* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Functional Microarchitecture of Cat Primary Visual Cortex
Axon guidance wikipedia , lookup
Animal echolocation wikipedia , lookup
Molecular neuroscience wikipedia , lookup
Activity-dependent plasticity wikipedia , lookup
Neuroesthetics wikipedia , lookup
Types of artificial neural networks wikipedia , lookup
Response priming wikipedia , lookup
Neuroethology wikipedia , lookup
Binding problem wikipedia , lookup
Neuroeconomics wikipedia , lookup
Nonsynaptic plasticity wikipedia , lookup
Single-unit recording wikipedia , lookup
Time perception wikipedia , lookup
Neural modeling fields wikipedia , lookup
Multielectrode array wikipedia , lookup
Convolutional neural network wikipedia , lookup
Functional magnetic resonance imaging wikipedia , lookup
Perception of infrasound wikipedia , lookup
Clinical neurochemistry wikipedia , lookup
Psychophysics wikipedia , lookup
Mirror neuron wikipedia , lookup
Caridoid escape reaction wikipedia , lookup
Neuroanatomy wikipedia , lookup
Biological neuron model wikipedia , lookup
C1 and P1 (neuroscience) wikipedia , lookup
Synaptic noise wikipedia , lookup
Central pattern generator wikipedia , lookup
Circumventricular organs wikipedia , lookup
Evoked potential wikipedia , lookup
Neural oscillation wikipedia , lookup
Development of the nervous system wikipedia , lookup
Neuropsychopharmacology wikipedia , lookup
Metastability in the brain wikipedia , lookup
Pre-Bötzinger complex wikipedia , lookup
Neural correlates of consciousness wikipedia , lookup
Premovement neuronal activity wikipedia , lookup
Optogenetics wikipedia , lookup
Stimulus (physiology) wikipedia , lookup
Nervous system network models wikipedia , lookup
Synaptic gating wikipedia , lookup
Channelrhodopsin wikipedia , lookup
Neural coding wikipedia , lookup
Diss. ETH N° 21392 Functional Microarchitecture of Cat Primary Visual Cortex A dissertation submitted to ETH Zurich For the degree of Doctor of Sciences Presented by Sylvia Schröder Master of Science, University of Zurich Born January 5th, 1984 Citizen of Germany Accepted on the recommendation of Prof. Dr. Kevan A. C. Martin Dr. Daniel Kiper, Prof. Dr. Fritjof Helmchen September 9th, 2013 Functional microarchitecture of cat primary visual cortex Table of contents List of figures........................................................................................................................ 4 Abbreviations ....................................................................................................................... 5 Summary.............................................................................................................................. 6 Zusammenfassung ................................................................................................................ 8 Declaration ........................................................................................................................ 10 1 Introduction................................................................................................ 11 1.1 Functional and anatomical architecture of primary visual cortex .................. 12 1.1.1 Receptive fields ........................................................................................... 12 1.1.2 Topographic maps and cortical columns ..................................................... 13 1.1.3 Cortical layers ............................................................................................. 16 1.2 Relevance of noise in neural responses ......................................................... 16 1.3 Adaptation to coding of natural stimuli ....................................................... 20 1.4 Neighbouring neurons ................................................................................ 22 1.5 Origin and physiological properties of the local field potential..................... 25 1.5.1 Origin and spatial extent of the LFP ............................................................ 25 1.5.2 Origin of oscillations ................................................................................... 27 1.5.3 Laminar differences ..................................................................................... 29 1.5.4 Stimulus dependence and tuning properties of oscillations .......................... 29 1.6 Relationship between LFP and neural spikes ............................................... 31 1.7 Function and relevance of oscillations ......................................................... 33 1.8 Aims of this study........................................................................................ 35 2 Methods ...................................................................................................... 36 2.1 Animal preparation ..................................................................................... 36 2.2 Electrophysiology and extracellular labelling ................................................ 37 2.3 Perfusion and Histology .............................................................................. 37 2.4 Visual stimuli .............................................................................................. 38 3 Functional heterogeneity in neighbouring neurons ...................................... 40 3.1 Introduction................................................................................................ 40 3.2 Methods ...................................................................................................... 42 3.2.1 Spike sorting ............................................................................................... 42 1 Table of contents 3.2.2 Tuning curves and phase analysis ................................................................ 42 3.2.3 Reconstruction of RFs from responses to visual noise .................................. 45 3.2.4 Correlation measures ................................................................................... 46 3.2.5 Significance test for correlation measures ..................................................... 47 3.2.6 Estimate of signal correlations between identical but noisy neurons ............. 48 3.2.7 Tests using bootstrapped signal and noise correlations ................................. 48 3.2.8 Control test for influence of time scale and signal correlations ..................... 48 3.3 Results ........................................................................................................ 50 3.3.1 Responses of neighbouring neurons differ substantially ............................... 51 3.3.2 Influence of time scale on signal correlations ............................................... 58 3.3.3 Relation between tuning differences and signal correlations ......................... 60 3.3.4 Signal correlations are similar for different stimulus classes .......................... 62 3.3.5 Noise correlations are small but similar across different stimulus classes....... 63 3.3.6 Relation between signal and noise correlations depends on stimulus class .... 66 3.3.7 Firing rates do not account for agreement between noise and signal correlations ................................................................................................................... 67 3.3.8 3.4 Dependence of response differences on cortical layer ................................... 69 Discussion ................................................................................................... 71 3.4.1 Comparison to other studies........................................................................ 71 3.4.2 Limitations of experimental approach.......................................................... 72 4 Relationship between the LFP and neighbouring neurons ........................... 74 4.1 Introduction................................................................................................ 74 4.2 Methods ...................................................................................................... 75 4.2.1 Preprocessing of LFP ................................................................................... 75 4.2.2 Spectral and phase analysis of LFP............................................................... 75 4.2.3 Measure of unreliability for LFP power and spike rate ................................. 76 4.2.4 Correlation measures ................................................................................... 76 4.3 Results ........................................................................................................ 78 4.3.1 Visual stimulation increases power of higher LFP frequencies ...................... 80 4.3.2 Tuning sensitivity of the LFP and nearby neurons ....................................... 81 4.3.3 Relationship between tuning curves of LFP and of neighbouring neurons ... 83 2 Functional microarchitecture of cat primary visual cortex 4.3.4 Unreliability and signal modulation of the LFP and neurons in response to different stimulus classes .............................................................................. 88 4.3.5 Relationship between LFP power and spike times or spike rate .................... 93 4.3.6 Locking of spikes to LFP phases .................................................................. 97 4.3.7 Comparison of LFP power and phase at times of reliable versus non-reliable spikes ........................................................................................................ 100 4.4 Discussion ................................................................................................. 102 4.4.1 Comparison to other studies...................................................................... 102 4.4.2 Limitations ................................................................................................ 107 5 Discussion ................................................................................................. 109 5.1 Cortical columns, functional heterogeneity and information processing .... 109 5.2 Is coding optimized to natural stimuli? ...................................................... 112 5.3 Relevance of rhythms in the LFP ............................................................... 112 5.4 Suggestions for future investigations .......................................................... 114 6 References ................................................................................................. 116 7 Acknowledgements.................................................................................... 131 8 Curriculum Vitae .................................... Fehler! Textmarke nicht definiert. 3 List of figures List of figures Figure 3.1 Overview of analyses. ......................................................................................... 40 Figure 3.2 Example of three simultaneously recorded neurons. ........................................... 50 Figure 3.3 Tuning curves and phase modulation of three simultaneously recorded neurons. ........................................................................................................................................... 51 Figure 3.4 Comparison between tuning differences of neighboring neurons and of randomly picked neurons. .................................................................................................................. 53 Figure 3.5 Tuning differences between neighboring neurons across all stimulus parameters. ........................................................................................................................................... 55 Figure 3.6 Signal correlations in response to artificial and natural stimuli. .......................... 57 Figure 3.7 Dependence of signal correlations on time scale. ................................................ 58 Figure 3.8 Correlation strength between tuning differences and signal correlations. ............ 61 Figure 3.9 Correlation strengths between signal correlations of different stimulus classes. ... 62 Figure 3.10 Noise correlations for all stimulus classes. ........................................................ 64 Figure 3.11 Correlation strengths between noise correlations of different stimulus classes. .. 65 Figure 3.12 Relation between noise and signal correlations on different time scales. ........... 66 Figure 3.13 Distribution of firing rates and their relation to signal or noise correlations. .... 67 Figure 3.14 Dependence of response differences between neighboring neurons on cortical layer. ........................................................................................................................................... 69 Figure 4.1 Example of simultaneously recorded neurons and LFP during 30 presentations of a movie. ................................................................................................................................ 78 Figure 4.2 Another example of simultaneously recorded neurons and LFP during 30 presentations of a movie. .................................................................................................... 79 Figure 4.3 Power spectra of LFP during visual stimulation and spontaneous activity. ......... 80 Figure 4.4 Tuning sensitivity of LFP and of neural firing rates in response to gratings. ....... 82 Figure 4.5 Correlation between tuning curves of LFP power and of neural firing rates in response to gratings. ........................................................................................................... 84 Figure 4.6 Relationship between tuning similarity of neighbouring neurons and tuning selectivity of LFP. ............................................................................................................... 88 Figure 4.7 Illustration of measures for unreliability and signal modulation of instantaneous signals. ............................................................................................................................... 90 Figure 4.8 Unreliability and signal modulation of LFP power, LFP phase and neural firing rate. ........................................................................................................................................... 91 Figure 4.9 Example showing the relationship between LFP power and spike rate in response to a movie. ......................................................................................................................... 94 Figure 4.10 Relationship between LFP power and spike rate during visual stimulation and spontaneous activity. .......................................................................................................... 96 Figure 4.11 Relationship between LFP phase and spike times. ............................................ 98 Figure 4.12 Differences between preferred LFP phases of neighbouring neurons. ............... 99 Figure 4.13 LFP at times of reliable and non-reliable spikes.............................................. 101 4 Functional microarchitecture of cat primary visual cortex Abbreviations AP Action potential CV Coefficient of variation EPSP/EPSC Excitatory postsynaptic potential/current GABA Gamma-aminobutyric acid FF Fano factor IPSP/IPSC Inhibitory postsynaptic potential/current LFP Local field potential MUA Multi-unit activity RF Receptive field SD Standard deviation SEM Standard-error of the mean SUA Single-unit activity V1 Primary visual cortex 5 Summary Summary The goal of this investigation was to quantify the differences and similarities in the responses to artificial and more complex stimuli of pairs or triplets of nearby neurons, which were situated in the same cortical “column” in cat primary visual cortex, and to relate the fingerprint of the neurons’ responses to that of the local field potential (LFP) recorded in close vicinity. We found that preferred direction, preferred orientation, and orientation tuning width were more clustered than would be expected from a random distribution. However, preferred phase, direction selectivity, relative modulation (F1/DC), and spatial frequency preference and tuning width showed no such clustering. By investigating the temporal patterns of neighbouring neurons in response to movies, visual noise and gratings, we found that stimulus-dependent responses, called “signals”, showed only small correlations (magnitude) on short time scales (10200 ms). The strengths of these signal correlations changed with bin size, but did not support the hypothesis that preferences to slowly changing stimulus features are more often shared between neighbouring neurons than preferences to rapidly fluctuating features. Although signal correlations were similar across all stimulus classes, they were only weakly related to differences between the neurons’ tuning curves. “Noise” in neural responses refers to stimulus-independent activity manifest in trial-to-trial fluctuations. The strength of noise correlations of two neurons is thought to reflect the degree of inputs shared between them. Generally, noise correlations in neighbouring neurons were small (magnitude) and exhibited similar strengths in response to different stimulus classes. They were strongly related to signal correlations in response to gratings or visual noise, but less so in response to movies, suggesting a special mode of processing of natural stimuli. The feature of the LFP that was most strongly related to the activity of nearby neurons was the high-frequency power of the LFP. Two results showed that power at frequencies above 30 Hz reflected best the summed activity of the surrounding neurons: firstly, tuning curves of LFP power were better related to the summed activity of two neighbouring neurons than to the tuning curve of a single neuron; secondly, the more similar the tuning of neighbouring neurons, the more similar was the tuning of LFP power to that of a nearby neuron and the higher was the tuning sensitivity of LFP power. Surprisingly, the degree of similarity between the tuning curves of LFP power and a nearby neuron was on average as high as that between the spikederived tuning curves of two neighbouring neurons, although the LFP integrates neural activity from a large neural population that probably extends over larger distances than the average distance of neurons recorded simultaneously. Comparisons of signal-to-noise ratios showed that single neurons are much more informative than any features of the LFP. The firing rate of single neurons was about 1.5 times more sensitive to changes in grating parameters than LFP power of high frequencies and exhibited a 1.5-4 times higher signal modulation (depending on the stimulus class). The magnitude of unreliability, on the other hand, was similar across LFP and neural firing rates. 6 Functional microarchitecture of cat primary visual cortex At fast temporal scales, the strongest relationship between LFP and neural activity was observed in the phase-locking of spikes to low frequencies of the LFP and in the single-trial correlations between instantaneous firing rates and LFP power, which was generally low, but highest for high-frequency power. Phase-locking strengthened with increasing power of low frequencies, and during reliable firing of the neurons (though the effect was weak). The difference between the average LFP phases to which two neighbouring neurons locked was as high as the difference between average phases of two random neurons, showing that neurons are not clustered according to their preferred LFP phases. We conclude that neurons within a cortical column express only weak response similarities, and re-evaluate the significance of cortical columns for information processing. The functional heterogeneity found among neighbouring neurons may have distinct advantages for cortical processing, and visual cortex might have adapted particularly to the processing of natural stimuli. 7 Zusammenfassung Zusammenfassung Ziel dieser Untersuchung war es, die Unterschiede und Gemeinsamkeiten der Antworten auf künstliche sowie komplexere Stimuli von zwei bis drei Neuronen, die sich in derselben kortikalen „Säule“ befinden, zu quantifizieren, und den „Fingerabdruck“ der Antworten dieser Neuronen zu dem des lokalen Feldpotentials (LFP), das in naher Umgebung aufgenommen wird, in Beziehung zu setzen. Wir konnten zeigen, dass sich die optimalen Bewegungsrichtungen, die optimalen Orientierungen und die Bandbreiten für bevorzugte Orientierungen in benachbarten Nervenzellen häufiger ähnelten, als man es in einer zufälligen Verteilung erwarten würde. Dies traf jedoch für andere Eigenschaften von benachbarten Nervenzellen nicht zu, nämlich deren optimalen Phasen, deren Selektivität für eine Bewegungsrichtung, deren relativen Modulationen (F1/DC), deren optimalen Raumfrequenzen sowie die Bandbreiten der bevorzugten Werte. Danach haben wir die Aktivität von benachbarten Neuronen in Reaktion auf natürliche Filme, dynamische Schachbrettmuster und bewegte Gittermuster (Gratings) auf einer feinen Zeitskala (eingeteilt in Intervalle von 10-200 ms) untersucht. Wir konnten feststellen, dass die Stimulus abhängigen Antworten („Signale“) nur schwach miteinander korreliert waren. Die Stärke dieser Signalkorrelationen hing von der verwendeten Zeitskala ab, aber die Hypothese, dass sich die Antworten von benachbarten Neuronen vor allem aufgrund sich langsam ändernden Stimuluseigenschaften ähneln, konnte nicht bestätigt werden. Obwohl Signalkorrelationen für verschiedene Stimulusklassen ähnlich stark waren, standen sie kaum mit den Unterschieden in den Antworten auf einzelne Stimuluseigenschaften („Tuning-curves“) in Zusammenhang. Das Störrauschen („Noise“) in neuronal Antworten bezieht sich auf Stimulus unabhängige Aktivität, die sich in den Fluktuationen von einer zur nächsten Wiederholung des gleichen Stimulus zeigt. Es wird angenommen, dass die Stärke von Noisekorrelationen zwischen zwei Neuronen den Umfang des synaptischen Inputs, den sie sich teilen, widerspiegelt. Noisekorrelationen zwischen benachbarten Neuronen waren im Durchschnitt schwach und unabhängig von der Stimulusklasse. Sie waren stark mit den Signalkorrelationen für die künstlichen Stimuli korreliert. Allerdings war die Korrelation zwischen Noise- und Signalkorrelationen für natürliche Filme war sehr viel schwächer als für die anderen Stimuli, was auf einen speziellen Modus der Verarbeitung von natürlichen Stimuli schließen lässt. Das Merkmal des LFPs, das die stärkste Verbindung zu der Aktivität der benachbarten Nervenzellen aufzeigte, war die Amplitude der hohen Frequenzen des LFPs. Zwei Ergebnisse zeigten, dass die Amplitude von Frequenzen über 30 Hz die Summe der Aktivitäten von nahegelegenen Neuronen widerspiegelt. Erstens waren die Tuning-curves des LFPs der Summe der Tuning-curves von zwei benachbarten Neuronen ähnlicher als der Tuning-curve eines der Neurone allein. Und zweitens waren sich die Tuning-curves des LFPs und eines nahegelegenen Neurons ähnlicher, wenn auch die Tuning-curves von zwei benachbarten Neuronen größere 8 Functional microarchitecture of cat primary visual cortex Ähnlichkeit zeigten. Des Weiteren zeigte das LFP unter dieser Bedingung eine höhere Sensibilität für Änderungen in den Eigenschaften des Stimulus. Überraschenderweise war der Grad, zu dem sich Tuning-curves von benachbarten Neuronen ähnelten, genauso hoch wie der Grad, zu dem sich Tuning-curves von LFP und einzelnen Neuronen ähnelten, obwohl das LFP neuronale Aktivität von einer Population integriert, die sich über größere Distanzen ausbreitet als die mittlere Distanz zwischen den Neuronen, deren Antworten wir gleichzeitig aufgenommen haben. Untersuchungen des Signal-Rausch-Verhältnisses zeigten, dass einzelne Neurone sehr viel informativer sind als irgendein Aspekt des LFPs. Die Feuerrate einzelner Neurone war ungefähr 1.5-mal so sensibel für Änderungen von Parametern des Gratingstimulusʼ wie die Amplitude der hohen Frequenzen des LFPs und zeigten eine 1.5- bis 4-mal höhere Signalmodulation (abhängig von der Stimulusklasse). Das Ausmaß der Unzuverlässigkeit der Antworten von einzelnen Neuronen war jedoch genauso groß wie das des LFPs. Auf einer feineren Zeitskala war die Beziehung zwischen LFP und neuronaler Aktivität in zwei Aspekten am stärksten: Neurone feuerten bevorzugt in bestimmten Phasen des LFPs („Phaselocking“), vor allem des niederfrequenten Signals, während die Feuerrate der Neurone am stärksten mit der Amplitude der hohen Frequenzen des LFPs korrelierte (allerdings war die Korrelation im Allgemeinen niedrig). Der Grad des Phase-lockings steigerte sich mit steigender Amplitude der niedrigen Frequenzen und während zuverlässigem Feuern der Neurone (obwohl der Anstieg gering ausfiel). Der Unterschied zwischen den bevorzugten LFP-phasen von benachbarten Neuronen war genauso groß wie der zwischen zufällig gewählten Neuronen. Dies zeigt, dass Nervenzellen mit ähnlichen Phasenpräferenzen nicht gehäuft nebeneinander auftreten. Wir kommen zu dem Schluss, dass Nervenzellen innerhalb einer kortikalen Säule nur wenige Ähnlichkeiten in ihren Antworten aufweisen, weshalb wir die Relevanz von kortikalen Säulen für die Informationsverarbeitung neu bewerten. Wir werden die Vorteile und Konsequenzen der funktionalen Heterogenität, die wir unter benachbarten Neuronen gefunden haben, diskutieren, sowie Hinweise auf die Anpassung des Gehirns an die Verarbeitung natürlicher Stimuli besprechen. 9 Declaration Declaration I hereby declare that the work in this thesis is original work, which I alone have authored and which is written in my own words, except for corrections made by Prof. Kevan A. C. Martin, Kevin Lloyd, and the anonymous reviewers of the published part of the thesis (first part of Results comprising section 3, Methods in section 2, and parts of the Discussion in section 5). Together with my supervisor, Prof. Kevan A. C. Martin, I have designed the research, and performed the experiments. In addition, the electrophysiological experiments were supported by Dr. Nuno da Costa and Dr. Elisha Ruesch. Histology of brain sections was supported by Simone Rickauer. Data analysis was performed by me, but was influenced by the feedback of the anonymous reviewers of the published part of the thesis, Prof. Kevan A. C. Martin and members of his research group, Sepp Kollmorgen, and Prof. J. Anthony Movshon. 10 Functional microarchitecture of cat primary visual cortex 1 Introduction The neocortex is a thin, extended, and in humans, greatly convoluted sheet of tissue, which forms the outer shell of the cerebrum. Its thickness of just about two millimetres in all mammals, might easily deceive us from its intricate composition: one cubic millimetre of neocortex holds 50-100 thousand neurons, about four kilometres of axons, and 300-1500 million synapses. This complex structure was the latest to evolve in the brain, and it is mainly due to its massive expansion and that of its connections that the size of hominid brains trebled within the last three million years. In humans, the neocortex and its connections take up about 80% of the brain’s volume (Passingham, 1982; Douglas et al., 2003; da Costa and Martin, 2010). The neocortex is involved in higher cognitive functions such as sensory perception, the generation of motor commands, and spatial reasoning, and enables humans to have conscious thought and language. The work of this thesis is specifically concerned with the first stage of visual processing in the neocortex, the primary visual cortex (V1). Although this area is the most studied region of the neocortex, experimental and theoretical difficulties in exploring its complex structure and function has greatly limited our understanding of the primary visual cortex (Olshausen and Field, 2004b; Carandini et al., 2005). This study here is an attempt to further our understanding of the functional architecture and, therefore, the computational processes carried out in this area. We focused here on a detailed comparison of the physiological properties of a given visual neuron to those of its neighbours and to the local population of nearby neurons. Because the structure of neuronal circuits is similar throughout neocortex (Douglas and Martin, 2011), we have reason to believe that to some degree our results can be generalized to other neocortical areas. The following sections first introduce the reader to the classic tuning properties of the neurons in V1 and the spatial arrangement of their functional properties along the horizontal and the vertical axis of visual cortex. Neurons do, however, not only respond to external stimuli, but exhibit activity that cannot be accounted for by the sensory input. Theories on how this socalled “noise” affects the coding capacity of neural populations and in what way it reflects the functional connectivity between neurons will be reviewed. The following section then considers the special role of natural stimuli in coding—what distinguishes natural visual stimuli from other stimuli and how the brain may have adapted to represent them efficiently. We then review the current knowledge of physiological properties of neighbouring neurons in the primary visual cortex, which is the focus of the first part of this study. The second part of the Introduction deals with the local field potential (LFP), which mainly reflects the synaptic input to the local population of neurons. We describe what the origin of the LFP and its oscillatory content is, how it changes with visual stimulation, and, most importantly, how it is related to neuronal spikes, which are the principal carriers of information in the brain. Finally, the relevance and hypothesized functions of oscillations in the LFP are presented. 11 1 Introduction 1.1 Functional and anatomical architecture of primary visual cortex 1.1.1 Receptive fields The receptive fields (RFs) of neurons in primary visual cortex fall into two classes or, as more recent studies suggest, along the continuum between two extremes (Chance et al., 1999; Mechler and Ringach, 2002): simple and complex RFs. Simple RFs are built of separate, elongated, parallel On- and Off-subfields, whose stimulation with light or dark spots, respectively, cause the neuron to fire. Their spatial profile was found to be well described by Gabor filters (Field and Tolhurst, 1986). In addition, simple cells react to temporal changes in a visual stimulus and often exhibit a preferred direction and speed of movement. The complete spatiotemporal characteristics of simple RFs define the neuron’s preferred orientation, direction, spatial frequency, temporal frequency, and phase, i.e. the position of On- and Off-subfields within the RF (see references in Carandini et al., 2005). These are some of the physiological properties we compared across nearby neurons. Complex RFs on the other hand have overlapping On- and Off-subfields resulting in invariance to contrast. A complex cell shows, in the extreme case, no or very little phase modulation, but otherwise exhibits selectivity to the same features as simple cells do. The most effective stimuli for both cell types are high contrast moving bars and gratings. Simple and complex RFs were first detected in cat area 17 (Hubel and Wiesel, 1959, 1962), later on in monkey primary visual cortex (Hubel and Wiesel, 1968) and mouse visual cortex (Niell and Stryker, 2008). At least simple cells appear to be ubiquitous in the visual system of mammals and were found in several species of monkeys, tree shrews, rodents, rabbits, and sheep (see references in Wielaard et al., 2001). As soon as Hubel and Wiesel (1962) first discovered simple and complex RFs, they suggested a possible wiring diagram that explained the emergence of these RFs given the circularly shaped, centre-surround RFs of geniculate neurons that form the only sensory input to primary visual cortex. They proposed that a simple cell receives input from geniculate neurons so that their RFs align with the simple cell’s subfields with matching polarity between each subfield and the centre-surround geniculate input. Complex cells were thought to receive input from several simple cells with the same RF orientation but adjacent retinal positions or shifted spatial phases. Current models are still based on the ideas of Hubel and Wiesel, but incorporate other observed properties like contrast-invariance, direction preference and the abundant recurrent connections within cortex (Suarez et al., 1995; Ferster and Miller, 2000; Douglas and Martin, 2007). Throughout the next section, it will become clear how Hubel and Wiesel’s ideas on the connectivity between geniculate neurons and the various cortical cell types influenced their thinking on the functional architecture of the primary visual cortex. Before describing the current knowledge of the functional architecture of primary visual cortex, it should be mentioned that simple and complex RFs do not capture all the physiological properties of visual neurons in V1 and are not the only RF types in this area. Some neurons in 12 Functional microarchitecture of cat primary visual cortex monkey V1 have circular, centre-surround RFs reminiscent of those of geniculate neurons (Hubel and Wiesel, 1968). More importantly, many neurons falling into the simple or complex cell type exhibit response nonlinearities such as surround suppression (already described as hypercomplex cells by Hubel and Wiesel, 1968) or facilitation, response saturation at high contrasts, nonspecific suppression, i.e. suppression of the response to the optimal stimulus by simultaneous presentation of stimuli that alone do not cause a response, to name just a few (Carandini et al., 2005). Such nonlinearities hamper the finding models that correctly predict responses of visual neurons to any kind of visual stimulus, and thus present a major difficulty for understanding visual processing. 1.1.2 Topographic maps and cortical columns Despite the neocortex’s anatomical complexity and relative uniformity across and within areas, it exhibits relatively clear physiological structures. The most obvious are topographic maps, in which adjacent neural populations represent neighbouring points or receptors in the periphery, such as neighbouring points in the retina, skin, and musculature, as well as neighbouring receptors in the cochlea coding for similar tone frequencies. Cortical areas are even defined by the representation of one complete topographic map. The first complete retinotopic map, i.e. the topographic map of the visual field, was measured in monkey V1 by Daniel and Whitteridge (1961). In addition to topographic maps, a number of functional response characteristics are clustered within so called cortical columns. These span the entire cortical thickness from the pial surface to the white matter and have a diameter of several 10s to 100s of microns, depending on the system and physiological property. The first evidence of such a columnar architecture was discovered in single neuron electrophysiology studies of the cat and monkey somatic sensory cortex (Mountcastle, 1957; Powell and Mountcastle, 1959). Neurons encountered in penetrations vertical to the cortical surface all responded either to superficial (skin, hair) or deep (joint, fascia) stimulation. In anatomical studies in the mouse, Lorente de Nó (1949) had previously described narrow chains of neurons extending vertically across all layers. Inspired by that, Mountcastle proposed that these “minicolumns” are the basic organisational units of cortex. A number of those minicolumns would then form a cortical column, the functional entity he had seen in somatic sensory cortex, via horizontal connections (reviewed in Mountcastle, 1997). Not long after Mountcastle’s discoveries, Hubel and Wiesel published their finding of two columnar systems for orientation and ocular dominance in cat and monkey primary visual cortex (Hubel and Wiesel, 1962, 1963, 1965, 1968). Ocular dominance columns contain neurons whose responses are at a similar level dominated by either the right or left eye. They are therefore directly related to features of the sensory receptors (similar to Mountcastle’s columns in somatic sensory cortex). Orientation selectivity, on the other hand, emerges in cortex most probably through the specific connectivity diagram suggested by Hubel and Wiesel (see previous section). They reasoned therefore that the functional significance of orientation columns 13 1 Introduction lies in the easier and more cost efficient wiring between neurons (Hubel and Wiesel, 1962, 1963). Generally, if neurons with similar RFs project to the same neuron or neuronal population information can be represented and processed more robustly given the noisy output of single neurons (see also section 1.6). These advantages are probably the most important ones that made the concept of cortical columns so compelling. The exact shape and arrangement of the columns stayed elusive for some time. Originally Hubel and Wiesel had the impression that orientation preference shifts in discrete steps along tracks parallel to the cortical surface. Today it is clear that orientation preference varies smoothly across most of cortical surface, except for sudden discontinuities like “fractures” or “pinwheels” where regions of different orientation preferences converge at one point (Bonhoeffer and Grinvald, 1991; Blasdel, 1992). But even near the centre of an orientation pinwheel, orientation preferences of single neurons in cat V1 appear highly ordered and not intermingled (Ohki et al., 2006). A complete 180º rotation of orientation preference, termed an “orientation hypercolumn”, is covered within approximately 0.5-1 mm along the cortical surface of cat and monkey (Hubel and Wiesel, 1974b, a). Similarly, an ocular dominance hypercolumn containing two columns each dominated by one of the two eyes covers a distance of 0.5-1 mm (Hubel and Wiesel, 1974a). Orientation and ocular dominance columns were observed to be independent systems, i.e. variations in orientation are not correlated with those in ocular dominance. Based on these results and the fact that neurons in primate V1 with horizontal distances of about 2 mm have adjacent, non-overlapping RFs, Hubel and Wiesel reasoned that “a 2 mm x 2 mm block of cortex contains by a comfortable margin the machinery needed to analyse a region of visual field roughly equal to the local field size plus scatter” (Hubel and Wiesel, 1974a, 1977). This functional architecture later became known as the “ice-cube model”. It was the basis for many studies on the existence and interrelation of columnar systems for further visual stimulus features. Other RF characteristics that were found to be clustered in V1 of cat include preferred direction of movement (Payne et al., 1981; Tolhurst et al., 1981), direction selectivity (Swindale et al., 2003), spatial frequency (Tootell et al., 1981; Tolhurst and Thompson, 1982; Shoham et al., 1997; Issa et al., 2000), and temporal frequency (Shoham et al., 1997). With the rise of optical imaging techniques for visualizing the responses of large neural populations in the upper layers of cortex, the specific geometric relationship between orientation and ocular dominance columns was confirmed and further columnar systems were integrated, such as that of spatial frequency (Hübener et al., 1997; Nauhaus et al., 2012) and direction of movement (Weliky et al., 1996; Swindale et al., 2003). These studies showed that the different map gradients tend to cross each other orthogonally. Following Hubel and Wiesel’s concept of their 2 mm x 2 mm “ice-cube” model of the cortical machinery, the functional significance of this specific geometric relationship between the columnar systems was sought in the accomplishment of complete coverage, i.e. the representation of all possible combinations of stimulus features for each position of the visual field. Indeed, theoretical studies confirm that columnar 14 Functional microarchitecture of cat primary visual cortex systems should be arranged orthogonal to each other to accomplish optimal coverage (Swindale et al., 2000, and references therein). More recently, the columnar systems were shown to have no fixed arrangement, meaning that the same cortical activation pattern could be evoked by different combinations of stimulus features (Basole et al., 2003). This can be explained by the dependence of a neuron’s selectivity to one stimulus feature, like orientation, on other features concurrent in the stimulus, e.g. the lengths of the presented bars. This is in fact expected given that V1 neurons can be described as filters that are selective for a range, not a single precise value, of orientations, spatial and temporal frequencies (Mante and Carandini, 2005). The model of Mante and Carandini (2005) shows that it is the RFs’ tuning for stimulus energy that is mapped on the cortical surface, not a fixed superposition of several stimulus feature maps. However, their results still entail the notion of a close functional similarity between neighbouring cortical neurons, which we aim to test in some detail in this thesis. In addition to the advantage of minimizing wiring costs, the cortical column is such a convincing concept because, as Horton and Adams (2005) phrased it, “[i]f one could understand a little piece of the cortex, and if this piece were representative of the whole, then our task [the scientist’s task to explain the function of cortex] would be simplified immensely.” Thus, during the last five decades cortical columns for many functional properties in many cortical areas were sought and found: for example frequency and binaural bands in auditory cortex, direction columns in motor cortex and neural clusters controlling the same muscle or muscle group, columns for axis and direction of motion in MT (middle temporal area), columns for similar complex shapes in IT (inferior temporal area), and columns for specific behaviours and functions in frontal association areas (reviewed by Mountcastle, 1997; Horton and Adams, 2005). However, the view that cortex is built of separate columns as well as the functional relevance of cortical column is questionable. Firstly, there is no structural signature of the functional column. The minicolumns described anatomically do not cluster or bind together via restricted short-range connections to form a larger column, nor are a single neuron’s proximal axonal boutons, the neuron’s output sites, restricted to the size of an orientation column (Horton and Adams, 2005; da Costa and Martin, 2010). Secondly, several species lack cortical columns for certain features, but neither the tuning selectivity of single neurons, nor behavioural discriminability, nor the size of the cortical area are found to correlate with the existence or non-existence of columns (Horton and Adams, 2005). Rodents, for example, have a salt-and-pepper organization of orientation preference. Nonetheless, squirrels belonging to the species of rodents have a very good visual acuity and a relatively large visual cortex. The abundant occurrence of cortical columns and their promise to be a key step in understanding cortex, might have led to an overestimation of their importance. Most studies on cortical columns were done on the spatial scale of maybe hundreds of neurons, not with single cell resolution. Furthermore, the temporal resolution of recorded responses was usually low, on the order of 100s of milliseconds to several seconds. Finally, cortical columns 15 1 Introduction and maps were most often mapped in response to artificial stimuli with a restricted set of stimulus features. In this investigation, two or more neighbouring neurons were recorded simultaneously together with the average activity of the surrounding population, as reflected in the local field potential. We analysed neural responses at a fine temporal resolution, and used artificial as well as natural visual stimuli to elicit neural responses. One of our goals was to investigate the functional relevance of the cortical columns under these conditions. 1.1.3 Cortical layers Compared to the variation of RFs along the horizontal dimension of the primary visual cortex, variation along the vertical axis is relatively minor. On the basis of cell morphology and density, six layers of neocortex can be distinguished. Layer 4 and 6 receive most of the cortical input from the lateral geniculate nucleus, layers 2 and 3 form the intra- and intercortical connections, and layers 5 and 6 project mainly to subcortical areas, but also form inter-areal projections. In the vertical dimension, all layers are strongly recurrently connected through the main loop from layer 4 termed the granular layer, over layers 2 and 3 (supragranular), to layers 5 and 6 (infragranular), and back to layer 4 (reviewed in Douglas and Martin, 2004). Physiologically, layer 4 contains the majority of simple cells and most neurons are dominated by the input of one eye, whereas supra- and infragranular layers contain mostly complex cells with binocular input (Hubel and Wiesel, 1962, 1968; Gilbert, 1977; Hubel and Wiesel, 1977; Martinez et al., 2005). These differences in cell type are presumably related to the laminar innervation of geniculate projections (LeVay and Gilbert, 1976). 1.2 Relevance of noise in neural responses The neural responses we have dealt with in the previous sections were average responses to a visual stimulus. These mean responses are thought to be driven purely by the stimulus and are termed the neuron’s “signal”. In the following, we will refer to any neural responses that are averaged across several repetitions of the same stimulus, including stimuli other than gratings and responses measured across various durations lasting from several milliseconds to several seconds (including the complete duration of the stimulus), as signal. However, neural responses do not only carry the stimulus related signal, but vary from one to another presentation of the same stimulus. These trial-to-trial fluctuations are often referred to as “noise”. Recently, it became clear that this term is not truly appropriate and rather confusing because deviations from the mean response are not only caused by random processes such as sensory noise (photons, for example, arrive at photoreceptors at a rate governed by a Poisson process) or stochastic processes at the biochemical and biophysical level of the cell (e.g. vesicle fusion or binding of neurotransmitters to receptors) (reviewed in Faisal et al., 2008), but can reflect internally generated processes of the current brain state, or response statistics similar to those during visual stimulation (reviewed in Destexhe, 2011). We will here continue to use the term “noise” simply to distinguish the stimulus-dependent response, i.e. the signal, from the remaining part of the response. 