Extended Data Fig. 6: Distributions of pairwise noise correlation coefficients do not differ significantly between pyramidal neurons in area V1 and higher-order visual areas.

a, Anatomical maps of visual cortical neurons that responded to each of the two stimuli. For these maps (but for no other analyses in the paper), we denoted a cell as responsive to one of the stimuli if, in at least one time bin during the 2-s-stimulation period (0.275 s per bin), the difference between the cell’s mean response and its mean activity trace during the inter-trial intervals was more than twice the sum of the s.e.m. values for these two traces. Cells that responded to stimulus A only are shown red, those that responded only to stimulus B only are shown blue, those that responded to both stimuli are shown purple. b, Mean Ca²⁺ responses (ΔF/F) of 25 example neurons to the two different moving grating stimuli, oriented at ± 30°. Ca²⁺ activity traces are shown coloured during the stimulation period (marked with light grey shading) and black otherwise. Coloured shading about each trace denotes the s.e.m. over 217 trials of each type. The inset shows a schematic of the two stimuli, which appeared for 2 s per trial and were presented in random order. c, d, Histograms of the estimated mean spiking rates of individuals neurons during visual stimulation (c) and the absolute values of the differential responses of the individual neurons to the two visual stimuli, |R_A – R_B| / (R_A + R_B) (d), where R_A and R_B denote the mean responses of a cell to stimuli A and B, respectively. The distributions of cells’ activity rates and preferences for one stimulus over the other were consistent with previous studies of rodent visual cortical neurons^{28,29,38,58,59}. Data shown are for N = 8,029 individual cells from N = 5 mice. Error bars are s.d. as estimated on the basis of counting errors. e, Histogram of noise correlation coefficients, r, between pairs of layer 2/3 pyramidal neurons, computed as in Fig. 2d, for V1 cell pairs (dashed lines) and cells pairs in higher-order visual areas (solid lines). The histograms show mean values across the two different visual stimuli for both the real neural activity traces, and for trial-shuffled data in which each cell’s responses to each stimulus presentation were randomly permuted across the set of all presentations of the same stimulus. r values were computed on the basis of cells’ responses integrated over t = [0.5 s, 2 s] from the start of each trial. Histogram bin, 0.01. (N = 1,331,109 V1 cell pairs from 5 mice; N = 2,428,437 cell pairs from higher-order visual areas in 5 mice). f, Box-and-whisker plots of the mean and FWHM values of the distributions in e (real data only). Both statistical metrics are similar for the two classes of visual cortical neurons. Open circles denote individual data points for N = 5 mice. g, h, Histograms (g) and cumulative probability distributions (h) of noise correlation coefficients for all cell pairs (based on all recorded V1 and higher-order visual cortical neurons) with similar or differently tuned mean evoked responses to the two visual stimuli. Unlike Fig. 2e, which shows these distributions for only the most active cells (the highest decile), here the distributions include all cell pairs with either positively (red curves) or negatively (blue curves) correlated mean responses to the two stimuli. Within these two groups of cell pairs, we computed the noise correlation coefficient, r, for each cell pair. Owing to the extremely large number of cell pairs, the two distributions of r values differed significantly (***P < 10⁻¹³ for all 5 individual mice; two-tailed Kolmogorov–Smirnov test; 3,482,186 positively correlated cell pairs in total; 3,464,094 negatively correlated pairs), even though the effect size was tiny and the two distributions were nearly identical. This result shows the difficulty of detecting information-limiting correlations by measuring pairwise noise correlations, because the variance in the individual r values is much greater than the difference between the mean values of the two distributions. i, Box-and-whisker plots of the mean values of the correlation coefficients in g, h. Open circles mark individual data points for N = 5 mice. b–i are based on 217–332 trials per stimulus condition in each of 5 mice. In f, i, boxes cover the middle 50% of values, horizontal lines denote medians, and whiskers span the full range of the data.