Adaptive Intervention in Probabilistic Boolean Networks

Probabilistic Boolean Networks (PBNs) have been recently introduced as a paradigm for modeling genetic regulatory networks. One of the objectives of PBN modeling is to use the network for the design and analysis of intervention strategies aimed at moving the network out of undesirable states, such as those associated with disease, and into desirable ones. To date, a number of intervention strategies have been proposed in the context of PBNs. However, most of these techniques assume perfect knowledge of the transition probability matrix of the PBN. Such an assumption cannot be satisfied in practice, and may lead to degraded, if not completely unacceptable, performance. To remedy the situation, one can adopt one of two main approaches:(i) design an intervention strategy that is "robust" or somewhat insensitive to the presence of a class of modeling errors, such as uncertainties in the transition probability matrix; or (ii) introduce on-line adaptation or learning into the intervention strategy to ensure satisfactory performance provided the modeling error belongs to a particular class. The first approach has already been developed in an earlier paper. The main goal of this paper is to demonstrate the feasibility of the second approach. Using simulation studies, it is shown that adaptive intervention works well in two different scenarios: first, when we have a family of PBNs whose individual transition probability matrices are reasonably well modeled and the predominant uncertainty is about which member of that family represents the underlying genetic regulatory network; and second, when we have a context sensitive PBN with a low probability of a context change so that there is sufficient time between context changes for the adaptive algorithm to learn the context and exploit it in the intervention design. These results agree quite well with intuitive expectations.