Integer Programming-Based Approach to Attractor Detection and Control of Boolean Networks

Abstract

The Boolean network (BN) can be used to create discrete mathematical models of gene regulatory networks. In this paper, we consider three problems on BNs that are known to be NP-hard: detection of a singleton attractor, finding a control strategy that shifts a BN from a given initial state to the desired state, and control of attractors. We propose integer programming-based methods which solve these problems in a unified manner. Then, we present results of computational experiments which suggest that the proposed methods are useful for solving moderate size instances of these problems. We also show that control of attractors is $\Sigma_2^p$-hard, which suggests that control of attractors is harder than the other two problems.