Stochastic models of genetic regulatory networks

Regulation of gene expression is a chemical process involving many coupled elementary chemical reactions modeled usually by systems of differential equations describing time evolution of molecular concentrations. However, due to low numbers of molecules involved in gene expression processes, random fluctuations may play a significant role. We will present an elementary introduction to stochastic models of such processes. Master, Fokker-Planck, and Langevin equations will be discussed. We will review a simple model of protein production which can be completely solved, that is one can obtain analytical expressions for the expected value and the variance of the number of protein molecules (Thattai and Oudenaarden, PNAS, 8614-8619, 2001). Then we will discuss specific models of mRNA- and protein-regulated networks, present some partial results and open problems.