Reducing the complexity of a PBN while preserving its dynamical structure

Owing to computational complexity, it is sometimes necessary to reduce the size of a gene regulatory network. This paper proposes a strategy to reduce the size of a probabilistic Boolean network (PBN) while preserving its dynamical structure, a crucial requirement for the development of intervention strategies based on control theory. In particular, we focus on the following two issues when deleting a gene from the network: (1) maintaining the same number of constituent Boolean Networks (BNs), and (2) preserving the attractor structure, the relative sizes of the basins of attraction, and the level structures of the state transition diagrams of the constituent BNs. Preservation of the attractor structure is critical because the attractors of a PBN determine its steady-state behavior.A&M University, Veterinary Physiology and Pharmacology, College Station, TX 77843, USA.