1Graduate Group in Biophysics, 2Departments of Physiology and Otolaryngology, 3Sloan-Swartz Center for Theoretical Neurobiology, and 4W. M. Keck Center for Integrative Neuroscience, University of California, San Francisco, California 94143-0444
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ABSTRACT |
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Lauritzen, T. Z., A. E. Krukowski, and K. D. Miller. Local Correlation-Based Circuitry Can Account for Responses to Multi-Grating Stimuli in a Model of Cat V1. J. Neurophysiol. 86: 1803-1815, 2001. In cortical simple cells of cat striate cortex, the response to a visual stimulus of the preferred orientation is partially suppressed by simultaneous presentation of a stimulus at the orthogonal orientation, an effect known as "cross-orientation inhibition." It has been argued that this is due to the presence of inhibitory connections between cells tuned for different orientations, but intracellular studies suggest that simple cells receive inhibitory input primarily from cells with similar orientation tuning. Furthermore, response suppression can be elicited by a variety of nonpreferred stimuli at all orientations. Here we study a model circuit that was presented previously to address many aspects of simple cell orientation tuning, which is based on local intracortical connectivity between cells of similar orientation tuning. We show that this model circuit can account for many aspects of cross-orientation inhibition and, more generally, of response suppression by nonpreferred stimuli and of other nonlinear properties of responses to stimulation with multiple gratings.
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INTRODUCTION |
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Cells in cat primary visual
cortex (V1) are tuned for the orientation of light/dark borders
(Hubel and Wiesel 1962). Understanding the circuitry
underlying this orientation selectivity remains a central problem in
systems neuroscience (reviewed in Ferster and Miller
2000
).
Clues to the underlying circuitry are provided by experiments involving
the superposition of two drifting sinusoidal luminance gratings. A
typical simple cell in layer 4 of cat V1 responds to a drifting grating
shown at its preferred orientation and is silent in response to a
drifting grating of the perpendicular (null) orientation. However,
superposition of the null grating with the preferred causes a reduction
in response relative to the response to the preferred grating alone, a
phenomenon known as "cross-orientation inhibition" (Bonds
1989; DeAngelis et al. 1992
; Morrone et
al. 1982
). More generally, superposition of a nonpreferred
grating can suppress responses to a preferred grating (Bonds
1989
; DeAngelis et al. 1992
).
This suppression suggests that a nonpreferred grating recruits
inhibition and/or disrupts the cell's excitatory drive. In particular,
the existence of cross-orientation inhibition has led to the suggestion
that inhibition from cells tuned to dissimilar orientations plays an
important role in setting the gain of cortical responses
(Carandini and Heeger 1994; Carandini et al.
1997
, 1999
; Heeger 1992
; Heeger et al.
1996
). However, evidence from intracellular recordings argues
against this idea. Such recordings show that the excitation and the
inhibition received by simple cells in cat layer 4 show similar
orientation tuning, with both peaked at the preferred orientation and
falling to small values at the orthogonal orientation (Anderson
et al. 2000a
; Ferster 1986
), and that
the orientation selectivity of voltage responses is neither created,
nor sharpened, by intracortical circuitry (Chung and Ferster
1998
; Ferster et al. 1996
).
In this paper, we show that a simple model circuit that is consistent
with the intracellular data can account for many of the two-grating
suppression effects, including cross-orientation inhibition. This model
circuit was originally inspired by the findings that the inhibition and
excitation received by a layer 4 simple cell have similar orientation
tuning (Anderson et al. 2000a; Ferster
1986
) but are in a "push-pull" or spatially opponent relationship (Ferster 1988
; Hirsch et al.
1998
): in ON subregions, where light evokes
excitation, dark evokes inhibition, and similarly dark evokes
excitation and light evokes inhibition in OFF subregions. Accordingly, we proposed (Troyer et al. 1998
) that
excitatory cells tend to make connections onto cells of similar
preferred orientation and similar absolute spatial phase (similar
locations in visual space of ON subregions and of
OFF subregions), while inhibitory cells tend to project to
cells of similar preferred orientation and opposite absolute spatial
phase. In addition, we assumed that the connections from the
lateral geniculate nucleus (LGN) to a simple cell are organized in an
oriented, subregion-specific manner (Chung and Ferster
1998
; Ferster et al. 1996
; Hubel and Wiesel 1962
; Reid and Alonso 1995
; Tanaka
1983
): ON center LGN inputs have receptive fields
aligned over the simple cell's ON subregions, and
OFF center inputs are aligned on OFF
subregions. We showed (Troyer et al. 1998
) that,
provided that the LGN-driven inhibition was stronger than the direct
LGN excitation, this circuitry could account for the invariance with
stimulus contrast of orientation tuning (Sclar and Freeman
1982
; Skottun et al. 1987
) and for a number of
other intracellular and extracellular observations. Here we show that
this circuitry can also account for cross-orientation inhibition and
more generally for a variety of two-grating suppression phenomena.
One of the more extensive experimental studies of such suppression was
done by Bonds (1989). He used as a visual stimulus a
preferred (base) grating at one temporal frequency and a superposed mask grating at a different temporal frequency. By analyzing the two
corresponding temporal components of the response, he separated the
base- and mask-driven response components and studied how each
component depended on the orientation, contrast, and spatial frequency
of the mask grating. In our modeling studies, we follow this procedure
to determine how closely our model is able to reproduce these
experimental observations. We also address two other experiments examining responses to superpositions of gratings with different temporal frequencies at the preferred orientation (Dean et al. 1982
; Reid et al. 1992
). These experiments found
that the modulation of the cell response to low-temporal-frequency
stimuli is suppressed by the superposition of high-temporal-frequency
stimuli, while the modulation of the cell response to
high-temporal-frequency stimuli is enhanced by superposition of
low-temporal-frequency stimuli. Here we reproduce these results and
explain some of the findings by a toy model.