16 Functional microarchitecture of cat primary visual cortex Because of the high degree of shared and recurrent connections between cortical neurons, noise is correlated between responses of nearby neurons (see for example Shadlen and Newsome, 1998). In most cases, noise correlations are defined as Pearson’s correlation (correlation between z-transformed variables) between two neurons’ trial-to-trial fluctuations, i.e. between their deviations from their mean responses. This correlation is not induced by the visual stimulus and thus cannot simply be explained by the similarity of two neurons’ RFs, although noise correlations are sensitive to stimulus properties (Kohn et al., 2009). For the purpose of this thesis, noise correlations are relevant for two aspects. Firstly, the correlation of noise exhibited by two neurons reflects their connectivity—not in a strict anatomical sense, but rather in a functional sense. Measuring noise correlations will thus allow us to relate the similarity between the signals and tuning properties of neighbouring neurons to their degree of functional connectivity. Secondly, noise and noise correlations are detrimental to information transmission and processing. Theories of neural coding, therefore, have to explain how the brain deals with neural noise and under which circumstances noise is specifically harmful to coding. These theories will help us interpreting the results of our comparison between signals and noise of neighbouring neurons and the local neural population. In the following, we will review experimental and theoretical studies on these two aspects. The strength of noise correlations is generally thought to reflect the degree of shared input between two neurons (for example Alonso and Martinez, 1998; Bair et al., 2001; Kohn and Smith, 2005). Using an artificial neural network of linear threshold units with biologically plausible connections, noise levels, and dynamic ranges, noise correlations between neurons were shown to increase with an increasing share of excitatory and inhibitory inputs (Shadlen and Newsome, 1998). The strength of noise correlations will, however, never reflect the absolute percentage of shared inputs or connections between the neurons. For once, a large fraction of the synaptic inputs to a neuron will not reach the spiking threshold so that many synchronous synaptic events arriving at two neurons will stay undetected in correlations of spike counts. Furthermore, Renart et al. (2010) used a neural network model of excitatory and inhibitory units with dense, strong, and random connections between each other and receiving shared input from another population of units to show that the magnitude of noise correlations can be far smaller than the magnitude of the actual correlated input to two neurons. The reason is that excitatory and inhibitory inputs cancel out if both are correlated to each other. The same effect—decorrelation through inhibition—was shown to cause the low noise correlations between nearby excitatory neurons in barrel cortex of actively whisking rats (Middleton et al., 2012). Nonetheless, common input to units in the model by Renart et al. (2010) had a noticeable influence on noise correlations, so that differences in common input were still distinguishable (see their supplementary material). Additional factors that influence the measurement of noise correlations are the firing rate of the neurons, the time window over which spikes are counted, spike sorting errors, and the internal brain state (de la Rocha et al., 2007; Cohen and Kohn, 2011). These considerations show that noise correlations need to be interpreted with great care when inferring the degree of connectivity between neurons. In this thesis, we 17 1 Introduction used noise correlations only to compare the strengths of shared input between pairs of neurons, not to infer absolute values of connectivity; additionally, we made an effort to exclude any experimental biases that might affect noise correlations. Considering coding of information, noise in any system is detrimental to information transmission and processing. Nonetheless, neurons in the cortex fire at noise levels comparable with a completely random process (Tolhurst et al., 1983; Softky and Koch, 1993). The high variability of neural spike trains in responses to the same stimulus might be a sign of energy efficiency because overcoming the noise intrinsic to molecular signalling mechanisms in favour of high precision is energetically very costly (Laughlin and Sejnowski, 2003). Neural network models further suggest that noisy responses are the drawback for achieving a plausible dynamic range of firing rates by balancing excitation with inhibition (Shadlen and Newsome, 1998). In fact, noise can even have positive effects by amplifying hidden periodic signals that are too weak to reach spiking threshold—a mechanism termed stochastic resonance (Buzsáki, 2006, pp. 155; McDonnell and Abbott, 2009). But how can the brain deal with such noisy processing units? One obvious solution is averaging across responses of many similarly tuned neurons (Shadlen et al., 1996; Parker and Newsome, 1998), which is possible through the redundant representation of information by many neurons in the columnar structure of cortex. If all neurons that participate in the coding of one quantity exhibited noise fluctuations independent from each other, the signal-to-noise ratio would increase steadily with the number of neurons (namely with the square root of the number of neurons in the coding population) (Zohary et al., 1994). If however the trial-to-trial fluctuations, i.e. the noise, of the participating neurons were correlated, the information capacity of the average population response would be severely limited and would saturate at a certain size of the neural population (Zohary et al., 1994; Shadlen and Newsome, 1998; Mazurek and Shadlen, 2002). Noise correlations are not in every case detrimental to coding, however. If the neurons exhibited different tuning preferences to the quantity they are jointly encoding and if the mechanism reading out the encoded quantity took advantage of this diversity in the neural responses (instead of simply performing an average), the coding accuracy could be retained and would increase with increasing population size (Abbott and Dayan, 1999; Averbeck and Lee, 2004). The conditions that need to be met for noise correlations to have a positive effect on coding is very well illustrated in the review by Averbeck et al. (2006). If two neurons have positive signal correlations, i.e. they are similarly tuned and their mean responses covary with changes in the stimulus parameters, positive noise correlations decrease information compared to independent noise responses. This is because the response distributions in this case will greatly overlap and the more mistakes will be made during decoding even if an optimal strategy is used. However, if signal and noise correlations have opposite polarity, i.e. one is positive and the other negative, coding capacity is increased compared to uncorrelated noise responses. So, it is the interaction between signal and noise correlations that determines the information contained in the population (see also Ecker et al., 2011). To implement such a decoding scheme, Chen 18 Functional microarchitecture of cat primary visual cortex et al. (2006) suggest a centre-surround summation where neural sensitivity is improved if responses at a cortical site that is uninformative of the encoded quantity is highly correlated with responses at an informative site. In that way, common noise could be estimated at the uninformative site, which does not respond to the stimulus quantity, and then removed from the responses at the informative cortical site. There are two further alternative ways for the brain to deal with noise, which may be briefly mentioned. One is that noise fluctuations in excitatory neurons can be tracked and thereby cancelled by highly correlated fluctuations in inhibitory neurons. High correlations between excitatory and inhibitory inputs have indeed been observed in the retina (Cafaro and Rieke, 2010) and, indirectly, in rat barrel cortex (Okun and Lampl, 2008) as well as between spiking activity putative excitatory and inhibitory neurons in rat barrel cortex (Middleton et al., 2012). The same mechanism, namely minimizing the effect of temporal correlations by time-lagged excitation and inhibition, was used to successfully decode neural population responses in a visual detection task (Chen et al., 2008). The other alternative to limit negative effects of noisy responses is using prior knowledge about the expected structure of sensory signals so that sensory processing can compensate for noise (Faisal et al., 2008). This is especially helpful if the sensory signals are highly structured and redundant as in the case of natural visual stimuli— we will take on this topic in more detail in section 1.3. We now give a short overview of the large number of studies that investigated noise correlations, what they are affected by, and how they are related to other measures such as cortical distance, time scales, and tuning properties. Across many brain areas, species, and states of the animal (anaesthetized, behavioural task, etc.), noise correlations were typically found to be small and positive, and were highest between neurons that are close to each other or have similar tuning properties (reviewed for studies in monkey in Cohen and Kohn, 2011). In cat primary visual cortex, noise correlations diminished when neuronal distances increased from a few 100 to 1000 microns or more (Ts'o et al., 1986; Das and Gilbert, 1999). The relationship between tuning similarity and noise correlations is not that clear cut. Whereas Ts'o et al. (1986) and DeAngelis et al. (1999) found higher noise correlations when tuning properties of two neurons were similar, Das and Gilbert (1999) found noise correlations to be independent of orientation preferences. Similarly in monkey V1, noise correlations were mostly found to be positively related to similarities in orientation preference (Kohn and Smith, 2005; Smith and Kohn, 2008; Cohen and Kohn, 2011), but others found no relationship between noise and signal correlations (Maldonado et al., 2000). As discussed above, a positive correlation between signal and noise correlations could be harmful to the coding accuracy of a neural population. A better understanding of the relationship between both measures and under which circumstances it changes is therefore still an important issue of investigation. It has been suggested that certain behavioural states like attention and arousal change the strength of noise correlations, and thereby improve coding efficiency. 19 1 Introduction However, the effects of these brain states are greatly conflicting across studies and still under debate (see review by Kohn et al., 2009). Difficulties in comparing the findings of several studies result from the various influences on noise correlations that are not always rigorously controlled, such as firing rates, brain states, or flaws in spike sorting (Cohen and Kohn, 2011). Different time scales also contribute to different results. The common observation is that noise correlations increase with longer time scales (Bair et al., 2001; Reich et al., 2001; Kohn and Smith, 2005). But two different mechanisms seem to shape correlations on two distinct time scales: correlations on brief time scales appear to arise from common input recruited by a particular stimulus, whereas correlations on long time scales reflect more spatially widespread fluctuations in cortical activity (Kohn and Smith, 2005; Kohn et al., 2009). Whereas precise synchrony between neurons is increased by presenting stimuli with the neurons’ preferred parameters, noise correlations on longer time scales are less stimulus dependent, but are generally reduced the stronger the external stimulation is (high contrast stimuli versus spontaneous activity) (Kohn and Smith, 2005; Smith and Kohn, 2008). In this study, we quantified noise and signal correlations in response to three stimulus classes of different complexities for the same pairs of neurons. This enables us to quantify the influence of the feature statistics of different stimulus classes on noise correlations as well as on the relationship between signal and noise correlations, which is relevant for coding efficiency. We avoided biases in the measurements of noise correlations by performing careful spike sorting, by accounting for the influences of firing rates on noise and signal correlations, and by examining both correlation measures on a variation of time scales from 10 milliseconds to several seconds. 1.3 Adaptation to coding of natural stimuli The great majority of studies undertaken to investigate neural processing and reviewed so far have probed neuronal responses using artificial stimuli such as bars and gratings. The rationale behind this strategy is that, on one hand, neurons in primary visual cortex tend to respond strongly to these kinds of stimuli, on the other hand, these stimuli are easily parameterized and therefore can be varied systematically. The goal of the study at hand is, however, to reveal aspects not only of the functional architecture of the primary visual cortex, but also of how neurons in a local population act in concert to represent and process visual information. Of particular interest is the neuronal interaction and functioning in response to “natural” stimulation that is reminiscent of the system’s visual experience in everyday life. This will reflect the “natural” working mode, which the brain has adopted to process the most probable stimuli it encounters. Natural images exhibit specific feature statistics, such as high correlations between luminance values of neighbouring locations and a distribution of spectral power of frequencies, f, according to 1/fn (n is approximately 2). But most importantly the statistics of natural images show redundancy, which can be reduced by an efficient representation and coding scheme. If the 20 Functional microarchitecture of cat primary visual cortex brain adapted to the statistics of natural images, the role of early sensory neurons might be the removal of this statistical redundancy (Simoncelli and Olshausen, 2001). Indeed, mechanisms of redundancy reduction such as de-correlation and whitening occur very early in visual processing, namely in the retina (reviewed in Simoncelli and Olshausen, 2001). In the case of primary visual cortex, Field (1987) noticed that natural images elicit small amplitude responses in the majority of neurons with RFs of the shape of Gabor filters (i.e. simple cells). He termed this important neural coding principle “sparseness”. Later, two forms of sparseness were distinguished to describe two related phenomena: “lifetime sparseness”, which means that each single neuron is stimulated only by a limited subset of natural stimuli, and “population sparseness”, which means that only few neurons participate in coding at the same time. The advantages of a sparse code include the reduction of metabolic costs, an increased storage capacity in associative memories, and an easy read-out of complex data at subsequent processing stages (Olshausen and Field, 2004a). Moreover, the concept of sparseness has also explanatory power. If an artificial neural network is trained to represent natural images under the constraint of a sparse and over-complete representation, the resulting RFs of the neural units take on the shape of Gabor filters resembling the RFs of simple cells (reviewed in Olshausen, 2003). Over-completeness means that the number of outputs is greater than the dimensions of the input. This property is desirable for tiling the input space in terms of spatial location, orientation, and spatial frequency, and is consistent with the massive expansions of the image representation in V1 compared to that coming from LGN. A later model shows that also complex cell properties can emerge from the principle of maximizing sparseness (Hyvärinen and Hoyer, 2001). Experimental evidence for sparse activity was found in the visual and other cortical areas (see review by Barth and Poulet, 2012). Neurons in primate V1 exhibited maximal lifetime sparseness in response to natural images (Willmore et al., 2011). In response to natural movies, nearby neurons in cat V1 responded with high lifetime and population sparseness (Yen et al., 2007). Moreover, lifetime and population sparseness in ferret V1 were higher in response to natural images than was predicted from a simple RF model incorporating spatial location, orientation and spatial frequency (Weliky et al., 2003). However, stimulation of the surround of the classical RF plays a crucial role. Both lifetime and population sparseness increased significantly if a natural movie extended outside the area of the classic RF compared to just the classic RF1 (Vinje and Gallant, 2000; Haider et al., 2010). Further evidence for the special role of natural stimuli in visual processing comes from measurements of increased reliability compared to responses to artificial stimuli (Tolhurst et al., 2009; Herikstad et al., 2011). The precision of neural responses might, however, simply depend on the time-scale of the visual stimulus, as was shown to be the case for neurons in the lateral geniculate nucleus (Butts et al., 2007), and is also increased by stimulation of the visual region surrounding the classic RF (Haider et al., 2010). 1 The classic RF here refers to the area of the visual field (circumscribed by a circle), in which small white and/or black squares or bars of optimal orientation elicit a response in the neuron. 21 1 Introduction A difference in the mode of processing of natural and artificial stimuli was seen in experiments measuring the population activity in cat V1 using voltage sensitive dye imaging (a method reflecting changes in synaptic potential in supragranular layers across several millimetres of cortex). In comparison to drifting gratings, natural movies elicited different activity patterns (spatially and temporally) with lower average excitation levels and less adaptation (Onat et al., 2011). Consistent with this observation, neural responses in primate V1 show generally stronger late inhibitory components in responses to natural movies compared to flashed gratings, and the RF structure, specifically the inhibitory profile, differs when mapped in response to the two stimulus classes (David et al., 2004). In particular the temporal RF profile seems to change as spatial profiles were seen to have greater similarity in response to artificial and natural stimuli (Ringach et al., 2002; Touryan et al., 2005). However, RF models do not capture neural responses to natural stimuli very well and predicting these responses still poses a great challenge. Even the best models explain less than half of the variance of the responses (Carandini et al., 2005). Finally, the brain’s adaptation to natural stimuli shows itself in the increasing similarity between spontaneous population activity patterns and those evoked by natural stimuli with increasing age (Fiser et al., 2004). Berkes et al. (2011) hypothesise that V1 implements an internal model that is adapted gradually during development to the statistical structure of the natural visual environment, and that spontaneous activity reflects the prior expectations of this internal model. In summary, there is evidence for the brain’s adaptation to natural stimuli in order to code their representation more efficiently and more robustly, and to implement an internal model to draw inferences about the external environment based on the visual input and prior expectations. Furthermore, neuronal responses to natural stimuli cannot be predicted well using current models. For these reasons, we recorded neuronal responses to natural movie scenes in addition to artificial stimuli so that a direct comparison between the effects of the different stimulus classes is possible. 1.4 Neighbouring neurons The major part of this study investigates physiological differences between cortical neurons that are situated adjacent to each other (judging from the size of recorded action potentials, far less than 100 μm apart from each other). Largely because of the multitude of columnar systems that were found in several cortical areas of many mammals, neighbouring neurons are expected to exhibit similar stimulus driven activity. The goal of our undertaking was to test this hypothesis at a fine spatial resolution, for as many stimulus features as possible, and for simple as well as complex stimuli. Nearby neurons are also most likely to participate together in the coding of the same information, because they have a high probability to receive similar input, to be connected to each other, and to project to similar cortical targets (at least at the resolution of topographic maps and laminar location). A detailed comparison of the physiology between nearby neurons will therefore help us to discover principles of cortical information processing 22 Functional microarchitecture of cat primary visual cortex at the level of local populations. Regarding the vast literature on the physiology of neurons in primary visual cortex, relatively few studies have described the spike responses of neighbouring neurons. Instead single neurons were recorded in isolation, or recording techniques were used that could not resolve responses of single neurons and instead averaged across the neural responses of a local population. However, the medium of communication between neurons in cortex are spikes, and it is not known how outputs of nearby neurons are further processed. Averaging across neural responses might, therefore, inadvertently disguise the actual operations performed by cortex. When Hubel and Wiesel (1962) discovered the orientation columns in cat V1, they noticed clear differences between simultaneously recorded, nearby neurons. They reported that only one third of neighbouring neurons had similar detailed RF organisations, and that differences in RF size and location, in ocular dominance, preferred direction and velocity were observable. (Nevertheless, they promoted their ice-cube model so successfully it is found in every neuroscience textbook). When individual neurons of local populations spanning several 100s of microns in area 18 of cats were probed with drifting gratings, orientation preferences were seen to be strongly clustered even near pinwheels (note, however, that only 4 to 8 different orientations were used), but preferences in direction showed sudden discontinuities where neighbouring neurons have opposite direction preferences (Ohki et al., 2005; Ohki et al., 2006). Also the tuning to spatial frequency was not very similar between neighbouring neurons in cat V1 (Molotchnikoff et al., 2007). The most detailed study on the comparison of RFs of neighbouring neurons was performed by DeAngelis et al. (1999). They mapped the spatiotemporal RFs of nearby simple cells in cat V1 by presenting sparse binary noise stimuli (i.e. flashed, small, black or white rectangles at the preferred orientation). The overall layout of the complete RFs including the temporal and both spatial dimensions were on average very different between neighbouring simple cells. Orientation and spatial frequency were the most similar features, RF width a little less similar (the contradiction to the aforementioned results on spatial frequency might originate from the restriction to simple cells in the study by DeAngelis et al.). Temporal parameters like the latency of peak response, the duration over which the visual stimulus is integrated, and the preferred temporal frequency were only modestly similar between nearby simple cells. For the strength of direction selectivity, preferred spatial phase (referring to the relative positions of On- and Off-subfields at the peak of the RF’s temporal profile), and preferred temporal phase (referring to the relative time point of contrast reversal in the temporal profile of the RF), neighbouring neurons showed differences as large as between two randomly chosen neurons. The similarity between two neurons’ responses to more complex stimuli than bars or gratings is commonly measured by the strength of their signal correlations, i.e. Pearson’s correlation between their responses averaged across several repetitions of the same stimulus. The range of signal correlations lies between -1 and 1, where -1 signifies opposite response profiles, 0 reflects uncorrelated responses, and 1 means a perfect match. Gawne et al. (1996b) found that the 23 1 Introduction strength of signal correlations between neighbouring neurons in V1 of awake monkeys decreases with the complexity of the stimulus. In response to static bar-like stimuli, 40% of the signal variance in one neuron could be explained by the mean responses of its neighbouring neuron (corresponding to a signal correlation of 0.63), whereas only 13% of the variance (signal correlation of 0.36) could be explained in response to Walsh patterns, which are similar to checkerboards (spike rates were averaged across the duration of the stimulus presentation of 267 ms). Reich et al. (2001) noticed that in response to binary dense noise stimuli the signal correlations of neurons in monkey V1 increase with increasing time scale (from about 0.05 when responses were measured in 2 ms time bins to about 0.5 for bins of 2 s). They suggested that preferences for stimulus attributes conveyed on short time scales might not be shared between neighbouring neurons. In response to natural movies, Yen et al. (2007) saw that neighbouring neurons in cat V1 often respond with very different peak firing rates, and exhibit high population and lifetime sparseness. Signal correlations were weak and comparable in strength to those between neurons that are up to 150 microns apart from each other (mean signal correlation was 0.21 measured on bins between 33 and 40 ms). These data speak for a large functional heterogeneity among nearby visual neurons, specifically in response to complex and natural stimuli. Noise correlations between neighbouring neurons are typically larger than those between more distant neurons. Such noise correlations increase with increasing time scale (Reich et al., 2001), but their strengths are independent of stimulus class and are similar even during spontaneous activity (Gawne et al., 1996b; Bair et al., 2001; Ecker et al., 2010) although stimulus parameters might influence noise correlations when measured at a very fine temporal resolution of a few milliseconds (Kohn and Smith, 2005; Smith and Kohn, 2008). Among neighbouring neurons, noise correlations are stronger between neurons with more similar tuning properties (DeAngelis et al., 1999; Bair et al., 2001; Ecker et al., 2010). The implications of this relationship were already reviewed above (section 1.2). Interestingly, the subthreshold membrane fluctuations of nearby neurons in cat V1 are far more strongly correlated with each other than their spike responses. In nearby neurons (<500 μm apart) of cat V1, Lampl et al. (1999) detected a mean correlation of 0.4 during spontaneous activity (analogous to noise correlations) when membrane potentials were measured at a resolution of 1 ms. Yu and Ferster (2010) saw even higher correlation strengths between the membrane potentials of neurons in cat V1 with similar cortical distances during spontaneous as well as visually evoked activity. Both studies agree that the correlation is stronger if both cells receive monosynaptic input from the LGN, or if both are polysynaptically driven from the LGN, and if both neurons are simple or both are complex cells. Furthermore, visual stimulation suppresses low frequency membrane potential synchrony (0-10 Hz) and often increases synchrony at high frequencies (20-80 Hz) (Yu and Ferster, 2010). In barrel cortex of awake mice, the strong correlation between membrane potentials of nearby neurons during behaviourally quiet periods decreases but stays significant during whisking activity. However, the spikes of the same neurons show very little or no synchronous activity 24 Functional microarchitecture of cat primary visual cortex (Poulet and Petersen, 2008). An explanation for this comes from the observation that not only are the net membrane potentials strongly correlated between nearby neurons, but their excitatory and inhibitory synaptic inputs are also synchronized, as seen in prefrontal cortex of anaesthetized ferrets and in barrel cortex of anaesthetized rats (Hasenstaub et al., 2005; Okun and Lampl, 2008). Based on these observations, Okun and Lampl (2008) reasoned that excitatory and inhibitory inputs to the same neuron are highly correlated as well (with inhibition slightly lagging behind excitation). This balance of excitation and inhibition might be an important reason for why the high membrane potential fluctuation between nearby neurons is not reflected as strongly in their spiking correlations. 1.5 Origin and physiological properties of the local field potential In addition to recording neighbouring neurons with a single pipette, we recorded the LFP, which largely reflects local synaptic inputs, using a second “piggy-back” pipette. This allowed us to investigate how activity of single neurons and, more interestingly, response differences between neighbouring neurons are related to the average activity of a larger, though still local neuronal population surrounding these neurons. The LFP is a signal of great interest because it is more easily recorded than single units, it is directly related to non-invasive methods such as the EEG (electro-encephalogram), which is the recording of electrical activity from the scalp, and it is more closely related to the BOLD signal (blood-oxygenation-level-dependent signal), measured in functional magnetic resonance imaging to map brain activity, than single or multiple neuron activity is (Logothetis et al., 2001). However, the gap between the micro-description of neural activity at the level of single units and the meso-description at the level of the field potentials is still not closed. As most previous studies recorded in addition to the LFP either only single neurons or multi-unit activity without distinguishing between single units, our comparison between the LFP and the activity of two or more neighbouring neurons can shed more light on the relationship between the two levels of description, specifically for visual stimuli or stimulus attributes eliciting diverse responses among neighbouring neurons. 1.5.1 Origin and spatial extent of the LFP The LFP is defined as the extracellular voltage potential measured in the frequency range below 100-200 Hz with respect to a reference potential usually placed outside but very close to the brain. The extracellular potential is generated by electric currents that are contributed from all active cellular processes within a volume of brain tissue and that superimpose at a given location. In other words, activities of neuronal ensembles create current sinks and sources in the extracellular space resulting from all individual microscopic membrane currents averaged across a certain volume. Current sources occur when outward currents (out of the intracellular space) dominate whereas current sinks appear during dominance of inward currents. The dynamics of these sinks and sources then cause the fluctuations in the LFP. As the LFP only reflects average currents, it is the magnitude, the polarity, and the temporal coordination of 25 1 Introduction the nearby transmembrane currents that shape the extracellular field potential. The further the distance of the transmembrane current to the recording site of the LFP, the smaller its influence will be on the amplitude of the LFP. The most important contributor of neural activity to the LFP is synaptic input because synaptic input currents are of a sufficient magnitude and slow enough to summate temporally whereas fast events like action potentials (APs) have larger amplitude, but much shorter durations, so reducing their possibility of summating. It has long been assumed that synaptic inhibition (mediated by the GABAA receptor) adds very little to the LFP because the chloride equilibrium is close to the resting potential so that hardly any current flows. The membrane of spiking neurons, however, is depolarized so that inhibitory synapses, being for from their reversal potentials, can also have a substantial impact on the LFP. Non-synaptic events that influence the LFP are voltage-dependent dendritic calcium spikes (triggered by excitatory postsynaptic potentials, EPSPs, or back-propagating APs), intrinsic resonance and oscillations of the membrane potential, synchronized after-hyperpolarisations after bursts of several spikes (e.g. elicited by unexpected stimuli), and membrane potential changes in non-neural cells such as glia (these mainly contribute to very slow <0.1 Hz field patterns). Spike activity mostly affects higher frequency bands above 100 Hz of the LFP (also see section 1.6). The geometry of neurons also has an important role in influencing the LFP. Synaptic inputs to pyramidal neurons have by far the biggest influence, because the long and thick apical dendrites of pyramidal cells generate a strong dipole with an extracellular current sink at the site of an EPSP and a current source at the soma. Because the dendrites of pyramidal neurons are aligned with each other, synchronous synaptic inputs of the same polarity generate a large potential. In contrast, spherically symmetric neurons like spiny stellate cells or thalamocortical neurons have less impact on the LFP. For more details on the biophysical underpinnings of the LFP see, for example, the reviews by Mitzdorf (1985), Buzsáki et al. (2012), and Berens et al. (2008a). The vast body of literature on the origin of LFP agrees that the major contributor is synaptic input. Less clear is, however, whether the synaptic input reflected in the LFP has local origin due to recurrent connections within the local population or originates from other brain regions. Khawaja et al. (2009) suggested that the LFP (especially high gamma frequencies of 65-140 Hz) might reflect input currents from lower areas of processing, because they saw that the tuning properties of the LFP in area MST of monkeys resembled those of single neurons of area MT, the main input area to MST, and not those of single neurons in MST. Most studies of the LFP in the primary visual area, however, find very similar tuning properties to those of the nearby single neurons or of the multi-unit activity (reviewed in section 1.5.4). Specifically, the LFP in V1 was found to be orientation selective, a tuning property that is not present (at least not at this strength) in neurons of the LGN, the main feed-forward input area to V1. For these reasons, the LFP in V1 most likely reflects synaptic input of more local origin. 26 Functional microarchitecture of cat primary visual cortex Exactly how local the neural population is that contributes to the LFP signal is still an issue of debate. Some studies estimated the spatial spread of the LFP to be only several hundred micrometres (Berens et al., 2008b; Katzner et al., 2009; Xing et al., 2009), whereas others estimated it to be much larger, up to several millimetres (Mitzdorf, 1985; Kajikawa and Schroeder, 2011). However, the extent of the volume conduction of the electric field depends on intricate relationships between the current sources and the features of the conductive medium (Buzsáki et al., 2012). A detailed biophysical model of a neuronal population revealed that the spatial extent of the region generating the LFP depends on the neuron morphology, the synapse distribution, and the correlation in synaptic activity (Lindén et al., 2011). Some LFP patterns can, therefore, be recorded far away from their source, while other patterns remain local. 1.5.2 Origin of oscillations A description of the LFP in terms of its frequency components provides in some cases more insight into its function. On one hand, if the LFP is not strictly phase-locked to the external stimulus, evoked potentials averaged across several trials of the stimulus would not reflect all fluctuations adequately. On the other hand, oscillations at several frequency bands are associated with different physiological processes or states. The most prominent feature of any field potentials recorded from the brain is the relationship between frequency, f, and power, which follows a power law according to 1/fn (where n is between 1 and 2). Three main reasons were identified for this relationship: the low-pass properties of long dendrites of pyramidal cells that attenuate high frequency when transmitting electric signals, the capacitive nature of the extracellular medium (an issue that is still debated, see Logothetis et al., 2007; Goto et al., 2010), and network mechanisms (Buzsáki et al., 2012). The latter refers to the hypothesis that during a short time window (the short cycle of fast oscillations) only a limited number of neurons can be recruited, whereas during a longer time window the activity of a larger number of neurons can contribute and generate a larger amplitude of slow oscillations in the LFP. Indeed, low frequency oscillations extend across large areas of the cortex, whereas faster oscillations are only locally coherent (Destexhe et al., 1999). The following frequency bands are most often distinguished: delta (0.5-4 Hz), theta (4-8 Hz), alpha (8-12 Hz), beta (12-30 Hz), gamma (30-80 Hz), and high-gamma (>80 Hz). The exact boundaries between the different rhythms are not agreed upon and vary more or less across studies. It is, however, thought that they vary independently of each other and that different mechanisms are underlying them although most of them are not known or not well understood (Buzsáki and Draguhn, 2004; Buzsáki, 2006; Jia and Kohn, 2011). Slow oscillations, such as delta, theta and slower, are often associated with sleep rhythms and quiescent networks, and with the switching between cortical states (Up- versus Down-states, or desynchronized versus synchronized states) (Harris and Thiele, 2011; Jia and Kohn, 2011). They are thought to be controlled by neuromodulatory inputs and thalamocortical projections (Steriade, 2006). Alpha oscillations appear to constitute the default rhythm of the cortex. They are observed in cortical slices disconnected from input of other areas and are strongest during disengagement from 27 1 Introduction external input, most prominently in the occipital cortex during closure of eyes (Buzsáki, 2006). Oscillations at higher frequencies, namely gamma and high-gamma rhythms, are mostly stimulus driven, but are also seen to be related to cognitive phenomena such as attention and memory (see for example Engel et al., 2001; Kohn et al., 2009; Harris and Thiele, 2011). Because of their relation to external stimulus drive and their relatively local extent, gamma oscillations are the most relevant for this study of physiological properties of local cortical populations. Two main models of the generation of gamma oscillations exist (Fries et al., 2007; Tiesinga and Sejnowski, 2009; Buzsáki and Wang, 2012). The first one is termed ING (interneuron gamma) or I-I model reflecting the importance of the interaction between inhibitory interneurons. It explains the gamma oscillations on the basis of mutually connected inhibitory neurons, the time constant of GABAA receptors, which equals the duration of one gamma cycle, and sufficient external drive to induce spiking in interneurons. The gamma oscillation emerges when a subset of interneurons begins to discharge together, thereby inducing inhibitory postsynaptic potentials (IPSPs) in nearby inhibitory neurons. Driven by the external input, the cycle begins anew when the GABAA receptor-mediated hyperpolarization has decayed, this time with a larger number of interneurons that are likely to spike synchronously. In this model, the gamma frequency is largely determined by the kinetics of the IPSPs and the net excitation of interneurons. The second model is termed PING (pyramidal interneuron gamma) or E-I model and is based on reciprocal connections between excitatory and inhibitory neurons. Here, synchronous increase of firing rates in the excitatory neurons leads to an increased drive of the inhibitory neurons, which in turn inhibit the excitatory cells, so that fast excitation alternates with delayed inhibition. The oscillation frequency of the PING model depends on the ratio between the firing rates of excitatory and inhibitory neurons. Experimental support was found for both models and the two mechanisms might work together in generating gamma rhythms (Tiesinga and Sejnowski, 2009; Buzsáki and Wang, 2012). The term gamma oscillation has to be used with care. The mechanisms just reviewed are not thought to underlie increases in broad-band oscillations of higher frequencies, which often occur together with greater spiking activity. Instead they underlie increases of power in a very restricted frequency band, which appears as a so-called “gamma bump” (Buzsáki and Wang, 2012). Studies in monkey V1 aiming to separate these two phenomena could show that power of the gamma bump varies independently from the power of broad-band gamma frequencies, which are tightly related to the firing rate and tuning of the local neural population (Ray and Maunsell, 2011a). The orientation tuning of the gamma bump is similar across large cortical distances and, therefore, not related to the tuning of local neurons (Jia et al., 2011). These studies showed that high-gamma frequencies reflect to a large degree power contained spike waveforms (see also section 1.6), and must be distinguished from those reflecting inhibitiondriven rhythms. 28 Functional microarchitecture of cat primary visual cortex 1.5.3 Laminar differences As the characteristics of the LFP depend on biophysical properties of neurons as well as neuronal geometry and circuitry, they might change across cortical layers, which accommodate distinct cell types, exhibit different cell densities, but also receive input from different neuronal populations. Probably due to differences in conductivity between cortical layers, the spatial spread of visually evoked LFPs reach about half of the extent (about 120 μm) in layer 4B in monkey V1 than in the other layers (about 250 μm) (Xing et al., 2009). Concerning oscillations, no differences in the power spectra across the cortical layers in cat V1 were seen in response to various stimuli including drifting gratings and natural movies (Kayser et al., 2003). In monkey, however, clear differences were observed. Gamma oscillations were often more prominent, stronger, and more sustained in middle and superficial layers compared to deep layers in V1 (Henrie and Shapley, 2005; Maier et al., 2010; Buzsáki and Wang, 2012; Xing et al., 2012a; Smith et al., 2013). Gamma rhythms within each zone, superficial or deep, were highly coherent, i.e. phase-locked, to each other but not across zones (Maier et al., 2010). Also, neuronal spikes had a stronger phase-locking to gamma oscillations in the upper than lower cortical layers, whereas their maximal coherence in deep layers was at low frequencies of 6-16 Hz (Buffalo et al., 2011), which were strong in all layers but peaked in the deepest layer (Smith et al., 2013). These differences may be due to the more abundant recurrent connections in supragranular layers (explaining stronger gamma oscillations) but also indicate that superficial and deep domains constitute two functional units entertaining different interaction with subcortical and other cortical areas (Maier et al., 2010; Buffalo et al., 2011; Xing et al., 2012a; Smith et al., 2013). 1.5.4 Stimulus dependence and tuning properties of oscillations Visual stimulation was generally observed to increase the power in higher frequencies above approximately 20 Hz (gamma range) in V1 of anaesthetized as well as awake cats and monkeys, no matter whether artificial stimuli like gratings or bars were used or more complex stimuli such as pink noise or natural stimuli. The power of lower frequencies in contrast does not change considerably or only at stimulus onset (Gray and Singer, 1989; Kayser et al., 2003; Siegel and König, 2003; Belitski et al., 2010), or are entrained by the temporal frequency of flicker stimuli (Rager and Singer, 1998). In response to drifting gratings or moving bars, gamma power (approximately >30 Hz) is consistently more selective to stimulus features like orientation, direction, spatial frequency, and temporal frequency than other frequencies, but is still less selective than single- or multi-unit activity recorded in the neighbourhood (Gray and Singer, 1989; Frien et al., 2000; Siegel and König, 2003; Kayser and König, 2004; Berens et al., 2008b; Burns et al., 2010a; Jia et al., 2011; Lashgari et al., 2012). With increasing contrast the power of gamma oscillations also increases (Henrie and Shapley, 2005). Although gamma oscillations exhibit tuning to stimulus features, it does not in all cases match the preferences of nearby neurons. Gray and Singer (1989) found similar orientation and direction preferences for gamma oscillations and MUA 29 1 Introduction in only a little more than half of their recordings in cat area 17 and 18. Lashgari et al. (2012) saw significant correlations between single units and LFP power for preferred orientation, direction selectivity, contrast, size, and phase especially in the high gamma band (90-200 Hz). In other studies, the similarity between the orientation and size tuning of MUA and LFP power increases with increasing frequency of the LFP (Jia et al., 2011; Zhang and Li, 2013). Also in response to natural movies, all frequencies above 70 Hz exhibit high signal correlations to MUA (Belitski et al., 2010). There is, however, an exception to the general trend of high-frequency power exhibiting similar tuning behaviour as activity of nearby neurons due to the fact that the frequencies in the typical gamma range are modulated by two different mechanisms reflected in broad-band gamma and the gamma bump (see above). By varying a number of features of drifting gratings, such as the size, the contrast, and the addition of masking noise, Jia et al. (2013a) could clearly distinguish the amplitude of the gamma bump from neuronal firing rates, but also from the peak frequency of the gamma bump, because all three measures are modulated independently by the stimuli (for differences in size tuning between MUA and gamma in cat V1, see Bauer et al., 1995). They saw that the gamma bump only occurs in response to very large gratings extending beyond the classic RF of the local neurons (also observed by Gieselmann and Thiele, 2008) and only at contrasts above 12%. Under these conditions, the orientation preference and tuning curves of the gamma bump (30-59 Hz) are highly similar across very distant cortical sites (up to 9 mm apart from each other) and, therefore, do not match the orientation tuning of local neurons (Berens et al., 2008b; Jia et al., 2011). Ocular dominance preference, however, is well correlated between the gamma bump power and MUA (Berens et al., 2008b). Oscillations at 35-80 Hz are also enhanced by slow drift of gratings and attenuated by fast movement changes of gratings, which rather generate low frequency oscillations that are phase-locked to the stimulus (Kruse and Eckhorn, 1996). Not surprisingly then, the LFP does not show such a prominent peak in the gamma range in response to natural scenes or other complex stimuli like pink noise and wavelet stimuli, which instead elicit increased power at frequencies above 80 Hz and a phasic response rather than the steady-state response for gratings (Kayser et al., 2003; Haslinger et al., 2012). Similar to gamma oscillations, frequencies at 8-23 Hz exhibit tuning selectivity for orientation, spatial frequency and temporal frequency. Other frequency bands (1-4 Hz, 23-36 Hz and > 109 Hz) show instead phase locking to natural movies (Kayser and König, 2004; Montemurro et al., 2008). This indicates that stimulus locking and feature selectivity prevail in complementary frequency bands. Consistent with this, power of low frequencies (around 4 Hz) conveys information about natural movies independent from high frequencies (around 70 Hz), which contain information more redundant to that conveyed by neural firing rates (Belitski et al., 2008; Belitski et al., 2010). Phase information in low frequencies carries even more information about the stimulus than power. Considering the low-frequency phase at the time of spikes boosts and stabilizes the information carried by spike patterns alone and, in the case of 30 Functional microarchitecture of cat primary visual cortex natural movies, conveys more than 50% of additional information beyond that conveyed by spike counts (Montemurro et al., 2008; Kayser et al., 2009). 