Extended Data Fig. 2: The spatial coordination index is a metric of the extent to which the activated neurons at an individual time point are spatially clustered.

a, Outline of the algorithm (Methods) used to compute the SCI at individual time points in the fluorescence Ca²⁺ movies. For each time point in a ΔF(t)/F₀ movie, we created an image of all cells that were coactive within 1 s of each other. A schematic of an example image (left) has a mixture of active (red) and inactive (white) cells. We computed the set of distances between all pairs of active cells in the image (middle). We then compared these values to the set of pairwise distances between active neurons in shuffled versions of the data from the same image, in which the identities of all the individual cells were randomly permuted while maintaining the same set of cell centroid locations. The shuffled dataset as a whole comprised 1,000 different random shuffles. We compared the cumulative probability distribution function (CDF) of all pairwise distances between active cells in the real image, to that for the shuffled data (right). We then tested two hypotheses, that the activated cells in the real image were either more spatially clustered than expected from a random pattern of activation, or less spatially clustered than expected from random activation. To test these two hypotheses, we performed a pair of one-sided Kolmogorov–Smirnov tests, comparing the real CDF values to those of the shuffled data. We determined the SCI by selecting the smaller of the two P values from these two tests, taking its logarithm, and assigning the sign of the index according to whether the CDF of the real data showed greater (positive sign) or less (negative sign) spatial clustering than the CDF of the shuffled data. b, Depictions of three images with different SCI values. The left image has an SCI >0, due to its many neighbouring coactive cells. The middle image has an SCI near zero, implying the activation pattern is consistent with that of a random distribution. The right frame has an SCI <0, indicating the active cells are further apart than generally expected of random activity. c, Examples of three image frames of different SCI values, from an actual Ca²⁺ movie acquired in a Drd1a^cre mouse. Active cells are shown enlarged and shaded white, whereas inactive cells are shaded grey. On the left is an image with multiple neighbouring coactive neurons and a high SCI. The middle image has a modest but positive SCI. The right image has a negative SCI, indicating that the activated cells are further apart than expected given a random pattern of activation. d, Distributions of pairwise distances between all pairs of active dSPNs for the three corresponding image frames shown in c. The distributions for the real data are shown in red, whereas those for the shuffled datasets are shown in grey. e, Mean time-dependent cross-correlation functions between mouse speed and the SCI of Ca²⁺ activity in dSPNs (left) and iSPNs (right). Cross-correlation values are shown normalized to their values for abscissa values of ±4 s (Methods). We computed the SCI from Ca²⁺ event traces to which we applied forward-smoothing, using one of five different filter values (coloured curves; Methods). Error bars are omitted for clarity in e, but are comparable to those shown in f. The centre-of-mass of the cross-correlation functions occurred at positive time lags (around 12–60 ms), indicating that rises in spatially coordinated Ca²⁺ activity preceded increases in mouse speed (P < 0.06 for both genotypes and all filter time constants; Wilcoxon signed-rank test), but there were no significant differences across the two mouse lines (P > 0.05 for all filter time constants; Wilcoxon rank-sum test; n = 37 cross-correlation functions from 16 Drd1a^cre mice and n = 52 from 21 Adora2a^cre mice). f, Mean cross-correlation functions between mouse speed and the SCI of Ca²⁺ activity in dSPNs and iSPNs computed from Ca²⁺ event rasters forward-smoothed with a 1,000-ms time constant. Shading indicates s.e.m. e, f, Values taken from n = 16 Drd1a^cre mice and n = 21 Adora2a^cre mice, aggregated over the 1-h recordings on day −5 and the 30-min recordings performed on days −4 to −1 after saline vehicle injection but before drug administration.