 |
 Previous Article | Next Article 
The Journal of Neuroscience, August 15, 1998, 18(16):6583-6598
Robust Temporal Coding of Contrast by V1 Neurons for Transient
But Not for Steady-State Stimuli
Ferenc
Mechler1, 2,
Jonathan D.
Victor1,
Keith
P.
Purpura1, and
Robert
Shapley2
1 Department of Neurology and Neuroscience, Cornell
University Medical College, New York, New York 10021, and
2 Center for Neural Science, New York University, New York,
New York 10003
 |
ABSTRACT |
We show that spike timing adds to the information content of spike
trains for transiently presented stimuli but not for comparable steady-state stimuli, even if the latter elicit transient responses. Contrast responses of 22 single neurons in macaque V1 to periodic presentation of steady-state stimuli (drifting sinusoidal gratings) and
transient stimuli (drifting edges) of optimal spatiotemporal parameters
were recorded extracellularly. The responses were analyzed for
contrast-dependent clustering in spaces determined by metrics sensitive
to the temporal structure of spike trains. Two types of metrics,
cost-based spike time metrics and metrics based on Fourier harmonics of
the response, were used. With both families of metrics, temporal coding
of contrast is lacking in responses to drifting sinusoidal gratings of
most (simple and complex) V1 neurons. However, two-thirds of all
neurons, mostly complex cells, displayed significant temporal coding of
contrast for edge stimuli. The Fourier metrics indicated that different
response harmonics are partially independent, and their combined use
increases information about transient stimuli. Our results demonstrate
the importance of stimulus transience for temporal coding. This finding
is significant for natural vision because moving edges, which are
present in moving object boundaries, and saccades induce transients. We
think that an abrupt change in the adapted state of the local visual circuitry triggers the temporal structuring of spike trains in V1
neurons.
Key words:
temporal coding; primary visual cortex; transient
stimuli; steady-state stimuli; edges; gratings; contrast response; simple cell; complex cell; metric spaces
| |
INTRODUCTION |
A prevailing view of neural coding
is that the meaningful signal is contained in the mean rate of the
action potential discharges of a neuron, and rate variability is
noise. Because this noise can be filtered out by averaging across time
or neuronal populations, rate coding performs robustly in the presence
of noise, but it has limited information capacity.
An alternative view is summarized by the term temporal coding; the
notion that the timing of individual spikes also carries information.
In principle, selective temporal mechanisms could exploit the high
intrinsic precision of cortical neurons to increase the efficiency of
neural coding.
It is natural to assume that rate coding plays a major role in neural
signaling, given its apparent simplicity. Decoding a rate code implies
temporal summation over periods of time long in comparison with the
mean interspike interval or summation across a population. On the other
hand, coincidence detection (Abeles, 1982 ; Bourne and Nicoll, 1993;
Softky, 1994; Konig et al., 1996; Cline, 1997; Volgushev et al., 1998),
refractory periods (Berry and Meister, 1998), activity-dependent
synaptic efficacy (Abbott et al., 1997; Gerstner et al., 1997;
Markram et al., 1997), post-tetanic potentiation (Alonso et al., 1996;
Volgushev et al., 1997), and other forms of temporal integration are
just as much a part of the qualitative description of neuronal signal
processing as is linear summation. Furthermore, neuronal spike
generation is intrinsically precise (Mainen and Sejnowski, 1995). Thus,
neurons are well equipped to generate and process temporal codes.
It is well recognized that temporally coded information is present in
spike trains of primate visual neurons (Optican and Richmond, 1987;
Richmond and Optican, 1987, 1990; Victor and Purpura, 1996, 1997).
Although studies in our laboratory and those of Optican and
Richmond (1987) made use of different stimuli and different analytical
tools, they shared two features: a focus on single spike trains rather
than response averages and transient presentation of stimuli. On the
other hand, many investigators use steady-state stimulation and
averaging methods such as poststimulus time histograms and Fourier
analysis, and they either ignore the possibility of temporal coding or
conclude that it is not present.
Thus, it is unclear whether the apparent presence or absence of
temporal coding is an artifact of the analytical method, or rather, is
related to physiological differences between transient and steady-state
regimens. To settle this issue, we looked for temporal coding in
contrast responses collected from the same V1 neurons in transient
(drifting edge) and steady-state (drifting grating) regimens. We found
strong evidence for temporal coding for the transient edges but not for
the steady-state gratings. The same results were obtained from cluster
analysis of the Fourier harmonics computed from individual spike
trains.
The major conclusion that we draw from this study is that the nature of
the visual stimulus, rather than the particular method of data
analysis, determines whether one finds temporal coding in the responses
of V1 neurons. The finding that transient stimuli generate temporally
coded responses has implications for natural vision.
Parts of this paper were presented at the 1997 Annual Meeting of the
Society for Neuroscience (Mechler et al., 1997).
| |
MATERIALS AND METHODS |
Physiological preparation. Standard acute preparation
techniques were used for electrophysiological recordings from single units in V1 of macaque monkeys (Kaplan and Shapley, 1982; Hawken et
al., 1988, 1996). Experiments were performed on two adult cynomolgus monkeys, Macaca fascicularis, weighing 1.8-4 kg. Before
surgery, animals were sedated with acepromazine (0.1 mg/kg, i.m.;
PromAce; Fort Dodge, Fort Dodge, IA) and then anesthetized with
ketamine (10 mg/kg, i.m.; Ketaset; Fort Dodge). Anesthesia was
maintained with sufentanil citrate (3-6
µg · kg 1 · hr1,
i.v.; Sufenta; Janssen Biochimica, Titusville, NJ), and muscle paralysis was induced (after all surgical procedures) and maintained with pancuronium bromide (0.1 mg · kg1 · hr1, i.v.;
Astra Pharmaceutical Products, Inc., Westborough, MA). Dexamethasone (1 mg/kg, i.m.; Elkins-Sinn, Cherry Hill, NJ) and gentamicin (5 mg/kg,
i.m.; Steris Laboratories, Inc., Phoenix, AZ) were given to prevent the
development of cerebral edema and infection, respectively. The animal
was ventilated through an endotracheal tube. Heart rate,
electrocardiogram, blood pressure, and end-tidal CO2 were
continuously monitored with a Hewlett-Packard 78354A patient monitor
and kept in the normal physiological range. Core body temperature was
maintained at 37°C using a thermostatically controlled heating pad.
The EEG was obtained from frontal leads and continuously monitored on
an oscilloscope.
A limited unilateral craniotomy was made posterior to the lunate sulcus
(the Horsley-Clarke stereotaxic coordinates were 12-14 mm posterior
and 10-20 mm lateral). A 1-2 mm durotomy was made for the recording
electrode, which was stabilized after insertion by agarose gel.
Experiments lasted for 4 d, at the end of which the animal was
sacrificed by infusion of a lethal dose of pentobarbital (Brevital; Eli
Lilly and Co., Indianapolis, IN). After transcardiac perfusion, a block
of the occipital lobe containing the penetration was saved for
histological reconstruction of the electrode track (Hawken et al.,
1988, 1996). Laminar positions of the recording sites were estimated in
relation to the pattern of cytochrome oxidase stain and Nissl density
in the reconstructed cortical section containing the track.
Optics. The eyelids were retracted and pupils were dilated
with 1% atropine sulfate (Atrosulf-1; Optics Laboratories, Co., Fairton, NJ). The corneas were protected with gas-permeable contact lenses (Metro Optics Inc., Houston, TX). External lenses were used to
correct refraction as first estimated by direct ophthalmoscopy and then
confirmed or improved by optimizing the high spatial frequency
responses of isolated neurons. Foveae were mapped by back-projection on
a tangent screen using a reversing ophthalmoscope (Eldridge, 1979). The
visual receptive fields of isolated neurons were mapped on the same
screen.
Extracellular recording. Microelectrode [glass-coated
tungsten (Merrill and Ainsworth, 1972); exposed tip, 5-15 µm;
typical resistance, 2 M ] penetrations were driven by a stepping
motor in 1 µm steps. The extracellular electrical signal was fed
through a differential amplifier and then further amplified and
bandpass-filtered (0.2-10 kHz). A window discriminator was adjusted to
generate brief (50 µsec) pulses on each occurrence of the isolated
spike. The discriminator input and output were fed to an audio monitor, and the times of occurrence of the pulses were recorded on a personal computer through a general purpose data aquisition box (CED 1401 plus;
Cambridge Electronic Design, Ltd., Cambridge, UK) with 1 msec
resolution. Single-unit isolation was aided by monitoring the window
levels multiplexed with the raw signal on an oscilloscope and
displaying the isolated spike on a separate storage oscilloscope. Isolation criteria used included an audible visually driven response, a
minimum interspike interval consistent with a physiological refractory
period (>1-1.5 msec), and a uniform, stable spike shape.
Only cells that were well and stably isolated throughout the runs
described below were included in this study. This restricted analysis
to 22 V1 cortical neurons (11 simple and 11 complex), 25% of all
neurons encountered. Of the two animals in the study, the first yielded
nine neurons (two complex and seven simple), and the second yielded 13 neurons (nine complex and four simple). Simple versus complex
categorization was based on (1) the modulation ratio of the fundamental
over the DC component of the response to drifting gratings of near
optimal spatial parameters (Movshon et al., 1978b; De Valois et al.,
1982; Skottun et al., 1991) and (2) the ratio of the first and second
harmonics in a spatial summation linearity test (Enroth-Cugell and
Robson, 1966; Hochstein and Shapley, 1976; Movshon et al., 1978a,b).
Receptive field positions were all located in the parafovea and
perifovea, between 1.5 and 6° eccentricity.
Visual stimulation. Stimuli were generated by a Silicon
Graphics Elan R4000 computer under the control of the personal
computer, displayed on a Barco CCD 7651B color monitor (60 Hz
noninterlaced refresh; 1024 × 768 pixels; 60 cd/m2 mean luminance, 8-bit intensity control). The
lookup tables controlling the voltages on the guns of the phosphors in
the monitors were linearized with the aid of a Photo Research 703-PC
spectroradiometer. The visual space subtended by the illuminated area
was 13 × 17° at a 114 cm viewing distance. The display area of
the modulated stimulus could be limited to a smaller patch within a
0.5-5° diameter aperture to optimize the response. Stimuli were
always centered on, and fully covered, the receptive field of the
neuron.
For quantitative analysis, we used two types of drifting
one-dimensional luminance waveforms: sinusoidal gratings and square waves of low spatial frequency for which we hereafter use the term
edges. The luminance profile of the drifting sinusoidal gratings is:
![I(x, t)=I<SUB>0</SUB>[1+C <UP>sin</UP>(2&pgr;(&kgr;x−&ohgr;t))].](/content/vol18/issue16/fulltext/6583/img001.gif)
|
(1)
|
Here, I(x,t) is the luminance
(candelas per square meter) at position x (degrees) along
the grating at time t (in seconds); I0 (candelas per square meter) is the mean
luminance of the unmodulated display; C is the Michelson
contrast of the stimulus;  (cycles per degree) is the spatial
frequency; and  (Hertz) is the temporal frequency. Similarly, the
luminance profile of the drifting edges is:
![I(x, t)=I<SUB>0</SUB>[1+C <UP>sgn</UP>(<UP>sin</UP>(2&pgr;(&kgr;x−&ohgr;t)))].](/content/vol18/issue16/fulltext/6583/img002.gif)
|
(2)
|
This is a square wave with a fundamental spatial frequency of
, temporal frequency of , and contrast of C.
