Download Short title: Thalamocortical computations during tactile sensation

Gutnisky et al
11/28/2016
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Mechanisms underlying a thalamocortical transformation during active
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tactile sensation
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Diego A. Gutnisky1, Jianing Yu1, S. Andrew Hires1,2, Minh-Son To3, Michael Bale4,5, Karel
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Svoboda1, David Golomb1,6
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Short title: Thalamocortical computations during tactile sensation
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Janelia Research Campus, HHMI, Ashburn, VA 20147, U.S.A.
Dept. of Biological Sciences, Neurobiology Section, University of Southern California, Los Angeles,
CA 90089, U.S.A.
Dept. of Human Physiology and Centre for Neuroscience, Flinders University,South Australia,
Australia.
Faculty of Life Sciences, University of Manchester, UK. 5School of Life Sciences, University of
Sussex, UK.
Depts. of Physiology and Cell Biology and Physics and Zlotowski Center for Neuroscience, Faculty of
Health Sciences, Ben Gurion University, Be’er-Sheva 8410501, Israel. ORCID ID: 0000-0001-65753685
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Correspondence should be addressed to [email protected] (K.S.); [email protected]
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(D.G.)
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Author contributions: D.A.G., K.S. and D.G. designed research; D.A.G., J.Y., and S.A.H.
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performed experiments; D. G., D.A.G. and K.S. contributed to circuit models; D.G.
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programmed the simulations; D.A.G., D.G. and K.S. analyzed data; D.A.G., K.S. and D.G.
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wrote the paper. J.Y, S.A.H., M.S.T and M.B. helped with data collection.
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The research was supported by a grant from the United States-Israel Binational Science
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Foundation (BSF), Jerusalem, Israel No. 2013033 (S.A.H, K.S. and D.G)., the Janelia Research
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Campus of the Howard Hughes Medical Institute (D.A.G., S.A.H., K.S. and D.G.), the Israel
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Science Foundation grant No. 88/13 (D.G.), and the Helmsley Charitable Trust through the
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Agricultural, Biological and Cognitive Robotics Center of Ben-Gurion University of the Negev
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(D.G.).
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Abstract
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During active somatosensation, neural signals expected from movement of the sensors are
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suppressed in the cortex, whereas information related to touch is enhanced. This tactile
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suppression underlies the brain’s ability to make fine tactile discriminations. Layer (L) 4
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excitatory neurons in the barrel cortex, the major target of the somatosensory thalamus (VPM),
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respond to touch, but have low spike rates and low sensitivity to the movement of whiskers.
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Most neurons in VPM respond to touch and also show an increase in spike rate with whisker
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movement. These data imply that signals related to self-movement are suppressed in L4. Fast-
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spiking (FS) interneurons in L4 respond similar to VPM neurons. Stimulation of halorhodopsin
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in FS interneurons causes a reduction in FS neuron activity and an increase in L4 excitatory
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neuron activity. To explain these experimental observations, we constructed a model of the L4
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circuit, with connectivity constrained by in vitro measurements. The model explores the
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various synaptic conductance strengths for which L4 FS neurons actively suppress baseline and
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movement-related activity in layer 4 excitatory neurons. Feedforward inhibition, in concert
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with recurrent intracortical circuitry, produces tactile suppression. Synaptic delays in
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feedforward inhibition allow transmission of temporally brief volleys of activity associated
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with touch. Our model provides a mechanistic explanation of a behavior-related computation
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implemented by the thalamocortical circuit.
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Author Summary
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We study how information is transformed between connected brain areas: the thalamus, the
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gateway to the cortex, and layer 4 (L4) in cortex, which is the first station to process sensory
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input from the thalamus. When mice perform an active object localization task with their
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whiskers, thalamic neurons and inhibitory fast-spiking (FS) interneurons in L4 encode whisker
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movement and touch, whereas L4 excitatory neurons respond almost exclusively to touch. To
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explain these observations, we constructed a computational model based on measured circuit
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parameters. The model reveals that without touch, when thalamic activity varies slowly, strong
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inhibition from FS neurons prevents activity in L4 excitatory neurons. Brief and strong touch-
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induced thalamic activity excites both excitatory and FS neurons in L4. FS neurons inhibit
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excitatory neurons with a delay of approximately 1 ms relative to ascending excitation,
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allowing L4 excitatory neurons to spike. Our results demonstrate that cortical circuits exploit
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synaptic delays for fast computations. Similar mechanisms likely also operate for rapid stimuli
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in the visual and auditory systems.
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Introduction
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Thalamocortical circuits represent model systems for multi-area computations [1]. Sensory
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information enters the cortex through the thalamus. Transformations in thalamocortical circuits
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have mostly been studied in anesthetized animals with passive sensory stimuli [2-8] or with
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artificial whisking [9]. In the somatosensory system these studies have revealed subtle
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differences in receptive field structure across neurons in the thalamocortical circuit [2-4].
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However, active sensation in awake animals involves dynamic interactions with the world,
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such as saccades [10], palpation with the digits of the hand [11], or movements of the whiskers
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on the face of rodents [12-14]. During haptic exploration, touch generates ‘exafferent’ signals,
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while movement itself activates peripheral sensors to produce ‘reafferent’ signals [15-21]. The
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brain needs to parse these different signals for perception [13]. During active sensation,
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movement attenuates the transmission of certain sensory signals to the cortex [22-24]. Tactile
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suppression is thought to enhance perception of salient events that cannot be predicted based
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on movement.
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The lemniscal pathway starts with mechanosensory afferents in the whisker follicle.
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Information then flows through the trigeminal ganglion, to the brainstem, thalamus (barreloids
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in the ventral posterior medial thalamic nucleus, VPM) and terminates in the primary
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somatosensory cortex (vS1). The main target of VPM axons is the Layer 4 (L4) barrels in vS1.
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The microcircuit of each L4 barrel is mostly contained within the barrel, and the connections
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between specific cell types within the barrel have been mapped: L4 excitatory neurons and L4
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fast-spiking, parvalbumin (PV)-expressing GABAergic interneurons (FS) are connected within
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type and across types [25, 26]. Apart from neuromodulation, the only known long-range input
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to L4 originates in VPM [27-29]. VPM excites all L4 neuron types, and L4 FS neurons inhibit
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the excitatory neurons to implement feedforward inhibition [30-33].
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Cell type-specific recordings from VPM, L4 excitatory [34] and L4 FS neurons [35] uncovered
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a fundamental computation performed by L4 barrels. Neurons in VPM respond to touch, but
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they also increase their activity during whisker movement (‘whisking’) [17-21]. L4 FS neurons
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have nearly identical dynamics as VPM neurons. In contrast, L4 excitatory neuron spikes are
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strongly coupled to touch, but respond only weakly to whisking [34]. L4 microcircuits
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therefore transmit touch signals and suppress reafferent signals generated by whisking. These
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observations indicate that the thalamocortical circuit accentuates salient tactile information by
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suppressing signals related to self-movement.
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Multiple observations regarding the L4 circuit remain to be explained [35]. First, the circuit
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suppresses self-movement signals but transmit touch signals. From a theoretical perspective,
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this selective filtering violates the linear response expected from theories of strongly coupled
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cortical networks [36, 37]. Second, whereas the baseline spike rates of VPM and L4 FS
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neurons are substantial during baseline conditions and more than double during whisking, the
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spike rate of L4 excitatory neurons is very low at baseline and does not increase during
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whisking. Third, when an inhibitory opsin (halorhodopsin) is excited in L4 FS neurons, the
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spike rates of FS neurons decrease and the spike rates of L4 excitatory neurons increase [35].
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Although this result is naively expected, it contradicts the "paradoxical effect" predicted from
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circuit models with strong synaptic coupling [38-40]. According to these models, both
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inhibitory and excitatory neurons should respond with increased spike rates at modest levels of
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inactivation of inhibitory neurons.
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To understand the mechanisms underlying these experimental observations we constructed and
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analyzed a conductance-based model of the L4 circuit. The synaptic circuits of L4 of the barrel
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cortex have been studied in great detail in brain slices. These measurements allowed us to
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constrain the numbers of neurons, neuronal properties, the patterns of connectivity, and the
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average synaptic strengths in the model. We studied how the model networks responds to
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thalamic input at baseline, during whisker movement and during touch. We used the model to
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disentangle the roles of feedforward synaptic connections from the thalamus and recurrent
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intracortical connections in shaping L4 dynamics. The model revealed an important role for
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synaptic delays and fast synaptic kinetics in shaping the L4 responses during behavior.
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Results
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Thalamocortical transformation of tactile information
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We first summarize recordings made in VPM and in L4 from excitatory and FS GABAergic
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interneurons in mice performing an object location discrimination behavior (Fig. 1a,b). Head-
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restrained mice had to localize a vertical pole with their whiskers for a water reward [41, 42].
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Whisker movement and touch were tracked on millisecond time scales with high-speed
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videography [43, 44] (Fig. 1a). Recordings were made with extracellular silicon probe
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recordings in VPM [35], and loose-seal cell-attached and whole cell recordings in L4 [34, 35,
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45].
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Fig. 1. Summary of experimental results in the object-localization task [35]. (a) Top,
