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Journal of Chemical Physics / Volume 135 / Issue 24 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 135, 244103 (2011); http://dx.doi.org/10.1063/1.3666988 (17 pages)

Exact on-lattice stochastic reaction-diffusion simulations using partial-propensity methods

Rajesh Ramaswamy and Ivo F. Sbalzarini

MOSAIC Group, Institute of Theoretical Computer Science and Swiss Institute of Bioinformatics, ETH Zurich, CH–8092 Zürich, Switzerland

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(Received 7 September 2011; accepted 18 November 2011; published online 23 December 2011)

Stochastic reaction-diffusion systems frequently exhibit behavior that is not predicted by deterministic simulation models. Stochastic simulation methods, however, are computationally expensive. We present a more efficient stochastic reaction-diffusion simulation algorithm that samples realizations from the exact solution of the reaction-diffusion master equation. The present algorithm, called partial-propensity stochastic reaction-diffusion (PSRD) method, uses an on-lattice discretization of the reaction-diffusion system and relies on partial-propensity methods for computational efficiency. We describe the algorithm in detail, provide a theoretical analysis of its computational cost, and demonstrate its computational performance in benchmarks. We then illustrate the application of PSRD to two- and three-dimensional pattern-forming Gray-Scott systems, highlighting the role of intrinsic noise in these systems.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. ON-LATTICE STOCHASTIC REACTION-DIFFUSION
    1. General concept
    2. Discretization-corrected propensities
    3. The next subvolume method (NSM) for on-lattice stochastic reaction-diffusion simulations
  3. THE PARTIAL-PROPENSITY STOCHASTIC REACTION-DIFFUSION METHOD
    1. General concept of PSRD
      1. Composition-rejection sampling to select the subvolume
      2. Partial propensities to sample the next reaction within a subvolume
        1. Partial propensities:
        2. Sampling using partial propensities:
    2. Detailed description of the PSRD algorithm
      1. Data structures
      2. Algorithms
  4. BENCHMARKS
    1. Colloidal aggregation model
    2. Linear chain model
  5. TWO- AND THREE-DIMENSIONAL SRD SIMULATIONS USING PSRD
  6. CONCLUSIONS AND DISCUSSION

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KEYWORDS and PACS

Keywords

master equation, noise, reaction kinetics theory, reaction-diffusion systems, stochastic processes

PACS

  • 82.20.Wt

    Computational modeling; simulation

  • 82.20.Fd

    Collision theories; trajectory models

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3666988

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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