1.6 Relationship between LFP and neural spikes In the previous section, we have concluded that the LFP mainly reflects the average synaptic input to neurons of a local population. Consistent with this, the LFP is strongly correlated with the membrane potential of nearby neurons, although this correlation weakens during active behaviour, probably because the activity of nearby neurons then also exhibits less correlation (Poulet and Petersen, 2008; Okun et al., 2010). The cross-correlation between the LFP and the membrane potential is dominated by low-frequency components (<25 Hz). High frequency components also show some but a much weaker similarity between the two signals. To understand the role of the LFP in information processing, however, it is necessary to understand its relationship to neuronal spikes as these are the main carriers of information in the brain. The strength and temporal relation between the LFP and the spikes of one neuron, referred to as the spike-triggered average (STA) of the LFP, is well reflected in the cross-correlation between the LFP and the neuron’s membrane potential. This indicates that a strong correlation between spikes and the LFP reflects high synchrony between the neuron’s synaptic input and the synaptic activity in the local network. For sparsely firing neurons (with rates of 0.01 Hz and less), however, this relationship might not hold as spikes of these neurons ride on top of synaptic bumps that are distinct from the average population synaptic activity. These observations were made in the primary somatosensory and the prefrontal cortex of awake rats (Okun et al., 2010). Unfortunately, no data are available to confirm the findings in other species or cortical areas. A large number of studies, however, did investigate the timing of spikes in relationship to the extracellular oscillations by measuring their coherence, which reflects both amplitude covariation and phase consistency of two signals. A coherence value of 0 means that there is no relationship, a value of 1 indicates a perfect relationship. In general, the spike-field coherence is low, never exceeding average values of 0.25, and with peak values in low frequencies (<10 Hz) and gamma frequencies (approximately 30-60 Hz) (Siegel and König, 2003; Henrie and Shapley, 2005; Burns et al., 2010a; Ray and Maunsell, 2011b; Lashgari et al., 2012; Jia et al., 2013b). Spike-field coherence increases with increasing firing rate (particularly in the gamma frequency range, 30-90 Hz) (Lashgari et al., 2012) as well as with stronger and more reliable stimulus-locking of spikes (Kayser et al., 2009). Also visual stimulation with natural movies or drifting gratings increases the coherence between the LFP and spikes where higher contrast of gratings shows higher effects (Siegel and König, 2003; Henrie and Shapley, 2005). In relation to low frequency oscillations, spikes are on average locked to the peak of the oscillation cycle, whereas they tend to occur at the trough of high frequency oscillations (>20 Hz). However, the diversity of phases that spikes are locked to at high frequencies seems much more extreme than at low frequencies (Rasch et al., 2008). This diversity may in part come from different phase-locking between different cell types. In cortical slices as well as in anaesthetized animals, 31 1 Introduction putative pyramidal neurons spiked on average during the down sweep of gamma cycles, whereas putative inhibitory neurons tended to spike during the trough (neuron types were distinguished based on the shape of their extracellular waveforms) (Hasenstaub et al., 2005). Some evidence suggests, that the high spike-field coherence in low frequencies reflects the strong phase-locking of spikes in this frequency range, whereas the coherence in high frequencies rather reflects the strong amplitude covariation of firing rates and oscillations (Rasch et al., 2008; Kayser et al., 2009). The latter is corroborated by the positive correlation of gamma power with spike-field coherence in the gamma range (Burns et al., 2010a; Jia et al., 2013b) and with neural firing rate (Nir et al., 2007). However, power in the broad-band gamma range needs to be distinguished from power of the gamma bump, which is not correlated with firing rates (see section 1.5.4 reviewing the independent tuning properties of the gamma bump and firing rates). The correlation between power in broad-band gamma and firing rates might be a consequence of “leakage” of slow transients contained in spike waveforms into the LFP. The LFP might then simply reflect the local spike rate rather than specific neural or network interaction. Ray and Maunsell (2011a) performed a careful study to resolve this problem and found that spike energy can be observed in the LFP power spectrum at frequencies as low as 50 Hz (adding less than one dB) with prominent impact above 100 Hz. They also confirmed that power in the broad-band gamma range is tightly correlated to firing rates whereas power in the gamma bump (centre frequency between 30 and 80 Hz with band width of about 20 Hz) is not. Enhanced gamma power is often taken as a sign of increased spike synchrony. Indeed, elevated and spatially coherent power in the gamma bump was associated with enhanced pairwise and higher-order neural correlations (Singer and Gray, 1995; Jia et al., 2013b). It was also observed that the strength of covariation between broad-band gamma power and neural firing rates was better explained by the strength of correlation between neighbouring neurons than by the mean firing rate of single neurons (Nir et al., 2007). This indicates that neural activity is more strongly reflected in the LFP if surrounding neurons engage in similar activity. The best test of how and how strongly the LFP is related to spiking activity of surrounding neurons is to try to predict the latter from the former. Taking on this endeavour, Rasch et al. (2008) found that only the low-frequency structure of spike trains (MUA) in the range of 100 ms, but not the exact spike times, can be inferred with reasonable accuracy from the nearby recorded LFP (in V1 of macaques). The prediction performance was very similar for spontaneous and visually driven activity and varied minimally across trials. However, performance depended a lot on the specific recording site, decreased with distance between LFP and spike recording sites (especially when activity was visually driven), and was better in anaesthetized than in awake animals. The most useful features in the LFP for spike prediction were, first, high frequency power (especially at 80-90 Hz) and, second, low-frequency information, particularly the phase at frequencies <10 Hz. The frequency band of 10-40 Hz and phase information in the gamma band (>40 Hz) were not informative about spike times. This is strong 32 Functional microarchitecture of cat primary visual cortex evidence for the underlying causes of high spike-field coherence at slow and high frequencies, respectively. Finally, we are interested in the interrelation between the LFP, neural spikes, and external stimulation. Spike prediction based on the presented visual stimulus (natural movies in this case) and the LFP, revealed that the LFP modulates firing rate by the same order as the stimulus but at a faster time scale (note, however, that total prediction performance was very low) (Haslinger et al., 2012). Periods of natural stimuli (whether auditory or visual) that elicited reliable LFP phase responses at low frequencies (4-8 Hz or 1-4 Hz, respectively) fell together with higher firing rates (Montemurro et al., 2008; Kayser et al., 2009). On the other hand, spikes that were reliably locked to the stimulus (natural sound) often occurred together with a consistent spike-phase relationship at frequencies of 4-8 Hz (Kayser et al., 2009). So far it is not clear which mechanisms induce phase-locking of spikes and stimulus-locking of low-frequency oscillations and how both processes influence each other. 1.7 Function and relevance of oscillations The functional role of oscillations and specifically of gamma is not clear. One possibility is that oscillations are a simple by-product of network activity. Alternatively, oscillations could be seen as the means of generating temporally restricted windows-of-opportunity for neurons to fire (during phases of depolarization) (Buzsáki, 2006). In the latter view, each oscillatory cycle is a temporal window signalling the beginning and the termination of the encoded or transferred message. Compelling evidence for this theory was seen in response latencies of V1 neurons after presentation of flashed light stimuli. LFP fluctuations in the gamma range that preceded response onset could be used to predict the latency of the neural response: negative going LFPs were associated with early, positive going LFPs with late response onsets (Fries et al., 2001). This would mean that the brain does not operate continuously, but chunks information in temporal packages. The wave-length of the oscillation thereby determines the length of the temporal windows of processing and indirectly also the size of the neuronal pool involved, because longer time windows permit a large number of neurons to be recruited. For at least two reasons, gamma oscillations are the most suitable rhythms to form cell assemblies of transiently interacting neurons. A presynaptic discharge within packages of 15-30 ms appears to be most effective in discharging downstream pyramidal neurons due to their temporal integration abilities (Harris et al., 2003). Furthermore, the length of the gamma cycle corresponds to the critical temporal window of spike-timing dependent plasticity, which refers to the strengthening of a synapse when the postsynaptic neuron is sufficiently depolarized and pre- and postsynaptic activity is appropriately timed (Buzsáki, 2006). Several theories on the functional relevance of gamma rhythms in coding and information processing have been proposed. First, gamma might serve as a temporal reference frame where the phase at which a spike occurs encodes stimulus strength. The idea is that after the activity of excitatory cells in the local pool has been reset by the synchronous activity of inhibitory 33 1 Introduction neurons (see mechanisms of gamma oscillations in section 1.5.2) the most strongly driven excitatory cells will fire first in the next gamma cycle. In that way, stimulus strength could be read out within one gamma cycle (Fries et al., 2007). Second, gamma may influence communication between distant neuronal populations. If the LFPs and spikes of both populations oscillate coherently adhering to a certain phase relationship their communication can be maximized as spikes sent by one population arrive during the time window of maximal sensitivity in the other population (Womelsdorf et al., 2007). This theory was termed communication through coherence (Fries, 2005). Coherence between cortical sites might be established through long-range projections of pyramidal or inhibitory neurons, or through interleaving cell assemblies. Slower temporal coordination among gamma oscillators may be achieved by modulating the gamma power by the phase of slower rhythms (Buzsáki et al., 2012). The third theory asserts that gamma links representations of multiple, distantly coded features of single objects through “binding by synchrony” (neurons coding features of the same object are bound by synchronous firing) (Gray et al., 1989). To date, it is not clear whether the proposers of functions of gamma rhythms will withstand their critics. The peak frequency of gamma rhythms varies with several stimulus parameters, so that only ensembles receiving visual input with matched contrast, noise perturbation, and size could maintain a consistent temporal relationship (Jia et al., 2013a). Even within the same stimulus, varying contrast across space generates gamma rhythms at different peak frequencies (Ray and Maunsell, 2010). This makes the idea of binding by synchrony seem implausible. Furthermore, gamma rhythms do not behave like a clock, meaning that they do not preserve a constant phase over longer time durations, which means that gamma is unlikely to be used as a temporal reference for spike times or as basis for a stable communication between cortical areas (Burns et al., 2010b; Burns et al., 2011; Xing et al., 2012b). Last, but not least, gamma oscillations make up only a small fraction (0.5-10%) of the total power of the LFP (Jia and Kohn, 2011). No matter whether and which theories on the function of LFP oscillations will be able to explain the data, the rhythms measured in the extracellular field are unlikely to play a genuinely causal role. In contrast to neuronal action potentials, the LFP and its oscillatory content is not actively transmitted. The only way the LFP can affect neurons is via ephaptic coupling, which refers to the impact of the extracellular field on the transmembrane potential of a neuron. Strong but naturally occurring spatial gradients in the LFP that can be caused by simultaneous activity of many neurons can indeed influence neuronal activity, specifically spike timing and spike-field coherence, and modulate the network activity that generated the LFP by a feedback loop (Fröhlich and McCormick, 2010; Anastassiou et al., 2011; Buzsáki et al., 2012). So, the extracellular field may enhance and amplify the local population activity, but does not cause neurons to spike synchronously particularly not across large distances. It also seems unlikely that neurons will “read out” the phase of any oscillation in the extracellular field. The rhythms in the LFP ought to be seen rather as a trace of processes and interactions within and between 34 Functional microarchitecture of cat primary visual cortex neurons and neural populations, which themselves may have an impact on the behaviour of single neurons and a causal role in information processing. 1.8 Aims of this study The aim of this study was to test rigorously the functional similarity between neighbouring neurons implicitly assumed in many models of columnar cortical architecture. Neurons in a local population of V1 are obvious candidates to form cell assemblies and code visual information together, because they represent stimuli at the same position in the visual field and receive similar input. As it is not known yet how multiple neurons act together and what aspects of each neuron’s response is most relevant, it is necessary to investigate neural activity at the level of single neurons and at a fine temporal resolution. Only few studies have done this, and even fewer have investigated responses of neighbouring neurons to different stimulus classes including natural stimuli. Here, we compared tuning preferences and sensitivities to parameters of drifting gratings between neighbouring neurons, and quantified the similarity of their stimulus-driven responses across three different stimulus classes (gratings, binary dense noise stimuli, and natural movies) at various time scales. We measured the latter using signal correlations, i.e. the correlation strength between two neurons’ instantaneous firing rates averaged across several presentations of the same stimuli. These analyses show us which stimulus parameters are likely to be represented together by multiple nearby neurons and at which time scale shared representations vary. Having quantified the strength of signal correlations between neighbouring neurons we go on to measure their functional connectivity reflected in their noise correlations. This tells us how strongly tuning similarity is related to the degree of shared input. At the same time, the relation between signal and noise correlations reflects the coding capacity of nearby neurons. A comparison across stimulus classes will reveal whether these relations change according to stimulus statistics. To date, it is still very demanding to measure activity of a great number of nearby neurons at a fine spatial and temporal resolution and with high accuracy. We therefore decided to seek a compromise and to record a few neurons at high resolution and simultaneously record activity at a very coarse spatial and temporal resolution, which is given by the LFP. Our main interests were to compare the stimulus preference and sensitivity of the LFP to those of the neighbouring neurons and to assess the relationship between the fluctuations in the LFP to the neural activity, i.e. to firing rates and spike times. We investigated which features of the LFP are most strongly tuned and most stimulus-locked, and how the diversity or similarity in the tuning of neighbouring neurons is reflected in the preference and selectivity of the LFP. We assessed the precise temporal relationship between the activity of neighbouring neurons and the LFP, and what this relationship is affected by. 35 2 Methods 2 Methods 2.1 Animal preparation All experiments, animal treatment, and surgical protocols were carried out with authorization and under a license granted to K.A.C.M. by the Cantonal Veterinary Office of Zürich, Switzerland. The data presented here originate from 15 adults cats (2.2-4.3 kg) of either sex. The animals were initially anaesthetized with a subcutaneous injection of xylazine (0.5 mg/kg; Rompun 2%, Bayer) and ketamine (15 mg/kg; Narketan 10, Vétoquinol). The femoral vein and artery and the trachea were cannulated while the cat was maintained under general anaesthesia with 2% halothane (Arovet) in oxygen/nitrous oxide (50%/ 50%) and with regular intravenous injections of alphaxalone/alfadolone (Saffan, Schering-Plough Animal Health). Throughout the experiment alphaxalone/alfadolone (5-14 mg/kg/h and 2-5 mg/kg/h, respectively; Saffan, Schering-Plough Animal Health) was continuously delivered intravenously to maintain general anaesthesia. The cat was artificially ventilated with oxygen/nitrous oxide (30%/70%) and the ventilation volume was adjusted so that end-tidal CO2 remained at a level of 4.5%. After opening the skull, the cat was given an intravenous injection of the muscle relaxant gallamine triethiodide (40 mg; Sigma-Aldrich) and thereafter gallamine triethiodide (7.3 mg/kg/h; Sigma-Aldrich) mixed with (+)-tubocurarine chloride hydrate (0.7 mg/kg/h; Sigma-Aldrich) was delivered intravenously to prevent eye movements. Lidocain gel (4%; G. Streuli) was applied to all pressure points (ear bars and rectal thermometer). Topical antibiotics (Voltamicin, OmniVision) and atropine (1%; Ursapharm; to prevent accommodation) was applied to the eyes before they were covered with gas-permeable, neutral power contact lenses. The nictitating membranes were retracted with phenylephrine (5%; Bausch & Lomb). During the course of the experiment, electroencephalogram (EEG, maintained in spindling state), electrocardiogram and blood pressure (measured via cannula in femoral artery) were continuously monitored. If needed, additional intravenous Saffan injections or halothane (0-2%; Arovet) could be given. A thermistor-controlled heating blanket, on which the cat was lying, kept the cat’s rectal temperature at 37°C. The location of the blind spot of each eye was marked on the screen used for mapping the receptive fields. This allowed the position of the area centralis to be estimated for each eye. Appropriate spectacle-lenses were used to focus the eyes onto the screen positioned 114 cm in front of the eyes. A small craniotomy was performed over area 17 (Horsley-Clark coordinates anteroposterior -3 to -6 and mediolateral 0 to 3). A recording chamber was mounted over the craniotomy and a tiny durotomy was made at the recording site. After the recording electrode was lowered to the surface of the brain the chamber was filled with agar (Sigma-Aldrich) for stabilization. 36 Functional microarchitecture of cat primary visual cortex 2.2 Electrophysiology and extracellular labelling To record spikes of single neurons, we used a glass micropipette with tip diameter of 2-4 μm (for 4 recordings the tip was bevelled), filled with 1 mol/l potassium acetate (in a few cases with 0.05 mol/l Tris and 0.2 mol/l KCl with 2% of horseradish peroxidase) and with a chlorided silver wire electrode. The pipettes had an average resistance of 25 MΩ (range of 6-90 MΩ). A second low impedance glass pipette was used to record the local field potential (LFP). It contained a chloride silver wire and was filled with a solution of 2% Pontamine Sky Blue (6B, Sigma-Aldrich) in 0.5 mol/l NaCl, 0.5 mol/l potassium acetate and 0.01 mol/l phosphate buffer. The pipette had a mean tip diameter of 10 μm (range of 3-14 μm) and a mean resistance of 4.4 MΩ (range of 2-14 MΩ). This second pipette was glued to the high impedance pipette at an average tip-to-tip distance of 34 μm (range of 16-60 μm). Using separate electrodes to record the two signals, LFP and spikes, has the advantage that the LFP signal is less polluted by simultaneously recorded spikes due to the distance between both electrodes. In addition, each electrode could be optimized for its purpose: high impedance increases the signal-to-noise ratio when recording spikes and warrants that the recorded neurons are very close to the tip of the electrode; a low impedance electrode, on the other side, is thought to be more suitable for picking up low frequency signals although the effects of electrode geometry on the recorded signal is still debated (Nelson and Pouget, 2010). The reference electrode (chlorided silver wire) for the recordings was attached to the scalp a few centimetres from the recording chamber. After successful recordings, the solution of the second, low impedance pipette was injected iontophoretically into the extracellular space with current pulses of 3 s on/3 s off, amplitude of 4-5 μA and lasting for 2-5 min. The injection left a blue spot in the tissue so that the cortical layer of the recording could be determined. The signals of both electrodes were recorded with an Axoprobe-1A system (Axon Instruments, CA, USA), further amplified and filtered, the spike signal from the high impedance electrode in a band of 100-8000 Hz, the LFP signal from the low impedance electrode in a band of 1-400 Hz (NeuroLog System, Hertfordshire, UK, and Kemo, Dartford, UK). Both signals were then digitized with a 12-bit resolution, the spike signal at 20 kHz and the LFP signal at 1 kHz (CED 1401 and Spike2 software, CED, Cambridge, UK). 2.3 Perfusion and Histology At the end of an experiment, the cat was given an overdose of anaesthetic i.v. sufficient to flatten the EEG. The cat was then perfused transcardially with normal 0.9% NaCl solution followed by a solution of 4% paraformaldehyde, 0.3% gluteraldehyde, and 15% saturated solution of picric acid in 0.1 mol/l phosphate buffer. After fixation the brain was stereotaxically cut and the block containing the recording sites was removed from the skull. Each block of brain tissue was vibratome sectioned at 80 μm in the coronal plane. After the slices were flat mounted onto glass slides, cell bodies were made visible with a Nissl or a neutral red stain so that cortical layers could be distinguished. 37 2 Methods 2.4 Visual stimuli Before each recording, the receptive field of one or more cells were plotted by hand and location, size, ocular dominance, orientation and direction preference, and receptive field type (simple or complex) were determined. The centres of the receptive fields had an average distance of about 4° from the estimated area centralis (always less than 10°) and an average size of 1.25° (along preferred orientation) × 1.2° (orthogonal to preferred orientation). Computer generated stimuli were presented on a Sony CPD-G500 monitor under control of a ViSaGe graphics card (Cambridge Research Systems). The monitor placed at 114 cm in front of the cat's eyes had an image area of 19.1° × 14.4° at a resolution of 800 × 600 pixels. Minimum and maximum luminance values were 0.39 cd/m² and 101.31 cd/m², respectively. The frame rate was 100 Hz. All stimuli were centred approximately on the centre of the manually measured receptive field, extended well beyond the classical receptive fields of the recorded neurons and were presented monocularly to the dominant eye (except for 2 cases, in which only binocular stimulation was effective). Sinusoidal drifting gratings were presented in a square aperture with edge lengths of 4°-6° on a mean grey background. Gratings were first varied in orientation and direction (in most cases), then in spatial frequency and then in temporal frequency using appropriate step sizes and ranges depending on the selectivity of the neurons. Orientation was varied in steps of 3.75° to 22.5° (median 18°), spatial frequency in steps of 0.08 to 0.25 cycles per degree (median 0.2), and temporal frequency in steps of 0.1 to 0.4 cycles per second (median 0.25). After the tuning to a given parameter was established, the parameter was fixed to a value close to the preferences of all simultaneously recorded neurons. In a few cases we fixed the parameter to each neuron’s optimum separately to measure the tuning to the other stimulus parameters. To find the optima for a given neuron, tuning curves were estimated online using online spike sorting (Spike2, Cambridge Electronic Design). Gratings had low contrasts of 10-50% to prevent response saturation. They were shown for 5 s (in 3 recordings for 3 s) and were interleaved for 2 s (in 1 case for 10 s) with a blank mean grey screen. Gratings were presented in random order and each one was in most cases repeated 10 times (but at least 5 times) except when the recording had to be stopped prematurely due to loss of cells. The natural movie scenes are digitized broadcasts from Dutch, British and German television taken from Hans van Hateren’s image and movie database (van Hateren and Ruderman, 1998). The movie images have a resolution of 128 × 128 pixels. To get an image size of 6.17° × 6.17° we magnified each frame to 256 × 256 pixels by quadruplicating each pixel. Grey scale values of each movie were discretized to 255 values and were scaled so that the brightest and darkest pixels reached maximal and minimal luminance, respectively. The movies were placed on a mean grey background. They were presented at 50 Hz (original frame rate of movies in database) or at 25 Hz (after averaging pairs of consecutive frames). Each movie clip lasted for 10 s, contained no video cuts, and was repeated 30 times (in 4 pair recordings, movies were repeated only 10-20 times). The clips were interleaved by 3.7-4.5 s of a blank mean grey screen. For 38 Functional microarchitecture of cat primary visual cortex neurons that were lost before the presentation was completed only data for movies (or parts thereof) that were presented for at least 5 trials were considered in further analyses. The third stimulus type was binary dense noise consisting of elongated bars at an orientation intermediate between the preferred orientations of the neurons. The bars occurred in a grid with 1-4 rows and 5-15 columns. The grid had a width of 2.6-6° and a height of 2.4-5.3° and appeared on a mean grey background. Each image was presented for 20 ms, i.e. for 2 video frames. The sequence of images was produced by changing the luminance value of each bar between white and black according to a pseudo random binary m-sequence of order 12 (Victor, 1992). The same sequence was used for each bar, but was temporally shifted so that luminance values of all bars were uncorrelated to each other (shifts were determined as ratio between the total length of the m-sequence in frames and the total number of bars resulting in 91 to 455 frames). The same image sequence was repeated 10 times without breaks between repetitions. In total, the complete presentation of the noise stimulus lasted for approximately 13 min and 39 s. 39 3 Functional heterogeneity in neighbouring neurons 3 Functional heterogeneity in neighbouring neurons 3.1 Introduction Despite the existence of various functional maps in primary visual cortex, physiological properties of neighbouring neurons were seen to differ in a number of ways. As reviewed in more detail in section 1.4, RFs of neighbouring neurons have on average strongly differing spatiotemporal layouts with the greatest differences being in their preferred spatial and temporal phases, and in their strengths of direction selectivity. Temporal features are only modestly sim- Figure 3.1 Overview of analyses. Upper row shows a grating stimulus and tuning curves, upon which the analysis of tuning differences are based. Below are data used for signal and noise correlations: responses to all stimuli of one class were used; spike times (depicted in raster plots) were binned and averaged across trials to determine the signals of the neurons; deviations from this signal in each trial constitute the noise of each neuron. 40 Functional microarchitecture of cat primary visual cortex ilar (DeAngelis et al., 1999). Other studies saw large variability in preferences for spatial frequency and occasionally opposite direction preferences (Ohki et al., 2005; Molotchnikoff et al., 2007). Responses to more complex stimuli, such as checkerboard-like patterns and natural movies, elicited maybe even higher heterogeneity (Gawne et al., 1996b; Reich et al., 2001; Yen et al., 2007). However, a direct comparison of the response similarity between all three stimulus classes is missing. Here, we used a single high-impedance electrode to record from two or more neurons simultaneously ensuring that their distance is minimal. We probed the neurons with sinusoidal drifting low-contrast gratings, with binary dense noise stimuli, and with natural movies to investigate their response properties for a variety of stimulus statistics. We then quantified tuning differences in response to gratings and signal correlations in response to all three stimulus classes. The latter compares stimulus-driven responses at a very fine as well as a coarse temporal scale (varying between 10 ms and several seconds) allowing us to examine how different time scales affect the similarity of the neurons’ signals. We then asked how well differences in the classic tuning properties are related to the strength of signal correlations and what influence the stimulus class has on signal correlations. As a measure of the degree of common input to the neurons, we quantified the strengths of the noise correlations, compared them between stimulus classes, and examined their relationship to the neurons’ signal correlations. To validate our results we controlled for the influence of firing rates on the magnitudes of and relations between the various correlations we investigated. Lastly, we compared all our measures of response differences across cortical layers. For an overview of the response measures we used to characterize neighbouring neurons see the illustration in Figure 3.1. Note that the results of this chapter were previously published (Martin and Schröder, 2013). 41 3 Functional heterogeneity in neighbouring neurons 3.2 Methods 3.2.1 Spike sorting Continuous voltage traces were recorded and action potentials were detected and sorted using the offline sorting algorithm WaveClus (Quiroga et al., 2004), which is a publicly available MATLAB (The MathWorks Inc., Natick, MA) toolbox. Before spike detection, the raw voltage traces were bandpass filtered between 200 and 3000 Hz with an elliptic filter in forward and reverse directions to prevent phase distortions. The spikes clustered by WaveClus were visually checked for possible false assignments. Spikes that were not assigned to any cluster or that were manually discarded were screened for possibly overlapping spikes originating from two neurons. Overlapping wave forms were decomposed by matching them with templates of the previously found spike clusters (Atiya, 1992). Matches were manually inspected and corrected if necessary. This procedure recovered spike occurrences that would go undetected with spike sorting algorithms only based on the similarity between waveforms. Examples of sorted spikes and resolved overlapping spikes are shown in Figure 3.2. 3.2.2 Tuning curves and phase analysis One approach to quantify response differences between neighbouring neurons is based on a comparison of their tuning curves. The curves are described by various functions fitted to the median responses of a neuron to sinusoidal drifting gratings that varied in one parameter while all other parameters were fixed. The magnitude of a neuron's response during one trial was determined depending on the receptive field type (see Cavanaugh et al., 2002). For “simple” RFs (criteria described below), spikes were aligned to the onset of each grating cycle, a Fourier transformation was applied, and the response, termed “F1”, was defined as half of the peak-topeak amplitude of the first harmonic. For “complex” RFs, the response in one trial, termed “DC”, was determined as mean spike rate during grating presentation minus the baseline firing rate, i.e. the mean spike rate during presentation of the blank screen immediately before and after the trial (the first 250 ms of these responses were not considered to discard any off-responses). The RF was classified as “simple” if the spatial frequency curve based on F1 responses had a larger maximum than the curve based on DC responses, otherwise the RF was classified as “complex” (Cavanaugh et al., 2002). If no responses to varying spatial frequency were recorded, the receptive field type was inferred from the neuron's orientation tuning curve in the same way. The ratio between the maxima estimated from F1 and DC responses is termed relative modulation and will be used for comparison of tuning properties between neighbouring neurons. For each of the stimulus parameters, orientation/direction, spatial frequency and temporal frequency, we fit several functions to the median responses of a neuron by minimizing the reduced -error between the observed and the estimated responses. We largely adopted the methods by Cavanaugh et al. (2002) and defined the reduced 42 -error as Functional microarchitecture of cat primary visual cortex where is the number of different values of the stimulus parameter, sponse to the stimulus), th value, is the estimated re- is the observed median response across all repetitions (at least 3 per is the squared mean absolute deviation from the mean, and are the degrees of freedom of the function used to fit the responses. To avoid very large values of set to be at least0.01 ∙ max , with 〈 / 〉 where 〈∙〉 is the mean across . , was is anal- ogous to variance-to-mean ratio. For each tuning property, we fitted the responses to at least one function that was chosen for each stimulus parameter separately according to the expected shape of the tuning curve. To control for the case that responses were not tuned, they were in addition fit to a horizontal line at variable height. If the fit to the horizontal line resulted in the smaller reduced -error, responses were not considered in the comparison between tuning properties. In all other cases, the best-fitting function was used to extract the relevant tuning properties, which are the neuron’s preferred feature value, tuning width, and the direction index for direction tuning. Responses to gratings varying in orientation and direction of movement were fit to a wrapped Gaussian, ∑ exp 180 ⁄ 2 , with 2 peaks separated by 180° (Swindale, 1998) if gratings of opposite directions of movements were shown (see Figure 3.3 A for examples of 3 neurons) or to a simple Gaussian if only gratings of directions within 180° were presented. The cell’s preferred orientation was defined as the value of the Gaussian’s peak modulo 180°, whereas preferred direction was defined as the value of the highest peak only if gratings of opposite directions were presented. The width of orientation tuning was determined from the width of the larger Gaussian at half height (i.e. half way between zero and the curve’s maximum). The direction selectivity of the cell was estimated by the direction index (DI) defined as DI tion, / , where is the response to the preferred direc- is the response to the opposite direction (as in Reid et al., 1987). For varying spatial frequencies, responses were fit to a double half-Gaussian as well as to a logarithmic double halfGaussian (examples of 3 neurons are depicted in Figure 3.3 B) (Baker et al., 1998). Responses to gratings varying in temporal frequency were fit to a Gaussian and to a logarithmic Gaussian (see examples in Figure 3.3 C) (Nover et al., 2005). Preferred spatial and temporal frequencies were taken as the values at the Gaussian’s peak, whereas the tuning width for each of both parameters was defined as width at half height in terms of octaves. For all stimulus features, we only considered tuning width of a neuron if the lower and upper value at half width was inside or very close to the range of sampled values. Therefore, we excluded 8 neurons from measurements of orientation tuning width and 8 neurons from measurements of spatial frequency tuning width (7 of those neurons were low-pass filtering cells). In the case of temporal frequency, we unfortunately often missed to sample values high enough to capture the complete tuning range of our cells. To prevent false estimates we only considered the neuron’s preferred temporal frequency if it was estimated to be smaller than at least the 3 largest sampled values. 43 3 Functional heterogeneity in neighbouring neurons The largest preferences of temporal frequency we included were about 2.5 cycles per second (see section 3.3.1.1 for how this affects our results on differences between neighbouring neurons). For the same reason we excluded temporal frequency tuning width in our comparison between neighbouring neurons. To fit the functions to the cell’s responses we employed an unconstrained nonlinear optimization procedure (function fminunc, MATLAB, The MathWorks Inc., Natick, MA) in case of the straight horizontal line, or a constrained nonlinear optimization procedure for the various other functions (function fmincon, MATLAB, The MathWorks Inc., Natick, MA). Constraints for the latter fitting procedure were introduced to prevent unreasonable fits and included restrictions on the position of the peak of the Gaussian and restrictions on its width. The goodness-of-fit of the curves was assessed by adjusted where ̅ is the mean across all 1 ∑ ∑ / ̅ / 1 , used for the tuning curve. If adjusted of the best fit was smaller than 0.3, the fitted function was not considered for comparison of tuning properties. The preferred phase of a neuron was determined from its response to the grating with its spatial frequency closest to the cell’s preferred spatial frequency (Figure 3.3 D shows responses of 3 neurons) or to the grating with its direction closest to the cell’s optimal direction if tuning to spatial frequency was not measured. If the cell was not sharply tuned to spatial frequency (or orientation), responses to all gratings varying in spatial frequency (or orientation) were considered. The preferred phase in each trial was determined by, first, aligning the neuron’s spikes to the start of each drift cycle of the grating stimulus. Second, the preferred phase was defined at the maximum of the first harmonic of the aligned spikes. The neuron was considered to have a preferred phase if the distribution of preferred phases in all considered trials was significantly different from a uniform distribution (p < 0.05, Rayleigh test). The test was performed using the MATLAB toolbox CircStat (Berens, 2009). This may include neurons classified as complex cells according to their relative modulation. To quantify tuning differences between neighbouring neurons, we measured the absolute differences between their tuning properties, or the ratio in case of preferred spatial and temporal frequency (larger value divided by smaller one). These difference measures were then compared to the absolute differences or ratios that would be expected between two randomly picked neurons in area 17. To estimate expected differences between random neurons we used a permutation test previously introduced by DeAngelis et al. (1999). We randomly picked neurons that were recorded at different sites and measured their absolute difference in the respective stimulus parameter. The number of random pairs we selected matched the number of original pairs. In this way, we generated 1000 random distributions for each stimulus feature, and used the medians of these distributions (termed random medians) for comparison to the median of our original data. Differences between neighbouring neurons were counted as significantly 44 Functional microarchitecture of cat primary visual cortex smaller than expected if the median of the original differences was smaller than at least 95% of the random medians. The degree of clustering of a tuning parameter was assessed with a measure called “clustering index”, also devised in the analyses of DeAngelis et al. (1999). It is the ratio between the median difference among neighbouring neuron and the median of all random medians (see above) for one tuning parameter. If the clustering index is 1, neighbouring neurons are as similar in the parameter as random neurons are. The more it exceeds 1, the stronger is the clustering in cortex. 3.2.3 Reconstruction of RFs from responses to visual noise A further tuning parameter we looked at is the position of the RF, which was reconstructed from the neurons’ responses to the visual noise stimuli (recorded in 12 pairs and one triplet). First, we determined the spike-triggered average (STA) and the eigenvector of the spike-triggered covariance matrix with the largest eigenvalue, as well as their significance, following the procedure outlined by Schwartz et al. (2006). For both quantities, we considered the last 10 frames (equivalent to 200 ms) that occurred before each spike. Although this time range not always covers the complete spatiotemporal RF of a neuron, it always includes its maximum, which is most important for the estimation of RF centre and spatial extension. In short, for calculating the STA and the first eigenvector we first subtracted the mean from the stimulus ensemble and whitened it. The STA consists of the stimulus frames occurring directly before the spikes averaged across all spike occurrences. The first eigenvector of the covariance matrix of the spike triggered stimulus ensemble was determined after the STA was projected out of the stimulus ensemble. To test the significance of both measures a distribution of random STAs and eigenvectors was generated by bootstrapping, which involved shifting the spikes by a random amount relative to the stimulus sequence. STA and eigenvector were considered significant if they exceeded 97.5% of the random distribution. Estimation of the centre of the RF was based on a two dimensional (one time and one space dimension) variant of each significant filter (STA or first eigenvector). For this, only one row of bars (orthogonal to their orientation) of each filter was considered (we chose the central row or the one with the largest amplitude). Each frame of these spatiotemporal filters was convolved with a Gaussian (with a standard deviation of 0.65 pixels and a radius of 2.5 pixels). The filter was then fit to an RF model constructed as the weighted sum of two space-time separable components as described by DeAngelis et al. (1999). Each component was modelled as the product of a spatial waveform, , and a temporal waveform, : . , is an overall scaling factor, and is a weight on the second separable subunit. Gabor function: ; exp 2 cos 2 45 ; , is a 3 Functional heterogeneity in neighbouring neurons where , , , and are free parameters. ; Gaussian RF envelope, oids. and differs from has the same form as by replacing ; the response duration, represent the center and width of the correspond to the spatial frequency and phases of the sinus- ; 90°). only by a shift in its phase by 90° ( ; , but describes the temporal dimension and is temporally skewed 2arctan with and / . now represents the peak latency response, the temporal frequency, and is phase shifted by 90° relative to ; the temporal phases. Again, . See DeAngelis et al. (1999) for a more detailed de- scription of the model and for depictions of fits to real data. The fits were evaluated by their fitting error, ∑ ∑ , , , , , , where , is the STA or the first ei- genvector. Only fits resulting in errors smaller than 0.45 were considered. The center of the RF was then defined by the spatial parameter of the fit that resulted in the smaller error. 