title: A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions.
abstract: Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.
authors.affiliation: Department of Biochemistry and Biophysics, California Institute for Quantitative Biosciences, University of California San Francisco, 1700 4th Street, San Francisco, California 94143-2542, USA.
authors.forename: Michael W
authors.initials: MW
authors.lastname: Chevalier
authors.affiliation: Department of Biochemistry and Biophysics, California Institute for Quantitative Biosciences, University of California San Francisco, 1700 4th Street, San Francisco, California 94143-2542, USA.
authors.forename: Hana
authors.initials: H
authors.lastname: El-Samad
mesh_terms: D001669:Biochemical Phenomena; D002462:Cell Membrane / Q000378:metabolism; D003198:Computer Simulation; D004058:Diffusion; D007700:Kinetics; D008390:Markov Chains; D008954:Models, Biological; D009038:Motion; D013269:Stochastic Processes