STIMULUS ENCODING BY 
MULTIDIMENSIONAL RECEPTIVE FIELDS 
IN SINGLE CELLS AND CELL POPULATIONS 
IN V1 OF AWAKE MONKEY 
Edward Stern 
Center for Neural Computation 
and Department of Neurobiology 
Life Sciences Institute 
Hebrew University 
Jerusalem, Israel 
Ad Aertsen 
Institut fur Neuroinformatik 
Ruhr-Universitat-Bochum 
Bochum, Germany 
Eilon Vaadia 
Center for Neural Computation 
and Physiology Department 
Hadassah Medical School 
Hebrew University 
Jerusalem, Israel 
Shaul Hochstein 
Center for Neural Computation 
and Department of Neurobiology, 
Life Sciences Institute 
Hebrew University 
Jerusalem, Israel 
ABSTRACT 
Multiple single neuron responses were recorded 
from a single electrode in V1 of alert, behaving 
monkeys. Drifting sinusoidal gratings were 
presented in the cells' overlapping receptive 
fields, and the stimulus was varied along several 
visual dimensions. The degree of dimensional 
separability was calculated for a large population 
of neurons, and found to be a continuum. Several 
cells showed different temporal response 
dependencies to variation of different stimulus 
dimensions, i.e. the tuning of the modulated 
firing was not necessarily the same as that of the 
mean firing rate. We describe a multidimensional 
receptive field, and use simultaneously recorded 
responses to compute a multi-neuron receptive 
field, describing the information processing 
capabilities of a group of cells. Using dynamic 
correlation analysis, we propose several 
computational schemes for multidimensional 
spatiotemporal tuning for groups of cells. The 
implications for neuronal coding of stimuli are 
discussed. 
377 
378 Stern, Aertsen, Vaadia, and Hochstein 
INTRODUCTION 
The receptive field is perhaps the most useful concept for understanding neuronal 
information processing. The ideal definition of the receptive field is that set of stimuli 
which cause a change in the neuron's firing properties. However, as with many such 
concepts, the use of the receptive field in describing the behavior of sensory neurons falls 
short of the ideal. The classical method for describing the receptive field has been to 
measure the "tuning curve" i.e. the response of the neuron as a function of the value of 
one dimension of the stimulus. This presents a problem because the sensory world is 
multidimensional: For example, even a simple visual stimulus, such as a patch of a 
sinusoidal grating, may vary in location, orientation, spatial frequency, temporal 
frequency, movement direction and speed, phase, contrast, color, etc. Does the tuning to 
one dimension remain constant when other dimensions are varied? i.e. are the dimensions 
linearly separable? It is not unreasonable to expect inseparability: Consider an oriented, 
spatially discrete receptive field. The excitation generated by passing a bar through the 
receptive field will of course change with orientation. However, the shape of this tuning 
curve will depend upon the bar width, related to the spatial frequency. This effect has not 
been studied quantitatively, however. If interactions among dimensions exist, do they 
account for a large portion of the cell's response variance? Are there discrete populations 
of cells, with some cells showing interactions among dimensions and others not? These 
question have clear implications for the problem of neural coding. 
Related to the question of dimensional separability is that of stimulus encoding: Given 
that the receptive field is multidimensional in nature, how can the cell maximize the 
amount of stimulus information it encodes? Does the neuron use a single code to 
represent all the stimulus dimensions? It is possible that interactions lead to greater 
uncertainty in stimulus identification. Does the small number of visual conical cells 
encode all the possible combinations of stimuli using only spike rate as the dependent 
variable? We present data indicating that more information is indeed present in the 
neuronal response, and propose a new approach for its utilization. 
The final problem that we address is the following: Clearly, many cells participate in the 
stimulus encoding process. Arriving at a valid concept of a multidimensional receptive 
field, can we generalize this concept to more than one cell introducing the notion of a 
multi-cellular receptive field? 
METHODS 
Drifting sinusoidal gratings were presented for 500 msec to the central 10 degrees of the 
visual field of monkeys performing a fixation task. The gratings were varied in 
orientation, spatial frequency, temporal frequency, and movement direction. We recorded 
from up to 3 cells simultaneously with a single electxode in the monkey's primary visual 
cortex (V1). The cells described in this study were well separated, using a template- 
matching procedure. The responses of the neurons were plotted as Peri-Stimulus Time 
Histograms (PSTHs) and their parameters quantified (Abeles, 1982), and offiine Fourier 
analysis and time-dependent crosscorrelation analysis (Aertsen et al, 1989) were 
performed. 
