Linear Mapping Approximation of Nonlinear Gene Regulatory Networks

The mathematical modeling of gene regulatory networks presents significant challenges when stochasticity is taken into account. Exact solutions to the chemical master equation are rare. This is particularly the case when gene regulatory networks have reactions which are second-order or higher since in this case the moment equations cannot be closed. In this talk I will present a novel type of approximation method which maps the master equation of a nonlinear gene regulatory network on to the master equation of a linear network. In so doing the method leads to a closed-form solution for the approximate time-dependent marginal probability distribution of nonlinear gene regulatory networks with two promoter states. An advantage of the method is that it does not assume time-scale separation as common in the literature. The high accuracy of the method is established by comparison with stochastic simulations for genetic feedback loops with cooperativity, bursty protein production and oscillatory transcription. If I have time I will discuss how we are using the method to map out the phase diagram of gene regulatory networks.