Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning

Abstract

The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian dynamics or Green’s function reaction dynamics, the RDME can be orders of magnitude faster if the lattice spacing can be chosen coarse enough. However, strongly diffusion-controlled reactions mandate a very fine mesh resolution for acceptable accuracy. It is common that reactions in the same model differ in their degree of diffusion control and therefore require different degrees of mesh resolution. This renders mesoscopic simulation inefficient for systems with multiscale properties. Mesoscopic-microscopic hybrid methods address this problem by resolving the most challenging reactions with a microscale, off-lattice simulation. However, all methods to date require manual partitioning of a system, effectively limiting their usefulness as “black-box” simulation codes. In this paper, we propose a hybrid simulation algorithm with automatic system partitioning based on indirect a priori error estimates. We demonstrate the accuracy and efficiency of the method on models of diffusion-controlled networks in 3D.

Authors:
 [1];  [1]; ORCiD logo [2]
+ Show Author Affiliations
  1. Uppsala Univ. (Sweden)
  2. Univ. of California, Santa Barbara, CA (United States)
Publication Date:
Research Org.:
Univ. of California, Santa Barbara, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1512930
Alternate Identifier(s):
OSTI ID: 1413550
Grant/Contract Number:  
SC0008975
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 147; Journal Issue: 23; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Hellander, Stefan, Hellander, Andreas, and Petzold, Linda. Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning. United States: N. p., 2017. Web. doi:10.1063/1.5002773.
Copy to clipboard
Hellander, Stefan, Hellander, Andreas, & Petzold, Linda. Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning. United States. https://doi.org/10.1063/1.5002773
Copy to clipboard
Hellander, Stefan, Hellander, Andreas, and Petzold, Linda. Fri . "Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning". United States. https://doi.org/10.1063/1.5002773. https://www.osti.gov/servlets/purl/1512930.
Copy to clipboard
@article{osti_1512930,
title = {Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning},
author = {Hellander, Stefan and Hellander, Andreas and Petzold, Linda},
abstractNote = {The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian dynamics or Green’s function reaction dynamics, the RDME can be orders of magnitude faster if the lattice spacing can be chosen coarse enough. However, strongly diffusion-controlled reactions mandate a very fine mesh resolution for acceptable accuracy. It is common that reactions in the same model differ in their degree of diffusion control and therefore require different degrees of mesh resolution. This renders mesoscopic simulation inefficient for systems with multiscale properties. Mesoscopic-microscopic hybrid methods address this problem by resolving the most challenging reactions with a microscale, off-lattice simulation. However, all methods to date require manual partitioning of a system, effectively limiting their usefulness as “black-box” simulation codes. In this paper, we propose a hybrid simulation algorithm with automatic system partitioning based on indirect a priori error estimates. We demonstrate the accuracy and efficiency of the method on models of diffusion-controlled networks in 3D.},
doi = {10.1063/1.5002773},
journal = {Journal of Chemical Physics},
number = 23,
volume = 147,
place = {United States},
year = {Fri Dec 15 00:00:00 EST 2017},
month = {Fri Dec 15 00:00:00 EST 2017}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1063/1.5002773
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 6 works
Citation information provided by
Web of Science

Figures / Tables:

Algorithm 1 Algorithm 1: Hybrid method.
All figures and tables (12 total)
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Coupled Mesoscopic and Microscopic Simulation of Stochastic Reaction-Diffusion Processes in Mixed Dimensions
journal, January 2012

  • Hellander, Andreas; Hellander, Stefan; Lötstedt, Per
  • Multiscale Modeling & Simulation, Vol. 10, Issue 2
  • DOI: 10.1137/110832148

Random Walks on Lattices. III. Calculation of First‐Passage Times with Application to Exciton Trapping on Photosynthetic Units
journal, April 1969

  • Montroll, Elliott W.
  • Journal of Mathematical Physics, Vol. 10, Issue 4
  • DOI: 10.1063/1.1664902

A general computational framework for modeling cellular structure and function
journal, September 1997

A convergent reaction-diffusion master equation
journal, August 2013

  • Isaacson, Samuel A.
  • The Journal of Chemical Physics, Vol. 139, Issue 5
  • DOI: 10.1063/1.4816377

Stochastic reaction-diffusion kinetics in the microscopic limit
journal, November 2010

  • Fange, D.; Berg, O. G.; Sjoberg, P.
  • Proceedings of the National Academy of Sciences, Vol. 107, Issue 46
  • DOI: 10.1073/pnas.1006565107

