Interconnection of asynchronous Boolean networks, asymptotic and transient dynamics

Abstract

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 non-deterministic 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).

A Formal Framework for Composing Qualitative Models of Biological Systems

“…For example, the properties of composing random Boolean network by computing the attractors compositionally is considered in [5]. Other work includes [15] in which a compositional approach is used to study a largescale network. Our approach based on merging entities and characterising the preservation of model behaviour appears to be new.…”

Relating Bisimulations with Attractors in Boolean Network Models

“…This allows us to minimize a model and still preserve the attractors. This is a well-known idea and several other methods to find attractor where developed after it (for instance, see [10]). On one hand, the method which we present can clusters sets of states which are not in the same SCC and, therefore, it clusters states which would not be clustered when we cluster the SCC's.…”

“…In [7], [10] some methods are presented. However, here, we present some new ideas that can lead to a new approach on this theme, based in bisimulations.…”

Measurement-induced Boolean dynamics and controllability for closed quantum networks

“…Boolean networks, introduced by Kauffman in the 1960s (Kauffman, 1969) and then extended to probabilistic Boolean networks (Shmulevich, Dougherty, Kim and Zhang, 2002), have been a classical model for gene regulatory interactions. The behaviors of Boolean dynamics are quite different compared to classical dynamical systems described by differential or difference equations due to their combinatorial natures, and their studies have been focused on the analytical or approximate characterizations to the steady-state orbits and controllability (Tournier and Chaves, 2013;Cheng and Qi, 2009). The contributions of the paper are summarized as follows:…”