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The Journal of Neuroscience, June 15, 1998, 18(12):4785-4799
Synaptic Depression and the Temporal Response Characteristics
of V1 Cells
Frances S.
Chance,
Sacha B.
Nelson, and
L. F.
Abbott
Volen Center and Department of Biology, Brandeis University,
Waltham, Massachusetts 02254-9110
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ABSTRACT |
We explore the effects of short-term synaptic depression on the
temporal dynamics of V1 responses to visual images by constructing a
model simple cell. Synaptic depression is modeled on the basis of
previous detailed fits to experimental data. A component of synaptic
depression operating in the range of hundreds of milliseconds can
account for a number of the unique temporal characteristics of cortical
neurons, including the bandpass nature of frequency-response curves,
increases in response amplitude and in cutoff frequency for transient
stimuli, nonlinear temporal summation, and contrast-dependent shifts in
response phase. Synaptic depression also provides a mechanism for
generating the temporal phase shifts needed to produce direction
selectivity, and a model constructed along these lines matches both
extracellular and intracellular data. A slower component of depression
can reproduce the effects of contrast adaptation.
Key words:
primary visual cortex; short-term plasticity; direction
selectivity; contrast adaptation; simple cells; temporal summation
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INTRODUCTION |
The responses of cortical neurons to
time-dependent stimuli display a paradoxical feature. In primary
visual, auditory, and somatosensory cortices of rats, cats, and
monkeys, many neurons exhibit responses to oscillatory stimuli that
peak at frequencies of a few Hertz and fall rapidly to zero above ~10
Hz. This might give the impression that cortical neurons act as
low-pass filters of the sensory stimuli that drive them. However, the
same neurons can exhibit vigorous responses to transients, such as
rapid stimulus onsets, that have much of their power above 10 Hz. Why
do these neurons respond to high-frequency stimuli that are novel and
fail to respond to sustained stimuli over the same frequency range?
Neurons in the mammalian primary visual cortex (V1) display this
paradoxical feature along with a number of other characteristics that
reflect nonlinear temporal dynamics. Responses of V1 neurons fall off
at lower temporal frequencies and at slower image velocities than those
of neurons in the lateral geniculate nucleus (LGN) (Movshon et al.,
1978 ; Orban et al., 1985; Hawken et al., 1996). Nevertheless, V1
neurons respond briskly to transients that contain high-frequency
components, and responses to sustained stimuli are more transient than
would be predicted on the basis of steady-state responses to
oscillating images (Ikeda and Wright, 1975; Movshon et al., 1978;
Kulikowski et al., 1979; Tolhurst et al., 1980). When visual images
oscillating at different temporal frequencies are combined, V1
responses show nonlinear temporal summation. Even simple cells, which
show approximately linear summation over different spatial regions of
their receptive fields (Ferster, 1994), display nonlinear summation in
the temporal domain. Combining two oscillating (counterphase) gratings
with different temporal frequencies decreases the response to the more
slowly oscillating image and enhances the response to the
higher-frequency oscillation (Dean et al., 1982). V1 cells respond to
temporally irregular visual stimuli formed from sums of sinusoidal
oscillations at temporal frequencies well above the response cutoff for
simple sinusoidal oscillations (Reid et al., 1992). The phases of the responses of V1 neurons to temporally oscillating images shift as a
function of contrast, again revealing temporal nonlinearity (Dean and
Tolhurst, 1986; Carandini and Heeger, 1994). Nonlinear temporal
dynamics is likely to contribute to a number of features exhibited by
V1 cells, including direction selectivity (Reid et al., 1991; Jagadeesh
et al., 1993; Tolhurst and Heeger, 1997) and velocity tuning (Orban et
al., 1985). Intracellularly recorded membrane potentials from
directionally selective neurons stimulated with sinusoidally
oscillating gratings at certain spatial phases are distinctly
nonsinusoidal (Jagadeesh et al., 1993). The mechanisms responsible for
these temporal nonlinearities have not been identified.
In this paper, we explore the idea that short-term synaptic plasticity,
in particular synaptic depression, is an important element in the
nonlinear temporal dynamics that leads to enhancement of transient
responses, nonlinear temporal summation, variable phase shifts, and
direction selectivity. We also study the suggestion that a slow form of
synaptic depression plays a significant role in contrast adaptation of
V1 neurons (Nelson, 1991b; Finlayson and Cynader, 1995; Nelson et al.,
1997; Todorov et al., 1997). Synaptic depression is a particularly
prominent feature of transmission at neocortical synapses (Shaw and
Teyler, 1982; Deisz and Prince, 1989; Thomson and West, 1993; Thomson
et al., 1993). Short-term depression has been observed in studies of
cat visual cortex (Stratford et al., 1996), in rodent somatosensory
(Markram and Tsodyks, 1996; Tsodyks and Markram, 1997), motor (Thomson
and Deuchars, 1994; Castro-Alamancos and Connors, 1996), and visual
(Abbott et al., 1997; Varela et al., 1997) cortices, and at cat
(Stratford et al., 1996) and rat (Gil et al., 1997) thalamocortical
synapses. In our study of the dynamics of excitatory transmission from
layer 4 to layer 2/3 in slices of rat primary visual cortex (Abbott et
al., 1997; Varela et al., 1997), we measured and modeled several components of short-term synaptic plasticity acting over a number of
time scales. Most prominent among these were two forms of synaptic depression: one rapid, setting in within 5-10 presynaptic action potentials and requiring 300-600 msec for recovery, and the other much
slower, requiring many action potentials to reach full extent and
recovering in ~10 sec. The recovery time for the rapid form of
synaptic depression is in the correct range to contribute to the
frequency dependence of cortical responses. It is nonlinear and,
although suppressing sustained responses, can transiently transmit
rapid stimulus onsets with high efficacy. The faster component of
depression also acts on a timescale appropriate for contributing to
response phase shifts, including those responsible for direction
selectivity (Nelson et al., 1997).
Responses of V1 cells adapt to the level of contrast during prolonged
visual stimulation (Movshon and Lennie, 1979; Ohzawa et al., 1985;
Maddess et al., 1988; Bonds, 1991; Nelson, 1991a). The slower form of
synaptic depression seen in the layer 4 to layer 2/3 pathway seems well
suited to contribute to this phenomenon. Its time course matches the
time constants measured for contrast adaptation in single-unit and
evoked-potential studies (Albrecht et al., 1984; Ho and Berkley, 1988;
Maddess et al., 1988; Giaschi et al., 1993).
To examine the role of synaptic depression in shaping the temporal
response properties of cortical neurons, we constructed a model of a V1
simple cell that receives its afferent drive via synapses that depress.
Although the circuitry in the model is highly simplified, the synaptic
dynamics is modeled quite accurately using a mathematical description
that fits experimental data (Abbott et al., 1997; Varela et al., 1997).
Although a number of mechanisms may contribute to temporal
nonlinearities in cortical responses, we focus rather exclusively on
synaptic depression within this modeling study to determine the limits
of what it can explain and thereby to establish whether it is an
important element in cortical dynamics.
