A spectral methods-based solution of the Chemical Master Equation for gene regulatory networks

We present a new method to approximate the time evolution of the probability density function (PDF) for molecule counts in gene regulatory networks modeled by the Chemical Master Equation (CME). A key feature of our method is that molecular states can be aggregated to reduce the computational burden without the need for assumptions like time-scales separation. The CME is amenable to the use of various spectral methods adapted from partial differential equations and our method results from expanding the solution using carefully selected basis functions. The method is illustrated in the context of an example taken from the field of systems biology.