Stimulus Encoding by Multidimensional Receptive Fields in Single Cells and Cell Populations 379 
RESULTS 
Recording the responses of visual cortical neurons to stimuli varied over a number of 
dimensions, we found that in some cases, the tuning curve to one dimension depended on 
the value of another dimension. Figure 1A shows the spatial-frequency tuning curve of a 
single cell measured at 2 different stimulus orientations. When the orientation of the 
stimulus is 72 degrees, the peak response is at a spatial frequency of 4.5 cycles/degree 
(cpd), while at an orientation of 216 degrees, the spatial frequency of peak response is 2.3 
cpd. If the responses to different visual dimensions were truly linearly separable, the 
tuning curve to any single dimension would have the same shape and, in particular, 
position of peak, despite any variations in other dimensions. If the tuning curves are not 
parallel, then interactions must exist between dimensions. Clearly, this is an example of 
a cell whose responses are not linearly separable. In order to quantify the inseparability 
phenomenon, analyses of variance were performed, using spike rate as the dependent 
variable, and the visual dimensions of the stimuli as the independent variables. We then 
measured the amount of interaction as a percentage of the total between-conditions 
1 
0.8, 
0.6. 
0.4. 
0.3 
0.2 
0.1 
0 
0.1 
A. Spatial Frequency 
Tuning Dependence upon 
Orientation 
B. Interaction effects between 
stimulus dimensions: 
Percentage of total variance 
25, 
Spatial Frequency (cpd) 
% of non-residual variance 
, ORI=72  ORI=216 
nfac=34 nfac=45 
Figure 1: Dimensional Inseparability of Visual Cortical Neurons. A: 
An example of dimensionsional inseparability in the response of a single 
cell; B: Histogram of dimensional inseparability as a percentage of 
total response variance. 
380 Stern, Aertsen, Vaadia, and Hochstein 
variance divided by the residuals. The resulting histogram for 69 cells is shown in Figure 
lB. Although there are several cells with non-significant interactions, i.e. linearly 
separable dimensions, this is not the majority of cells. The amount of dimensional 
inseparability seems to be a continuum. We suggest that separability is a significant 
variable in the coding capability of the neurons, which must be taken into account when 
modeling the representation of sensory information by cortical neural networks. 
We found that the time course of the response was not always constant, but varied with 
stimulus parameters. Conical cell responses may have components which are sustained 
(constant over time), transient (with a peak near stimulus onset and/or offset), or 
modulated (varying with the stimulus period). For example, Figure 2 shows the responses 
of a single neuron in V1 to 50 stimuli, varying in orientation and spatial frequency. Each 
response is plotted as a PSTH, and the stippled bar under the PSTH indicates the time of 
4.5 
2.3 
1.5 
0.8 
0.4 
Orientation 
t80' 216  252' 288* 324  
3Ol 
Figure 2: Spatial Frequency/Orientation Tuning of Responses 
of V1 Cell 
Stimulus Encoding by Multidimensional Receptive Fields in Single Cells and Cell Populations 381 
the stimulus presentation (500 msec). The numbers beneath each PSTH are the f'u'ing rate 
averaged over the response time, and the standard deviations of the response over 
repetitions of the stimulus (in this case 40). Clearly, the cell is orientation selective, and 
the neuronal response is also tuned to spatial frequency. The stimulus eliciting the 
highest firing rate is ORI=252 degrees; SF=3.2 cycles/degree (cpd). However, when 
looking at the responses to lower spatial frequencies, we see a modulation in the PSTH. 
The modulation, when present, has 2 peaks, corresponding to the temporal frequency of 
the stimulus grating (4 cycles/second). Therefore, although the response rate of the cell is 
lower at low spatial frequencies than for other stimuli, the spike txain carries additional 
information about another stimulus dimension. 
If the visual neuron is considered as a linear system, the predicted response to a drifting 
sinusoidal grating would be a (rectified) sinusold of the same (temporal) frequency as that 
of the stimulus, i.e. a modulated response (Enroth-Cugell & Robson, 1966; Hochstein & 
Shapley, 1976; Spitzer & Hochstein, 1988). However, as seen in Figure 2, in some 
stimulus regimes the cell's response deviates from linearity. We conclude that the 
linearity or nonlinearity of the response is dependent upon the stimulus conditions 
(Spitzer & Hochstein, 1985). A modulated response is one that would be expected from 
simple cells, while the sustained response seen at higher spatial frequencies is that 
expected from complex cells. Our data therefore suggest that the simple/complex cell 
categorization is not complete. 
A further example of response time-course dependence on stimulus parameters is seen in 
Figure 3A. In this case, the stimulus was varied in spatial frequency and temporal 
frequency, while other dimensions were held constant. Again, as spatial frequency is 
raised, the modulation of the PSTH gives way to a more sustained response. Furthermore, 
as temporal frequency is raised, both the sustained and the modulated responses are 
replaced by a single transient response. When present, the frequency of the modulation 
follows that of the temporal frequency of the stimulus. Fourier analysis of the response 
histograms (Figure 3B) reveals that the DC and fundamental component (FC) are not 
tuned to the same stimulus values (arrows indicating peaks). We propose that this 
information may be available to the cell readout, enabling the single cell to encode 
multiple stimulus dimensions simultaneously. 