3.2.4 Correlation measures The second approach for comparing stimulus-dependent responses of neighbouring neurons was to measure their signal correlations at various time scales. Signal correlations that were measured on complete trials of grating stimuli are termed “trial correlations”. They are defined as Pearson’s correlation between average firing rates of two neurons in response to all presented grating stimuli: rho where n i 1 ( X i X )(Yi Y ) i 1 ( X i X )2 n (1) i 1 (Yi Y )2 n is the mean firing rate of one neuron for the complete duration of grating stimulus i averaged across all repetitions, the second neuron, and is the mean across all , and are the analogous data of is the total number of stimuli. We normalized the set of firing rates for each stimulus parameter (e.g. orientation) separately before combining across all parameters (see Figure 3.6 A). Specifically, we applied a z-transformation, i.e. subtracting the mean and dividing by one standard deviation, to all responses given to stimuli varying in orientation before combining them with the z-transformed responses to stimuli varying in spatial frequency and temporal frequency, respectively. Only then was the trial correlation calculated. This was necessary to compensate for differences in responsiveness due to different sets of fixed parameters, which could have led to spurious correlations (fixing orientation to the preferred one might lead to generally higher firing rates than fixing another parameter while orientation is varied). As a good estimate of signal correlations depends on an accurate estimate of the neurons’ firing rates, we only took reliable responses into account. To test for reliability we paired responses , to the same stimulus but from different trials and and pooled together paired responses from all stimuli that were varied in one parameter. If the two vectors and (for all 1, . . . , and all 1, . . . , 1, 2, . . . , , where is the number of trials) were significantly correlated (p < 0.05, permutation test, see below for description), the neuron’s responses to this stimulus parameter were said to be reliable and 46 Functional microarchitecture of cat primary visual cortex were considered for trial correlation. Furthermore, the trial correlation of a pair was only taken into account if responses to at least 10 stimuli were measured and reliable for both neurons. Each stimulus was repeated at least 5 times. Signal correlations at shorter time scales of 10-200 ms are defined in a similar way as above: rho where and and , (X n L i 1 b 1 n L i 1 b 1 ( X i ,b X )(Yi ,b Y ) 2 i ,b X ) represent firing rates in bin , i 1 b 1 (Yi ,b Y )2 n L (2) averaged across all repetitions of stimulus , are the averages across all stimuli and all bins, and is the number of bins. For each stimulus class, responses to all stimuli of that class were considered in calculating a pair’s signal correlation. As was done for trial correlations, binned responses to gratings varying in one stimulus parameter were z-transformed separately before signal correlation was determined. All responses to stimuli that did not elicit reliable responses were discarded. Again, we constructed vectors , and 1, . . . , , and for all trials , for all , 1, . . . , 1, 2, . . . , , . The responses to the stimulus were considered reliable if the vectors were significantly correlated with each other. Signal correlations were considered only if responses to at least 10 bins were measured, and if stimuli were repeated at least 5 times. Noise correlations compare the neurons’ response deviations from their mean response and are commonly attributed to shared input between the neurons. Noise correlations were determined in a similar way as shown in formulas (1) and (2) above. In formula (1), by / , where ulus in trial , and was replaced by is the mean firing rate for the complete duration of grating stim- is the standard deviation across all trials. Similarly in formula (2), , / , where , is the firing rate in bin of stimulus averaged is the standard deviation of responses in bin of stimulus . In both , , across all trials, and was replaced , , formulas, the analogous replacements are done for responses of the second neurons and a sum across trials is added in the nominator and denominator. Similar to signal correlations, we measured noise correlations at complete trials of grating stimuli and at bins of 10-200 ms for all stimulus classes and considered only reliable responses (see above). All stimuli that belong to one class and that were repeated at least 5 times were used to calculate each pair’s noise correlation. 3.2.5 Significance test for correlation measures To test the significance of the strength of a correlation between vectors X and Y we performed a permutation test. This means we randomly permuted the entries in Y to get Y’ and then measured the correlation between X and Y’. We repeated this 1000 times. The p-value is the fraction of random correlation strengths (between X and Y’) whose absolute value are larger than the absolute value of the correlation between X and Y. 47 3 Functional heterogeneity in neighbouring neurons 3.2.6 Estimate of signal correlations between identical but noisy neurons We estimated the maximal possible signal correlation between two identical but noisy neurons by what we call the “identical cell signal correlation”. Instead of comparing the signals of two different neurons, we divided the trials of a single neuron into odd and even trials, determined the signal for each group of trials by averaging across them, and then calculated signal correlations as described above. Again, only stimuli that elicited reliable responses were considered and at least 10 trials must have been recorded. We compared identical cell signal correlations and pairwise signal correlations in Figure 3.6 E. 3.2.7 Tests using bootstrapped signal and noise correlations The confidence intervals of signal and noise correlations were determined by bootstrapping. For each pair of neurons, we sampled with replacement responses from as many trials as were recorded and then determined signal and noise correlations as described above. We repeated this procedure 500 times. We used the bootstrapped distribution of a pair’s signal correlations to test whether they differ across bin sizes (Kruskal-Wallis test with p < 0.05) and whether they monotonically increase (or decrease) by checking that the signal correlation for bin size i+1 is not significantly smaller (or significantly larger) than that for bin size i (using the comparison intervals resulting from Tukey’s honestly significant difference criterion for multiple comparisons with a significance level of 5%). The confidence intervals of noise correlations determined from the bootstrapped distributions are shown in Figure 3.10 D to demonstrate the robustness of their estimates. Furthermore, the bootstrapped distributions were used to get confidence intervals for the strength of correlation between noise correlations of different stimulus classes (Figure 3.11) as well as between signal and noise correlations (Figure 3.12 B). 3.2.8 Control test for influence of time scale and signal correlations When signal correlations are compared across bin sizes, differences could arise due to noisier estimates of firing rates on smaller bins compared to larger ones. In order to estimate the strength of this effect, we simulated data based on a fixed firing rate to which random noise is added in each trial. As we wanted to measure the effect of different noise levels, we simulated data so that signal correlations on different bin sizes would be equal if no noise was added. We therefore used the mean firing rate that was measured on bins of 200 ms as the baseline rate. To simulate a neuron’s response for a bin size of 10 ms, we binned the baseline rate into 10 ms intervals and added normally distributed noise to each bin. The magnitude of the noise depended on the variance of firing rate measured on the 10 ms bins. As this variance increases linearly with firing rate, we first related the two quantities by a linear regression. Now the standard deviation of the normally distributed noise could be determined by looking up the variance observed for the bin’s firing rate. In this way, as many trials were simulated as were measured, and signal correlation was calculated between the simulated responses of two neurons as described above. Signal correlations for other bin sizes were simulated accordingly. 48 Functional microarchitecture of cat primary visual cortex These simulations show how much signal correlations are expected to change with bin size due to noise characteristics only. 49 3 Functional heterogeneity in neighbouring neurons 3.3 Results The analyses are based on recordings of 122 neurons in area 17 of 15 adult cats. Pairs of neurons (n = 46) and triplets (n = 3) were recorded with a single high impedance pipette. An additional 21 single neurons were included in control statistics (for comparison of tuning differences between neighbouring neurons with those between randomly chosen neurons, see following section). Figure 3.2 shows an example voltage trace containing spikes of three simultaneously recorded neurons (Figure 3.2 A), together with examples of overlapping spikes that could be distinguished in the spike sorting procedure (Figure 3.2 B). Figure 3.2 C shows raster plots for the simultaneous responses of the three neurons to multiple trials of a drifting sinusoidal grating featuring the neurons’ optimal orientation and direction, a monochrome natural Figure 3.2 Example of three simultaneously recorded neurons (cat0810 P1C2). A, This example of a bandpass-filtered recorded voltage trace contains spike shapes of three different neurons. All detected and identified spikes are marked by triangles of a different colour for each neuron. B, Three examples of almost simultaneously occurring, overlapping spikes originating from neurons recorded in A. Spikes are marked with the same colour code as in A and were distinguished using a semi-automated algorithm matching spike templates to the given voltage trace (see Materials and Methods). C, Raster plots depict the spike times of the same three neurons as in A and B during 5 seconds of a drifting sinusoidal grating, a natural movie scene, and a noise stimulus, respectively (small images at the left are example frames from each stimulus class, not the particular stimuli shown to these neurons). The grating and the movie were presented 30 times, the visual noise stimulus 10 times. Colours refer to same neurons as in A and B. 50 Functional microarchitecture of cat primary visual cortex movie scene, and binary dense noise stimuli consisting of high contrast black and white bars presented at the optimal orientation. For 16 pairs of simultaneously recorded neurons, responses to all three stimulus classes could be recorded, whereas the remaining pairs were lost before the end of the stimulus protocol or were unresponsive to some of the stimuli. 3.3.1 Responses of neighbouring neurons differ substantially 3.3.1.1 Tuning differences The first step in our comparison of neighbouring neurons was to estimate the similarities of their receptive fields (RFs) in response to drifting sine wave gratings. For each pair or triplet we determined their preferences for orientation, direction, spatial and temporal frequency, their tuning widths for orientation and spatial frequency, their direction index (indicating how much more the neuron prefers motion into one direction over the opposite), and their preferred phase. Figure 3.3 A-C shows examples of tuning curves of the three simultaneously Figure 3.3 Tuning curves and phase modulation of the same three simultaneously recorded neurons in Figure 3.2 (same colours for neuron identity). A-C, All tuning curves of the neurons were based on their median responses across all repetitions of each grating (dots). In this case the RFs of all three neurons were classified as simple, so the response refers to the amplitude of the first harmonic of the spike pattern in response to one cycle of the grating (F1 responses). Error bars show the mean absolute deviation from the mean response divided by the square root of the number of trials (see section 3.2.2). A, Responses of each neuron were fit to two wrapped Gaussians whose peaks have a fixed distance of 180°. The angle of the grating refers to its direction of motion orthogonal to its orientation. B, Tuning curves for spatial frequency were determined by fitting either two halves of two Gaussians (purple and green curves) or of two logarithmic Gaussians (orange curve) to the neurons’ responses. The better fit determined which of the two options was chosen. C, Responses to different temporal frequencies of the gratings were fit with a Gaussian (purple and green curves) or a logarithmic Gaussian (orange curve). D, Instantaneous firing rate of each neuron during the course of one drift cycle of the grating. 51 3 Functional heterogeneity in neighbouring neurons recorded neurons whose raw data are shown in Figure 3.2. The responses were fit with Gaussian functions or variations thereof. Figure 3.3 A shows that the orientation preferences of one neuron differed from the other two, but that all had the same direction preference. Direction indices ranged from 0.23 for the neuron indicated in orange, which had similarly strong responses to both directions, to 0.85 for the neuron indicated in purple. All three neurons had similar spatial frequency tuning (Figure 3.3 B) but one cell differed markedly from the other two in its temporal frequency tuning (Figure 3.3 C). As can be seen in Figure 3.3 C, we sampled temporal frequencies very finely but, unfortunately, missed out values high enough to get the full tuning range of the neuron with the purple curve. In such cases (see section 3.2.2 for details) we did not consider the neuron’s preference for temporal frequency. Consequently, our analyses on temporal frequency preferences are limited to lower values up to 2.5 cycles per second. To determine the preferred phase of a neuron its spikes were aligned to the start of each drift cycle of the grating stimulus. The preferred phase was then defined at the maximum of the first harmonic of the aligned spikes. The example neurons in Figure 3.3 D had very different phase preferences. Note that this definition of preferred phase incorporates spatial and temporal aspects of the neuron’s phase preference. In contrast to stationary contrast-reversal gratings, drifting gratings do not allow for a distinction between these two aspects. The greater part of phase differences we measured on the basis of our definition, however, can most likely be ascribed to differences in spatial aspects. DeAngelis et al. (1999) found that the preferred temporal phases in simple cells were confined to a narrow range, whereas preferred spatial phases were distributed uniformly over the range of possible values and contributed most to differences between spatiotemporal RFs of neighbouring simple cells . Furthermore, our measure of phase difference does not take into account the distance between RFs. It cannot, for example, distinguish between two overlapping and structurally equal RFs that just differ in the polarity of their subfields (Off-region of one neuron overlaps with On-region of the other neuron and vice versa) and two equal RFs shifted in space by the width of one subfield. However, phase differences, as we define them, do reflect absolute positional differences between the RFs’ subfields that have the same polarity (On or Off). To compare the tuning across all neuron pairs and triplets, we measured the absolute differences between the tuning properties of neighbouring neurons and compared these with the absolute differences that would be expected if receptive field properties were not clustered in cortex (Figure 3.4). Expected differences were estimated by pairing randomly selected neurons from different recording sites (see section 3.2.2 for details). Figure 3.4 A shows that the difference between the preferred orientations of two neighbouring neurons (black bars) was often much smaller than between two randomly selected neurons (red line). Similarly, preferred direction of movement (Figure 3.4 B), and tuning width for orientation (Figure 3.4 D) were significantly more similar in adjacent neurons than in two randomly chosen cells (p < 0.05, permutation test, see section 3.2.2). To quantify the degree of clustering for each 52 Functional microarchitecture of cat primary visual cortex Figure 3.4 Comparison between tuning differences of neighbouring neurons and of randomly picked neurons. A, Distribution of differences between the preferred orientations of two neighbouring neurons (black bars); left y-axis indicates the number of observed pairs. Black triangle at the top indicates the median difference. Red outline shows distribution of differences in pairs of two randomly selected neurons that were not simultaneously recorded (red y-axis to the right depicts percentage of these pairs; scales of red and black y-axes are equivalent). This distribution resulted from pooling all 1000 random distributions (see section 3.2.2). Red triangle indicates the median of all random medians, red horizontal line the confidence interval (5% to 95%). B-I, Same as in A but for different tuning properties. In each panel, the number of pairs that were considered is given by n. Not all tuning curves could be measured for all pairs and not all tuning properties could be determined from the neurons’ responses, so n differs across the stimulus parameters. J, The clustering index (see Results) for each stimulus parameter is depicted. Two stars indicate a highly significant difference (p < 0.01, permutation test) between the actual and the chance distribution of differences between neurons, one star indicates a significant difference (p < 0.05). 53 3 Functional heterogeneity in neighbouring neurons tuning property, we devised a measure previously introduced by DeAngelis et al. (1999) termed the “clustering index” (see section 3.2.2). It is the ratio between the expected difference, i.e. the difference seen between randomly chosen neurons, and the observed difference between adjacent neurons (Figure 3.4 J). If the clustering index is larger than 1, neighbouring neurons are more similar to each other than two randomly picked neurons. Again, preferred direction and preferred orientation were very strongly clustered within cortex. Although preferred temporal frequencies had a high clustering index, the neighbouring neurons were not significantly more similar than expected. This is probably due to the small number of pairs. Furthermore, the differences in the chance distribution of preferred temporal frequencies were most probably underestimated as we only sampled low values of temporal frequencies and missed out neurons with higher preferences. On the other side, our estimate of differences between neighbouring neurons is probably a fairly good description for the whole population of pairs, because data from DeAngelis et al. (1999) shows that differences in preferred temporal frequency between neighbouring simple cells are fairly constant and independent of the absolute preferred values (see their Figure 11 F). We therefore expect that temporal frequency shows clustering in cortex when the complete range of preferences is considered. Other tuning properties, particularly direction index, tuning width for spatial frequency, and preferred phase (see also Figure 3.4 E, F, and H, respectively), were randomly distributed among neighbouring neurons. For these tuning properties, clustering indices were close to 1 and differences between neighbouring neurons were not significantly smaller than differences between randomly selected neurons. These data suggest that some tuning properties do not cluster on a fine spatial scale within primary visual cortex. Having measured differences in single tuning parameters, we then asked how differences across parameters are combined and whether some pairs of neighbouring neurons have very similar tuning properties on the whole. To do this we rescaled differences in each tuning property so that they were directly comparable to each other. For each tuning property, therefore, the differences between two cells were expressed in percentiles of the expected differences between two randomly selected neurons (see Figure 3.5 A and B). So, if the difference between two neighbouring neurons falls into the nth percentile the cells are as similar as the n% most similar random pairs. The tuning differences of each recorded neuron pair are represented in Figure 3.5 C. Differences for each tuning property are depicted in a different colour, whereas a pair’s mean difference across all properties is shown as circle. The neuron pairs were ranked from the most similar to the most dissimilar pair. Only for 4 of 49 pairs were all measured tuning differences smaller than the 50th percentile of the chance distribution. Most pairs had some tuning properties in common, but the great majority showed large differences in at least one tuning property. 54 Functional microarchitecture of cat primary visual cortex Figure 3.5 Tuning differences between neighbouring neurons across all stimulus parameters. A, Same plot as in Figure 3.4 D. Differences between the neurons’ width of orientation tuning is given in degrees. Black bars depict differences between neighbouring neurons, the red line differences between randomly chosen neurons. B, Same data as in A, but now differences between the neurons’ tuning width (black bars) are given in percentiles of the chance distribution, i.e. in terms of the differences between randomly picked neurons (see main text). The distribution of differences between randomly chosen neurons (chance distribution; red line) is, therefore, flat. C, Tuning differences for all stimulus parameters plotted for each pair of neighbouring neurons, expressed in percentiles of the chance distribution as in B. Neuron pairs were ranked with the most similar pair, i.e. the one with the lowest mean tuning difference across all measured parameters, at the left. Colour of each square refers to the stimulus parameter. Mean differences depicted as black circles. 3.3.1.2 Signal correlations in response to artificial and natural stimuli The “signal” of a neuron is its purely stimulus-related response and is estimated by averaging the neuron’s responses across trials assuming that deviations from that signal, commonly referred to as “noise”, are independent across trials. The signal correlation of two neurons is thus a measure of the similarity between their stimulus-related responses. We calculated signal correlations here as Pearson’s correlation (covariance divided by product of standard deviations) between each neuron’s average firing rates in response to all presented stimuli of one class (gratings, movies, or visual noise; for details see section 3.2.4). We measured firing rates on various bin sizes to assess the influence of different time scales on the strength of signal correlations. As the calculation of signal correlation depends on a good estimate of the average firing rates of each neuron, we only considered responses to stimuli if both neurons fired in a fairly reliable manner across trials (see section 3.2.4). First, we considered signal correlations in response to gratings. In Figure 3.6 A firing rates of two adjacent cells were assessed over the complete duration of a grating stimulus lasting for 5 s. Each dot represents the mean responses of both neurons and is coloured according to which stimulus parameter (orientation, spatial 55 3 Functional heterogeneity in neighbouring neurons frequency, or temporal frequency) was varied. To avoid spurious signal correlations, firing rates in response to variations of a single stimulus parameter were z-transformed (mean subtracted and divided by standard deviation) before the signal correlation on all transformed responses was determined (see section 3.2.4 for details). We will from now on refer to this measure as “trial correlation”, because firing rates were estimated from complete trials as supposed to smaller time bins, which we will investigate in the following paragraphs. The example in Figure 3.6 A shows a pair with a fairly high positive trial correlation of 0.53 (p < 0.001). The population results (Figure 3.6 B) show that 48% of the pairs of neighbours (12 of 25 pairs) had positive trial correlations larger than 0.5. The median trial correlation across all pairs was 0.48, indicating a high heterogeneity in response properties between neighbouring neurons. The differences between neighbouring neurons grew even larger when their responses were compared on finer temporal scales. Signal correlations determined from firing rates on small bins ranging from 10 to 200 ms were used to quantify such differences. An example for two neurons is shown in Figure 3.6 C, which plots the average responses in bins of 50 ms to repetitions of a 10 s movie sequence. To assess the signal correlation of the cells, their binned firing rates in response to all movies (in this case two movies) were correlated with each other (illustrated in Figure 3.6 D). In this pair, the signal correlation for movies had a very high value of 0.81 (p < 0.001). Across all neuron pairs, however, the median signal correlation was always close to zero and the absolute strength of signal correlation for 50% of the pairs (interquartile range) stayed well below 0.5, no matter which stimulus class was presented (Figure 3.6 E). Signal correlations in the same range were seen for neighbouring neurons in cat area 17 in response to movies (Yen et al., 2007), but were higher in V1 of anaesthetized or awake monkeys in response to visual noise stimuli (Gawne et al., 1996a; Reich et al., 2001). The strength of signal correlation for two neurons depends on how well the average firing rates of the neurons can be estimated and ultimately on how noisy their responses are. We thus compared the signal correlations measured for pairs of neighbouring neurons to signal correlations that are expected in identical but noisy neurons. These reflect the maximal strength of signal correlation that can be reached by two neurons given the level of noise. We estimated this by dividing the trials of a single neuron into two groups, as if they originated from two different neurons (see section 3.2.6). Given that the neuron was recorded for a sufficient number of trials, the correlation between the average firing rates of each of the two trial groups is an estimate of the signal correlation between identical neurons. The median of these “identical cell signal correlations” across all single cells is depicted as diamonds in Figure 3.6 E for each bin size and stimulus class. The noise in single cell responses dramatically lowered the expected signal correlation for identical neurons, specifically for the slowly varying gratings and the smallest bin size of 10 ms (median of 0.177). Nevertheless, the median “identical cell signal correlation” was always larger than 80% of the pairwise signal correlations. In case of movies and visual noise, it was exceeded by at most 2 out of 18 or 1 out of 15 pairwise signal 56 Functional microarchitecture of cat primary visual cortex Figure 3.6 Signal correlations in response to artificial and natural stimuli. A, Firing rates in response to gratings measured on complete trials and averaged across all presentations of each grating stimulus are plotted for two simultaneously recorded neurons (cat0210 P3C4). The firing rates in response to gratings varying in one stimulus feature, namely in orientation and direction (black), spatial frequency (dark grey) or temporal frequency (light grey), were z-transformed separately (see main text). The signal correlation in this example was 0.53 (p < 0.001) B, Histogram of signal correlations for gratings (complete trials) for all n pairs of neighbouring neurons. Black bars indicate significant correlations (p < 0.05), white bars non-significant correlations. C, Firing rates of the same two neurons as in A (purple and orange trace, respectively) in response to a 10 s long movie sequence. Spikes were binned into 50 ms intervals and firing rates averaged across 30 presentations of the same movie. D, Firing rates of both neurons plotted against each other for each time bin in C as well as for data from a second movie presented to the same pair of neurons The signal correlation in this example was 0.81 (p < 0.001). Dashed line represents the linear regression line. E, Signal correlations for all three stimulus classes, gratings, movies and visual noise, determined using various bin sizes. For comparison the distribution of signal correlations measured on mean spike counts of complete trials (3 or 5 seconds in duration) is also included (rightmost box). The boxes extend from the 25th to the 75th percentiles, median indicated by black dot. Whiskers show the whole range of signal correlations, whereas outliers (further than 1.5 times the box length away from the box edge) are marked by circles. Distributions whose medians were significantly different from zero are labelled with a triangle above the box (p < 0.05, signed rank test). Diamonds represent median signal correlations expected from identical but noisy neurons (see main text and section 3.2.6). 57 3 Functional heterogeneity in neighbouring neurons correlations. In case of movies and visual noise, it was exceeded by at most 2 out of 18 or 1 out of 15 pairwise signal correlations, respectively. Signal correlations in neighbouring neurons were much lower than can be explained by the noise in the neurons’ individual responses. 3.3.2 Influence of time scale on signal correlations Although the median of signal correlations stayed close to zero for bin sizes from 10 to 200 ms, their range increased. When we examined signal correlations for each pair separately (data shown in Figure 3.7 A-C) we found that their absolute strengths increased significantly with increasing bin sizes from 10 to 200 ms in 27 of 65 recordings (taken from 37 pairs) in response Figure 3.7 Dependence of signal correlations on time scale. A, Dependence of signal correlations on bin sizes is shown for each pair of neighbouring neurons separately. Each grey line connects the signal correlations of one pair. Data for the largest bin size were measured on complete trials. For this panel all signal correlations were determined from responses to gratings. Filled dots represent significant signal correlations (p < 0.05). B and C, Same as in A but for signal correlations in response to movies and visual noise, respectively. D, Measured signal correlations (red dots) and distributions of simulated signal correlations (grey boxes) in response to gratings for one pair of neighbouring neurons (same pair as in Figure 3.2, indicated with purple and orange spikes). Simulated signal correlations were based on firing rates measured on bins of 200 ms and response noise dependent on the according bin size (see section 3.2.8). They were used to simulate the effect of the varying noise characteristics on signal correlations (see main text). E and F, As in D but for two other pairs in response to movies (E, same neurons indicated with purple and green spikes in Figure 3.2) and in response to gratings (F, same neurons indicated with orange and green spikes in Figure 3.2). G and H, Trend indices for simulated (grey boxes) and measured (red dots) signal correlations that are shown in plots D and E, respectively. (For definition of “trend index” see main text.) 58 Functional microarchitecture of cat primary visual cortex to gratings, movies or visual noise (considering only recordings, for which signal correlations on 200 ms and at least one smaller bin size existed). In detail: signal correlations for these recordings were significantly different between bin sizes (p<0.05, Kruskal-Wallis test on bootstrapped signal correlations; see section 3.2.7 for details), the signal correlation on the largest bin (200 ms) was significantly different from zero (p < 0.05, permutation test), and there was a monotonic increase or decrease of signal correlations with increasing bin sizes (see section 3.2.7). Figure 3.7 D and E (red dots) shows two pairs with a significant negative and positive trend, respectively, whereas the pair in Figure 3.7 F (red dots) shows no monotonic trend as was the case in 7 of 65 recordings. In the remaining recordings (31 of 65), signal correlations on 200 ms bins were not significant. The significant trends seen in some of the recordings might reflect a dependence of signal similarity between neighbouring neurons on the temporal stimulus statistics. A second possibility is that firing rates estimated on smaller bins are more susceptible to noise in the neuron’s responses than those estimated on larger bin sizes. The increase of absolute strength of signal correlations might therefore be explained by varying noise statistics across time scales rather than by the temporal stimulus statistics. To test for this, we generated neural responses from an assumed “true” signal emitted in response to the stimulus and additional noise with a magnitude depending on the considered bin size. The assumed true signal was taken from the neuron’s mean firing rate measured on bins of 200 ms, because these estimates were the least variable, and was then parcelled into smaller bins if necessary. The noise that was added was based on the measured variance of firing rate for each bin size (see section 3.2.8). If no noise had been added to the simulated neural responses, signal correlations would have been the same across all bin sizes. Thus, any differences in correlations of the simulated signals that are observed between different bin sizes can be attributed to the different noise levels and the different numbers of bins used to generate the signals. Examples of signal correlations based on simulated data in comparison to the measured signal correlations are given in Figure 3.7 D-F (grey boxes). The examples show that simulated signal correlations decreased in absolute strength the smaller the bin size was, i.e. the more noise was added to the original signal. To assess the strength of the trend in simulated and measured signal correlations we calculated the normalized difference between the signal correlation on 200 ms bins, bin size, : / , and on a smaller . We refer to this measure as the “trend index”. The measured trends of signal correlations in the pairs in Figure 3.7 D and E were much stronger than those from the simulated responses for all bin sizes (compare red dots with grey boxes in Figure 3.7 G and H). This shows that the trend of increasing strengths of signal correlations cannot be explained alone by the varying noise statistics across bin sizes. The same was true for about 30% of all recordings where a positive or negative trend was observed (8 of 27, Gratings: 3 with positive and 2 with negative trends, Movies: 3 with positive trends; p < 0.05, 2-way ANOVA with measured and simulated trend indices as one factor and bin size as second factor). In contrast, signal correlations at larger time scales of several seconds that we measured in response to gratings were not significantly correlated to those at smaller time scales 59 3 Functional heterogeneity in neighbouring neurons (p > 0.16 for all bin sizes, permutation test).These results show that the time scale at which signals are compared between neurons does matter and should be chosen with care. The reasons for a change in signal correlations with a change in time scale probably lie in the interplay between differences in the neurons’ RFs and the spatiotemporal stimulus statistics. If a stimulus causes two neurons to respond with an elevated firing rate during approximately the same extended time periods but without high precision, they will have a low signal correlation on small time scales, which then increases on larger bin sizes. Examples of this are the neurons indicated with purple and green spikes in Figure 3.2 C responding to the movie. In the opposite case, namely when the neurons fire during non- or almost non-overlapping extended time periods (as the neurons indicated with purple and orange spikes in Figure 3.2 C responding to gratings), their signal correlations will have a negative trend with increasing time scale. 3.3.3 Relation between tuning differences and signal correlations Our data indicate that neighbouring neurons have low signal correlations for a variety of stimuli. Furthermore, only a few tuning properties, viz. preferred orientation, direction, and width of orientation tuning, seem to be similar between neighbouring neurons. But how much can differences between neighbouring neurons in such classic tuning parameters tell us about their signal correlations measured in response to various stimulus classes? Our data give only an approximate answer to this question, because the analyses required not just the assessment of tuning differences, but also the responses to movies or visual noise. These analyses could only be made for a relatively small number of neuron pairs. The correlation strengths between differences in tuning characteristics and the pairs’ signal correlations are plotted in Figure 3.8 A. All tuning differences except for RF offsets (see below) were measured in percentiles of the chance distribution, i.e. the distribution of differences between any two neurons in primary visual cortex (see above and Figure 3.5 A and B). A number of tuning characteristics, viz. preferred orientation, preferred spatial frequency, and direction index, showed a relatively high and significant relationship to trial correlations in response to gratings explaining 27% to 50% of the variance (filled blue squares in Figure 3.8 A). This result is not unexpected as these tuning parameters have the strongest influence on the shape of the neurons’ tuning curves and, therefore, largely determine their trial correlations. Note, however, that signal correlations are calculated from mean firing rates whereas tuning curves are based on the neurons’ F1 or DC responses according to their receptive field type (see Materials and Methods). The scatter plots of these data (tuning differences versus trial correlations of each pair of neighbouring neurons) are shown in Figure 3.8 B-D. Signal correlations measured on shorter time scales had almost no significant correlations with tuning differences. The only exception to this were signal correlations in response to movies measured on bin sizes of 100 and 200 ms, which were significantly correlated to differences in relative modulation (filled red circles in Figure 3.8 A, column F1/DC). This means that if the neurons were to a similar degree phase modulated in response to drifting gratings, they would also respond more similarly to movies. The scatter plot for all pairs is shown in Figure 3.8 E. 60 Functional microarchitecture of cat primary visual cortex Figure 3.8 Correlation strength between tuning differences and signal correlations. A, Plot shows the correlation strengths between the pairs' signal correlations and their tuning differences in single preferred stimulus parameters, as well as in direction index, in relative modulation, and their RF offset (shown in different columns). The y-axis signifying the correlation strengths is reversed, because a close relationship between tuning differences and signal correlations would result in negative correlation coefficients. Tuning differences in each parameter were related to signal correlations for different stimulus classes (blue, red and green) and for various bin sizes (the lighter the colour, the smaller the bin size). Note that signal correlations on complete trials were only measured for grating stimuli (blue squares). Filled symbols mark significant correlations (p < 0.05). The letters next to some points mark significant correlations between tuning differences and signal correlations and refer to the plots, B-F, which show the underlying data. B, Signal correlations measured on complete grating trials are plotted against the neurons’ differences in preferred orientation. The correlation strength between both measures is depicted in A (square marked with B). C-F, Same as in B but for other tuning parameters and signal correlations on other bin sizes and for different stimulus classes (see label of axes). Although differences in preferred phase seem to be highly correlated with signal correlations in response to visual noise, the low “n” (in this case only 9 to 10 pairs) did not lead to significant results. Differences in tuning width for orientation or spatial frequency (not shown in Figure 3.8 A) had no significant relation to signal correlations. A further difference between RFs that could substantially influence the strength of signal correlations is the offset between RFs, which we here measured as the distance between both neurons’ RF centres. The RF centres were estimated from the responses to visual noise, which were used to reconstruct spatiotemporal RFs by either determining the spike-triggered average, or the eigenvectors of the spike-triggered covariance (see section 3.2.3). The reconstructed spatiotemporal RFs were then fit to an RF model to determine the centre of the RF. In this way, we measured the position of the RF centres of neurons in 13 pairs, which showed RF centre offsets of between 0.02 and 1.4 visual degrees (median offset was 0.32 visual degrees). The last column in Figure 3.8 A shows that only signal correlations in response to visual noise were significantly correlated to these offsets (also see Figure 3.8 F). In summary, most tuning differences we considered here were more closely related to trial correlations, which were measured in response to drifting gratings on a time scale of several seconds. At smaller time scales, 61 3 Functional heterogeneity in neighbouring neurons signal correlations had very weak relationships to most of the tuning differences and the strength of this relationship varied across stimulus classes. 3.3.4 Signal correlations are similar for different stimulus classes In the previous section we found that differences between neighbouring neurons in most tuning parameters poorly predict signal correlations on short time scales for any of the three stimulus classes. We now turn to the question of whether the neurons’ signal correlations are similar across the different stimulus classes we used, i.e., gratings, movies, and visual noise. Any differences that occur will necessarily be caused by the different stimulus statistics. Full-field gratings, for example, have only one spatial dimensional (luminance along the second dimension does not change), whereas natural movies are two-dimensional in space. If the responses of neurons were sufficiently described by a linear RF the shape of a Gabor function, which is itself one-dimensional in space, signal correlations in response to gratings and movies should be roughly similar. However, there are many parameters that are not captured by the one-dimensional linear RF, such as surround effects or the degree of contrast adaptation, that may differentially modulate the responses of both neurons and lead to differences in signal correlations across stimuli. Furthermore, some differences between the neurons’ RFs may be revealed by one but not the other stimulus class, e.g. due to different temporal and spatial resolutions. Therefore, neurons are not expected to have similar signal correlations in response to different stimulus classes. Note, however, that the converse argument is not valid: similar signal correlations across different stimulus classes are not proof of linear RFs. Our results show that signal correlations for different stimulus classes were strongly related to each other (Figure 3.9). Regardless of the bin size used, correlation coefficients were between 0.58 and 0.81 when signal correlations for movies were compared to those for gratings or visual Figure 3.9 Correlation strengths between signal correlations of different stimulus classes. A, Signal correlations measured on responses to gratings and to movies are plotted against each other for each pair of neighbouring neurons. The responses were binned in intervals of 50 ms. Inset shows the correlation coefficients between signal correlations using bin sizes of 10 ms, 20 ms, 50 ms, 100 ms and 200 ms, respectively. B and C, Same as in A but for signal correlations measured on responses to different stimulus classes. Black bars in the insets signify highly significant correlations (p < 0.01), grey bars stand for significant correlations (p < 0.05), n is the number of pairs. 62 Functional microarchitecture of cat primary visual cortex noise stimuli (Figure 3.9 A and C). They were even higher, namely between 0.8 and 0.91, when signal correlations for gratings and noise stimuli were compared to each other (Figure 3.9 B). Below we will show that this agreement cannot be explained by firing rates of the pairs alone. In addition, we found no systematic differences between the strengths of signal correlation in response to different stimulus classes (p > 0.06, pairwise signed rank test). From these results we conclude that the similarity between the stimulus-dependent responses of two neighbouring neurons is largely independent of the stimulus class. In particular, even simple artificial gratings elicit average responses that are as similar or different between neighbouring neurons as their responses to movies or visual noise stimuli. 