Application of dynamic programming in genetic regulatory networks

Probabilistic Boolean networks (PBN´s) have been recently introduced as a rule-based paradigm for modeling gene regulatory networks. Such networks, which form a subclass of Markovian genetic regulatory networks, provide a convenient tool for studying interactions between different genes while allowing for uncertainty in the knowledge of these relationships. In an earlier paper, we introduced external control into Markovian genetic regulatory networks. More precisely, given a Markovian genetic regulatory network whose state transition probabilities depend on an external (control) variable, a procedure was developed by which one could choose the sequence of control actions that minimized a given performance index over a finite number of steps. The procedure was based on the theory of controlled Markov chains and made use of the classical technique of dynamic programming. Furthermore, the choice of the finite horizon performance index was motivated by cancer treatment applications where one would ideally like to intervene only over a finite time horizon, then suspend treatment and observe the effects over some additional time before deciding if further intervention was necessary. The control algorithm in that paper, however, can be implemented only when one has perfect knowledge of the states of the Markov chain. Since such a requirement is unlikely to be satisfied in the real world, this paper considers a control strategy that can be implemented in the imperfect information case. Such a control strategy makes use of the available measurements which are assumed to be probabilistically related to the states of the underlying Markov chain.