Parvalbumin-Expressing Interneurons Linearly
Transform Cortical Responses to Visual Stimuli
Bassam V. Atallah,1,* William Bruns,2Matteo Carandini,3and Massimo Scanziani2,*
1Computational Neurosciences Graduate Program, University of California San Diego, La Jolla, California, 92093-0634, USA
2Howard Hughes Medical Institute and Center for Neural Circuits and Behavior and Neurobiology Section, Division of Biology,
University of California San Diego, La Jolla, California, 92093-0634, USA
3UCL Institute of Ophthalmology, University College London, London EC1V 9EL, UK
*Correspondence: email@example.com (M.S.), firstname.lastname@example.org (B.V.A.)
The response of cortical neurons to a sensory stim-
ulus is shaped by the network in which they are
embedded. Here we establish a role of parvalbumin
(PV)-expressing cells, a large class of inhibitory
neurons that target the soma and perisomatic
compartments of pyramidal cells, in controlling
cortical responses. By bidirectionally manipulating
PV cell activity in visual cortex we show that these
neurons strongly modulate layer 2/3 pyramidal cell
spiking responses to visual stimuli while only
modestly affecting their tuning properties. PV cells’
impact on pyramidal cells is captured by a linear
transformation, both additive and multiplicative,
with a threshold. These results indicate that PV cells
are ideally suited to modulate cortical gain and
establish a causal relationship between a select
neuron type and specific computations performed
by the cortex during sensory processing.
Inhibition in the cortex is generated by a variety of different types
neuron types transforms sensory responses is central to estab-
lishing a mechanistic understanding of cortical processing. To
date, however, the specific role played by these distinct types
of inhibitory neurons in sensory processing is still unknown.
processing in vivo have been challenged by the discrepancy
between the exquisite specificity of inhibitory circuits and the
unspecific nature of the pharmacological tools at hand. While
the different subcellular compartments of cortical pyramidal
(Pyr) cells are inhibited by distinct GABAergic interneurons, the
action of GABAergic antagonists used to experimentally affect
inhibition (Sillito, 1975; Katzner et al., 2011) is general and
diffuse. This discrepancy has prevented the selective perturba-
tion of inhibitory transmission mediated by specific interneuron
types or generated onto a specific cellular compartment.
To circumvent this problem we have directly manipulated the
activity of a genetically identified type of inhibitory interneuron,
the parvalbumin (PV)-expressing cell, using microbial opsins,
and examined the resulting effect on the response of Pyr cells
to visual stimuli. This approach has allowed us to bidirectionally
control the activity of PV cells in vivo during sensory stimulation
and determine how this cell type contributes to the fundamental
operations performed by layer 2/3 Pyr cells in primary visual
Among the various interneurons that inhibit Pyr cells, those
rons in the cortex (Celio, 1986; Gonchar and Burkhalter, 1997;
Kawaguchi and Kubota, 1997). PV cells are known to inhibit
the somatic and perisomatic compartments of Pyr cells (Kawa-
guchi and Kubota, 1997), appear to respond less selectively to
specific sensory stimulus features as compared to Pyr cells
(Sohya et al., 2007; Niell and Stryker, 2008; Kerlin et al., 2010;
Cardin et al., 2007), and play a role in shaping the timing and
dynamic range of cortical activity (Cobb et al., 1995; Sohal
et al., 2009; Cardin et al., 2009; Pouille and Scanziani, 2001;
Gabernet et al., 2005; Cruikshank et al., 2007; Pouille et al.,
2009). Despite this wealth of knowledge, how PV cells contribute
to the operations performed by the cortex during sensory stimu-
lation is not known. Here we show that PV cells profoundly
modulate the response of layer 2/3 Pyr cells to visual stimuli
while having a remarkably small impact on their tuning proper-
ties. This modulation of cortical visual responses by PV cells is
described by a linear transformation whose effects are visible
in firing rate once above spike threshold and is well captured
by a conductance-based model of the Pyr cell. These results
indicate that PV cells are ideally suited to modulate response
gain, an essential component of cortical computations that
changes the response of a neuron without impacting its recep-
tive field properties. Gain control has been implicated, for
example, in the modulation of visual responses by gaze direction
(Brotchie et al., 1995; Salinas and Thier, 2000) as well as by
attention (Treue and Martinez-Trujillo, 1999; McAdams and
To control the activity of PV cells we conditionally expressed the
light-sensitive proton pump Archeorhodopsin (Arch-GFP; to
suppress activity; Chow et al., 2010) or the light-sensitive cation
channel Channelrhodopsin-2 (ChR2-tdTomato; to increase
activity; Boyden et al., 2005; Nagel et al., 2003) in V1 using viral
Neuron 73, 159–170, January 12, 2012 ª2012 Elsevier Inc. 159
injection into PV-Cre mice (Hippenmeyer et al., 2005). Targeted
electrophysiological recordings were performed in anesthetized
mice under the guidance of a two-photon laser-scanning
Visual Responses of PV Cells Are Distinct from Those
of Pyr Cells
We characterized PV cells in the adult PV-Cre mouse line immu-
nohistochemically and electrophysiologically (Figure 1; Fig-
ure S1, available online). We fluorescently labeled the cells
expressing Cre by crossing PV-Cre mice with a tdTomato
reporter line (Madisen et al., 2010). tdTomato was present
exclusively in neurons that were also immunopositive for PV,
confirming that cells expressing Cre also expressed PV (97% ±
2%; mean ± standard deviation [SD]; n = 400 cells in 4 mice; Fig-
ure S1). Targeted loose-patch recordings from fluorescently
labeled PV cells in layer 2/3 of the primary visual cortex in vivo
(spontaneous rate: 2.1 ± 3.1 spikes/s; n = 79) showed that their
spike-waveforms (Figure S1) had faster kinetics than non-PV
cells recorded using the same configuration, consistent with
these cells being of the fast-spiking type (McCormick et al.,
1985; Connors and Kriegstein, 1986; Swadlow, 2003; Ander-
mann et al., 2004; Mitchell et al., 2007). Because the vast
majority (?90%) of the non-PV cells in layer 2/3 are Pyr cells
(Gonchar and Burkhalter, 1997), from here on we will refer to
non-PV cells as Pyr cells.
PV cells gave strong responses to drifting gratings of various
contrasts and orientations presented to the contralateral visual
tent with earlier reports, however, these responses were barely
modulated by stimulus orientation (Sohya et al., 2007; Niell and
Stryker, 2008; Kerlin et al., 2010; Zariwala et al., 2011; Ma
et al., 2010; Bock et al., 2011; Hofer et al., 2011). To estimate
the overall selectivity for stimulus orientation we computed the
orientation selectivity index (OSI), the ratio of the modulation in
response caused by changing orientation to the average
OSI = 0.11
OSI = 0.85
PYR cell response
PV cell response
osi (1-circ. variance)
visually evoked rate
5 10 15 20 25
Figure 1. Distinct Visual Response Properties of PV Cells versus Pyr Cells
(A) Left: configuration for two-photon targeted loose-patch recordings in mouse V1; PV cell expressing tdTomato targeted for recording with green electrode.