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METHODS |
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We study a model previously described ("computational model"
of Troyer et al. 1998). The major difference in the
present work is that N-methyl-D-aspartate (NMDA)
receptors have been included at excitatory synapses onto excitatory
cells. Here we present only the basics of that model along with details
of any differences in the present implementation.
Our LGN model consists of 7,200 LGN X cells arranged in four overlying
30 × 30 sheets of ON cells and four similar sheets of
OFF cells, with ON and OFF lattices
offset by one-half square lattice spacing, covering 6.8 × 6.8°
of the visual field. LGN firing rates in response to a single grating
were calculated by assuming rates were sinusoidally modulated, up to
rectification at zero rate, about background rates of 10 and 15 Hz for
ON and OFF cells, respectively, with the
amplitude of the sinusoidal modulation chosen so that the first
harmonic (F1) of the rectified responses matched values at a given
contrast and temporal frequency reported by Sclar
(1987). To compute responses to multiple gratings, we added the
sinusoidal rate modulations induced by each grating and then rectified
the result. Spikes were then generated from these rates in a random
(Poisson) fashion. Overlaying cells have 25% correlation in their
spike trains (each of 4 overlaying cells picked spikes with probability
1/4 from a common set of 4 Poisson spike trains), to match data showing
correlations among LGN cells with overlapping receptive fields
(Alonso et al. 1996
).
The cortical model includes 1,600 excitatory- and 400 inhibitory layer
4 simple cells, representing a 2/3 × 2/3-mm patch of cortex,
corresponding to 0.75 × 0.75° in visual angle. Each cortical cell was assigned a Gabor-function describing its receptive field, with
orientation given by a measured orientation map from cat V1, spatial
frequency of 0.8 cycles/°, retinotopic position progressing uniformly
across the sheet, and spatial phase assigned randomly to each cell. The
precise parameters used for the Gabor functions were those specifying
the "broadly tuned" cells in Troyer et al. (1998),
which were designed to reproduce the observed (Anderson et al.
2001a
; Ferster et al. 1996
) 35° half-width at
half-height of the orientation tuning of intracellular voltage
modulations in response to optimal sinusoidal gratings. The connection
strength from LGN cells to a cortical cell was determined as in
Troyer et al. (1998)
by a probabilistic sampling of the
cell's Gabor function, where positive regions of the Gabor are
converted to probabilities of a connection from an ON cell
centered on that point and negative regions converted to probabilities
of OFF cells connecting.
Cortical cells were modeled as single-compartment
conductance-based integrate-and-fire neurons as in Troyer et al.
(1998), with the following differences. The cortical background
excitatory input (Poisson) received by all cells was set to a rate of
6,000 Hz, resulting in background firing rates of approximately 0.5 Hz
for excitatory cells and 20-30 Hz for inhibitory cells. The amplitude
of the adaptation conductance,
); this
yielded reasonable levels of excitatory cell gain as measured from
plots of firing rate versus instantaneous membrane potential.
Finally, synaptic conductances were identical to those used in
Troyer et al. (1998) except that we have included
NMDA-mediated conductances, in addition to the AMPA-mediated
conductances, in all of the excitatory synapses except for the
thalamocortical synapses onto inhibitory cells, which were purely AMPA
mediated. NMDA receptors were included simply because we believe they
make the model more realistic and allow the model to explain cortical temporal frequency tuning (Krukowski and Miller 2001
) as
well as orientation tuning (Troyer et al. 1998
);
inclusion of NMDA receptors has therefore become the "default" for
our lab's studies of the correlation-based circuit. We used parameters
determined in other studies (Krukowski 2000
;
Krukowski and Miller 2001
) and did not tune parameters
to address the present issues. The inclusion of NMDA receptors impacts
the present issues only in reducing the F1/DC ratio at higher temporal
frequencies, which turns out to be crucial to explaining the effects of
mixing low- and high-temporal frequency gratings (see
Modulation changes with multiple gratings in
RESULTS and DISCUSSION).
The decay of the NMDA conductances is modeled as a double exponential
with a fast and a slow time constant
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The probability that a cortical cell connected to any other cortical
cell depended on the correlation between their sets of LGN inputs, as
in Troyer et al. (1998): the probability of a connection from an excitatory cell monotonically increased with the degree of
correlation, while the probability of a connection from an inhibitory
cell monotonically increased with the degree of anticorrelation. This
connectivity rule yields the basic cortical circuit structure within a
single iso-orientation column shown in cartoon form in Fig.
1A. For simplicity, the
inhibitory cells received only thalamocortical input. Previous
simulations have demonstrated that intracortical excitatory connections
onto inhibitory cells do not have a significant effect on the behavior
of the model (Krukowski 2000
; Troyer et al.
1998
). An important feature of the model is that the inhibition is dominant over feedforward excitation, rather than precisely balancing it.
