Master equations in chemical kinetics: CME and beyond

Abstract: Chemical reactions happening inside the cell are discrete, stochastic events widely modeled through the Chemical Master Equation (CME) and solved either directly, by trajectorial approaches (SSA) and their coarse-grained approximation, or by hybrid methods that bridge these two approaches. However, the CME assumes molecular well-mixedness and is prone to lack accuracy in the presence of multi-stage reactions that involve time delays and/or spatial inhomogeneities. Including these aspects requires approaches that go beyond the classical CME approach. We will give a review of stochastic, temporal and spatio-temporal approaches within the Master Equation framework. Especially, we will focus on two generalizations of the classical CME, the CME for reaction kinetics with delays (DCME) (Barrio et al., 2006; Tian et al., 2007) and for compartment-based reaction-diffusion (RDME) (Hattne et al., 2005; Isaacson, 2009) and explain their relationship. In this context, we will also bridge from corresponding trajectorial approaches, namely delay SSAs (Bratsun et al. 2005; Barrio et al.