Right: spiking response of the same PV cell to each of 12 directions of a drifting sinusoidal grating (2 s duration, shaded gray box).
(B) Raster plots and peristimulus time-histograms (PSTHs) illustrate the cell’s spiking response to repeated grating presentations. Same cell as in (A).
(C) Top: tuning curve, i.e., the average spike-rate during the stimulus presentation of the 12 grating directions, illustrated both on Cartesian and on polar axes
(same cell as A). The tuning curve plotted on Cartesian axes is fitted with adouble Gaussian. The cell’s spontaneousfiring rate is illustrated by the dotted line. The
cell’s poor modulation as a function of orientation is reflected in a low orientation selectivity index (OSI).
Bottom: spiking response of a different PV cell as a function of contrast, fit with a hyperbolic ratio function (line). Error bars are the standard error of the mean
(D) Top left: histogram of visually evoked spike rates (PV: n = 79; Pyr: n = 80). Top right: histogram of OSI (PV: n = 63; Pyr: n = 60). Inset: median PV and Pyr cell
tuning curves normalized to thepeak and fit withdouble Gaussian (shaded areas illustrated the2ndand 4thquartile). NotethatPyr cells haveafar greater OSIthan
PV cells. Bottom left: histogram of tuning sharpness, measured as the half-width at half-height (HWHH) of the double Gaussian fit (PV: n = 63; Pyr: n = 60). Inset:
median PV and Pyr cell HWHH.
and fit (shaded area is the SEM).
(E) Raster plots and PSTH illustrate the spiking response of a Pyr cell to 12 directions of oriented grating stimuli.
(F) Top: tuning curve of the cell in (E). Note the cell’s high OSI as compared to the PV cell in (C). The cell’s spontaneous firing rate is illustrated by the dotted line.
Bottom: spiking response of a different Pyr cell as a function of contrast, fit with the hyperbolic ratio function (line). Error bars are the SEM.
PV Cells Linearly Transform V1 Responses
160 Neuron 73, 159–170, January 12, 2012 ª2012 Elsevier Inc.
responseacross orientations. OSIwasextremelylowforPVcells
(0.1 ± 0.1; n = 63), significantly lower than in Pyr cells (0.4 ± 0.2;
n= 60; p <1 3 10?11Wilcoxon rank-sum test; Figure 1). Only3%
of PV cells, as compared to 65% of Pyr cells, had an OSI > 0.25
(Figure 1D). Furthermore PV cells were more broadly tuned than
Pyr cells. To estimate the tuning sharpness we calculated the
half width at half height (HWHH) of a double Gaussian fit to the
tuning curve of each cell; PV cells: 52 ± 24 degrees; n = 63;
Pyr cells: 42 ± 23 degrees; n = 60; p < 0.05). Finally, the contrast
response function of PV cells differed in two clear ways from that
of Pyr cells (Figure 1D). First, the maximal firing rate was two
times higher for PV cells than for Pyr cells (9.1 ± 5.6 spikes/s;
n = 43; versus 4.5 ± 3.0 spikes/s; n = 30). Second, the increase
in firing rate of PV cells with increasing contrast, captured
by the exponent of the curve fitted to contrast responses, for
PV cells was significantly shallower than for Pyr cells (2 ± 2;
n = 43; versus 3.0 ± 2.5; n = 30; p < 0.005). Thus, in contrast to
a previous report (Runyan et al., 2010) the response properties
Bidirection Control of PV Cell Activity
Next, we assessed the impact of optogenetic manipulation on
the visual responses of PV cells. We recorded from Arch- or
ChR2-expressing layer 2/3 PV cells at least two weeks after viral
LED (470 nm, Figure 2). Since strong suppression of inhibition
of PV cells can completely silence cortical activity (not shown),
we perturbed PV cell firing over a moderate range chosen to
fall within the reported firing rates of these neurons in active
awake mice (Niell and Stryker, 2010). Control measurements in
uninjected animals established that illumination by itself did not
affect visual responses (Figure S5).
targeted PV cells, both spontaneous (from 3.0 ± 3.5 to 1.9 ± 3.4
spikes/s; n = 31; p < 0.02 paired Wilcoxon sign-rank test) and
visually evoked (from 9.2 ± 7.3 to 6.6 ± 7.0 spikes/s; n = 31;
p < 0.0001; Figure S2A). PV cell firing rate decreased at all
contrasts tested (Figure 2D) and was well described by a linear
fit (0.6 3 control rate ? 0.4 spikes/s). Thus, PV cell firing rates
decreased by approximately the same factor, 0.6, minus an
offset, 0.4 spikes/s, regardless of stimulus contrast (Figure 2D).
Photo stimulation of ChR2-expressing PV cells had the dia-
metrically opposite effect, increasing both their spontaneous
firing (from 3.0 ± 3.8 to 5.8 ± 6.1 spikes/s; n = 16; p < 0.01)
and their visually evoked firing (from 13.6 ± 13.2 to 18.0 ± 15.1
spikes/s; n = 16; p < 0.01; Figure S2B). As for Arch-mediated
suppression of PV cells, the fractional increase in PV cell firing
rate with ChR2 was similar for all presented contrasts (linear fit:
1.2 3 control rate + 2.0 spikes/s; Figure 2E).
Thus, we could bidirectionally modulate visually evoked
offset, independently of how strongly these neurons were driven
by the visual stimulus.
PV Cells Tightly Control Visual Responses of Pyr Cells
To assess how PV cell activity impacts cortical responses to
visual stimuli, we asked how their suppression or activation
changes the visual responses of layer 2/3 Pyr cells. We concen-
trated on three response attributes: response to contrast, overall
selectivity for orientation and direction, and sharpness of tuning.
Optogenetic modulation of PV cell activity strongly affected
the response of Pyr cells to visual stimuli. Suppressing PV cell
activity by photo stimulating Arch led to an increase in the spike
rate of Pyr cells (change in firing rate: 0.8 ± 1.5 spikes/s; 73% ±
85%; n = 43 cells; p < 0.005; Figure S2C). This increase was
again well described as a linear transformation (1.4 3 control
rate + 0.3 spikes/s) independently of the contrast tested (Fig-
ure 2F). Complementarily, activating PV cells by photo stimu-
lating ChR2 resulted in decreased Pyr cell spike rates (change
in firing rate: ?3.7 ± 2.2 spikes/s; ?38% ± 30%; n = 19 cells,
rate ? 0.3 spikes/s; Figure 2G).
of Pyr cells, and they do so in a manner that is independent of
stimulus contrast. Indeed, manipulation of PV cell activity scaled
the response of Pyr cells, with little effect on the shape of their
contrast responses curves. PV cells, therefore, control the
response but not the contrast sensitivity of Pyr cells.