3.3.5 Noise correlations are small but similar across different stimulus classes In contrast to a neuron’s signal, which reflects its stimulus-dependent response, its trial-to-trial fluctuations in response to the same stimulus are commonly referred to as noise. Noise correlations measure the co-variation of trial-to-trial fluctuations of two neurons independent of the stimulus. They are thought to arise primarily from inputs shared between the neurons (Bair et al., 2001; Kohn and Smith, 2005; Smith and Kohn, 2008). Although noise correlations cannot be used to infer how many inputs the neurons share in absolute terms (see sections 1.2 and 5.1), a comparison between stimulus classes can still tell us whether the amount of shared input changes. We computed the noise correlation of a neuron pair based on each neuron’s deviation from its mean response to the stimulus divided by the standard deviation. As for the case of signal correlation, only reliable responses of the neurons were taken into account (see section 3.2.4). Pearson’s correlation was then calculated on the normalized spike count deviations pooled across all stimuli of the same class (see section 3.2.4). As time scales of noise correlations in cortex were estimated to range from 10s of milliseconds (Bair et al., 2001) to 100s of milliseconds (Reich et al., 2001; Kohn and Smith, 2005; Mitchell et al., 2009), we considered spike counts on bins of 10 to 200 ms and, in response to gratings, of several seconds. Figure 3.10 shows the noise correlations between adjacent neurons for the three stimulus classes. Figure 3.10 A depicts an example of deviations from the mean responses of two neighbouring neurons for two repetitions of a movie scene and Figure 3.10 B shows the pair's noise correlation for the two different movie scenes that were presented during the recording. We found that across the whole population of pairs of neighbouring neurons median noise correlations were generally small, always staying below a value of 0.08 for bin sizes up to 200 ms, regardless of stimulus class (Figure 3.10 C). As noise correlations depend on a good estimate of the neurons’ mean firing rates and as the number of trials for some stimuli was relatively small in our dataset, we measured how robust our estimates of noise correlations were by performing a bootstrap analysis. Bootstrapped noise correlations were calculated from responses of randomly sampled trials (see section 3.2.7). Their relation to measured noise correlations is shown in Figure 3.10 D for bin sizes of 10 ms. The medians of the bootstrapped noise correlations were very similar to the measured values for all stimulus classes, and the 95% confidence 63 3 Functional heterogeneity in neighbouring neurons Figure 3.10 Noise correlations for all stimulus classes. A, For two simultaneously recorded neurons (purple and orange traces, respectively; cat0210 P3C4), trial-to-trial fluctuations are plotted for two different presentations (continuous and dashed lines, respectively) of the same 10 s movie sequence. Mean responses of the same neurons to this movie sequence are shown in Figure 3.6 C. Response deviations were determined on bins of 50 ms and z-transformed for each bin with the mean and standard deviation across all 30 stimulus repetitions. B, Normalized response deviations from the mean are plotted for both neurons for all presentations of two different movie scenes. Dashed line shows the linear regression line. The noise correlation between these two neurons in response to movies was 0.08 (p < 0.001). C, Distribution of noise correlations on different bin sizes and for different stimulus classes are depicted as box plots (see caption of Figure 3.6 E for details on box plot representation). The last box shows the distribution of noise correlations measured on complete grating trials (for better visibility, 2 outliers with noise correlations of -0.8 and -0.55 are not shown). The medians of all distributions were significantly larger than zero (p < 0.05, signed rank test). D, Measured noise correlations are plotted against median of bootstrapped noise correlations for each pair. Lines depict the 95% confidence interval of the bootstrapped distribution. Dotted grey lines mark equality. Typical number of samples used to determine noise correlations is about 14000 for gratings, 60000 for movies, and 82000 for visual noise. These differences might underlie the larger confidence intervals for gratings. E, Dependence of noise correlations on bin sizes for each pair of neighbouring neurons separately. Grey lines connect noise correlations of each pair. All noise correlations were determined in response to gratings and were measured on complete trials for the largest bin size. Filled dots represent significant noise correlations (p < 0.05). F and G, As in E but for noise correlations in response to movies and visual noise, respectively. 64 Functional microarchitecture of cat primary visual cortex intervals in most cases were small demonstrating the robustness of the measurements (larger confidence intervals in case of gratings are most likely due to smaller numbers of samples used to calculate noise correlations, see caption of Figure 3.10 D). The range of noise correlations in our dataset is consistent with several previous studies (Bair et al., 2001; Reich et al., 2001; Kohn and Smith, 2005; Mitchell et al., 2009), as is the small trend of increasing noise correlations with increasing bin sizes from 10 to 200 ms visible in Figure 3.10 C. When measured on long time scales of several seconds in response to gratings the median noise correlations reached a value of 0.16. Figure 3.10 E-G shows that noise correlations of several pairs increased with bin size, but decreased for only very few of them. Noise correlations measured on any two different bin sizes (between 10 and 200 ms) were highly correlated to each other (pooled across stimulus classes, rho > 0.7, p < 0.001, permutation test); those measured on complete grating trials were less well related to noise correlations at smaller time scales (rho = 0.36, p = 0.06 for 10 ms bins, rho = 0.65, p < 0.001 for 200 ms bins). Bair et al. (2001) showed that noise correlations are equivalent to the integral of the neurons' cross-correlogram (CCG) normalized by their auto-correlograms when limits of integration match the bin size of the noise correlations. Noise correlations in their recordings had the smallest variance across stimuli when the integration limits just enclosed the peak of the CCG but not its variable flanks. The CCGs of our pairs that showed signs of significant correlations had in average very narrow peaks extending over delays of 10-20 ms (data not shown). Accordingly, the noise correlations we measured on bins of 10 and 20 ms yield the best, i.e. the most robust, estimates. Noise correlations in response to different stimulus classes were similar to each other. A comparison between noise correlations for gratings and movies showed that they were highly correlated to each other (Figure 3.11). Noise correlations in response to visual noise were somewhat less well related to noise correlations in response to the other stimulus classes (specifically for bin sizes of 10 and 20 ms) and this relation did not always reach a 5% significance level due to the small number of data points. Underlying these differences might the faster temporal dynamics of visual noise stimuli (20 ms frame rate) and their high contrast changes from frame Figure 3.11 Correlation strengths between noise correlations of different stimulus classes. A, Strength of correlation between noise correlations for gratings and movies measured on bin sizes of 10 ms, 20 ms, 50 ms, 100 ms and 200 ms, respectively. Bar colour refers to significance level (black: p < 0.01, dark grey: p < 0.05, light grey: p < 0.1, white: p > 0.1). Grey lines signify the 95% confidence interval based on the bootstrapped noise correlations (see section 3.2.7). n gives the number of pairs, which differs slightly for different bin sizes. B and C, Same as in A but for different stimulus classes. 65 3 Functional heterogeneity in neighbouring neurons to frame. The more rapidly changing firing rates (see Figure 3.2 C) might influence both the dynamics of the neural noise response, as well as the accuracy of its estimation. However, none of the stimulus classes led to consistently larger noise correlations (p > 0.08 for any bin size, pairwise signed rank test). In the next section we investigate the degree to which stimulusdependent similarities in the responses of neighbouring neurons, as reflected in their signal correlations, were related to their noise correlations. 3.3.6 Relation between signal and noise correlations depends on stimulus class To test for the possible influence of common inputs on signal correlations, we plotted the latter against noise correlations, which were measured on bins of 10 ms as these are the most robust estimates (see above) and correlate best with signal correlations. Figure 3.12 A shows signal correlations on bin sizes of 10 ms plotted against noise correlations and Figure 3.12 B depicts the strength of this relation for different time scales. The correlation strength between the two measures varied between 0.4 for trial correlations in response to gratings and 0.85 in response to visual noise. For nearby neurons, positive relations between noise and signal correlations or another measure of tuning similarity have also been found in monkey area MT (Zohary et al., 1994; Bair et al., 2001). Comparing different time scales, our results show that in response to gratings signal correlations on larger bins were less well related to noise correlations. We speculate that signal correlations on larger time scales are less dependent on differences between certain RF parameters of the neurons (Figure 3.8 A suggests that, for preferred phase and RF offset, differences in these parameters might be averaged out for larger bin sizes). These differences may, however, be reflected in the degree of common input and thereby also in the strength of noise correlations of the neurons, which then leads to mismatch between signal and noise correlations. Further analyses will be necessary to substantiate this point. Secondly, and more importantly, Figure 3.12 B shows that signal and noise correlations were more closely related to each other for gratings and visual noise than for movies. Similar results were observed Figure 3.12 Relation between noise and signal correlations on different time scales. A, Noise and signal correlations both measured on bins of 10 ms for each pair of neighbouring neurons. Shade of the dots refers to stimulus class (black: gratings, grey: movies, white: visual noise). B, The correlation between noise correlations on 10 ms bins and signal correlations on varying bin sizes is shown for each stimulus class separately. For the last bar, signal correlations were calculated from the spike counts of complete grating trials. Grey lines at top of bars depict the 95% confidence interval based on the bootstrapped signal and noise correlations (see section 3.2.7). The number of pairs used for each stimulus class is given by n. All correlations were significant (p < 0.05), except for movies on bin sizes of 100 ms and for grating on complete trials. 66 Functional microarchitecture of cat primary visual cortex when noise correlations were measured on larger bin sizes, or if we took into account only those pairs for which data to all three stimulus classes were recorded (not shown). The data in Figure 3.12 A suggest that the smaller agreement between signal and noise correlations in response to movies is explained by very small noise correlations in pairs that respond similarly to movies (signal correlations higher than 0.2). Whether this is caused by some form of decorrelation is outside the scope of this study. However, this effect might show specific adaptation of visual cortex to natural stimuli as low correlations between signal and noise correlations are thought to increase coding capacities (see section 5.2). 3.3.7 Firing rates do not account for agreement between noise and signal correlations Previous studies have suggested that higher firing rates of neurons could lead to increased noise correlations (de la Rocha et al., 2007; Cohen and Maunsell, 2009). If noise correlations in our data were strongly correlated with firing rates of the neurons, and if the same held true for signal correlations, the agreement between signal and noise correlation would be a trivial consequence. Also the relation of the correlation measures across stimulus classes might be affected Figure 3.13 Distribution of firing rates and their relation to signal or noise correlations for gratings (A, D, G), movies (B, E, H), and visual noise (C, F, I). A, Distribution of firing rates that were averaged across all grating stimuli. B and C, same as in A but in response to movies and visual noise, respectively. D, Correlation between minimum firing rates in response to gratings and the signal correlations for gratings measured on bins of 10 ms, 20 ms, 50 ms, 100 ms, 200 ms, and on complete trials. n gives the number of pairs, which differs somewhat across bin sizes. Significance levels of correlations are marked by the shade of the bars (dark grey: p < 0.05, light grey: p < 0.1, white: p > 0.1). E and F, Same as in D but for responses to movies and visual noise stimuli, respectively. G-I, Same as in D-F but for noise instead of signal correlations. Number of pairs is the same as for signal correlations. 67 3 Functional heterogeneity in neighbouring neurons by firing rates. In this section, we will show that firing rates alone cannot explain our results. The distribution of firing rates (Figure 3.13 A-C) shows that the median firing rates for gratings, movies and visual noise stimuli were 8.5 Hz, 4.5Hz, and 6.0 Hz, respectively. Firing rates in response to gratings were significantly larger than in response to movies (p < 0.05, KruskalWallis test across all stimulus classes and Bonferroni correction for multiple comparisons), whereas visual noise evoked firing rates that had magnitudes in between the other two stimulus classes and were not significantly different to them. For the comparison to signal and noise correlations, the firing rate of a pair was calculated from the firing rate of the less active neuron in the pair averaged across all stimuli of a class to which the neuron responded reliably. We considered the minimum rate in the pair rather than the commonly used geometric mean rate, because simulations showed that spike count correlations depend more on the minimum response of two neurons than on their mean rate (see figure 2d in Cohen and Kohn, 2011). (The results did not change qualitatively when we used the geometric mean instead of minimum rates.) Figure 3.13 D-F shows that signal correlations were positively and significantly correlated with firing rates only in response to gratings and when measured on complete trials (p < 0.05, permutation test). For movies and visual noise stimuli, correlations were negative and not significant. The strengths of noise correlations had a positive and significant relationship to firing rates only in response to gratings on bin sizes of 10 ms (Figure 3.13 G-I). The relationship in all other cases was non-significant (p > 0.05). We then tested whether firing rates can explain the observed agreements between the correlation measures by determining semi-partial correlations. The semi-partial correlation between a predictor variable X and a response variable Y expresses the unique contribution of X to the total variance of Y by removing the contribution of another predictor variable Z. Technically, one correlates the residuals from the linear regression of X and Z, which removes the effect of Z, with Y. In our analysis, X and Y are distributions of signal or noise correlations, whereas Z is the distribution of firing rates. We first consider the variance of signal correlations for one stimulus class that can be explained by signal correlations for another stimulus class (see Figure 3.9). On average 13.8% (and at most 36.9%) of this variance could be accounted for by firing rates (when comparing the squared correlation coefficient with the squared semi-partial correlation coefficient). The strength of correlation between signal correlations of any two stimulus classes was still significant when the explanatory effect of firing rates was accounted for (p < 0.05, permutation test for semi-partial correlation). In case of noise correlations (see Figure 3.11), firing rates accounted on average for 5.9% (maximally for 39.7%) of the variance that could be explained by noise correlations of another stimulus class. In most cases, significant relationships between noise correlations of two stimulus classes (see Figure 3.11) remained significant after the effect of firing rates was accounted for (the only exceptions to that occurred for noise correlations in response to movies and visual noise). Finally, we checked whether the relation between signal and noise correlations of the neuron pairs (see Figure 3.12 B) could be explained by their firing rates. In all cases where this relation was significant, maximally 20.9% of the variance in signal correlations that could be explained by noise correlations, or vice versa, 68 Functional microarchitecture of cat primary visual cortex was explained by the minimum firing rates of the pairs (significance levels stayed very similar). Overall, these results indicate that the relationship between the various correlation measures of neighbouring neurons cannot be explained by their firing rate alone. 3.3.8 Dependence of response differences on cortical layer Neurons situated in different cortical layers play qualitatively different roles in information processing and transmission, and thus we investigated whether the magnitude of response differences or functional differences was influenced by the cortical layer in which the pair or triplet was located. By marking each recording site with Pontamine Sky Blue, we determined the laminar position of 40 pairs. We found 8 pairs in layer 2/3, 14 pairs in layer 4, 13 pairs in layer 5, and 5 pairs in layer 6. Because there are few data, we pooled pairs of layer 5 and 6 together for the statistical analyses, but still plot them separately in the figures. The comparison of tuning differences, signal and noise correlations revealed only minor differences between cortical layers. Figure 3.14 A shows differences in orientation preference, which were smaller between neighbouring neurons in layer 4 than in layers 5/6 (p = 0.029, signed rank test). However, differences between layers were minor, because no significant differences were found when we tested the distributions of all 3 groups (layer 2/3, 4 and 5/6) simultaneously (p = 0.11, KruskalWallis test). In fact, preferred phase was the only tuning property for which differences between neighbouring neurons were not equally distributed across layers (p = 0.0027, Kruskal-Wallis test). A pairwise test between layers accounting for multiple comparisons revealed that neighbouring neurons in layer 2/3 as well as in layer 4 had larger differences between preferred phases than neighbouring neurons in layers 5/6 (p < 0.05, Bonferroni correction; Figure 3.14 B). Differences between preferences for all other tuning parameters and between tuning widths were very similar between neighbouring neurons of all cortical layers. Figure 3.14 Dependence of response differences between neighbouring neurons on cortical layer. A, Differences between preferred orientations of neighbouring neurons plotted against the cortical layer of the pair. Differences were expressed as percentiles of the chance distribution, i.e. the differences in preferred orientations between randomly paired neurons. Each circle represents one pair of neighbouring neurons. B, Same as in A but for differences in preferred phases of neighbouring neurons. Significant differences between layer 2/3, layer 4 and layers 5 and 6 (pooled together) are marked with a star (p < 0.05 for Kruskal-Wallis test and accounting for multiple comparisons, see main text). 69 3 Functional heterogeneity in neighbouring neurons In agreement with these findings, signal correlations were very similar for all cortical layers, regardless of bin size and stimulus class. For noise correlations, we also found no significant differences between layers. Overall, our results show that the functional neighbourhood relationship between neurons in V1 remains fairly similar throughout all cortical layers. The relatively small data set, however, means these observations are provisional. 70 Functional microarchitecture of cat primary visual cortex 3.4 Discussion 3.4.1 Comparison to other studies The tuning differences we found between neighbouring neurons in cat V1 largely agree with previous studies, most notably with results of DeAngelis et al. (1999). In that study, comparison were made between spatiotemporal RFs determined by reverse correlation of neural responses to binary sparse noise. Making use of the same measure to quantify the degree of clustering, both our results and theirs show strong clustering of orientation, somewhat weaker clustering of temporal frequency, and no clustering of preferred phase2 and strength of direction selectivity. Furthermore, we observed a similar range of RF offsets and a similar tendency for neighbouring neurons to exhibit the same preferred direction. In contrast to our results, DeAngelis et al. (1999) observed a far stronger clustering for orientation and spatial frequency, the latter not being significantly clustered in our data. These differences can most likely be explained by DeAngelis et al. restricting themselves to pairs of simple cells, whereas we also included complex cells. Indeed, when we restricted our analyses to only simple cells, clustering of preferred orientation and spatial frequency became stronger (in the latter case even significant). Other studies in cat area 17 report that the preferred spatial frequencies of adjacent cells sometimes show large differences (Tolhurst and Thompson, 1982) or that spatial frequency tuning curves are as similar between neighbouring as between randomly selected neurons (Molotchnikoff et al., 2007). Our analyses of tuning differences add to this by showing that almost all pairs of neighbouring neurons exhibit a strong difference (as strong as between two random neurons) in at least one tuning property. For shorter time scales of 10s to 100s of milliseconds, a few previous studies showed large response differences between neighbouring neurons. The strengths of signal correlations we measured, however, are about a third to a half of the strengths that others have observed in V1 of awake and anaesthetized monkeys in response to stimuli similar to our binary noise stimuli (Gawne et al., 1996b; Reich et al., 2001)3. In response to natural movies, signal correlations measured by Yen et al. (2007) in V1 of anaesthetized cats had a similar range to our measurements but a high median (0.18 versus 0.01 in our data). Reasons for these differences are not obvious and could be manifold, including differences between species, recording electrodes, size and precise statistics of the stimuli. On the other hand, differences between the studies 2 Note that phase is used differently in our and DeAngelis et al.’s study. Whereas they distinguish between temporal and spatial phase, our measure of phase integrates both factors (see section 3.3.1.1). Moreover, both spatial and temporal phase as defined by DeAngelis et al. are determined relative to the spatial and temporal peak of the RF, respectively, whereas we defined phase relative to the position of the grating in visual space so that the reference for simultaneously recorded neurons is the same with respect to the stimulus. Therefore, the phase differences we found make a stronger prediction for heterogeneous responses, because in DeAngelis et al.’s case phase differences could be large although the cells’ On- and Off-subfields are largely overlapping. 3 Signal correlations measured by Gawne et al. cannot be directly compared to ours, because they preprocessed the neural signals (low-pass filtered spike responses and then only used the 1st principle component of the each neuron’s response vector). 71 3 Functional heterogeneity in neighbouring neurons (specifically in the last case) might be expected from the limited sampling size of neural pairs and stimuli and might not be significant. The increase in signal correlations with increasing time scale, previously seen by Reich et al. (2001), was most noticeable in our data for the visual noise (similar to stimuli Reich et al. used). We analysed this effect in more detail and found the following: firstly, less than half of the pairs showed a significant change of signal correlations with longer time scales; secondly, signal correlations for some of those pairs became more negative (particularly in response to gratings); and thirdly, most of these observations could be explained by changing statistics of noise in the data when responses are pooled in larger bins. Contrary to the conclusion by Reich et al. (2001), these results indicate that neighbouring neurons do not have a tendency to respond similarly to more slowly changing stimulus features but that temporal differences between their RFs exist at all time scales. The strengths of noise correlations up to time scales of 100 ms in our data match those measured between neighbouring neurons in V1 of anaesthetized monkeys (Reich et al., 2001). Noise correlations on longer time scales (>100 ms) were seen to be somewhat larger than ours (Gawne et al., 1996b; Reich et al., 2001), except for one study that saw noise correlations between nearby neurons of less than 0.01 at a time scale of 500 ms in V1 of awake monkeys (Ecker et al., 2010). However, the extremely low values of the latter study might be caused by very low firing rates (discussed in Cohen and Kohn, 2011). The strengths of noise correlations in our dataset were not significantly different across cortical layers, in contrast to a study in monkey V1 that found very low values (0.01) in the input layer (layer 4) and considerably higher correlation values in the superficial and deep layers (between 0.7 and 1.1) (Smith et al., 2013). In this case, noise correlations were averaged across pairs of neurons with distances of up to 1.8 mm. Laminar differences might thus be due to larger dendritic trees and farther reaching axons of neurons in upper and lower layers, so that distant neurons in those layers express larger correlations than neurons in the middle layer. These data do not, therefore, contradict our finding of similar noise correlations between nearby neurons across all cortical layers. A strong and positive relationship of noise correlations to signal correlations or tuning similarity has been previously observed for neighbouring neurons in monkey area MT (Zohary et al., 1994; Bair, 1999), as well as in cat V1 (DeAngelis et al., 1999). We confirmed these observations, and additionally showed that the relationship between noise and signal correlations is time scale dependent in response to gratings, and varies significantly across stimulus classes, specifically between visual noise and natural movies. 3.4.2 Limitations of experimental approach Cohen and Kohn (2011) identified four factors that can bias estimates of noise correlations (and to some degree of signal correlations): response strengths, the time period for counting spikes (i.e. bin size), spike sorting, and fluctuations in internal states. We controlled for the first two biases by showing that firing rates alone cannot explain our results concerning signal and noise correlations, and by considering various time scales for noise and signal correlations, 72 Functional microarchitecture of cat primary visual cortex including temporal resolutions of 10 and 20 milliseconds. This range corresponds to the duration of observed membrane time constants and is thus the timescale where correlated activity most strongly affects the responses of downstream neurons (see review by Salinas and Sejnowski, 2001). The third potential bias—faulty spike sorting—can lead to an overestimation of correlations, when spikes of multiple cells are not distinguished, as well as to an underestimation, when too many spikes are discarded. We minimized both types of error by achieving a high signal-to-noise ratio in our recordings and by careful screening and identification of all spikes. Finally, slow variations in brain states, the fourth bias, are generally very hard to assess. We kept the physiological state as constant as possible, as indicated by the vital signs, including the EEG. However, fluctuations on long time scales (several trials) seem to have only a minor influence on noise correlations (Bair et al., 2001), indicating that they arise in large part from fluctuations on faster time scales (see also Cohen and Kohn, 2011). Signal correlations, on the other hand, could be overestimated if by chance all trials for one stimulus fell into a state of low or high firing rates. It is impossible to exclude such a scenario but randomization of the stimulus sequence during presentation circumvents this problem in the best possible way. A further difficulty in measuring signal correlations is that they are completely dependent on the stimulus set. We attempted to find a meaningful measure of signal correlation by choosing gratings of preferred and non-preferred values, and by sampling more finely if on-line analyses indicated that tuning curves were very narrow. For the visual noise and especially for movie stimuli, no such strategy exists and the stimulus space is even larger. Signal correlation still appeared to us as the best measure for tuning similarities as it is independent of any assumptions about the RF structure. However, its limitations must be kept in mind when interpreting our results. 73 4 Relationship between the LFP and neighbouring neurons 4 Relationship between the LFP and neighbouring neurons 4.1 Introduction The LFP and specifically elevated gamma power in the LFP is seen as signature of increased and synchronous neural activity (see section 1.6). The results of the previous chapter showed, however, that neighbouring neurons in cat primary visual cortex are not equally tuned to changes in grating parameters, nor are their signal and noise correlations very strong. This observation led us to the question of how the LFP, which reflects the average synaptic input largely produced by the local neuronal population itself, is in fact related to the heterogeneity of multiple single neurons in its vicinity, and how well it reflects stimulus properties under these circumstances. Although a number of studies have investigated the interrelation between external stimulation, neural activity and the LFP, the experimental approach of this project offers a few advantages that were not exploited before: (1) the LFP was recorded using a separate electrode from that recording spike of nearby neurons to reduce effects of leakage from spike waveforms into the LFP, (2) two or more single neurons were distinguished so that not only each cell’s individual response properties but also the differences between cells can be related to changes in the LFP, and (3) the impact of three different stimulus statistics on the relation of the LFP to the stimuli and to neural activity can be compared. Here, we first examine the influence of visual stimulus on the frequency content of the LFP using the three different stimulus classes. We then compare the tuning curves and sensitivities of features of the LFP (power and evoked potentials) to those of neural firing rates and relate the former to tuning differences between neighbouring neurons. As a next step, we quantify the reliability and strength of modulation of instantaneous changes in LFP features (power and phase) in comparison to those of firing rates in neighbouring neurons. At last, we examine the relationship between the LFP (power and phase) and neuronal spikes at a fine time scale and how this relationship changes during strong versus weak stimulus-locking of neural responses. 74 Functional microarchitecture of cat primary visual cortex 4.2 Methods 4.2.1 Pre-processing of LFP To remove very low frequency fluctuations from the recorded LFP (see section 2.2, Electrophysiology and extracellular labelling, for details), a local detrending procedure was applied (function locdetrend of MATLAB toolbox chronux, http://chronux.org). It performed a linear regression on overlapping data segments of 1 s length moving in steps of 0.5 s, and averaged the regression lines to obtain the fit that was then subtracted. The LFP was then filtered, first, using a high-pass filter with cut-off frequency of 1 Hz and, second, using a low-pass filter with cut-off frequency of 100 Hz. Both were Butterworth filters of order 5 and were applied in forward and reverse direction to ensure zero-phase distortion. To remove line noise, a notch filters were applied to the LFP at the frequencies with maximum power around 50, 100, and 150 Hz corresponding to the frequency of the line noise and its harmonics. The bandwidth of each notch filter was set manually for each dataset. One dataset (cat0310 P1C1, file 3) was recorded at a sampling rate of 20 kHz and was down-sampled to 1 kHz after the local detrending using the MATLAB function decimate, first, with reduction factor 5, then, with reduction factor 4. 4.2.2 Spectral and phase analysis of LFP Power of the LFP was measured by employing the multitaper method (for details, see Mitra and Bokil, 2008). Spectral estimation was averaged over two Slepian tapers. In most cases, power was estimated on small moving time windows (shifted by 50 ms) whose length was varied depending on frequency to allow for a good compromise between accurate power estimation and fine temporal resolution. Time widows of 1 s, 0.5 s, 0.2 s, and 0.15 s were used for frequencies between 1-5.5, 5.5-11, 11-20, and 20-100 Hz, respectively. To reach a constant time-bandwidth product of 1.5 the half-bandwidth of the tapers for these four frequency bands were set to 1.5, 3, 7.5, and 10 Hz, respectively. These settings are comparable to those chosen by Rasch et al. (2008). For cases where LFP power was estimated over the complete trial duration of 3 or 5 s (section 4.3.3, Relationship between tuning curves of LFP and of neighbouring neurons), the same half-bandwidths were used for the tapers, which in turn resulted in increased time-bandwidth products. To calculate power spectra and spectrograms of the LFP the MATLAB toolbox chronux (http://chronux.org) was used. For instantaneous measures of LFP power on small time windows of 40 ms as well as for phase estimates measured on small time bins (1/4 of oscillation cycle), the LFP was filtered within bands of 2 Hz using a Kaiser window FIR filter with 60 dB attenuation in stop-bands, 0.01 dB pass-band ripple, and transition bands of 1 Hz. The Hilbert transform of the filtered LFP was then used to estimate phase in 1 ms bins, and the squared absolute value of the Hilbert transform resulted in estimates of LFP power in 1 ms bins. Estimates were averaged across the appropriate number of bins. As the FIR filters had very large sizes (a few seconds), only data 75 4 Relationship between the LFP and neighbouring neurons recorded at least 10 s after the start and at least 10 s before the end of each recording were considered to circumvent filter on- and offset artefacts. To determine mean and SD of a phase distribution and to test for its uniformity appropriate functions of the MatLab toolbox CircStat for statistics on circular distributions were used (Berens, 2009). 4.2.3 Measure of unreliability for LFP power and spike rate Unreliability of LFP power was based on measurements of instantaneous LFP power (see previous section) binned in windows of 40 ms. Mean and SD of power of one frequency measured across trials and pooled over all stimuli of one class were fit with a weighted linear regression (function lscov, MATLAB, The MathWorks Inc., Natick, MA). The weights were defined by / , 0.04 , where is the number of trials, and , is the mean power in bin of stimulus . Unreliability of LFP power of one frequency and for one stimulus class was then defined as the slope of the weighted linear regression relating the SD to the mean power of each bin and each stimulus: ∙ , , . Unreliability of spike rate was defined analo- gously but using variance instead of SD. 4.2.4 Correlation measures Tuning similarity of LFP power and neural firing rate was quantified by measuring signal correlations on responses averaged across complete presentations of grating stimuli. As in chapter 3, we defined signal correlation as Pearson’s correlation between the two signals ∑ , ∑ where ∑ is the mean LFP power for stimulus averaged across trials and across frequencies in bands of 4 Hz, is the number of stimuli, is the mean across all , and and are the analogous quantities for neural firing rate, either of a single neuron or of the summed responses of two neighbouring neurons. In Figure 4.5 C, signal correlations for several 4 Hz frequency bands were averaged for each neuron or neuron pair, respectively. Signal correlations were determined for each grating parameter (orientation, spatial and temporal frequency) separately. Correlations between instantaneous LFP power and firing rates as well as between instantaneous firing rates of two neurons were defined similarly. In the case of correlations between single trial responses, and each represent the response in a certain time bin of a certain stimulus during a certain trial, and index enumerates all time bins of all stimuli of one class for all trials. For correlations between trial averaged responses, and each represent the response in a certain time bin of a certain stimulus averaged across all trials, and index enumerates all time bins of all stimuli of one class. The size of the time bins equalled that of time bins used to quantify LFP power (see section 4.2.2, Spectral and phase analysis of LFP), i.e. 1, 0.5, 0.2, 76 Functional microarchitecture of cat primary visual cortex and 0.15 s depending on the frequency. Bins were overlapping, shifted in steps of 50 ms. The same bins were used to measure instantaneous spike rate. 77 4 Relationship between the LFP and neighbouring neurons 4.3 Results For this study, we made use of the same data as presented in chapter 3 (Functional heterogeneity in neighbouring neurons). But in addition to recording spiking activity of one to three neurons simultaneously using a high impedance pipette, we recorded at the same time the LFP using a pipette with lower impedance. Both pipettes were glued together so that their tips had a distance of approximately 30μm. In total, we recorded the LFP in 2 cases together with a triplet of neurons, in 42 cases with a pair, in 27 cases together with a single neuron, and in 4 cases without any single units. An example of data we collected during multiple presentations of a movie is given in Figure 4.1 showing the raster plot of two simultaneously recorded neurons (A), the LFP traces (B), and the average spectrogram of the LFP (C). These data exemplify several issues that we will investigate in more detail in the following sections: (1) the amplitude of higher frequencies of the LFP was strongly stimulus locked (Figure 4.1 B and C show a strong and reliable increase of high frequency amplitude around second 2 after stimulus onset), Figure 4.1 Example of simultaneously recorded neurons and LFP (cat0210 P3C4) during 30 presentations of a movie. A, Raster plot of two neurons (purple and orange, respectively). B, LFP recorded simultaneously with the neurons in A. Scale bar to the right depicts the magnitude of voltage fluctuations for all trials. C, Spectrogram of the LFP traces shown in B averaged across all trials. Colour codes for LFP power in units of mV2/Hz at a logarithmic scale (see colour bar to the right). Vertical dotted lines in all panels mark the onsets and offsets of the movie presentations. 78 Functional microarchitecture of cat primary visual cortex Figure 4.2 Another example of simultaneously recorded neurons and LFP (cat0610 P1C1) during 30 presentations of a movie. See Figure 4.1 for further explanations. whereas (2) the time course of low frequency fluctuations varied more or less randomly across trials and showed no obvious locking to the stimulus, and (3) the amplitude of high frequency fluctuations was tightly related to the firing rates of nearby neurons (the increase of high frequency amplitude in panels B and C coincided with a marked increase in activity in both simultaneously recorded neurons shown in panel A). The relationship of the LFP to the visual stimulus or to activity of nearby neurons was not always as strong as in the previous example. Data collected in a different animal and in response to a different movie (Figure 4.2) showed a much weaker relationship of high frequency amplitudes to the visual stimulus. A clear difference in this example to the previous one was that the responses of the two neurons agreed less well with each other. Nevertheless the responses of both were to some degree reflected in the LFP. How the heterogeneity of responses of neighbouring neurons relates to the LFP will be described in later sections. 79 4 Relationship between the LFP and neighbouring neurons 4.3.1 Visual stimulation increases power of higher LFP frequencies As a first step, we checked whether the average power of any LFP frequencies changed significantly depending on the stimulus class that was presented. Figure 4.3 compares the average power spectra elicited by gratings, movies, visual noise, and blank screens, the last of which elicits only spontaneous activity not driven by any stimulus. Figure 4.3 A shows that power spectra of the LFP recorded at a single site were very similar in response to different stimulus classes. To quantify the change in power across stimulus classes, we looked at the ratio of the mean power of the LFP in response to visual stimulation and during spontaneous activity. Although results at single recording sites clearly differed between each other (compare ratios of example in Figure 4.3 B with population data in Figure 4.3 C), on average power spectra in response to visual stimulation were different to those recorded during spontaneous activity, independently of the stimulus class. High frequencies above 20 Hz exhibited higher power, whereas power of lower frequencies did not differ greatly from that observed during spontaneous activity (Figure 4.3 C). The origin of the inflexion between 50 and 60 Hz occurring in response to visual noise is not known. As the frame rate of the full-contrast visual noise stimuli was 50 Hz, one might expect higher power at this frequency because neural responses might lock to the frame onsets. This power was, however, most likely removed together with the removal of line noise at 50 Hz using a notch filter applied to each recording. Possibly, the filter attenuated the signal in this frequency range more strongly than in response to the other stimuli. Note, however, that the inflexion rarely occurred in single datasets and that its magnitude is comparable to that of the SEM. In summary, these results give a quantitative indication that power of high frequencies are related to higher neural firing rates elicited by visual stimulation, Figure 4.3 Power spectra of LFP in response gratings (blue), movies (red), visual noise (green), and blank screens (black), respectively. A, Power spectra of LFP recorded at the same site as data in Figure 4.1 (cat0210 P3C4). Lines and patches show mean LFP power ± 1 SD taken across time, trials and stimuli of each stimulus class (SDs larger and smaller than the mean were determined separately). B, Same data as in A plotted as ratio of mean LFP power in response to visual stimulation (gratings, movies, or visual noise) and mean LFP power during spontaneous activity (presentation of blank screens). C, Ratio of the LFP power (mean ± 1 SEM across all recording sites) in response to visual stimulation with gratings, movies, or visual noise, and during blank screens (n = 71, 71, 28, and 26 for blanks, gratings, movies, and visual noise, respectively). For each recording site, the mean power spectrum in response to each stimulus class was calculated first, then the ratios between these mean power spectra were averaged across recording sites. For blanks, this ratio equals one (black line). 80 Functional microarchitecture of cat primary visual cortex whereas low frequencies are not related to firing rates. Similar increases of LFP power in response to visual stimulation were observed in previous studies in cat area 17 and 18 (Gray and Singer, 1989) and monkey V1 (Henrie and Shapley, 2005; Belitski et al., 2008; Berens et al., 2008b; Burns et al., 2010a). 4.3.2 Tuning sensitivity of the LFP and nearby neurons In this section, we compare the sensitivity of the LFP and of nearby neurons to varying parameters of sinusoidal drifting gratings. The analyses will show us, what aspects of the LFP vary most strongly to changes in grating parameters and how the strength of this modulation compares to that of the neural spike rates. One aspect of the LFP we considered is the evoked fluctuations at the onset and offset of the grating stimuli, termed “evoked potentials”. These have been described to exhibit tuning to sensory stimuli and to motor actions in previous studies (Kreiman et al., 2006; Asher et al., 2007; Berens et al., 2008b). Figure 4.4 A and B shows the onset and offset evoked LFP averaged across responses from all recording sites and across all presented gratings. The strength of the onset and offset response during a single trial was measured as the root-mean-square of the potential between 0 and 200 ms after grating onset or offset, respectively. This corresponds to the time window where evoked potentials were on average clearly different from zero. The second aspect of the LFP whose tuning sensitivity we investigated is the mean power during grating presentation. Figure 4.4 C shows for one recording site the orientation tuning curves of onset evoked potentials and LFP power at 24-56 Hz, as well as of the firing rate of two neighbouring neurons. In this example, the neurons were very sensitive to variations in orientation, i.e. they clearly fired at different rates for different orientations. LFP power was far less sensitive to orientation, whereas the onset evoked potentials had no clear preferred orientation and responses between orientations varied to a similar degree as responses to repetitions of the same orientation (reflected in large SDs). To quantify tuning sensitivity we used the d’-index: max min max where max max and and min min , min are the maximal and minimal mean responses across all orientations, and are the variances of these responses across all trials. Hence, the larger the d’- index, the better stimuli can be distinguished based on single trial responses, and the higher is the tuning sensitivity. The d’-indices in the previous example (Figure 4.4 C) were 9.57 for neuron 1, 2.51 for neuron 2, 1.02 for LFP power at 25-56 Hz, and 0.81 for onset evoked LFP. 81 4 Relationship between the LFP and neighbouring neurons Figure 4.4 Tuning sensitivity of LFP and of neural firing rates in response to gratings. A, LFP (mean ± 1 SEM across all recording sites) evoked by onset of grating stimuli at 0 ms (n = 65). Before average was taken across recording sites, the onset evoked LFP was first averaged across all grating stimuli for each recording site. Dashed vertical lines at 0 and 200 ms depict the time window over which the response strength of the evoked LFP was quantified (using the rootmean-square). B, Same as in A, but for the LFP evoked by the offsets of gratings depicted at 0 ms (n = 65). C, Response strengths (mean ± 1 SD across all trials) of firing rates of two neurons (blue and green, respectively), LFP power at 24-56 Hz (black), and the onset evoked LFP (brown). All data were taken from cat0610 P1C1 (same recording site as in Figure 4.2). Each tuning curve was normalized by dividing all values by the maximum. Most gratings in this example was repeatedly presented for 10 times. D, d’-indices (i.e. normalized difference between maximum and minimum response in tuning curve, see main text for details) of LFP power for tuning curves of orientation (turquoise), spatial frequency (pink) and temporal frequency (green). Depicted are mean d’-indices ± 1 SEM across all recording sites (n = 64, 61, 61 for orientation, spatial frequency, and temporal frequency, respectively). E, d’-indices (mean ± 1 SEM across all datasets) of the onset and offset evoked LFP (EP), and of neural firing rates for tuning curves of the same grating parameters as in D (n = 62, 40, 30 for evoked LFPs; n = 105, 64, 46 for spike responses). F, Lines show the portion of datasets, for which LFP power differed significantly in response to different parameter values (p < 0.05, one-way ANOVA). G, Same as in F, but for onset and offset evoked LFP, and for firing rates of neurons. We quantified tuning selectivity as reflected by d’-indices for each varied grating parameter, i.e. orientation, spatial frequency, and temporal frequency, separately. For each parameter, d’indices of LFP power averaged across all recording sites (Figure 4.4 D) had values around 1 for 82 Functional microarchitecture of cat primary visual cortex frequencies below 20 Hz (i.e. the difference between maximum and minimum response was as large as one SD), then increased markedly from 20 to 40 Hz to reach a plateau of about 2 for frequencies above 40 Hz. Onset and offset evoked potentials had d’-indices of about 1, similar to the power of low frequencies (Figure 4.4 E, left and centre). Neurons reached a mean d’-index of around 3 for each of the three grating parameters (Figure 4.4 E, right). These results show that on average neurons are about 1.5 times as sensitive as power of the most sensitive LFP frequencies, whereas power at low frequencies as well as evoked potentials are not modulated by changing stimulus features and, therefore, carry very little stimulus information. As a second measure of tuning sensitivity, we tested whether the responses to different parameter values differed significantly between each other (p < 0.05, ANOVA). In contrast to d’indices, this measure incorporates responses to all parameter values, not only those eliciting the maximum and minimum responses. However, it does not reflect the strength of the difference between responses. The ratios of datasets with significant differences in LFP power, evoked potentials and neural firing rate are depicted in Figure 4.4 F and G and showed similar trends as those seen for d’-indices. For substantial numbers of recording sites, LFP power at frequencies below 20 Hz and the strength of evoked potentials exhibited no significant differences in response to different orientations, spatial or temporal frequencies. On the other hand, LFP power at higher frequencies in most cases and neural firing rates in almost all cases differed significantly across varying values of a grating parameter. Both measures of tuning sensitivity showed that power of high frequencies (>40 Hz) in the LFP reflect changes in orientation, spatial and temporal frequency better than any other aspect of the LFP (low frequencies or evoked potentials). However, spike rates of single were still much more sensitive to these stimulus changes. 