Spatial summation in the receptive fields of MT neurons

Abstract

Receptive fields (RFs) of cells in the middle temporal area (MT or V5) of monkeys will often encompass multiple objects under normal image viewing. We therefore have studied how multiple moving stimuli interact when presented within and near the RF of single MT cells. We used moving Gabor function stimuli, <1 degrees in spatial extent and approximately 100 msec in duration, presented on a grid of possible locations over the RF of the cell. Responses to these stimuli were typically robust, and their small spatial and temporal extent allowed detailed mapping of RFs and of interactions between stimuli. The responses to pairs of such stimuli were compared against the responses to the same stimuli presented singly. The responses were substantially less than the sum of the responses to the component stimuli and were well described by a power-law summation model with divisive inhibition. Such divisive inhibition is a key component of recently proposed "normalization" models of cortical physiology and is presumed to arise from lateral interconnections within a region. One open question is whether the normalization occurs only once in primary visual cortex or multiple times in different cortical areas. We addressed this question by exploring the spatial extent over which one stimulus would divide the response to another and found effective normalization from stimuli quite far removed from the RF center. This supports models under which normalization occurs both in MT and in earlier stages.

Fig. 1.

Single Gabor motion impulse depicted as a function of space and time. A, Two-dimensional representation of typical stimulus. This portrays the default values for spatial parameters used in these experiments, which were only varied if these proved ineffective in driving the cell. Aspect ratio was always 2:1, but the ratio of carrier period to Gaussian envelope was more variable. The numbered points indicate the successive locations of an arbitrary spatial reference point in seven successive frames of the stimulus; the white numbers are only for graphic clarity. B, Contrast as a function of time. Eachpoint represents a single frame, corresponding to the locations indicated in A. In a sequence of continuously presented stimuli, the next stimulus frame 0 would immediately follow frame 8, producing an overall interval of 125 msec between successive stimuli.

Fig. 2.

Spatial arrangement of Gabor impulses, schematically illustrated over an MT cell RF (circle). Stimuli could either be presented individually or else in pairs (illustrated). The direction of the stimuli (arrows) was adjusted to match the preference of the cell, and the dimensions were adjusted so the corner stimuli gave approximately equal, very small responses.

Fig. 3.

Grand average temporal envelope of MT response to single motion impulses. The responses of each cell were individually normalized and then averaged to produce the histogram shown. Thevertical dashed lines indicate the boundaries of the temporal window used to calculate the rates used as the principal response metric in this paper. The bold horizontal lineabove the histogram denotes the stimulus period. The histogram peaks to which these responses were normalized averaged 102 impulses/sec across our sample of cells, and the average integrated response above baseline, in the center of each RF, was 61 impulses/sec.

Fig. 4.

Responses of two representative MT cells, shown as PSTHs. Each small axis shows the response to the stimuli presented in the corresponding spatial location. Each is only 150 msec in duration; the responses of each cell were individually normalized, and the vertical calibration is indicated in the bottom left PSTH. The locations of each stimulus grid are indicated in degrees relative to the center of gaze. The vertical calibration bars express firing rate in impulses/sec. The ratios of the size of the sampling grid to the derived RF size (see Fig. 5) were 1.84 for the cell in A and 0.84 for the cell in B. The geometric mean of this ratio was 1.33 for our sample of cells.

Fig. 5.

RF size to eccentricity relationship estimated from the single motion impulses. Eccentricity was the center point of the best-fit two-dimensional Gaussian function fit to the spike rate data. Size was the sum of the ς_x and ς_y parameters, or average diameter.

Fig. 6.

Responses of 2 MT cells to pairs of Gabor motion stimuli. The x- and y-axes show the responses to each component stimulus presented individually (arbitrarily assigned to x or y), and thevertical axis shows the observed response to the pair presented simultaneously. Dots connected to thex–y plane show observed data points, whereas the surfaces and associated contour lines show the best-fit model (Eq. 3).A, Cell for which linear summation provided good account of the data. B, Different cell, which shows summation closer to winner take all.

Fig. 7.

Sample average summation. Each response (including the z-axis, or gray scale value) is normalized to the same value: the height of the two-dimensional Gaussian fit to the single-stimulus data. Each individual paired-stimulus condition was binned according to the observed response to the components of the pair, and then the bins were averaged. The surface was mirror-reflected across the diagonal for graphical clarity.

Fig. 8.

Comparison of predictions of three models for this experiment. A, Linear model: a = 0.5; n = 1. B, Winner-take-all model: a = 1; n = 100.C, Summation followed by squaring: a= 0.0025; n = 0.5. For comparison, the fit values for the two cells portrayed in Figure 6 were Figure6A: a = 0.72;n = 1.36; Figure 6B:a = 0.93; n = 6.68.

Fig. 9.

Comparison of variance accounted for by three models. Variance accounted for was calculated as 100 * (1 − var(obs − pred)/var(obs)). A, Linear model compared against the model of Simoncelli and Heeger (1998).B, Linear model compared against the generalized power-law summation model. Note that all three models provided fair accounts of the data but also that the generalized model provided the consistently lowest errors.

Fig. 10.

Sample histograms for the two key parameters of the generalized power-law summation model. See Results for details.

Fig. 11.

Responses and model residuals as a function of spatial location of the component stimuli. A, Average responses normalized as in Figure 7. B, Residuals from the best-fit generalized power-law summation model, also normalized to the same value, the amplitude of the Gaussian function fit to the single stimulus data.

Fig. 12.

Effects of time on responses to paired stimuli.A, Responses to single-motion impulses, shown as a function of time within a trial. Z scores were calculated relative to the entire distribution of responses to each stimulus location, independent of time, and then averaged for each time position, across stimulus location. Responses clearly decline rapidly in the first 500 msec of each trial (four stimuli). B, Responses to pairs of stimuli, compared against the expected response for that location and time position. Because the stimulus sequence was random, many stimulus location–time position combinations were not represented in any given experiment, but all that were presented contribute to this average. For both Aand B, the error bars denote the SEM across cells.