PV Cells Only Modestly Impact Pyr Cell
Despite the strong influence of PV cells on the firing rate of Pyr
cells, bidirectional modulation of PV cell activity only modestly
impacted the tuning of Pyr cells for stimulus orientation.
Suppression of PV cells with Arch increased Pyr responses to
all stimulus orientations (Figure 3A), and activation of PV cells
with ChR2 suppressed Pyr responses to all orientations (Fig-
ure 3B). Neither manipulation, however, had much of an effect
on the shape of Pyr cell tuning curves (see e.g., normalized
tuning curves in Figures 3A and 3B). Indeed, the changes in PV
activity had hardly had any impact on the relative responses of
Pyr cells to each grating direction (Pearson’s correlation =
0.8 ± 0.2; n = 45).
Accordingly, PV cell suppression or activation caused only
modest changes in the overall selectivity of Pyr cells. Suppres-
sion of PV cells with Arch stimulation caused an increase in Pyr
firing rate at all orientations. In relative terms, however, it
increased responses less at the preferred orientation than at
the orthogonal orientation. This resulted in a small but significant
decrease of the OSI by ?0.06 ± 0.08 (n = 31 Pyr cells; p < 0.001;
Figure 3C; 13/31 individual cells showed significant changes in
OSI). Activation of PV cells with ChR2 led to the opposite effect:
a modest (but significant) increase in the OSI of Pyr cells (mean
cells showed significant changes; Figure 3B).
ically on the change in Pyr cell firing rate caused by PV cell
perturbation. A linear regression of the percentage change in
spiking response at the preferred orientation versus OSI re-
vealed a highly significant correlation (r = ?0.6; n = 45 cells;
p < 0.0001; Figure 3C). In other words, the Pyr cells that dis-
played the greatest increase in response also experienced the
largest decrease in OSI. Conversely, the Pyr cells that displayed
the greatest decrease in response experienced the largest
increase in OSI. This said, the changes in OSI were minor even
PV Cells Linearly Transform V1 Responses
Neuron 73, 159–170, January 12, 2012 ª2012 Elsevier Inc. 161
PV cell Suppression by ARCH
PV cell Activation by ChR2
L 5 L 2/3
L 1L 4
L 5 L 2/3
Change in Contrast Resp
All PV cells
Single PV cell
0 10 20
y = 1.2 x + 2y = 0.6 x - 0.4
Pyr response to PV cell Suppression
PV cell Suppression
PV cell Activation
Pyr response to PV cell Activation
y = 0.7 x - 0.3y = 1.4 x + 0.3
Change in Contrast Resp
All PV cells
Single PV cell
Change in Contrast Resp
All Pyr cells Single Pyr cell
Change in Contrast Resp
All Pyr cells Single Pyr cell
Figure 2. Bidirectional Modulation of PV Cell Activity Demonstrates Their Tight Control of Pyr Cell Contrast Response
(A) Top: coronal section of V1 from a PV-Cre x tdTomato reporter mouse injected with Cre depend Arch-GFP AAV-vector. In red: the naive expression of
tdTomato; in green: Arch-GFP expressing cells (anti-GFP immunostaining). Bottom: image detail. Note that Arch-GFP expression only occurs in tdTomato
expressing, and hence PV expressing, cells.
(B) Left: PV cell expressing Arch-GFP targeted for loose-patch recording with red electrode. Right: raster plot and PSTH of spiking response to grating during
interleaved trials: either control (cyan, no led) or during PV cell suppression by Arch photo stimulation (green, LED on). Gray area on the raster plot illustrates the
PV Cells Linearly Transform V1 Responses
162 Neuron 73, 159–170, January 12, 2012 ª2012 Elsevier Inc.
their response 3-fold before undergoing a change in OSI of only
0.1, a tenth of the distance separating an untuned cell from
a perfectly tuned cell.
As with orientation selectivity, the direction selectivity of Pyr
cells changed only modestly while perturbing PV cell activity.
Upon PV cell suppression the direction selectivity index (DSI,
see Experimental Procedures) decreased by 0.08 ± 0.16 (over
the population of n = 31 cells; p < 0.01; 7/31 individual cell had
significant changes; Figure 3A). Conversely, PV cell activation
increased the DSI by 0.07 ± 0.11 (n = 14 cells; p < 0.05; 4/14 indi-
vidual cell had significant changes; Figure 3B). As with OSI,
changes in DSI were small but highly significantly correlated
with changes in response (r = ?0.5; n = 45 cells; p < 0.001;
Remarkably, neither PV cell suppression nor activation had
any systematic impact on tuning sharpness. We have already
seen that PV cell modulation had no effect on the shape of the
Pyr tuning curves for the two example neurons (see normalized
tuning curves in Figures 3A and 3B). This effect was common
to the whole sample. While perturbing PV cell activity slightly
changed the tuning sharpness in a subset of Pyr cells (PV cell
suppression: 9/31 cells; DHWHH = 7 ± 11 degrees; PV cell acti-
vation: 3/14 cells; DHWHH = ?4 ± 9 degrees), there was no
significant impact on the tuning sharpness across the population
of Pyr cells (PV cell suppression: HWHH, mean change: 2.5 ±
14.6 degrees; n = 31 cells; p = 0.5; PV cell activation: ?3.7 ±
8.2 degrees; n = 14 cells; p = 0.2). Regression analysis further
confirmed that perturbing PV cells did not systematically impact
Pyr cell tuning sharpness perturbation (p = 0.8; n = 45 cells).
Taken together, these results demonstrate that while PV cells
significantly impact the visually evoked responses of layer 2/3
Pyr cells, modulating spiking by as much as 60% below and
250% above baseline rates (Figure 3C), they do so while only
modestly impacting orientation and direction selectivity, with
no systematic effects on tuning sharpness.
A Linear Function Describes How PV Cells Control Pyr
Cell Visual Responses
of PV cells on the responses of Pyr cells to visual stimuli. We
plotted the control responses of Pyrcells tostimuli of each orien-
tation (the black points in Figure 4A) against the responses re-
corded while activating or suppressing PV cells (the red or green
points in Figure 4A). Strikingly, the effect of activating or sup-
pressing PV cells on Pyr cell responses was linear (Figure 4B).