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schematic illustrates measurement of whisker position (azimuthal angle θ), instances of touch
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and an example trace of whisker position. (b) Schematics of the thalamocortical circuit and
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relevant cell-types. (c) Spike rate aligned to transitions from non-whisking to whisking. (d)
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Average spike rate as a function of whisking amplitude. (e) Average population response
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aligned to touch. Data and figures corresponding to previously reported datasets [34, 35].
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VPM neurons have significant spike rates (mean, 5.1 Hz), even in the absence of whisker
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movement and touch (Table 1; Fig. 1c, d; see S1 Fig, S2 Fig. for representative examples) [35].
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VPM neurons were also highly sensitive to whisking (S1 Fig. B,C). Spike rates increased after
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whisking onset (average, 3-fold; Fig. 1c, d;). VPM neurons also responded to active touch with
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a brief increase in spike rate (0.6 spikes per touch) (Fig. 1e). The peri-stimulus time histogram
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(PSTH) aligned to touch onset shows a sharp peak in spike rate, with short latency after touch
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(3.1±0.6 ms) and brief duration (2.9±1.7 ms) (S1 Fig. i,n,s). Exafferent touch signals and
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reafferent whisking signals were multiplexed in individual VPM neurons (S1 Fig.).
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The modulation of L4 FS neurons to touch and whisker movement were similar to VPM
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neurons (Fig. 1c-e; S1 Fig., S2 Fig.). L4 FS neurons increased their spike rate after onset of
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whisking (average, 3-fold). L4 FS neurons responded reliably to touch. The response onset had
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slightly longer latency (5-15 ms) and longer duration (2-15 ms) than for VPM neurons. The
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increased latency is expected from the propagation time delay between VPM and L4 (2 ms)
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[35] [46].
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The responses of L4 excitatory neurons differed profoundly from those of VPM and L4 FS
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neurons [34] (Fig. 1 c-e, S2 Fig.). The baseline spike rate of L4 excitatory neurons was much
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lower and did not increase significantly after onset of whisking. The response after touch onset
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occurred with longer latency and longer duration than for the VPM neurons, and similar to L4
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fast-spiking neurons (Fig. 1e).
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The transformation performed by L4 circuits can be summarized by three main findings (Fig.
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1c-e; Table 1). First, baseline spike rates are high in VPM and L4 FS neurons, and low in L4
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excitatory neurons. Second, VPM and L4 FS neurons elevate their spike rates further during
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periods of whisker movement, whereas L4 excitatory neuron spike rates remain low. The spike
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rates of VPM and L4 FS neurons during periods of whisking are more than one order of
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magnitude larger than those of L4 excitatory neurons. Third, all three neuron types respond to
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touch reliably (Table 1; Fig. 1e). The L4 circuit therefore performs a behaviorally relevant
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computation by propagating information related to external stimuli and suppressing responses
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to whisker movement, a predictable stimulus.
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Area
Figure
N
Spikes/touch
Non-whisking
Whisking
-
-
-
spks
spks/s
spks/s
VPM
4
29
0.6±0.5
5.1±5.5
13.5±12.7
L4 FS
4
18
1.9±1.0
9.3±8.5
21.1±15.8
L4e
4
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0.3±0.4
0.4±0.6
0.6±0.9
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Table 1. Summary experimental results for VPM, L4 excitatory and L4 FS neurons. Data are
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taken from [35]. The increase of the average spike rate of L4 excitatory neurons from non-
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whisking to whisking conditions was found to be insignificant. Values are reported as mean ±
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standard deviation.
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The dynamics of FS neurons during whisker movement suggest that these neurons suppress
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whisker movement-related activity in L4 excitatory cells. Consistent with this view,
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optogenetic reduction of activity in a subset of L4 FS neurons expressing the light-gated,
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inhibitory chloride pump eNphHR3.0 (L4I-hr+) unmasks movement-related activity in L4
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excitatory neurons [35] (Fig. 2a,b). Photostimulation of L4I-hr+ neurons decreases the activity
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in L4 FS neurons on average and increases the activity in L4 excitatory neurons. The
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suppression of L4I-hr+ neurons causes an increase in response in L4 excitatory neurons during
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whisker movements (Fig. 2c) and an overall increase in the number of spikes per touch (Fig.
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2d). This result implies that suppression of whisking response in L4 excitatory neurons
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involves inhibition from FS neurons.
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Fig. 2. Summary of effect of photoinhibition of L4 FS neurons on L4 neurons. (a)
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Schematic of the hr+ experiment. A subset of L4 FS neurons do not express hr (hr- neurons).
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(b) Photostimulation of hr+ neurons decreases the activity in L4 FS neurons and increases the
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activity in L4 excitatory neurons. (c) Response of L4 excitatory neurons during whisker
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movements. (d) Response to touch of L4 excitatory neurons. This figure is adapted from Yu et
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al (2016).
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Membrane potential measurements provide additional mechanistic clues [35]. L4 excitatory
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neurons depolarize substantially (6 mV) and briefly after touch. Touch-related inhibitory input
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(from FS neurons) to L4 excitatory neurons is delayed by approximately 0.5 ms with respect to
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excitatory input. It has been proposed that this short ‘window of opportunity’ [2, 33] allows L4
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excitatory neurons to spike after touch, typically with one spike [34], before inhibition
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suppresses L4 excitatory activity. During whisker movement excitation is matched by
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inhibitory input, keeping the L4 excitatory neuron membrane potential well below spike
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threshold. Suppression of self-movement signals is therefore implemented by inhibition within
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L4.
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Yu et al. (2016) also showed that activating halorhodopsin in L4I-hr+ neurons during whisker
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movement suppresses activity in these neurons. This result poses a new question. The major
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cellular effect of activation of halorhodopsin is hyperpolarization [47, 48]. Theoretical
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investigations of cortical circuits, consisting of recurrently connected excitatory neurons
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stabilized by inhibitory neurons, have investigated the effects of hyperpolarization of inhibitory
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neurons [39]. Over a large range of conditions, hyperpolarization of inhibitory neurons leads to
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increased spike rates in both excitatory and also inhibitory neurons. This "paradoxical effect"
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is common to multiple network regimes, including networks with strong synaptic conductances
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that fire in an asynchronous manner [38] and networks with moderate synaptic conductances, if
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the excitatory-to-excitatory synaptic coupling gEE is sufficiently strong [39]. Does the L4
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circuit lie outside of the modeled parameter regimes, or can other factors explain the lack of
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paradoxical effect?
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A computational model of tactile suppression in L4
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To explain the dynamical response of the L4 circuits to thalamic input, and to understand the
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roles of feedforward and recurrent connections, we constructed and analyzed a detailed
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computational model of the L4 circuit. L4 excitatory and L4 FS neurons make connections
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within type and across types with high connection probability (Fig. 3a; Table 2).
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thalamocortical circuit of the rodent whisker system is one of the most extensively studied
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mammalian circuits. In vitro and in vivo studies have measured many fundamental parameters
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that are required to construct a realistic computational model of the thalamocortical circuit. Our
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model circuit consists of 1600 L4 excitatory (E) neurons and 150 L4 FS (I) neurons [26]
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receiving input from 200 VPM (T) neurons (Fig. 3a). When referring to modeling results we
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denote VPM neurons as T, L4 excitatory neurons as L4E, and GABAergic interneurons as L4I
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(Fig. 3b, c). Since we know little about non-FS GABAergic interneurons during behavior we
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model only one inhibitory neuronal population.
The
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Fig. 3. Neural network model of L4. (a) Diagram of the recurrent model of L4 network. (b)
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Spike shape of VPM (schematic), L4E and L4I neurons. (c) Temporal dynamics of individual
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EPSPs for the different synaptic connections (T = VPM; I = L4 FS; E = L4E). The convention
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is that that the first letter corresponds to the post-synaptic neuron and the second letter to the
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presynaptic neuron. (d) Thalamic generating function FT (Eq. 1). The panels on the right show
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the same figure in a magnified scale.
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
Populations Synaptic  delay
Kαβ gαβ
Vextr Kαβ
Vextr
2
Receptor (ms)
mS/cm (mV)
(mV)
experimental experimental
values
values
a
ET
AMPA 1.0 50 0.15
1.1 100
0.5a, 2.4±2b (response to
first spike in a train), ~1b
(spike train ~10 Hz).
c
IT
AMPA 1.0 75 0.2
1.03 150
4.1±3b (response to first
spike in a train), ~1b (spike
train ~10 Hz), 3c
EE
AMPA 1.0 200 0.2
0.73 400e
1.1±1.1b, 0.52d, 1.6±1.6e
IE
AMPA 1.0 400 0.6
1.33 800b
2.2±2.2b
EI
GABAA 0.85 25 0.7
-1.92 50b
-1.1b, -1.0f
II
GABAA 0.5 25 0.55
-1.28 50d
-1.8f
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
Table 2. Network parameters in the reference parameter set:  delay
- synaptic delay , Kαβ -
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average number of presynaptic inputs , gαβ - synaptic conductance, Vextr - the extremal value
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of the unitary synaptic membrane potential change. The corresponding experimental values for
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Kαβ and Vextr are written in the two right columns. Those values are taken from the following
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references: a - [46], b - [49], c - [32], d- [26], e – [50], f - [25].
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Cortical neurons were simulated using a conductance-based model with a single compartment
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per neuron [51, 52]. Synaptic conductances are denoted as gαβ, where β is the presynaptic
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population and α is the postsynaptic population (Fig. 3a). Model parameters, including
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numbers of neurons, unitary synaptic conductance, connection probability, resting potential,
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and membrane time constants are based on neurophysiological measurements in brain slices
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[25, 26, 49, 53] with small adjustments (see Methods). VPM provides the only external input
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to the model circuit, with connectivity estimates based on in vivo and brain slice measurements
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[32, 46]. Spike trains of T neurons were modeled as independent inhomogeneous Poisson
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processes with a generating function FT representing thalamic activity during quiescence,
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whisking or whisking and touch (Fig. 3d; see Methods).
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
 2 t
 C
FT (t )  AT 1  BT sin 
     T (t  n w  tc ) (n w  tc   c  t )
 w
  c

