Exact computation of probability landscape of stochastic networks of Single Input and Coupled Toggle Switch Modules

Gene regulatory networks depict the interactions between genes, proteins, and other components of the cell. These interactions often are stochastic that can influence behavior of the cells. Discrete Chemical Master Equation (dCME) provides a general framework for understanding the stochastic nature of these networks. However solving dCME is challenging due to the enormous state space, one effective approach is to study the behavior of individual modules of the stochastic network. Here we used the finite buffer dCME method and directly calculated the exact steady state probability landscape for the two stochastic networks of Single Input and Coupled Toggle Switch Modules. The first example is a switch network consisting of three genes, and the second example is a double switching network consisting of four coupled genes. Our results show complex switching behavior of these networks can be quantified.