Stimuli were presented monocularly to the preferred eye in trials that
spanned several cycles of the periodic stimulus and lasted typically 4 sec (range, 2-16 sec). A brief preliminary qualitative exploration of
the spatiotemporal tuning preferences of a unit was followed by a basic
set of quantitative characterization experiments, in which the tuning
for orientation, then spatial frequency, then temporal frequency, and
occasionally orientation again, of a unit were measured using drifting
sinusoidal luminance gratings of 64% contrast. The optimal value for
each tuning parameter was assessed sequentially and then kept fixed in
subsequent tuning experiments for the other parameters. In each tuning
experiment, the tuning parameter was varied in random order, and blank
trials were randomly interleaved. The blank condition consisted of a uniform display at a luminance identical to the spatiotemporal mean of
all modulated stimuli. Orientation and temporal frequency tuning
(velocity tuning at fixed spatial frequency) experiments were also
performed with drifting edges. Edges had a fundamental spatial
frequency of 0.1-0.3 cycles/°.
In the contrast-response experiments, 4 sec trials of drifting
gratings or edges of optimal spatiotemporal parameters were interleaved
with blank trials of equal duration. Patterned stimuli were presented
in order of increasing contrast. Blank trials were intended to minimize
the variable effects of contrast adaptation. Each block of trials,
representing a full set of contrast levels, was repeated several
(typically two to four) times in identical trial order, typically
yielding 8-16 sec of recorded spike trains in each condition.
Data analysis: metric spaces and clustering of spike trains.
The data analysis determines the extent to which there is a
reproducible dependence of spike counts and spike times on the contrast
of the stimulus. It consists of two separate stages (see in detail below); the construction of a metric space from a set of responses, followed by an analysis of response clustering. For the first stage, we
use spike counts and a family of spike time metrics (Victor and
Purpura, 1997), both as originally conceived as well as in a
modification that makes them more appropriate for analyzing responses
to periodic stimulation. We will also introduce new metrics to connect
this approach to standard Fourier analysis. We performed the Fourier
analysis in addition to the abstract spike time metric space analysis
because (1) Fourier components are conventionally and frequently used
response measures for periodic stimulation and, (2) more importantly,
they naturally give rise to vector spaces unlike the cost-based
metrics. Because of point 1, some readers will find the Fourier
approach more appealing then the cost-based metric space approach.
Because of point 2, the nontrivial question of whether the two
independent methods of analysis lead to similar results needs to be
answered empirically, which we do here. Although the result of the
analysis of clustering in the second stage is dependent on the choice
of the particular metric in the first stage, the clustering algorithm
itself is not. In this way, coding based on spike counts and coding
based on temporal pattern can be compared on an equal footing. The
following paragraphs give the reader the basics of the analyses. A
rigorous treatment of this material has been published (Victor and
Purpura, 1997).
Spike time metrics. We assess the extent to which spike
trains elicited by stimuli of different contrasts appear more
"dissimilar" than spike trains elicited by stimuli of the same
contrast. This assessment is performed for multiple notions of
dissimilarity, or distance, between spike trains, known as metrics. We
use a family, Dspike[q], of
metrics of the distances between spike trains, parametrized by a cost,
q, that specifies a presumed time scale (1/q) for
the systematic stimulus dependence of spike timing.
For Dspike[q], two spike
trains are considered similar if the number of spikes is similar and if
their timing agrees to within 1/q. To formalize this notion,
we define the distance between two spike trains as the "cost" of
transforming one into the other. The transformation from one spike
train into the other is via a sequence of elementary steps, consisting
of (1) spike elimination, (2) spike insertion, and (3) shifting a spike
in time. Each elementary step is associated with a definite cost. For
eliminating or inserting a spike, the cost is unity. To shift a spike,
the cost is equal to q t, where t
is the extent of the shift. The factor q has units of
seconds1. Given these preliminaries,
let
|
(3)
|
be a path that leads from Sa to
Sb through a finite sequence of intermediate
spike trains, in which each spike train
S j + 1 is obtained from the
preceding one, Sj, via one of the
three types of elementary steps (deletion, insertion, and a finite
shift of a single spike). Given a fixed q cost parameter,
let
Kq(Sj,Sj + 1) denote the cost of that elementary transformation. The cost of the
transformation of spike train Sa to
Sb via the pathway P is the sum of the cost of all the elementary transformations along that
pathway:
|
(4)
|
Then, for a given cost parameter, q, the distance
Dspike[q](Sa,
Sb) between Sa and
Sb in the metric
Dspike[q] is defined as the
minimum total cost of transforming Sa to Sb:
=<LIM><OP><UP>min</UP></OP><LL>{ P<SUB>&agr;</SUB> }</LL></LIM>{K<SUB><UP>q</UP></SUB>(P<SUB>&agr;</SUB>)},](/content/vol18/issue16/fulltext/6583/img005.gif)
|
(5)
|
where the minimum is taken over all possible pathways that lead
from Sa to Sb via any
sequence of elementary transformations.
The cost parameter q is the measure of the sensitivity of
the metric to the timing of individual spikes. Shifting a spike by an
amount of time t >1/q is greater in cost than
deleting it altogether. In like manner, shifting a spike by an amount
of time t >2/q is greater in cost than
deleting it and reinserting it in the new location. Thus, spikes whose
times differ by t >1/q sec are viewed by
Dspike[q] as unrelated. For
q = 0, there is no cost associated with shifting spikes
in time (but inserting and deleting spikes are still associated with
unit cost). Hence Dspike[0] is a metric
in which the distance between two spike trains is simply the difference
in the number of spikes they contain, and which therefore we denote
Dcount.
The diagram in Figure
1A illustrates a
sequence of elementary steps associated with the calculation of the
distance in metric Dspike[q]
between spike trains Sa and
Sb. The arrows indicate shifts of spikes in
time. Spike deletions and insertions are indicated by the asterisk.
Depending on the cost of the shifts (as determined by the cost
parameter q) of a metric, the total cost of transformation may be lower if we deleted a spike and reinserted it at the exact required time. Train Sa consists of five spikes,
four of which are shifted in time to coincide with spikes in train
Sb. However, the first spike in
Sa rather than shifted, is deleted and then reinserted into Sb as the next to the last
spike. Insertions or deletions are also necessary when the number of
spikes in the two trains are not equal. An example of this is the last
spike in Sb. An efficient algorithm is available
to find the sequence of transformations that have minimal total cost,
and thus calculate the distance
Dspike[q] between spike
trains (Victor and Purpura, 1997).
View larger version (20K):
[in this window]
[in a new window]
|
Figure 1.
Quantifying the dissimilarity of spike trains via
the spike time metrics
Dspike[q] and
Dspike,circ[q]. The
distance between spike trains Sa and
Sb is the minimum cost of transforming
Sa into Sb via a
sequence of elementary steps, as detailed in Materials and Methods.
A, Spike time metric
Dspike[q]. Spike
trains are considered to be segments of time, and the periodicity of
the stimulus is ignored. The direction of time is indicated at the
bottom left. Transformation of spike train
Sa into Sb
involves the deletion of the first spike of
Sa (marked by asterisk),
insertion of the last two spikes of Sb (also
marked by asterisk), and shifts of the other spikes, as
diagrammed by the arrows from
Sa to the virtual spike train
S'. B, The spike time metric adapted to
periodic stimuli,
Dspike,circ[q]. The
spike trains Sa and
Sb are now considered to be cyclic, with a
period corresponding to that of the stimulus. This modification allows
shifts of spikes to wrap around across the cycle boundaries. In the
example illustrated, this modification changes the minimum-cost set of
transformations to one in which the initial spike of
Sa (marked by asterisk) is
shifted across a cycle boundary to coincide with the last spike of
Sb. For spike trains that differ in the
illustrated manner, the distances in this modified "circular"
Dspike,circ[q]
metric will be smaller than those defined by the open-ended form,
Dspike[q].
|
|
In summary, some important properties of the spike time metrics are (1)
the distance Dspike[q]
between two spike trains is small if the number of spikes in them is
similar, and their times match within a temporal window of width
1/q; (2) if q is zero, only the spike count
matters; and (3) if q is very large, almost all spike trains
are far apart, unless the spike times are almost identical, because the
metric considers spikes that differ by t
>1/q to be unrelated.
Spike time metrics adapted to periodic responses. We
modified the above procedure for computing distances between spike
trains to make it more appropriate for responses to periodic stimuli. The issue addressed by this modification is illustrated in Figure 1B. The first spike in train
Sa is distant from the last spike in
Sb, but it is similar in response phase.
Because of the way that
Dspike[q] is defined, this
kind of similarity is neglected, as a consequence of the partitioning
of the response into successive epochs. But for periodic stimuli, it
might make sense to recognize this kind of similarity by allowing for
cyclic wraparound of spikes. That is, for the purpose of shifting
spikes in time, individual responses are considered to be on a circular
time axis, and each circular segment corresponds to one stimulus cycle.
This modification can reduce the cost of transformation of one
spike train to another by allowing a shift across the point of
wraparound. As the diagram (Fig. 1B) shows, with this
modified spike time metric,
Dspike,circ[q], it is now
cheaper to shift, rather than to delete and then reinsert, the leftmost
spike in spike train Sa.
We used both the original spike time metric
(Dspike[q]) and the
modification that allowed for cyclic wraparound
(Dspike,circ[q]) on all data
sets, with no noticeable difference in the results. Only the results of
analyses with the modified
Dspike,circ[q] are
presented.
For a periodic stimulus, there is some arbitrariness inherent in
the choice of the phase to use as the cut point for partitioning the
spike train into individual responses. One approach is to choose the
onset time of the stimulus cycle as the cut point. A second approach is
to position the cut point in a region of low firing rate, i.e., between
the peaks of the response histogram. We used this second approach,
although a control computation on a few data sets showed no significant
dependence on this choice.
Metrics based on Fourier components. For the purpose
of Fourier analysis, an action potential at time
tj is treated as a unitary event described by a
delta function  (t  tj) centered at
tj, and a spike train is described by the
sum of delta functions centered on the time of occurrence of each spike
in the train. A set of m responses may be represented by
|
(6)
|
corresponding to m cycles of the stimulus
s of period Ts (and temporal
frequency = 1/Ts). We calculate the
first n Fourier harmonics of these m
responses,
|
(7)
|
We considered families of metrics based on these Fourier
components. For each harmonic of the stimulus cycle, the corresponding Fourier component can be thought of as a two-component vector (the real
and imaginary parts). A set of k Fourier components thus
corresponds to a real vector space of 2k dimensions. In a vector space, a natural distance is defined by the Pythagorean rule,
and this Euclidean vector-space distance can also serve as a metric.
We explored four families of such metrics, each parametric in
n, the largest Fourier harmonic considered: (1)
Fsingle[n], the Pythagorean
distance based on the nth harmonic alone; (2)
Fall[n], the Pythagorean
distance based on all of the first n components; (3)
Feven[n], the Pythagorean
distance based on the even harmonics up to n; and (4)
Fodd[n], the Pythagorean
distance based on the odd harmonics up to n. The temporal
frequency of the nth harmonic, n, plays a role similar to that of the cost parameter q; for both, the
reciprocal specifies the time scale over which details in the temporal
structure of the spike train affect the corresponding metric. With this in mind, we allowed n to span a comparable range to that
of q in our calculations (see below).
