Optimal control for probabilistic Boolean networks

Aberrant gene functions usually contribute to the pathology or diseases. Avoiding undesirable cellular phenotypes as many as possible is a major purpose of external control for gene regulatory networks. An interesting question is how to control a gene network subjected to the condition that the genes reach some undesirable states with minimal probability during a cell cycle. In this paper, we make use of the theory of the first passage model for discrete-time Markov decision processes to determine the optimal control for a gene intervention model. Specifically, we first use a control model for a probabilistic Boolean network to model interactions among genes and then solve an optimal control problem for maximising the probability of the first arrival time to desirable gene states. In order to illustrate the validity of our approach, examples are also displayed.