title: Efficient parametric analysis of the chemical master equation through model order reduction.
abstract: BACKGROUND
  Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state space dimension of these equations, numerical simulations are computationally expensive. This is a particular problem for analysis tasks requiring repeated simulations for different parameter values. Such tasks are computationally expensive to the point of infeasibility with the chemical master equation.
  
  
  RESULTS
  In this article, we apply parametric model order reduction techniques in order to construct accurate low-dimensional parametric models of the chemical master equation. These surrogate models can be used in various parametric analysis task such as identifiability analysis, parameter estimation, or sensitivity analysis. As biological examples, we consider two models for gene regulation networks, a bistable switch and a network displaying stochastic oscillations.
  
  
  CONCLUSIONS
  The results show that the parametric model reduction yields efficient models of stochastic biochemical reaction networks, and that these models can be useful for systems biology applications involving parametric analysis problems such as parameter exploration, optimization, estimation or sensitivity analysis.
authors: Institute for Systems Theory and Automatic Control, University of Stuttgart, Pfaffenwaldring 9, Stuttgart, Germany. waldherr@ist.uni-stuttgart.de
authors: Steffen
authors: S
authors: Waldherr
authors: Bernard
authors: B
authors: Haasdonk
mesh_terms: D053263:Gene Regulatory Networks; D008954:Models, Biological; D013223:Statistics as Topic; D013269:Stochastic Processes