Cluster analysis. Each of the above metrics formalizes a
notion of similarity between spike trains. A candidate notion of similarity is only relevant to coding if the observed responses to
distinct stimuli tend to be more dissimilar than responses to the same
stimulus (Victor and Purpura, 1997). The goal of the second step in our
analysis is to ask, for each of the metrics, the extent to which this
is the case. The answer is summarized by a single value, the
transinformation (Abramson, 1963). We use transinformation as a measure
of stimulus-dependent clustering for each metric. If it is high, then
each stimulus leads to distinct response clusters in the abstract space
defined by the metric under consideration. That is, the responses to
different contrasts are much more dissimilar (i.e., lie in distinct
clusters) than responses to the same contrast. If the transinformation
is low, then (for the particular metric under consideration), responses to stimuli of different contrasts are largely overlapping. Note that we
use transinformation to quantify the extent to which clustering of
spike trains, not spikes, in metric spaces of responses systematically depends on a stimulus parameter (contrast).
The experiment is considered to consist of C stimuli
s1,
s2, ...,
si ..., sC. We
classify an individual spike response S according to its
average distance from all the responses
Sa = {S'} elicited by each
particular stimulus sa. A spike train S  Si elicited by stimulus
si will be classified as belonging to response class rj if it was closer on average to the
Sj responses elicited by stimulus
sj than to the responses elicited by any
other stimulus. For this purpose, the average distance between a
spike train S and all the responses
Sa elicited by stimulus
sa is defined by:
|
(8)
|
for any metric D, which may include
Dspike,circ[q],
Fsingle[n],
Fall[n], etc.
This classification procedure is then applied to each spike train.
Results are summarized in a confusion matrix,
N(si,
rj), which tallies the instances in which
a stimulus si elicited a response that was
categorized as belonging to response class rj. That is, N(si,
rj) is the number of instances in which a
response to stimulus si would be confused with a
response to a stimulus sj, based on the
similarities of the recorded spike trains. If this matrix is diagonal,
responses are in perfect correspondence to the stimuli that elicited
them, and the extent of stimulus-dependent clustering is maximum. If,
on the other hand, the confusion matrix elements are all equal, then
the metric leads to an apparently random association between stimuli
and responses. In this instance, the extent of stimulus-dependent
clustering is minimum.
The confusion matrix N(si,
rj) depends on the metric via the
clustering algorithm. The transinformation indicates, for any metric,
where be- tween the extremes of stimulus-dependent clustering the confusion matrix N(si,
rj) lies. It is given by
|
(9)
|
H takes on non-negative values (in bits), with
H = 0 corresponding to minimum clustering. The maximum
value of H depends on the choice of stimuli. (For this
reason, we used sets of comparable contrasts for the edge and grating
experiments.) For C equally likely stimuli, perfect
stimulus-dependent clustering corresponds to H = log2C. In our data sets, stimuli of different
contrast were not equally likely. Each stimulus of nonzero contrast was presented an equal number of times, but the blank (zero contrast) was
presented a number of times equal to the total number of nonblank presentations. For C 1 nonblank stimuli and 1 blank
presented with these probabilities, perfect contrast-dependent
clustering corresponds to H = 1 + 0.5 log2(C 1). For C = 7, H ~2.29, the ideal maximum for our contrast experiments.
However, much smaller values of H indicate significant
stimulus-dependent clustering. For example, a 70% correct performance
in a two-alternative forced choice situation corresponds to
H = 0.12.
When the set of available responses is limited, as in real data, the
estimate of the transinformation H contains a positive bias
(Carlton, 1969; Treves and Panzeri, 1995). This is because even if
clustering is at chance levels, there may not be an equal number of
counts in each cell of the confusion matrix. A conservative approach to
correction of this bias is to subtract an empirical estimate of the
bias in H caused by chance clustering. We derived this
estimate by recalculating the transinformation after several random
reassignments (typically 10) of the responses across stimuli. We found
that this bias estimate for H was small compared with H and also relatively independent of q. Hence,
our results would not change had we elected to not subtract the
correction. Further discussion of the bias and the algorithm to compute
H is given in Victor and Purpura (1997).
The shape and maximum of the H(q) function
describes the temporal coding capabilities of the neuron. If, for
example, the spike count carries all of the potential information in a
response of a neuron, then H(q) will achieve its
maximum at q = 0, because timing of individual spikes
[which affects H(q) for q > 0]
does not depend systematically on the stimulus and thus degrades
clusters. On the other hand, if the timing of spikes systematically
depends on the stimulus, then we expect that H(q)
will be maximal in the neighborhood of q, which is the
inverse of the meaningful temporal precision of the firing of the
neuron. We computed H(q) at q = 0 and typically 14 additional points in logarithmic steps along the
q axis from 1 to 512, corresponding to increasing temporal sensitivities from the order of a second through a few milliseconds. For the metrics based on Fourier harmonics, the characteristic frequency n takes the role of q. For
H(n), n was varied, in a range
comparable to that of q, in 14 steps.
| |
RESULTS |
In previous work, evidence for temporal coding of contrast in V1
neurons was obtained in experiments that used several types of
transient stimuli, including flashed gratings and patterns (Victor and
Purpura, 1996, 1998; Richmond et al., 1997). Those experiments did not
include steady-state grating stimuli-stimuli, which are commonly used
in vision research but which are not typically analyzed for the
presence of a temporal code. This leaves open the question of whether
the transient nature of the stimulus is essential for temporal coding,
or, alternatively, whether the apparent presence of temporal coding is
primarily attributable to the analytical approach. To address this
question, we compared (for the same neurons) the coding of contrast in
responses to two classes of stimuli: drifting sinusoidal gratings and
drifting low-frequency square waves, or edges. The drifting square
waves were presented with at most one edge within the receptive field at any time. Unlike sustained presentation of drifting gratings that
provide a spatiotemporal steady-state input for the local cortical
circuit, a drifting sharp edge engages only parts of that same circuit
at any time, and only in a transient manner.
Contrast responses to drifting sinusoidal gratings as well as drifting
square waves (edges) of 22 isolated neurons were extracellularly recorded in the primary visual cortex of the anesthetized macaque monkey. For stimuli of both classes, the orientation, direction, and
temporal frequency (and, for gratings only, spatial frequency) were
optimized for the selectivity of the receptive field of each neuron.
Details of the optimization are given in Materials and Methods. The
contrast levels spanned a wide range in approximately logarithmic
steps, 8-78% for gratings and 11-90% for edges. (Note that the
contrast of the first harmonic component of an edge was approximately
equal to the contrast of a corresponding grating in the set. We needed
to explore a similar response range for edges and gratings. With the
convention we used, the contrasts, response sizes, and clustering
estimates for the two stimulus classes were comparable.) Thus, a
complete data set for one neuron consists of a set of responses at six
nonzero contrast levels and the blank condition, for both gratings and
edges. We first present results of the analysis based on spike time
metrics and then those based on Fourier components. For each set of
metrics, we begin by showing the analysis of responses from several
typical units, and then present results across the population of
neurons in our sample.
Cluster analysis based on spike time metrics
Single-unit example: complex cell
Figure 2 shows the data obtained
from a complex cell, typical of our sample. For this cell, a
nondirectional layer 6 neuron, the stimulus parameters were 0.2 cycle/°, 1 Hz (edge), and 1.6 cycles/°, 5 Hz (grating). Responses
to edges (Fig. 2A-C) and to gratings
(Fig. 2D-F) are presented in
identical format. This complex cell, when measured with both gratings
and edges, had a threshold contrast of ~5% (data not shown) and a
monotonically increasing response up to 60-80% contrast. For
gratings, the contrast-response function saturated at the highest
contrasts (Fig. 2E).
View larger version (41K):
[in this window]
[in a new window]
|
Figure 2.
Analysis of temporal coding in contrast
responses of a layer 6 nondirectional complex cell (mt926).
A, Cycle-by-cycle raster plots of responses to edges
(0.2 cycle/°, 1 Hz, 24 cycles at each contrast) at the seven
different contrasts indicated on the right. Only a
subset of the blank runs are shown. B, Semilogarithmic
plot of the contrast-response function for edges based on the DC
component of responses. Error bars are ±1 SD. C, Level
of contrast-dependent clustering (uncorrected for chance clustering),
H(q), for edge responses
(thick line with plus symbols), and the
estimated level of chance clustering (dashed line) for
the metrics
Dspike,circ[q], as a
function of the cost parameter (q). For the
estimate of the level of chance clustering, 10 random reassignments
were used, and the SE values of these estimates are indicated by the
shaded region. D, Cycle-by-cycle raster
plots of responses of the same complex cell to gratings (1.6 cycle/°,
5 Hz, 40 cycles at each contrast) at seven different contrasts. Only a
subset of the blank runs are shown. E,
Contrast-response function for gratings, based on the DC component of
responses. F, H(q)
for the grating responses, plotted as in C.
|
|
The raster plots in Figure 2A show the cycle-by-cycle
responses to drifting edges. Each of the six runs contained four cycles of the stimulus; the illustrated rasters were obtained by segmenting each of these runs at the onset of each stimulus cycle, for a total of
24 cycles. This neuron, like most complex cells, had nonzero
spontaneous activity in the presence of the blank (zero contrast) and
responded to the passage of edges of both polarities with similar
bursts. (Each cycle of the drifting square wave introduces two edges of
opposite contrast, half a cycle apart.) The average number of spikes in
these bursts monotonically increased with increasing contrast. There is
a moderate phase advance, more noticeable in the first response of each
raster line, as contrast increases. The usefulness of this form of
temporal information about the stimulus contrast is unclear, because of
trial-to-trial variability.
The DC component of the responses (for each contrast, the average spike
count divided by the stimulus period) was used to construct the
contrast-response function in Figure 2B. The error bars (±1 SD of the mean firing rate) indicate a considerable
cycle-by-cycle variability in the responses. This variability limits
the ability of the cell to discriminate contrast levels based on the
spike counts in its response.
To compare the usefulness of changes in spike counts and spike timing,
we used the cost-based metric approach described in Materials and
Methods. This procedure results in a function
H(q) that measures the extent to which changes in
contrast result in reproducible changes in firing pattern. When q
= 0, the assessment of firing pattern ignores spike timing
altogether and is sensitive only to the number of spikes in each
response. For q > 0, the assessment of firing pattern
is sensitive to spike timing, with a precision of 1/q.
Thus, in examining H(q), we focus on the temporal
precision qmax at which the level of
contrast-dependent clustering is maximal, Hmax = H(qmax), and we compare
Hmax with the level of contrast-dependent clustering obtained by spike counts alone,
Hcount = H(0). The difference
H = Hmax Hcount is a measure of temporal coding in
responses of a neuron. If spike timing does not contribute to coding of
contrast, then we would find that qmax = 0 and
H = 0. We emphasize that we are not so much
interested in the absolute transinformation values H, as in
how H(q) depends on temporal sensitivity
(q), and in how the relative temporal contributions compare
across the two classes of stimuli.