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Simulations for a given grating or multi-grating stimulus were run as follows. We first allowed the network to run for 1 s of simulated time while LGN cells fired at their background rates. We then started the grating stimulus and allowed the simulation to run an additional 0.25 s to suppress transients, then recorded data for 1 s of simulated time as the grating stimulus continued. Peristimulus time histograms (PSTHs) of 20 such simulations (each with different seeds for the random number generator controlling the Poisson sampling of LGN spikes) were made for the spiking results. Cells of all orientation preferences are represented in the cortical network. To be certain of avoiding artifacts of alignment of the grid with the stimulus, the preferred-orientation stimulus was always at an orientation of 128°, and we sampled our results from the 35 excitatory cells with preferred orientations within ±2.5° of 128°.
Toy rate model
In modeling responses to sums of two grating stimuli at the
preferred orientation at different temporal frequencies, we considered both the full model as described in the preceding text and a simple toy
model. The toy model was based on the mean (DC) and first harmonic (F1)
of the feedforward input (the LGN-driven input, both direct LGN
excitation and indirect inhibition via interneurons) observed in the
full model. We assumed that the feedforward inputs due to the two
sinusoids were simply added and the result passed through a linear
threshold input/output curve. We considered 2 sine curves:
y2 Hz(t) = sin
(4t)
2 Hz,
y8 Hz(t) =
[sin
(16
t)
8 Hz], where
t is in seconds,
is the amplitude of the 8-Hz grating
relative to that of the 2-Hz grating, and the
's are the
inhibitory total feedforward DC (the sum of LGN excitation and inhibition from LGN-driven inhibitory interneurons). We estimated the size of the
's in the full model by examining the total
synaptic current evoked when the membrane potential is clamped at spike threshold in response to a 2-Hz grating alone and an 8-Hz grating alone, where grating contrasts were chosen so that evoked current F1's
were comparable (2-Hz grating at 20% contrast, 8-Hz grating at 40%
contrast, ratio of 2-Hz F1 to 8-Hz F1 is approximately 0.9). Defining
as DC/F1 of the resulting currents, we found
8
Hz = 0.42 and
2 Hz = 0.019. We
considered a linear rectified model of response
r(t) to an input waveform
i(t): r(t) = [i(t)
]+, where
is a
threshold (values used given in RESULTS) and
[x]+ = x, x > 0;
[x]+= 0, x
0. To model
single sinusoids, i(t) is set equal to
y2 Hz(t) or
y8 Hz(t); for double
sinusoids, i(t) = y2
Hz(t) + y8 Hz(t). We then examined the Fourier component of r(t) at
2 and/or 8 Hz.
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RESULTS |
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Basic concepts of the model circuit
To understand our results, it is important to recall the main ideas of our circuit model, which will figure prominently in the following results (Fig. 1). We define feedforward input to excitatory cells as the sum of the direct LGN excitatory input and the LGN-driven input from inhibitory neurons. Due to the dominant antiphase inhibition, the mean feedforward input evoked by grating stimuli is inhibitory. Cortical excitatory simple cells can only be driven to fire by the temporal modulation of this input: inhibition and excitation are driven at opposite phases of the modulation, so that one goes up when the other goes down. This modulation allows excitation to periodically dominate over inhibition and drive responses even though inhibition dominates in the mean (Fig. 1B).
The mean LGN input evoked by a grating does not depend on grating orientation (because this mean is just the weighted sum of the mean rates of the individual LGN inputs to the simple cell, and the responses of LGN cells are assumed to be untuned for orientation). But the modulation of the LGN input varies strongly with orientation. In response to a preferred orientation stimulus, all of the LGN inputs to a cell modulate their firing rates together so the total LGN input to the cell is strongly modulated and the cell periodically fires (Fig. 1B). As the stimulus orientation is moved away from the preferred, the different LGN inputs to a cell come to be increasingly desynchronized in their rate modulations. These modulations at different phases wash out so that the net input to the cell becomes temporally steady and unmodulated, albeit with the same mean, and the cell is inhibited (Fig. 1C).
The net feedforward inputthat is, the sum of the LGN input and the
antiphase inhibition
is determined by the LGN input as follows. The
mean LGN input evokes a net inhibitory mean feedforward input due to
the dominance of inhibition in our circuit. The anti-phase inhibition
amplifies the modulation of the LGN input, yielding a stronger
modulation of the net feedforward input. We previously showed that this
combination of net inhibitory mean feedforward input, which is untuned
for stimulus orientation, and the orientation tuning of the modulation
of the feedforward input could account for the contrast-invariance of
cortical orientation tuning (Troyer et al. 1998
). Here
we show that the same principles can explain suppression effects such
as cross-orientation inhibition.
Finally, we introduce our terminology. We characterize a response to a periodic stimulus by the mean response, referred to as the "DC" of the response, and the amplitude of the response modulation at the temporal frequency of the stimulus, referred to as the "F1" of the response (for "first harmonic"). Note that the peak value of the response is roughly given by the sum DC + F1.
Cross-orientation inhibition
In the model circuit, the response to a base grating at the preferred orientation is suppressed by simultaneous presentation of a mask grating at the null orientation (the orientation perpendicular to the preferred). Two factors contribute to this suppression (Fig. 2). First, the preferred-orientation stimulus evokes synchronized modulation of the firing rates of the LGN inputs to a simple cell, but superposition of the null stimulus disrupts this synchronization. This reduces the F1 of the net LGN input to a simple cell. This is a small effect in the model. Second, superposition of the null stimulus increases the mean spiking rate of the LGN inputs and thus the DC of the net LGN input to a simple cell. This is converted by the dominant antiphase inhibition in the circuit into an increased negative feedforward DC input to the simple cell. The combination of these two effects provides sufficient suppression to match many aspects of the suppression observed experimentally, including the illustrated cross-orientation inhibition. Note that the superposition of the second grating yields an increase in the peak input (DC + F1) of the LGN input, so that simple cell responses would be increased by addition of the second grating if only LGN input were considered.
