Predicting the asymptotic dynamics of large biological networks by interconnections of Boolean modules

The dynamics of Boolean networks can be represented by asynchronous transition graphs, whose attractors describe the system's asymptotic behavior. This paper shows that the attractors of the feedback interconnection of two Boolean modules can be fully identified in terms of cross-products of the attractors of each module. Based on this observation, a model reduction technique is proposed, aiming at analysing the asymptotic behavior of a high-dimensional network through the computation of the dynamics of two isolated smaller subnetworks. The method is applied to a large network which models cell-fate decision: all the attractors of the full network are exactly calculated by representing the network as an interconnection of two 3-input/3-output modules.