Steady-state analysis of genetic regulatory networks modeled by nonlinear ordinary differential equations

Abstract

Although Ordinary Differential Equations (ODEs) have been used to model Genetic Regulatory Networks (GRNs) in many previous works, their steady-state behaviors are not well studied. However, a phenotype corresponds to a steady-state gene expression pattern and steady-state analysis of GRNs can provide valuable information on the stability of the GRNs, insights into cellular regulatory mechanisms underlying disease development as well as possible interventions for disease control. In this study, the steady-state behaviors of the nonlinear GRN models are analyzed based on time series data. The steady-state solutions and stability of nonlinear GRNs including polynomial model, sigmoidal model and S-system model are discussed in details.