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Contrast dependence of cross-orientation inhibition
The amount of suppression is dependent on the mask contrast. The
mean spike response to a base grating at the preferred orientation decreases with the contrast of a mask grating at a nonpreferred orientation, both in a cell from Bonds (1989) (Fig.
3A) and in simulations (Fig.
3C). The curve of response versus base contrast is shifted
downward or rightward with increasing mask contrast, with little change
in slope, both in an experimental cell (Fig. 3B) and in
simulation (Fig. 3D). Both response versus base contrast and
suppression versus mask contrast are stronger in the experimental cells
illustrated than in simulation, but the degree of suppression for a
given ratio of base to mask contrast is more comparable.
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Recent experiments by Sengpiel et al. (1998) also
addressed the effect of inhibition by a second grating on the
contrast-response curve. They described the contrast-response function
by a hyperbolic ratio function, R = Rmax
(Fig. 4A). The
inhibition in the model is similarly described well by a rightward
shift of the contrast response function (Fig. 4B).
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Effect of cross-orientation inhibition on orientation tuning
We examined the effects of a mask stimulus at the null orientation on the response tuning for the orientation of a base grating (Fig. 5). The mask-induced suppression does not significantly alter the orientation tuning in the model: when the response tuning curve in the presence of the mask is scaled to have the same height as the response tuning curve in the absence of the mask, the two curves become almost identical. Thus the effect of the suppressing grating on the orientation tuning curve is predicted to be mainly divisive.
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Dependence of suppression on mask orientation
The initial concept of cross-orientation inhibition has been
broadened by several experiments to that of a more general, nonspecific suppression of the response to a preferred stimulus by superposition of
a second stimulus (Bonds 1989; DeAngelis et al.
1992
). Here we focus on the experiments of Bonds
(1989)
, who used as stimuli superimposed pairs of sine
gratings: a base grating at the preferred orientation and 2-Hz temporal
frequency, and a mask grating at 3 Hz (or other temporal frequencies,
considered later) and various orientations, as illustrated in Fig.
6. By decomposing the cell's response
into two F1's, one at each temporal frequency, as well as a DC, the
separate response to each grating was assessed: the F1 at 2 Hz
represents response to the base grating, while the F1 at 3 Hz
represents response to the mask grating. This allowed Bonds
(1989)
to determine the effect of the orientation of the mask
grating on the response to the base grating.
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We have mimicked this procedure in our simulations (Fig.
7). In both experiments and simulations,
the mask grating at nonpreferred orientations suppressed the DC spike
response, and the tuning of this DC response with mask orientation is
similar to the excitatory orientation tuning curve to a single grating
(Fig. 7, A and E). Similarly, both experiment and
simulation show tuning of the 3-Hz (mask) F1 component of the response
with the mask orientation, again following the excitatory
orientation-tuned response of the cell (Fig. 7, B and
F). The effects of the mask on the 2-Hz (base) F1 component
of the response is more complex. Experimentally, Bonds
(1989) found 11 of 14 cells showed suppression of the base component that was untuned for mask orientation (Fig. 7C),
while 3 of 14 cells showed broad tuning for mask orientation (Fig.
7D). In simulations, we find that the 2-Hz component of the
intracellular current shows suppression that is untuned for mask
orientation (Fig. 7G), but the 2-Hz component of the spiking
response shows broadly tuned suppression (Fig. 7H) akin to
that seen in a minority of cells by Bonds. This tuning of the base
spike response arises from the addition of an untuned base current
component and a tuned mask current component followed by a
rectification to give the spike response.
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Neither simulation results nor experimental results (Bonds
1989) depended on the relative spatial phase of the two
gratings (not shown).
Temporal frequency dependence of the suppression
By keeping the base grating at 2 Hz and varying the temporal
frequency of the mask grating, Bonds (1989) investigated
the temporal characteristics of the cortical suppression. We first examine the dependence of suppression on mask contrast and temporal frequency (Fig. 8). In the experiments,
strong suppression is found for lower temporal frequencies (2 and 8 Hz), with a decrease in suppression at 16 Hz. In simulations, 8- and
16-Hz masks evoke greater suppression than the 2-Hz mask, but the
suppression does decrease between 8 and 16 Hz.
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We next examine the dependence of suppression on mask orientation and temporal frequency (Fig. 9). In experiments, the total (DC) response (Fig. 9A) shows suppression for masks at OFF orientations that decreases with mask temporal frequency until, for a mask of 32 Hz, there is no inhibitory effect at all. When the mask is at the preferred orientation, the lowest frequencies evoke no suppression. The mask response (Fig. 9B) is, not surprisingly, tuned with mask orientation, and the excitation decreases with temporal frequency. The excitation actually cuts off earlier than the suppression: at 16 Hz, there is little excitatory effect of the mask, while there is still a significant inhibition of the DC and base responses. The suppression of the base response (Fig. 9C) is untuned with mask orientation, and the inhibition is highest for low temporal frequencies and decreases with increasing temporal frequencies, as in Fig. 8. Our simulations (Fig. 9, D-F) are similar except that, again, 3-Hz gratings evoke less suppression than higher temporal frequencies, and the base component of the spiking response shows orientation tuning (although again, the base component of the current response is untuned).