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MATERIALS AND METHODS |
The model
Simple-cell model. The model simple cell that we
study is a single-compartment, integrate-and-fire neuron that receives
synaptic input in the form of transient conductance changes at both
excitatory and inhibitory synapses. The total excitatory and inhibitory
synaptic conductances at time t are denoted by
GE(t) and
GI(t) and are computed by
summing contributions from all of the excitatory and inhibitory
synapses, respectively. For convenience, we define synaptic
conductances in dimensionless units so that
GE and GI are
the usual synaptic conductances divided by the resting membrane conductance of the cell. The membrane potential is computed by numerically integrating the first-order differential equation describing a resistance-capacitance (RC) circuit with additional synaptic conductances:
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(1)
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where  m equals 30 msec and is the
membrane time constant, V0 equals  70 mV and is
the resting potential, and VE and
VI equal 0 and 90 mV and are the reversal
potentials for the excitatory and inhibitory synapses, respectively.
When the membrane potential reaches the threshold value of 55 mV, an
action potential is fired, and the membrane potential is reset to 58 mV. The relatively high reset value was used to make the voltage traces
match typical somatic recordings. Use of a lower value did not change
the behavior of the model in any significant way.
When a presynaptic spike occurs on an excitatory afferent, the
excitatory conductance is increased by the substitution:
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(2)
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where j is a label identifying which afferent fired.
The parameter gj is a constant that sets
the strength of synapse j, and
Dj and Sj are
factors describing its degree of fast and slow depression as discussed
below. If the synapse for afferent j is inhibitory, a
similar increment is made in the inhibitory conductance:
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(3)
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Between presynaptic action potentials, the synaptic conductances
decay exponentially to zero with time constants
E = 2 msec and I = 10 msec:
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(4)
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Synaptic depression. Synaptic depression is modeled
using the same formalism and parameter values used to fit slice data (Abbott et al., 1997; Varela et al., 1997). The general procedure is
related to methods used previously to describe short-term plasticity at
the neuromuscular junction (Liley and North, 1952; Magleby and Zengel,
1975; Krausz and Friesen, 1977; Zengel and Magleby, 1982; Sen et al.,
1996) and adapted for our purposes (Abbott et al., 1997; Varela et al.,
1997; see also Grossberg, 1984; Tsodyks and Markram, 1997). Each time a
presynaptic action potential arrives at synapse j, the
factors Dj and
Sj for that synapse are reduced by
multiplicative factors:
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(5)
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The fixed parameters dj and
sj (with 0  dj, sj 1)
determine the amount of depression at synapse j induced by
each spike and thereby control the depression onset rate. Between
presynaptic action potentials, Dj and
Sj recover exponentially toward the value
one:
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(6)
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The time constants D and
S determine the depression recovery rates.
This model provides a good fit of experimental data (Varela et al.,
1997). The two sets of equations listed above can be combined by
writing:
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(7)
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and:
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(8)
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where tµ is the time of a presynaptic
spike labeled by the index µ and  (t tµ) is the Dirac function. These equations are convenient for determining average values of the depression factors, although this requires some care in taking the averages of the
function terms. If afferent j fires a Poisson spike
train at rate Rj, the average steady-state
values of the depression terms are:
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(9)
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The parameter values we use lie within the range seen in the
experimental data. For all of the simulations,
D = 300 msec, and S = 20 sec. We use the values s = 0.99 in all of the
simulations where contrast adaptation is considered and
s = 1.0 when we simulate experiments involving a
constant level of adaptation. (We write the depression factors
sj and dj without the index j when their values do not depend on
j.) Turning off the slow form of depression in this way is a
convenience to avoid having to duplicate the sorts of manipulations
that must be done in an experimental setting to avoid adaptation
effects. The value of d varies between 0.4 and 1.0 in
different simulations as noted.
The model of synaptic depression and parameters values used come from
studies of slices of rat primary visual cortex. The data on visually
evoked neural responses that we use to test the model come primarily
from experiments on cats. Therefore, our model relies on two
extrapolations, from in vitro to in vivo
preparations and from rat to cat cortices. The extrapolation from rat
to cat is supported by the fact that results on cat visual cortical
synapses (Stratford et al., 1996) show short-term plasticity very
similar to that seen in the rat. Measurements on slices of ferret
visual cortex also reveal synaptic depression with similar properties (J. A. Varela and S. B. Nelson, unpublished observations).
The relationship between short-term plasticity in vivo and
in vitro has not been examined in detail in the visual
system. However, synaptic depression has been observed in parallel
in vivo and in vitro studies of rodent
somatosensory cortex (Castro-Alamancos and Connors, 1996; Gil et al.,
1997).
Synaptic inputs. To isolate the role that synaptic
depression plays in shaping the temporal characteristics of V1
responses, we drive the model simple cell exclusively with feedforward
inputs (Hubel and Wiesel, 1962). Although, in reality, V1 cells are
part of a recurrent network, studying a feedforward model allows us to
identify the essential features caused by synaptic depression without
having to deal with the complexities of recurrent network dynamics. In
a recurrent circuit, the nonlinear properties we study on the output of
a model simple cell are also present on its inputs. To avoid this
problem, we give all of the inputs to our model V1 cell, both
excitatory and inhibitory, the spatial and temporal characteristics of
linear LGN cells.
The model of synaptic depression we use is based on properties of the
layer 4 to layer 2/3 pathway within visual cortex that provides the
major excitatory synaptic drive to upper layer neurons (Abbott et al.,
1997; Varela et al., 1997). Recent results indicate that LGN inputs to
neurons in the primary visual and somatosensory cortices display
depression similar to that seen for synapses between pyramidal cells
(Stratford et al., 1996; Gil et al., 1997). Currently, less information
is available about the short-term synaptic plasticity of feedforward
inhibition. Synapses from inhibitory interneurons onto pyramidal cells
of rat primary visual cortex show the faster form of synaptic
depression but to a lesser degree than excitatory synapses (Song et
al., 1997). Unfortunately, we do not know how LGN-interneuron synapses
contribute to the total short-term plasticity along the feedforward
pathway. In the absence of these data, we simply assumed that the total
synaptic depression of the inhibitory drive to the model V1 cell is the
same as that of the excitatory drive. We also studied a feedforward
model with exclusively excitatory drive. This model produced results
similar to those described below, although, of course, there was no
hyperpolarization below the resting potential.
The synaptic input to the model neuron is derived from the model of LGN
center-surround receptive fields described in the next section. The
structure of the receptive field of the model V1 simple cell is
established by the spatial arrangement of the receptive fields of its
on- and off-center afferents. Because we use contrast gratings that
only vary spatially in one dimension as visual stimuli, we use a
one-dimensional spatial arrangement of afferent receptive fields. To
study response phase shifts, we consider a simple linear arrangement
that produces a three-lobed, off-on-off V1 receptive field. This is
obtained by dividing the afferents of the model into three groups with
receptive fields at three different spatial locations (see Fig.
