Master equations in chemical kinetics: CME and beyond

  • Leier A, Marquez-Lago T T
  • Published 2009

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 reactiondiffusion (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., 2006; Cai, 2007; Anderson 2007) and spatial SSAs (Hattne et al., 2005; Marquez-Lago and Burrage, 2007; Erban et al., 2007), to particle tracking models and discuss current research topics.

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Cite this paper

@inproceedings{A2009MasterEI, title={Master equations in chemical kinetics: CME and beyond}, author={Leier A and Marquez-Lago T T}, year={2009} }