Suppressing PV cell spiking with Arch linearly increased the
activity of Pyr cells: control responses were multiplied by
a constant factor of 1.2 and a constant amount was added (Fig-
ure 4B, green). Similarly, activating PV cells with Chr2 linearly
decreased Pyr cell activity: control responses were multiplied
by a constant factor of 0.7 and a constant amount was sub-
lead to negative firing rates, the lowest control firing rates were
suppressed to approximately zero spikes/s. Thus, a simple
threshold-linear function with only two parameters (one where
the firing rate is zero up to a threshold for activation and then
grows linearly) provides a good fit to the data (Figure 4B, lines).
tive effects of PV cells on Pyr cell responses, with no free param-
eters (Figure 4C, green and red curves). The function captures
the fact that suppression of PV cell activity with Arch linearly
scales responses regardless of stimulus orientation (Figure 4).
(DOSI = ?0.11 ± 0.06) but there is no change in tuning sharpness
(DHWHH = 0 ± 0.1 degrees). Similarly, the function explains that
an increase in PV cell activity with ChR2 linearly scales
responses regardless of stimulus orientation, except where the
responses are pushed below zero (Figures 4B and 4C, gray).
As a result, there is an increase in overall selectivity for orienta-
with no change in tuning sharpness (DHWHH = 3 ± 5 degrees).
Thus, PV cells perform a remarkably simple linear operation on
the response of Pyr cells to visual stimuli in layer 2/3 of mouse
primary visual cortex.
Suppressing PV Cells Reduce Synaptic Inhibition
in Pyr Cells
By what mechanisms do PV cells transform the Pyr cell
responses? The suppression of PV cells could in principle have
two immediate effects on neighboring Pyr cells: direct reduction
duration of the visual stimulus; shaded area on the PSTH is the bootstrapped 95% confidence interval (cyan and green). LED illumination is illustrated with
horizontal blue bar. Note that the time course of PV cell suppression tightly matches the time course of LED illumination.
(C) Left: PV cell expressing Chr2-tdTomato targeted for loose-patch recording with green electrode. Right: raster plot and PSTH of spiking response to grating
during interleaved trials: either control (cyan, no LED) or during PV cell activation with ChR2 photo stimulation (red, LED on). Shaded area and horizontal bar as in
(B). Note that the time course of PV cell inactivation tightly matches the time course of led illumination.
(D) Left: example of contrast response of a single PV cell in control (cyan) and during suppression by Arch photo stimulation (green). Error bars are the SEM.
Right, gray: visually evoked spike rate of PV cells under control conditions versus during Arch photo stimulation (circles; 8 different contrasts for each cell; n = 14
cells) Lines: linear fits to each cell; green line: average linear fit; dotted line at unity.
(E) Left: example of contrast response of a single PV cell in control (cyan) and during activation with ChR2 (red). Error bars are the SEM.
Right, gray: visually evoked spike rate of PV cells undercontrol conditions versus during ChR2 photo stimulation (circles; 8 different contrasts for eachcell; n = 11
cells). Lines: linear fits to each cell; red line: average linear fit; dotted line at unity.
(F) Left: contrast response of a single Pyr cell in control (black) and during suppression of PV cells (green). Error bars are the SEM.
Right, gray: visually evoked spike rate of Pyr cells under control conditions versus during PV cell suppression (circles; 8 different contrasts for each cell; n = 17
cells). Lines: linear fits to each cell; green line: average linear fit; dotted line at unity.
(G) Left: example of contrast response of a single Pyr cell in control (black) and during activation of PV cells (red). Error bars are the SEM.
Right,gray: visuallyevoked spike rate of Pyr cells under controlconditions versus during PVcell activation (circles; 8different contrasts for each cell; n = 10cells).
Lines: linear fits to each cell; red line: average linear fit; dotted line at unity.
PV Cells Linearly Transform V1 Responses
Neuron 73, 159–170, January 12, 2012 ª2012 Elsevier Inc. 163
rect effect results from the fact that cortical Pyr cells within layer
2/3 are recurrently connected; thus, an increase in firing rate of
Pyr cells in response to PV cell suppression (as observed above)
may lead to an increase in the amount of excitation received by
the Pyr cells themselves.
To quantify the net decrease in visually evoked inhibition
during Arch-mediated suppression of PV cells we recorded in
the whole-cell voltage-clamp configuration from layer 2/3 Pyr
cells (targeted with two-photon microscopy) using a Cs-based
internal solution. When the membrane potential of Pyr cells
was clamped at the reversal potential of glutamate-mediated
synaptic excitation (?15mV), photo suppression of PV cells
decreased by 10% the postsynaptic inhibitory currents evoked
by visual stimuli in Pyr cells (?9% ± 20%; n = 13 cells, p <
0.03; Figure 5A). To quantify the impact of PV cell suppression
on excitation, Pyr cells were voltage clamped at the reversal
potential for GABAA receptor-mediated inhibition (?80mV).
Photo suppression of PV cells led to a small but significant
increasein spontaneous excitatory
0.02 nS; n = 10; p < 0.004), demonstrating that our recordings
are indeed sensitive to changes in excitation. However no signif-
icant increase was measured in visually evoked excitatory
conductance (n = 10; p = 0.5; Figure 5B). Thus, PV cell suppres-
sion results in little change in excitation but a net decrease in
synaptic inhibition on to Pyr cells.
A Conductance-Based Model Captures How PV Cells
Transform Pyr Cell Responses
Can this relatively small decrease in inhibition explain the
observed linear transformation of Pyr cell spiking activity? To
test this we constructed a simple conductance-based model
of Pyr cell spiking activity and studied its dependence on stim-
ulus orientation. To fully capture the linear transformation, not
Figure 3. Slight Modulation of Pyr Cell Tuning Properties by PV Cells
(A) Left: PSTH of Pyr cell response to drifting gratings during control (black) or Arch-mediated suppression of PV cells (green). Horizontal bars: black, stimulus
The tuning curves plotted on Cartesian axes are fitted with a double Gaussian. Note the slight reduction in both orientation and direction selectivity indexes.
Bottom: the Gaussian fits under control (black) and PV cell suppression (green) are normalized to the peak and superimposed for comparison. Error bars are the
SEM. Note that the tuning sharpness during PV cell suppression remains essentially unaffected.
(B) Left: PSTH of Pyr cell response to drifting gratings during control (black) or ChR2-mediated activation of PV cells (red). Horizontal bars: black, stimulus
presentation; blue, LEDillumination.Right:the tuning of the cellis illustrated onpolar (top)and Cartesian (middle)axes(black:control; red:PV cell activation). The
tuning curves plotted on Cartesian axes are fitted with a double Gaussian. Note the increase in both orientation and direction selectivity indexes. Bottom: the
Gaussianfitsunder control (black)and PVcellactivation(red) arenormalized tothepeak andsuperimposed forcomparison. ErrorbarsaretheSEM.Notethatthe
tuning sharpness during PV cell activation remains essentially unaffected.