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To understand the temporal-frequency tuning of suppression in our model, we examined the thalamocortical and full-circuit input to cells when adding a varying-temporal-frequency mask grating at the orientation orthogonal to a preferred-orientation 2-Hz base grating (Fig. 10). We assume that the 2-Hz component of the response is roughly determined by the sum of the DC and the 2-Hz F1, representing the peak reached by the 2-Hz component when ignoring the other modulating components. The LGN input shows an increased DC component for 8- and 16-Hz masks relative to that for a 3-Hz mask, while the 2-Hz F1 component is slightly reduced. The cortical circuit amplifies both the DC and 2-Hz F1 component and reverses the DC component. The superposition of the 2-Hz F1 and DC then results in a peak input (F1 + DC) that is lower for the higher-temporal-frequency masks.
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According to the experiments, the peak input should increase for the
higher mask temporal frequencies, suggesting flaws in our models either
of the LGN DC and/or F1 or of inhibitory cell temporal tuning. However,
after this work was completed, we learned of recent experiments
(Durand et al. 2001; A. B. Bonds, unpublished data)
suggesting that the temporal tuning of suppression actually is more
like that predicted by the model; we return to this in the
DISCUSSION.
Spatial-frequency dependence of the suppression
Cortical cells show band-pass tuning for the spatial frequency of
a grating. This band-pass tuning is expected to also influence suppressive effects. Figure 11 shows
experiments (Bonds 1989) and simulations of cell
responses with varying spatial frequency of the base and mask. The
experiments show that tuning of the suppression for mask
spatial-frequency is broader than the cell's excitatory spatial tuning
bandwith. Furthermore the bandwith of the suppression increases with
mask contrast. In our simulations, inhibitory cells and excitatory
cells have similar spatial frequency tuning (they have identical
Gabor-functions defining their receptive fields), and as a result, the
suppression and excitatory tuning have similar bandwidth, suggesting a
flaw in our model of inhibitory cell receptive fields. However, the
simulations do show some broadening of the tuning of suppression with
contrast.
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Modulation changes with multiple gratings
When stimulating simple cells with a superposition of a high- and
a low-temporal-frequency grating, the F1 of the spike response at the
lower frequency is decreased relative to that evoked by the
low-temporal-frequency grating alone. At the same time the F1 at the
higher temporal frequency is enhanced compared with its value for a
single grating. This was shown by Dean et al. (1982),
who obtained results for 18 simple cells at 1.25- and 7.75-Hz temporal
frequency using counter-phase gratings. When restricted to cells for
which the ratio of the response amplitudes to each frequency presented
alone was between 0.8 and 1.2, they found a mean relative response
modulation (ratio of F1 when 2 gratings shown together to F1 of single
grating alone) of 0.77 at 1.25 Hz and 1.23 at 7.75 Hz. Across all
cells, they found mean changes in the same directions (Dean et
al. 1982
, Fig. 2). In our simulations, we use drifting rather
than counterphase gratings so that the modeled responses will not
depend on the absolute spatial phase of the cells, allowing cells of
all absolute spatial phases to be studied simultaneously. Using 2- and
8-Hz gratings with contrasts chosen to yield similar responses to each
grating alone, we find a relative response modulation of 0.60 at 2 Hz and 1.09 at 8 Hz (Fig. 12A).
Thus the strength of suppression and the direction, although not the
strength, of enhancement are roughly replicated by our model.
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This can be understood from a simple toy model as illustrated in Fig.
13. We assume that each grating alone
evokes both a sinusoidal oscillation and a negative DC; the
superposition of the gratings is modeled simply by adding their
oscillations and DCs. The resulting waveform is rectified at a
threshold and the F1 of the rectified response is computed. The model
has four parameters: the threshold , expressed as a percentage of
the amplitude of the 2-Hz oscillation; the sizes
2 Hz
and
8 Hz of the negative DCs, relative to the amplitude
of their respective sinusoidal oscillations; and the amplitude
of
the 8-Hz oscillation relative to that of the 2 Hz. This toy model is
similar to one considered by Dean et al. (1982
, their
Fig. 1), except that their model did not include the negative DCs,
i.e., in their model,
2 Hz =
8
Hz = 0. They found that their toy model could not
explain their results, and indeed we shall find that the negative DCs
are critical to our explanation of the results.
|
In simulations of the full model, we find 8 Hz = 0.4232 and
2 Hz = 0.0187 (see METHODS), and so
accordingly in our toy model, we initially consider
8 Hz = 0.4 and
2 Hz = 0. We first choose
so that, after
rectification, the 2-Hz grating alone and the 8-Hz grating alone evoke
similar F1's. Examining results across values of the threshold (Fig.
12B), we find that for thresholds less than 0.3, this simple
model replicates the basic result of the experiment: the low-frequency
F1 decreases, and the high-frequency F1 increases, when the two
sinusoids are added together. Next we fix the threshold at 0.2 and find
that across all values of
, the same basic result is obtained (Fig.
12C).