2A). In the central region, we place on-center
afferents that act on the model V1 neuron via excitatory synapses and
off-center afferents that act via inhibitory synapses. In the two
flanking regions, the situation is reversed so that the excitatory
inputs have off-center receptive fields and the inhibitory inputs have
on-center receptive fields. For the directionally selective model
neuron, we use two such arrangements of afferent receptive fields
shifted from each other by one-half the size of the receptive field
center (see Fig. 3A). Because our primary purpose is to
model the temporal response properties of V1 simple cells, we do not
model spatial receptive fields in detail. We have obtained similar
results from a variant of the model in which the spatial structure of
the receptive field is matched to a Gabor function by adjusting the
values of the synaptic weights of the inputs, but we use the simple
geometric model here.
In the nondirectionally selective model (see Fig.
2A), all of the excitatory synaptic strengths were
set to gj = 0.009, and the inhibitory
synapses all had gj = 0.0025 (for
exceptions, see Fig. 2B, middle and
bottom, where values 2.4 and 10 times larger were used to
compensate for the increased degree of depression). For the
directionally selective model (see Fig. 3A), the
nondepressing excitatory synapses had gj = 0.0075, and the nondepressing inhibitory synapses had
gj = 0.002. For the depressing synapses,
these values were increased by a factor of 10. Some scaling of these
values was done from figure to figure to produce firing rates within a
range that matched data for a particular cell. In some cases (see Figs.
4-6), all of the synaptic conductances were multiplied by 1.25. When
we activated the slower form of synaptic depression to model contrast
adaptation, we had to increase the synaptic conductances to compensate
for the average tonic level of slow depression. The synaptic
conductances were multiplied by factors of 5.5, 4, and 6.25 (see Figs.
7-9, respectively). Responses of the model without simulated visual
images and using gj = 0.05 are also shown
(see Fig. 1).
We use a sufficient number of afferents to drive our model V1 cell to
reduce the Poisson noise in the membrane potential and the variability
in the firing rate of the model simple cell to a level that allows us
to perform single-trial simulations. This was done merely for
convenience; using a smaller number of afferents and averaging over
trials (as is done in experimental work) can yield similar results. In
the receptive field, each circle represents 80 (see Fig.
2A) or 40 (see Fig. 3A) excitatory and
inhibitory afferents. In another case (see Fig. 1), a total of 200 afferents was used.
Model of afferent firing rates. To model the afferent spike
sequences that drive the V1 cell, we use a standard LGN model that
produces a Poisson spiking output at a rate computed from a linear
space-time filter acting on the luminance of the visual input (see,
for example, Wörgötter and Koch, 1991). The particular implementation we use is from the work of Maex and Orban (1996). The
spatial structure of the afferent receptive fields is center-surround described by the difference of two Gaussian functions. The temporal response of both the center and the surround is given by the difference of two  functions with the surround response slower than the center
response. The difference between the stimulus luminance at the point
(x, y) at time t and the average
background luminance is denoted I(x,
y, t). The firing rate of afferent j
at time t in response to this stimulus is given by the
difference of center (c) and surround (s)
contributions:
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(10)
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Rb is the background firing rate
set to 5 Hz (for an exception, see Fig. 8 where we used a background
rate of 15 Hz to get better agreement with the data), and
A(C) is a contrast-dependent amplitude
factor discussed below with C a measure of contrast that
varies from zero to one. The choice of plus or minus in this equation
determines whether the afferent is of the on-center (+) or off-center
() type. The spatial filters for the center (c) and
surround (s) are:
|
(11)
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where (xj,
yj) is the location of the center of the
receptive field for afferent j. The receptive field size is
set by the parameters  c = 0.3° and
s = 1.5°. The temporal filters used to
model the afferents are:
|
(12)
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with 1/c = 8 msec,
1/s = 16 msec, and 1/ = 32 msec.
The computed firing rate Rj is used to
drive a Poisson spike generator that produces action potentials on
afferent j to the model V1 simple cell. The Poisson spike
generator produces an action potential during a short time period of
duration  t around the time t with probability
Rj(t)t. If
Rj(t) < 0, no spike is fired.
LGN firing rates do not increase linearly as image contrast is
increased; they saturate. The afferent model described by the above
equations is linear as a function of the stimulus function I, but we include this nonlinear effect via the contrast
amplitude factor A(C). To do this, we
restrict I to lie in the range 1 I 1. Afferent responses at contrast level C are scaled by the contrast amplitude factor:
|
(13)
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obtained by fitting data of Ohzawa et al. (1985). We only use
Equation 13 in the range C > 0.015 (1.5% contrast)
where the logarithm is positive. To simulate images with no contrast,
we set A = 0. We have also used the fit A
Cn/(C50n + Cn) (Cheng et al., 1995) in the
model and found that it gives similar results.
Comparison with data. We compare the results of the model
with previously published data (see Figs. 3, 4, 7, 8). We have
extracted the data curves or points in these figures from the cited
references using the graph tracing program DataThief and then redrawn
the figures.
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RESULTS |
Transient responses
The temporal response characteristics of the model simple cell we
have constructed are affected by the temporal dynamics of the LGN cell
model of the afferents and by synaptic depression. Nonlinear dynamics
in the model V1 cell can arise from rectification of afferent and V1
firing rates as well as from nonlinear synaptic depression. Before
analyzing the complete model, we present a simulation that reveals the
basic features arising solely from the rapid form of synaptic
depression. To isolate these features, we drive the model V1 neuron by
manipulating directly the firing rate of its afferents rather than by
using simulated visual images. Inhibitory afferents were not activated
in this simulation. Furthermore, we study the membrane potential of the
model simple cell with action potentials blocked. These steps eliminate
the effects of temporal filtering by the LGN-like afferent model and of
output firing rate rectification.
The frequency-response characteristics of the model V1 cell are shown
in Figure 1B. To
generate this figure, we modulated identically the firing rates of all
the excitatory afferents to the model V1 cell, although individual
action potentials were generated independently on each afferent. The
common afferent firing rate oscillated over time at a variety of
frequencies and took the form of a rectified sine wave with a peak
firing rate of 100 Hz. Two different cases were considered, a periodic
pattern formed from a rectified sine wave as shown on the
top of Figure 1A and a single pulse
consisting of one cycle of a rectified sine wave as shown in the
middle of Figure 1A. Figure
1B is a plot of the amplitude of the membrane
potential fluctuations produced in the model V1 cell by these patterns
of afferent firing. The solid circles and
triangles correspond to the case in which the rapid form of
depression was present with d = 0.75. The open
symbols show the results without any synaptic depression
(d = 1.0) for comparison purposes. In both cases, the
slow form of synaptic depression was eliminated by setting
s = 1. Conductance strengths were adjusted so that the
peak responses to periodic input-rate oscillations were the same with
and without synaptic depression.
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Figure 1.
