Noise correlations in cortical area MT and their potential impact on trial-by-trial variation in the direction and speed of smooth-pursuit eye movements

Abstract

Smooth-pursuit eye movements are variable, even when the same tracking target motion is repeated many times. We asked whether variation in pursuit could arise from noise in the response of visual motion neurons in the middle temporal visual area (MT). In physiological experiments, we evaluated the mean, variance, and trial-by-trial correlation in the spike counts of pairs of simultaneously recorded MT neurons. The correlations between responses of pairs of MT neurons are highly significant and are stronger when the two neurons in a pair have similar preferred speeds, directions, or receptive field locations. Spike count correlation persists when the same exact stimulus form is repeatedly presented. Spike count correlations increase as the analysis window increases because of correlations in the responses of individual neurons across time. Spike count correlations are highest at speeds below the preferred speeds of the neuron pair and increase as the contrast of a square-wave grating is decreased. In computational analyses, we evaluated whether the correlations and variation across the population response in MT could drive the observed behavioral variation in pursuit direction and speed. We created model population responses that mimicked the mean and variance of MT neural responses as well as the observed structure and amplitude of noise correlations between pairs of neurons. A vector-averaging decoding computation revealed that the observed variation in pursuit could arise from the MT population response, without postulating other sources of motor variation.

FIG. 1.

Computer simulation showing the impact of noise correlations between pairs of neurons on decoding of stimulus speed and direction. A1: the color of each pixel indicates each neuron's mean number of spikes across 200 simulated repetitions of a stimulus moving at the direction of 135° and at the speed of 16°/s, and the location of each pixel indicates the neuron's preferred speed and direction. A2: responses on 20 trials for neurons with preferred speed equal to stimulus speed, plotted as a function of preferred direction. A3: responses on 20 trials for neurons with preferred direction equal to stimulus direction, plotted as a function of preferred speed. In A2 and A3, black curves show the population responses from individual trials and red curves show the mean response. B and C: plots of the variance of the decoded target speed (B) and direction (C) as a function of the number of neurons for different amplitudes of noise correlations, shown by different colors. The numbers in the key indicate the maximum correlation coefficient among neuron pairs (see methods for details of models). Filled orange symbols show predictions with uniform correlations that averaged 0.3 across the model population. All other symbols show predictions from model populations with structured correlations of different amplitudes. For the model populations in these simulations, the direction bandwidth was 98°, the SD of speed-tuning curves was 1.45, and the response amplitude was 11.5 spikes.

FIG. 2.

Absence of effect of exact location of random dots on noise correlations. A: spike count correlation of the responses from an example middle temporal visual area (MT) neuron pair with r = 0.64. Each symbol represents data from a single trial and shows spike counts in z-scores of 2 simultaneously recorded neurons. Visual stimuli comprised presentations of 201 different random-dot textures moving coherently in a fixed direction at 16°/s. B: scatterplot of the correlation coefficients computed from trials that used different vs. the same dot texture on every repetition of the stimulus. Each symbol shows data from one pair of MT neurons and the oblique dashed line has a slope of 1. C and D: averaged cross-correlograms (CCGs) under the random- (C) and fixed-seed (D) conditions for 27 neuron pairs that showed significant spike timing correlation. The y-axes plot the firing rate of one neuron at each time lag conditional on a spike at time 0 in the other neuron, defined as the number of coincidences in each bin of the CCG divided by the bin width of 1 ms. All responses were calculated during the total 500-ms motion presentation.

FIG. 3.

Structure of the relationships between spike count correlation r_sc and the difference between the preferred speeds (PS) (A, D), preferred directions (PD) (B, E), and the separation of receptive field (RF) centers (C, F) of the neuron pairs. Each symbol plots the correlation coefficient for one neuron pair. The red symbols represent statistically significant correlations (P < 0.05). A–C: correlation coefficients were based on the initial 150 ms of the neurons' responses to moving stimuli. D–F: correlation coefficients were based on the overall responses during the 500-ms motion presentation period. The gray bands in A and B show the mean ± 1SD of the correlations between pairs. In B and E, “Non-DS” refers to the pairs in which at least one neuron was not directionally selective (DSI <0.5).

FIG. 4.

Structure of spike count correlations. Black and gray histograms show the distributions of spike count correlation r_sc for neuron pairs whose preferred speed differences were <20°/s and >20°/s (A, D), whose preferred direction differences were <60° and >60° (B, E), and whose receptive field centers differed by <7.5° and >7.5° (C, F). A–C: correlation coefficients were based on the initial 150-ms of the neurons' responses to moving stimuli. D–F: correlation coefficients were based on the overall responses during the 500-ms motion presentation period. In each graph, the black and gray arrowheads show the mean value of r_sc for the cell pairs with the smaller vs. larger difference in response properties. All pairs are included, without regard for the statistical significance of r_sc.

FIG. 5.

Three-dimensional plots of spike count correlation r_sc in relation to the differences in PS and PD between the 2 neurons in each pair. Filled circles show pairs with significant positive correlations. Correlation coefficients were based on the overall responses to 500 ms of motion. The graph shows data for 143 pairs of directional-selective MT neurons.

FIG. 6.

Correlation maps as a function of time during the response to stimulus motion. The color of each pixel shows the mean correlation coefficient as a function of the times within the response of the 2 neurons. A: averages across all 165 neuron pairs. B and C: pairs with significant positive (n = 72) or negative (n = 18) correlations. All 3 correlation maps use the same color bar. Correlation coefficients were based on a series of 100-ms analysis windows incremented in 10-ms steps through the response. D: correlation along the diagonal of the 3 correlation maps plotted as a function of time from the onset of the neural response. Black, red, and blue traces show correlations for all neurons and neurons with significant positive or negative correlations. Time t in the plots indicates the time from t to t + 100 ms and t = 0 signifies the start of the neural response. The axes run to 250 ms, representing data from 0 to 350 ms after the onset of the response. Because some neurons had response latencies as long as 150 ms, 350 ms of data comprise the entire response for some neurons.