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where AT is the spike rate averaged over a whisker movement cycle, BT is the modulation depth,
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and CT is the number of spikes per touch, τw is the whisking period, tc is the time of touch onset
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within a whisking cycle, n is the cycle number, and Θ is the Heaviside function. During
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whisker movements AT increases above a baseline, with sinusoidal modulation phase-locked to
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a single preferred phase ϕ. Touch is represented by adding a rectangular function at touch onset
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t=tc (with respect to the whisking cycle), stretched over τc = 3 ms with an integral of CT =0.6
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spikes per touch (Eq. 1). The population-average spike rate of neurons within a population over
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whisking cycles is denoted by να (α=T,E,I), and the population-average spiking response to
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touch is denoted by Rα. Note that without touch, νT = AT. A ‘reference parameter set’ is
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described in Methods and used unless otherwise stated.
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Response of the model circuit to whisker movement and touch
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We start by simulating the model for whisking without touch (thalamic spikes per touch, CT=0).
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L4E spike rates were low (νE < 1 Hz) compared to those of L4I neurons (Fig. 4a, b). The
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average rates νE and νI depend on AT (the population- and time-average thalamic spike rate
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during whisking only) but are almost independent of the modulation depth BT (Eq. 1). Except
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near threshold, νI was proportional to AT, inconsistent with theoretical results for large and
(1)
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sparse neuronal networks with strong synapses, in which strong excitation is compensated by
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inhibition (balanced networks) [36]. The L4E spike rate νE increased linearly with AT, but with
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a much smaller slope compared to νI.
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Fig. 4. A neural network model of L4 explains suppression of whisker movement signals
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in L4 excitatory neurons. The colors black, grey and red denote T, L4E and L4I neuronal
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populations respectively. (a) Example L4E and L4I membrane potential during simulated
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whisking (green). (b) The population- and time average spike rates νE and νI of the L4E and
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L4I neurons respectively as function of the thalamic input AT in the absence of touch. L4I
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neurons follow linearly the thalamic input while L4E neurons increase only weakly with AT
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beyond firing threshold. Inset, zoom in. (c) Membrane potential for an example neuron during
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whisking and touch (black dots). (d) Population PSTH aligned to touch onset. Inset, zoom in.
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The linearity of the νI-AT curve fit empirical observations (Table 1, Figure 1c; spike rates of
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both VPM and L4 FS neurons more than double in the transition from non-whisking to
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whisking). The average spike rate of L4 excitatory neurons, νE, is low [35]. During transition
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from non-whisking to whisking, the average spike rate of L4 excitatory neurons barely changes
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(from 0.4 Hz to 0.6 Hz; Table 1). The spike rates of L4E neurons in our model show similar
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dynamics.
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L4E neurons fire at most one spike each after touch, whereas L4I neurons fire more than one
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EI
(up to two) spikes per touch (Fig. 4c, d). The synaptic delay,  delay
, is a critical factor in
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EI
determining the strength of the touch response (Fig. 5a). For  delay
 0 , the average normalized
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response of L4E neurons after touch, RE, is small (RE=0.01 spikes/touch), and L4I neurons fire
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RI=0.64 spikes/touch. Strong inhibition overwhelms excitation before L4E neurons have a
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chance to spike. The delay between the appearance of excitation and feed-forward inhibition in
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the L4E neuron has been termed ‘window of opportunity’ [2, 33, 54-56]. This ‘window of
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EI
opportunity’ increases with  delay
, but is not equal to it because it is affected by the durations of
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thalamocortical synaptic process and the time needed for the L4I to fire in response to the brief
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EI
and strong thalamic input. For a more realistic value,  delay
 0.85ms , L4E and L4I fire 0.33
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and 1.3 spikes/touch respectively, similar to experimental measurements (Table 1).
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Fig. 5. Touch response in function of synaptic delay, AMPA receptors’ time constant and
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parameters defining thalamic input. In each panel, Response to touch in L4E and L4I
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neurons (RE and RI, in grey and red respectively) are plotted, as well as the thalamic response
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in black. Spikes per touch were counted up to 25 ms after touch onset, and baseline computed
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by counting spikes 25 ms before touch is subtracted. Responses to touch are plotted as
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EI
functions of (a) I-to-E synaptic delay  delay
, (b) the AMPA receptor time constant tAMPA, (c) the
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thalamic response to touch, CT, and (d) the thalamic spike rate AT during whisker movements
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without touch.
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The response of the network to touch depends on the time-course of synaptic conductances.
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Without touch signals, L4E neurons are inhibited by L4I neurons and spike at low rates
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(Fig. 4a, b). Touch produces strong, brief and synchronous thalamic excitation (Fig. 1e), which
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depolarizes L4E neurons and enables them to fire before inhibition terminates the response.
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This mechanism demands that excitatory synaptic conductance changes at thalamocortical
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synapses are brief. Touch responses of L4E and L4I neurons decrease with tAMPA, the decay
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time of AMPA-mediated EPSCs (Fig. 5b). Substantial touch responses in L4E neurons require
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tAMPA < 2-3 ms, consistent with the brief excitatory conductances measured at thalamocortical
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synapses [53].
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Touch responses of L4E and L4I neurons increased with the strength of the thalamic touch
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signal (Fig. 5c), consistent with graded responses to touch strength measured in L4E neurons
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[34]. The response saturates at one and two spikes/touch for L4E and L4I respectively; this is
323
in part due to the intrinsic properties of these neurons, which preclude them from firing more
324
spikes in response to brief thalamic input.
325
We have shown that a L4 network with parameters similar to experimentally determined
326
values can replicate major experimental findings. L4E excitatory neurons exhibit low baseline
327
activity, low activity in response whisker movement, and significant response to touch.
328
However, during behavior the responses of L4 excitatory neurons is not all-or-none: L4
329
excitatory neurons are tuned to multiple sensory features including touch direction, intercontact
330
interval, strength of touch, and likely other factors [34]. Our simulation results indicate that
331
L4E and L4I neurons respond to touch in a graded manner and robustly respond to touch at
332
different whisking amplitudes. Specifically, our simulations show that RE and RI decrease with
333