4.3.3 Relationship between tuning curves of LFP and of neighbouring neurons Given that power of higher LFP frequencies showed modulation by changes in grating parameters and given the known relationship between the LFP and neural spike rates, we expected that the tuning curves of those frequencies resemble to some degree the tuning curves of firing rates of single nearby neurons. Here, we quantify the strength of this resemblance. In contrast to most previous studies on this topic, we were also able to compare the similarity between responses of two neighbouring neurons to the similarity the LFP had to each one of those neurons. 83 4 Relationship between the LFP and neighbouring neurons Figure 4.5 Correlation between tuning curves of LFP power and of neural firing rates in response to gratings. A, Orientation tuning curves of two neurons (purple and orange, respectively) and the LFP power in the bands of 1-4 Hz (grey) and 24-56 Hz (black) (data from cat0210 P3C4, same recording site as in Figure 4.1). Lines and patches show the mean responses ± 1 SD across all trials (for each trial, power of all frequencies within one band was averaged). Magnitude of neural responses (in Hz) is shown on the left axis (red), magnitude of the LFP power on the right axis (black). Tuning curves for LFP power of both frequency bands were scaled so that maximum and minimum values are 1 and 0, respectively. B, Same as in A, but for spatial frequency tuning. C, Signal correlations (mean ± 1 SEM across all datasets) between tuning curves of neurons and of LFP power (for different frequency bands, for details see section 4.2.4). Correlations were calculated for each tuning parameter (orientation, spatial frequency, and temporal frequency) separately. Filled circles on solid lines show signal correlations between LFP power and responses of single neurons, open squares on dashed lines show signal correlations between LFP power and summed responses of two neighbouring neurons (n = 86/33, 48/17, 43/15 (single neurons/pairs) for orientation, spatial frequency, and temporal frequency, respectively). D, Signal correlations between LFP power (24-56 Hz) and single neurons are plotted against signal correlations between LFP power and summed responses of neighbouring neurons. Signal correlations were determined on mean responses to all grating stimuli (not separately for the different parameters). Connected dots represent data from two neighbouring neurons (each correlated with LFP power). E, Signal correlations between neighbouring neurons (x-axis) are plotted against signal correlations between LFP power (24-56 Hz) and single neurons. Again, signal correlations were calculated on mean responses to all gratings, and connected dots show data from neighbouring neurons. 84 Functional microarchitecture of cat primary visual cortex The only aspect of the LFP we compared to neural spike rates was LFP power, because the strength of evoked potentials after stimulus on- and offset was not tuned, as we saw above (Figure 4.4 E). Figure 4.5 A and B shows tuning curves for orientation and spatial frequency of two neighbouring neurons and of power of the nearby recorded LFP within two frequency bands. In these examples, LFP power of lower frequencies (1-4 Hz) not only exhibited higher variability across trials (consistent with smaller tuning sensitivity of low frequencies, as seen in the previous section) but had different preferences for orientation and spatial frequency compared to those of the nearby neurons. Power of higher frequencies (24-56 Hz), on the other side, was less variable across trials and exhibited similar tuning as the adjacent neurons. We quantified the similarity of tuning using a measure termed signal correlation, which is Pearson’s correlation between the “signals”, i.e. the mean responses, of LFP power and of a neuron’s firing rate (see section 4.2.4). In response to changing orientation (Figure 4.5 A), the signal correlations between the two neurons and low frequency (1-4 Hz) LFP power was -0.18 and 0.07, respectively. For high frequency (24-56 Hz) LFP power, the signal correlation with the neurons increased to values of 0.43 and 0.60, respectively. Responses of the two neighbouring neurons were correlated with a strength of 0.51. When spatial frequency was varied (Figure 4.5 B), low frequency LFP power had correlation strengths with the neural responses of 0.44 and 0.54, but high frequency LFP power reached correlation strengths of 0.93 and 0.87, respectively. The two neurons had a signal correlation of 0.94. The trend that LFP power of higher frequencies have more similar tuning to nearby neurons than power of lower frequencies was also found in the population data. Figure 4.5 C shows signal correlations between LFP power of various frequency bands and neural responses as well as between two neighbouring neurons for the complete population. Signal correlations were measured separately for tuning curves of orientation, spatial and temporal frequency (different colours in Figure 4.5 C) and then averaged across all recording sites. We also distinguished between signal correlations of LFP power with the firing rate of a single neuron (solid lines with filled circles) and with the summed firing rates of two neighbouring neurons (dashed lines with open squares). The results show that tuning of LFP power of low frequencies up to 12 Hz was clearly uncorrelated to tuning of neural responses, independent of what grating parameter was varied. Signal correlations between LFP power of high frequencies above 24 Hz and neural responses on the other hand reached values between 0.27 and 0.69. The absolute strengths of signal correlations at higher frequencies (above 24 Hz) depended on the varied grating parameter. Signal correlations for orientation tuning were significantly smaller than those for spatial and temporal frequency tuning (p < 0.05, ANOVA and Tukey’s honestly significant difference criterion for correction of multiple comparisons; only exception: signal correlations involving summed neural responses were not significantly different between orientation and spatial frequency tuning). Previously, when preferences for certain stimulus parameters were compared between the LFP and neural activity, differences between the two measures were ascribed to the integration volume of the LFP (Berens et al., 2008b; Katzner et 85 4 Relationship between the LFP and neighbouring neurons al., 2009; Xing et al., 2009). So, the shorter the cortical distances at which two neurons change their tuning preferences, the larger are the expected tuning differences between the LFP and a single neuron recorded in its vicinity. The same effect might underlie the tuning differences we observed: if orientation preference changed more strongly than spatial or temporal preferences across the same cortical distance, orientation tuning would be more different between the LFP and neural firing rates than frequency tuning. However, when measuring signal correlations, as in our case, not only the preferred values but the complete tuning curves are compared, so that also differences in tuning width play a role. If the tuning width is very small compared to the range of values represented by the neurons, signal correlations will be very sensitive to small differences in preferred values. This seems to be the case for orientation tuning, because even neighbouring neurons tend to have smaller signal correlations between their tuning curves for orientation than between those for spatial or temporal frequency (see Figure 4.5 C; differences were, however, not significant; p > 0.12, ANOVA) although they are known to have more similar preferences for orientation than spatial or temporal frequency (DeAngelis et al., 1999, also see section 3.3.1.1). Most likely the same reason underlies the greater signal correlations between LFP power and firing rates for temporal and spatial frequency than for orientation. A different explanation for the results could lie in different mean firing rates elicited by the three stimulus parameters. We saw that mean firing rates in orientation tuning curves were significantly smaller than those in spatial frequency tuning curves, which were in turn smaller than the mean firing rates in temporal frequency tuning curves (p < 0.05, paired Wilcoxon rank test; median differences were smaller than 2.4 Hz). Furthermore, the correlation between LFP power (at 24-56 Hz) and firing rates was weakly but significantly correlated to the firing rate of the neuron (rho = 0.18, p < 0.02). Therefore, responses to varying temporal and spatial frequencies could have been more strongly coupled to LFP power than the somewhat weaker responses to varying orientations, but the effect was probably small. In summary, the smaller tuning similarity between LFP power and firing rates for orientation does not indicate that the LFP’s integration volume is much larger than orientation columns, but rather reflects the tight orientation selectivity of single neurons. Figure 4.5 C also shows that LFP power of higher frequencies is slightly better correlated to the summed activity of two nearby neurons (dashed lines) than to the activity of each single nearby neuron (solid lines). Pooled across all three grating parameters signal correlations for summed neural responses were in fact significantly higher than for single neuron responses (p = 0.025, ANOVA with two factors: frequency band and single neuron/pair responses). To investigate this on a pairwise level, we plotted in Figure 4.5 D the signal correlations between LFP power at 24-56 Hz and firing rates of single neurons against the signal correlations between LFP power and the summed firing rates of both neurons of the pair. Here signal correlations were determined on responses pooled over all gratings, not for each varied parameter separately. Clearly, tuning of LFP power was more similar to tuning of the summed neural responses than to tuning of single neuron responses. This difference was significant for LFP power of all frequency bands above 24 Hz (p < 0.001, paired t-test). Given that the LFP reflects 86 Functional microarchitecture of cat primary visual cortex the average activity and input of the local cell population, the sum of nearby neural activity is expected to relate better to the LFP than single neuron activity. It is surprising, however, how big this effect of adding activity of one more neuron is considering the number of neurons that presumably contribute to the LFP. It might indicate that part of the spiking signal is captured and reflected in the LFP. The effect occurred however for low frequencies (24-56 Hz), which are usually thought to contain no or very little of the neurons’ action potential waveform (see section 4.4.2.1 for further discussion on this issue). Finally, we investigated how the tuning similarity between neighbouring neurons compares to the tuning similarity between LFP power and each neuron of the pair. In Figure 4.5 E signal correlations between LFP power (24-56 Hz) and firing rates of nearby neurons are plotted against signal correlations between the two nearby neurons. Both signal correlations, in other words tuning similarities, were significantly correlated to each other for LFP power of all frequency bands above 12 Hz. The strength of this correlation increased with increasing frequency starting at 0.31 for the frequency band of 12-24 Hz and reached a value of 0.53 for the frequency band of 80-100 Hz. This relationship shows that LFP power and nearby neurons are more similarly tuned the more similar tuned the neurons are themselves. Pooling responses across all varied grating parameters may have favoured such a relationship because the average strength of signal correlations varied across parameters (see Figure 4.5 C) and for some recording sites tuning was measured only for a subset of grating parameters. This could have resulted in lower correlation strengths for orientation and higher correlation strengths for spatial and temporal frequency. Results were, however, qualitatively similar to those presented when tuning of each parameter was considered separately. These results are consistent with the notion that the LFP reflects the average activity of the surrounding neural population, but also indicate that two similarly tuned neighbouring neurons tend to be surrounded by neurons with the same tuning properties, whereas differently tuned neurons tend to be situated in a more diversely tuned population. In light of the observation that LFP power had on average a lower tuning sensitivity than neural firing rates (compare Figure 4.4 D and E in previous section), it is interesting to note that tuning similarity between two neighbouring neurons and tuning similarity between a neuron and the LFP power of frequencies above 24 Hz were not significantly different in strength (p > 0.2, paired t-test). In other words, the tuning curve of a neuron was on average as similar to the tuning curve of a neighbouring neuron as it was to the more “diluted” average tuning curve of the surrounding population as reflected by the LFP. But is the LFP also more selective to changes in grating parameters if the nearby neurons exhibit more similar tuning? Figure 4.6 A shows the relationship between the strength of signal correlations between two neighbouring neurons and the tuning selectivity of the LFP power (24-56 Hz) as reflected by the d’-index. The figure demonstrates that tuning selectivity of LFP power does not necessarily increase with increasing tuning similarity between neighbouring neurons. Both measures are only weakly correlated to each other (rho = 0.25, p = 0.025). Figure 4.6 B shows that tuning selectivity of LFP power of higher frequencies was about equally well related to the tuning similarity between 87 4 Relationship between the LFP and neighbouring neurons Figure 4.6 Relationship between tuning similarity of neighbouring neurons and tuning selectivity of LFP. A, Signal correlation between tuning curves of neighbouring neurons is plotted against d’-Index (tuning selectivity) of LFP power (24-56 Hz). Measures were taken for each grating parameter separately (marked by colour of circles). B, Strength of correlation between neural signal correlations and d’-Indices of LFP power for different frequency bands are depicted. Bar colour refers to significance of the correlation (black: p < 0.01, dark grey: p < 0.05, light grey: p < 0.1, white: p > 0.1). neighbouring neurons. For lower frequencies, the two measures were independent of each other (as expected from the low signal correlations between low frequency LFP power and neural firing rates). In summary, the main results of this and the previous section are that LFP power of higher frequencies are more sensitive to changes in stimulus parameters and are more closely related to neural firing rates than LFP power of low frequencies. Our observations support the notion that the LFP reflects the average population activity within the surrounding volume. The higher diversity in this local population is expressed in a lower match between the shape of the tuning curve of the population (reflected by LFP power) and that of the constituent neurons. However, the signal-to-noise ratio or tuning selectivity of the population signal is only weakly related to the tuning similarity between the nearby neurons. 4.3.4 Unreliability and signal modulation of the LFP and neurons in response to different stimulus classes Results in the previous sections were all based on average responses to sinusoidal gratings presented for several seconds. In this section, we quantify the sensitivity of LFP and neural firing rate to stimuli other than gratings and at a time scale smaller than several seconds. Similar to tuning sensitivity measured in section 4.3.2, these analyses will point to those aspects of the LFP that are most strongly and most reliably modulated by the stimuli of each class. The aspects of the LFP we investigated are LFP power and LFP phase. LFP phase is closely related to evoked potentials (which we did not analyse because of the lack of an appropriate measure of sensitivity) as the latter will reach a significant magnitude only if the phase of the LFP is stimulus locked, otherwise potentials measured throughout several repetitions will cancel out when averaged. Furthermore, LFP phase has gained relevance through several studies ascribing it an important role in coding of external stimuli (Montemurro et al., 2008; Kayser et al., 2009; Kayser et al., 2012). 88 Functional microarchitecture of cat primary visual cortex In section 4.3.2, we measured tuning sensitivity using the d’-index, which incorporates the magnitude of signal modulation by determining the difference between the maximum and minimum mean response. The unreliability or magnitude of noise of the responses was obtained by dividing by the mean SD. In response to more complex time varying stimuli, the same method cannot be adapted reasonably. Instead we measured unreliability and signal modulation separately. In the following we use the term “signal” to refer to the mean response either of the LFP or of neurons averaged across several repetitions of the same stimulus, where responses were measured on relatively small time bins of 10s of milliseconds. Intuitively, one would measure unreliability by means of response variability in relation to the magnitude of the signal so that high variability will be considered less unreliable if the magnitude of the signal is large. However, signal and unreliability change over time in response to non-static stimuli and across different stimuli. Figure 4.7 A shows example data of LFP power measured in time bins of 40 ms in response to all presented grating stimuli. For each time bin, the mean LFP power at 19-21 Hz is plotted against the SD across trials. To get to a measure of unreliability across all these data points we made use of the observation that, in case of LFP power, mean and SD were approximately linearly related to each other as can be seen in this example but also in the other recordings (not shown). Although the relationship is not perfectly linear (specifically for high mean power values), the great majority of the data is well captured. Therefore, we defined unreliability of LFP power as the slope of a weighted linear regression on the means and SDs of LFP power of a certain frequency (see section 4.2.3). LFP power was measured in time bins of 40 ms in response to all stimuli of one class. This definition is closely related to the coefficient of variation (CV), which is the ratio of SD and mean, and will be termed “noise CV of LFP power”. The larger the noise CV, the less reliable were the responses. In a similar way, we defined unreliability of spike rate. In this case, however, mean spike rate was linearly related to its variance, not its SD. This is shown in the example in Figure 4.7 C, where for each time bin of 40 ms mean spike rate is plotted against variance for all grating stimuli. Unreliability was now defined as the slope of a weighted linear regression through these data points and was termed “noise Fano factor (FF) of spike rate” due to its close relationship to the FF, i.e. the ratio between variance and mean. The third measure, LFP phase, is a circular quantity so that deviations from zero do not translate into signal strength. Unreliability of LFP phase was therefore simply defined as the SD of LFP phase across trials averaged across small time bins (the size of bins is chosen depending on the frequency whose phase is considered) and is termed “noise SD of LFP phase”. Figure 4.7 B shows the distribution of LFP phase SDs across all time bins for one recording in response to grating stimuli. 89 4 Relationship between the LFP and neighbouring neurons Figure 4.7 Illustration of measures for unreliability and signal modulation of instantaneous LFP power, instantaneous LFP phase, and instantaneous neural firing rate in response to gratings. AC, Example data from cat0210 P3C4 in response to gratings illustrating the measure of unreliability. A, Mean and SD across trials of instantaneous LFP power at 19-21 Hz are plotted against each other. Each dot represents LFP power in a time bin of 40 ms. The fit with weighted linear regression is depicted by the red line (unreliability defined by slope is 0.97). B, Histogram of SDs across trials of instantaneous LFP phase at 19-21 Hz. Here, LFP phase in each trial was estimated in time bins of 13 ms approximating a quarter of one oscillation cycle. Unreliability of LFP phase defined as average SD across all time windows (red triangle) was 1.36. C, Mean and variance across trials of instantaneous firing rate are plotted against each other. Each dot represents firing rate in a time bin of 40 ms. Unreliability of firing rate was determined from weighted linear regression (red line) and had a slope of 32.51. D-F, Data from all recording sites in response to gratings illustrating the measure of signal modulation. D, For each recording site, mean and SD across time of the LFP power signal (LFP power in time bins of 40 ms averaged across all trials) for frequencies of 19-21 Hz are plotted against each other. The average signal CV of LFP power across all recording sites is 0.45. E, For each recording site, the SD of the LFP phase signal (LFP phase in time bins of 13 ms averaged across trials) for frequencies of 19-21 Hz was determined across time bins. Histogram shows distribution of these SDs over all recording sites. The mean signal modulation of LFP phase across all recording sites was 1.4. F, For each recording site, mean and variance across time of the spike rate signal (spike rate in time bins of 40 ms averaged across trials) are plotted against each other. The average signal Fano factor of LFP phase across all recorded neurons is 12.2. A measure of signal modulation, on the other hand, ought to reflect how much the average response, i.e. the signal, is varied by the stimulus across time and across the range of stimuli. The greater the modulation the better can the stimulus be encoded. The general idea of measuring signal modulation closely follows the approach of measuring unreliability: we measured variability of the signal across time and stimuli in relation to the signal averaged across time and stimuli. In case of LFP power, we defined signal modulation of a recording site in response to one stimulus class as the ratio between SD and mean of the LFP power signal across time and all presented stimuli of that class. We termed it “signal CV of LFP power”. Figure 4.7 D shows the mean and SD of the LFP power signal for each recording site. Analogously for spike rate, signal modulation of a neuron was defined as ratio between variance and mean of the spike rate signal and was termed “signal FF of spike rate” (see Figure 4.7 F for data of all 90 Functional microarchitecture of cat primary visual cortex Figure 4.8 Unreliability and signal modulation of LFP power, LFP phase and neural firing rate in response to gratings, movies and visual noise. A-C, Absolute measures of unreliability and signal modulation for LFP power, LFP phase, and spike rate. A, Solid lines and surrounding patches depict the mean noise CVs (± 1 SEM) of LFP power for frequencies between 1 and 100 Hz taken across all recording sites. Dashed lines and surrounding patches show the mean signal CVs (± 1 SEM) of LFP power for frequencies between 1 and 100 Hz taken over all recording sites. Noise and signal CVs were determined in response to each stimulus class (gratings, movies, and visual noise) separately (represented by different colours). B, Similar to A, solid lines depict mean noise SDs of LFP phase, dashed lines mark mean signal SDs of LFP phase. Shades represent the mean ± 1 SEM. C, Filled circles show mean noise Fano factors (± 1 SEM) of spike rate in response to the three stimulus classes. Open circles show mean signal Fano factors (± 1 SEM) of spike rate. D-F, Ratio between unreliability of original and control data for LFP power, LFP phase, and spike rate, respectively. D, Mean ratio (± 1 SEM) between original and control data for noise CVs of LFP power. The dotted line marks equality between original and control data. E, F, Same as in D but for noise SDs of LFP phase and for noise Fano factors of spike rate, respectively. G-I, Ratio between signal modulation of original and control data for LFP power, LFP phase, and spike rate, respectively. G, Mean ratio (± 1 SEM) between original and control data for signal CVs of LFP power. The dotted line marks equality between original and control data. H, I, Same as in G but for signal SDs of LFP phase and for signal Fano factors of spike rate, respectively. Note that for reasons of visibility the scale of the y-axis of panel I differs from those of panels G and H (extent of panels G and H depicted by grey area in panel I). neurons). At last, signal modulation of LFP phase was defined as the SD of the LFP phase signal, termed “signal SD of LFP phase” (see Figure 4.7 E for population data). As mentioned above, a normalization with the mean LFP phase signal is unreasonable because phase is a circular quantity. 91 4 Relationship between the LFP and neighbouring neurons Now we have measures at hand to quantify the unreliability and signal modulation of LFP power, LFP phase and spike rate in response to visual stimulation. Figure 4.8 A-C shows the magnitude of these measures in response to gratings, movies, and visual noise averaged across all recording sites or neurons, respectively. Noise CVs of LFP power (solid lines in Figure 4.8 A) were very similar across stimulus classes and were generally smaller for frequencies above 20 Hz than for lower frequencies. Signal CVs of LFP power (dashed lines in Figure 4.8 A) on the other hand had about half or less of the magnitudes of noise CVs showing that variability across trials is much larger than signal variability caused by visual stimulation. Signal CVs of LFP power were similar across stimulus classes for frequencies above 50 Hz, but were smaller in response to movies than in response to gratings and visual noise for LFP power of lower frequencies. For LFP phase, Figure 4.8 B shows that noise SDs were actually smaller than signal SDs. Signal SDs of LFP phase were similar across stimulus classes and almost reached the value expected of a uniform distribution of phases (SD would be 1.41). Noise SDs on the other hand were largest in response to movies and smallest in response to visual noise. This means that phase was more strongly locked to the full-contrast noise stimuli in which contrast was reversed on a fast temporal scale and that were optimized to the orientation preference of the nearby neurons. For spike rate, noise and signal FFs were relatively similar across stimulus classes (Figure 4.8 C). As for LFP power, noise FFs were larger in magnitude than signal FFs, however, the average ratio between signal and noise FFs of spike rate was for each stimulus class smaller than the ratio between signal and noise CVs of LFP power of all frequencies. In summary, these results show that the strength of signal modulation of LFP power, phase and spike rate was only weakly dependent on the stimulus class. Similarly, unreliability of LFP power and spike rate had similar magnitudes across stimulus classes. Only LFP phase was more reliable in response to visual noise than to gratings and was most unreliable in response to movies. When considering the relationship between signal modulation and unreliability, spike rate appears to be the least favourable response signal because noise FFs are so much larger than signal FFs, whereas LFP phase seems to be the optimal response signal. However, the distribution of occurring spike rates, which was skewed a lot towards small values, differed greatly from the distribution of occurring LFP phases, which was approximately uniform. Hence, expected values of signal modulation and unreliability for random data, i.e. data not locked to a stimulus, will differ a lot between spike rate and LFP phase. Analogously, distributions of LFP power, phase and spike rate might differ between stimulus classes and lead to different expected magnitudes of signal modulation and unreliability for random data. To take these differences in distributions into account, we looked at the ratio between signal modulation of the original data, i.e. the data we measured, and signal modulation of control data, as well as at the equivalent ratio for unreliability. Control data were constructed by randomly shifting responses within each repetition of the same stimulus. This was repeated 200 times. Figure 4.8 D-F shows the ratios between unreliability of original and control data for LFP power, LFP phase, and spike rate, respectively. Noise CVs of LFP power were as large as expected in response to gratings, somewhat smaller in the range of 20-30 Hz in response to visual noise, and decreased 92 Functional microarchitecture of cat primary visual cortex with respect to expected values with increasing frequency in response to movies. The dip of noise CV ratio at 25 Hz in response to movies is most likely due to the movies’ frame rate of 25 Hz. Noise SDs of LFP phase, on the other hand, were larger than expected in response to gratings. They were just below expected values in response to movies and only decreased for very low frequencies of 1-5 Hz and again at 25 Hz, the movie frame rate. In response to visual noise, ratios between unreliability of original and control data for LFP phase reached the lowest values. In case of spike rate, unreliability of original data compared to control data was similarly low for all stimulus classes, and was on average lower than for LFP power and LFP phase. In total, the ratios between original and control data had similar magnitudes across LFP power, phase, and spike rate. Figure 4.8 G-I shows the ratios between signal modulation of original and control data. In line with decreases in noise (Figure 4.8 D), signal modulation of LFP power was up to 1.4 times higher than expected for higher frequencies in response to movies, and up to 1.1 times higher than expected in the range of 20-30 Hz in response to visual noise, whereas signal modulation of LFP power in response to gratings was at the same level as expected values. Signal modulation of LFP phase (Figure 4.8 E) showed no dependence on frequency, and was close to expected values in response to movies and gratings, whereas it was about 1.1 times higher for original than for control data in response to visual noise. Much larger ratios between original and control data were reached by signal modulations of spike rate. On average it was 4 times higher than expected in response to movies, 2.3 times higher than expected in response to visual noise, and 1.5 time higher than expected in response to gratings. From these results we conclude: when response statistics are accounted for, spike rate is more sensitive to visual stimulation than LFP power and phase is. Moreover, sensitivity was strongest in response to movies, which is also reflected in the LFP power of higher frequencies, and which might be related to different distributions of instantaneous spike rate and LFP power across stimulus classes. 4.3.5 Relationship between LFP power and spike times or spike rate In this and the following section, we investigate how the LFP is related to the firing rate and to the spike times of nearby neurons during visual stimulation and during spontaneous activity. The question is: to what degree is the neural spiking activity reflected in the LFP? First, we concentrate on LFP power. Figure 4.9 A shows an example of single trial responses to 10 presentations of a 10 s long movie. For each trial, the spike times of two neighbouring neurons (purple and orange tick marks, respectively) and the LFP once filtered within a band of 1-3 Hz (grey curve) and once filtered within a band of 59-61 Hz (black curve) are plotted. In these single trial responses, it is hard to see any consistent rules governing the relationship between spike times and LFP power. There was, however, a tendency for spikes to occur during time intervals when 60 Hz fluctuations in the LFP had higher power (the correlation strengths in this example were 0.12 for each of the two neurons; see section 4.2.4 for details). LFP power of low frequencies was in single trials even slightly decorrelated with the firing rates of the two 93 4 Relationship between the LFP and neighbouring neurons Figure 4.9 Example showing the relationship between LFP power and spike rate in response to a movie (data from cat1310 P2C2). A, For the first 10 repetitions of the movie, spike times of two neurons (purple and orange tick marks, respectively), and the LFP filtered between 1 and 3 Hz (grey lines) as well as filtered between 59 and 61 Hz (black lines) are depicted. Scale bar indicates 2 mV for the low frequency LFP and 0.1 mV for the high frequency LFP. B, Firing rates (mean ± 1 SD across all 30 repetitions of the movie) of the same neurons as in A. C, LFP power (mean ± 1 SD across all 30 repetitions of the movie) for frequencies between 1 and 3 Hz (top, power averaged across frequencies) and for 60 Hz (bottom). Note that the power in the two frequency bands differs by two orders of magnitude. 94 Functional microarchitecture of cat primary visual cortex neurons (correlation strengths were -0.08 and -0.05, respectively). Responses averaged across trials are depicted in Figure 4.9 B for firing rates of the same neurons as in panel A, and in Figure 4.9 C for LFP power of frequencies between 1 and 3 Hz (top) as well as for 60 Hz (bottom). Average responses, i.e. signals, were similarly related to each other as single trial responses were: whereas low frequency power was not positively correlated with firing rates of the nearby neurons (in this example, correlation strengths were -0.02 and -0.25 for each neuron, respectively), power of higher frequencies matched more closely the neural activity (correlation strengths were 0.14 and 0.30 for each neuron, respectively). Note, however, the large SD for firing rates and LFP power of both frequency bands. These are ignored in the calculation of signal correlations assuming that only the average responses are the important stimulusinduced quantities. As a side note, unreliability of LFP power (defined in section 4.3.4), i.e. the ratio between SD and mean of power, was for this movie larger at 1-3 Hz (1.1) than at 60 Hz (1.03). To see how spikes are related to LFP power, we plotted the spectrum of LFP power at spike times of nearby neurons averaged across all neurons we recorded (Figure 4.10 A). These spectrograms look very similar to those in Figure 4.3 C, where average LFP power throughout visual stimulation is depicted. There are almost no differences visible across stimulus classes, and the decreased power of high frequencies at times of spikes occurring during spontaneous activity (presentation of blank screens) compared to visual stimulation is due to the generally decreased power of high frequencies during spontaneous activity. If for each stimulus class power at spike times is plotted relative to the mean power occurring throughout the presentation of stimuli of that class (Figure 4.10 B), the same effect occurred across stimulus classes: LFP power of frequencies below 10 Hz did not change during the occurrence of spikes, whereas LFP power of frequencies above 20 Hz was higher at spike times compared to any time during visual stimulation (about 0.25 SDs larger than the mean of the distribution of power occurring at all time points throughout stimulation). To investigate the relationship between the time varying fluctuations of LFP power and neural firing rate during visual stimulation, we quantified the correlation between them. We measured correlations between responses averaged across all repetitions of the stimuli, which reflects the stimulus driven part of the responses. We also measured correlations on single trial responses, which also reflects the trial-to-trial fluctuations. Figure 4.10 C shows the average correlations between firing rate and LFP power as a function of frequency where both quantities are measured in single trials (dashed lines), and where both quantities were first averaged across trials (solid lines). The latter corresponds to the signal correlation between LFP power and firing rates as shown in Figure 4.5 C (correlation between tuning curves) but now measured on smaller bin sizes of 150-1000 ms and in response to movies and visual noise in addition to gratings. Consistent with the observed relationship between single spikes and LFP power (Figure 4.10 B), correlations between single trial responses increased from around 0 for LFP power of low frequencies, to about 0.1 for LFP power of frequencies above 30 Hz. Again, no differences between stimulus classes were apparent. 95 4 Relationship between the LFP and neighbouring neurons Figure 4.10 Relationship between LFP power and spike rate in response to gratings (blue), movies (red), visual noise (green), and blank screens (black). A, LFP power at spike times (mean ± 1 SEM across all recorded neurons; n = 108, 43, 42, and 78 for gratings, movies, visual noise, and blank screens, respectively). LFP power at each frequency was first averaged across all spikes of each neuron, then across all neurons. B, Same data as in A, but here mean LFP power at spike times is plotted in relation to mean LFP power measured during all times of stimulus presentation (complete power distribution). For each neuron, the mean LFP power of the complete distribution is subtracted from LFP power at each spike time and divided by the standard deviation of the complete distribution. These normalized values were then averaged across all spikes of the same neuron, and thereafter averaged across all neurons. The dotted line at zero marks the normalized mean LFP power of the complete distribution. C, Correlation (mean ± 1 SEM across all neurons) between instantaneous LFP power and firing rate as well as between firing rates of neighbouring neurons. Dashed lines show the mean correlation between LFP power and firing rate measured during single trials, solid lines show the mean correlation between LFP power and firing rate averaged across all repetitions of each stimulus. Filled circles with solid errorbars depict signal correlations (mean ± 1 SEM) between firing rates of neighbouring neurons, open circles with dashed errorbars depict single-trial correlations (mean ± 1 SEM) between firing rates of neighbouring neurons. Both correlations were measured using bins of 150 ms, the same bin size used for correlations between firing rate and LFP power of frequencies above 20 Hz. Correlation strengths of trial averaged responses (solid lines), i.e. stimulus-induced signals, were generally larger than those for single trial responses, especially in response to movies and gratings. This shows that when stimulus-independent noise is added to the stimulus-induced responses in single trials, the correlation was weakened between neurons and the surrounding population reflected by LFP power of higher frequencies. Hence, noise had a significant magnitude (consistent with large unreliability compared to signal modulation, see Figure 4.8 A) and was less correlated between neurons in a local population than their stimulus-induced responses were. Interestingly, signal correlations between neighbouring neurons (filled circles in Figure 4.10 C) were not larger than signal correlations between LFP power of high frequencies and neural 96 Functional microarchitecture of cat primary visual cortex firing rates when both were measured using the same bin sizes (150 ms). This shows that the stimulus-induced responses of two neighbouring neurons were as similar to each other as the average stimulus-induced activity of the surrounding population was to the activity of each of the single neurons. Furthermore, single-trial and signal correlations between neighbouring neurons showed no difference in strength whereas single-trial correlations between LFP power and neural firing rate were weaker than signal correlations. This indicates that stimulus-independent noise was more strongly correlated between neighbouring neurons than between more distant neurons. Indeed, this was previously seen in a number of studies in cat (Ts'o et al., 1986; Das and Gilbert, 1999) and monkey (Kohn and Smith, 2005; Smith and Kohn, 2008). Unexpectedly, the signal correlations between LFP power and neural firing rate in response to movies were significantly stronger than those in response to the other two stimulus classes (Figure 4.10 C). We did not see this effect in signal correlations between neighbouring neurons, which were not significantly different in strength across stimulus classes, nor did single-trial correlations differ across stimulus classes. We have no ready explanation for this result. 4.3.6 Locking of spikes to LFP phases The LFP is thought to reflect synchronized activity of neural populations and the phase of the LFP marks the oscillation period of the population oscillator. In the previous section, we saw that the magnitude of LFP power reflects the magnitude of firing rates. The relationship between LFP phase and spike times shows what degree of synchrony (at a very fast time scale) is reflected in measured LFP oscillations. We therefore investigated the relationship between spike times and LFP phase, and how this relationship changes with LFP power. Figure 4.11 A shows the spike-triggered averages (STAs) of LFP for two neighbouring neurons (purple and orange traces, respectively). The top plot represents the STAs of the complete frequency content of the LFP, whereas for the bottom plot the LFP was first band-pass filtered between 24 and 56 Hz (using a Butterworth filter of order 10). From the two plots, one gets the impression that spikes of both neurons occur before the peak of low frequencies and approximately at or just before the trough of higher frequency oscillations. Giving a more precise view onto phase locking of spikes, Figure 4.11 B and C shows for each neuron the probability of a spike occurring at a certain LFP phase as a function of frequency. Consistent with the STAs in panel A, spiking probability was higher before the peak of an oscillation cycle of very low frequencies, as well as at and before the trough of higher frequencies. Note also that the first neuron (Figure 4.11 B and purple trace in A) spiked a little earlier in the oscillation cycles of higher frequencies than the second neuron whose spikes tended to appear closer to the trough (Figure 4.11 C and orange trace in A). We defined the preferred LFP phase of a neuron for a certain frequency as the mean LFP phase across all spike times. A neuron was said to have a preferred LFP phase for a frequency only if its spikes were significantly locked to any LFP phase for that frequency, i.e. if the distribution of LFP phases, at which the spikes occurred, was not uniformly distributed (p < 0.05, Rayleigh 97 4 Relationship between the LFP and neighbouring neurons Figure 4.11 Relationship between LFP phase and spike times. A, Example showing spike-triggered averages (STAs) of the LFP for two simultaneously recorded neurons (purple and orange, respectively) during the presentation of gratings (data from cat1410 P4C1). Top, LFP was only pre-processed (as described in section 4.2.1), bottom, LFP was, in addition to pre-processing, band-pass filtered between 24-56 Hz before averaging across spikes. Dotted vertical lines at zero mark the times of spikes. 