Interconnection of asynchronous Boolean networks, asymptotic and transient dynamics

The dynamics of the interconnection of two Boolean networks is analyzed directly from the properties of the two individual modules. Motivated by biological systems where multiple timescales are present, we consider asynchronous Boolean networks, whose dynamics can be described by nondeterministic transition graphs. Two new objects are introduced, the asymptotic and the cross graphs, constructed from the strongly connected components of the modules' transition graphs. It is then proved that the asymptotic graph actually recovers the attractors of the interconnected system, while reducing overall computational cost. Illustrated by various biological applications, this method is applied to analyze a composition of several well known modules (multicellular modeling), or to analyze a high dimensional model through its decomposition into smaller input/output subnetworks (model reduction).