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. 2021 Jul 9;12:4237. doi: 10.1038/s41467-021-24306-2

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 1 — A A schematic representation of the connectome showing different connection types in the brain. Given a distinction between hub nodes (red outline) and nonhub nodes (gray outline), we can delineate three classes of connections: rich links—connections between two hubs (red); feeder links—connections between a hub and a nonhub (yellow); and peripheral links—connections between two nonhubs (blue). B Connectome-wide heritability analysis. We use structural equation modeling to fit a classic ACTE biometric model to every connection within the brain, resulting in estimates of genetic and environmental influences for each link. C Analysis of transcriptional coupling. (I) Each of 3702 tissue samples in the Allen Human Brain Atlas (AHBA) is mapped to a given region in our brain parcellation. (II) Expression values are then subjected to quality control and processing pipeline⁴⁰ to construct a region × gene matrix of expression values. (III) We estimate correlated gene expression (CGE) between each pair of brain regions as the Pearson correlation between region-specific gene-expression profiles. (IV) Inter-regional CGE is corrected for spatial autocorrelation of the expression data via regression of an exponential distance trend⁴⁰. D Schematic representation of how values assigned to each edge are compared across connection types. We compare the mean of edge-level (pairwise) measures of heritability and CGE for rich, feeder, and peripheral links across all possible hub-defining thresholds (horizontal axis). As k increases, the definition of a hub becomes more stringent and identifies the actual hubs of the network. Thus, if a given effect is stronger for rich links, we expect the pairwise estimates to increase as a function of k, with the increase for rich links being particularly large relative to the feeder and peripheral links.