Temporal response properties arising from synaptic
depression. A, The model neuron was stimulated by
modulating the rate of Poison spike sequences on its afferents. Action
potentials were blocked. Top, Middle, The
temporal pattern of afferent firing rates used in B,
either single (triangles) or multiple
(circles) cycles of a rectified sine wave with a peak of
100 Hz. B, Plots of the peak-to-peak membrane potential
fluctuation evoked by the pattern of presynaptic stimulation in
A are shown. The circles refer to
periodic afferent firing rates, and the triangles refer
to single-pulse stimulation. The solid symbols
correspond to depressing synapses (d = 0.75),
whereas the open symbols show the results without
synaptic depression (d = 1). C, The
membrane potential response to a step change in the afferent firing
rates. The solid curve is with depression
(d = 0.75), and the dashed curve is
without depression (d = 1). D,
Synaptic depression causes nonlinear summation. The afferent firing
rates were modulated around a background of 50 Hz by the sum of a 0.5 and a 3 Hz sine wave. The solid curve is the resulting
membrane potential. The dashed curve is a membrane
potential obtained by summing the separate responses to the background
rate and the two different oscillations. Differences between the two
curves show the effect of nonlinear summation.
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For low afferent oscillation frequencies, the response amplitudes
plotted in Figure 1B for the periodic and transient
cases are identical, but the frequency-response curves with and
without depression are different. Without depression, the frequency
response is approximately that of a resistance-capacitance circuit, and it peaks at zero frequency. With depression, the response peaks at ~2
Hz. The increase in response amplitude between 0 and 2 Hz is
attributable to the onset of depression during the rising phase of the
afferent firing rate increase. At low modulation frequencies, depression sets in well before the afferent rate reaches its peak value. At higher frequencies, the afferent firing rate increases quickly enough so that it can get closer to its peak value before depression sets in. The peak response frequency depends on the value of
d, and for typical values seen in the slice data (Varela et
al., 1997), such as d = 0.75, it falls in a range that
matches peak response frequencies for V1 neurons responding to
oscillating images. Above a few Hertz, the response amplitude for
single pulse afferent rates without depression and for periodic
afferent rates with and without depression all fall off rapidly as a
function of frequency. This is the result of the low-pass filtering
properties of the equivalent circuit model of the neuron [for a
discussion of a bandpass filtering model, see Maex and Orban (1992)].
Synaptic depression causes the response to periodic afferent rate
fluctuations to roll off slightly more rapidly than when depression is
absent. This is because, for high-frequency oscillations, there is
insufficient time for the synapses to recover from depression between
successive pulses of afferent firing. The solid
triangles in Figure 1B show that synaptic
depression has a dramatic effect on responses to transient,
single-pulse fluctuations in the afferent firing rates. For such
transients, the response amplitude continues to rise as a function of
frequency until it peaks at ~10 Hz. This occurs because, for single
pulses, recovery from depression between pulses is not an issue and the
rapid onset of a high-frequency pulse allows the firing rate to get
closer to its maximum value before depression sets in. The eventual
roll off above 10 Hz is due to the filtering properties of the
postsynaptic cell. The effects of synaptic depression seen in Figure
1B reproduce characteristic features of cortical
responses: the rise in response amplitude at low frequency, the
response peak at a few Hertz, and the increase in both response
amplitude and response cutoff frequency for transient as opposed to
periodic stimuli.
Figure 1C shows the membrane potential of the model neuron
in response to a sudden step in the afferent firing rates from 0 to 50 Hz. The dashed curve, showing the response without
synaptic depression, resembles a typical capacitive charging curve.
When synaptic depression is included, the membrane potential overshoots by approximately a factor of two and then settles to its steady-state value. Similar overshoots are a common feature of the firing rates of
cortical neurons in response to sudden stimulus onsets (Maunsell, 1987).
The reduced model, in which synaptic depression is the only
nonlinearity, displays nonlinear temporal summation as seen in Figure
1D. The membrane potential trajectory indicated by
the solid line in Figure 1D was
evoked by setting all of the excitatory afferent firing rates to an
expression involving the sum of two sinusoids: r = 50 Hz [1 + 0.5 sin(2 f1t) + 0.5 sin(2 f2t)], with
f1 = 0.5 Hz and f2 = 3 Hz. The dashed line in Figure 1D was computed by summing the membrane potential trajectories generated by
the DC term and the two sinusoids in this expression separately. The
failure of linear summation is evident. The response of the model to a
combined stimulus like this, consisting of a sum of low- and
high-frequency oscillations, can be separated into corresponding low-
and high-frequency components by Fourier analysis. When this is done,
we find that in the model, as in the data (Dean et al., 1982), the
amplitude of the low-frequency component is smaller than when the
low-frequency signal is presented alone, whereas the amplitude of the
high-frequency component is larger than when the high-frequency
stimulus is presented alone. This latter effect can be seen by
carefully comparing the two traces in Figure 1D. This
figure also reveals that the low-frequency oscillation induces more of
a multiplicative amplitude modulation in the response to the
high-frequency stimulus than a linear additive shift.
We can use the result in Equation 9 to understand the nonlinear
summation seen in Figure 1D. Suppose that
R = A + B sin(2 f1t) + C sin(2
f2t) as in Figure
1D, f1 is small enough so that the depression factor D remains near its steady-state value
during the slower oscillations, and f2 is large
enough so that oscillations at this frequency have a minimal temporal
effect on synaptic depression. In this case, D  rD/[rD + A + B sin(2
f1t)], where
rD = 1/[(1 d)D]. The level of postsynaptic
drive attributable to an afferent firing at rate R via a
synapse depressed to a level D is approximately
DR. Thus, the effect of these two different sinusoids is
approximately rD [A + B sin(2 f1t) + C sin(2
f2t)]/[rD + A + B sin(2
f1t)]. The rapidly varying part of
this expression, rD C sin(2
f2t)/[rD + A + B sin(2
f1t)], shows the effect seen in
Figure 1D, in which the amplitude of the
high-frequency oscillation is modulated by a low-frequency term in a
multiplicative rather than in an additive form.
Temporal phase shifts
Having illustrated the basic features introduced by synaptic
depression, we now include the LGN-like afferent model in our simulations and drive the model V1 neuron with simulated visual input.
The basic arrangement considered in this section is shown in Figure
2A. The afferent
receptive fields are arranged to form a V1 receptive field consisting
of a central "on" region and two flanking "off" regions. The
visual image used in these simulations is a grating with sinusoidal
variations in both space and time. The maximum contrast and temporal
oscillation frequency of the grating were varied, but its spatial
wavelength was held fixed at a value that maximized the V1
response.
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Figure 2.
Synaptic depression causes temporal phase shifts.
A, Schematic of the arrangement of afferent receptive
fields used to drive the model simple cell. Areas marked OFF correspond
to the central regions of off-center afferents with excitatory synapses
onto the simple cell and of on-center afferents with inhibitory
synapses. Conversely, within the ON region, the central regions of
on-center afferents excite the model V1 cell, and of off-center
afferents inhibit it. For B-E, the stimulus used was a
contrast grating that varied as sin(2 ft) sin(2
x/ ), where f is the temporal frequency
and is the spatial wavelength. The spatial wavelength was set to
match the spacing of the afferent receptive fields, whereas the
temporal oscillation frequency or contrast was varied.
B, Membrane potential as a function of time in response
to a 2 Hz oscillating grating (100% contrast) for different levels of
synaptic depression. Top, no depression;
middle, d = 0.75;
bottom, d = 0.4. C,
Response phase relative to the phase of the oscillating grating for
different oscillation frequencies at 100% contrast. Open
circles correspond to no depression, and solid
circles correspond to d = 0.75. D, The difference between the response phases in
C with and without synaptic depression plotted as a
function of stimulus frequency. E, The response phase
relative to the stimulus for an oscillation frequency of 2 Hz as a
function of stimulus contrast. Open circles correspond
to no depression, and solid circles correspond to
d = 0.75.