For the edge responses of this cell, the calculated
H(q) is shown in Figure 2C by the
thick line and the plus symbols. The cost parameter q
(seconds1) was sampled at 0, and from 1 to 512 in
14 logarithmic steps, with the extremes corresponding to equivalent
temporal precision of a second and two milliseconds, respectively. As
seen in Figure 2C, H(q) rises from a
low value at q = 0 (Hcount = 0.35) to a maximum (Hmax = 0.83) at
qmax = 64 sec1, indicating
that the level of clustering is maximal for a temporal sensitivity of
the underlying spike time metric of ~16 msec (1/q). H(q) takes a sharp downward turn for
q > 100 sec1. This cutoff at the
high end indicates that paying attention to details of spike timing on
the order of  10 msec makes spike trains elicited by the same stimulus
seem too dissimilar in the underlying metric to allow meaningful
clustering.
The dashed line in Figure 2C indicates the estimate for the
level of chance clustering which, as previously reported (Victor and
Purpura, 1997), is relatively insensitive to q. Thus, the features described above (the location of qmax
and the large positive H = Hmax Hcount),
remain after subtracting the correction for chance clustering. We thus
conclude that, for this response of this neuron to edges, taking into
consideration spike timing yields much greater levels of
stimulus-dependent clustering than would be obtained by counting spikes
alone. That is, stimulus contrast may be determined from the responses
with greater certainty if the timing of spikes is not ignored. This
finding is typical of the complex cells in our sample.
The same analysis was also applied to the responses elicited from this
complex cell by the gratings, the steady-state stimuli (Fig.
2D-F). This neuron, like most
complex cells, responds to gratings of optimal frequency with a rather
unmodulated elevation of the spike rate. The response rasters (Fig.
2D) show a relatively irregular distribution of
spikes over the time course of the stimulus and a considerable
variation of their timing from trial to trial. As in the edge
responses, the contrast-response function has a monotonic rise over
most of the available contrast range (Fig. 2E), with
a large variance of spike counts, as indicated by the error bars. The
clustering analysis is shown in Figure 2F. Unlike what was seen for edges, for gratings H(q)
(thick line with filled circles) is maximal
at q = 0 (Hcount = 0.63). As
q increases, H(q) runs a rather flat
course up to q ~50 sec1, after which
there is a sharp cutoff. The important difference between edge
responses and grating responses in this neuron is that for drifting
grating responses, Hcount maximizes
H(q). This indicates that once spikes are
counted, the temporal structure of the grating responses provides no
additional information concerning their contrast.
Given the mostly flat, irregular response time course with little
discernible systematic variation with increasing grating contrast of
the complex cell, this is perhaps not a surprising result, but it is
not merely confirmation of the intuition that there are no spikes with
precise timing buried in the raster. As we see below, the lack of a
temporal contribution to the level of contrast-dependent clustering of
grating responses was found in most of the neurons in our sample,
including simple cells that gave strongly modulated responses to
gratings.
Single unit example: simple cell
Figure 3 shows an analysis of edge
responses (Fig. 3A-C) and grating responses
(Fig. 3D-F) for a typical simple cell, in
the same format as the analysis of complex cell responses in Figure 2.
For this cell, a nondirectional layer 6 neuron, the stimulus parameters
were 0.3 cycle/°, 3 Hz (edge); 1.2 cycles/°, 5 Hz (grating). For
both gratings and edges, contrast sensitivity was typical for our
sample (threshold contrast was ~5%), and response was monotonic up
to 30-40% contrast. At higher contrasts, the contrast-response function saturated and perhaps even turned down (Fig.
3B,E).
View larger version (30K):
[in this window]
[in a new window]
|
Figure 3.
Analysis of temporal coding in contrast
responses of a layer 6 nondirectional simple cell (mt928). Data are
plotted as in Figure 2. A-C, Edge
responses (0.3 cycle/°, 3 Hz, 24 cycles at each contrast).
D-F, Grating responses (1.2 cycle/°, 5 Hz, 40 cycles at each contrast). A, D,
Cycle-by-cycle rasters of spikes. Only a subset of the blank runs are
shown. B, E, Contrast-response function.
C, F,
H(q) (uncorrected, thick
lines with symbols; correction for the level of
chance clustering, dashed line; SE values of the
correction estimates, shaded region).
|
|
This neuron, like most simple cells, had no spontaneous activity in the
presence of the blank (0% contrast in Fig.
3A,D). For edges of increasing
contrast, the response consisted of a burst of spikes of increasing
intensity up to a saturating level near 30% contrast. Like most simple
cells, it responded to the passage of an edge of one polarity but not
the other. That is, there is only one response transient in the rasters
(Fig. 3A), unlike the pair of transients seen for responses
of typical complex cells to the drifting low-frequency square wave
(Fig. 2A). There is also a moderate phase advance in
the responses with increasing contrast, as was seen in the responses to
edges of the complex cell. Because this shortening of latency (Gawne et
al., 1996) occurs for contrasts in which the spike count has saturated,
it might be especially useful in discriminating among the higher contrast levels. However, given the trial-to-trial variability of the
response onset, the utility of latency in signaling contrast is unclear
from mere inspection of the rasters. The response magnitude is also
quite variable, as indicated by the error bars in Figure 3B.
The function H(q) is plotted in Figure
3C (thick lines with plus
symbols). H(q) has an initial jump from
Hcount = 0.61 (at q = 0) to a
higher value at q = 1 sec1, the
lowest nonzero value of q examined. The course of
H(q) is a plateau over most of the sampled range,
with a suggestion of a maximum near q = 50 sec1 (Hmax = 0.82).
H(q) declines sharply above q = 250 sec1. Subtracting the correction for the level
of chance clustering (dashed line) does not change
these general features. That is, a positive H = Hmax Hcount remains,
indicating the presence of temporal coding of contrast in the responses
of a simple cell to edges. As in this example, most other simple cells
in our sample also had evidence of a temporal contribution to coding
edge contrast, but the relative size of this contribution was usually
smaller than in complex cells.
Figure 3D-F shows the results obtained in this
simple cell with gratings. Unlike the complex cell of Figure 2, the
response time course is not uniform. As contrast increases, the rasters (Fig. 3D) indicate increasingly compact responses, and there
is the suggestion of a burst structure at the highest contrasts. The
contrast-response function saturates at intermediate levels (Fig.
3E). Trial-to-trial variability is large, both in terms of
onset time (Fig. 3D) and spike counts (Fig. 3E).
Despite the similarity in the response waveforms seen for this simple
cell to both gratings and edges, H(q) has a
different shape. For gratings (Fig. 3F, filled circles
and thick line), H(q) is
maximal at Hcount = H(0). That is,
the changes seen in the response time course with increasing contrast
are not reliable enough to add to the signaling of contrast. As in the
case of the complex cell of Figure 2, the details of the temporal
structure of spike trains do not add significantly to the
contrast-dependent segregation of clusters of responses to
gratings.
Other examples
This difference in temporal contribution to contrast information
for edges and gratings was found in most of the neurons in our sample.
Figure 4, A and B,
shows examples of this for two more neurons. For each cell, the measure
of stimulus-dependent clustering, H(q), based on
the circular spike time metrics, with the level of chance clustering
subtracted, is presented for edges (plus symbols) and
gratings (filled circles). Figure
4A shows results from a layer 4C nondirectional
complex cell. For edges, H(q) has a maximum,
Hmax = 0.72, at qmax = 22 sec1, yielding a large H, several
times larger than Hcount = H(0). This
is an example in which the spike count severely underestimates the
ability of the neuron to signal contrast of edges. The position of
qmax indicates that the level of
contrast-dependent clustering is optimal for a temporal resolution of
45 msec; note that the period of the edge was 2000 msec. For the
response of the same cell to gratings, H(q) is
maximal at q = 0 (Hcount = 0.56, see arrowhead), indicating that spike counts carry the
maximum contrast information. The analysis for the simple cell in
Figure 4B is a variation on this theme. For this
neuron, there is evidence for the presence of temporal coding of
contrast for both edges and gratings, but H, the maximum
increase in H(q) over H(0) associated with temporal coding, is larger for edges (0.28, 120% of
Hcount) than for gratings (0.08, 14% of
Hcount). For both gratings and edges,
Hmax values are comparable in magnitude and
occur at similar positions qmax ~20
sec1 (corresponding to ~50 msec precision). This
neuron had the largest H among the simple cells in our
sample.
View larger version (18K):
[in this window]
[in a new window]
|
Figure 4.
Comparison of the level of
contrast-dependent clustering,
H(q), for edges
(plus symbols), and gratings
(filled circles), for three V1 neurons.
H(q) is determined for the metrics
Dspike,circ[q], and
the level of chance clustering has been subtracted. An
arrowhead points to the maximum of each
H(q) curve. A and
B are typical examples, C is an
exceptional cell for which temporal structure contributes more strongly
to the maximum of H(q) for
responses to gratings than to edges. A, Layer 4C
nondirectional complex cell (mt918). Edges, 0.3 cycles/°, 0.5 Hz, 12 cycles at each contrast; gratings, 4 cycles/°, 6 Hz, 48 cycles at
each contrast. B, Layer 4C nondirectional simple cell
(mt838). Edges, 0.2 cycle/°, 3 Hz, 24 cycles at each contrast;
gratings, 0.6 cycle/°, 5 Hz, 80 cycles at each contrast.
C, Layer 4B nonoriented simple cell (mt942). Edges, 0.15 cycle/°, 3 Hz, 24 cycles at each contrast; gratings, 0.5 cycle/°,
10 Hz, 80 cycles at each contrast.
|
|
The simple cell in Figure 4C is one of three neurons in our
sample that showed evidence for temporal coding for gratings but not
for edges. This simple cell had the largest H (0.26, 300% of Hcount) for gratings among all
the neurons in our sample, whereas the other two neurons (a simple and
a complex cell) both exhibited very small H for gratings.
The peaks in the two clustering curves in Figure 4C are
comparable in height. The curve for the edges is maximized by
Hcount, whereas clustering for gratings
reaches its peak near q = 100 sec1
(equivalent to a temporal resolution of 10 msec).
Analysis across cells
In most neurons, evidence for temporal coding of contrast was
stronger for edges than for gratings. To quantify this difference across the population of the 22 V1 neurons in this study, we
plotted (Fig. 5) the
level of contrast-dependent clustering obtained with spike count alone
(Hcount) on the horizontal axis against
the maximum level (Hmax) on the vertical
axis. The estimate of the level of chance clustering was subtracted
from each value. In this plot, each neuron is plotted twice, with plus
symbols for edges and with filled circles for gratings. If the stimulus
dependency of clustering is most reliable at q = 0, then Hmax = Hcount, and the corresponding symbol
falls on the identity line (diagonal). This indicates
the absence of a detectable temporal contribution to the coding of
contrast. If, however, stimulus-dependent clustering was most reliable
at q > 0, then Hmax > Hcount, and the symbol falls above the
identity line. This indicates a temporal contribution to the coding of
contrast. Most of the points corresponding to gratings fell on or near
the diagonal, and the largest vertical displacements from the diagonal
are seen for edges.
View larger version (15K):
[in this window]
[in a new window]
|
Figure 5.
Comparison of the levels of contrast-dependent
clustering obtained with spike counts and spike time metrics in 22 V1
neurons. Hcount, the level
achieved with Dcount = Dspike,circ[0], is plotted against
Hmax, the level achieved with the
optimal spike time metric
Dspike,circ[qmax].