AT (Fig. 5d) for all parameter values consistent with the data. Mechanistically, increasing
334
thalamic input causes larger inhibition in the cortical circuit that decreases touch response.
335
Future experiments could test this model prediction.
336
Contributions of intracortical connections in tactile suppression
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337
The model allows us to explore how specific synaptic connections within L4 contribute to fine-
338
tuning L4 function. These connections currently cannot be specifically manipulated, making
339
them difficult to evaluate experimentally. Recurrent excitation (gEE) can only be tuned over a
340
limited range before runaway excitation is triggered (for about gEE~0.4 mS/cm2), even during
341
baseline or whisking (Fig. 6a-b). The conductance gEE does not modify the slope of the νE-AT
342
curve (Fig. 6b), but shifts this curve upward. gEE amplifies touch responses RE and RI (Fig. 6c)
343
[57], mostly by increasing the duration of touch responses (Fig. 6d-i).
344
345
Fig. 6. Effects of varying intracortical recurrent excitatory conductances gEE on the
346
function of L4E neurons. (a) The circuit with changing gEE emphasized in green. (b) RT, RE
347
and RI as functions of gEE. Other parameters: AT = 14 spikes/s, CT = 0.6). (c) νE vs. AT during
348
whisker movements only, for 11 values of gEE from 0 (light green) to 0.4 mS/cm2, that is twice
349
the reference parameter value (dark green). Recurrent excitation gEE increases νE while not
350
affecting the slope of the νE-AT curve far from spiking threshold substantially. (d) PSTH
351
aligned to touch onset for L4E and without recurrent excitation (gEE=0 mS/cm2). (e) Same as C
352
for L4I. (f-g) Same as c-d for gEE=0.2 mS/cm2. (h-i): Same as c-d for gEE=0.35 mS/cm2.
353
Beyond ~gEE=0.4 mS/cm2 the network exhibits runaway excitation.
354
355
The dynamics of L4E neurons are shaped in subtle ways by L4 inhibition. Figure 7 shows how
356
parameters involving inhibition (gII, gEI, gIE) affect circuit responses, while holding the other
357
parameters at their reference values. Intracortical excitation of inhibition (gIE) is necessary to
358
prevent runaway excitation, and thus keeps the spike rates of neurons in the network moderate
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359
(Fig. 7a,b). Reducing gIE shifts the νE-AT curve during whisking upward, without modifying its
360
slope.
361
decreasing the slope of the linear section of this sigmoid (Fig. 7c).
For touch responses, gIE shift the touch-response RE-CT curve to the right while
362
363
Fig. 7. Inhibition in L4 controls the response to L4E neurons. (a-c) Changing gIE from 0 to
364
1.2 mS/cm2 (d-f) Changing gEI from 0 to 1.4 mS/cm2. (g-i) Changing gII from 0 to 1.1 mS/cm2.
365
In the top panels, the synaptic connection that its strength is varied is plotted in green. In the
366
middle and bottom panels, curve are plotted for 11 values of the relevant g from 0 (light green)
367
to its maximal value, that is twice the reference parameter value (dark green). (b, e, h) The
368
response of L4E neurons, νE, to slowly varying thalamic input, which correlates with the
369
amplitude of whisking. (c, f, i) The response of L4E neurons to spikes, RE, associated with
370
touch.
371
372
Inhibition to L4E neurons (gEI) is also required to prevent runaway excitation (Fig. 7d,e). For
373
low values of gEI (but above values for runaway excitation) and large values of gII (Fig. 7g,h),
374
νE scales linearly with thalamic input AT. This linear scaling is known from balanced networks
375
with strong synaptic coupling [36, 38]. The situation is different for sufficiently strong
376
inhibition (relatively high gEI, moderate gII), where the response of L4E neurons to slowly-
377
varying thalamic input during whisking, νE, is independent, and even decreasing, with AT (Fig.
378
7e, h). For small enough gII, L4E are quiescent except of near firing threshold. In addition, low
379
gET and large gIT values are critical to keep νE low for all whisker movement amplitudes (Fig.
380
8a,b,d,e). Furthermore, these low values νE are nearly independent of AT. This regime is
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381
consistent with experimental data, where L4 FS neurons increase their spike rate with whisker
382
movement, whereas L4 excitatory neuron spike rates remain low (Fig. 1d, Table 1).
383
384
Fig. 8. Effect of varying thalamocortical conductances on the function of L4E neurons.
385
Symblols and lines are as in Figure 7. (a) Changing gET.. (b) νE vs. AT during whisker
386
movements only. (c) RE vs. CT. (d) Changing gIT. (e-f) Same as b-c.
387
388
Increasing values of gEI and gII shifts the touch-response RE-CT curve to the right and to the left
389
respectively (Fig. 7f, i). In addition, gEI, but not gII, decreases the slope of the linear section of
390
this sigmoid (Fig. 7f). Similarly, gET and gIT shift the RE-CT curve to the left and to the right
391
respectively (Fig. 8c, f).
392
The effects of halorhodopsin activation in L4 FS neurons
393
Yu et al. (2016, Fig. 8, supplementary Fig. 13) expressed halorhodopsin in FS neurons in L4
394
and explored how the responses of excitatory and FS neurons in L4 to under baseline
395
conditions, whisking and touch vary under halorhodopsin activation. L4 excitatory neurons
396
increase their spike rates and L4 FS neurons decrease their spike rates, both during baseline
397
and whisking conditions. Similarly, L4 excitatory neurons increase their spiking responses to
398
touch and L4 FS neurons decrease their responses.
399
The halorhodopsin expression levels in FS neurons likely varied widely across individual
400
neurons [58]. We therefore divided the L4I neurons in the model into hr expressing neurons
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401
and non-expressing neurons (hr+ and hr- respectively). The fraction of hr+ neurons among L4I
402
neurons is denoted by fhalo.
403
404
Manipulation of the components of neural networks can cause complex and counterintuitive
405
change in network dynamics (‘paradoxical’ response; [38-40, 59]: injecting negative current to
406
all inhibitory neurons in a network, that includes spiking excitatory neurons, increases the
407
average spike rates in inhibitory neurons). If the synaptic conductance strengths are moderate
408
and the excitatory-to-excitatory synaptic conductance is above a certain level, injecting
409
negative current to the inhibitory neurons causes the spike rates of excitatory neurons νE to
410
increase, and as a result the network dynamics causes the spike rates of inhibitory neurons νI to
411
increase as well [39, 40, 59]. Alternatively, if synaptic conductances are strong and the
412
excitatory population is active, the condition that the activity of excitatory neurons should be
413
moderate (non-zero and not epileptic) causes νI to increase under negative current injection to
414
inhibitory interneurons [38]. The major effect of halorodopsin is to hyperpolarize FS neurons
415
(see Methods). Therefore, if all inhibitory neurons in the model are assumed to express
416
halorodopsin equally (fhalo=1), halorhodopsin activation will cause both L4E and L4I neurons
417
to increase their spike rates.
418
419
We simulated the response of L4E and L4I neurons to whisking for fhalo=1 without and with
420
halorhodopsin activation, and replicated the 'paradoxical effect': the average responses of L4E
421
and L4I neurons to whisking, νE and νI, increase with simulated light activation. The simulation
422
result for L4I neurons is in contrast to experimental observations showing that most L4 FS
423
neurons increase their spike rates. This discrepancy is resolved if we assume fhalo =0.5. For this
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424
value, spike rates during whisking increase, on average, for L4E neurons (Fig. 9a), decrease
425
for almost all L4I-hr+ neurons (Fig. 9b), and increase for inhibitory neurons that do not express
426
halorhodopsin (L4I-hr-).
427
428
Fig. 9. Simulated light activation of halorhodopsin expressed in L4I-Hr+ neurons.
429
Simulations with fhalo=0.5 reveals a reduction in the whisking suppression and an enhancement
430
of touch responses by L4E neurons. (a) Halorhodopsin activation in L4I-Hr+ causes an average
431
increase in response of L4E during whisking and no touch, with a wide distribution of
432
halorhodopsin–induced modifications. (b) Most L4I-Hr+ neurons reduce their activity during
433
whisking while L4I-Hr- neurons increase it. (c) Increase in the touch responses in L4E neurons
434
during suppression of L4I-Hr+. (d) Increase in the touch responses in L4I neurons. (e,f)
435
Population PSTH of L4E (e) and L4I (f) neurons with and without L4I-Hr+ activity suppression.
436
(g) Reduction of L4I-Hr+ activity diminishes the whisking suppression effect in L4E neurons.
437
Black line: T neurons; solid grey line: L4E neurons without halorhodopsin activation; dashed
438
grey line: L4E neurons during halorhodopsin activation. (h) Reduction of L4I-Hr+ activity
439
diminishes the whisking response in L4I-Hr+ neurons. Solid red line: L4I-Hr+ neurons without
440
halorhodopsin activation; dashed red line: L4I-Hr+ neurons during halorhodopsin activation.
441
Solid blue line: L4I-Hr- neurons without halorhodopsin activation; dashed blue line: L4I-Hr-
442
neurons during halorhodopsin activation.
443
444
445
The spike responses of L4E neurons to touch increase moderately for fhalo =0.5, especially for
446
neurons with low baseline response (Fig. 9c, e), whereas the spike response of and L4I-hr-
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447
inhibitory neurons remains about the same and that of L4I-hr+ increases somewhat (Fig. 9d, f).
448
These dynamics stem from the fact that the initial response to touch, before feedforward
449