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The membrane potential of the model neuron, with action potentials
blocked, in response to an oscillating grating with different degrees
of depression is shown in Figure 2B. Without
depression (d = 1.0), the membrane potential varies
approximately sinusoidally because the transform from image luminance
to membrane potential is approximately linear in the model. When
depression is included (d = 0.75 and d = 0.4), a temporal nonlinearity is immediately evident because the
waveform in response to a sinusoidal input is not sinusoidal. The time
of peak depolarization (and peak hyperpolarization) advances via the
effects of synaptic depression until it shifts by almost 90°. This
occurs because depression sets in during the rising phase of the
afferent response. The magnitude of the phase shift depends on both the
frequency and the level of contrast. To quantify this effect, we
computed the phase of the Fourier component of the membrane potential
at the frequency of the stimulus. This is plotted as a function of
stimulus frequency in Figure 2C. The response phase of a
resistance-capacitance circuit varies as a function of frequency and
can account for the major part of the dependence of response phase on
frequency. However, depression produces an appreciable phase advance
for frequencies between ~0.25 and 6 Hz relative to the phase of the
nondepressing case (Fig. 2C, open circles).
The phase advance attributable to depression is plotted in Figure
2D. Note that the phase shift computed in this way is
considerably smaller than the phase shift of the peak of the membrane
potential depolarization seen in Figure 2B.
For a linear system, the phase cannot depend on amplitude or, in this
case, contrast. When synaptic depression is eliminated, the phase of
the model V1 cell membrane potential oscillations is indeed insensitive
to contrast (Fig. 2E, open circles).
Depression causes the phase to advance as the contrast is increased
(Fig. 2E, solid circles). Phases of
experimentally recorded V1 responses advance as the contrast is
increased in qualitative agreement with the results of Figure
2E, but the magnitude of the effect is considerably
larger in the data (Dean and Tolhurst, 1986; Hamilton et al., 1989;
Reid et al., 1991; Carandini and Heeger, 1994). There are some
complications in relating the phase of the membrane potential to the
phase extracted from the principal Fourier component of a spike
sequence. As we have mentioned, the peak phase of the membrane
potential advances more than the phase of its principal Fourier
component. The phases extracted from spikes, from the peak potential,
and from subthreshold oscillations are all different, and the
relationship between them depends on details of the membrane potential
waveform and on the value of the spiking threshold. Synaptic depression
is only one potential contributor to response phase shifts. Additional
LGN shifts, spike-rate adaptation, conductance changes, and
intracortical effects are other possible sources (Priebe et al., 1997;
Carandini et al., 1998).
Direction selectivity
Models of direction selectivity in neuronal responses to moving
images are based on a combination of temporal and spatial phase shifts
(Barlow and Levick, 1965; Adelson and Bergen, 1985; Watson and Ahumada,
1985; Borst and Egelhaaf, 1989; Heeger, 1993; Smith and Snowden, 1994;
Suarez et al., 1995; Maex and Orban, 1996). In these models, inputs
from different spatial locations within the receptive field are
subjected to different temporal delays or advances so that an image
moving in the preferred direction produces synchronous excitation and a
large response. Movement in the opposite direction leads to
asynchronous excitation and a weaker response. A spatial phase shift
between different sets of inputs to a V1 neuron can be established by
appropriate positioning of the receptive fields of its afferents. The
source of the temporal phase shift is more problematic. Potential
sources include lagged responses in the LGN (Mastronarde, 1987; Saul
and Humphrey, 1990) or delays caused by cortical loops (Suarez et al.,
1995; Maex and Orban, 1996). In both of these cases, the relevant
temporal phase shift is a delay. Figure 2B shows that
synaptic depression is another candidate, although in this case the
temporal phase shift is an advance not a delay.
Figure 3 shows how the phase advance
attributable to synaptic depression can give rise to directionally
selective responses. The key element in the model is a correlation
between the spatial location of a given input and the degree of
depression it displays. We discuss arrangements with multiple
components and graded degrees of depression below, but first we
consider the simplest possible scheme. As seen in Figure 3A,
the model V1 neuron is driven by two sets of inputs each consisting, as
before, of a central on region flanked by two off regions. The two sets
are shifted in space relative to each other by one-half the size of the
central region of the afferent receptive field. This produces the
spatial shift needed in the model. The temporal shift is generated by connecting these two sets of inputs to the model cortical neuron via
synapses exhibiting different degrees of depression. In this example,
one set has no depression (d = 1), and the other has a
fairly large amount of depression (d = 0.4). The
membrane potential fluctuations produced in the model V1 cell (with
action potentials blocked) by these two sets of inputs separately are
shown on the left of Figure 3B. These traces were
generated by a temporally oscillating, stationary grating positioned to
produce the maximum response in each case. The set of nondepressing
inputs evokes an approximately sinusoidal oscillation (dashed
curve) like that seen in the top of Figure
2B. Input through the depressing synapses generates a
sawtooth waveform (solid curve) similar to that seen in the bottom of Figure 2B. The sawtooth
waveform is advanced in phase relative to the sinusoidal form.
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Figure 3.
Model of a directionally selective simple cell.
A, The arrangement of afferent receptive fields. Each
row of circles is identical to that shown
in Figure 2A, and the two rows are
displaced from each other in the horizontal direction by one-half the
width of the central region of an afferent receptive field (the
vertical displacement of the two rows in the figure is
only for clarity; the V1 receptive field is one-dimensional). The
upper circles represent afferents coupled to the V1 cell
without synaptic depression, and the lower circles are
inputs with synapses that depress (d = 0.4).
B, Left, Model V1 cell membrane
potentials evoked by driving the two rows of inputs
separately using a sinusoidal counterphase grating oscillating at 2 Hz.
The solid curve is the potential caused by driving the
afferents with depressing synapses (shaded circles in
A), and the dashed curve corresponds to
driving the afferents with nondepressing synapses (open
circles in A). Right, The two
principal components replotted from Kontsevich's (1995) analysis of
the intracellular recordings of Jagadeesh et al. (1993).
C, Plots of the membrane potential of the model simple
cell in response to a grating moving in the preferred direction.
Upper, The peak membrane potential fluctuations induced
separately by the depressing (solid curves) and
nondepressing (dashed curves) inputs are in phase.
Lower, When both components are present, the model
neuron fires action potentials. D, Plots of the membrane
potential of the model simple cell in response to a grating moving in
the nonpreferred direction. Upper, The membrane
potential fluctuations induced separately by the depressing
(solid curves) and nondepressing (dashed
curves) inputs are out of phase. Lower, When
both components are present, the model neuron fails to fire any action
potentials.
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Intracellular recordings of direction-selective neurons in cat visual
cortex have been made by Jagadeesh et al. (1993). We compare the
membrane potential of our model neuron with their results in Figure 4.