Each neuron is represented by two data points: one for edges
(plus symbols) and one for gratings
(filled circles). Symbols lying above the
diagonal Hcount = Hmax indicate a contribution of the temporal
pattern of spikes to coding of contrast.
|
|
Table 1 summarizes the average level of
contrast-dependent clustering based on spike counts
(Hcount), the average peak level of
clustering (Hmax) obtained with the
metrics Dspike,circ[q], the
average relative contribution at the peak level from temporal coding
(H/Hcount), and the number
of cells with significantly positive H. These averages
are given for edges and gratings and for simple and complex cells. The
level of chance clustering is subtracted in all cases. For most
neurons, the stimulus dependency of clustering of responses to edges
became more reliable when the underlying metric was sensitive to the
temporal details of the spike trains. The average size of the increase
was 47% of the average Hcount (60% in complex
cells, 33% in simple cells; two-sample t test, significant
difference at p < 0.05). However, for gratings, the
spike count metric usually provided the most reliable
stimulus-dependent clustering. Only a minority of neurons showed
evidence for a temporal contribution to the coding of grating contrast,
and the size of this improvement was small (7% on average over spike
counts).
The average contrast-dependent clustering estimated as the population
mean ± 1 SD of Hmax, was 0.60 ± 0.26 for gratings and 0.56 ± 0.23 for edges (n = 22), not significantly different (paired t test,
p > 0.14). This difference across stimulus types
tended to be larger for simple cells than for complex cells, but was not statistically significant in either case. In keeping with the above
difference in temporal contributions for gratings and edges, there was
a significantly greater (p < 0.01) level of
clustering via spike counts alone for gratings (0.57 ± 0.27) than
for edges (0.38 ± 0.23).
Figure 5 and Table 1 provide an estimate of the contribution of
temporal coding for gratings and edges but do not allow the comparison
within cells. Figure 6 shows the
contribution of temporal structure to the peak levels of clustering of
responses to gratings (HG) and edges
(HE) for each neuron. Open symbols
represent simple cells, and filled symbols represent complex cells. For most of the neurons the measured contribution of temporal structure to
contrast-dependent clustering was greater for edges than for gratings.
Nine neurons exhibited a positive contribution exclusively for edges,
but only three neurons (two simple and one complex cell) showed
temporal contribution exclusively for gratings, and in only one of
these three (Fig. 4C) was the contribution large. Four
neurons had no significant temporal contribution to the level of
contrast-dependent clustering for either stimulus class. Figure 6 sums
up, in essence, the major finding of this study.
View larger version (15K):
[in this window]
[in a new window]
|
Figure 6.
Comparison of the temporal contribution to the
maximum level of contrast-dependent clustering in the responses of 22 V1 neurons to gratings (HG = Hmax, Grating Hcount,
Grating) versus edges (HE = Hmax, Edge Hcount, Edge). Neurons for which temporal
pattern contributes to contrast-dependent responses for edges but not
gratings occupy the top left region along the
HE axis in the scatter plot. Neurons with
the opposite behavior are represented by symbols scattered near the
HG axis. As the scatter shows, most V1
neurons belong to the first group. Simple cells are represented with
open symbols, complex cells with filled
symbols.
|
|
We characterized the resolution of the temporal structure that
contributes to the level of stimulus-dependent clustering via the cost
parameter that maximizes H(q),
qmax. The distribution of
qmax is shown in Figure
7A. Each of the 22 neurons
yielded two values of qmax: one derived from the
edge responses, and one from the grating responses. Two-thirds of the
data sets exhibited temporal coding (Hmax > Hcount, qmax > 0). For these, the distribution of qmax is wide,
sampling a range of equivalent temporal resolution (1/qmax) from 10 msec to 1 sec. The
geometric mean of qmax was 17 sec1 overall (18 sec1 for
edges and 16 sec1 for gratings; not significantly
different, p > 0.7), indicating, on average, a
temporal resolution for contrast of ~60 msec. Although overall
temporal resolution was not significantly different in simple and
complex cells, we found a significantly finer temporal resolution for
edges in complex cells (29 sec1) than in simple
cells (10 sec1; p < 0.02). Within
complex cells, temporal resolution for edges was significantly higher
than for gratings (11 sec1, p < 0.01).
View larger version (19K):
[in this window]
[in a new window]
|
Figure 7.
A, Distribution of the cost
parameter (qmax, plotted
logarithmically except for qmax = 0) that
maximizes H(q) based on
Dspike,circ[qmax].
Each of the 22 neurons is represented by two values, one for
edges and one for gratings. The geometric mean of the nonzero values of
qmax was 17 sec1,
indicating an average temporal resolution of 60 msec for the optimal
spike time metric in those neurons in which temporal pattern
contributed to stimulus-dependent clustering. The dark
portion of the histogram is the distribution of complex cells.
B, Distribution of the temporal frequency
(tfmax = nmax)
of the highest Fourier harmonic that was needed to maximize
H(n) based on the metric family
Fall (Fig. 8). The geometric mean of
the nonzero values of tfmax was 9.6 Hz.
Distribution of complex cells is indicated by the dark
portion as in A.
|
|
The relative contribution (~50% of the average
Hcount) of temporal structure to
Hmax of edge responses is comparable to what we
found for contrast responses of V1 neurons to stationary gratings flashed for 256 msec in the anesthetized macaque [contrast data of
Victor and Purpura (1998) pooled across spatial phase]. In that study,
which included responses to gratings of nonoptimal spatial frequency
and orientation, population averages (after correction for the level of
chance clustering) were Hcount = 0.044, Hmax = 0.068, H = 54% of
Hcount, with a positive H
in 28 of 32 data sets. A data set comprising 15 contrast-response
functions of V1 neurons of the awake behaving macaque (Victor and
Purpura, 1996; reanalyzed) yielded somewhat larger values for these
average quantities and for the relative contribution of temporal
structure: Hcount = 0.10;
Hmax = 0.31; H = 210% of
Hcount. In 12 of 15 data sets there was a
positive H. The stimulus conditions in the latter study
were the same as those of Victor and Purpura (1998).
The geometric mean value of qmax obtained in the
present study (17 sec1) agrees well with values
found for contrast coding of flashed stimuli in V1 of awake [21
sec1; Victor and Purpura (1996), their Fig.
6A] and anesthetized macaques [18
sec1; contrast data of Victor and Purpura (1998),
pooled across spatial phase].
Results of the present study and the previous two cited above indicate
that the stimulus-dependent temporal contribution to contrast coding is
too large (~50% or more) to be overlooked in evaluating the function
of a neuron. Comparable contributions of temporal structure were also
found for stimulus modalities other than contrast, such as spatial
frequency and orientation, both in the awake study of V1 and V2 neurons
(Victor and Purpura, 1996) and in the study in anesthetized macaques
(Victor and Purpura, 1998). The implication is that classical tuning
curves based on the average firing rates can seriously underestimate
the potential for visual neurons to signal characteristics of the
stimulus. Such estimates critically influence our understanding of the
neural mechanisms underlying behavior. For example, underestimating
dynamic range in V1 neurons would result in overestimating the minimum size of the neuronal population over which pooling of signals is
necessary to explain behaviorally measured contrast discrimination.
Cluster analysis based on Fourier components
The above results demonstrate that within the same neuron,
temporal coding (i.e., a systematic dependence of the temporal structure of the response on a nontemporal aspect of the stimulus) is
prominent for one class of stimuli (drifting edges) and much less
important for another (drifting gratings). It is conceivable, however,
that the identification of temporal coding is in some way related to
the unconventional analysis technique, i.e., a metric-space embedding
in which any possible additive structure is simply ignored.
For these reasons, we also analyzed our data in a manner based on
Fourier components of the response. As will be seen below, Fourier
components can be used to define several sequences of metrics, each of
which forms the basis for a clustering calculation. In contrast to the
spike time metrics, the Fourier metrics are also Euclidean distances
that respect the additive and Euclidean structure of a vector space of
responses. Thus, we will be able to determine whether the above results
depend on the use of a nonEuclidean distance. On the other hand, if
temporal coding is robust, it should be manifest in the analysis based
on Fourier metrics as well.
Because the Fourier metrics and the spike time metrics look at the same
signals (the former in the frequency domain and the latter in the time
domain), intuition suggests that the results obtained by the two
approaches should closely correspond. However, this correspondence is
not guaranteed because the algorithms involved in the Fourier approach
are not simply transforms of algorithms used in the spike time
analysis. Thus, a secondary motivation for the Fourier-based analysis
is to determine whether the temporal coding we have identified in the
time domain corresponds to specific harmonics or specific frequency
ranges within the response.
The first step in construction of the Fourier-based metrics is
cycle-by-cycle Fourier analysis of the responses of a neuron to each
trial of a particular stimulus at integer multiples of the fundamental
stimulus frequency. A set of estimates of k Fourier components of a response can be considered to be a set of 2k
real numbers, representing the cosine and sine components at each of the k harmonics. These 2k-tuples are points in a
2k-dimensional vector space, and as such, are associated
with a natural distance: the Pythagorean rule. This distance is
Euclidean, but it depends on the number of harmonics (k),
and on which k harmonics are chosen. Once these distances
were calculated, we used the same clustering algorithm and measure of
stimulus-dependent clustering (H) that we used for
the spike time metrics, thereby allowing for a direct comparison of
results obtained using the different kinds of metrics.
We considered four families of Fourier metrics, all parametric in a
single frequency parameter, the highest (nth) response harmonic included in the analysis. These families are (1)
Fsingle[n], which includes
only the single nth harmonic; (2)
Fall[n], which includes all
harmonics up to the nth harmonic; (3) Feven[n], which includes all
even harmonics up to the nth harmonic, including the DC
component; and (4) Fodd[n],
which includes all odd harmonics up to the nth harmonic and the DC component as well. Analysis based on the family
Fsingle[n] quantifies the
relative importance of single response harmonics in temporal coding of
contrast. For n = 0, 1, and 2, it considers only the
DC, first, and second harmonics of the response, which are commonly
used to describe responses of V1 neurons to periodic visual
stimulation. The other three families
(Fall[n],
Feven[n], and
Fodd[n]) provide a fuller
characterization of the spike responses than single harmonics. For
example, typical complex cell responses to drifting edges are
double-peaked, but not necessarily sinusoidal, a feature that motivates
Feven[n]. On the other hand,
typical simple cell responses to both gratings and edges are
approximately half-wave rectified, indicating the presence of a mixture
of at least one significant odd harmonic (the first) and perhaps
several significant higher even harmonics. In both cases, analysis
based on these metrics will indicate the extent to which the distinct
harmonics have the potential to provide independent information
concerning contrast.
For each metric, the highest temporal frequency considered is equal to
n, where is the temporal frequency of the stimulus. This combination plays a role that is similar to the role of the cost
parameter q in the analysis based on spike time metrics. Both parameters have dimensions of reciprocal time
(sec1) and both specify, in the inverse sense, a
temporal scale above which details of the temporal structure in spike
trains affect the calculated distance between them. We therefore
analyze the level of stimulus-dependent clustering H as a
function of the frequency of the nth harmonic, and we will
display the results as a function of n. The main
quantities of interest will be the relative contribution of temporal
pattern to the maximum level of clustering, as quantified by
H = Hmax Hcount, as well as the temporal frequency
at which maximum is obtained. (Note that for all four families,
n = 0 considers only the DC response and is thus
identical to the spike count metric.)
