Spatial and Temporal Scales of Neuronal Correlation in Primary Visual Cortex

Comparison of correction methods for CCGs. A, Diagram of the method used for CCG correction. Data from 5 simulated trials is shown on the left, with a different color labeling for the spikes from each trial. The trials were divided into bins based on the jitter window size (demarcated by the dashed vertical lines). From the original data, a raw CCG was computed. The original data were then resampled. For each spike in each jitter bin, a new spike was chosen randomly, without replacement, from the set of all spikes in the same jitter bin on all trials. B, Raw CCG and correction terms. From the original data, we computed a raw CCG (red line, shown for an example pair of neurons). The most common method of correcting CCGs is shuffling the trial labels, which produces the correction term shown with the dashed line for this pair. The jitter correction terms, for jitter window sizes of 50, 250, and 1000 ms, are shown here with gray lines (dark, thin lines represent the larger jitter windows). C, Corrected CCGs (subtracting the correction term from the raw CCG). In the shuffle-corrected CCG (dashed line), significant correlation is evident on both slow and fast time scales as broad and narrow peaks, respectively. Using jitter correction with large windows (250 and 1000 ms), the broad peak is reduced but still evident. When the jitter window is small (50 ms, thick gray line), the broad peak is removed and only the short time scale correlation remains.

Dependence of r_sc on distance and tuning similarity. A, The dependence of r_sc on distance for pairs grouped based on their orientation tuning similarity (r_signal, thicker lines are for pairs with the most similar orientation tuning). The distance bins start at 0.25 mm and extend to 4.25 mm in 0.5 mm increments. The average of all the data are plotted at the center value of each bin. Data from dual-recording experiments (567 pairs) are shown with separate symbols to the right of the axis. Error bars on this and all subsequent plots indicate ±1 SEM; the points are shifted slightly from their true value along the abscissa for illustration purposes only. In this and all subsequent plots, only data points corresponding to 5 or more neuronal pairs are shown. B, The dependence of r_sc on r_signal for pairs grouped by their separation, thinner and darker lines are for more distant pairs. The average of all the data are plotted at the center value of each bin. C, The dependence of r_sc on both distance and tuning similarity. The scale of the color plot is indicated by the bar at the right. The original data in this and all subsequent surface plots were smoothed with a two-dimensional Gaussian (SD of 1 bin).

Effect of distance on the time scale of correlation. A, Surface plot showing the value of r_ccg for different integration windows and distances between electrodes. The color scale is shown to the left of E. B, r_ccg as a function of integration window for different distance groups (thinner and darker lines for more distant pairs). C, Surface plot showing the value of r_ccg for different integration windows and tuning similarity. The color scale is shown on the right. D, r_ccg as a function of integration window for different r_signal groups (thinner and darker lines indicate pairs with less similar tuning preferences). E, For neurons in three distance groups (thinner and darker lines are more distance), the value of r_ccg is shown as a ratio to its value at the longest distance (3–4 mm). F, Average shuffle-corrected CCGs for pairs of neurons grouped by distance. The tick marks to the left of the CCGs indicate a value of 0 coinc./sp.

CCGs after removing long time scale correlation. A, Average CCGs, after jitter correction, for pairs of neurons grouped by distance. A large peak, centered on zero time lag, is evident at close distances. The increasing noise in the lower plots is due to the smaller number of pairs at those distances. The tick marks to the left of the CCGs indicate a value of 0 coinc./sp. The tick mark at the bottom of the CCGs indicates zero time lag. B, The area under the CCG peak, within ±10 ms of zero, falls off quickly with distance, reaching zero for pairs >3 mm apart.

Dependence of synchrony on distance and tuning similarity. A, The dependence of synchrony, quantified by the area under the CCG peak, on distance for pairs grouped based on their orientation tuning similarity (r_signal, thicker lines are for more similar orientation tuning). B, The dependence of synchrony on orientation tuning similarity for pairs grouped by distance (r_signal, thinner lines are for more distant pairs of neurons). C, The relationship of synchrony to both distance and tuning similarity (conventions are as in Fig. 3C).

Dynamics of correlation. A, In a separate data collection period in 6 of the 7 array implants, we recorded 15–30 min of spontaneous activity. The value of r_sc for 2738 pairs decreased with distance, but was much higher at all distances than during the evoked response. Using a smaller 0.1 s epoch, the same as in B and C, resulted in a lower value for r_sc. However, it was still significantly higher than that observed in the ISI after the end of the visual stimulus (C). B, The average geometric mean firing rate across all 12 stimulus directions and all neurons. The stimulus period (1.28 s) is indicated by the gray shaded region, and the nonshaded regions represent the blank interstimulus intervals. Each data point represents the average value for a 100 ms window centered at the time on the abscissa. C, The value of r_sc computed in the same 100 ms windows as above.