Hybrid numerical solution of the chemical master equation - Henzinger, Thomas A; Mateescu, Maria; Mikeev, Linar; Wolf, Verena; CMSB: Computational Methods in Systems Biology (Trento, Italy : Springer, 2010)
We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe net- works 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 prob- ability distribution of the discrete stochastic variables and the values of the continuous deterministic variables. We im- plemented the algorithm and we demonstrate its usefulness and efficiency on several case studies from systems biology.
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Keywords: conference paper