Jahnke, T. and Huisinga, W.
(2007)
*Solving the Chemical Master Equation for Monomolecular Reaction Systems Analytically.*
J. Math. Biol., 54
(1).
pp. 1-26.

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Official URL: http://dx.doi.org/10.1007/s00285-006-0034-x

## 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.

Item Type: | Article |
---|---|

Subjects: | Mathematical and Computer Sciences > Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group |

ID Code: | 41 |

Deposited By: | Admin Administrator |

Deposited On: | 03 Jan 2009 20:20 |

Last Modified: | 03 Mar 2017 14:39 |

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