Boolean Networks in Systems Biology

It is commonly accepted that many biological networks, such as gene regulatory or metabolic networks, are “modular,” in the sense that networks exhibit a structure of regions in which nodes are highly connected, called modules, with sparse connections between modules. Versions of such “community structures” can be found throughout the complex systems field. Since networks in molecular biology are often dynamic by nature, the natural question arises whether and how structural modularity is reflected in network dynamics. And if it is, then this modular structure should be recognizable in the dynamic models we frequently use to describe them. One common type of dynamic model in systems biology is that of Boolean networks, characterizing dynamics in terms of logical rules of regulation. This talk will propose, for the Boolean network framework, a definition of module, present a decomposition theorem that characterizes the modular structure of Boolean networks, and show that this decomposition theorem induces a decomposition of the resulting network dynamics in terms of the dynamics of the structural modules. The talk will also discuss some related open mathematical problems. The preprint arxiv.org/abs/2206.04217 contains details.