Multiscale Reaction-Diffusion Algorithms: PDE-Assisted Brownian Dynamics
journal, January 2013

  • Franz, Benjamin; Flegg, Mark B.; Chapman, S. Jonathan
  • SIAM Journal on Applied Mathematics, Vol. 73, Issue 3
  • DOI: 10.1137/120882469

A hybrid continuous-discrete method for stochastic reaction–diffusion processes
journal, September 2016

  • Lo, Wing-Cheong; Zheng, Likun; Nie, Qing
  • Royal Society Open Science, Vol. 3, Issue 9
  • DOI: 10.1098/rsos.160485

Multiscale reaction-diffusion simulations with Smoldyn: Fig. 1.
journal, March 2015

Stochastic Simulation Service: Bridging the Gap between the Computational Expert and the Biologist
journal, December 2016

Hybrid approaches for multiple-species stochastic reaction–diffusion models
journal, October 2015

Stochastic modelling of reaction–diffusion processes: algorithms for bimolecular reactions
journal, August 2009

MOLNs: A Cloud Platform for Interactive, Reproducible, and Scalable Spatial Stochastic Computational Experiments in Systems Biology Using PyURDME
journal, January 2016

  • Drawert, Brian; Trogdon, Michael; Toor, Salman
  • SIAM Journal on Scientific Computing, Vol. 38, Issue 3
  • DOI: 10.1137/15M1014784

Lost in presumption: stochastic reactions in spatial models
journal, December 2012

  • Mahmutovic, Anel; Fange, David; Berg, Otto G.
  • Nature Methods, Vol. 9, Issue 12
  • DOI: 10.1038/nmeth.2253

Fast Monte Carlo Simulation Methods for Biological Reaction-Diffusion Systems in Solution and on Surfaces
journal, January 2008

  • Kerr, Rex A.; Bartol, Thomas M.; Kaminsky, Boris
  • SIAM Journal on Scientific Computing, Vol. 30, Issue 6
  • DOI: 10.1137/070692017

Reaction-diffusion master equation in the microscopic limit
journal, April 2012

Green’s-function reaction dynamics: A particle-based approach for simulating biochemical networks in time and space
journal, December 2005

  • van Zon, Jeroen S.; ten Wolde, Pieter Rein
  • The Journal of Chemical Physics, Vol. 123, Issue 23
  • DOI: 10.1063/1.2137716

An adaptive algorithm for simulation of stochastic reaction–diffusion processes
journal, January 2010

  • Ferm, Lars; Hellander, Andreas; Lötstedt, Per
  • Journal of Computational Physics, Vol. 229, Issue 2
  • DOI: 10.1016/j.jcp.2009.09.030

The pseudo-compartment method for coupling partial differential equation and compartment-based models of diffusion
journal, May 2015

  • Yates, Christian A.; Flegg, Mark B.
  • Journal of The Royal Society Interface, Vol. 12, Issue 106
  • DOI: 10.1098/rsif.2015.0141

The Role of Type 4 Phosphodiesterases in Generating Microdomains of cAMP: Large Scale Stochastic Simulations
journal, July 2010

The Role of Dimerisation and Nuclear Transport in the Hes1 Gene Regulatory Network
journal, May 2013

  • Sturrock, Marc; Hellander, Andreas; Aldakheel, Sahar
  • Bulletin of Mathematical Biology, Vol. 76, Issue 4
  • DOI: 10.1007/s11538-013-9842-5

Noise-Induced Min Phenotypes in E. coli
journal, January 2006

Flexible single molecule simulation of reaction–diffusion processes
journal, May 2011

Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases
journal, December 2004

URDME: a modular framework for stochastic simulation of reaction-transport processes in complex geometries
journal, January 2012

  • Drawert, Brian; Engblom, Stefan; Hellander, Andreas
  • BMC Systems Biology, Vol. 6, Issue 1
  • DOI: 10.1186/1752-0509-6-76

Convergence of methods for coupling of microscopic and mesoscopic reaction–diffusion simulations
journal, May 2015

Spatial Stochastic Dynamics Enable Robust Cell Polarization
journal, July 2013

STEPS: efficient simulation of stochastic reaction–diffusion models in realistic morphologies
journal, January 2012

  • Hepburn, Iain; Chen, Weiliang; Wils, Stefan
  • BMC Systems Biology, Vol. 6, Issue 1
  • DOI: 10.1186/1752-0509-6-36

