Identification of periodic attractors in Boolean networks using a priori information

Boolean networks (BNs) have been developed to describe various biological processes, which requires analysis of attractors, the long-term stable states. While many methods have been proposed to detection and enumeration of attractors, there are no methods which have been demonstrated to be theoretically better than the naive method and be practically used for large biological BNs. Here, we present a novel method to calculate attractors based on a priori information, which works much and verifiably faster than the naive method. We apply the method to two BNs which differ in size, modeling formalism, and biological scope. Despite these differences, the method presented here provides a powerful tool for the analysis of both networks. First, our analysis of a BN studying the effect of the microenvironment during angiogenesis shows that the previously defined microenvironments inducing the specialized phalanx behavior in endothelial cells (ECs) additionally induce stalk behavior. We obtain this result from an extended network version which was previously not analyzed. Second, we were able to heuristically detect attractors in a cell cycle control network formalized as a bipartite Boolean model (bBM) with 3158 nodes. These attractors are directly interpretable in terms of genotype-to-phenotype relationships, allowing network validation equivalent to an in silico mutagenesis screen. Our approach contributes to the development of scalable analysis methods required for whole-cell modeling efforts.Author summary: Systems biology requires not only scalable formalization methods, but also means to analyze complex networks. Although Boolean networks (BNs) are a convenient way to formalize biological processes, their analysis suffers from the combinatorial complexity with increasing number of nodes n. Hence, the long standing O(2n) barrier for detection of periodic attractors in BNs has obstructed the development of large, biological BNs. We break this barrier by introducing a novel algorithm using a priori information. We show that the proposed algorithm enables systematic analysis of BNs formulated as bipartite models in the form of in silico mutagenesis screens.