FIG. 7.

Analysis of the growth of noise correlation as a function of the duration of the analysis window. A: scatterplot comparing correlation coefficients based on the responses during the initial 150 ms of the neural response vs. the full 500 ms of the stimulus. The solid line has a slope of 1 and the dashed line shows the regression fit with a slope of 0.75. B: the averaged correlation coefficient across 165 MT neuron pairs as a function of the duration of the analysis window. C: average Fano factor of spike count as a function of the duration of the analysis windows. In B and C, the point at an analysis interval of 500 ms shows results for analysis of the entire 500-ms duration of the motion stimulus, starting from the onset of the stimulus motion. All other intervals started from the time of response onset. Error bars indicate SEs.

FIG. 8.

Speed dependence of noise correlation in 3 example MT neuron pairs. A: scatterplots showing the trial-by-trial neuronal responses of one example pair for 8 stimulus speeds. The numbers above each scatterplot and in the bottom right corner indicate the correlation coefficient (r) and stimulus speed (S). B–D: speed tuning of neural response and r_sc for 3 example MT neuron pairs. Dashed curves show normalized speed-tuning curves for the 2 neurons in each pair. Connected symbols show r_sc. Filled circles indicate speeds that yielded statistically significant correlations (P < 0.05). For B–D, the scales on the left axes are the same and calibrate the dashed lines showing neural responses. The scale on the right of D applies to B–D and calibrates the connected symbols showing the values of the spike count correlations. A and B show data for the same neuron pair.

FIG. 9.

Speed dependence of noise correlation summarized for 70 neuron pairs with similar stimulus preferences. A: averaged joint speed-tuning curve across pairs. B: averaged correlation coefficients across pairs as a function of stimulus speed. Error bars in A and B indicate SEs. C: summary of the relationship between the speed of the largest value of r_sc and the joint preferred speed. Each symbol is sized to indicate the number of pairs that plotted at each site in the graph. The 4 symbol sizes indicate that 1, 2, 3, or 5 pairs corresponded to each location in the graph. Data are for 50 neuron pairs that showed significantly positive correlation at one or more stimulus speeds. C1: marginal distribution of the speed of the largest r_sc. C2: marginal distribution of the joint preferred speed.

FIG. 10.

Contrast dependence of noise correlations. A and B: distributions of the noise correlation coefficients at stimulus contrasts of 5 and 20%. C: the mean correlation coefficient as a function of stimulus contrast. The error bars indicate SEs. Data are from 87 neuron pairs that were studied for stimuli of different contrasts. Horizontal dashed line shows the mean r_sc obtained when the stimulus was a high-contrast random-dot patch, averaged across the 43 neuron pairs studied with both patches and square-wave gratings.

FIG. 11.

Structure of spike count correlations for neuron pairs in a typical model MT population response. The parameters used in the model were: r_max = 0.36, and τ_s = 0.3, and τ_d = 0.4. A: relationship between r_sc and the difference between the preferred speeds of model neuron pairs whose preferred directions were equal to stimulus direction. The mean r_sc across all 1,035 pairs of model neurons was 0.072. B: relationship between r_sc and the difference between the preferred directions of 4,005 model neuron pairs whose preferred speeds were equal to stimulus speed. The mean r_sc across all 4,005 pairs of model neurons was 0.079. The gray ribbons are replotted from Fig. 3 and show the mean ± 1SD of the noise correlations in our sample of pairs of MT neurons.

FIG. 12.

Impact of response parameters of the model population on the variance of decoded estimates of target speed and direction. A: filled and open symbols show variances of speed and direction readouts as a function of response amplitude in the model population. B–F: effect of changing the speed and direction tuning in the model population on the variance of the decoded estimates of target speed (B, C), the mean estimate of target speed (D), and the variance of the estimates of target direction (E, F). B and E: variance is plotted as a function of the bandwidth (the full width at half-height) of the direction tuning of neurons in the model population; different sets of connected points indicate curves for different values of speed-tuning SD, indicated by the numbers in the key. C and F: variance is plotted as a function of the SD of the speed tuning of neurons in the model population; different sets of connected points indicate curves for different values of bandwidth of the direction tuning, indicated by the numbers in the key. D: bandwidth of direction tuning did not affect the mean speed, so only one curve is shown for a direction bandwidth of 72°.

FIG. 13.

Speed and direction variances of decoded estimates of target speed and direction match the variances of eye speed and direction during open-loop pursuit. A and B: speed variance plotted as a function of the SD of speed tuning in the model MT population. C and D: direction variance plotted as a function of the SD of speed tuning. The 2 columns summarize the performance of models chosen to reproduce different sets of data. Filled and open symbols in the left column (A, C) show 2 models designed to match the average performance of monkey subjects from Osborne et al. (2007). The horizontal lines indicate the average variances of those subjects and the vertical dashed lines are plotted at values of the SD of speed tuning that allow the models to reproduce the average variances. The right column (B, D) shows models designed to match the performance of 2 monkeys that represent extremes of data obtained in our laboratory. The horizontal dotted and solid lines indicate the variances obtained from monkey Pk, who showed very reliable pursuit initiation, and monkey Mo, who showed the most variable pursuit initiation among recent subjects in our laboratory. Open and filled symbols show models that could reproduce the variances of monkeys Mo and Pk, respectively. The vertical dashed lines indicate the values of the SD of speed tuning that allowed the models to succeed. Parameters of the successful population models are given in the text.