Calibrating a parameterized stochastic Boolean network model of gene regulation using a single steady-state gene expression profile

Boolean networks (BNs), due to their capacity to replicate non-linear dynamics despite their simplicity, have garnered significant interest among researchers. BNs can be used to simulate the effect of perturbations in biological systems, including changes in environmental conditions, genetic mutations, or the introduction of a drug. A major application of dynamic gene regulatory network (GRN) models is to identify how a specific perturbation shifts a GRN’s behavioral mode towards another one. To this end, a gene expression profile, which snapshots the cell transcriptome at (quasi-)steady-state, can be exploited to adjust a stochastic Boolean GRN under a certain condition. Such tailored GRNs hold numerous implications for drug target discovery, novel therapeutic strategies, and personalized medicine. In this study, we introduce a methodology for estimating the parameters of a parameterized stochastic BN model of gene regulation using a single steady-state gene expression measurement. We employ certain simplifying assumptions to reformulate the problem as a system of linear equations, ensuring ergodicity and the existence of a unique solution. However, even under these simplifying conditions, the high time and space demand to solve the problem can be challenging. In the present study, we applied a simulation-based approach to estimating parameters, rather than explicitly deriving and solving the set of linear equations. Finally, we show the applicability and relevance of our approach on a set of randomly generated BNs as well as establishing “personalized” BNs for non-small cell lung cancer cell lines (NSCLC).