Optimal Finite-Horizon Perturbation Policy for Inference of Gene Regulatory Networks

Abstract

A major goal of systems biology is to model accurately the complex dynamical behavior of gene regulatory networks (GRNs). Despite several advancements that have been made in inference of GRNs, two main issues continue to make the problem challenging: 1) nonidentifiability of parameters and 2) limited amounts of data. Thus, it becomes necessary to experimentally perturb or excite the system into different states. This perturbation process disrupts the expression of genes from active to inactive, or vice versa, at each time point. Another issue is the partial observability of the gene states, which must be inferred indirectly from noisy gene expression measurements. In this article, this latter issue is accounted for by employing the partially observed Boolean dynamical system signal model for the data and applying optimal state estimation. Then, the optimal finite-horizon perturbation policy is derived to achieve the highest possible expected performance for the maximum a posteriori estimator under a small perturbation cost. Performance is assessed through numerical experiments using the well-known p53-MDM2 negative-feedback loop regulatory model and synthetic GRNs.