1 SEM plotted around the mean was smaller than the thickness of the lines (n = 21510, 12511 for neuron 1 and neuron 2, respectively). B, Example showing the distribution of LFP phases at spike times for neuron 1 based on same data as in panel A (purple traces) in response to gratings. Top, illustration of LFP phase in accordance with x-axis of bottom panel. Bottom, for each frequency (y-axis), the normalized probability of a spike ( ) given the LFP phase ( ), | ⁄∑ | , is illustrated by the colour code (see colour bar to the left of panel C). C, Same as in B, but for neuron 2 based on same data as in panel A (orange traces). D, Bottom left, for each frequency, preferred LFP phase (mean ± 1 SEM across all neurons) is plotted in response to gratings (blue), movies (red), visual noise (green), and blank screens (black). First, LFP phases at all spike times of one neuron were averaged, then the average across neurons was taken. Only neurons whose distribution of LFP phases at spike times was significantly different from uniform (p < 0.05, Rayleigh test for uniformity of circular data) were taken into account (total number of neurons n = 110, 45, 41, 110 for gratings, movies, visual noise, and blank screens, respectively). Top left, illustration of LFP phase. Right, ratio of neurons with non-uniform distribution of LFP phases at spike times. E, Top, illustration of LFP phase. Bottom, average LFP phase (mean ± SEM across neurons and stimulus classes) for spikes occurring during time points of high LFP power (solid line) and during time points of low LFP power (dashed line). LFP power for a certain frequency was considered high when it exceeded the median power measured during blank screens. Otherwise, power was considered low (for distributions see inset in F). Again, only neurons with a non-uniform distribution of phases at spike times were considered (n = 169-246 and 48-193 for high and low power across frequencies, respectively). F, SD of LFP phases (mean ± 1 SEM across all neurons and stimulus classes) at spikes occurring during high LFP power (solid line) and low LFP power (dashed line) (n = 265 and 245 for high and low power, respectively). In case, all neurons were considered, not only those exhibiting significant LFP phase locking. Inset, spectra (mean ± 1 SEM across all neurons) of LFP power at spike times that occurred during time windows of high power (solid line) and of low power (dashed line). First, power spectra were averaged across all spikes of each neuron, then across all neurons. test for uniformity of circular data). The population data in Figure 4.11 D shows that the preferred LFP phases that neurons on average locked to were very similar to those in our previous example. The plot only includes data of neurons that were significantly locked to an LFP phase and it shows that preferred LFP phases did not differ across stimulus classes. During 98 Functional microarchitecture of cat primary visual cortex spontaneous activity, however, only about 50% of neurons had a significant phase locking for frequencies above 20 Hz, whereas more neurons were phase locked in response to visual stimulation (Figure 4.11 D, right plot). At very low frequencies <8 Hz, the large majority of neurons (between 80% and 100%) exhibited phase locking independent of stimulus class. To investigate the influence of LFP power on phase locking, we sorted the spikes of each neuron into two groups according to whether they occurred during high or low LFP power. LFP power was considered high if it exceeded the median power that occurred during spontaneous activity; below the median power it was considered low. The inset in Figure 4.11 F depicts the spectra of high and low LFP power, each averaged across all neurons. It shows that the two power distributions were clearly different from each other. However, the average preferred LFP phases of all recorded neurons and for all frequencies did not change depending on LFP power (Figure 4.11 E). The average SDs of LFP phases at high versus low power spikes are shown in Figure 4.11 F. Surprisingly, higher LFP power did not increase the strength of phase locking, Figure 4.12 Differences between preferred LFP phases of neighbouring neurons in response to different stimulus classes. A, Solid black line with dark grey shading depicts differences between preferred phases (mean ± SEM across all pairs) of neighbouring neurons in response to gratings. Only pairs for which both neurons had non-uniform distributions of phases at spike times were considered (n = 21-45). Dashed grey line with light grey patch shows differences between preferred phases (mean and 95% confidence interval) of neurons from two different recording sites, also in response to gratings. Differences between phases are expressed in radians divided by π so that 0.5 marks a difference of a quarter an oscillation cycle. B-D, Same as in A, but in response to stimuli of different classes (n = 7-28, 7-14, 8-14 for blank screens, movies, and visual noise, respectively). 99 4 Relationship between the LFP and neighbouring neurons i.e. did not decrease the SD, very much for frequencies above 20 Hz, but did so only for frequencies below about 14 Hz. In summary of the two last sections, spikes were more likely to occur during times of high power of frequencies above 20 Hz, whereas power of lower frequencies was not correlated with increased spiking probability, but with stronger locking of spikes to certain oscillation phases. We then asked whether spikes of neighbouring neurons are locked to more similar LFP phases than spikes of two random neurons. It might be suspected that neighbouring neurons, compared to more distant neurons, are likely to get more similar synaptic input, maybe exhibit more membrane fluctuations and therefore also lock to more similar LFP phases. Figure 4.12 shows these differences between neighbouring neurons and between two neurons from two different recording sites (500 pairs were generated for the control) in response to each stimulus class separately. For the large majority of frequencies, differences in preferred LFP phases between neighbouring neurons fell within the confidence interval of expected differences, i.e. differences between random neurons, in response to all stimulus classes. Neurons, which exhibit phase locking, are therefore not clustered in visual cortex according to their preferred LFP phase. 4.3.7 Comparison of LFP power and phase at times of reliable versus non-reliable spikes When investigating the relationship of the LFP to spikes we wondered whether spikes that occur during epochs of reliable responses to a stimulus, i.e. responses are very similar across trials, take on a special role. Our rationale was that reliable responses of a neuron are likely to be caused by synchronous synaptic inputs, which should be reflected in the LFP. We defined a spike to be reliable if the average firing rate at the time point of its occurrence (relative to stimulus onset) crossed a certain threshold (namely the 95th percentile of the spike rate distribution of that neuron measured in response to all stimuli of one class) and if in at least 50% of trials (or in at least 33% of trials if the total number of trials exceeded 21) some spikes occurred during the same period of elevated firing rate. An example of reliable and non-reliable spikes of two neighbouring neurons is given in Figure 4.13 A. The relationships of the LFP to reliable versus non-reliable spikes are compared in Figure 4.13 B-F. Figure 4.13 B shows that power spectra at the occurrence of spikes from the two groups look very similar. The ratio of LFP power at reliable spikes and at non-reliable spikes plotted in Figure 4.13 C shows that on average the peak ratio of 1.15 is reached for frequencies between 60 and 80 Hz. LFP power at reliable spikes, however, is not consistently larger than LFP power at non-reliable spikes across all neurons. In fact, the percentage of neurons for which power was significantly larger at non-reliable spikes compared to reliable spikes varied between 10 and 20% for most frequencies (plotted in Figure 4.13 D), whereas for only 4050% of neurons power at reliable spikes was significantly larger than at other spikes (p < 0.05, t-test). The preferred LFP phases of the two spike groups did not differ either (Figure 4.13 E). 100 Functional microarchitecture of cat primary visual cortex Figure 4.13 LFP at times of reliable and non-reliable spikes. A, Example showing raster plot of reliable and non-reliable spikes of two neighbouring neurons (purple and orange dots, respectively) in response to 30 repetitions of a movie (cat1310 P2C2). Times of reliable responses are marked by shading of the same colour as the neuron’s spike times. Reliable spikes are presented in a darker colour than non-reliable spikes. B, LFP power (mean ± 1 SEM across all neurons) at times of reliable spikes (solid line with dark grey patch) and of non-reliable spikes (dashed line with light grey patch) (n = 70 for both reliable and non-reliable spikes). For each neuron, spikes of all stimulus classes were pooled together. C, Ratio between LFP power at reliable spikes and LFP power at non-reliable spikes (mean ± 1 SEM across all neurons, n = 70). First, the ratio between mean power at reliable and non-reliable spikes was calculated for each neuron, then ratios were averaged across neurons. D, Portion of neurons whose reliable spikes occurred at significantly higher power than their non-reliable spikes (solid line) versus portion of neurons whose non-reliable spikes occurred at significantly higher power than their reliable spikes (dashed line). E, Average LFP phase of reliable spikes (solid line) and of non-reliable spikes (dashed line) (n = 75 for both reliable and non-reliable spikes). Lines and patches show the mean ± 1 SEM across neurons, respectively. F, SD (mean ± 1 SEM across all neurons) of LFP phase at reliable spikes (solid line) and non-reliable spikes (dashed line). Only the SD of LFP phases at which reliable spikes occurred was somewhat smaller than for non-reliable spikes especially for frequencies between 15 and 30 Hz (Figure 4.13 F) meaning that reliable spikes tended to have a stronger phase-locking. In summary, we did not see large differences in the relationship between the LFP and reliable versus non-reliable spikes, which indicates that fluctuations in a single cell’s synaptic input that led to reliable spike times were too small to show up in the LFP. Furthermore, we saw previously that neighbouring neurons were very differently tuned to stimuli of any class (Figure 3.6) indicating that significant fluctuations in the membrane potential of one neuron were most likely not mirrored as such in nearby neurons. 101 4 Relationship between the LFP and neighbouring neurons 4.4 Discussion 4.4.1 Comparison to other studies 4.4.1.1 Tuning of LFP in comparison to neural firing rates The d’-index we determined for the tuning to orientation, spatial frequency, and temporal frequency can be seen as a measure of the signal-to-noise ratio (as it is defined as the difference between the most extreme response amplitudes, divided by the mean standard deviations of both responses). Similar to our results (using a similar index), Siegel and König (2003) found in V1 of awake cats higher orientation sensitivity for frequencies above 45 Hz compared to lower frequencies. Sensitivity, however, peaked at about 60 Hz and then slowly declined. In awake behaving monkeys, Berens et al. (2008b) saw the highest sensitivity for orientation in the LFP at 60 Hz. Their d’-index incorporated the responses to the preferred and the orthogonal orientation (instead of the orientation eliciting the minimal response), and resulted in smaller values than we saw. However, the orientation sensitivity of gamma power was, similar to our results, half or less of that of multi-unit activity. Both studies observed gamma bumps in their LFP recordings, which might be the reason for the peak of sensitivity around 60 Hz compared to the plateau we observed for frequencies above 30 Hz. Further studies looked at the tuning depth for orientation, which refers to the normalized response difference between different orientations (either considering all orientations or just the most and the least driving orientations), but does not consider the noise, i.e. the variation of the responses. Results agree that power of high frequencies (>30 Hz) of the LFP have a larger tuning depth than power of lower frequencies, but smaller tuning depth than MUA (Frien et al., 2000; Jia et al., 2011). Only Kayser and König (2004) saw an equally large tuning depth at low frequencies (8-23 Hz) for orientation, spatial and temporal frequency in V1 of awake cats4. In contrast to the majority of investigations including those reviewed above, we compared the tuning of the LFP to that of single neurons, not multi-unit activity. To the best of our knowledge, the only other study that followed the same approach was conducted by Lashgari et al. (2012) in V1 of awake monkeys. From their results they concluded that responses of single neurons have a far greater signal-to-noise ratio (in fact 50 times greater) than LFP power, which is in stark contrast to our finding of about two times the signal-to-noise ratio in neural responses compared to high-frequency LFP power (determined by the d’-index). However, the measure of signal-to-noise ratio used by Lashgari et al. (2012) is defined as the mean power of the LFP in responses to a certain orientation divided by the mean power of the baseline (when 4 A previous study of the same lab also found an increase of the d’-index in these lower frequencies (Siegel and König, 2003). The values stayed, however, much lower than those for higher frequencies (>45 Hz). Both studies together indicate that the tuning depth at low frequencies is large, but that the variation of the responses at lower frequencies are much larger so that the signal-to-noise ratio is relatively small. 102 Functional microarchitecture of cat primary visual cortex no stimulus is presented), averaged across all presented orientations. Trial-to-trial variations were not considered. Following their definition, signal-to-noise ratios of single neuron responses are expected to be very large because of their generally low spontaneous firing rates (which corresponds to their baseline values). The tuning depths observed by Lashgari et al. (2012), on the other hand, show far greater similarity between single units and LFP power5. For orientation, LFP power exhibits on average at least 60% of the tuning depth of single units, whereas for temporal frequency, LFP power and single units have no significantly different tuning depths (unfortunately, they only report average values, not the variation seen in their population). However, there is another great difference to our study: they analysed not the firing rates of single neurons but the amplitudes of different frequency bands of their responses. The relationship between the two measures is not obvious and at least two studies found great differences between the tuning (in this case size tuning) of firing rates and spectral power of multi-unit spike responses in V1 of cats (Bauer et al., 1995; Zhang and Li, 2013). Lashgari et al. (2012) also compared the tuning preferences between spectral power of single unit activity and the LFP and found high correlations for preferred orientation at low and high gamma bands (30-90 Hz and 90-200 Hz, respectively), which is compatible with our results. Preferred temporal frequencies were, in contrast to our findings, not correlated in their data, which might be due to their analysis of frequency content of single unit responses instead of firing rates (only the power of theta frequencies, 4-8 Hz, during the transient response directly after stimulus onset were significantly correlated between the LFP and single neurons). The similarity of orientation tuning between high-frequency power of the LFP and MUA was confirmed by Jia et al. (2011) in monkey V1, but only as long as the gratings are small and do not elicit a gamma bump (see also Berens et al., 2008b). The same relationship between LFP power and neural activity was seen in response to natural movies. Belitski et al. (2008) observed strong signal correlations between LFP power and MUA for frequencies above 70 Hz (values of 0.4-0.6). The correlations were greater than in our data (signal correlations reached values of 0.25 in response to movies), which might be explained by our recording of single instead of multiple neurons (remember that signal correlations of tuning curves increased between LFP power and neural activity when we considered summed firing rates of two neurons). In summary, we confirmed the observation that high-frequency LFP power is more sensitive to changes in orientation than low-frequency power but less so than neural activity, and that 5 Note, however, that Lashgari et al. (2012) did not measure tuning depths of single recording sites. Instead they, first, averaged tuning curves across all LFP recordings and across all neurons, separately (after dividing each by its maximum value and aligning them to preferred parameter values for orientation and spatial phase), and then compared tuning depths between these two averages. Differences in tuning width and, maybe more importantly, differences in preferred and non-preferred parameter values across recording sites could greatly diminish the tuning depth of the average compared to the single tuning curves. Significance values, on the other hand, were determined by comparing the distributions of tuning depths of single tuning curves. 103 4 Relationship between the LFP and neighbouring neurons both high-frequency power and neural activity have similar orientation tuning. Our results add to the existing body of research by showing that this relationship also holds for the tuning of single neurons (based on their firing rates), that the relationship improves if firing rates of multiple neurons are considered, and that it holds for further stimulus parameters, namely spatial and temporal frequency. 4.4.1.2 Temporal relation between spikes and the LFP Consistent with the many studies finding the largest coherence between LFP and spikes at very low (<10 Hz) and high frequencies (>30 Hz) (reviewed in section 1.6), we saw greater phaselocking of spikes at frequencies <14 Hz (especially during epochs of high power) than higher frequencies, as well as stronger correlations between firing rate and high- rather than low-frequency LFP power (section 1.6 explains the connection of those relations to spike-field coherence). Only few investigations have looked directly at the relationship between neural firing rates of single or multiple units and high-frequency power of the LFP but they have consistently found positive correlations—in human auditory cortex (Nir et al., 2007) as well as in V1 of awake monkeys, except at frequencies that exhibit a gamma bump (Ray and Maunsell, 2011a). In the latter study, the correlation is highest at a zero time lag (at which our measures of correlation are taken) showing that there is no temporal delay between spike activity and the related LFP fluctuations (Ray and Maunsell, 2011a). The preferred LFP phases that spikes locked to in our data—namely before the peak of low frequencies and just before or at the trough of higher frequencies—was the same as that seen in MUA recorded in monkey V1 (Montemurro et al., 2008; Rasch et al., 2008). Both of those studies also saw that phase-locking is strongest for low frequencies. Their data, however, cannot conclusively distinguish between the following two interpretations: firstly, that several neurons could be tightly phase-locked to high frequencies preferring very different phases or, secondly, that each neuron has only a very weak phase-locking to high frequencies with similar preferred phases. Our recordings from single neurons shows that the latter interpretation is correct. In auditory cortex of awake monkeys, phase-locking of spikes (MUA and SUA) at low frequencies is more strongly preserved across stimulus repetitions than for higher frequencies, and often occurs during reliable spike patterns (Kayser et al., 2009), consistent with our results. Averaging phases at spike times across time might, however, underestimate the strength of locking. In auditory cortex, different periods of natural sounds are associated with somewhat different but reliable phases at spike times (for frequencies of 4-8 Hz) (Kayser et al., 2009). Furthermore, spike times of individual neurons in visual cortex of awake monkeys systematically shift their position in the gamma cycle as a function of firing rate (Vinck et al., 2010), which might explain the weaker phase-locking compared to that at lower frequencies. To understand the significance of phase-locking, a closer look at its relationship to other factors, such as the neural activity of the same and surrounding neurons or the stimulus-locking of neural activity and the LFP, is needed (see also section 5.3). 104 Functional microarchitecture of cat primary visual cortex 4.4.1.3 Differences across stimulus classes Very few investigations have actually compared features of the LFP across different stimulus classes. To our knowledge, none has done so for the relationship between the LFP and spikes. Kayser et al. (2003) have compared LFP power spectra and their temporal dynamics measured in V1 of awake cats in response to drifting gratings, natural movies, modified natural movies (wavelet-filtered), and two kinds of noise stimuli (pink and wavelet noise). They found similar LFP activity patterns and amplitude strengths for the natural movies, their modifications, and the noise stimuli. After a first onset response where power at all frequencies was elevated, these stimuli elicited a phasic response with large variations of activity over time and, on average, elevated power at frequencies >80 Hz, mostly within frequency ranges that we did not consider. Kayser et al. (2003) argue that the temporal variations are caused by irregular motion patterns present in all the mentioned stimuli. Gratings, on the other hand, show a very different response profile. They elicit stable steadystate responses with increased power mostly in the gamma range (30-60 Hz) and less power in the higher frequencies compared to that elicited by natural movies (Kayser et al., 2003). Similarly, Haslinger et al. (2012) observed a prominent gamma bump in the LFP power spectrum in response to grating stimuli compared to that during natural scenes when recording in V1 of awake monkeys (although they did not observe greater high-frequency power for natural movies). In summary, the main difference to our results is the occurrence of the gamma bump in the LFP spectrum in response to gratings, which can probably be explained by our use of relatively small gratings spanning 4-6°, whereas in both cited studies large stimuli of more than 20° were used. We will review results on when the gamma bump is or is not observed in section 4.4.1.5. 4.4.1.4 Stimulus information contained in the LFP A number of studies found that certain frequencies (specifically very low, <8 Hz, and sometimes higher, 60-100 Hz, frequencies) of the LFP carry more stimulus information than other frequencies. In general, high information values result from good separability of the different stimuli which profits from both distinct mean responses and high trial-to-trial reliability. We assessed both by measuring signal and noise CVs of LFP power and phase but saw only minor differences across frequencies. Noise CVs, i.e. unreliability, of LFP power was even higher at low frequencies. We will now try to resolve these contradicting results. In recordings of the LFP in V1 of anaesthetized monkeys, Belitski et al. (2008) found that LFP power of frequencies at 1-8 Hz and 60-100 Hz are the most informative about the presented natural movies. Similar to our results, they saw that power of low frequencies is less reliable than of high frequencies. However, signal modulation was greatest at high frequencies (60-100 Hz) and very low frequencies, which counteracted their unreliability and resulted in high information rates at both frequency bands. The same pattern of unreliability and signal modulation (measured by noise and signal CV) for LFP power was observed by Montemurro et al. 105 4 Relationship between the LFP and neighbouring neurons (2008). In contrast, we found only minimal variation of signal modulation across frequencies. The strong signal modulation at low frequencies might be strongly linked to the high power seen at low frequencies of the temporal profile of their movies (Belitski et al., 2008), which might not be the case for our movies and would explain the low signal modulation at low frequencies. Furthermore, both cited studies (Belitski et al., 2008; Montemurro et al., 2008) evaluated noise and signal CVs at time bins of 2 s, whereas we used time bins of 40 ms. A later investigation by the same group found that noise CVs, and thus unreliability, generally increases with shorter time scales, whereas information rates decrease, especially at high frequencies (Belitski et al., 2010). Stimulus information in higher frequency bands is, therefore, dependent on time scale and is larger when the energy is averaged over several hundreds of milliseconds. This shows that time scale plays a crucial role. Unfortunately, changes of signal modulation were not directly studied across varying time scales. Two studies concentrated on the stimulus information contained in the LFP phase and found higher information rates at low frequencies (<8 Hz) (Montemurro et al., 2008; Kayser et al., 2009), whereas we did not see differences in unreliability or signal modulation of LFP phase across frequencies. We think that this discrepancy originates from differences in firing rates, because stimulus-locking of LFP phase is stronger during higher rates, and firing rates of both studies seem to be higher than those we recorded (judging from presented exemplary data). Furthermore, the time scales of measured phases plays a crucial role in determining their reliability across stimulus repetitions. At higher frequencies, a complete cycle through all phases is traversed within only few milliseconds so that only very bins are reasonable for estimating the average phase of a certain time window after stimulus onset. Montemurro et al. (2008) show that phase variance across trials increases for higher frequencies but do not state the size of time bins they used. If they used the same (relatively large) time bin for all frequencies, this result is expected. For this reason, we adjusted the time bin for each frequency to match approximately the duration of a quarter of a cycle. 4.4.1.5 Occurrence of the gamma bump In theories of the mechanisms and functions of the gamma rhythm (see section 1.7), the term “gamma bump” refers to the occurrence of elevated power at a narrow frequency band typically in the range of 30-60 Hz. Elevations of power at broad-band frequencies between approximately 30 Hz and well beyond 100 Hz occur under different conditions and are thus thought to underlie different mechanisms of generation (see section 1.5.2). According to these definitions, we did not observe genuine gamma rhythms in our population data, and also did not see it in single datasets. A few studies in monkey V1 investigated the conditions that elicit gamma rhythms and gamma bumps. During presentation of gratings at the preferred orientation of the gamma power, gamma rhythms only occur if the grating is large or if it has a high contrast6 (Gieselmann and Thiele, 2008; Ray and Maunsell, 2011a; Jia et al., 2013a). For cat 6 To elicit a gamma bump in the LFP power spectrum, gratings need to have a size of around 0.5°-2° even at full contrast, whereas a minimum contrast of more than 12% is necessary for large gratings (10°). 106 Functional microarchitecture of cat primary visual cortex V1, results on the necessary conditions are not as clear. Bauer et al. (1995) did not show systematically how the LFP power spectrum changes with stimulus size. Data for only two values are presented: no gamma occurs for a stimulus size of 2.5°, but it is clearly visible for a size of 30°, in both cases for gratings at full contrast. Zhang and Li (2013), on the other hand, show population data where a gamma bump is present for full-contrast gratings at sizes of 1° (and larger). In their exemplary data for one recording site, however, a gamma bump is visible even during spontaneous activity. Additionally, they observe a decrease of gamma power with increasing stimulus size (surround inhibition), which is in contradiction to a number of previous observations (Bauer et al., 1995; Gieselmann and Thiele, 2008; Ray and Maunsell, 2011a; Jia et al., 2013a). The reasons for these discrepancies are unclear. Given these results, we suppose that the absence of gamma bumps in our data is due to the relatively small size of around 4°-6° and the relatively low contrasts of 10-50% used in the gratings we presented. That we did not observe gamma bumps in response to natural movies and visual noise is not surprising, because fast movements have been seen to abolish gamma rhythms (Kruse and Eckhorn, 1996) and no previous study has reported gamma bumps in response to natural stimuli (Kayser et al., 2003; Belitski et al., 2008; Montemurro et al., 2008; Haslinger et al., 2012). What the relevance of gamma rhythms might be, given these observations, will be discussed later in section 5.3. 4.4.2 Limitations 4.4.2.1 Spike leakage Several of our results show that the amplitude of frequencies >20-30 Hz is related to the activity of nearby recorded neurons, raising the question whether this relationship is a trivial consequence of spike leakage into the LFP. We tried to minimize this effect by using two separate electrodes for the recording of spikes and the LFP. However, as the average distance between the electrodes is only 30 microns, we cannot exclude that the remnants of the spike waveforms had an impact on the LFP signal. Ray and Maunsell (2011a) studied the relationship between spikes and the LFP in the time-frequency domain when both are recorded from the same electrode in monkey V1. Their analyses show that spike energy can be observed in the LFP power spectrum at frequencies as low as 50 Hz, and that the impact of spikes is very prominent above 100 Hz. The energy due to spiking activity is locked to a narrow time window of a few milliseconds around the time of the spike. Zanos et al. (2011) took a different approach but reached a similar conclusion. They performed simulations in which spike waveforms are added to phase-randomized LFP signals, such that the spectral profile of the LFP is maintained but the actual LFP-spike relationship is not. When they estimated LFP by low-pass filtering the simulated signal, their analysis shows artificial spike-field coherence and phase-locking for frequencies >50 Hz, whereas tuning curves of LFP power are not influenced by spike contamination even at frequencies up to 140 Hz. Similar artefacts occurred in real data recorded in macaque V1 when analysed with commonly used low-pass filters in comparison to when spikes were removed first. These studies show that spike contamination cannot explain the similarity in 107 4 Relationship between the LFP and neighbouring neurons tuning properties between LFP power and firing rates, nor can it explain the correlation between LFP power and spike occurrence or firing rate at low frequencies of 30 Hz. It is, however, very likely that correlations between the LFP and spikes are due to postsynaptic activity caused by the spikes of the recorded neurons. 4.4.2.2 Anaesthesia Anaesthetics have direct effects on the physiology of neurons and may, thus, lead to results different from those seen in awake animals. The main anaesthetic agent we used is alphaxalone (contained in Saffan), which is a steroidal general anaesthetics. It primarily prolongs the decay of IPSCs elicited by GABA, but does not affect their rise time or amplitude (Belelli and Lambert, 2005). Halothane was used by us only occasionally during the recordings and at low doses of about 0.5%. At doses of 1.2%, it depresses the amplitude and considerably prolongs the decay time of evoked IPSCs in both pyramidal cells and inhibitory interneurons (Nishikawa and MacIver, 2000). The same study also revealed that halothane increases the frequencies of miniature IPSCs (spontaneously occurring synaptic currents) in both types of neurons and increases the failure rate of synaptically evoked action potentials. These effects could have influenced the signals we recorded in the LFP and specifically could have reduced or even abolished the gamma rhythm, which is thought to depend on the time constant of GABA receptors (see section 1.5.2). Several studies were, however, conducted in anaesthetized cats and elicited clearly visible gamma bumps (Bauer et al., 1995; Kruse and Eckhorn, 1996; Fries et al., 2001). Although only halothane and no alphaxalone was used, it seems unlikely that the anaesthetics we used caused the absence of gamma bumps as the effects of halothane of the physiology of the neurons appear to be even stronger than those of alphaxalone. 108 Functional microarchitecture of cat primary visual cortex 5 Discussion 5.1 Cortical columns, functional heterogeneity and information processing One possible advantage of cortical maps is that stimulus features can be better estimated when a downstream neuron pools across responses of neurons with similar tuning properties (Parker and Newsome, 1998; Mazurek and Shadlen, 2002). Indeed, neurons in cat V1 are more selective to orientation, which shows a high degree of clustering, than to spatial frequency (Webster and De Valois, 1985). The heterogeneity we and others observe, therefore, raises a number of questions: how can information be coded and processed, is the clustering of some tuning properties within cortical columns relevant in processing complex stimuli, does the observed functional heterogeneity have any advantages, and what does the underlying circuit look like? Pooling across responses of neurons with a similar tuning property requires that these responses reach the downstream neuron within its temporal window of integration (i.e. within the time that a unitary postsynaptic potential decays back to baseline). The length of such a window depends on various factors, such as the membrane time constant of the neuron, replenishment of neurotransmitters at the presynaptic terminal, actual resistance of the membrane, receptor types, and the immediate spiking history of the neuron, and can extend over 10s to a few 100s of milliseconds (Buzsáki, 2006, p. 151). Since we found that signal correlations between neighbouring neurons were relatively low for time scales of up to 200 ms, pooling across their responses seems inefficient in driving a downstream neuron. This holds even for neighbouring neurons that are similarly tuned for a stimulus feature like orientation, because tuning similarity was only very weakly or not at all related to the strength of signal correlations. When Reich et al. (2001) measured signal correlations between neighbouring neurons in monkey V1 in response to visual noise stimuli, they observed that signal correlations on average increase with increasing time scales. They concluded that information conveyed on short (<15 ms), but not on long (>60 ms), time scales is largely independent, which might indicate that rapidly varying stimulus attributes are not shared between neighbouring neurons, whereas slowly varying features are jointly represented. Our analyses showed, however, that stronger signal correlations on longer time bins can be largely explained by more robust response estimates, which are essential for the calculation of signal correlations. So, slowly varying stimulus features do not form a basis for strong clustering among nearby neurons. On the other hand, response characteristics of neurons in a local population are not completely disparate and the degree of response similarity seems to be more or less constant across larger distances than those between simultaneously recorded neurons. This was reflected by similar strengths of signal correlations between LFP power and nearby neurons, on the one hand, and between two neighbouring neurons, on the other hand (for tuning curves as well as instantaneous activity). If the similarity between stimulus-driven responses was rapidly decreasing with cortical distance, the correlation between LFP power and nearby neurons would have been much lower. Yen et al. (2007) 109 5 Discussion consistently found indistinguishable strengths of signal correlations between neurons recorded on the same electrode and neurons recorded on electrodes with a distance of 150 μm. Whatever response characteristics underlie this weak similarity, it is not obvious whether cortical columns and the degree of clustering within them form the basis for a wiring-cost efficient pooling process. This means, it is not clear whether signal correlations between neurons within a cortical column are sufficiently strong to be more advantageous for pooling than between neurons situated in different columns. Sufficiently detailed models of neural networks capturing the functional heterogeneity we have observed here could reveal what conditions, i.e. what connectivity principles and integration time scales, are necessary to implement efficient pooling in downstream neurons. One step in this direction is provided by topographic models maximizing sparseness and temporal coherence in response to natural stimuli (Hyvärinen and Hoyer, 2001; Hyvärinen et al., 2003). These used two-layer networks with fixed neighbourhood relationships and found that neurons adopt simple-cell and complex-cell like RFs in each layer, respectively, when applying sparseness and temporal coherence constraints on the second layer. In addition, this model shows emergence of a strong retinotopic and orientation map, a weaker spatial frequency organization, and random spatial phase distributions. It remains to be seen whether models constrained to more biologically plausible implementations will find similar results. At first sight, the functional heterogeneity we saw between neighbouring neurons comes as a surprise. Because of the extensive overlap of their dendritic trees, neighbouring neurons are expected to share a large amount of their inputs (Douglas et al., 1995). Indeed, dual intracellular recordings in cat area 17 show that the membrane potentials of nearby cells are highly correlated with each other (Yu and Ferster, 2010). However, not every synaptic input will drive the membrane potential of a neuron to threshold. Unsynchronized synaptic activity, or a balance between excitatory and inhibitory inputs, will be ineffective. Only synchronized excitatory inputs, or synchronized inhibitory withdrawal reflected in fast fluctuations in the membrane potential, play a decisive role in triggering spikes (Lampl et al., 1999; Hasenstaub et al., 2005; Banitt et al., 2007). Therefore, spike-spike (or noise) correlations are weaker and narrower than expected from the correlation of the membrane potential of two nearby neurons (Lampl et al., 1999). Moreover, noise correlations are weakened if the shared excitatory and inhibitory inputs to two neurons are synchronized. This also means that noise correlations do not reflect the full degree of shared input (see section 1.2, and Renart et al., 2010). Even neurons receiving the same input might process it in different ways due to different dendritic morphologies, different channel distributions along the dendrite, or different spiking thresholds. Therefore, noise correlations only reflect the relevant common input that leads to spikes in both neurons. As our results show a fairly strong relation between noise and signal correlations, it is this relevant fraction of common input that strongly determines the similarity of the stimulus driven responses of neighbouring neurons. In line with this, data of Monier et al. (2003) show that orientation and direction preference is often determined by merely a slight excess of the mean excitatory compared to the mean inhibitory conductance. This indicates 110 Functional microarchitecture of cat primary visual cortex that even small differences in input could lead to different tuning properties. All together, these results could explain the functional heterogeneity among neighbouring neurons despite their shared inputs. Furthermore, recurrent inhibition within a population of excitatory cells receiving similar input could lead to competition in a winner-take-all fashion. This competition may—possibly also through long-term effects of plasticity—ultimately lead to functional heterogeneity among nearby neurons. An often cited advantage of functional heterogeneity in local neural populations is that pooling across neurons with mixed preferences for one stimulus parameter could help establishing invariance to the parameter in downstream neurons, as observed for the phase invariance in complex cells. However, other non-clustered tuning parameters, like direction selectivity, still play a crucial role in higher visual areas (Gizzi et al., 1990). In that case, connections to downstream neurons might be highly specific and arise only from neurons that have the same direction selectivity. Some hint of such specificity comes from rodent studies in visual cortex. These showed that adjacent supragranular pyramidal neurons that are connected to each other share common excitatory input from layer 4 neurons and other superficial neurons, thereby forming functional subnetworks (Yoshimura et al., 2005). In addition, if supragranular neurons prefer similar orientations or respond similarly to natural stimuli, they are connected to each other with a higher probability compared to neurons with dissimilar preferences (Hofer et al., 2011; Ko et al., 2011). Whether the same principles hold for connections across cortical areas and whether they exist in other mammals, specifically in those with orientation columns, is not yet known. An indication for pooling of responses originating from only a subset of neurons within an orientation column comes from anatomical studies. Intracortical axonal projections of layer 2/3 neurons in V1 form patches in distant cortical regions, which to some degree exhibit similar orientation preferences to those of the projecting neurons (e.g. Gilbert and Wiesel, 1989; Bosking et al., 1997). The number of patches to which a single neurons sends its axon does, however, not match the number of patches formed by the local surrounding neural population. This suggests some selectivity in intracortical long-range connections (Ruesch, 2011). On the other hand, functional heterogeneity in local populations and in downstream inputs does not prohibit high selectivity in postsynaptic neurons as suggested by experimental and theoretical studies. Jia et al. (2010) showed that inputs at individual dendritic sites of neurons in mouse V1 are orientation tuned, but that different sites exhibit a large diversity of orientation preferences. Nonetheless, the spike outputs of the receiving neurons show clear orientation selectivity. Simulations of neural networks with random recurrent connectivity and feed-forward orientation selective input show that, despite the weak orientation selectivity of the excitatory and inhibitory inputs, strong orientation selectivity emerges in the spike responses of the output neurons if the network operates in a regime of balanced excitation and inhibition (Hansel and van Vreeswijk, 2012). Pooling across differently tuned neurons is also less likely to amplify noise, which is shared to higher degrees between neurons with similar tuning properties. Finally, a diversity of inputs may be a great advantage for coding the multitude of contexts a given neuron encounters during the processing of natural scenes. 111 5 Discussion 5.2 Is coding optimized to natural stimuli? A common observation is that noise correlations are largest for neurons with similar tuning properties (see review by Cohen and Kohn, 2011). Several theoretical studies have indicated that such a correlation structure is highly detrimental for population coding, because responses are harder to decode under these conditions and therefore carry less information about the external stimulus (Abbott and Dayan, 1999; Sompolinsky et al., 2001; Averbeck et al., 2006; see also section 1.2). Our results on neighbouring neurons showed a smaller dependence of noise correlations on signal correlations, indicative of a more efficient coding, in response to natural movies than to artificial stimuli. In line with this, Vinje and Gallant (2002) found higher information transmission rates for movies than for gratings. To substantiate this apparent adaptation of the brain for efficient coding of natural stimuli, it will be necessary to discover whether and how noise correlations depend on individual stimuli. Stimulus dependence was observed in monkey V1 (Kohn and Smith, 2005) and might largely affect information coding, because stimulus discrimination depends on how far the range of responses to different stimuli overlap (Averbeck et al., 2006). The theory of sparse coding argues that natural scenes activate a minimal number of neurons at each point of time (Olshausen and Field, 2004a). The significance of this theory comes from its ability to explain the RF structure of simple cells and, more recently, of complex cells, as well as the degree of clustering of RF parameters like preferred orientation, spatial frequency and phase (Hyvärinen and Hoyer, 2001). Low signal correlations and rare synchronous activity of neighbouring neurons are consistent with this idea of sparse coding. However, signal correlations were similarly small for all stimulus classes we considered, not just movies. Also lifetime sparseness (a measure of how selectively neurons respond to stimuli) of neurons in awake monkey V1 was similar in response to natural vision and gratings (Vinje and Gallant, 2000). In this sense, there is no sign of a specific adaptation to natural stimuli. However, theoretical predictions as to what the values of sparseness should be in response to artificial stimuli versus natural stimuli do not yet exist. 