Sparse grids and hybrid methods for the chemical master equation

  • Markus Hegland
  • Andreas Hellander
  • Per Lötstedt


The direct numerical solution of the chemical master equation (CME) is usually impossible due to the high dimension of the computational domain. The standard method for solution of the equation is to generate realizations of the chemical system by the stochastic simulation algorithm (SSA) by Gillespie and then taking averages over the trajectories. Two alternatives are described here using sparse grids and a hybrid method. Sparse grids, implemented as a combination of aggregated grids are used to address the curse of dimensionality of the CME. The aggregated components are selected using an adaptive procedure. In the hybrid method, some of the chemical species are represented macroscopically while the remaining species are simulated with SSA. The convergence of variants of the method is investigated for a growing number of trajectories. Two signaling cascades in molecular biology are simulated with the methods and compared to SSA results.

Key words

stochastic chemical kinetics master equation sparse grids hybrid method 


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Copyright information

© Springer Science + Business Media B.V. 2008

Authors and Affiliations

  • Markus Hegland
    • 1
  • Andreas Hellander
    • 2
  • Per Lötstedt
    • 2
  1. 1.Centre for Mathematics and its Applications, MSIAustralian National UniversityCanberraAustralia
  2. 2.Division of Scientific Computing, Department of Information TechnoloyUppsala UniversityUppsalaSweden

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