inhibition hyperpolarizes the neuron, is determined mainly by feedforward excitation. While
450
halorhodopsin activation hyperpolarizes inhibitory neurons and increase the difference
451
between spiking threshold and their membrane potentials before touch onset, the driving force
452
of excitation (the difference between the reversal potential of APMA-mediated excitation and
453
their membrane potential) increases as well and enhances excitation.
454
455
The reduction in response in L4I-hr+ neurons partially disrupts whisker movement suppression
456
in L4E neurons, and increases the slope of the νE-AT curve (Fig. 9g). During photostimulation
457
of L4I-hr+ neurons, their response to increasing whisker movements becomes shallower (Fig.
458
9h). This change in response of L4-hr+ neurons in turns causes a steeper response to whisker
459
movements in L4E neurons (Fig. 9g).
460
461
Finally we explored how the previous results depend on fhalo. The mean touch responses for all
462
neuronal populations is non-monotonic: it increases when fhalo increase from zero, and then
463
decreases for higher values (Fig. 10a). For our parameter set, simulated halorhodopsin
464
activation increases touch response (in comparison with no activation) for fhalo < 0.78. During
465
whisker movements, the spike rates of all neuronal populations increases with fhalo, and the
466
average spike rate of L4I-hr+ neurons during simulated halorhodopsin activation is lower than
467
that with no activation for fhalo < 0.74 (Fig. 10b). Interestingly, L4-hr+ neurons reduce their
468
spiking response to touch in response to halorhodopsin activation for large values of fhalo, but
469
reduce their spike rates in response to whisking for small fhalo values.
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470
Fig. 10. Effects of light activation of halorhodopsin expressed in L4I-Hr+ neurons. Effects
471
of halorhodopsin light activation on touch response and whisking response for the L4E (grey),
472
L4I-Hr+ (red) and L4I-Hr- (blue) neuronal populations are plotted as functions of fhalo, the
473
fraction of L4I-Hr+ neurons among all L4I neurons. (a) Spikes per touch, R, for L4 neuronal
474
populations as functions of fhalo. (b) Average spike rates, ν, during whisking for L4 neurons as
475
functions of fhalo.
476
477
478
Discussion
479
We computationally dissected how information is transformed between thalamus and barrel
480
cortex at the level of defined neural circuits [34, 35] (Fig. 1). Our model defines the
481
mechanisms that enable the L4 circuit to transmit touch-related information and suppress self-
482
motion signals in L4. Here we summarize our main modeling results and how they explain
483
major experimental observations.
484
Transmission of touch signals while suppressing whisking signals
485
We compared our model to recordings from VPM projection neurons (Fig. 1; S1 Fig., S2 Fig.),
486
L4 FS neurons, and L4 excitatory neurons [35] during performance of an object localization
487
task, while whisker movements and touches were tracked with millisecond time scale precision
488
[34, 42, 45, 60]. VPM and L4 FS neurons respond to whisker movement and touch, whereas
489
L4 excitatory neurons responded almost exclusively to touch. During whisking, excitation to
490
L4 excitatory neurons from VPM is only slowly modulated in time and is matched by
491
feedforward and feedback inhibition from L4 FS neurons, which cancels self-movement
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492
signals. In contrast to the self-movement input, touch-related inputs are brief and synchronous
493
(Fig. 1e). Our model establishes the conditions for a ‘window of opportunity’, in which L4
494
excitatory neurons can fire before inhibition catches up [33, 55, 57, 61, 62]. The I-to-E
495
EI
synaptic delay  delay
must be sufficiently large (say, ~1 ms) and the AMPA-mediated synaptic
496
conductances should be brief (Fig. 6a,b). The brief duration of this window diminishes the
497
chance of L4 excitatory neurons to fire multiple spikes upon touch, producing low trial-to-trial
498
variability in spike count after touch [34, 63].
499
Spike rates during baseline and whisking
500
During baseline and whisking, L4 FS neurons spike on average at tens of Hz, while L4
501
excitatory neurons spike on average below 1Hz. The average spike rates of VPM and L4 FS
502
excitatory neurons, νT and νI, more than double after whisking onset, while the average spike
503
rates of L4 excitatory neurons remains below 1 Hz. Low spike rates of L4E neurons require
504
particular combinations of synaptic parameters: gIE,, gEI and gIT need to be strong, and gEE,, gII
505
and gET should be weak (Figs. 6c,7,8). If gET is too small or gET is too large, L4E neurons will
506
be quiescent. Similarly, L4E neurons will not spike if gII is too small (Fig. 7h). For moderate
507
gII, νE can remain about constant with AT.
508
Touch responses
509
The response of L4E neurons to touch, RE, increases with CT (the thalamic response to touch)
510
in a sigmoid manner, because the intrinsic properties of L4E neurons in the model impose a
511
refractory period that in general precludes rapid firing of more than one spike. Synaptic
512
parameters that increase νE during whisking shift the sigmoid function leftward, and those that
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513
decrease νE shift that function rightward (Figs. 7,8). In our model, the inhibitory neuronal
514
population spikes at significant rates (20-40 Hz) even at baseline. This allows the number of
515
spikes/touch RE to be smaller than one and vary gradually with input strength (Fig. 7f). As a
516
result, stronger thalamic responses to touch, for example as a result of stronger touch,
517
generates proportionally stronger L4E responses, consistent with experimental results (Fig. 1e)
518
[34].
519
Effects of photostimulation of L4-hr+ neurons
520
In response to halorhodopsin activation, L4 excitatory neurons increase their average spike
521
rates and L4-hr+ FS neurons reduce their spike rates [35]. The model does not replicate this
522
behavior if halorhodopsin is "expressed" in all inhibitory neurons, because νI increases with
523
simulated photostimulation. This discrepancy is resolved if a sufficient number of L4 I neurons
524
lack halorhodopsin (or express halorhodopsin at very low levels) (Figs. 9, 10b). With
525
photostimulation, L4-hr+ I neurons decrease their spike rates if their fraction among I neurons,
526
fhalo, is below a certain value (0.74 in Fig. 10a), while L4-hr- FS neurons increase their spike
527
rates. Future work is needed to determine whether including more populations of inhibitory
528
interneurons, for example somatostatin-positive neurons [64] will generate parameter regimes
529
in which L4-hr+ neuron decrease their responses to both whisking and touch upon light
530
activation.
531
Modeling approach
532
The emergence of powerful computing resources has enabled simulations of entire cortical
533
columns of diverse neurons with realistic morphologies and biophysically plausible membrane
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534
conductances [65, 66]. Because of the profusion of parameters, detailed models are difficult to
535
analyze to extract the underlying principles. So far these detailed models have failed to explain
536
any neural computation [67]. Here we took a different approach. We implemented a
537
computational model based on hard won numbers for connection probability, connection
538
strength, neuron numbers and basic cellular parameters for the whisker thalamocortical circuit.
539
The neurons themselves were generic single compartment models. Given the reduced nature of
540
the model, it is possible to analyze the model in detail. This analysis yields testable predictions.
541
For example, the dependence of average spike rates of neuronal populations on the average
542
spike rates of thalamic neurons (Fig. 4b). These predictions could be tested in experiments
543
where stimuli, applied for example with a magnetic stimulator, are applied during whisker
544
movement at different amplitudes.
545
The main characteristics of the thalamocortical circuit are: (i) Strong external inputs to fast-
546
spiking inhibitory neurons and excitatory neurons. (ii) Strong inhibition within L4,
547
implementing feedforward and lateral inhibition. (iii) Recurrent excitation. iv) A brief but
548
nonzero delay between intracortical inhibitory and external excitatory input. Parameters based
549
from neurophysiological measurements produce a model circuit with behavior that is in
550
qualitative agreement with in vivo measurements over a large range of conditions. However, it
551
was necessary to adjust the model parameters slightly (i.e. within a factor of 2-3; Methods) to
552
best match experimental data (reference parameter set, Methods). Experimental inaccuracy,
553
sampling errors, and differences across biological conditions (such as in vitro brain slices
554
versus behaving brain) likely preclude more accurate estimation of synaptic parameters.
555
Changing even a single parameter could lead to quantitative, and sometimes even qualitative
556
changes in behavior (Fig. 6-8), as has been noted in other contexts [68]. This means that the
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557
detailed parameters matter. For example, if gII is too strong then L4I neurons do not respond
558
sufficiently briskly to reduce whisking signals in L4E neurons (Fig. 7g, h); on the other hand,
559
if gII is too weak then inhibition shuts down L4E neurons. Similarly, gEE > 0 is required to
560
amplify touch signals, but elevating gEE by a factor of two beyond the optimal level causes run-
561
away excitation (Fig. 6b). Moreover, the kinetics matter, such as the durations of the I-to-E
562
EI
