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Fokker–Planck approximation of the master equation in molecular biology

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Computing and Visualization in Science

Abstract

The master equation of chemical reactions is solved by first approximating it by the Fokker–Planck equation. Then this equation is discretized in the state space and time by a finite volume method. The difference between the solution of the master equation and the discretized Fokker–Planck equation is analyzed. The solution of the Fokker–Planck equation is compared to the solution of the master equation obtained with Gillespie’s Stochastic Simulation Algorithm (SSA) for problems of interest in the regulation of cell processes. The time dependent and steady state solutions are computed and for equal accuracy in the solutions, the Fokker–Planck approach is more efficient than SSA for low dimensional problems and high accuracy.

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Author notes

  1. Johan Elf

    Present address: Department of Chemistry and Biology, Harvard University, Cambridge, MA, 02138, USA

Authors and Affiliations

  1. Division of Scientific Computing, Department of Information Technology, Uppsala University, P.O. Box 337, 75105, Uppsala, Sweden

    Paul Sjöberg & Per Lötstedt

  2. Department of Cell and Molecular Biology, Uppsala University, P.O. Box 596, 751 24, Uppsala, Sweden

    Johan Elf

Authors
  1. Paul Sjöberg
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  2. Per Lötstedt
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  3. Johan Elf
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Corresponding author

Correspondence to Per Lötstedt.

Additional information

Communicated by G. Wittum.

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Sjöberg, P., Lötstedt, P. & Elf, J. Fokker–Planck approximation of the master equation in molecular biology. Comput. Visual Sci. 12, 37–50 (2009). https://doi.org/10.1007/s00791-006-0045-6

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  • DOI: https://doi.org/10.1007/s00791-006-0045-6

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