Kontsevich (1995) (see also Ferster, 1994) has analyzed this
intracellular data and discovered that it can be fit quite well using a
phenomenological model based on two principal components. The
components extracted by Kontsevich (Fig. 3B,
right) are quite similar to the two components that
contribute to the membrane potential in our model (Fig. 3B,
left). This similarity first led us to consider synaptic
depression as a mechanism for direction selectivity.
Figure 3, C and D, shows how the model of
direction selectivity works. When a grating moves in the preferred
direction (Fig. 3A, from left to
right), it aligns with the receptive fields of the afferents
with nondepressing synapses before it aligns with those that
depress. Nevertheless, synaptic depression advances the response so
that the peak of the depolarization caused by the depressing synapses
(Fig. 3C, upper, solid curve)
occurs at approximately the same time as the peak of the contribution
of the nondepressing synapses (Fig. 3C, upper,
dashed curve). When the two contributions are added
together, they produce sufficient depolarization to make the model
neuron fire action potentials (Fig. 3C, lower).
When the direction of motion is reversed, the grating aligns with the
nondepressing inputs after it aligns with the receptive
fields of the depressing synapses. In this case, the contribution of
the depressing synapses to the membrane potential (Fig. 3D,
upper, solid curve) is out of phase with
that of the nondepressing synapses (Fig. 3D,
upper, dashed curve). When the two are
summed, the total depolarization is subthreshold, and no firing results
(Fig. 3D, lower).
Figure 4 compares the membrane potential
in our model with the intracellular recordings of Jagadeesh et al.
(1993). A stationary oscillating grating was used as the stimulus for
both the model and the experiments, and the different traces show the
responses for different positions of the grating. In both cases, the
response at 0° spatial phase is approximately sinusoidal. In the
model, this occurs because the grating in this position aligns with the receptive fields of the inputs without synaptic depression. At approximately 90° spatial phase, the membrane potential in both the
model and the data has the sawtooth shape that we have seen before. In
the model, this occurs because the grating now aligns with the
receptive fields of the afferents with synapses that depress.
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Figure 4.
A comparison of the membrane potential of the
model simple cell with in vivo intracellular recordings
from a neuron in area 17 of a cat. In both cases, the stimulus was a
stationary counterphase grating oscillating at 2 Hz and positioned at
different spatial phases as indicated. A, Membrane
potential of the model neuron. B, Recorded membrane
potentials replotted from Jagadeesh et al. (1993). Calibration:
horizontal, 100 msec; vertical, 10 mV for the model and 2.5 mV for the
data.
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Any model of direction selectivity must account for the fact that
neurons can remain directionally selective over a wide range of
contrasts. Figure 5A shows
that this is true for our model. The firing rate of the model V1 neuron
increases as a function of contrast for motion in both the preferred
and nonpreferred directions. However, the direction index is constant
and near one over the entire contrast range shown (the direction index is the difference between the firing rates in the preferred and nonpreferred directions divided by the firing rate in the preferred direction). Figure 5B shows that the firing rate evoked by a
grating moving in the preferred direction varies with temporal
frequency in the typical manner of a cortical response, peaking at ~2
Hz and falling off above ~10 Hz (for a moving grating, the temporal frequency is the speed of the motion divided by the spatial wavelength of the grating). Although the response in the preferred direction is
greatly decreased at low temporal frequencies, the model neuron remains
at least somewhat directionally selective. Directionally selective
neurons show a wide variety of frequency and contrast-response characteristics, and those shown in Figure 5 fall within observed ranges (Orban et al., 1986; Reid et al., 1991; Tolhurst and Dean, 1991;
Saul and Humphrey, 1992).
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Figure 5.
Direction selectivity as a function of contrast
and frequency. A, The firing rate of the model V1 cell
shown in Figures 3 and 4 as a function of the contrast of the moving
grating for motion in the preferred (solid circles) and
nonpreferred (open circles) directions. The upper
curve (+ symbols) is the directional index,
plotted as a percentage. B, The firing rate in response
to a grating of 100% contrast moving in the preferred (solid
circles) and nonpreferred (open circles)
directions as a function of frequency.
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The directionally selective model of Figures 3-5 is based on having
two populations of inputs with different spatial phases and different
degrees of depression. It is possible to avoid such a simplistic scheme
and construct models that involve a continuous variation in the degree
of synaptic depression. The critical component in these models is that
the degree of depression for a given input must be correlated with its
spatial phase. We have constructed such a model with spatial receptive
fields divided into two groups, as in Figure 3A, but with a
continuous range of depression factors. These factors fell in the range
0.4 dj 1.0. Afferents with dj 0.7 shared one spatial placement,
and those with dj > 0.7 had the second spatial
placement. The firing rates, direction index, and frequency-response
curves for this model are shown in Figure
6. The graded model tends to be less
directionally selective than the simple two-component model, although
it retains a constant directional index as a function of contrast (Fig.
6A). The difference in the frequency-response
profile of this model neuron (Fig. 6B) for motion in
the nonpreferred direction compared with that in Figure 5B
is attributable primarily to its higher firing rate compared with that
of the model of Figure 3A and is not a necessary correlate
of this architecture.
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Figure 6.
Directional selectivity in a model with graded
amounts of depression. A, The firing rate of the model
cell as a function of the contrast of the moving grating for motion in
the preferred (solid circles) and nonpreferred
(open circles) directions. The horizontal
curve (+ symbols) is the directional index,
plotted as a percentage. B, The firing rate in response
to a grating of 100% contrast moving in the preferred (solid
circles) and nonpreferred (open circles)
directions as a function of frequency.
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We have used oscillating stimuli and discussed phase shifts in our
presentation of the directionally selective model, and that might leave
the impression that it requires oscillating stimuli to be directionally
selective. We have verified that this is not the case. For example, the
response of the model neuron to two spatially displaced gratings that
are flashed transiently depends on the order in which they appear in a
manner consistent with its direction selectivity.
Contrast adaptation
The effects we have discussed thus far are caused by the fast
component of synaptic depression. We now turn our attention to the
slower component that, when activated by setting s = 0.99 (rather than s = 1), causes the responses of the
model simple cell to change slowly over time as the slow depression
either sets in or recovers from previous activity. Figure
7 compares a model simulation with an
experiment on contrast adaptation in neurons of cat area 17 performed
by Ohzawa et al. (1985). The stimulation sequence in Figure 7 goes from
top to bottom. In both the simulation and the
experiment, the firing rate at 0% contrast is essentially zero. After
a 30 sec period during which contrast adaptation to the 0% stimulus
takes place, the response to a low-contrast grating is transiently
vigorous but then relaxes to a lower firing rate. After another 30 sec
adaptation period, the response to a high-contrast grating once again
consists of a transient period of rapid firing followed by steady-state
firing at a lower rate. When the low-contrast grating is presented for
a second time, there is no initial response because of the previous
adaptation to the high-contrast stimulus. The steady-state response is
established after a slow buildup period. The model neuron, with
contrast adaptation arising solely from slow synaptic depression,
duplicates the results seen in the experimental recordings quite
well.
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Figure 7.
Contrast adaptation from slow synaptic depression.