Finally we examine the dependence of the results on the two
's, that is, on the size of the negative DC offset evoked by the
two gratings, for fixed values of the threshold and relative amplitude
(Fig. 12, D-F). Small or negative values of
2
Hz and high (positive) values of
8 Hz yield
changes in the experimentally observed directions: for these values of
the
's, the 2-Hz F1 is decreased (negative "2-Hz F1 difference"
in Fig. 12D) and the 8-Hz F1 is increased (positive "8-Hz
F1 difference" in Fig. 12E) when the two sinusoids are
added together. To better ascertain the parameter range over which each
F1 is changed in the appropriate direction, we multiply the negative
region of the 2-Hz change (positive values set to 0) with the positive
region of the 8-Hz change (negative values set to 0) and take the
absolute value of the result; contours of this result are shown in Fig.
12F. The contours increase with approach toward the lower
right corner, that is, as
8 Hz increases and
2
Hz decreases. (The parameter region that gives the desired
result increases when the threshold is decreased or the relative 8-Hz
amplitude is increased, not shown.) Thus we conclude that it is
critical to the observed result that an 8-Hz grating evoke a larger
negative DC, relative to its F1, than a 2-Hz grating. (This occurs in
our full model due to the slow time course of NMDA conductances, which
lowers the F1/DC ratio for higher frequencies; see
DISCUSSION.)
Reid et al. (1992) studied the superposition of eight
counter-phase gratings of increasing temporal frequencies. As in the two-grating paradigm of Dean et al. (1982)
, they found
that the modulation of low temporal frequencies is depressed and that
of high temporal frequencies is enhanced in the superposition relative to that of the constituent sinusoids. We again use drifting gratings, and examine the F1 responses of our full model at each of eight stimulus frequencies, in response to each of the eight individual sinusoids alone and in response to their superposition (Fig.
14). As in the experiments, the F1's
at lower temporal frequencies are decreased and those at higher
temporal frequencies are increased in the superposition, relative to
the single gratings. We find a cross-over point from depression to
elevation between 4 and 5 Hz slightly lower than, but comparable to,
the experimentally found cross-over of 6-8 Hz (Reid et al.
1992
).
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DISCUSSION |
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We have shown that a simple correlation-based local circuit can account for many aspects of cortical responses to multiple gratings, including many features of the dependence of suppression or enhancement on a mask grating's orientation, spatial frequency, and temporal frequency as well as the effects of mixing sinusoids of multiple temporal frequencies. The model predicts that superposition of a mask grating orthogonal to the preferred orientation should cause little change in orientation tuning to a base grating, having a primarily divisive effect on the orientation tuning curve; to our knowledge this has not been tested. It also predicts that high-temporal-frequency (e.g., 8 Hz) gratings should evoke a stronger negative DC for a given F1 amplitude than low-temporal-frequency gratings (e.g., 2 Hz), and that this larger DC at higher frequencies is critical to explaining the effects of mixing sinusoids of multiple temporal frequencies (see Figs. 12 and 13).
The circuit model that attains these results (Troyer et al.
1998) rests on three basic assumptions. First, both the
excitation and inhibition received by a simple cell come from other
cells of similar preferred orientation (Anderson et al.
2000
), but the excitation and inhibition are evoked by opposite
polarities (light or dark) at any given point in the receptive field
(Ferster 1988
; Hirsch et al. 1998
).
Second, the inhibition dominates, rather than balances, excitation in
the cortical circuitry. This dominance is supported by experiments
showing that even slight movement of a spot stimulus across a subregion
boundary is sufficient to cause the spot to evoke net inhibition
(Hirsch et al. 1998
), as well as by experiments showing
that nonspecific shock of the LGN evokes massive inhibition in cortex
(Ferster and Jagadeesh 1992
). It is this excess
inhibition that primarily accounts for the cross-orientation (or
"second grating") suppression. Third, the inhibitory neurons in the
model respond to all orientations, although they are orientation-tuned: their tuning curves resemble a tuned hill atop an untuned platform (Troyer et al. 1998
). Recent results find two types of
inhibitory interneurons in cat V1 layer 4: simple cells that show good
orientation tuning and complex cells that are untuned for orientation
(Hirsch et al. 2000
). It is possible that these
separately embody the two components of inhibitory tuning
the tuned
hill and the untuned platform
that we are attributing to a single
class of cells.
The model points to two basic sources of second-grating suppression. In
the model, the degree of activation of a cell is determined by the size
of the temporal modulation or F1 of a simple cell's LGN input,
relative to the size of the mean level or DC of this input: the F1
leads to activation, while the DC is transformed by the dominant
antiphase inhibition into a net suppression. Thus the second grating
may suppress responses in either of two ways: by lowering the F1 of a
simple cell's LGN input, e.g., due to desynchronization of the rate
modulations of the individual LGN inputs to a cell, and/or by raising
the DC level of the cell's LGN inputs, evoking net inhibition. In our
hands, the change in F1 is a small effect, but our model of LGN
response is currently very simple: we assume LGN spike-rate responses
to the two gratings add linearly up to rectification at zero firing
rate. Furthermore, short-term synaptic depression of geniculocortical
synapses, which we have not considered here, can lower the base F1 of
the LGN input in the presence of a mask, as discussed in the following text. Thus it is possible that in reality this could be a larger effect. In our hands, the increase in DC and the resulting inhibition is the primary source of suppression. However, synaptic depression can
suppress this DC at lower temporal frequencies, discussed in the
following text. Furthermore Bonds (1989) shows results from a few LGN cells suggesting that the response to two gratings is
sublinear relative to the response to each grating alone with little
change in DC. It will be important to better characterize both the
degree to which the DC of the LGN input grows, and the manner in which
the F1 of the total LGN input received by a simple cell alters, when a
mask grating is added to the base grating.
