NDLI: Solving the chemical master equation for monomolecular reaction systems analytically

Content Provider	Springer Nature Link
Author	Jahnke, Tobias Huisinga, Wilhelm
Copyright Year	2006
Abstract	The stochastic dynamics of a well-stirred mixture of molecular species interacting through different biochemical reactions can be accurately modelled by the chemical master equation (CME). Research in the biology and scientific computing community has concentrated mostly on the development of numerical techniques to approximate the solution of the CME via many realizations of the associated Markov jump process. The domain of exact and/or efficient methods for directly solving the CME is still widely open, which is due to its large dimension that grows exponentially with the number of molecular species involved. In this article, we present an exact solution formula of the CME for arbitrary initial conditions in the case where the underlying system is governed by monomolecular reactions. The solution can be expressed in terms of the convolution of multinomial and product Poisson distributions with time-dependent parameters evolving according to the traditional reaction-rate equations. This very structured representation allows to deduce easily many properties of the solution. The model class includes many interesting examples. For more complex reaction systems, our results can be seen as a first step towards the construction of new numerical integrators, because solutions to the monomolecular case provide promising ansatz functions for Galerkin-type methods.
Ending Page	26
Page Count	26
Starting Page	1
File Format	PDF
ISSN	03036812
e-ISSN	14321416
Journal	Journal of Mathematical Biology
Issue Number	1
Volume Number	54
Language	English
Publisher	Springer-Verlag
Publisher Date	2006-09-05
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Convergence to steady state Explicit solutions and reductions Chemical master equation Continuous-time Markov process Mathematical Biology in General Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) Applications of Mathematics Explicit solution formula Continuous-time Markov processes on general state spaces
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Agricultural and Biological Sciences Modeling and Simulation

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