Model Reconstruction for Moment-based Stochastic Chemical Kinetics
  Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains. The analysis of such processes is, however, computationally expensive and sophisticated numerical methods are required. Here, we propose an analysis framework in which we integrate a number of moments of the process instead of the state probabilities. This results in a very efficient simulation of the time evolution of the process. In order to regain the state probabilities from the moment representation, we combine the fast moment-based simulation with a maximum entropy approach for the reconstruction of the underlying probability distribution. We investigate the usefulness of this combined approach in the setting of stochastic chemical kinetics and present numerical results for three reaction networks showing its efficiency and accuracy. Besides a simple dimerization system, we study a bistable switch system and a multi-attractor network with complex dynamics. 
Andreychenko Alexander and Mikeev Linar and Wolf Verena
math.NA