Differential Equations and Chemical Master Equation Models for Gene Regulatory Networks

Synonyms

Chemical kinetics; Gene networks; Systems biology

Introduction

Gene regulatory networks (GRN) are composed of genes, DNA binding sites, transcription factors, mRNA and protein products, and even small ions. The molecules that are part of a GRN interact between and among themselves through biological processes. A GRN’s input collects the biological information from its environment. The GRN’s response, delivered through its output, is a result of the GRN’s computation on its input. Part of the output may be feed back into its input, creating loops into the GRN’s structure. Graphical representations for a GRN are not yet standardized, and mathematical models associated with a given GRN structure are not unique. One possibility to describe the computational processes that take place in a GRN is through differential equations. These mathematical models are deterministic in the sense that the concentration of the molecules of a GRN is considered as precise numbers at any given time....