synaptic delay  delay
(Fig. 5a), axonal delays, the time-courses of synaptic conductances (Fig.
563
5b), and intrinsic neuronal properties.
564
Comparison with previous L4 models
565
Rate models have been used to study cortical responses to fast-rising stimuli in the whisker
566
system [8, 54] and elsewhere [64]. These previous models of L4 aimed to account for fast
567
cortical responses to passive whisker deflections [8], but rate models cannot reliably describe
568
brief responses to rapidly-varying stimuli [69]. Moreover, in important aspects these models
569
have opposite behavior to our experimental and modeling results and to the known anatomy
570
and physiology of L4 circuits. First, the modeled L4 neurons show activity in the absence of
571
input, in contradiction to recent measurements [35, 70]. Second, L4 neurons exhibit strong and
572
EI
brief response to touch even for  delay
 0 , in contrast to our model.
573
The propagation of synchronous and brief activity in cortical circuits has been investigated [2,
574
56, 57, 71, 72]. In these models, excitatory inputs produce strong inhibition in local circuits,
575
which is slightly delayed with respect to the excitation. In L4 of the barrel cortex, the
576
convergence of thalamocortical input onto L4 FS neurons is higher than for L4 excitatory
577
neurons (probabilities of connections are 0.75 vs 0.4) [32] and thalamic stimuli produce larger
578
synaptic potentials in L4 FS than L4 excitatory neurons [33]. These features allow propagation
Gutnisky et al
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29
579
of brief synchronous activity across network layers. These models can respond to brief, strong
580
stimuli by brief responses of the L4 E and I neuronal populations. Our model goes beyond this
581
effect by showing how this brief touch response can be obtained together with large νI and
582
small νE in response to baseline and whisking. For example, simple feedforward models such
583
as [33] cannot exhibit small νE for a wide range of AT, corresponding to both baseline and
584
whisking. That model, however, explores the development of cortical responses of L4E and
585
L4I neurons over the long time scale of short-term synaptic plasticity. Conducting of such a
586
study in a model that includes recurrent connections and comparing its outcome to
587
experimental result in vivo remains to be carried out.
588
Models of networks of strongly-coupled neurons compensated by inhibition have been studied
589
extensively [36-38, 51, 73]. If inhibition on the excitatory neurons is not too large, the
590
population-average response of excitatory and inhibitory neuron (νE and νI) scales linearly with
591
the external (here, thalamic) input AT [37, 74]. The slope of the νE vs. AT increases with gII and
592
decreases with gIE.. If inhibition is too strong, νE =0 and νI scales linearly with AT. In our
593
network, the numbers of neurons and the strengths of synaptic conductances are not very large.
594
As a result, when νE is small (νE
595
of near firing threshold, namely the AT values for which cortical neurons start firing) increase
596
weakly with AT, be independent of AT, or even decrease with AT (Fig. 7e,h, Fig. 8b,e). Similar
597
behavior was obtained in rate models of V1 [75, 76]. This result mimics the empirical
598
observation that during transition from non-whisking to whisking, the spike rates of VPM
599
neurons more than double, the spike rates of L4I neurons increase proportionally, but the spike
600
rates of L4E neurons remains low, with no significant increase with thalamic input strength.
601
For larger νE (> 2 Hz), νE depends linearly on AT. Larger νE could be obtained with larger gII or
~ 1 Hz), similar to measured values [34, 35], νE can (except
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602
smaller gEI (Fig. 7b,e,h), or by suppressing a fraction of L4I neurons using halorhodopsin
603
activation (Fig. 9g).
604
Based on the linearity of strongly-coupled networks, one would expect that if responses of L4E
605
neurons to whisking is an order of magnitude smaller than that of VPM neurons, the same
606
proportions will maintain for the responses to touch, whereas experimentally the touch
607
responses of L4 excitatory and VPM neurons differ by only a factor of two. We explain this
608
EI
effect by the fact that, with  delay
, inhibition lags excitation in response to brief and strong
609
EI
thalamic input. Indeed, for  delay
 0 , the response to L4E neurons is significantly reduced (Fig.
610
5a).
611
612
Materials and Methods
613
Experimental methods
614
The experimental methods were described in Yu et al (2016). In brief, we performed chronic
615
multi-electrode silicon probe recordings from VPM and cell-attached recordings from L4
616
excitatory and L4 fast spiking neurons. To search for VPM neurons we lightly anesthetized the
617
mice (0.6-1.2 % isoflurane) and stimulated individual whiskers during extracellular recordings.
618
We mapped the principal whisker (PW) to assess whether the PW was one of the large
619
whiskers that can be tracked reliably during behavior. We stimulated several individual
620
whiskers around the PW with a piezoelectric stimulator at multiple frequencies (i.e. 5,10,20,40
621
Hz) and recorded the neural activity. Before and/or after each day of behavioral recording we
622
confirmed that neurons respond to stimulation of the PW (we re-positioned the electrode drive
623
daily). In addition, after placing the animal in the behavioral apparatus, we usually maintained
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31
624
the anesthesia for several minutes to check that neurons still responded to the PW (by manual
625
stimulation and/or by contacting the whiskers with the pole).
626
behavioral task shortly after anesthesia was withdrawn.
627
Statistical analyses. Data is presented as mean ± s.d. or mean ± s.e.m. as noted. Statistical
628
comparisons use the non-parametric, two-sided Wilcoxon rank sum test. All statistical analyses
629
were performed in Matlab (Mathworks).
Animals performed the
630
631
Behavior, videography and recordings. In Yu et al (2016) we recorded from VPM neurons in
632
mice trained to localize an object using their whiskers [42]. In each trial, during a sample
633
epoch lasting a few seconds (1.1 - 2.5, mean 1.9 s), a pole appeared in one of multiple
634
locations on the right side of the head (Fig. 1a). Animals had to withhold licking when the pole
635
was presented in the most anterior location (typically out of reach of the whiskers), or lick to
636
obtain a reward when the pole was in the posterior locations. High-speed videography and
637
automated whisker tracking quantified whisker movement (azimuthal angle, ; whisking phase,
638
), changes in curvature caused by the forces exerted by the pole on the whisker (change in
639
curvature, ∆)[34, 44, 77], and contact time, all with 1 millisecond temporal precision [43, 45].
640
Mice touched the pole multiple times (mean number of touches, 8.9±4.2 before reporting
641
object location with licking (mean reaction time 416 ± 165 ms; mean ± s.d.). Recordings were
642
made in trained mice (71±7 % correct responses). To examine the relationship of VPM activity
643
and tactile behavior we aligned spikes of individual neurons recorded in VPM with high-speed
644
recordings of whisker movement and touch [34, 44, 45].
645
646
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32
647
Neuronal network model of a layer 4 barrel
648
Comprehensive neuroanatomical and neurophysiological data sets are revealing the
649
connectivity between defined cell types over multiple spatial scales [26, 78-82]. But links
650
between neural representations, computation and detailed anatomy are rarely achieved [6, 83].
651
One challenge is a lack of knowledge about strengths and dynamics of synapses between
652
specific cell types during behavior. Most of such studies were carried out in slices, and there
653
are differences between intrinsic and synaptic properties measured in slices and in vivo and
654
between different in vivo states. Therefore, our strategy is to set parameter values (synaptic
655
conductances, connectivity) close to measured in vitro values. However, differences between
656
in vitro and in vivo conditions and experimental errors (e.g. estimates of unitary synaptic
657
strengths) currently preclude exact quantification of the synaptic and connectivity properties
658
(e.g., [46]). We define a set of parameter values, named "reference parameter set" [84], close to
659
measured values when known (Fig. 3), allowing for adjustment over a restricted range (mostly
660
within a factor of 2 relative to empirical values), such that the circuit displays dynamics similar
661
to experimentally-observed behavior. The reference parameter set specified below is used
662
unless otherwise stated. Then, we vary one or two parameters to explore the role of those
663
parameters on the system dynamics (e.g., Figs. 6-8).
664
Network architecture. We modeled one barrel in layer 4 (L4) of the vibrissa primary
665
somatosensory cortex (vS1). Our model circuit consists of L4 excitatory (E) neurons and L4
666
FS (I) neurons [26] receiving input from VPM (T) neurons (Fig. 3a). When referring to
667
modeling results we denote VPM neurons as T, L4 excitatory neurons as L4E, and GABAergic
668
interneurons as L4I (Fig. 3b, c). Non-FS interneurons have not been studied during behavior
669
and are therefore not included in the model.
Gutnisky et al
11/28/2016
33
670
671
672
Dynamics of single cortical neurons. Intrinsic neuronal properties of L4 neurons have not been
673
fully characterized. Therefore, following previous work on cortical dynamics [51, 52], single
674
neurons are governed by a modified Wang-Buzsáki model [51, 52] with one compartment. The
675