Left, The different stimuli used and the sequence in
which they were presented. Each stimulus presentation lasted for 30 sec. Middle, The firing rate of the model V1 neuron in
response to each stimulus, starting from the time of stimulus onset.
Right, Data from recordings of cat area 17 neurons
replotted from Ohzawa et al. (1985). In both cases, the stimulus was a
2 Hz grating moving in the preferred direction.
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Figure 8 compares the contrast-response
curves for the model neuron and a cat area 17 neuron recorded by Ohzawa
et al. (1985) under a variety of preadapted conditions. Contrast
adaptation causes the curves to shift rightward in the model as in the
data. We can approximate the effect of synaptic depression on contrast response using some of the results derived when we discussed the model
of depression. The total drive coming from an afferent with firing
R is R times the level of depression of its
synapse onto the V1 neuron. The average steady-state level of
depression is given by Equation 9. After adaptation to a sustained
firing rate Radapt, this drive is equal
to R/([1 + (1 dj)DR]
[1 + (1 sj)SRadapt]).
Synaptic depression thus implements a form of divisive contrast
normalization similar but not identical to that discussed by Heeger
(1992) and Carandini and Heeger (1994). Synaptic depression causes the
postsynaptic response to begin to saturate when the input rates are
larger than rD = 1/[(1 d)D]. In agreement with
experimental data (Albrecht and Hamilton, 1982; Skottun et al., 1986),
the saturation level depends on the afferent firing rate and hence on
the contrast level, not on the firing rate of the postsynaptic V1
neuron.
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Figure 8.
Contrast-response curves for different levels of
adaptation. Each curve shows the response as a function of contrast
after the neuron has been fully adapted to the level of contrast
indicated. The stimulus was a 2 Hz grating moving in the preferred
direction. A, Contrast-response curves of the model
neuron. B, Contrast-response curves of a cat area 17 neuron redrawn from Ohzawa et al. (1985).
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Recently two groups have recorded intracellularly in anesthetized cats
during contrast adaptation protocols (Ahmed et al., 1997; Carandini and
Ferster, 1997). Ahmed et al. (1997) found no clear intracellular
correlate of contrast adaptation in the recorded subthreshold membrane
potentials. Carandini and Ferster (1997) have reported that the
dominant effect of contrast adaptation on the recorded membrane
potentials was a DC hyperpolarization. In the majority of cells,
contrast adaptation did not significantly alter the amplitude of the
membrane potential oscillations evoked by an oscillating stimulus. Our
model is not in complete agreement with these results. Figure
9 shows the membrane potential of the model simple cell in response to oscillating gratings at 0, 5, and
100% contrast. The solid curves show the response
after adaptation to a 100% contrast grating, and the dashed
curves show the response after adaptation to a 5% contrast
grating. Adaptation to the high-contrast grating causes a DC
hyperpolarization (Fig. 9A-D) in agreement with the results
of Carandini and Ferster (1997). However, the amplitude of the
oscillations in response to the 5% (Fig. 9B) and 100%
(Fig. 9C) contrast stimuli is clearly smaller for
high-contrast adaptation than for low-contrast adaptation, an effect
not seen by Carandini and Ferster (1997) in the majority of cells they recorded. In Figure 9A-C, action potentials have been
blocked in the model to show the membrane potential oscillations
without the spiking nonlinearity. Figure 9D shows the
membrane potential of the model under the same conditions used in
Figure 9C but with the model producing spikes every time the
neuron rises to the threshold potential (for clarity, the spikes have
been truncated in this figure). The spike generation mechanism in the
model clips the membrane potential oscillation so that it does not rise
above the action potential threshold. Clearly, if action potentials are
not integrated into the potential in some way, spiking seriously distorts the picture and greatly reduces the amount by which contrast adaptation modifies the amplitude of membrane potential oscillations. The effects of spikes have been included in the data from the intracellular recorded membrane potentials by a method of averaging and
interpolation (Carandini and Ferster, 1997), but, ideally, the results
of the model should be compared with intracellular recordings with
action potentials internally blocked. Nevertheless, as Carandini and
Ferster (1997) have noted, the data seem to suggest the presence of a
tonic component in the synaptic input that slowly depresses, and this
is not present in the model we have described.
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Figure 9.
Membrane potential oscillations evoked by a 4 Hz
oscillating grating at different contrast levels and for different
degrees of adaptation. The solid curves show the
response of the model V1 cell (with action potentials blocked) after
prolonged exposure to an oscillating 100% contrast grating. For the
dashed curves, the adapting stimulus was a 5% grating.
A, Response to a 0% grating. The different levels of
contrast adaptation cause a DC shift in the membrane potential.
B, Response to a 5% grating. C, Response
to a 100% contrast grating. In B and C,
the different levels of contrast adaptation cause both a DC shift in
the membrane potential and a change in the amplitude of the membrane
potential oscillations. D, Same as C but
with the spike generation mechanism in the model activated. Spikes have
been truncated to reveal the underlying subthreshold membrane potential
more clearly.
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DISCUSSION |
Simple cells exhibit nonlinear behavior in both the spatial and
temporal domains, but the nature and source of these nonlinearities appear to be different. A large body of data suggests that spatial summation of subthreshold inputs to simple cells is linear and that the
dominant source of nonlinearity in the spatial domain is the action
potential threshold (Ferster, 1994). Nonlinear behavior in the time
domain seems to be richer and difficult to explain as arising purely
from a spiking threshold. Transient and sustained visual responses
exhibit different types and degrees of nonlinear behavior. Transient
responses show strong temporal nonlinearities, including enhancement of
high-frequency components (Ikeda and Wright, 1975; Movshon et al.,
1978; Kulikowski et al., 1979; Tolhurst et al., 1980). Sustained
responses show more subtle temporal nonlinearities, in particular the
failure of linear summation (Dean et al., 1982; Reid et al., 1992). We
have found that the synaptic depression measured and modeled from
experiments involving slices of primary visual cortex (Abbott et al.,
1997; Varela et al., 1997) can account for nonlinear temporal effects
in responses to both sustained and transient stimuli. Synaptic
depression is particularly well suited to explain the marked
differences between the responses to transient and periodic stimuli,
including both the higher response frequency range and the increased
response amplitude for transient stimuli.
Perceptual and single-unit studies have revealed the existence of
sustained and transient channels in vision (for review, see Maunsell,
1987). Although a number of factors, including retinal and LGN cell
type, contribute to this distinction, our studies indicate that
differences in the degree and type of short-term synaptic plasticity
can dramatically affect the temporal character of cortical
responses.
Despite its extreme simplicity, our simple-cell model does a fairly
good job of matching data on nonlinear temporal summation, direction
selectivity as a function of frequency and contrast, and contrast
adaptation. Results on the contrast dependence of response phase shifts
suggest that synaptic depression may be a significant contributor to
this effect (see also Priebe et al., 1997).
Previous models of directionally selective simple cells have used a
variety of mechanisms to generate the necessary temporal phase shifts
(Saul and Humphrey, 1990; Suarez et al., 1995; Maex and Orban, 1996).
