Time-dependence in chemical kinetics: system size expansion and finite state methods for reaction extents #

Konstantinos Alexiou, James Holehouse, Giorgos Minas

Poster session

Abstract #

In this poster we provide analytic solutions to the master equation describing reaction extents, i.e., the number of reactions of each type that have occurred. It provides more information than the chemical master equation, and can be used to discuss the probability of a reaction having fired $n$ times in some time period. Notably, molecule numbers are not uniquely described by a single vector of the reaction extents, but there is a one-to-one mapping from reaction extents to molecules numbers. We start by applying the system size ansatz to the reaction extents chemical master equation (RECME) and derive the linear noise approximation, and then use a mesoscopic result to provide more accurate analytics in small volumes. We then use these approximations in order to provide system bounds to solve the RECME exactly within a finite state truncated system using linear algebraic methods previously used to solve the 1D 1-step master equation in time. This is part of my PhD project and a joint work with Dr. James Holehouse (The Santa Fe Institute) and Dr. Giorgos Minas (University of St Andrews).