Single-unit examples
The two illustrated cells (Fig. 8),
one complex (top panels) and one simple (bottom
panels), are typical and illustrate the main points of the
Fourier-based cluster analysis. For each cell, data obtained with
gratings are shown in the left panels, and data obtained with edges are
shown in the right panels. The five curves in each panel indicate the
level of stimulus-dependent clustering H(q)
obtained with the family of
Dspike,circ[q] of spike time
metrics (thick solid line), and
H(n) obtained with the four families of
Fourier-based metrics (dotted line for Fsingle[n]; thin
lines with asterisks for
Fall[n]; thin
lines with plus symbols for
Feven[n]; and thin
lines with open circles for
Fodd[n]). For the Fourier
metrics, H is plotted as a function of n, where is the temporal frequency of the stimulus (in Hertz) and n is the highest harmonic of this frequency used in the
metric. For all curves, the estimated level of chance clustering has
been subtracted.
View larger version (32K):
[in this window]
[in a new window]
|
Figure 8.
Comparison of
H(n) based on four families of Fourier
metrics (Fsingle, thin dotted
lines; Fall, thin line
with asterisk;
Feven, thin lines with
plus symbols; Fodd,
thin lines with open circles), and
H(q) based on spike time metrics
(thick line with no symbols) in two typical V1 neurons.
A, B, Analysis of grating
(A) and edge (B) responses
of a layer 4C complex cell (mt918, stimulus conditions as in Fig.
4A). C, D, Analysis
of grating (C) and edge (D)
responses of a layer 6 simple cell (mt829; edges, 0.36 cycle/°, 1.25 Hz, 15 cycles at each contrast; gratings, 6.1 cycles/°, 4 Hz, 32 cycles at each contrast). For each data set, the five H
curves are shown on comparable abscissae; for the Fourier metrics, as a
function of the frequency (in Hertz) of the highest harmonic used, for
the spike time metrics, as a function of the cost parameter
q (sec1).
|
|
All curves share the same value of H(0) because this is the
measure of contrast-dependent clustering based on spike counts only. In
each panel, H(n) obtained with one or more of
Fall,
Feven, and
Fodd run a course similar to that of the
H(q) curve. However,
H(n) based on
Fsingle always has a very different
course; it decreases after the first few harmonics but then maintains a
relatively constant low level thereafter, often crossing the other
curves after they decline at high frequencies. The H curves
based on the metric family Fsingle
exhibit low levels of information content and more variation than those
based on cumulative use of Fourier harmonics because of the low
signal-to-noise in single harmonic components at intermediate-to-high temporal frequencies.
The peak of the H(n) curve based on
Fsingle was always at one of the first
three (n = 0, 1, or 2) harmonics. Except for data sets in which there was no evidence of temporal coding (i.e., those in which
maximal level of clustering occurred for the spike count metric), this
peak was not as high as the peaks attained by one or more of the other
Fourier metric series or by the series of spike time metrics. Thus,
using a single response harmonic results in underestimation of temporal
coding, even if much of the signal in the response power is at one or
only a few frequencies. In other words, distinct Fourier components of
the response are not redundant and contain at least partially
independent contrast information.
The other common feature of the data is that at very high frequencies
and values of q, H(n) based on
Fsingle exceeds
H(n) based on the other metrics. Most likely,
this is because at high frequencies, all response amplitudes are very small, but there is likely a persistent small stimulus-related signal
carried in the phase. The lack of a sharp decline in
H(n) calculated with
Fsingle is consistent with this notion
because phase differences tend to scale in proportion to frequency. On
the other hand, the high-frequency cutoff in
H(n) obtained with metrics that use harmonics
in a cumulative manner indicates that the stimulus-related signals across high-frequency harmonics are redundant and that their cumulative use mostly accumulates noise. Thus, the curves of
H(n) based on
Fall,
Feven, and
Fodd decline rapidly at high frequencies
and cross the curve of H(n) based on
Fsingle.
The three metric families that make cumulative use of the Fourier
harmonics show differences in the H(n)
function for the edge data that shed new light on the known properties
of simple and complex cells. For the complex cell,
Feven shows evidence of temporal coding
to an extent comparable to Dspike,circ,
but the persistent low values of H(n) for
Fodd indicate that the odd harmonics have
no consistent stimulus-dependent behavior (Fig. 8B).
For the simple cell (Fig. 8D), the reverse is seen:
Fodd and
Dspike,circ give rise to comparable
values of H(n), but
Feven gives rise to smaller values of
H(n). The result for complex cells is expected
because it responds almost equally well to passes of both polarities of
an edge, so its response is concentrated in the even harmonics. This
also explains the strong magnitude alternation between odd and even
harmonics up to the eighth harmonic seen in the H curve
based on Fsingle (Fig.
8B). For the simple cell, it is not surprising that
the odd harmonics contribute to signaling. However, two points are unexpected: for both kinds of cells, different low-harmonic components are nonredundant (i.e., combining multiple components leads to a
greater level of stimulus-dependent clustering than any single frequency alone), and for simple cells, even-harmonic components do not
provide any independent temporal information.
In the grating data (Fig. 8A,C),
analysis based on Fourier components confirms what was found with spike
time metrics: the DC component (or spike count) gives rise to similar
or higher values of H to those obtained with metrics that,
in using the higher harmonics, exploit temporal structure. For the
complex cell (Fig. 8A) neither
H(q) nor any of the Fourier metrics showed evidence for temporal coding. The sharp drop in
Fsingle for all nonzero frequencies is
not surprising, because a typical complex cell responds to a drifting
sinusoidal grating near its spatial frequency optimum primarily by
elevating its spike rate (Movshon et al., 1978a; Skottun et al.,
1991).
For the simple cell (Fig. 8C), the first harmonic alone
leads to a greater level of stimulus-dependent clustering than the DC
component, as seen in the initial two values of
H(n), obtained with
Fsingle (dotted line in
bottom left). Significant levels of stimulus-dependent clustering based on the first harmonic is expected because a typical grating response of a simple cell typically resembles a half-wave rectified sinusoid, which is dominated by a DC component and its first
harmonic. A metric that uses the DC and the first harmonic component
together (Fodd for n = 1, plotted at 4 Hz) leads to the maximal level of
H(n) within Fodd
and also across the other Fourier metrics. However, the difference between the maximum in H(n) and
Hcount is slight, indicating little temporal
coding.
Analysis across cells
To make an overall comparison between the time-domain analysis
and the Fourier metrics, we compared H(q) based
on Dspike,circ with
H(n) based on
Fall. As seen in Table 1, the extent of
the contribution of temporal structure was comparable for both stimulus
classes and both cell types. Across the sample of complex cells,
Hmax based on Fall
and Feven were similar and, for edges,
greater than the maximum levels of contrast-dependent clustering based
on Fodd, as in the example of Figure
8B. Across the sample of simple cells,
Hmax based on
Fall,
Feven, and
Fodd were similar.
To correlate the estimates of the temporal resolution, we compared
qmax as determined from
H(q), based on
Dspike,circ, with the frequency
tfmax for which H(n),
based on Fall, achieves maximum (Fig.
7B). (tfmax = nmax, where nmax is
the harmonic for which
Fall[n] achieves maximal
clustering, and is the fundamental temporal frequency of the
stimulus.) The geometric mean of tfmax is very nearly half of the geometric mean of qmax. This
twofold difference was seen within individual neurons, too (Fig. 8).
This factor of two likely reflects a difference in the way that the
quantities q and n enter into their respective
metrics; shifting a spike by an amount 1/q is equivalent to
removing it altogether, but shifting it by only 1/(2n)
(half of the period 1/n) results in a maximal change in
the nth Fourier component. Another way of looking at this is
that the minimum temporal interval required to sample a single
frequency is half of its period (i.e., the Nyquist limit).
The following features of the Fourier-based analysis of temporal coding
were found in all cells of our sample. Evidence for temporal coding
(i.e., H > 0) was found for the Fourier-based metrics when and only when it was found with the spike time metrics. Moreover, provided that the appropriate family of Fourier metrics was
used (i.e., edge responses for complex cells, assessed with Feven, and for simple cells, assessed
with Fodd), Hmax
was within 10% of the maximum of H(q) determined
from the spike time metrics
Dspike,circ[q]. The temporal
frequency at which H(n) had its maximum
Hmax was correlated well with
1/qmax (r = 0.82;
p < 0.01), and the shapes of
H(n) and H(q) were
similar, up to the factor of two translation discussed above.
| |
DISCUSSION |
We use the term temporal coding to indicate the presence of
reproducible stimulus-dependent changes in the temporal structure of a
spike train. This work focuses on the identification and characterization of such changes. The rate coding versus temporal coding distinction is not a dichotomy; rather, it is a matter of
identifying the time scale over which instantaneous firing probability
depends systematically on the stimulus. If this interval is short, then
the detailed temporal pattern contains information about the stimulus.
If this interval is long (i.e., comparable to the entire response
duration), then the temporal code effectively reduces to a rate code.
The idealized properties of neurons (i.e., linearity of spatial and/or
temporal summation) provide mechanisms for rate coding. Well documented
and prominent deviations from these ideal behaviors (i.e., thresholds
and time- and voltage-dependent conductances, among others) provide
mechanisms for temporal coding.
Despite the potential advantages and plausibility of temporal coding
(see introductory remarks), the extent to which the brain actually
makes use of it is unclear. In other sensory systems, in audition
(Abeles and Gerstein, 1988; Middlebrooks et al., 1994) and in olfaction
(Laurent et al., 1996; Wehr and Laurent, 1996), temporal pattern can
convey information that firing rate overlooks. A direct demonstration
that temporal coding is used is very difficult: it would require
experimental manipulation of the detailed structure of spike trains
without changing their mean rate and observation of the presence (or
absence) of a behavioral change. The technical difficulties of such an
experiment are compounded by the fact that temporal coding and rate
coding are not mutually exclusive; indeed, stimulus-dependent changes
in temporal structure typically occur along with stimulus-dependent
changes in firing rate (Victor and Purpura, 1996). Thus, changes in
temporal structure (e.g., synchrony) might contribute to the behavioral
changes that are observed when rate is manipulated (Salzman and
Newsome, 1994). Furthermore, physiological changes in temporal
structure might be coupled to changes in mean rate, thus precluding a
direct experimental dissection.
Several studies (Purpura et al., 1993; Victor and Purpura, 1996;
Richmond et al., 1997; K. Purpura and L. M. Optican, unpublished observations) have provided evidence for temporal coding of contrast in
neurons of the macaque visual cortex. In these studies, transiently presented static stimuli (textures or gratings) were used. Because drifting sinusoids are commonly used in vision research, but responses are not analyzed for temporal coding, it is unclear whether the transient nature of the stimulus is essential for temporal coding, or,
alternatively, whether apparent "temporal coding" is merely an
artifact of complex analytic techniques. We resolve this question by
comparing, within the same V1 neurons, responses to transient stimuli
(drifting square waves of low spatial frequency, called edges) and
steady-state stimuli (optimal drifting sinusoidal gratings).
