Decomposition of Boolean networks: An approach to modularity of biological systems

Abstract: This paper presents the foundation for a decomposition theory for Boolean networks, a type of discrete dynamical system that has found a wide range of applications in the life sciences, engineering, and physics. Given a Boolean network satisfying certain conditions, there is a unique collection of subnetworks so that the network can be reconstructed from these subnetworks by an extension operation. The main result of the paper is that this structural decomposition induces a corresponding decomposition of the network dynamics. The theory is motivated by the search for a mathematical framework to formalize the hypothesis that biological systems are modular, widely accepted in the life sciences, but not well-defined and well-characterized. As an example of how dynamic modularity could be used for the efficient identification of phenotype control, the control strategies for the network can be found by identifying controls in its modules, one at a time.