Understanding complex systems through differential causal networks.

In the evolving landscape of data science and computational biology, Causal Networks (CNs) have emerged as a robust framework for modelling causal relationships among elements of complex systems derived from experimental data. CNs can efficiently model causal relationships emerging in a single system while comparing multiple systems, allowing to understand rewiring in different cells, tissues, and physiological states with a deeper perspective. Despite the existence of network models, namely differential networks, that have been used to compare coexpression and correlation structures, causality needs to be introduced in differential analysis to robustly provide direction to the edges of such networks, in order to better understand the flows of information, and also to better intervene in their functioning, for example for agricultural or pharmacological purposes. Resolved to reach this ambitious goal, we introduce Differential Causal Networks (DCNs), a novel framework that represents differences between two existing CNs. A DCN is obtained from experimental data by comparing two CNs, and it is a power tool for highlighting differences in causal relations. After a careful definition and design of DCNs, we test our algorithm to model possible differential causal relationships between genes responsible for the onset of type 2 diabetes mellitus-related pathologies considering patients' sex at the tissue level. DCNs allowed us to shed light on causal differences between sexes across nine tissues. We also compare differences among three possible definitions of DCNs to highlight similarities and differences of biological importance. Code, Data and Supplementary Information are available at https://github.com/hguzzi/DifferentialCausalNetworks .