It appears that temporal coding is present under circumstances in which
the dynamic contrast gain control mechanism (Albrecht and Geisler,
1991; Bonds, 1991; Heeger, 1992; Victor et al., 1997) is active. This
mechanism (which could be viewed as short-term contrast adaptation) is
a prominent nonlinearity in V1 that acts on the order of 1 sec. The
area over which the contrast signal is pooled by the gain control is
local, comparable to a receptive field size (DeAngelis et al., 1992).
For edges and flashed stimuli, the contrast signal changes rapidly and
provides a dynamic input to the nonlinearities of the contrast gain
control. For gratings, however, the contrast signal is constant and
does not engage the nonlinearities of the gain control.
Contrast-reversed standing gratings may represent intermediate stimuli
in that the temporal modulation function determines whether there is an
abrupt change in contrast adaptation level.
We show here that drifting edges generate responses in which the
temporal pattern of spikes robustly contributes to the signaling of
contrast, especially for complex cells. Responses to drifting gratings,
even if phasic, show almost no evidence of temporal coding. These
results were obtained by two types of analysis: a time-domain approach
that used non-Euclidean spike time metrics, and a frequency-domain
approach that used a vector space (Euclidean) metric. Thus, temporal
coding is not an artifact of the particular choice of the analytic
approach but is rather associated with the nature of the stimulus.
Our results provide evidence for robust temporal coding of contrast
information in V1 responses for transients. The temporal contribution
to contrast coding is too large to be overlooked in evaluating the
function of a neuron. Underestimating the dynamic range in V1 neurons
(by reliance on spike counts alone) might result in overestimating the
minimum size of the neuronal population necessary to explain behavioral
contrast discrimination (Parker and Newsome, 1998).
Regardless of the method of analysis, the temporal resolution of the
code for contrast transients was found to be, on average, ~50 msec,
with a range of 10-100 msec, in agreement with earlier estimates in
V1. It has been argued that the latency of V1 neuronal responses, which
can change by as much as 50 msec across contrasts, is important for
coding of contrast (Gawne et al., 1996). Given our precision estimate,
response latency (or phase at any single frequency) is not the only
form of the available temporal information. The typical response of a
V1 neuron to a drifting edge contains several (up to a dozen or more)
response harmonics. For most neurons, combining phases and amplitudes
at several harmonics, up to a certain frequency, increases the ability
of the neuron to discriminate contrasts.
One of the most enduring issues in the physiology of vision is the
function of V1 neurons classified as simple and complex. Simple cells
have long been viewed (Hubel and Wiesel, 1962, 1968) as excellent
candidates for edge or feature detection, whereas complex cells have
been considered to be better suited for Fourier-based texture analysis
(Albrecht et al., 1980; De Valois and De Valois, 1980; De Valois et
al., 1982, 1985). Our work shows that complex cells are as well
equipped as simple cells to distinguish edges on the basis of contrast,
provided that the temporal structure of the response is considered.
(This does not necessarily imply that complex cells signal the contrast
polarity, position, or time of passage of an edge more precisely than
simple cells).
In natural viewing, the world is presented to our visual system in a
succession of transients because of moving object boundaries and also
because of saccadic eye movements (Viviani, 1990). Transients and
object boundaries are salient natural features that effectively direct
attention and trigger saccades (Yantis and Jonides, 1996). The neuronal
mechanism involved in attention grabbing must be fast, efficient, and
reliable. In the V1 neurons of this study, consistent with other
studies (Gawne et al., 1996), higher-contrast transients triggered
quicker and brisker onset signals that were often burst-like. Several
lines of evidence indicate that bursts are more reliably transmitted
across central synapses than single spikes (Lisman, 1997). Thus bursts
may provide the substrate for such fast, efficient, and reliable
low-level neural mechanisms that must underlie the effectiveness of
transient stimuli at orienting attention.
It is worthwhile to consider how the appearance of temporal coding
might be associated with stimulus transience. At the time of a
transient visual input (either attributable to a saccadic eye movement
or to a transient visual stimulus), many neurons fire a burst of
spikes. This burst, although perhaps not specific to the visual
stimulus, nevertheless provides a reset or reference point in time,
thereby enhancing the informative value of the timing of later spikes
(Victor and Purpura, 1996). With the exception of an ideal Poisson
process, the information in the timing of a single spike increases if
there is knowledge of the time of the preceding spike. The
integrate-and-fire neuron (Knight, 1972) provides an example: the
interspike interval precisely indicates the mean level of the stimulus
over this interval. A more elaborate example of this idea is contained
in a model recently proposed (Hopfield, 1995) in which delay times
represent sensory quantities. The cortex has neural mechanisms that may
exploit the resetting effect of a stimulus transient. These mechanisms
include not only sensitivity to coincidences but also long inhibitory
time constants that could extend the time over which a subpopulation of
neurons remains reset by the stimulus (Buzsaki and Chrobak, 1995;
Douglas et al., 1995).
| |
FOOTNOTES |
Received April 8, 1998; revised June 1, 1998; accepted June 3, 1998.
This work was supported by National Institutes of Health Grants EY9314
(J.D.V. and F.M.), NS01677 (K.P.P.), and EY01472 (R.S.). Special thanks
to Dario Ringach and Mike Hawken for their help in all phases of the
data acquisition. We also thank Matteo Carandini, Mike Hawken, and
Daniel Reich for their advice and helpful comments.
Correspondence should be addressed to Ferenc Mechler, Department of
Neurology and Neuroscience, Cornell University Medical College, 1300 York Avenue, New York, NY 10021.
| |
REFERENCES |
-
Abbott LF,
Varela JA,
Sen K,
Nelson SB
(1997)
Synaptic depression and cortical gain control.
Science
275:220-224.
-
Abeles M
(1982)
Role of the cortical neuron: integrator or coincidence detector?
Isr J Med Sci
18:83-92[Web of Science][Medline].
-
Abeles M,
Gerstein GL
(1988)
Detecting spatiotemporal firing patterns among simultaneously recorded single neurons.
J Neurophysiol
60:909-924[Abstract/Free Full Text].
-
Abramson N
(1963)
In: Information theory and coding. New York: McGraw-Hill.
-
Albrecht DG,
Geisler WS
(1991)
Motion selectivity and the contrast-response function of simple cells in the visual cortex.
Vis Neurosci
7:531-546[Web of Science][Medline].
-
Albrecht DG,
De Valois RL,
Thorell LG
(1980)
Visual cortical neurons: are bars or gratings the optimal stimuli?
Science
207:88-90[Abstract/Free Full Text].
-
Alonso JM,
Usrey WM,
Reid RC
(1996)
Precisely correlated firing in cells of the lateral geniculate nucleus.
Nature
383:815-819[Medline].
-
Berry II MJ,
Meister M
(1998)
Refractoriness and neural precision.
J Neurosci
18:2200-2211[Abstract/Free Full Text].
-
Bonds AB
(1991)
Temporal dynamics of contrast gain in single cells of the cat striate cortex.
Vis Neurosci
6:239-255[Web of Science][Medline].
-
Bourne HR,
Nicoll R
(1993)
Molecular machines integrate coincident synaptic signals.
Cell
72:65-75.
-
Buzsaki G,
Chrobak JJ
(1995)
Temporal structure in spatially organized neuronal ensembles: a role for interneuronal networks.
Curr Opin Neurobiol
5:504-510[Web of Science][Medline].
-
Carlton AG
(1969)
On the bias of information estimates.
Psychol Bull
71:108-109[Web of Science].
-
Cline H
(1997)
Coincidence detection in the nervous system.
Trends Neurosci
19:566-567.
-
DeAngelis GC,
Robson JG,
Ohzawa I,
Freeman RD
(1992)
Organization of suppression in receptive fields of neurons in cat visual cortex.
J Neurophysiol
68:144-163[Abstract/Free Full Text].
-
De Valois RL,
De Valois KK
(1980)
Spatial vision.
Annu Rev Psychol
31:309-341[Web of Science][Medline].
-
De Valois RL,
Albrecht DG,
Thorell LG
(1982)
Spatial frequency selectivity of cells in macaque visual cortex.
Vision Res
22:545-559[Web of Science][Medline].
-
De Valois RL,
Thorell LG,
Albrecht DG
(1985)
Periodicity of striate-cortex-cell receptive fields.
J Opt Soc Am
2:1115-1123.
-
Douglas RJ,
Koch C,
Mahowald M,
Martin KA,
Suarez HH
(1995)
Recurrent excitation in neocortical circuits.
Science
269:981-985[Abstract/Free Full Text].
-
Eldridge JL
(1979)
A reversible ophthalmoscope using a corner-cube.
J Physiol (Lond)
295:1P-2P[Free Full Text].
-
Enroth-Cugell C,
Robson JG
(1966)
The contrast sensitivity of retinal ganglion cells of the cat.
J Physiol (Lond)
187:517-561.
-
Gawne TJ,
Kjaer TW,
Richmond BJ
(1996)
Latency: another potential code for feature binding in striate cortex.
J Neurophysiol
76:1356-60[Abstract/Free Full Text].
-
Gerstner W,
Kreiter AK,
Markram H,
Herz AVM
(1997)
Neural codes: firing rates and beyond.
Proc Natl Acad Sci USA
94:12740-12741[Abstract/Free Full Text].
-
Hawken MJ,
Parker AJ,
Lund JS
(1988)
Laminar organization and contrast sensitivity of direction-selective cells in the striate cortex of the Old World monkey.
J Neurosci
8:3541-3548[Abstract].
-
Hawken MJ,
Shapley RM,
Grosof DH
(1996)
Temporal-frequency selectivity in monkey visual cortex.
Vis Neurosci
13:477-492[Web of Science][Medline].
-
Heeger DJ
(1992)
Normalization of cell responses in cat striate cortex.
Vis Neurosci
9:181-197[Web of Science][Medline].
-
Hochstein S,
Shapley RM
(1976)
Quantitative analysis of retinal ganglion cell classifications.
J Physiol (Lond)
262:237-264[Abstract/Free Full Text].
-
Hopfield JJ
(1995)
Pattern recognition computation using action potential timing for stimulus representation.
Nature
376:33-36[Medline].
-
Hubel DH,
Wiesel TN
(1962)
Receptive fields, binocular interaction and functional architecture in the cat's visual cortex.
J Physiol (Lond)
160:106-154.
-
Hubel DH,
Wiesel TN
(1968)
Receptive fields and functional architecture of monkey striate cortex.
J Physiol (Lond)
195:215-243[Abstract/Free Full Text].
-
Kaplan E,
Shapley RM
(1982)
X and Y cells in the lateral geniculate nucleus of macaque monkeys.
J Physiol (Lond)
330:125-143[Abstract/Free Full Text].
-
Knight BW
(1972)
Dynamics of encoding in a population of neurons.
J Gen Physiol
59:734-766[Abstract/Free Full Text].
-
Konig P,
Engel AK,
Singer W
(1996)
Integrator or coincidence detector? The role of the cortical neuron revisited.
Trends Neurosci
19:130-137[Web of Science][Medline].
-
Laurent G,
Wehr M,
Davidowitz H
(1996)
Temporal representations of odors in an olfactory network.
J Neurosci
16:3837-3847[Abstract/Free Full Text].
-
Lisman JE
(1997)
Bursts as a unit of neural information: making unreliable synapses reliable.
