Hybrid numerical solution of the chemical master equation

Authors:
Thomas A. Henzinger;Linar Mikeev;Maria Mateescu;Verena Wolf
Affiliations:
Institute of Science and Technology, Austria;Saarland University, Germany;Ecole Polytechnique Fédérale de Lausanne, Switzerland;Saarland University, Germany
Venue:
Proceedings of the 8th International Conference on Computational Methods in Systems Biology
Year:
2010

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Abstract

We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is based on the construction of a stochastic hybrid model in which certain discrete random variables of the original Markov chain are approximated by continuous deterministic variables. We compute the solution of the stochastic hybrid model using a numerical algorithm that discretizes time and in each step performs a mutual update of the transient probability distribution of the discrete stochastic variables and the values of the continuous deterministic variables. We implemented the algorithm and we demonstrate its usefulness and efficiency on several case studies from systems biology.