State-Space Approach to Modeling Dynamics of Gene Regulation in Networks

Genetic networks are a key to unraveling dynamic properties of biological processes and regulation of genes plays an essential role in dynamic behavior of the genetic networks. A popular characterization of regulation of the gene is a kinetic model. However, many kinetic parameters in the genetic regulation have not been available. To overcome this difficulty, in this report, state-space approach to modeling gene regulation is presented. Second-order systems are used to characterize gene regulation. Interpretation of coefficients in the second order systems as resistance, capacitance and inductance is studied. The mathematical methods for transient response analysis of gene regulation to external perturbation are investigated. Criterion for classifying gene into three categories: underdamped, overdamped and critical damped is discussed. The proposed models are applied to yeast cell cycle gene expression data.