Supplementary Figure 7: Spatial autocorrelation structure in gene expression and group-averaged T1w/T2w maps.

(a) Spatial autocorrelation in the parcellated cortical gene expression data is well-approximated by a decaying exponential function of distance. Gene co-expression is defined as the pairwise Spearman rank correlation between cortical parcels’ gene expression values, here for the 2413 brain-specific genes. Proximal cortical parcels exhibit more similar gene expression values compared to distal parcels. Pairs of parcel with geodesic separation distance less than 100 mm (8247 of 16,110 total pairs) were used to fit the characteristic scale of spatial autocorrelation, illustrated in red (i.e., exp(−d/d₀)), where d is geodesic distance and d₀ = 25 mm. Each data point corresponds to the co-expression of a pair of cortical parcels. Top: Mean co-expression value as a function of geodesic distance bin. (b) Gene co-expression values after correcting for spatial autocorrelation structure by subtraction of the fitted exponential in a. After correction, the mean co-expression value is near zero across all geodesic distance bins. (c) Example randomized surrogate maps with spatial autocorrelation structure matched to the empirical T1w/T2w map (see Methods). Autocorrelation structure-preserving surrogate maps are used for nonparametric calculation of statistical significance values for PCA results in Figs. 5 and 6, and Supplementary Figs. 6 and 10. (d) Distribution of pairwise Spearman rank correlations between 39,800 pairs of surrogate T1w/T2w maps.