Optimal Control for Generalized Asynchronous Probabilistic Boolean Networks†

As a paradigm for modeling gene regulatory networks, synchronous or asynchronous probabilistic Boolean networks (PBNs) provide us an effective tool to design therapeutic intervention strategies. However, most of the previous works focused on the former and only few studied the latter. This paper deals with an optimal control problem in a generalized asynchronous PBN by applying the theory on semi-Markov decision processes. Specifically, we first formulate a control model for a generalized asynchronous PBN as a first passage model for semi-Markov decision processes and then solve the corresponding optimal control problem by choosing optimal constituent Boolean networks in the asynchronous PBN such that the risk probability that the first passage time to some undesirable states associated with disease does not exceed a certain time is minimal. Numerical simulations are also provided to demonstrate the effectiveness of the proposed optimality approach.