(C) Linear regression (line) of percentage change in Pyr cells firing rate at their preferred orientation versus the change in their tuning properties during PV cell
photo suppression (green dots; n = 31) or PV cell photo activation (red dots; n = 14). p values (black) indicate the significance of correlation between in change
firing rate and tuning property. Left: distributions of respective tuning properties (negative values indicate decrease in tuning property; p value indicates
confidencethat there isasignificantdifference;green:Arch versuscontrol;red: ChR2versuscontrol).Bottom:distribution of change infiringrate. Arrowspoint to
PV Cells Linearly Transform V1 Responses
164 Neuron 73, 159–170, January 12, 2012 ª2012 Elsevier Inc.
only must the decrease in inhibition result in a robust ? 40%
increase in Pyr cells response, but it must do so while having
only slight impact on tuning properties and, in particular, tuning
To set up the fundamentals of the model we first considered
the orientation tuning under control conditions. To this end, we
recorded excitatory and inhibitory conductances in layer 2/3
Pyr cells as a function of orientation. Stimulus-evoked excitatory
currents (Figure 5C, red trace) recorded at the reversal potential
for GABAAreceptor-mediated inhibition showed clear tuning:
tation than at the nonpreferred orientation. In contrast, inhibitory
currents (Figure 5C, blue trace) recorded at the reversal potential
of glutamate-mediated synaptic excitation were less tuned,
being only 1.2-fold (n = 5) larger at the preferred compared to
the nonpreferred orientation (consistent with Liu et al., 2010).
The membrane potential tuning was then calculated directly
from these two opposing conductances (Figure 5D) and the
model cell’s intrinsic properties (Figure 5E). The spike generation
orientation selectivity and tuning sharpness of spikes matched
experimentally measured Pyr cell spike tuning properties
(modeled suprathreshold OSI = 0.7 and HWHH = 24 deg; Fig-
ure 5F, black trace).
To test the impact of PV cell suppression on model Pyr cell
responses, we decreased the inhibitory conductance by 10%,
Figure 4. A Linear Function with a Threshold
Describes How PV Cells Transform Pyr Cell
(A) Median response of Pyr cell population to 12 directions
under control conditions (black circles) and upon PV cell
photo suppression (green circles; n = 31) or PV cell photo
activation (red circles; n = 14). Error bars are bootstrapped
95% confidence intervals. Black solid lines: double
Gaussian fits to median control response.
(B) Median response of Pyr cell population to 12 directions
during PV cell photo suppression (green circles) or PV cell
photo activation (red circles) plotted against control
conditions (same data as A). Solid lines: threshold-linear
function fit to data (green: slope of 1.2 and offset of 11%;
red: slope 0.7 and offset of ?13%). Gray dashed line
extends the red linear fit to negative Pyr cell firing rates
(i.e., the linear function without applying the threshold).
Gray solid line is at unity.
(C) Same data as (A), with the addition of the quantitative
prediction of Pyr cell tuning curves (green and red lines)
based on the threshold-linear functions in (B).
Note the threshold-linear functions illustrates that activa-
tion/suppression of PV cells linearly scales Pyr cell
responses regardless ofstimulusorientation exceptwhere
the responses are pushed below zero (gray lines). As
aresult, there isno change inHWHH and asmall change in
orientation and direction selectivity.
as experimentally determined. Notably, this
reduction in inhibition not only resulted in
a substantial increase in the modeled spiking
response (?50%) but did so in a manner that
observed linear transformation—i.e., a small decrease in OSI
(DOSI = 0.08) and no impact on tuning sharpness (DHWHH < 2
degrees; Figure 5F, Inset). The model robustly accounted for
the transformation of Pyr cells over the wide range of Pyr cell
orientation selectivity (Figure S3).
Thus, this conductance-based model provides insight into
how even slight changes in PV cell-mediated inhibition can
lead to robust changes in response of Pyr cells to visual stimuli
without having a major impact on their tuning properties.
By manipulating the activity of PV cells bidirectionally we have
determined that while these neurons minimally affect tuning
properties, they have profound impact on the response of cortex
and basic computation contributed by these neurons during
cortical visual processing: a linear transformation of Pyr cell
responses, both additive and multiplicative. This linear transfor-
mation of course operates in the presence of a threshold, as
firing rates cannot be reduced below zero. The bidirectional
control of PV cells during visual stimulation has also allowed us
to demonstrate the consistency of this transformation over
control levels (Figure 2). While suppressing PV cell activity with
Arch revealed their function under control conditions, increasing
PV Cells Linearly Transform V1 Responses
Neuron 73, 159–170, January 12, 2012 ª2012 Elsevier Inc. 165
PV cell activity with ChR2 demonstrates their further potential for
linearly transforming visual responses in layer 2/3 of the cortex.
Finally we showed, using in vivo whole-cell recordings, that the
robust changes caused by PV cell perturbation on visually
evoked responses in Pyr cells result from relatively small modu-
lations in synaptic inhibition. A conductance-based model
provides a likely explanation for how this small yet systematic
change in inhibition can lead not only to the observed change
in spiking responsebut also
Because of their powerful effect on firing rate, minor effect on
direction and orientation selectivity and no systematic effects on
tuning sharpness, PV-expressing interneurons appear ideally
suited to modulate response gain in layer 2/3 of visual cortex
to the observedlinear
(Figure 4). The results obtained here, therefore, provide a causal
basis for the view that the response gain of neurons in visual
cortex is under the control of GABAa mediated inhibition, as
had been postulated based on pharmacological experiments
(Katzner et al., 2011). Moreover, our experiments identify
a specific role of PV cells in this control of response gain.
Quantification of PV Cell Perturbation
The changes in firing rate that we caused in PV cells are consis-
tent with the changes in inhibitory conductance that we
observed in Pyr cells. We chose to perturb PV cells over
a moderate range, increasing or decreasing their activity by
3–4 spikes/s (i.e., ?40%; Figures 2D, 2E, and S2) of the average
visual evoked firing rate of ?10 spikes/s (Figure 1D). Given that
Figure 5. A Model Based on Experimentally Determined Synaptic Conductances Captures Linear Transformation of Pyr Cell Responses
(A) Left: visually evoked inhibitory postsynaptic currents (IPSC) recorded in a Pyr cell during control (cyan) and PV cell suppression (green). Average of 38 sweeps
at each condition. Horizontal bars: black, stimulus presentation; blue, LED illumination. Brackets: black, baseline; gray, time over which average IPSC amplitude
is computed. Right: scatter plot of visually evoked inhibitory conductance in control versus during PV cell photo suppression (open circles); ‘‘X’’ marks individual
cells with significant change in conductance. Solid circle illustrates mean. Average decrease ?10%; n = 13; p < 0.03.