A paradigm we have not addressed here is that when a cell is tonically
excited by a one-dimensional noise stimulus at the preferred
orientation , a counterphase grating at the null orientation
=
+ 90° induces frequency-doubled suppression (Morrone et al. 1982
). This has led to the suggestion that suppression may be mediated by complex cells or a pool of simple cells of many preferred phases preferring the null orientation
(Bonds
1989
; DeAngelis et al. 1992
; Morrone et
al. 1982
). We have not attempted to simulate either noise or
counterphase stimuli, but it is worth noting that this frequency
doubling is expected in our model. Each of the two opposite phases of
the counterphase grating at angle
will excite roughly half the LGN
inputs to an inhibitory cell preferring angle
and inhibit the other
half. The LGN inputs that are excited can raise their firing rates much
more than those that are inhibited can lower their firing rates
(because lowering is bounded at 0 firing rate), so the net result is
that each phase produces a pulse of increased LGN input causing the
inhibitory cell to respond. Because inhibition dominates excitation,
the feedforward inhibition evoked by the pulses of LGN input will exceed the feedforward excitation they evoke, and a frequency-doubled suppression of excitatory cell responses will result.
Role for synaptic depression?
Since this work was completed, Carandini and colleagues have
reported that cross-orientation suppression has temporal frequency tuning like that of LGN inputs (Durand et al. 2001) and
is not affected by a period of adaptation to a cross-oriented stimulus (Freeman et al. 2001
). Based on these results and
previous findings that cross-orientation suppression is largely, though
not entirely, monocular (Walker et al. 1998
), they
proposed that cross-orientation suppression does not stem from the
firing of cortical cells but rather from short-term synaptic depression
of geniculocortical synapses (Durand et al. 2001
;
Freeman et al. 2001
).
We had examined the effects of including such depression in our model
(modeled as in the "pulse" parameters of Kayser et al. 2001) and found that it does not substantially alter our
results as to the contrast, temporal, spatial, and mask orientation
tuning of mask suppression or the effects of combining two or more
gratings of different temporal frequencies (unpublished data). However, we have now reexamined this and found that inclusion of depression does
alter the mechanism of suppression: in the presence of
synaptic depression, the base F1 component of the LGN input is
substantially decreased by the presence of a mask. Synaptic depression
also substantially lowers the DC of the LGN input to low temporal
frequencies (e.g., 3 Hz) but not to higher temporal frequencies (e.g.,
8 Hz) (Krukowski 2000
). The result is that when the base
grating is combined with a low-temporal-frequency mask, the DC is near
zero so the inhibition plays little role, and most of the mask
suppression is due to the lowering of the base F1 by synaptic
depression. However, when the base grating is combined with a
high-temporal-frequency mask, the DC is substantial, and so the
combination of the suppression of the base F1 by depression and the
reversal of the DC by antiphase inhibition is needed to explain mask suppression.
A strong argument for a role of inhibition is that, when a cell's
firing rate is elevated by iontophoresis of an amino acid, a
cross-oriented stimulus reduces responses (Ramoa et al.
1986). This has no obvious explanation in terms of synaptic
depression of geniculocortical synapses but is easily explained by inhibition.
An important distinction between feedforward inhibition and synaptic
depression as mechanisms mediating mask suppression is that the former
should have essentially instantaneous effects while the latter should
take some time to develop. While feedforward inhibition involves an
extra synapse relative to LGN excitation, inhibitory cells have lower
thresholds and are the first to spike in response to LGN excitation so
that feedforward inhibition arrives within a few milliseconds of the
arrival of LGN excitation (Ferster and Jagadeesh 1992).
However, it is possible that the effects of geniculocortical depression
become substantial over the time in which a cortical cell integrates
its inputs before spiking so that depression effects also would appear
to be instantaneous in extracellular recording. Both theoretical
studies of the time course of mask suppression expected from synaptic
depression, and experimental characterization of the time course of
mask suppression, will be of great interest.
The finding that adaptation to a cross-oriented stimulus does not alter
the strength of cross-orientation suppression (Freeman et al.
2001) suggests that the layer 4 inhibitory neurons in our model
should not show contrast adaptation or at least not in response to a
cross-oriented stimulus. To our knowledge, the presence of contrast
adaptation in inhibitory neurons has never been tested; it would be
very interesting to test this prediction. However, it will also be
important to determine whether adaptation affects the strength of
cross-orientation suppression induced by higher-temporal-frequency masks since it is these masks that should elicit the strongest inhibition in the presence of synaptic depression.
Failures of the model
While the model captures a wide array of results, it also fails in
two or three notable ways. One apparent failure is that suppression in
the experiments of Bonds (1989) is tuned to lower mask
temporal frequencies than in the model. However, after this work was
completed, we learned of new experiments by Bonds (unpublished data)
and by Durand et al. (2001)
, both reporting the
high-temporal-frequency cutoff of suppression to be in the range of
16-20 Hz, similar to our findings (also seen in Morrone et al.
1982
). Thus what appeared to be a flaw in the model may instead
turn out to be an accurate prediction. This high cutoff arises in our
model because the temporal frequency tuning of the inhibitory neurons
follows that of the LGN input.
This leaves two remaining problems. First, suppression in experiments
is more broadly tuned for mask spatial frequency than in the model
(also seen in DeAngelis et al. 1992; Morrone et
al. 1982
). Second, the majority of cells studied experimentally
showed no tuning for mask orientation of the base component of
response, whereas in the model there is such tuning.