In these models, direction selectivity arises from a temporal delay
combined with a spatial phase shift. In our model, direction
selectivity arises from a phase advance. The intracellular recordings
of Jagadeesh et al. (1993) shown in Figure 4 and the principal
components extracted from these data by Kontsevich (1995) shown in
Figure 3B suggest that the more nonlinear component is phase
advanced relative to the more linear (that is, sinusoidal) component.
If the source of the nonlinearity and the source of the phase shift are
the same, as they are in our model, the phase shift must be an advance
not a delay. A model based on a delay mechanism must use an
approximately linear delay mechanism and then explain by a separate
mechanism the nonlinear behavior in the other component. The
intracellular recordings can potentially be explained by a single
mechanism if the source of direction selectivity is a phase
advance.
In the directionally selective model, we have adjusted the relative
strengths of the depressing and nondepressing synapses so that their
steady-state amplitude is approximately equal. As a result, the
synaptic conductance parameter that sets the synaptic strength in the
model was larger for depressing synapses than for nondepressing
synapses. This is consistent with the assumption that these two sets of
synapses differ in the probability of vesicle release. It is observed
experimentally that depression is maximal for synapses with high
release probabilities and decreases when the release probability is
smaller (Atwood and Wojtowicsz, 1986; Zucker, 1989; Tsodyks and
Markram, 1997; Varela et al., 1997). Because the synaptic strength
parameter gj is proportional to release
probability, this is exactly the type of relationship used in the
directionally selective model.
The directionally selective model requires a correlation between the
spatial phase of a particular afferent and the degree of depression at
its synapse onto the V1 cell. Deficits in strobe-reared cats suggest
that activity may play a role in establishing direction selectivity
(Pasternak et al., 1985). The correlations needed in our model could
arise from an activity-dependent learning rule that adjusts the degree
of synaptic depression on the basis of the spatial phase of the input.
Markram and Tsodyks (1996) have found that a long-term potentiation
(LTP) paradigm that enhances the amplitude of postsynaptic currents in
response to a single presynaptic spike also increases the degree of
synaptic depression, so that the steady-state response to repetitive
presynaptic input remains unchanged. A form of LTP that targets the
degree of synaptic depression is exactly what is needed for
activity-dependent development of directional selectivity via synaptic
depression. Modeling work on correlation-based activity-dependent
development (Miller, 1992) of direction selectivity in other models
(Miura et al., 1995; Feidler et al., 1997) may provide the mechanism
needed to correlate activity-dependent modification of the degree of
depression with the spatial phase of a particular input, although this
has not yet been verified.
Synaptic transmission at a synapse that exhibits depression depends on
the relation of presynaptic activity to the activity that immediately
preceded it. The presynaptic spiking pattern that produces the largest
postsynaptic current is a period of silence followed by a high rate of
activity. Visual neurons often respond most vigorously if the
appearance of an optimal image is preceded by an "opposite" image,
for example, contrast reversed. Recently Ringach et al. (1997) have
measured reverse correlations for orientation tuning at short time
intervals. Their data show this "reversal" effect; many neurons
respond most vigorously if an optimally oriented image is preceded by
an orthogonal orientation [the effects of synaptic depression on the
dynamics of orientation tuning have been considered by O. Artun, H. Shouval, and L. Cooper (personal communication)]. Optimal stimuli that
are anticorrelated in this way arise naturally from synaptic
depression.
We have studied the idea that synaptic depression may also play an
important role in contrast adaptation. The onset of synaptic depression
depends on the number of presynaptic action potentials and thus is both
rate and contrast dependent. Consistent with this, the magnitude and
onset rate of adaptation increase as the temporal frequency of the
visual stimulus increases (Maddess et al., 1988; Bonds, 1991; Nelson,
1991a). Pharmacological manipulations (Nelson, 1991b; McLean and
Palmer, 1996) and intracellular recordings (Carandini and Ferster,
1997) support the hypothesis that contrast adaptation is caused by a
reduction in excitatory synaptic drive. A number of experiments suggest
a synaptic, rather than a cellular, adaptation mechanism. Contrast
adaptation can occur locally within a portion of the receptive field of
a cell (Marlin et al., 1991; Nelson, 1991a), the sensitivity of a
neuron to a particular stimulus can be reduced without reducing its
maximal firing rate (Ohzawa et al., 1985), and contrast adaptation can
be induced by stimuli that do not cause the cortical neuron to fire
(Vidyasagar, 1990; Geisler and Albrecht, 1992; Allison and Martin,
1997). On the other hand, recent results show that contrast adaptation
can also be evoked by current injection without visual stimulation,
suggesting that a cellular mechanism may also contribute (Sanchez-Vives
et al., 1997).
We have constructed our model specifically to investigate the impact of
synaptic depression and thus have tried to avoid other sources of
temporal nonlinearity that would complicate the study of this
particular mechanism. We are not proposing that all of the temporal
response properties of cortical neurons arise solely from synaptic
depression. Undoubtedly, neuronal adaptation and cortical circuit
effects play a role in these phenomena. Some of the effects of the
interplay between recurrent synaptic connections, cortical
amplification (Douglas et al., 1995), and synaptic depression have been
discussed by Todorov et al. (1997), Priebe et al. (1997), and Sen
(1997). Interplay between the different forms of short-term plasticity
seen in intracortical excitatory-excitatory, excitatory-inhibitory, and inhibitory-excitatory synapses, as well as the rich dynamics of
recurrent neural circuits, will make the study of more realistically connected models both challenging and interesting.
The most direct way to test our model experimentally is to modify
synaptic depression in vivo. Recently, we and others have shown that manipulations that diminish transmitter release also diminish synaptic depression in slices (Gil et al., 1997; Tsodyks and
Markram, 1997; Varela et al., 1997). These manipulations include reducing extracellular calcium, applying neuromodulators including adenosine and acetylcholine, and activating presynaptic GABA-B receptors. According to our model, reducing depression should make V1
responses more linear in the temporal domain, and the response
properties that we have attributed to depression, such as enhancement
of transient and reduction of steady-state responses, nonlinear
temporal summation, contrast-dependent phase shifts, directional
selectivity, and contrast adaptation, should be altered. Unfortunately,
manipulations that modify transmitter release do not target synaptic
depression exclusively; they also affect response amplitude and
synaptic facilitation. Spiking threshold effects in extracellular
recordings can make it difficult to untangle these combined
modulations. Nevertheless, the model makes clear predictions about the
impact that modifying synaptic depression will have on visual
responses, and with sufficient pharmacological specificity and clever
data analysis, it should be possible to test them.
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FOOTNOTES |
Received Jan. 8, 1998; revised March 27, 1998; accepted April 1, 1998.
This research was supported by the National Science Foundation Grants
DMS-95-03261 and IBN-95-11094, the W. M. Keck Foundation, National
Eye Institute Grant EY-11116, and the Alfred P. Sloan Foundation.
Correspondence should be addressed to Dr. Larry Abbott, Volen Center,
MS 013, Brandeis University, 415 South Street, Waltham, MA 02254-9110.
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Top
Abstract
Introduction
![−0.6×W<SUB>s</SUB>(x, y)K<SUB>s</SUB>(t−t′)]I(x, y, t′).](/content/vol18/issue12/fulltext/4785/img011.gif)
