Branching process approach for Boolean bipartite networks of metabolic reactions

TL;DR

This paper extends the branching process approach to Boolean bipartite networks of metabolic reactions, enabling analysis of avalanche dynamics in these complex systems by reducing bipartite structures to unipartite networks.

Contribution

It introduces a method to adapt the BP approach for bipartite metabolic networks by integrating out OR gates, providing a new way to analyze avalanche phenomena.

Findings

BP approach successfully applied to model metabolic networks

Effective branching ratio derived for bipartite Boolean networks

Simulation results confirm analytical predictions

Abstract

The branching process (BP) approach has been successful in explaining the avalanche dynamics in complex networks. However, its applications are mainly focused on unipartite networks, in which all nodes are of the same type. Here, motivated by a need to understand avalanche dynamics in metabolic networks, we extend the BP approach to a particular bipartite network composed of Boolean AND and OR logic gates. We reduce the bipartite network into a unipartite network by integrating out OR gates, and obtain the effective branching ratio for the remaining AND gates. Then the standard BP approach is applied to the reduced network, and the avalanche size distribution is obtained. We test the BP results with simulations on the model networks and two microbial metabolic networks, demonstrating the usefulness of the BP approach.