Trends Neurosci
20:38-43[Web of Science][Medline].
-
Mainen ZF,
Sejnowski TJ
(1995)
Reliability of spike timing in neocortical neurons.
Science
268:1503-1506[Abstract/Free Full Text].
-
Markram H,
Lubke J,
Frotscher M,
Sakmann B
(1997)
Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs.
Science
275:213-215[Abstract/Free Full Text].
-
Mechler F,
Victor JD,
Purpura K,
Shapley R
(1997)
Temporal encoding of contrast by V1 neurons is greater for transient than steady-state stimuli.
Soc Neurosci Abstr
23:567.
-
Merrill EG,
Ainsworth A
(1972)
Glass-coated platinum-plated tungsten microelectrodes.
Med Biol Eng
10:662-672[Web of Science][Medline].
-
Middlebrooks JC,
Clock AE,
Xu L,
Green DM
(1994)
A panoramic code for sound location by cortical neurons.
Science
264:842-844[Abstract/Free Full Text].
-
Movshon JA,
Thompson ID,
Tolhurst DJ
(1978a)
Spatial summation in the receptive fields of simple cells in the cat's striate cortex.
J Physiol (Lond)
283:53-77[Abstract/Free Full Text].
-
Movshon JA,
Thompson ID,
Tolhurst DJ
(1978b)
Receptive field organization of complex cells in the cat's striate cortex.
J Physiol (Lond)
283:79-99[Abstract/Free Full Text].
-
Optican LM,
Richmond BJ
(1987)
Temporal encoding of two-dimensional patterns by single units in primate inferior temporal cortex. III. Information theoretic analysis.
J Neurophysiol
57:162-178[Abstract/Free Full Text].
-
Parker AJ,
Newsome WT
(1998)
Sense and the single neuron: probing the physiology of perception.
Annu Rev Neurosci
21:227-277[Web of Science][Medline].
-
Purpura K,
Chee-Orts MN,
Optican LM
(1993)
Temporal encoding of texture properties in visual cortex of awake monkey.
Soc Neurosci Abstr
19:771.
-
Richmond BJ,
Optican LM
(1987)
Temporal encoding of two-dimensional patterns by single units in primate inferior temporal cortex. II. Quantification of response waveform.
J Neurophysiol
57:147-161[Abstract/Free Full Text].
-
Richmond BJ,
Optican LM
(1990)
Temporal encoding of two-dimensional patterns by single units in primate primary visual cortex. II. Information transmission.
J Neurophysiol
64:370-380[Abstract/Free Full Text].
-
Richmond BJ,
Gawne TJ,
Jin GX
(1997)
Neuronal codes: reading them and learning how their structure influences network organization.
Biosystems
40:149-157[Web of Science][Medline].
-
Salzman CD,
Newsome WT
(1994)
Neural mechanisms for forming a perceptual decision.
Science
264:231-237[Abstract/Free Full Text].
-
Skottun BC,
De Valois RL,
Grosof DH,
Movshon JA,
Albrecht DG,
Bonds AB
(1991)
Classifying simple and complex cells on the basis of response modulation.
Vision Res
31:1079-1086[Web of Science][Medline].
-
Softky W
(1994)
Sub-millisecond coincidence detection in active dendritic trees.
Neuroscience
58:13-41[Web of Science][Medline].
-
Treves A,
Panzeri S
(1995)
The upward bias in measures of information derived from limited data samples.
Neural Comput
7:399-407[Web of Science].
-
Victor JD,
Purpura KP
(1996)
Nature and precision of temporal coding in visual cortex: a metric-space analysis.
J Neurophysiol
76:1310-1326[Abstract/Free Full Text].
-
Victor JD,
Purpura KP
(1997)
Metric-space analysis of spike trains: theory, algorithms and application.
Network
8:127-164.
-
Victor JD, Purpura KP (1998) Spatial phase and the temporal
structure of the response to gratings in V1. J Neurophysiol, in
press.
-
Victor JD,
Conte MM,
Purpura KP
(1997)
Dynamic shifts of the contrast-response function.
Vis Neurosci
14:577-587[Web of Science][Medline].
-
Viviani P
(1990)
Eye movements in visual search: cognitive, perceptual and motor control aspects.
Rev Oculomot Res
4:353-393[Medline].
-
Volgushev M,
Voronin LL,
Chistiakova M,
Singer W
(1997)
Relations between long-term synaptic modifications and paired-pulse interactions in the rat neocortex.
Eur J Neurosci
9:1656-1665[Web of Science][Medline].
-
Volgushev M,
Chistiakova M,
Singer W
(1998)
Modification of discharge patterns of neocortical neurons by induced oscillations of the membrane potential.
Neuroscience
83:15-25[Web of Science][Medline].
-
Wehr M,
Laurent G
(1996)
Odour encoding by temporal sequences of firing in oscillating neural assemblies.
Nature
384:162-166[Medline].
-
Yantis S,
Jonides J
(1996)
Attentional capture by abrupt onsets: new perceptual objects or visual masking?
J Exp Psychol Hum Percept Perform
22:1505-1513[Web of Science][Medline].
Copyright © 1998 Society for Neuroscience 0270-6474/98/18166583-16$05.00/0
This article has been cited by other articles:
|
|
|
|
 
D. J. Tolhurst, D. Smyth, and I. D. Thompson
The Sparseness of Neuronal Responses in Ferret Primary Visual Cortex
J. Neurosci.,
February 25, 2009;
29(8):
2355 - 2370.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
C. Huetz, B. Philibert, and J.-M. Edeline
A Spike-Timing Code for Discriminating Conspecific Vocalizations in the Thalamocortical System of Anesthetized and Awake Guinea Pigs
J. Neurosci.,
January 14, 2009;
29(2):
334 - 350.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
B. Zhang, E. L. Smith III, and Y. M. Chino
Postnatal Development of Onset Transient Responses in Macaque V1 and V2 Neurons
J Neurophysiol,
September 1, 2008;
100(3):
1476 - 1487.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
U. Hasson, E. Yang, I. Vallines, D. J. Heeger, and N. Rubin
A Hierarchy of Temporal Receptive Windows in Human Cortex
J. Neurosci.,
March 5, 2008;
28(10):
2539 - 2550.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
N. Y. Masse and E. P. Cook
The Effect of Middle Temporal Spike Phase on Sensory Encoding and Correlates with Behavior during a Motion-Detection Task
J. Neurosci.,
February 6, 2008;
28(6):
1343 - 1355.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
J. V. Verhagen and D. B. Katz
More Time to Taste. Focus on "Variability in Responses and Temporal Coding of Tastants of Similar Quality in the Nucleus of the Solitary Tract of the Rat"
J Neurophysiol,
February 1, 2008;
99(2):
413 - 414.
[Full Text]
[PDF]
|
|
|
|
|
|
|
F. Mechler, I. E. Ohiorhenuan, and J. D. Victor
Speed Dependence of Tuning to One-Dimensional Features in V1
J Neurophysiol,
March 1, 2007;
97(3):
2423 - 2438.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
J. D. Victor, E. M. Blessing, J. D. Forte, P. Buzas, and P. R. Martin
Response variability of marmoset parvocellular neurons
J. Physiol.,
February 15, 2007;
579(1):
29 - 51.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
B. C. Motter
Modulation of transient and sustained response components of V4 neurons by temporal crowding in flashed stimulus sequences.
J. Neurosci.,
September 20, 2006;
26(38):
9683 - 9694.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
R. E. Kass, V. Ventura, and E. N. Brown
Statistical Issues in the Analysis of Neuronal Data
J Neurophysiol,
July 1, 2005;
94(1):
8 - 25.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
P. E. Williams, F. Mechler, J. Gordon, R. Shapley, and M. J. Hawken
Entrainment to Video Displays in Primary Visual Cortex of Macaque and Humans
J. Neurosci.,
September 22, 2004;
24(38):
8278 - 8288.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
S. V. David, W. E. Vinje, and J. L. Gallant
Natural Stimulus Statistics Alter the Receptive Field Structure of V1 Neurons
J. Neurosci.,
August 4, 2004;
24(31):
6991 - 7006.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
R. A. Frazor, D. G. Albrecht, W. S. Geisler, and A. M. Crane
Visual Cortex Neurons of Monkeys and Cats: Temporal Dynamics of the Spatial Frequency Response Function
J Neurophysiol,
June 1, 2004;
91(6):
2607 - 2627.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
J. M. Samonds and A. B. Bonds
From Another Angle: Differences in Cortical Coding Between Fine and Coarse Discrimination of Orientation
J Neurophysiol,
March 1, 2004;
91(3):
1193 - 1202.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
G. Ariav, A. Polsky, and J. Schiller
Submillisecond Precision of the Input-Output Transformation Function Mediated by Fast Sodium Dendritic Spikes in Basal Dendrites of CA1 Pyramidal Neurons
J. Neurosci.,
August 27, 2003;
23(21):
7750 - 7758.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
D. Aronov, D. S. Reich, F. Mechler, and J. D. Victor
Neural Coding of Spatial Phase in V1 of the Macaque Monkey
J Neurophysiol,
June 1, 2003;
89(6):
3304 - 3327.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
I. Kagan, M. Gur, and D. M. Snodderly
Spatial Organization of Receptive Fields of V1 Neurons of Alert Monkeys: Comparison With Responses to Gratings
J Neurophysiol,
November 1, 2002;
88(5):
2557 - 2574.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
F. Mechler, D. S. Reich, and J. D. Victor
Detection and Discrimination of Relative Spatial Phase by V1 Neurons
J. Neurosci.,
July 15, 2002;
22(14):
6129 - 6157.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
D. S. Reich, F. Mechler, and J. D. Victor
Temporal Coding of Contrast in Primary Visual Cortex: When, What, and Why
J Neurophysiol,
March 1, 2001;
85(3):
1039 - 1050.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
D. S. Reich, F. Mechler, and J. D. Victor
Formal and Attribute-Specific Information in Primary Visual Cortex
J Neurophysiol,
January 1, 2001;
85(1):
305 - 318.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
G. Kreiman, R. Krahe, W. Metzner, C. Koch, and F. Gabbiani
Robustness and Variability of Neuronal Coding by Amplitude-Sensitive Afferents in the Weakly Electric Fish Eigenmannia
J Neurophysiol,
July 1, 2000;
84(1):
189 - 204.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
D. V. Buonomano
Decoding Temporal Information: A Model Based on Short-Term Synaptic Plasticity
J. Neurosci.,
February 1, 2000;
20(3):
1129 - 1141.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
M. C. Wiener and B. J. Richmond
Using Response Models to Estimate Channel Capacity for Neuronal Classification of Stationary Visual Stimuli Using Temporal Coding
J Neurophysiol,
December 1, 1999;
82(6):
2861 - 2875.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
M. W. Oram, M. C. Wiener, R. Lestienne, and B. J. Richmond
Stochastic Nature of Precisely Timed Spike Patterns in Visual System Neuronal Responses
J Neurophysiol,
June 1, 1999;
81(6):
3021 - 3033.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
D. S. Reich, J. D. Victor, and B. W. Knight
The Power Ratio and the Interval Map: Spiking Models and Extracellular Recordings
J. Neurosci.,
December 1, 1998;
18(23):
10090 - 10104.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
Top
Abstract
Introduction
