Optimal control of context-sensitive probabilistic Boolean networks using integer programming

Boolean networks are well-known as one of the models of biological networks such as gene regulatory networks. In this paper, we propose a solving method of the optimal control problem of context-sensitive probabilistic Boolean networks (CS-PBNs), which are one of the extended models of Boolean networks. In the existing solving methods, it is necessary to compute state transition diagrams with 2ⁿ nodes for a given CS-PBN with n states. So the existing methods cannot be applied to large-scale networks. To avoid the computation of state transition diagrams, an integer programming-based approach is proposed. In the proposed method, a CS-PBN is transformed into a linear system with binary variables, and the optimal control problem is reduced to an integer linear programming problem, which can be computed relatively easier than the existing methods using state transition diagrams.