5.3 Relevance of rhythms in the LFP The oscillations visible in the LFP are thought to provide a temporal framework for the spike output of neurons in a window-of-opportunity fashion (see section 1.7). According to this hypothesis, our results indicate that slow rhythms of the LFP are more likely to constitute such a gating mechanism, because phase-locking of spikes was stronger and significant in a larger number of neurons for lower frequencies than for higher frequencies. Spikes of single neurons were on average more strongly locked to phases of low frequencies if power at those frequencies was higher, whereas phase-locking hardly increased with power at high frequencies. Still, the SD of spike-phases at low frequencies was on average relatively large (approximately 0.4 π during high power epochs). Also, we found merely weak indication for a role of phase-locking in relation to stimulus-locked, i.e. reliable, spikes. The strength of phase-locking increased 112 Functional microarchitecture of cat primary visual cortex somewhat for reliable spikes, most strongly at around 20 Hz, but a decrease of SD of spikephases from 0.44 π to 0.42 π does not seem to make a significant difference. LFP power increased significantly at reliable spikes only in a subset neurons, and even decreased in a substantial number of neurons. These result show that the “gate” set up by the oscillations is either very wide, which casts doubt on the relevance of the gating mechanism, or it is flexible in time. The latter was suggested by a study on spike-phase coding in auditory cortex of awake monkeys (Kayser et al., 2009). Spikes that were reliably locked to a natural auditory stimulus occurred reliably during the same low-frequency phase, but at somewhat different phases for different stimulus epochs. It is not clear whether a similar phenomenon would be observed in visual cortex and what mechanism actually underlies the systematic phase shift. A different kind of phase shift was seen by Vinck et al. (2010) in neurons of V1 of awake monkeys. Here, spikes shifted to earlier phases of the gamma cycle when their firing rate increased, which was tested by stimulating neurons with their preferred and non-preferred orientations. This is direct evidence for the theory of gamma as temporal reference frame (see section 1.7) where spike-phase is an instantaneous analogue representation of the neuron’s excitation and, therefore, of stimulus attributes the neuron codes for. Furthermore, early spikes in the gamma cycle might execute enhanced impact on postsynaptic neurons, first, by escaping the rhythmic inhibition of gamma oscillations for longer time periods than other spikes and, second, by diminishing later spikes through winner-take-all mechanisms (Vinck et al., 2010). However, low frequencies (<10 Hz) and phase-locking during non-cyclic natural stimuli were not analysed, so that no unifying picture of phase-shifting has emerged as yet. In the Introduction (section 1.7), we have reviewed further potential functions of the gamma rhythm. Here, we want to discuss how relevant gamma rhythms actually are. As gamma rhythms, i.e. a distinct bump in the power spectrum of the LFP at frequencies of 30-80 Hz, did not appear in our data, we reviewed, in section 4.4.1.5, conditions under which the gamma rhythm did and did not appear. In short, grating stimuli had to have a minimum size or/and a minimum contrast and had to be moved with a constant velocity to elicit gamma rhythms. But more importantly, we have not found one study on primary visual cortex (neither in awake nor anaesthetized animals) that showed a gamma bump in response to natural movies. In our opinion, this is a very strong indication that gamma rhythms as defined by elevated power in a restricted frequency band cannot play an important role in early visual areas under natural circumstances. In addition, the tuning similarity between gamma power and the firing of nearby neurons is somewhat controversial and cannot easily be explained. Several studies find no relationship between gamma and neurons for orientation and size tuning (Bauer et al., 1995; Berens et al., 2008b; Gieselmann and Thiele, 2008; Jia et al., 2011; Ray and Maunsell, 2011a; Jia et al., 2013a), whereas one study found similar size tuning (Zhang and Li, 2013, see section 4.4.1.5 for a critical evaluation of this study) and another investigation saw similar 113 5 Discussion ocular dominance tuning between gamma and neural firing rates (Berens et al., 2008b) 7 . Astonishingly, orientation tuning of gamma power in the study by Jia et al. (2011) was similar between recording sites with distances of up to 9 mm (in monkey V1). How this globally coherent gamma rhythm is generated is not yet clear but it shows strikingly that the amplitude of gamma rhythm is not related to the activity of a locally restricted neural population. This limits the relevance of gamma rhythms in coordinating the communication between cortical regions that interact in coding a specific quantity or information as suggested by the theory of communication through coherence or binding by synchrony (see section 1.7). 5.4 Suggestions for future investigations The functional heterogeneity among neurons in local populations of primary visual cortex that was observed in this study raises two main questions that should be addressed in future research: (1) how do downstream neurons deal with the heterogeneity in the neural pools from which they receive input, and (2) how does the heterogeneity in tuning for some stimulus features together with the similarity in other stimulus features develop? Both questions should be approached—not only, but also—under natural conditions, i.e. when natural stimuli are processed. Regarding the first question, we previously hypothesized that connectivity might be specific according to similar response characteristics. To test this theory, methods used by the various studies on functional subnetworks in rodents could serve as templates (Hofer et al., 2011; Ko et al., 2011). Using two-photon microscopy in primary visual cortex of mammals with cortical columns, such as cat or monkey, one could identify neurons with more similar tuning properties or stronger signal correlations than normally observed between neurons in a local population. In a second step, connectivity between those neurons could be determined, previously done by slicing the same brain tissue and patch-clamping those neurons whose physiology data was collected before. New powerful genetic tools might even enable the investigation of subnetworks extending across layers or cortical areas by directly combining structural and functional analysis of neural circuits. Rabies viruses in combination with other viral vectors could be used to exclusively mark, stimulate and record from single neurons together with the neurons projecting to it (for proof of concept, see Osakada et al., 2011). These tools allow one to assess whether functional networks exist for non-clustered stimulus features within columnar architectures of V1, and whether different functional subnetworks emerge in response to different stimulus statistics. Knowing the input neurons to a single downstream neuron and at the same time being able to record their responses would also help to understand how a neuron processes and responds to “natural” synaptic inputs (as supposed to artificially generated input) 7 Note that all of these statements refer to the relationship between gamma power and the firing rate of neurons. Power of the frequency content of spiking activity was mostly seen to be more similar to gamma power for the tuning of several parameters (see for example Bauer et al., 1995; Lashgari et al., 2012). 114 Functional microarchitecture of cat primary visual cortex while being embedded in its “natural” context (not cut off from a large number of cortical and subcortical input, as is the case for recordings in slices). Regarding the second question, the observation of how response characteristics of single and multiple neurons in a local population change during development can further the understanding of coding principles. Long-term observations of population activity using electrophysiology or two-photon imaging (for long-term experiments in monkey, see Heider et al., 2010) make these changes visible. It is expected that neurons will become more selective to visual stimulation during development, but will they at the same time differentiate their responses so that response characteristics will become less and less correlated among nearby neurons? Or will subsets of neurons adjust their response properties to reach greater similarity? Combining such functional investigations with the study of the underlying circuits could lead to an understanding of whether functional similarity or diversity is first setup by thalamic inputs or whether it is more strongly regulated by intracortical connections. A very important step in this direction was made by Ko et al. (2013). They combined two-photon imaging in vivo with structural analysis in vitro (the same way as was done in their earlier experiments, see previous paragraph) during different stages of development in mouse V1. Their data reveals that functional specificity in local populations, i.e. higher connection probability for neurons exhibiting more similar orientation preferences or higher signal correlations in response to movies, only develops after eye opening although neurons are already selective to visual features before that. Simulations using artificial neural networks suggest that thalamic input patterns structure the recurrent cortical connectivity by activity-dependent mechanisms of synaptic plasticity. Similar experiments conducted in V1 of mammals expressing cortical columns could reveal how some features cluster and at the same time other response characteristics, specifically for natural stimuli, differentiate among neighbouring neurons. 115 6 References 6 References Abbott LF, Dayan P (1999) The effect of correlated variability on the accuracy of a population code. Neural computation 11:91-101. Alonso JM, Martinez LM (1998) Functional connectivity between simple cells and complex cells in cat striate cortex. Nature neuroscience 1:395-403. Anastassiou CA, Perin R, Markram H, Koch C (2011) Ephaptic coupling of cortical neurons. Nature neuroscience 14:217-223. Asher I, Stark E, Abeles M, Prut Y (2007) Comparison of direction and object selectivity of local field potentials and single units in macaque posterior parietal cortex during prehension. Journal of neurophysiology 97:3684-3695. Atiya AF (1992) Recognition of multiunit neural signals. IEEE transactions on bio-medical engineering 39:723-729. Averbeck BB, Lee D (2004) Coding and transmission of information by neural ensembles. Trends in neurosciences 27:225-230. Averbeck BB, Latham PE, Pouget A (2006) Neural correlations, population coding and computation. Nature reviews Neuroscience 7:358-366. Bair W (1999) Spike timing in the mammalian visual system. Current opinion in neurobiology 9:447-453. Bair W, Zohary E, Newsome WT (2001) Correlated firing in macaque visual area MT: time scales and relationship to behavior. The Journal of neuroscience : the official journal of the Society for Neuroscience 21:1676-1697. Baker GE, Thompson ID, Krug K, Smyth D, Tolhurst DJ (1998) Spatial-frequency tuning and geniculocortical projections in the visual cortex (areas 17 and 18) of the pigmented ferret. The European journal of neuroscience 10:2657-2668. Banitt Y, Martin KA, Segev I (2007) A biologically realistic model of contrast invariant orientation tuning by thalamocortical synaptic depression. The Journal of neuroscience : the official journal of the Society for Neuroscience 27:10230-10239. Barth AL, Poulet JF (2012) Experimental evidence for sparse firing in the neocortex. Trends in neurosciences 35:345-355. Basole A, White LE, Fitzpatrick D (2003) Mapping multiple features in the population response of visual cortex. Nature 423:986-990. Bauer R, Brosch M, Eckhorn R (1995) Different rules of spatial summation from beyond the receptive field for spike rates and oscillation amplitudes in cat visual cortex. Brain research 669:291-297. Belelli D, Lambert JJ (2005) Neurosteroids: endogenous regulators of the GABA(A) receptor. Nature reviews Neuroscience 6:565-575. 116 Functional microarchitecture of cat primary visual cortex Belitski A, Panzeri S, Magri C, Logothetis NK, Kayser C (2010) Sensory information in local field potentials and spikes from visual and auditory cortices: time scales and frequency bands. Journal of computational neuroscience 29:533-545. Belitski A, Gretton A, Magri C, Murayama Y, Montemurro MA, Logothetis NK, Panzeri S (2008) Low-frequency local field potentials and spikes in primary visual cortex convey independent visual information. The Journal of neuroscience : the official journal of the Society for Neuroscience 28:5696-5709. Berens P (2009) CircStat: A MATLAB Toolbox for Circular Statistics. J Stat Softw 31:1-21. Berens P, Keliris GA, Ecker AS, Logothetis NK, Tolias AS (2008a) Feature selectivity of the gamma-band of the local field potential in primate primary visual cortex. Frontiers in neuroscience 2:199-207. Berens P, Keliris GA, Ecker AS, Logothetis NK, Tolias AS (2008b) Comparing the feature selectivity of the gamma-band of the local field potential and the underlying spiking activity in primate visual cortex. Frontiers in systems neuroscience 2:2. Berkes P, Orban G, Lengyel M, Fiser J (2011) Spontaneous cortical activity reveals hallmarks of an optimal internal model of the environment. Science 331:83-87. Blasdel GG (1992) Orientation selectivity, preference, and continuity in monkey striate cortex. The Journal of neuroscience : the official journal of the Society for Neuroscience 12:3139-3161. Bonhoeffer T, Grinvald A (1991) Iso-orientation domains in cat visual cortex are arranged in pinwheel-like patterns. Nature 353:429-431. Bosking WH, Zhang Y, Schofield B, Fitzpatrick D (1997) Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. The Journal of neuroscience : the official journal of the Society for Neuroscience 17:2112-2127. Buffalo EA, Fries P, Landman R, Buschman TJ, Desimone R (2011) Laminar differences in gamma and alpha coherence in the ventral stream. Proceedings of the National Academy of Sciences of the United States of America 108:11262-11267. Burns SP, Xing D, Shapley RM (2010a) Comparisons of the dynamics of local field potential and multiunit activity signals in macaque visual cortex. The Journal of neuroscience : the official journal of the Society for Neuroscience 30:13739-13749. Burns SP, Xing D, Shapley RM (2011) Is gamma-band activity in the local field potential of V1 cortex a "clock" or filtered noise? The Journal of neuroscience : the official journal of the Society for Neuroscience 31:9658-9664. Burns SP, Xing D, Shelley MJ, Shapley RM (2010b) Searching for autocoherence in the cortical network with a time-frequency analysis of the local field potential. The Journal of neuroscience : the official journal of the Society for Neuroscience 30:4033-4047. Butts DA, Weng C, Jin J, Yeh CI, Lesica NA, Alonso JM, Stanley GB (2007) Temporal precision in the neural code and the timescales of natural vision. Nature 449:92-95. Buzsáki G (2006) Rhythms of the brain: Oxford University Press. 117 6 References Buzsáki G, Draguhn A (2004) Neuronal oscillations in cortical networks. Science 304:19261929. Buzsáki G, Wang XJ (2012) Mechanisms of gamma oscillations. Annual review of neuroscience 35:203-225. Buzsáki G, Anastassiou CA, Koch C (2012) The origin of extracellular fields and currents-EEG, ECoG, LFP and spikes. Nature reviews Neuroscience 13:407-420. Cafaro J, Rieke F (2010) Noise correlations improve response fidelity and stimulus encoding. Nature 468:964-967. Carandini M, Demb JB, Mante V, Tolhurst DJ, Dan Y, Olshausen BA, Gallant JL, Rust NC (2005) Do we know what the early visual system does? The Journal of neuroscience : the official journal of the Society for Neuroscience 25:10577-10597. Cavanaugh JR, Bair W, Movshon JA (2002) Nature and interaction of signals from the receptive field center and surround in macaque V1 neurons. Journal of neurophysiology 88:2530-2546. Chance FS, Nelson SB, Abbott LF (1999) Complex cells as cortically amplified simple cells. Nature neuroscience 2:277-282. Chen Y, Geisler WS, Seidemann E (2006) Optimal decoding of correlated neural population responses in the primate visual cortex. Nature neuroscience 9:1412-1420. Chen Y, Geisler WS, Seidemann E (2008) Optimal temporal decoding of neural population responses in a reaction-time visual detection task. Journal of neurophysiology 99:1366-1379. Cohen MR, Maunsell JH (2009) Attention improves performance primarily by reducing interneuronal correlations. Nature neuroscience 12:1594-1600. Cohen MR, Kohn A (2011) Measuring and interpreting neuronal correlations. Nature neuroscience 14:811-819. da Costa NM, Martin KA (2010) Whose Cortical Column Would that Be? Frontiers in neuroanatomy 4:16. Daniel PM, Whitteridge D (1961) The representation of the visual field on the cerebral cortex in monkeys. The Journal of physiology 159:203-221. Das A, Gilbert CD (1999) Topography of contextual modulations mediated by short-range interactions in primary visual cortex. Nature 399:655-661. David SV, Vinje WE, Gallant JL (2004) Natural stimulus statistics alter the receptive field structure of v1 neurons. The Journal of neuroscience : the official journal of the Society for Neuroscience 24:6991-7006. de la Rocha J, Doiron B, Shea-Brown E, Josic K, Reyes A (2007) Correlation between neural spike trains increases with firing rate. Nature 448:802-806. 118 Functional microarchitecture of cat primary visual cortex DeAngelis GC, Ghose GM, Ohzawa I, Freeman RD (1999) Functional micro-organization of primary visual cortex: receptive field analysis of nearby neurons. The Journal of neuroscience : the official journal of the Society for Neuroscience 19:4046-4064. Destexhe A (2011) Intracellular and computational evidence for a dominant role of internal network activity in cortical computations. Current opinion in neurobiology 21:717725. Destexhe A, Contreras D, Steriade M (1999) Spatiotemporal analysis of local field potentials and unit discharges in cat cerebral cortex during natural wake and sleep states. The Journal of neuroscience : the official journal of the Society for Neuroscience 19:45954608. Douglas R, Markram H, Martin KAC (2003) Neocortex. In: The Synaptic Organization of the Brain (Shepherd GM, ed), p 736: Oxford University Press. Douglas RJ, Martin KA (2004) Neuronal circuits of the neocortex. Annual review of neuroscience 27:419-451. Douglas RJ, Martin KA (2007) Mapping the matrix: the ways of neocortex. Neuron 56:226238. Douglas RJ, Martin KA (2011) What's black and white about the grey matter? Neuroinformatics 9:167-179. Douglas RJ, Koch C, Mahowald M, Martin KA, Suarez HH (1995) Recurrent excitation in neocortical circuits. Science 269:981-985. Ecker AS, Berens P, Tolias AS, Bethge M (2011) The effect of noise correlations in populations of diversely tuned neurons. The Journal of neuroscience : the official journal of the Society for Neuroscience 31:14272-14283. Ecker AS, Berens P, Keliris GA, Bethge M, Logothetis NK, Tolias AS (2010) Decorrelated neuronal firing in cortical microcircuits. Science 327:584-587. Engel AK, Fries P, Singer W (2001) Dynamic predictions: oscillations and synchrony in topdown processing. Nature reviews Neuroscience 2:704-716. Faisal AA, Selen LP, Wolpert DM (2008) Noise in the nervous system. Nature reviews Neuroscience 9:292-303. Ferster D, Miller KD (2000) Neural mechanisms of orientation selectivity in the visual cortex. Annual review of neuroscience 23:441-471. Field DJ (1987) Relations between the statistics of natural images and the response properties of cortical cells. Journal of the Optical Society of America A, Optics and image science 4:2379-2394. Field DJ, Tolhurst DJ (1986) The structure and symmetry of simple-cell receptive-field profiles in the cat's visual cortex. Proceedings of the Royal Society of London Series B, Containing papers of a Biological character Royal Society 228:379-400. 119 6 References Fiser J, Chiu C, Weliky M (2004) Small modulation of ongoing cortical dynamics by sensory input during natural vision. Nature 431:573-578. Frien A, Eckhorn R, Bauer R, Woelbern T, Gabriel A (2000) Fast oscillations display sharper orientation tuning than slower components of the same recordings in striate cortex of the awake monkey. European Journal of Neuroscience 12:1453-1465. Fries P (2005) A mechanism for cognitive dynamics: neuronal communication through neuronal coherence. Trends in cognitive sciences 9:474-480. Fries P, Nikolic D, Singer W (2007) The gamma cycle. Trends in neurosciences 30:309-316. Fries P, Neuenschwander S, Engel AK, Goebel R, Singer W (2001) Rapid feature selective neuronal synchronization through correlated latency shifting. Nature neuroscience 4:194-200. Fröhlich F, McCormick DA (2010) Endogenous electric fields may guide neocortical network activity. Neuron 67:129-143. Gawne TJ, Kjaer TW, Hertz JA, Richmond BJ (1996a) Adjacent Visual Cortical Complex Cells Share About 20% of Their Stimulus-Related Information. Cerebral Cortex 6:482-489. Gawne TJ, Kjaer TW, Hertz JA, Richmond BJ (1996b) Adjacent visual cortical complex cells share about 20% of their stimulus-related information. Cerebral cortex 6:482-489. Gieselmann MA, Thiele A (2008) Comparison of spatial integration and surround suppression characteristics in spiking activity and the local field potential in macaque V1. The European journal of neuroscience 28:447-459. Gilbert CD (1977) Laminar differences in receptive field properties of cells in cat primary visual cortex. The Journal of physiology 268:391-421. Gilbert CD, Wiesel TN (1989) Columnar specificity of intrinsic horizontal and corticocortical connections in cat visual cortex. The Journal of neuroscience : the official journal of the Society for Neuroscience 9:2432-2442. Gizzi MS, Katz E, Schumer RA, Movshon JA (1990) Selectivity for orientation and direction of motion of single neurons in cat striate and extrastriate visual cortex. Journal of neurophysiology 63:1529-1543. Goto T, Hatanaka R, Ogawa T, Sumiyoshi A, Riera J, Kawashima R (2010) An evaluation of the conductivity profile in the somatosensory barrel cortex of Wistar rats. Journal of neurophysiology 104:3388-3412. Gray CM, Singer W (1989) Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. Proceedings of the National Academy of Sciences of the United States of America 86:1698-1702. Gray CM, König P, Engel AK, Singer W (1989) Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature 338:334-337. 120 Functional microarchitecture of cat primary visual cortex Haider B, Krause MR, Duque A, Yu Y, Touryan J, Mazer JA, McCormick DA (2010) Synaptic and network mechanisms of sparse and reliable visual cortical activity during nonclassical receptive field stimulation. Neuron 65:107-121. Hansel D, van Vreeswijk C (2012) The mechanism of orientation selectivity in primary visual cortex without a functional map. The Journal of neuroscience : the official journal of the Society for Neuroscience 32:4049-4064. Harris KD, Thiele A (2011) Cortical state and attention. Nature reviews Neuroscience 12:509523. Harris KD, Csicsvari J, Hirase H, Dragoi G, Buzsáki G (2003) Organization of cell assemblies in the hippocampus. Nature 424:552-556. Hasenstaub A, Shu Y, Haider B, Kraushaar U, Duque A, McCormick DA (2005) Inhibitory postsynaptic potentials carry synchronized frequency information in active cortical networks. Neuron 47:423-435. Haslinger R, Pipa G, Lima B, Singer W, Brown EN, Neuenschwander S (2012) Context matters: the illusive simplicity of macaque V1 receptive fields. PloS one 7:e39699. Heider B, Nathanson JL, Isacoff EY, Callaway EM, Siegel RM (2010) Two-photon imaging of calcium in virally transfected striate cortical neurons of behaving monkey. PloS one 5:e13829. Henrie JA, Shapley R (2005) LFP power spectra in V1 cortex: the graded effect of stimulus contrast. Journal of neurophysiology 94:479-490. Herikstad R, Baker J, Lachaux JP, Gray CM, Yen SC (2011) Natural movies evoke spike trains with low spike time variability in cat primary visual cortex. The Journal of neuroscience : the official journal of the Society for Neuroscience 31:15844-15860. Hofer SB, Ko H, Pichler B, Vogelstein J, Ros H, Zeng H, Lein E, Lesica NA, Mrsic-Flogel TD (2011) Differential connectivity and response dynamics of excitatory and inhibitory neurons in visual cortex. Nature neuroscience 14:1045-1052. Horton JC, Adams DL (2005) The cortical column: a structure without a function. Philosophical transactions of the Royal Society of London Series B, Biological sciences 360:837-862. Hubel DH, Wiesel TN (1959) Receptive fields of single neurones in the cat's striate cortex. The Journal of physiology 148:574-591. Hubel DH, Wiesel TN (1962) Receptive fields, binocular interaction and functional architecture in the cat's visual cortex. The Journal of physiology 160:106-154. Hubel DH, Wiesel TN (1963) Shape and arrangement of columns in cat's striate cortex. The Journal of physiology 165:559-568. Hubel DH, Wiesel TN (1965) Binocular interaction in striate cortex of kittens reared with artificial squint. Journal of neurophysiology 28:1041-1059. 121 6 References Hubel DH, Wiesel TN (1968) Receptive fields and functional architecture of monkey striate cortex. The Journal of physiology 195:215-243. Hubel DH, Wiesel TN (1974a) Uniformity of monkey striate cortex: a parallel relationship between field size, scatter, and magnification factor. The Journal of comparative neurology 158:295-305. Hubel DH, Wiesel TN (1974b) Sequence regularity and geometry of orientation columns in the monkey striate cortex. The Journal of comparative neurology 158:267-293. Hubel DH, Wiesel TN (1977) Ferrier lecture. Functional architecture of macaque monkey visual cortex. Proceedings of the Royal Society of London Series B, Containing papers of a Biological character Royal Society 198:1-59. Hübener M, Shoham D, Grinvald A, Bonhoeffer T (1997) Spatial relationships among three columnar systems in cat area 17. The Journal of neuroscience : the official journal of the Society for Neuroscience 17:9270-9284. Hyvärinen A, Hoyer PO (2001) A two-layer sparse coding model learns simple and complex cell receptive fields and topography from natural images. Vision research 41:24132423. Hyvärinen A, Hurri J, Väyrynen J (2003) Bubbles: a unifying framework for low-level statistical properties of natural image sequences. Journal of the Optical Society of America A, Optics, image science, and vision 20:1237-1252. Issa NP, Trepel C, Stryker MP (2000) Spatial frequency maps in cat visual cortex. The Journal of neuroscience : the official journal of the Society for Neuroscience 20:8504-8514. Jia H, Rochefort NL, Chen X, Konnerth A (2010) Dendritic organization of sensory input to cortical neurons in vivo. Nature 464:1307-1312. Jia X, Kohn A (2011) Gamma rhythms in the brain. PLoS biology 9:e1001045. Jia X, Smith MA, Kohn A (2011) Stimulus selectivity and spatial coherence of gamma components of the local field potential. The Journal of neuroscience : the official journal of the Society for Neuroscience 31:9390-9403. Jia X, Xing D, Kohn A (2013a) No consistent relationship between gamma power and peak frequency in macaque primary visual cortex. The Journal of neuroscience : the official journal of the Society for Neuroscience 33:17-25. Jia X, Tanabe S, Kohn A (2013b) Gamma and the coordination of spiking activity in early visual cortex. Neuron 77:762-774. Kajikawa Y, Schroeder CE (2011) How local is the local field potential? Neuron 72:847-858. Katzner S, Nauhaus I, Benucci A, Bonin V, Ringach DL, Carandini M (2009) Local origin of field potentials in visual cortex. Neuron 61:35-41. Kayser C, König P (2004) Stimulus locking and feature selectivity prevail in complementary frequency ranges of V1 local field potentials. The European journal of neuroscience 19:485-489. 122 Functional microarchitecture of cat primary visual cortex Kayser C, Salazar RF, König P (2003) Responses to natural scenes in cat V1. Journal of neurophysiology 90:1910-1920. Kayser C, Ince RA, Panzeri S (2012) Analysis of slow (theta) oscillations as a potential temporal reference frame for information coding in sensory cortices. PLoS computational biology 8:e1002717. Kayser C, Montemurro MA, Logothetis NK, Panzeri S (2009) Spike-phase coding boosts and stabilizes information carried by spatial and temporal spike patterns. Neuron 61:597608. Khawaja FA, Tsui JM, Pack CC (2009) Pattern motion selectivity of spiking outputs and local field potentials in macaque visual cortex. The Journal of neuroscience : the official journal of the Society for Neuroscience 29:13702-13709. Ko H, Hofer SB, Pichler B, Buchanan KA, Sjöström PJ, Mrsic-Flogel TD (2011) Functional specificity of local synaptic connections in neocortical networks. Nature 473:87-91. Ko H, Cossell L, Baragli C, Antolik J, Clopath C, Hofer SB, Mrsic-Flogel TD (2013) The emergence of functional microcircuits in visual cortex. Nature 496:96-100. Kohn A, Smith MA (2005) Stimulus dependence of neuronal correlation in primary visual cortex of the macaque. The Journal of neuroscience : the official journal of the Society for Neuroscience 25:3661-3673. Kohn A, Zandvakili A, Smith MA (2009) Correlations and brain states: from electrophysiology to functional imaging. Current opinion in neurobiology 19:434-438. Kreiman G, Hung CP, Kraskov A, Quiroga RQ, Poggio T, DiCarlo JJ (2006) Object selectivity of local field potentials and spikes in the macaque inferior temporal cortex. Neuron 49:433-445. Kruse W, Eckhorn R (1996) Inhibition of sustained gamma oscillations (35-80 Hz) by fast transient responses in cat visual cortex. Proceedings of the National Academy of Sciences of the United States of America 93:6112-6117. Lampl I, Reichova I, Ferster D (1999) Synchronous membrane potential fluctuations in neurons of the cat visual cortex. Neuron 22:361-374. Lashgari R, Li X, Chen Y, Kremkow J, Bereshpolova Y, Swadlow HA, Alonso JM (2012) Response properties of local field potentials and neighboring single neurons in awake primary visual cortex. The Journal of neuroscience : the official journal of the Society for Neuroscience 32:11396-11413. Laughlin SB, Sejnowski TJ (2003) Communication in neuronal networks. Science 301:18701874. LeVay S, Gilbert CD (1976) Laminar patterns of geniculocortical projection in the cat. Brain research 113:1-19. Lindén H, Tetzlaff T, Potjans TC, Pettersen KH, Grün S, Diesmann M, Einevoll GT (2011) Modeling the spatial reach of the LFP. Neuron 72:859-872. 123 6 References Logothetis NK, Kayser C, Oeltermann A (2007) In vivo measurement of cortical impedance spectrum in monkeys: implications for signal propagation. Neuron 55:809-823. Logothetis NK, Pauls J, Augath M, Trinath T, Oeltermann A (2001) Neurophysiological investigation of the basis of the fMRI signal. Nature 412:150-157. Lorente de Nó R (1949) Cerebral cortex: architecture, intracortical connections, motor projections. In: Physiology of the nervous system: Oxford University Press. Maier A, Adams GK, Aura C, Leopold DA (2010) Distinct superficial and deep laminar domains of activity in the visual cortex during rest and stimulation. Frontiers in systems neuroscience 4. Maldonado PE, Friedman-Hill S, Gray CM (2000) Dynamics of striate cortical activity in the alert macaque: II. Fast time scale synchronization. Cerebral cortex 10:1117-1131. Mante V, Carandini M (2005) Mapping of stimulus energy in primary visual cortex. Journal of neurophysiology 94:788-798. Martin KA, Schröder S (2013) Functional heterogeneity in neighboring neurons of cat primary visual cortex in response to both artificial and natural stimuli. The Journal of neuroscience : the official journal of the Society for Neuroscience 33:7325-7344. Martinez LM, Wang Q, Reid RC, Pillai C, Alonso JM, Sommer FT, Hirsch JA (2005) Receptive field structure varies with layer in the primary visual cortex. Nature neuroscience 8:372-379. Mazurek ME, Shadlen MN (2002) Limits to the temporal fidelity of cortical spike rate signals. Nature neuroscience 5:463-471. McDonnell MD, Abbott D (2009) What is stochastic resonance? Definitions, misconceptions, debates, and its relevance to biology. PLoS computational biology 5:e1000348. Mechler F, Ringach DL (2002) On the classification of simple and complex cells. Vision research 42:1017-1033. Middleton JW, Omar C, Doiron B, Simons DJ (2012) Neural correlation is stimulus modulated by feedforward inhibitory circuitry. The Journal of neuroscience : the official journal of the Society for Neuroscience 32:506-518. Mitchell JF, Sundberg KA, Reynolds JH (2009) Spatial attention decorrelates intrinsic activity fluctuations in macaque area V4. Neuron 63:879-888. Mitra PP, Bokil H (2008) Observed Brain Dynamics: Oxford University Press. Mitzdorf U (1985) Current source-density method and application in cat cerebral cortex: investigation of evoked potentials and EEG phenomena. Physiological reviews 65:37100. Molotchnikoff S, Gillet PC, Shumikhina S, Bouchard M (2007) Spatial frequency characteristics of nearby neurons in cats' visual cortex. Neuroscience letters 418:242247. 124 Functional microarchitecture of cat primary visual cortex Monier C, Chavane F, Baudot P, Graham LJ, Frégnac Y (2003) Orientation and direction selectivity of synaptic inputs in visual cortical neurons: a diversity of combinations produces spike tuning. Neuron 37:663-680. Montemurro MA, Rasch MJ, Murayama Y, Logothetis NK, Panzeri S (2008) Phase-of-firing coding of natural visual stimuli in primary visual cortex. Current biology : CB 18:375380. Mountcastle VB (1957) Modality and topographic properties of single neurons of cat's somatic sensory cortex. Journal of neurophysiology 20:408-434. Mountcastle VB (1997) The columnar organization of the neocortex. Brain : a journal of neurology 120 ( Pt 4):701-722. Nauhaus I, Nielsen KJ, Disney AA, Callaway EM (2012) Orthogonal micro-organization of orientation and spatial frequency in primate primary visual cortex. Nature neuroscience 15:1683-1690. Nelson MJ, Pouget P (2010) Do electrode properties create a problem in interpreting local field potential recordings? Journal of neurophysiology 103:2315-2317. Niell CM, Stryker MP (2008) Highly selective receptive fields in mouse visual cortex. The Journal of neuroscience : the official journal of the Society for Neuroscience 28:75207536. Nir Y, Fisch L, Mukamel R, Gelbard-Sagiv H, Arieli A, Fried I, Malach R (2007) Coupling between neuronal firing rate, gamma LFP, and BOLD fMRI is related to interneuronal correlations. Current biology : CB 17:1275-1285. Nishikawa K, MacIver MB (2000) Membrane and synaptic actions of halothane on rat hippocampal pyramidal neurons and inhibitory interneurons. The Journal of neuroscience : the official journal of the Society for Neuroscience 20:5915-5923. Nover H, Anderson CH, DeAngelis GC (2005) A logarithmic, scale-invariant representation of speed in macaque middle temporal area accounts for speed discrimination performance. The Journal of neuroscience : the official journal of the Society for Neuroscience 25:10049-10060. Ohki K, Chung S, Ch'ng YH, Kara P, Reid RC (2005) Functional imaging with cellular resolution reveals precise micro-architecture in visual cortex. Nature 433:597-603. Ohki K, Chung S, Kara P, Hübener M, Bonhoeffer T, Reid RC (2006) Highly ordered arrangement of single neurons in orientation pinwheels. Nature 442:925-928. Okun M, Lampl I (2008) Instantaneous correlation of excitation and inhibition during ongoing and sensory-evoked activities. Nature neuroscience 11:535-537. Okun M, Naim A, Lampl I (2010) The subthreshold relation between cortical local field potential and neuronal firing unveiled by intracellular recordings in awake rats. The Journal of neuroscience : the official journal of the Society for Neuroscience 30:44404448. 125 6 References Olshausen BA (2003) Principles of image representation in visual cortex. In: The Visual Neurosciences (Chalupa LM, Werner JS, eds), pp 1603-1615: Cambridge, MA: MIT Press. Olshausen BA, Field DJ (2004a) Sparse coding of sensory inputs. Current opinion in neurobiology 14:481-487. Olshausen BA, Field DJ (2004b) What is the other 85% of V1 doing. In: Problems in Systems Neuroscience, pp 182-211: Oxford University Press. Onat S, König P, Jancke D (2011) Natural scene evoked population dynamics across cat primary visual cortex captured with voltage-sensitive dye imaging. Cerebral cortex 21:2542-2554. Osakada F, Mori T, Cetin AH, Marshel JH, Virgen B, Callaway EM (2011) New rabies virus variants for monitoring and manipulating activity and gene expression in defined neural circuits. Neuron 71:617-631. Parker AJ, Newsome WT (1998) Sense and the single neuron: probing the physiology of perception. Annual review of neuroscience 21:227-277. Passingham R (1982) The Human Primate. Oxford and San Francisco: W.H. Freeman. Payne BR, Berman N, Murphy EH (1981) Organization of direction preferences in cat visual cortex. Brain research 211:445-450. Poulet JF, Petersen CC (2008) Internal brain state regulates membrane potential synchrony in barrel cortex of behaving mice. Nature 454:881-885. Powell TP, Mountcastle VB (1959) Some aspects of the functional organization of the cortex of the postcentral gyrus of the monkey: a correlation of findings obtained in a single unit analysis with cytoarchitecture. Bulletin of the Johns Hopkins Hospital 105:133162. Quiroga RQ, Nadasdy Z, Ben-Shaul Y (2004) Unsupervised spike detection and sorting with wavelets and superparamagnetic clustering. Neural computation 16:1661-1687. Rager G, Singer W (1998) The response of cat visual cortex to flicker stimuli of variable frequency. The European journal of neuroscience 10:1856-1877. Rasch MJ, Gretton A, Murayama Y, Maass W, Logothetis NK (2008) Inferring spike trains from local field potentials. Journal of neurophysiology 99:1461-1476. Ray S, Maunsell JH (2010) Differences in gamma frequencies across visual cortex restrict their possible use in computation. Neuron 67:885-896. Ray S, Maunsell JH (2011a) Different origins of gamma rhythm and high-gamma activity in macaque visual cortex. PLoS biology 9:e1000610. Ray S, Maunsell JH (2011b) Network rhythms influence the relationship between spiketriggered local field potential and functional connectivity. The Journal of neuroscience : the official journal of the Society for Neuroscience 31:12674-12682. 126 Functional microarchitecture of cat primary visual cortex Reich DS, Mechler F, Victor JD (2001) Independent and redundant information in nearby cortical neurons. Science 294:2566-2568. Reid RC, Soodak RE, Shapley RM (1987) Linear mechanisms of directional selectivity in simple cells of cat striate cortex. Proceedings of the National Academy of Sciences of the United States of America 84:8740-8744. Renart A, de la Rocha J, Bartho P, Hollender L, Parga N, Reyes A, Harris KD (2010) The asynchronous state in cortical circuits. Science 327:587-590. Ringach DL, Hawken MJ, Shapley R (2002) Receptive field structure of neurons in monkey primary visual cortex revealed by stimulation with natural image sequences. Journal of vision 2:12-24. Ruesch E (2011) Functional architecture of superficial layer pyramidal neurons in the cat primary visual cortex. In, p 374. Zürich: ETH Zürich. Salinas E, Sejnowski TJ (2001) Correlated neuronal activity and the flow of neural information. Nature reviews Neuroscience 2:539-550. Schwartz O, Pillow JW, Rust NC, Simoncelli EP (2006) Spike-triggered neural characterization. Journal of vision 6:484-507. Shadlen MN, Newsome WT (1998) The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. The Journal of neuroscience : the official journal of the Society for Neuroscience 18:3870-3896. Shadlen MN, Britten KH, Newsome WT, Movshon JA (1996) A computational analysis of the relationship between neuronal and behavioral responses to visual motion. The Journal of neuroscience : the official journal of the Society for Neuroscience 16:14861510. Shoham D, Hübener M, Schulze S, Grinvald A, Bonhoeffer T (1997) Spatio-temporal frequency domains and their relation to cytochrome oxidase staining in cat visual cortex. Nature 385:529-533. Siegel M, König P (2003) A functional gamma-band defined by stimulus-dependent synchronization in area 18 of awake behaving cats. The Journal of neuroscience : the official journal of the Society for Neuroscience 23:4251-4260. Simoncelli EP, Olshausen BA (2001) Natural image statistics and neural representation. Annual review of neuroscience 24:1193-1216. Singer W, Gray CM (1995) Visual feature integration and the temporal correlation hypothesis. Annual review of neuroscience 18:555-586. Smith MA, Kohn A (2008) Spatial and temporal scales of neuronal correlation in primary visual cortex. The Journal of neuroscience : the official journal of the Society for Neuroscience 28:12591-12603. Smith MA, Jia X, Zandvakili A, Kohn A (2013) Laminar dependence of neuronal correlations in visual cortex. Journal of neurophysiology 109:940-947. 127 6 References Softky WR, Koch C (1993) The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. The Journal of neuroscience : the official journal of the Society for Neuroscience 13:334-350. Sompolinsky H, Yoon H, Kang K, Shamir M (2001) Population coding in neuronal systems with correlated noise. Physical review E, Statistical, nonlinear, and soft matter physics 64:051904. Steriade M (2006) Grouping of brain rhythms in corticothalamic systems. Neuroscience 137:1087-1106. Suarez H, Koch C, Douglas R (1995) Modeling direction selectivity of simple cells in striate visual cortex within the framework of the canonical microcircuit. The Journal of neuroscience : the official journal of the Society for Neuroscience 15:6700-6719. Swindale NV (1998) Orientation tuning curves: empirical description and estimation of parameters. Biological cybernetics 78:45-56. Swindale NV, Grinvald A, Shmuel A (2003) The spatial pattern of response magnitude and selectivity for orientation and direction in cat visual cortex. Cerebral cortex 13:225238. Swindale NV, Shoham D, Grinvald A, Bonhoeffer T, Hübener M (2000) Visual cortex maps are optimized for uniform coverage. Nature neuroscience 3:822-826. Tiesinga P, Sejnowski TJ (2009) Cortical enlightenment: are attentional gamma oscillations driven by ING or PING? Neuron 63:727-732. Tolhurst DJ, Thompson ID (1982) Organization of neurones preferring similar spatial frequencies in cat striate cortex. Experimental brain research Experimentelle Hirnforschung Experimentation cerebrale 48:217-227. Tolhurst DJ, Dean AF, Thompson ID (1981) Preferred direction of movement as an element in the organization of cat visual cortex. Experimental brain research Experimentelle Hirnforschung Experimentation cerebrale 44:340-342. Tolhurst DJ, Movshon JA, Dean AF (1983) The statistical reliability of signals in single neurons in cat and monkey visual cortex. Vision research 23:775-785. Tolhurst DJ, Smyth D, Thompson ID (2009) The sparseness of neuronal responses in ferret primary visual cortex. The Journal of neuroscience : the official journal of the Society for Neuroscience 29:2355-2370. Tootell RB, Silverman MS, De Valois RL (1981) Spatial frequency columns in primary visual cortex. Science 214:813-815. Touryan J, Felsen G, Dan Y (2005) Spatial structure of complex cell receptive fields measured with natural images. Neuron 45:781-791. Ts'o DY, Gilbert CD, Wiesel TN (1986) Relationships between horizontal interactions and functional architecture in cat striate cortex as revealed by cross-correlation analysis. The Journal of neuroscience : the official journal of the Society for Neuroscience 6:1160-1170. 128 Functional microarchitecture of cat primary visual cortex van Hateren JH, Ruderman DL (1998) Independent component analysis of natural image sequences yields spatio-temporal filters similar to simple cells in primary visual cortex. Proceedings Biological sciences / The Royal Society 265:2315-2320. Victor JD (1992) Nonliear Systems Analysis in Vision: Overview of Kernel Methods. In: Nonlinear vision: determination of neural receptive fields, function, and networks (Pinter RB, Nabet B, eds), pp 1-38: Boca Raton: CRC PRess. Vinck M, Lima B, Womelsdorf T, Oostenveld R, Singer W, Neuenschwander S, Fries P (2010) Gamma-phase shifting in awake monkey visual cortex. The Journal of neuroscience : the official journal of the Society for Neuroscience 30:1250-1257. Vinje WE, Gallant JL (2000) Sparse coding and decorrelation in primary visual cortex during natural vision. Science 287:1273-1276. Vinje WE, Gallant JL (2002) Natural stimulation of the nonclassical receptive field increases information transmission efficiency in V1. The Journal of neuroscience : the official journal of the Society for Neuroscience 22:2904-2915. Webster MA, De Valois RL (1985) Relationship between spatial-frequency and orientation tuning of striate-cortex cells. Journal of the Optical Society of America A, Optics and image science 2:1124-1132. Weliky M, Bosking WH, Fitzpatrick D (1996) A systematic map of direction preference in primary visual cortex. Nature 379:725-728. Weliky M, Fiser J, Hunt RH, Wagner DN (2003) Coding of natural scenes in primary visual cortex. Neuron 37:703-718. Wielaard DJ, Shelley M, McLaughlin D, Shapley R (2001) How simple cells are made in a nonlinear network model of the visual cortex. The Journal of neuroscience : the official journal of the Society for Neuroscience 21:5203-5211. Willmore BD, Mazer JA, Gallant JL (2011) Sparse coding in striate and extrastriate visual cortex. Journal of neurophysiology 105:2907-2919. Womelsdorf T, Schoffelen JM, Oostenveld R, Singer W, Desimone R, Engel AK, Fries P (2007) Modulation of neuronal interactions through neuronal synchronization. Science 316:1609-1612. Xing D, Yeh CI, Shapley RM (2009) Spatial spread of the local field potential and its laminar variation in visual cortex. The Journal of neuroscience : the official journal of the Society for Neuroscience 29:11540-11549. Xing D, Yeh CI, Burns S, Shapley RM (2012a) Laminar analysis of visually evoked activity in the primary visual cortex. Proceedings of the National Academy of Sciences of the United States of America 109:13871-13876. Xing D, Shen Y, Burns S, Yeh CI, Shapley R, Li W (2012b) Stochastic generation of gammaband activity in primary visual cortex of awake and anesthetized monkeys. The Journal of neuroscience : the official journal of the Society for Neuroscience 32:13873-13880a. 129 6 References Yen SC, Baker J, Gray CM (2007) Heterogeneity in the responses of adjacent neurons to natural stimuli in cat striate cortex. Journal of neurophysiology 97:1326-1341. Yoshimura Y, Dantzker JL, Callaway EM (2005) Excitatory cortical neurons form fine-scale functional networks. Nature 433:868-873. Yu J, Ferster D (2010) Membrane potential synchrony in primary visual cortex during sensory stimulation. Neuron 68:1187-1201. Zanos TP, Mineault PJ, Pack CC (2011) Removal of spurious correlations between spikes and local field potentials. Journal of neurophysiology 105:474-486. Zhang L, Li B (2013) Surround modulation characteristics of local field potential and spiking activity in primary visual cortex of cat. PloS one 8:e64492. Zohary E, Shadlen MN, Newsome WT (1994) Correlated neuronal discharge rate and its implications for psychophysical performance. Nature 370:140-143. 130 Functional microarchitecture of cat primary visual cortex 7 Acknowledgements First of all, I thank my supervisor Professor Kevan Martin for providing me with the challenge of conducting this research project. He gave me great freedom to follow my own path and to make my own mistakes, so that I learned a lot more than scientific facts and methods. I thank him for always encouraging me to present my work, for providing a rich and interdisciplinary research environment, and for the delicious cakes he regularly prepares for all lab members. Finally, I am very grateful that he continuously showed me his appreciation and care for the animals we work with. I thank Nuno da Costa for his tireless and selfless support and help. I got to know him as a very patient teacher. Furthermore, I thank Elisha Ruesch for his help in performing the experiments and Sepp Kollmorgen for many discussions on data analysis, Simone Rickauer for performing most of the histological processing, John Anderson, Andreas Keller, and Isabelle Spühler for their support during the experiments, as well as Kevin Lloyd for his corrections of the Discussion parts. Finally, I thank everyone who took the time to engage in lively discussions about science, which makes up a large portion of why I enjoy doing science. 131