Optimal Bayesian Biomarker Selection for Gene Regulatory Networks under Regulatory Model Uncertainty

Gene regulatory networks (GRNs) are large and complex dynamical systems often monitored through RNA sequencing or microarray technologies. Genomics studies often focus on a small subset of genes and analyze only these genes due to the huge cost and time-limit constraints. Therefore, selecting a small subset of genes that carries the highest information about the underlying process of these complex systems is highly desired. The existing biomarker selection techniques rely on unrealistic assumptions such as direct observability of genes’ states as well as the availability of perfect knowledge about the modeling process. To address the aforementioned issues, this paper models GRNs with uncertain regulatory models with the signal model of partially-observed Boolean dynamical systems (POBDS) and derives the optimal Bayesian biomarker selection framework given the noisy available gene-expression data. The proposed framework is built on the multiple-model adaptive estimation (MMAE) framework and the optimal minimum mean-square error (MMSE) state estimator for POBDS, called Boolean Kalman smoother (BKS). The proposed framework is an optimal solution relative to the uncertainty class, and its high performance is demonstrated using the mammalian cell-cycle Boolean network model and the p53-MDM2 negative feedback loop observed through gene-expression data.