(B) Left: visually evoked excitatory postsynaptic currents (EPSC) recorded in a Pyr cell during control (red) and PV cell photo suppression (green). Average of 62
sweeps at each condition; horizontal bars and brackets as above. Note that while there is no change in the visually evoked EPSCs relative to baseline (black
bracket), a significant increase in EPSC amplitude occurred systematically at led onset (asterisk; 0.1 ± 0.02 nS; n = 10; p < 0.004). Right: scatter plot of visually
evoked excitatory conductance in control versus during PV cell photo suppression (open circles); ‘‘X’’ marks individual cells with significant change in
conductance; solid circle illustrates mean. Excitatory conductance did not change significantly; n = 10; p = 0.5).
(C) Top: visually evoked IPSCs (cyan) and EPSCs (red) recorded in a layer 2/3 Pyr cell during the presentation of six sinusoidal grating orientations.
Bottom, dots: summary of excitatory (red; n = 4) and inhibitory (cyan; n = 5) tuning as a function of orientation. Error bars are the SEM. Lines are the respective
(D) Tuning of excitatory synaptic conductance (red) and inhibitory synaptic conductance (cyan: control; green:during PV cell suppression, i.e., 10% reduction) as
a function of orientation. Lines are the Gaussian fits from (C).
(E) Net depolarization in the membrane potential of modeled cell (resulting from conductances in D) as a function of orientation under control conditions (black)
and during PV cell suppression (green). The dotted line illustrates the spike threshold. Note that under control conditions the membrane potential is above
threshold at most orientations.
(F) Model cell’s orientation tuning, i.e., firing rate as a function of orientation under control conditions (black; OSI = 0.67; HWHH = 24 degrees) and during PV cell
suppression(green;OSI= 0.59;HWHH= 26degrees).Inset,left:theexpansivenonlinear threshold orpowerlaw, i.e., thefiringrate asafunctionofnetmembrane
potential depolarization. Inset, right: orientation tuning curves in normalized to the peak. A 10% decrease in inhibition, as experimentally determined, results in
PV Cells Linearly Transform V1 Responses
166 Neuron 73, 159–170, January 12, 2012 ª2012 Elsevier Inc.
PV cells are 30%–50% of all inhibitory interneurons (Gonchar
and Burkhalter, 1997), and that 90% of PV cells were virally in-
fected (88% ± 6%; n = 5 mice), a simple calculation reveals
that the observed change in PV cell firing rate should result in
a 13% ± 8% change in inhibition, consistent with the experimen-
tally observed 10% reduction in synaptic inhibitory current (Fig-
ure 5A). Moreover, since our perturbation of PV cells was chosen
to be moderate, and thus fall within the range of firing rates
spanned by these neurons during awake-behaving states in
mice (Niell and Stryker, 2010), we believe that PV cells are likely
While changing the firing rate of the PV cells by 3–4 spikes/s
(?40%) resulted in an opposite change in layer 2/3 Pyr cell
responses by ?0.5–1 spikes/s (?40%; Figures 2F, 2G, and
S2), a small fraction (<10%) of Pyr cells exhibited ‘‘paradoxical’’
effects. That is, upon photo stimulation of Arch-expressing PV
cells these Pyr cells were also suppressed rather than activated,
or upon photo stimulation of ChR2-expressing PV cells Pyr cells
were activated rather than suppressed (Figures 2F, 2G, and S2).
These paradoxical effects in Pyr cells probably occur because
a small subset (<10%) of PV cells also exhibited paradoxical
effects. That is, upon photo stimulation, a few visually identified
Arch-expressing PV cells were activated rather than suppressed
or ChR2-expressing PV cells were suppressed rather than acti-
vated (Figures 2E and S2A). This may be explained by the fact
that PV cells not only contact Pyr cells but also inhibit one
another (Galarreta and Hestrin, 2002). Thus, in a fraction of PV
cells the changes in synaptic inhibition caused by perturbing
PV cell activity may outweigh the direct effects of opsin activa-
tion. The potential for paradoxical effects during optogenetic
manipulation further highlights the importance of directly quanti-
fying the impact of the perturbation.
Perturbing PV Cells Affects Synaptic Inhibition with
Little Change in Excitation
We find that PV cells substantially impact the response of layer
2/3 Pyr cells to visual stimuli. In principle, this action can occur
via two mechanisms: the direct reduction in synaptic inhibition
and, due to the recurrent nature of the layer 2/3 circuit, the indi-
rect increase in excitation. Whole-cell recordings from Pyr cells
yet relatively small, decrease in synaptic inhibition and negligible
changes in excitation. This underscores the exquisite sensitivity
of cortical sensory responses to even small changes in synaptic
inhibition. The fact that synaptic excitation did not change in
a consistent manner, despite clear increases in Pyr cell spiking,
implies that recurrent excitatory connections between layer 2/3
Pyr cells contribute little to the overall excitatory input onto these
cells during visual stimulation, as suggested by a recent study
(Hofer et al., 2011).
PV Cells Linearly Transform Visual Responses
of Pyr Cells
The computation performed by PV cells, i.e., how these neurons
control the visual responses of layer 2/3 Pyr cells, is quantita-
tively summarized by a simple linear equation, both additive
and multiplicative with a threshold (which accounts for the
spiking threshold of neurons). While Pyr cell responses are
most significantly transformed by the multiplicative factor, which
has no impact on tuning properties, the small additive compo-
nent of this transformation accounts for the minor changes in
The simplicity of this transformation relies in part on the fact
that, in mice, PV cells generate inhibition that varies little with
orientation (Figure 1; Sohya et al., 2007; Niell and Stryker,
2008; Kerlin et al., 2010; Ma et al., 2010). Accordingly, within
each condition (control or Arch or ChR2 stimulation), as long
as the stimuli were presented at constant contrast (Figure 4)
the activity of PV cells must have been approximately constant,
regardless of stimulus orientation. In other species, like cats,
where due to the presence of large orientation domains the
responses of inhibitory neurons are tuned to orientation (Ander-
son et al., 2000) (although PV cells are likely to be less turned
than other neurons; Cardin et al., 2007; Nowak et al., 2008),
more complex models may be necessary to describe their
impact on visual responses (Ferster and Miller, 2000; Katzner
et al., 2011). In the primate, however, where orientation domains
have an anatomically smaller scale (Nauhaus et al., 2008), indi-
vidual PV cells may sample excitation from several domains
and, hencesimilarto mice,controlgainbygenerating orientation
Interestingly, despite the fact that cortical responses as a
function of contrast and cortical responses as a function of
orientation are independent of each other (Niell and Stryker,
2008; Finn et al., 2007), PV cell perturbation affected both
responses linearly and in a quantitatively similar fashion (i.e.,
PV cell suppression multiplied both responses by ?1.4 and
added a small offset). This further demonstrates that PV cells
are ideally suited to globally modulate gain.
Modulation of Pyr Cell Response without Systematic
Changes in Tuning Sharpness
How can PV cell perturbation so robustly modulate Pyr cell
response without systematically affecting tuning sharpness?
