Coding of stimulus sequences by population responses in visual cortex

Abstract

Neuronal populations in sensory cortex represent time-changing sensory input through a spatiotemporal code. What are the rules that govern this code? We measured membrane potentials and spikes from neuronal populations in cat visual cortex (V1) using voltage-sensitive dyes and electrode arrays. We first characterized the population response to a single orientation. As response amplitude grew, the population tuning width remained constant for membrane potential responses and became progressively sharper for spike responses. We then asked how these single-orientation responses combine to code for successive orientations. We found that they combined through simple linear summation. Linearity, however, was violated after stimulus offset, when responses exhibited an unexplained persistence. As a result of linearity, the interactions between responses to successive stimuli were minimal. Our results indicate that higher cortical areas may reconstruct the stimulus sequence from V1 population responses through a simple instantaneous decoder. Therefore, spatial and temporal codes in area V1 operate largely independently.

Fig. 1

Population responses to an oriented stimulus. (a) Average maps of VSD fluorescence triggered on the appearance of a 90° grating, at various delays from grating onset. Scale bar indicates 1 mm. (b) Combining maps obtained with multiple stimulus orientations yields a map of orientation preference. Hue indicates the preferred orientation and brightness indicates tuning strength. (c) Summary of the membrane potential responses of the population. Responses of pixels with similar orientation preference were averaged and the result plotted as a function of preferred orientation (relative to stimulus orientation). The mean across orientations was removed. Black curves indicate best fitting Gaussian functions, error bars indicate ±1 s.e. (across 6 stimulus orientations). (d) Two superimposed population responses separated by 20 ms interval. (e) Summary of the spike responses of the population. The same methods as those in a–c were applied to the firing rate measured with the electrode array. (f) Two superimposed population responses separated by 20 ms interval. Panels a–d are from experiment 56-4-1, panels e,f from experiment 75-5-16.

Fig. 2

Properties of single-orientation responses. (a) Time course of response amplitude (from Gaussian fits in Fig. 1c,e) for membrane potential (dark gray) and spikes (light gray). Shaded regions indicate ±1 s.e. (n=8 hemispheres for membrane potential, 6 hemispheres for spikes). Black dots indicate data points above background level. (b) Same, for the tuning width (half-width at half height). Only values corresponding to amplitudes above background level (black dots in a) are shown. (c) Time course of response amplitude for isolated single units (n=31). (d) Time course of tuning width for isolated single units for time points above background level (black dots in panel c). (e) Population responses for membrane potential (e) and spikes (f) were decomposed into two additive terms: a tuned component (which varies both in orientation and in time, shown on the bottom) and a baseline component (which varies only in time, shown by the black curve on top). To account for variability, responses are expressed as z-scores (mean across repeats divided by standard deviation across repeats). (f) Tuned component of the spike responses with the unturned component shown on top as well. Panel e is from experiment 56-4-1, panel f is from experiment 75-5-16.

Fig. 3

Predicting the membrane potential responses of the population to the full stimulus sequence. (a) The stimulus expressed as an image, with ones (dots) indicating the sequence of stimulus orientations as function of time, and zeros elsewhere (gray). For graphical purposes, the orientation axis was duplicated to cover the full 360° range. Thus each grating appears as two dots separated by 180°. Only 2 s of stimulation are shown here (typical stimuli lasted 30 s). Dots have been shifted in time by 74 ms to compensate for the delay of the membrane potential signal. (b) Elemental population response to a single orientation (from Fig. 2e0). The asterisk denotes convolution. (c) Population responses predicted by convolving the stimulus with the elemental response. For graphical purposes we advanced these responses in time by 58 ms to appear roughly contemporaneous with the stimulus. (d) The measured population responses, similarly shifted in time. (e) Relationship between model predictions and measured responses. Dots are mean values taken across n=8 hemispheres. Gray regions indicate ±1 s.d. Panels a–d are from experiment 56-4-1.

Fig. 4

Predicting the spike responses of the population to the full stimulus sequence. Format as in Fig. 3. Panels a–d are from experiment 75-5-16.

Fig. 5

Predicting the interactions between population responses to successive orientations. (a) Average membrane potential responses of the population to two successive stimuli of the same (top panel) or different orientations. The schematic at left describes the stimulus. From top to bottom, successive stimuli differing in orientation by 0°, 90°, −45°, and +45°. (b) Predictions of the summation model for the data in a. (c–d) Same as a–b, for the spike responses of the population. (e) Attraction of population response profiles during ±45° jumps in orientation. Profiles are measured at the peak time of the second response (60.5±1.7 ms from the onset of the second stimulus). Curves are model predictions. Average of 5 hemispheres. (f) Same as in e, for the spike responses of the population. Panels a–b are from experiment 69-1-5, panels c–d are from experiment 75-5-16.

Fig. 6

Unexplained persistence of population responses after stimulus offset. (a) When the visual stimulus is removed (stimulus-to-blank conditions, as shown on top by the contrast change), membrane potential activity in the population persists for well over 50 ms. Gray symbols indicate that before and after the stimulus-blank sequence, the stimulus could have any orientation or be blank (b) Same as in a, for spike responses. (c–d) The prediction of the summation model is substantially shorter for both spike responses and membrane potential. (e) The persistence is tuned for orientation: a separable model obtained through singular-value decomposition of the response shown in a yields a very similar profile. (f) Same as in e, for spike responses. (g–h) Temporal dynamics of responses (red) and predictions (black). Shaded areas indicate ±1 s.d. (n = 6 conditions). (i) Difference between the predicted and actual time courses averaged over hemispheres. Shaded areas indicate ±1 s.d. (n=8 hemispheres). (j) Same, for the firing rate of the population responses (n=6 hemispheres). Panels a,c,e from experiment 68-3-5, panels b,d,f from experiment 75-5-16.

Fig. 7

Decoding stimulus orientation from the population responses. (a) The average response to an individual stimulus orientation. The dotted lines indicate the interval when this response is significantly higher than baseline. (b) Probability that a spike response is evoked by a specific orientation (computed within the time interval indicated in a). (c) Firing rates of the population in response to a stimulus sequence, averaged over 10 trials. (d) Firing rates for an individual trial. (e) Stimulus likelihood estimated by the instantaneous Bayesian decoder from the single-trial responses. (f) The stimulus sequence (shifted by 50 ms to compensate for response delay). (g) Confusion matrix comparing the estimated orientation to the actual stimulus orientation. (h) The average stimulus likelihood when a stimulus is followed by a blank. Panels a–h are from experiment 79-12-16.