membrane potential Vi , where α=E,I and i=1,…, Nα obeys
dVi




C
  I L, i  I Na,
i  I Kdr,i  I KZ,i  I syn,i
dt
676
(2)
677
678
where C is the neuron capacitance,
679



I L,
i  gL (Vi  VL )
680
(3)
681
is the leak current, the conductance of the leak current is gL=0.05 mS/cm2 and 0.1 mS/cm2 for
682

the excitatory and inhibitory neurons, respectively, and VL = -65 mV. The current I syn,i
is the
683
3
total synaptic input into the neuron. The other ionic currents are: I Na  g Na m h(V  VNa ) where
684
m   m (V) / ( m (V)  m (V)) , I Kdr  g Kdr n 4 (V  VK ) , and I KZ  gKZ z(V VK ) . The kinetics
685
of h and n are given by:
686
687
dh / dt   h (V )(1  h)  h (V )h  , dn / dt   n (V )(1  n)  n (V )n 
(4)
The functions α(V) and β(V), for V in mV, are:
688
689
 m (V )  0.1(V  30) /{1  exp[0.1(V 30)]}
(5)
690
m (V )  4exp[(V  55) /18]
(6)
Gutnisky et al
11/28/2016
34
691
h (V )  0.7exp[(V  44) / 20)]
(7)
692
h (V )  10 / {1  exp[0.1(V  14)]}
(8)
693
n (V )  0.1(V  34) / {1  exp[0.1(V 34)]}
(9)
694
n (V )  1.25exp[(V  44) / 80] .
695
We set ϕ=0.2 to produce wider spikes than in [52]. The gating variable z of the adaptation
696
current IKZ is governed by the equation:
(10)
697
698
dz / dt  [ z (V )  z ] /  z
(11)
699
700
Where z (V)  1/{1  exp[0.7(V 30)]} and τz = 60 ms. The parameters of the model are:
701
gNa=100 mS/cm2, VNa= 55 mV, gKdr=40 mS/cm2, VK= -90 mV, C=1µF/cm2. Excitatory neurons
702
have gKZ=0.5 mS/cm2, whereas inhibitory neurons do not possess this current (gKZ=0).
703
704
Network architecture. The network consists of NE excitatory neurons and NI inhibitory neurons.
705
The L4 neurons receive input from NT thalamic relay neurons in one barreloid. For the
706
simulations, NE = 1600, NI = 150, and NT = 200 [26]. Each neuron, whether excitatory or
707
inhibitory, receives excitation and inhibition from the excitatory and inhibitory cortical
708
neuronal populations respectively, as well as excitation from VPM thalamic neurons. The
709
probability that a neuron from the βth, pre-synaptic population forms a synapse on a neuron
710
from the αth, post-synaptic population is K / N  [85]. Therefore, a neuron from the αth
711
population receives, on average, Kαβ synaptic inputs from neurons in the βth population. We
Gutnisky et al
11/28/2016
35
712
define the matrix Cij to be 1 if the jth neuron from the βth population projects to the ith
713
neuron from the αth population, and 0 otherwise.
714
715
Synaptic input. We consider only fast synapses corresponding to AMPA and GABA A receptors.
716
The total synaptic input a cell i from population α receives is the sum of the synaptic currents
717
from all the pre-synaptic populations:

I syn,
i 
718


T,E,I



Gsyn,
i (t ) Vi  Vsyn 
(12)
719
720
 ,
The total conductance Gsyn,i
for β = T,E,I is:
721

Gsyn,
i (t ) 
 syn,all
K
N
g  Cij s
(t )
j
(13)
j 1
722
where the normalization constant τsyn,all is set to be 1 ms. The value s
denotes a synaptic
j
723
variable of the pre-synaptic neuron j from the βth population projecting to the αth population.
724
Those variables for AMPA and GABAA conductances are:
725
s
j (t ) 
1
tsyn
 exp (t  t    
k
k
delay

) / tsyn  (t tk   delay
)
(14)
726
The pre-synaptic neuron fires at times tk , k is the spike index, tsyn is the time constant of
727

synaptic decay, Θ is the Heaviside function, and  delay
is the time delay between the firing by a
728
spike from a presynaptic neuron from the βth population and the onset of the post-synaptic
729
conductance in the post-synaptic neuron from the αth population. Unless specified otherwise,
730
we use time constants tsyn = tAMPA = 2 ms for AMPA-mediated synapses and tsyn = tGABAA = 3 ms
731
for GABAA-mediated synapses. The reversal potentials are VAMPA=0 and VGABAA=-85 mV.
Gutnisky et al
11/28/2016
36
732