Based on the classical ‘‘iceberg’’ model of a cell’s membrane
potential tuning (Carandini and Ferster, 2000) this seems coun-
terintuitive. The iceberg model illustrates the fact that, due to
the spike threshold, the spike output of the neuron is generally
more sharply tuned than the underlying membrane potential
(where a mountain shaped iceberg is the membrane potential
tuning curve and the water level is the spike threshold). Accord-
ing to this model, depolarization of the membrane (e.g., by
decreasing inhibition through PV cell suppression) is like
lowering the water level around the iceberg and results in
a broader spiking response as a function of orientation, i.e.,
a decrease in tuning sharpness. Importantly, this model implies
that some of the iceberg is under the water level, i.e., that
some of the membrane potential tuning curve is below threshold
for spike generation. This is clearly the case in Pyr cells, like the
one illustrated in Figures 1E and 1F, that do not generate any
spike to stimuli of the nonpreferred orientation. However, such
cells are the exception rather than the rule. The average tuning
curve of layer 2/3 Pyr cells (e.g., Figure 1D inset and Figure 4)
PV Cells Linearly Transform V1 Responses
Neuron 73, 159–170, January 12, 2012 ª2012 Elsevier Inc. 167
shows that spiking responses are generated even by the
nonpreferred orientations, although at much lower rates as
compared to preferred orientations. In other words, thanks in
part to fluctuations in membrane potential (Carandini, 2007;
Finn et al., 2007) the iceberg is almost completely out of
the water: further depolarization will increase the firing rate at
all orientations but will not result in a broadening of the tuning
Our conductance-based model (Figure 5E) where the
membrane potential tuning curve results from experimentally
determined excitatory and inhibitory synaptic currents (Fig-
ure 5D) illustrates exactly this fact: the membrane potential
tuning curve is above threshold at most orientations (arrow in
Figure 5E). This mechanism enables PV cells to produce large
increases in layer 2/3 Pyr cell response with little impact on
tuning sharpness (furthermore, this mechanisms holds over
a wide range of OSIs; Figure S3).
Clearly, stronger PV cell activation will eventually enhance
tuning sharpness of Pyrcells,astheir membrane potential tuning
curve is hyperpolarized below threshold. Indeed in 20%–30% of
Pyr cells PV cell perturbation led to small yet significant change
in tuning sharpness. Overall, however, our results illustrate that
perturbing PV cells such as to modulate the response of layer
2/3 Pyr cells over a wide range (from 60% below to 250% above
baseline) had no significant effect on the tuning sharpness of the
population average, nor resulted in a significant relationship
between changes in individual pyramidal cell response and
tuning sharpness (Figure 3C).
To our knowledge this is the first time a specific role in cortical
sensory processing has been directly attributed to distinct
neuron type. PV cells target the somatic and perisomatic
compartments of Pyr cells; however, these cells represent only
one class among the several types of inhibitory neurons that
populate the cortical network (Callaway, 2002; Kawaguchi and
Kubota, 1997). Future comparisons between how PV cells and
other types of inhibitory cells, such as those that target distinct
subcellular domains of Pyr cells, impact visually evoked
responses will be exciting.
All procedures were conducted in accordance with the National Institutes of
Health guidelines and with the approval of the Committee on Animal Care at
Adult, PV-Cre (Jax: 008069), or PV-Cre x tdTomato reporter line (Jax: 007908)
pigmented mice were anesthetized with 2% isoflurane. Then < 1 mm2area of
skull over V1 (2 mm lateral to the midline, 0.2 mm rostral to lambda) was
thinned and 0.1–0.4 mm2craniotomy performed with a 20 G needle. The virus
was delivered using a glass micropipette attached to either a Nanoject II
(Drummond) or UMP3 (WPI). Over a 10 min period, 100–250 nL of virus
AAV2/9.flex.CBA.Arch-GFP.W.SV40 (Addgene 22222) was injected at a depth
of 300–500 mm from the cortical surface. We then sutured the scalp, and
administered an analgesic (0.1 mg/kg Buprenex) to help the recovery from
AAV2/1.CAGGS.flex.ChR2.tdTomato.SV40 (Addgene 18917) was injected
micropipette (tip diameter 40–60 mm) was then used to puncture the scalp and
skulland 60nLinjectedinthreebolusesof20nLatboth200and 400mmbelow
the surface of the scalp.
In Vivo Physiology
Recordings were made from 2- to 8-month-old mice, at least 2 weeks after
virus injection. Animals were injected with 5 mg/kg chlorprothixene and
1.5 g/kg urethane. After reaching a surgical plane of anesthesia (10–20 min),
the mice were secured with a stereotaxic bite bar, eye-lash hairs were cut,
and a thin, uniform layer of silicone oil (30,000 centistokes) was applied to
the cornea to prevent drying. The scalp was then removed and a head plate
attached with dental cement. A ?1.5 mm2craniotomy was performed over
V1 (2 mm lateral to the midline, 0.7 mm rostral of lambda). The craniotomy
was covered with a thin < 1 mm layer of 1% agarose; dura was left intact for
loose-patch recordings and a durotomy performed for whole-cell recordings.
Two-photon imaging was performed with a Sutter MOM, coupled to
a Coherent Chameleon Laser at 1000–1020 nm. PV cells were targeted based
on their expression of tdTomato or eGFP, while Pyr cells were targeted using
the ‘‘shadow-patching’’ method (Kitamura et al., 2008; Komai et al., 2006).
Targeted recordings were performed using 3–5 MU glass electrodes filled
with 50 mM Alexa 488/594 or 25 mM Sulfur rhodamine dye in aCSF for loose-
patch (in mM: 142 NaCl, 5 KCl, 10 dextrose, 3.1 CaCl21.3 MgCl2, pH 7.4)
and Cs-based internal solution for whole-cell voltage-clamp recordings
(in mM: 130 Cs-methylsulfonate, 3 CsCl, 10 HEPES, 1 EGTA, 10 phosphocre-
atine, 2 Mg-ATP, 7.4 pH). Pyr cells were voltage clamped at the reversal
potential for excitation (20mV ± 1mV n = 13 cells) and inhibition (?80mV ±
0mV, n = 10 cells) to record inhibitory and excitatory postsynaptic currents
(IPSCs and EPSCs), respectively. Series resistance, assessed using an instan-
taneous voltage step in voltage-clamp configuration, was 31 ± 17 MU (n = 21
cells). Voltages were not corrected for the experimentally determined junction
potential (?9.8mV ± 0.2mV; n= 3). Atthe end of the recordings, the animal was
sacrificed by administering 2.5% isoflurane followed by decapitation. For
histology and/or immunohistochemistry, the brain was extracted, fixed in
4% PFA, and sliced (30 mm).