It will be important to determine these properties for cells in layer
4, the layer that we are modeling. If they hold in layer 4, it would
suggest that two types of improvements are needed in the model. First,
we may need to consider inhibitory cell models that have broader tuning
or a broader variety of tunings for spatial frequency. The model
presently assumes that inhibitory neurons have the same
multiple-subregion Gabor receptive field shape as excitatory neurons. A
source for broader tuning was suggested by Toyama et al.
(1981), who reported that inhibition onto layer 4 simple cells
with multiple ON-OFF subregions may come primarily from
inhibitory layer 4 simple cells with single-subregion receptive fields.
Second, the tuning for mask orientation of the base response component
is a threshold effect: the addition of the untuned base component and
the tuned mask component of current, followed by rectification by the
spike threshold, yields a tuned base component of the spiking response.
Sufficient voltage noise can smooth away many threshold effects, and
voltage noise appears comparable in size to stimulus-induced voltage
modulations (Anderson et al. 2000b
; Arieli et al.
1996
; Paré et al. 1998
; Tsodyks et
al. 1999
), suggesting that exploration of higher-noise regimes
might remove the threshold-induced tuning.
Suppression and contrast
The modeled experiments (Bonds 1989) and other
reported results (DeAngelis et al. 1992
; Morrone
et al. 1982
) display a wide range of suppression strengths.
There does not seem to be any systematic connection between suppression
strengths and cell response properties or cortical position except that
simple cells are reported to show stronger suppression than complex
cells (Morrone et al. 1982
). Our cells often required
higher contrasts of both base and mask than in experiments to see a
given level of response or suppression, although the relative contrast
of base versus mask for a given strength of suppression was often
similar. Strength of overall responses can be varied without otherwise
altering circuit behavior by varying circuit parameters in a
coordinated way (Troyer et al. 1998
); thus the most
robust issue seems to be the relative contrast required to achieve a
given degree of suppression, rather than the absolute contrasts.
Furthermore, the relative contrast necessary to achieve a given degree
of suppression is also parameter-dependent in the model, depending in
particular on the overall strength of inhibition. We have used the
model as tuned for other experiments and not altered it to fit these data. The strength of response and suppression also depends on our LGN
model, which as we have noted is very simple and needs better characterization.
Modulation changes with multiple gratings
Our model reproduces the qualitative effects of modulation changes
for pairs of gratings found by Dean et al. (1982). The simple toy model we considered for this paradigm accords well with
this, showing the experimentally observed effect across parameters provided that the 8-Hz grating evokes a stronger negative DC for a
given F1 than the 2-Hz grating. This stronger negative DC at higher
frequencies arises in our full model due to the presence of NMDA
conductances in excitatory synapses; the slow time course of these
conductances suppresses the high-frequency F1 without altering the DC,
resulting in a higher DC/F1 ratio (e.g., Fig. 2.28, Krukowski
2000
). Frequency-dependent synaptic depression in
geniculocortical synapses can play a similar role, by differentially lowering the DC/F1 ratio of low-frequency stimuli (Krukowski
2000
).
Our result for the extension to eight sine gratings, Fig. 14, agrees
with the experimentally observed response amplitudes of cortical cells
(Reid et al. 1992). Reid et al. (1992)
further reported a decrease in integration time of the response to the eight sine gratings as determined by the slope of the curve of response
phase versus temporal frequency; the cells appear to respond faster.
They argue that these effects must be of cortical origin. We do not see
a change in integration time in our simulations (data not shown). We
have found (Kayser et al. 2001
) that increases in
contrast can advance the phase of response due to a number of
mechanisms including synaptic depression, spike-rate adaptation, and
increases in conductance. We can speculate that such effects might
contribute to the experimental result, since there is greater overall
contrast in the eight-grating stimulus than in the single-grating stimuli, although we do not see an effect in the present simulations.
Conclusion
Correlation-based or "push-pull" connectivity with dominant
inhibition has been shown to account for many experimentally observed properties of layer 4 of cat primary visual cortex. These include contrast-invariant orientation tuning (Troyer et al.
1998), cortical temporal frequency tuning that cuts off at much
lower frequency than LGN tuning (Krukowski and Miller
2001
), and various contrast-dependent nonlinearities
(Kayser et al. 2001
). The present results suggest that
this framework can also explain a range of suppression and enhancement
effects observed with multiple-grating stimuli. However, they also
suggest some modifications may be needed: in particular, our
inhibitory cell models may need to be modified to explain the broader
spatial-frequency tuning of suppression observed experimentally and we
may need to explore regimes with more realistic levels of voltage noise.
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ACKNOWLEDGMENTS |
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We thank A. B. Bonds and T. Troyer for many useful discussions and the anonymous reviewers for many useful suggestions.
This work was supported by a predoctoral fellowship from the Danish Research Agency (T. Z. Lauritzen) and National Eye Institute Grant RO1-EY-11001.
Present address of A. E. Krukowski: NASA Ames Research Center, Mail Stop 262-2, Moffett Field, CA 94035-1000.
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FOOTNOTES |
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Address for reprint requests: K. D. Miller, Dept. of Physiology, University of California, 513 Parnassus, San Francisco, CA 94143-0444 (E-mail: ken{at}phy.ucsf.edu).
Received 30 January 2001; accepted in final form 14 June 2001.
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