The values of gαβ, Kαβ and  delay
are based on [25, 26, 32, 46, 49, 53] (Table 2). Compared to
733
literature values the Kαβ were reduced by a factor of 2 to counteract strong synchrony in the
734
cortical circuits. Alternatively this could have been achieved by modeling highly variable
735
synaptic strengths [86].
736
The experimental evolution of the response of VPM and L4 neurons to consecutive touch
737
events has not reported yet. In this work, we do not address how the responses to whisking and
738
touch vary over the long time scale of short-term plasticity. For these reasons, and to keep the
739
model and its analysis simple, the synapses in the model do not have depression and
740
facilitation properties.
741
Spike rates of thalamic neurons. Spike trains of T neurons were modeled as statistically-
742
independent inhomogeneous Poisson processes. All T neuron share the generating function FT
743
mimicking thalamic activity during quiescence, whisking or whisking and touch (Fig. 3d):
744

 2 t
 C
FT (t )  AT 1  BT sin 
     T (t  n w  tc ) (n w  tc   c  t )
 w
  c

745
The first term in Eq. 1 represents the baseline and whisking modulation contribution to the
746
instantaneous spike rate, and the second term represents spikes added by touch. The parameter
747
AT is the spike rate averaged over a whisker movement cycle without touch, BT is the
748
modulation depth, and CT is the average number of additional spikes per touch, τw is the
749
whisking period, tc is the time of touch onset within a whisking cycle, and n is the cycle
750
number. During whisker movements, AT increases above a baseline, with sinusoidal
751
modulation phase-locked to a single preferred phase ϕ (several neurons in VPM exhibit phase-
752
locking activity to the whisking cycle; Yu et al, 2016). Touch is represented by adding a
(15)
Gutnisky et al
11/28/2016
37
753
rectangular function at touch onset t=tc (with respect to the whisking cycle), stretched over
754
3 ms with an integral of CT =0.6 spikes per touch (Eq. 1). We use the parameters: BT = 0.25, τc
755
= 3 ms, T=100 ms, ϕ=π/2. The parameter tc is set to be 0.5T because thalamic neurons reach
756
their maximal spike rate during whisking at around maximal retraction (Yu et al., 2016). The
757
parameters AT and CT are 6 Hz and 0 during no-whisking states, 14 Hz and 0 during whisking
758
states and 14 Hz and 0.6 during whisking-and-touch states. For simplicity, we take the same
759
values of AT, BT and CT for all thalamic neurons. Because of the large convergence of thalamic
760
inputs into L4E and L4I neurons, our results are not modified significantly if we allow those
761
thalamic parameters to be taken from a uniform distribution with the same average values.
762
763
Population- and time-averaged quantities. We define να to be the population- and time-
764
averaged spike rates of all the neurons in the αth population over many whisking cycles. Touch
765
response of a neuron is defined to be the difference between the number of spikes fired by that
766
neuron during a time window of 25 ms after touch onset and the number of spikes fired by the
767
neuron 25 ms before touch onset. We define Rα to be the population- and time-average of the
768
spiking response to touch of all the neurons in the αth population over many touch events.
769
770
Simulations of halorhodopsin activation. We model activation of halorhodopsin, a light-gated
771
chloride pump, expressed in L4I FS neurons (Fig. 9,10). Halorhodopsin expression levels
772
likely varied widely across individual neurons [58]. We therefore assume that halorhodopsin is
773
expressed in only a fraction fhalo of the inhibitory neurons, 0  f halo  1. Activation by light of
774
the ith FS neurons that express halorhodopsin was modeled by two processes. First, as a
775
chloride pump, its activation has an effect of negative current injection to the neuron. The
Gutnisky et al
11/28/2016
38
776
amplitude of this current in the ith neuron is I halo,i  I halo,0  I halo,1 xi , where xi is taken randomly
777
from a uniform distribution between -1 and 1, Ihalo,0=-2 µA/cm2, and Ihalo,1=1 µA/cm2. As a
778
result, I halo,i varies between -3 µA/cm2 and -1 µA/cm2. Second, the GABAA reversal potential
779
is depolarized [87, 88] by a value VGABAA,i   I halo,i , where   4mVcm2 /μA . The second
780
process has only a small quantitative effect on the spiking responses of cortical neurons. Note
781
that non-expressing neurons can be interpreted as non-FS neurons, or L4 FS neurons with low
782
halorhodopsin expression levels.
783
784
Numerical methods. Simulations were performed using the fourth-order Runge-Kutta method
785
with time step Δt = 0.05 ms. Simulations with smaller Δt reveal similar statistics of neuronal
786
firing patterns, such as spike rates ν (averaged over many whisking cycles), touch responses R
787
or levels of synchrony. Differences between individual voltage time courses, however,
788
diverged over large integration time interval This divergence is expected because of the chaotic
789
nature of the sparse network dynamics [36, 37, 89]. Statistics were computed after removing a
790
transient of 0.5 s, over 60 s for panels showing dynamical properties of one realization (Fig.
791
4a,c,d, 6d-i, 9a-f ) and over 5.5 s for panel showing dependence on parameters (Fig. 4b, 5, 6b,c,
792
7, 8, 9g,h, 10) where each data point is computed by averaging over 10 network realizations.
793
794
Acknowledgements
795
We thank David Kleinfeld, Rasmus Petersen, Rony Azouz, for helpful discussions, Amy Hu,
796
Brian Barbarits, Sun Wei-Lung, Tim Harris for help with experiments.
Gutnisky et al
11/28/2016
797
Conflict of interest
798
The authors declare no conflict of interest.
799
800
801
39
Gutnisky et al
802
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Supporting Information
1005
1006
S1 Fig. Example neurons recorded in VPM during whisker-based object localization. (a)
1007
Chronic silicon probe recordings in VPM. (b,c) Two example trials from the same neuron
1008
showing increases in activity with whisker movements without touch. Blue line, whisker
1009
azimuthal angle. Black ticks, spikes. (d,e) Two example trials showing increases in spike rate
1010
after touch. (f) Touch rasters (black dots; sorted by last touch in a trial). The magenta line
1011
shows when the pole was moved within reach of the whiskers. The green line represents the
1012
last touch in each trial. (g) Whisker movement amplitude. Red rectangle, epoch of high
1013
whisker movement amplitude and high spike rate (same as in h). Orange rectangle, epoch of
Gutnisky et al
11/28/2016
45
1014
low amplitude and low spike rate (same as in h). (h) Spike raster for an example neuron in
1015
VPM (blue dots, spikes). The black arrow in g-h indicates onset of whisker twitching [90]. The
1016
twitching is triggered by an auditory signal generated by the brief activation of a shutter. (i)
1017
Peri-stimulus-time-histogram (PSTH) showing response for touch. (j) Spike rate as a function
1018
of whisker movement amplitude. (k-o) Same as f-j for another example VPM neuron with low
1019
baseline spike rate. (p-t) Same as f-j for another example VPM neuron that does not show
1020
modulation with whisking amplitude.
1021
1022
S2 Fig. Example neurons across the thalamocortical circuit. (a) Touch raster (black dots;
1023
sorted by last touch in a trial). The magenta line shows when the pole was moved within reach
1024
of the whiskers. The green line represents the last touch in each trial. (b) Whisker movement
1025
amplitude. Red rectangle, epoch of high whisker movement amplitude and high spike rate.
1026
Orange rectangle, epoch of low amplitude and low spike rate. (c) Spike raster of an example
1027
neuron in VPM (blue dots, spikes). Red and orange regions of interest correspond to B. (d)
1028
PSTH showing response for touch. (e) Spike rate as a function of whisker movement amplitude.
1029
(f-j) Same as a-e for a L4 FS neuron. (k-o) Same as a-f for a L4 excitatory neuron. The few
1030
spikes that occur during whisking are phase-locked to movement.
1031