Altering steady-state probabilities in probabilistic Boolean networks

External control of a genetic regulatory network is used for the purpose of avoiding undesirable states, such as those associated with disease. Heretofore, intervention has focused on finite-horizon control, i.e., control over a small number of stages. This paper considers the design of optimal infinite-horizon control for probabilistic Boolean networks (PBNs). The stationary policy obtained is independent of time and dependent on the current state. The average-cost-per-stage problem formulation is used to generate the stationary policy for a PBN constructed from melanoma gene-expression data. The results show that the stationary policiy obtained is capable of shifting the probability mass of the stationary distribution from undesirable states to desirable ones.