Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation

In systems biology, the stochastic description of biochemical reaction kinetics is increasingly being employed to model gene regulatory networks and signalling pathways. Mathematically speaking, such models require the numerical solution of the underlying evolution equation, known as the chemical master equation (CME). Up to now, the CME has primarily been treated by Monte-Carlo techniques, the most prominent of which is the stochastic simulation algorithm (Gillespie 1976). The paper presents an alternative, which focuses on the discrete partial differential equation (PDE) structure of the CME. This allows to adopt ideas from adaptive discrete Galerkin methods as first suggested in (Deuflhard, Wulkow 1989) for polyreaction kinetics and independently developed in (Engblom 2006). Among the two different options of discretizing the CME as a discrete PDE, Engblom had chosen the method of lines approach (first space, then time), whereas we strongly advocate to use the Rothe method (first ti...

• Type: Journal
• Year: 2008
• Where: SIAMSC
• Authors: Peter Deuflhard, Wilhelm Huisinga, T. Jahnke, Michael Wulkow
• Keywords: Adaptive Discrete, Chemical Master Equation, Reaction Kinetics, SIAMSC 2008