Download Functional Microarchitecture of Cat Primary Visual Cortex

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
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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.
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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
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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.
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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.
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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).
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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.
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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).
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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.)
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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
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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,
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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.
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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
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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.
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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.
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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.
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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.
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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,
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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).
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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.
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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).
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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,
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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.
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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.
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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.
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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).
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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.
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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.
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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.
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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
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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).
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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.
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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
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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.
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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
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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
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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.
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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.
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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
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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
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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
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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).
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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).
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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.
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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.
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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.
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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).
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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.
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(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°).
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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
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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.
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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)
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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
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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.
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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
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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
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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
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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