Analysis of Modular Organisation of Interaction Networks Based on Asymptotic Dynamics

This paper investigates questions related to modularity in discrete models of biological interaction networks. We develop a theoretical framework based on the analysis of their asymptotic dynamics. More precisely, we exhibit formal conditions under which agents of interaction networks can be grouped into modules, forming a modular organisation. As main results, we show that the conventional decomposition in strongly connected components fulfills the formal conditions of being a modular organisation and we propose a modular and incremental algorithm for an efficient equilibria computation. Furthermore, we point out that our framework enables a finer analysis providing a decomposition in elementary modules, possibly smaller than strongly connected components.