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. 2021 Apr 26;22:304. doi: 10.1186/s12864-021-07593-3

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© The Author(s) 2021

Open AccessThis 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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.

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Fig. 8 — Diagram describing the process of constructing directed networks from Granger causality. a Lagged correlated expression between two genes (Granger causality) leads to the construction of a directed edge between two genes (nodes), which in turn is used to build directed lead-lag network models of putative interactions among genes. Edges can be positive or negative, based on the sign of lead-lag correlation between the two genes. b Bivariate associations are calculated between two genes at a time, while multivariate associations adjust for potential indirect association from all other genes in the gene set