Reaction rates for mesoscopic reaction-diffusion kinetics
journal, February 2015

Stochastic simulation of chemical reactions with spatial resolution and single molecule detail
journal, August 2004

Reaction rates for reaction-diffusion kinetics on unstructured meshes
journal, February 2017

  • Hellander, Stefan; Petzold, Linda
  • The Journal of Chemical Physics, Vol. 146, Issue 6
  • DOI: 10.1063/1.4975167

Stochastic reaction-diffusion simulation with MesoRD
journal, April 2005

Reaction rates for a generalized reaction-diffusion master equation
journal, January 2016

The Reaction-Diffusion Master Equation as an Asymptotic Approximation of Diffusion to a Small Target
journal, January 2009

  • Isaacson, Samuel A.
  • SIAM Journal on Applied Mathematics, Vol. 70, Issue 1
  • DOI: 10.1137/070705039

E-CELL: software environment for whole-cell simulation
journal, January 1999

Spatio-temporal correlations can drastically change the response of a MAPK pathway
journal, January 2010

  • Takahashi, K.; Tanase-Nicola, S.; ten Wolde, P. R.
  • Proceedings of the National Academy of Sciences, Vol. 107, Issue 6
  • DOI: 10.1073/pnas.0906885107

The two-regime method for optimizing stochastic reaction–diffusion simulations
journal, September 2011

  • Flegg, Mark B.; Chapman, S. Jonathan; Erban, Radek
  • Journal of The Royal Society Interface, Vol. 9, Issue 70
  • DOI: 10.1098/rsif.2011.0574

Second quantization representation for classical many-particle system
journal, September 1976

Random Walks on Lattices. II
journal, February 1965

  • Montroll, Elliott W.; Weiss, George H.
  • Journal of Mathematical Physics, Vol. 6, Issue 2
  • DOI: 10.1063/1.1704269

ReaDDy - A Software for Particle-Based Reaction-Diffusion Dynamics in Crowded Cellular Environments
journal, September 2013

A diffusional bimolecular propensity function
journal, October 2009

  • Gillespie, Daniel T.
  • The Journal of Chemical Physics, Vol. 131, Issue 16
  • DOI: 10.1063/1.3253798

Simulation of Stochastic Reaction-Diffusion Processes on Unstructured Meshes
journal, January 2009

  • Engblom, Stefan; Ferm, Lars; Hellander, Andreas
  • SIAM Journal on Scientific Computing, Vol. 31, Issue 3
  • DOI: 10.1137/080721388

Exact Solution of the Reversible Diffusion-Influenced Reaction for an Isolated Pair in Three Dimensions
journal, February 1999

Diffusion-controlled reaction rates
journal, August 1949

Spatial Stochastic Dynamics Enable Robust Cell Polarization
text, January 2013

Multiscale reaction-diffusion algorithms: PDE-assisted Brownian dynamics
preprint, January 2012

A Convergent Reaction-Diffusion Master Equation
text, January 2012

Convergence of methods for coupling of microscopic and mesoscopic reaction-diffusion simulations
preprint, January 2013

Reaction rates for a generalized reaction-diffusion master equation
text, January 2015

Hybrid approaches for multiple-species stochastic reaction-diffusion models
text, January 2015

    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    eGFRD in all dimensions
    journal, February 2019

    • Sokolowski, Thomas R.; Paijmans, Joris; Bossen, Laurens
    • The Journal of Chemical Physics, Vol. 150, Issue 5
    • DOI: 10.1063/1.5064867

    Using Spatial Partitioning to Reduce the Bit Error Rate of Diffusion-Based Molecular Communications
    journal, April 2020

    • Riaz, Muhammad Usman; Hamdan, Awan; Chou, Chun Tung
    • IEEE Transactions on Communications, Vol. 68, Issue 4
    • DOI: 10.1109/tcomm.2020.2969861
      Sort by:
      [ × clear filter / sort ]

      Figures / Tables found in this record:

      Algorithm 1 (p. 6)figure
      FIG. 1 (p. 7)figure
      Algorithm 2 (p. 8)figure
      FIG. 2 (p. 8)figure
      Algorithm 3 (p. 9)figure
      Algorithm 4 (p. 10)figure
      FIG. 3 (p. 11)figure
      TABLE I (p. 11)table
      FIG. 4 (p. 12)figure
      FIG. 5 (p. 12)figure
      TABLE II (p. 12)table
      FIG. 6 (p. 13)figure
        [ × clear filter / sort ]
        Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

        Similar Records in DOE PAGES and OSTI.GOV collections: