Classification of State Trajectories in Gene Regulatory Networks

Gene-expression-based phenotype classification is used for disease diagnosis and prognosis relating to treatment strategies. The present paper considers classification based on sequential measurements of multiple genes using gene regulatory network (GRN) modeling. There are two networks, original and mutated, and observations consist of trajectories of network states. The problem is to classify an observation trajectory as coming from either the original or mutated network. GRNs are modeled via probabilistic Boolean networks, which incorporate stochasticity at both the gene and network levels. Mutation affects the regulatory logic. Classification is based upon observing a trajectory of states of some given length. We characterize the Bayes classifier and find the Bayes error for a general PBN and the special case of a single Boolean network affected by random perturbations (BNp). The Bayes error is related to network sensitivity, meaning the extent of alteration in the steady-state distribution of the original network owing to mutation. Using standard methods to calculate steady-state distributions is cumbersome and sometimes impossible, so we provide an efficient algorithm and approximations. Extensive simulations are performed to study the effects of various factors, including approximation accuracy. We apply the classification procedure to a p53 BNp and a mammalian cell cycle PBN.