Thus, a complete description of the receptive field must be multidimensional in nature. 
Furthermore, in light of the evidence that the spike train is not constant, one of the 
dimensions which must be used to display the receptive field must be time. 
Figure 4 shows one method of displaying a multidimensional response map, with time 
along the abscissa (in 10 msec bins) and orientation along the ordinate. In the top two 
figures, the z axis, represented in gray-scale, is the number of counts (spikes) per bin. 
Therefore, each line is a PSTH, with counts (bin height) coded by shading. In this 
example, cell 2 (upper picture) is tuned to orientation, with peaks at 90 and 270 degrees. 
The cell is only slightly direction selective, as represented by the fact that the 2 areas of 
high activity are similarly shaded. However, there is a transient peak at 270 degrees which 
382 Stern, Aertsen, Vaadia, and Hochstein 
Spatial Frequency (cpcl) 
U.6 0.8 1.1 1.5 2.1 
D ha normalized values 
16 
TF (cycles/second) 
F 
1.5 
1.1 
O.8 
0.6 
SF (cpd) 
Figure 3: A. TF/SF Tuning of response of V1 cell. 
B. Tuning of DC and FC of response to stimulus parameters. 
is absent at 90 degrees. The middle picture, representing a simultaneously recorded cell 
shows a different pattern of activity. The orientation tuning of this cell is similar to that 
of cell 2, but it has stronger directional selectivity, (towards 90 degrees). In this case, the 
transient is also at 90 degrees. The bottom picture shows the joint activity of these 2 
cells. Rather than each line being a PSTH, each line is a Joint PSTH (JPSTH; Aertsen et 
al, 1989). This histogram represents the time-dependent correlated activity of a pair of 
cells. It is equivalent to sliding a window across a spike train of one neuron and 
Stimulus Encoding by Multidimensional Receptive Fields in Single Cells and Cell Populations 383 
324 
216 
108 
0 
cell 2 
I I I 
counts/bin 
250 
200 
150 
0 
324 
216 
108 
0 
cell 3 
I I I 
324 
216 
108 
0 
cell 2,3 coincidence 
I I i 
30 
20 
0 250 500 750 1000 
time (msec) SF=4.5 cpd 
Figure 4: Response Maps. 
Top, Middle: Single-cell Multidimensional Receptive Fields; 
Bottom: Multi-Cell Multidimensional Receptive Field 
asking when a spike from another neuron falls within the window. The size of the 
window can be varied; here we used 2 msec. Therefore, we are asking when these cells 
fire within 2 msec of each other, and how this is connected to the stimulus. The z axis is 
now coincidences per bin. We may consider this the logical AND activity of these cells; 
if there is a cell receiving information from both of these neurons, this is the receptive 
field which would describe its input. Clearly, it is different from the each of the 2 
individual cells. In our results, it is more narrowly tuned, and the tuning can not be 
predicted from the individual components. We emphasize that this is the "raw" JPSTH, 
which is not corrected for stimulus effects, common input, or normalized. This is because 
we want a measure comparable to the PSTHs themselves, to compare a multi-unit 
384 Stern, Aertsen, Vaadia, and Hochstein 
receptive field to its single unit components. In this case, however, a significant (p<0.01; 
Palm et al, 1988) "mono-directional" interaction is present. For a more complete 
description of the receptive field, this type of figure, shown here for one spatial frequency 
only, can be shown for all spatial frequencies as "slices" along a fourth axis. However, 
space limitations prevent us from presenting this multidimensional aspect of the 
multicellular receptive field. 
CONCLUSIONS 
We have shown that interactions among stimulus dimensions account for a significant 
proportion of the response variance of V 1 cells. The variance of the interactions itself 
may be a useful parameter when considering a population response, as the amount and 
location of the dimensional inseparability varies among cells. We have also shown that 
different temporal characteristics of the spike txains can be tuned to different dimensions, 
and add to the encoding capabilities of the cell in a neurobiologically realistic manner. 
Finally, we use these results to generate multidimensional receptive fields, for single cells 
and small groups of cells. We emphasize that this can be generalized to larger populations 
of cells, and to compute the population responses of cells that may be meaningful for the 
cortex as a biological neuronal network. 
Acknowledgements 
We thank Israel Nelken, Hagai Bergman, Volodya Yakovlev, Moshe Abeles, Peter 
Hillman, Robert Shapley and Valentino Braitenberg for helpful discussions. This study 
was supported by grants from the U.S.-Israel Bi-National Science Foundation (BSF) and 
the Israel Academy of Sciences. 
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