Multiscale Simulation of Stochastic Reaction-Diffusion Networks

  • Stefan Engblom
  • Andreas Hellander
  • Per LötstedtEmail author


The most commonly employed spatial stochastic simulation methods for biochemical systems in molecular systems biology are reviewed from a multiscale perspective. Three levels of approximation are distinguished: macroscopic, mesoscopic, and microscopic levels. The relation between the levels of approximation is discussed for both reactions between molecules and transport of the molecules through a solvent. Computational methods are described for each level separately and for hybrid methods involving two levels. Free software implementing these methods in space and time is surveyed.

2010 Mathematics Subject Classification.

Primary: 65C40; Secondary: 60H35; Tertiary: 92C05 



Generous support has been received from the Swedish Research Council, the eSSENCE strategic collaboration on e-Science, the UPMARC Linnaeus Center of Excellence, and the NIH under grant no. 1R01EB014877-01. The contents are solely the responsibility of the authors and do not necessarily reflect the opinions of these agencies. The authors would also like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Stochastic Dynamical Systems in Biology: Numerical Methods and Applications where this paper was conceived. This programme was supported by EPSRC grant no EP/K032208/1.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Stefan Engblom
    • 1
  • Andreas Hellander
    • 1
  • Per Lötstedt
    • 1
    Email author
  1. 1.Division of Scientific Computing, Department of Information TechnologyUppsala University05 UppsalaSweden

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