Stimuli were created using Matlab with Psychophysics Toolbox and displayed
with a gamma-corrected LCD screen (Dell 30 3 40 cm, 75 Hz refresh rate,
mean luminance 50 cd/m2) placed 25 cm from the mouse. The preferred
spatial frequency (within the range 0.01 and 0.5 cycles/degree) and stimulus
size (while ?75% of neurons preferred full-screen stimuli, the remainder fired
more robustly to a smaller circular stimulus of diameter 7–20 degrees) were
determined for each neuron. Orientation and direction selectivity was then
determined using sinusoidal gratings of 2–3 s duration presented at the
preferred spatial frequency, temporal frequency of 2 Hz, 100% contrast, and
drifting at 12 randomly interleaved directions. Each stimulus presentation
was called a trial. Contrast-response curves were determined by presenting
the same drifting grating at the preferred orientation at eight contrast levels
logarithmically spanning the range from 1% to 100% contrast.
Photo stimulation of ChR2 or Arch was performed using a 470 nm fiber-
coupled LED (1 mm diameter; 0.5 NA; Doric lenses) position approxi-
mately 7 mm from the cranial window. Light intensities in the range of
0.1–1 mW/mm2. To ensure that under our experimental configuration cortical
illumination did not itself (in the absence of ChR2/Arch) impact visual
responses, we performed control experiments on PV-CRE mice that had not
received ChR2/Arch virus injection (Figure S5). There were no differences
between the control responses (i.e., in the absence of photo stimulation) of
in ChR2 versus Arch injected animals for either Pyr (Figure S5) or PV (data
not shown) cells.
In Arch- and ChR2-expressing mice we first recorded from PV cells, quan-
tified PV cell suppression/activation and subsequently recorded visually
evoked responses in Pyr cells using the same light intensity of photo stimula-
tion. Photo stimulation with light intensities ?0.1–0.5 mW/mm2in animals ex-
pressing Arch reliably suppressed PV cells, without generating aberrant
responses (Figure S4). The level of suppression that we chose was submax-
imal: rather thancompletely preventing PV cells from spiking, we reduced their
spike rate by ?3–4 spikes/s (Figures 2D and S2; Supplementary Experimental
Procedures). Similarly, in animals expressing ChR2 we found that light intensi-
ties of ?0.05–0.2 mW/mm2wouldmoderately activate PVcells without entirely
PV Cells Linearly Transform V1 Responses
168 Neuron 73, 159–170, January 12, 2012 ª2012 Elsevier Inc.
silencing Pyr responses. So in mice where we did not record from PV cells
we used this range of light intensity, i.e., light intensity was set to
0.05–0.1 mW/mm2, and increased until change in the activity Pyr cells was
observed. The population response of the visual cortex to visual stimuli was
monitored using local field potential recordings during this process. Light
intensities never exceeded 1 mW/mm2.
When recording from PV cells while photo stimulating Arch or ChR2
(Figure 2) cortical illumination started before the visual stimulus (to monitor
the effect on spontaneous activity) and ended before the end of the visual
stimulus (to determine the kinetics of recovery to visually evoked firing rates).
Spontaneous spike rate was calculated asthe averagefiring rate during a0.5 s
period before the presentation of the stimulus. The visual response to a given
stimulus was the average rate over the stimulus duration or over the period
when both cortical illumination and visual stimulus occurred (1–2 s). Orienta-
tion selectivity index (OSI) was calculated as 1 ? circular variance (Ringach
et al., 1997). Responses to the 12 grating directions were fit with orientation
tuning curves i.e., a sum-of-Gaussians (Figures 1, 3, and 4). The Gaussians
are forced to peak 180 degrees apart, and to have the same tuning sharpness
(s) but can have unequal height (Aprefand Anull, to account for direction selec-
tivity), and a constant baseline B. The tuning sharpness was measured as s
(2 ln(2))1/2, i.e., the half-width at half height (HWHH). Direction selectivity index
(DSI) was calculated as (Rpref– Rnull) / (Rpref+ Rnull), where Rprefis the response
at the preferred direction and Rnullis the response 180 degrees away from the
preferred direction.Contrast-responsecurveswerefitwiththehyperbolic ratio
equation (Albrecht and Hamilton, 1982): R(C) = Rmaxcn/ (C50n+ cn) + Roffset,
where c is contrast, C50is the semisaturation contrast, and n is a fitting
exponent that describes the shape of the curve, Rmaxdetermines the gain,
and Roffsetis the baseline response.
To obtain the threshold-linear fit, we first computed a summary of Pyr cell
responses in layer 2/3. The tuning curves of all cells were aligned to the
same preferred orientation, a nominal value of 0 degrees and the maximal
response was scaled to a nominal value of 100% (Figure 4A). We then plotted
themedian Pyr cellresponse measured during the suppression or activation of
PV cells against the median response measured in the control condition (Fig-
ure 4B). The bootstrapped distribution of median responses was used to
calculate errors bars in OSI, DSI, and HWHH. Please see Supplemental Exper-
imental Procedures for more details.
The membrane potential tuning, or net depolarization, as a function of orienta-
tion, q, was modeled as:
gx=gmin+ðgmin? gmaxÞ e?q2
Where x is either E (excitation) or I (inhibition); s is the tuning sharpness; gmax
and gminare the conductances at preferred and nonpreferred orientation
(see Table 1). R is the reversal potential of the respective conductance.
Vr(?50mV) is the cell’s resting potential.
The firing rate was computed as [DV(q) ? Vthres]n+, where Vthres, the spike
threshold, was 4mV (relative to rest) and exponent n was 3 (Priebe et al.,
2004). The subscript ‘‘+’’ indicates rectification, i.e., that values below zero
were set to zero.
The tuning properties of excitatory and inhibitory synaptic conductances
(i.e., s, gmin, gmax) in layer 2/3 Pyr cells were determined using whole-cell
recordings voltage-clamp configuration where cells were held at the reversal
potential for inhibition and excitation, respectively. The average visually
evoked conductance was then determined for each of the six orientation of
drifting gratings presented (Figure 5C). The result was fit with a Gaussian, gX.
Statistical significance was determined using the Wilcoxon sign rank, and
rank sum tests where appropriate.
Supplemental Information includes Supplemental Experimental Procedures
and five figures and can be found with this article online at doi:10.1016/j.
We would like to thank C. Niell and M. Stryker for providing expertise and
sharing code at the initial stages of this project; H. Adesnik for his help
implementing optogenetic approaches; S.R. Olsen for his insights and help
in developing the visual recording configuration; and J. Evora, A.N. Linder,
and P. Abelkop for histology and mouse husbandry. M.C. holds the
GlaxoSmithKline / Fight for Sight Chair in Visual Neuroscience. B.V.A. was
supported by NIH NS061521. This work was supported by the Gatsby
Charitable Foundation and HHMI.
Accepted: December 13, 2011
Published: January 11, 2012
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RE= 0 mV (see Figure 5)
s = 70 deg; gmax= 7 nS; gmin6 nS;
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