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

Title: Efficient reactive Brownian dynamics

Abstract

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and dissociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently process reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as reaction-diffusion master equation algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction-limited and diffusion-limited irreversible association in three dimensions and compare tomore » existing theoretical predictions at low and moderate densities. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium and compare to recent theoretical predictions. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. Our studies reinforce the common finding that microscopic mechanisms and correlations matter for diffusion-limited systems, making continuum and even mesoscopic modeling of such systems difficult or impossible. We also find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.« less

Authors:
 [1];  [2];  [3]
+ Show Author Affiliations
  1. New York Univ. (NYU), NY (United States)
  2. New York Univ. (NYU), NY (United States); Univ. of California, Berkeley, CA (United States)
  3. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1435110
Alternate Identifier(s):
OSTI ID: 1417424
Grant/Contract Number:  
AC02-05CH11231; SC0008271
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 148; Journal Issue: 3; Related Information: © 2018 Author(s).; 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

Donev, Aleksandar, Yang, Chiao-Yu, and Kim, Changho. Efficient reactive Brownian dynamics. United States: N. p., 2018. Web. doi:10.1063/1.5009464.
Copy to clipboard
Donev, Aleksandar, Yang, Chiao-Yu, & Kim, Changho. Efficient reactive Brownian dynamics. United States. https://doi.org/10.1063/1.5009464
Copy to clipboard
Donev, Aleksandar, Yang, Chiao-Yu, and Kim, Changho. Sun . "Efficient reactive Brownian dynamics". United States. https://doi.org/10.1063/1.5009464. https://www.osti.gov/servlets/purl/1435110.
Copy to clipboard
@article{osti_1435110,
title = {Efficient reactive Brownian dynamics},
author = {Donev, Aleksandar and Yang, Chiao-Yu and Kim, Changho},
abstractNote = {We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and dissociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently process reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as reaction-diffusion master equation algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction-limited and diffusion-limited irreversible association in three dimensions and compare to existing theoretical predictions at low and moderate densities. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium and compare to recent theoretical predictions. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. Our studies reinforce the common finding that microscopic mechanisms and correlations matter for diffusion-limited systems, making continuum and even mesoscopic modeling of such systems difficult or impossible. We also find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.},
doi = {10.1063/1.5009464},
journal = {Journal of Chemical Physics},
number = 3,
volume = 148,
place = {United States},
year = {Sun Jan 21 00:00:00 EST 2018},
month = {Sun Jan 21 00:00:00 EST 2018}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1063/1.5009464
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 17 works
Citation information provided by
Web of Science

Figures / Tables:

Fig. 1 Fig. 1: Conversion from microscopic to macroscopic reaction rates for (partially) diffusion-limited systems (ƒ = k0/kS ∼ 1/2) at finite packing densities φ. Error bars are smaller or comparable to symbol size. (Left) Correction to the low-density rate k0, given by (1) for SRBD and by (3) for RDME, formore » coagulation, A + A → A and ∅ → A. For SRBD, we use two different time step sizes (see the legend) and extrapolate to the exact result without splitting errors. For the RDME, an exact renormalization calculation gives the leading order non-analytic φ1/2 correction, which matches our numerical results for sufficiently small densities. For SRBD, the result is well fit by the empirical fit k/k0 = 1 + 1.215φ1/2 + 0.312φ (dotted black line). (Right) Deviation k/k0 = nB/nA from the low-density rate k0 given by (1) for SRBD for annihilation, A + B → B and ∅ → A, for several time step sizes (see the legend). For Δt = 1, we show results obtained using a system that is twice larger (i.e., eight times the number of particles) and see no measurable finite-size effects. There is no theory for finite densities but the result is consistent with the empirical fit k/k0 ≈ 1 + 0.458φ1/2.« less
All figures and tables (6 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:

A First-Passage Kinetic Monte Carlo algorithm for complex diffusion–reaction systems
journal, May 2010

  • Donev, Aleksandar; Bulatov, Vasily V.; Oppelstrup, Tomas
  • Journal of Computational Physics, Vol. 229, Issue 9
  • DOI: 10.1016/j.jcp.2009.12.038

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

Do the internal fluctuations blur or enhance axial segmentation?
journal, May 2011

Validity of the Law of Mass Action in Three-Dimensional Coagulation Processes
journal, March 2012

Stochastic operator-splitting method for reaction-diffusion systems
journal, November 2012

  • Choi, TaiJung; Maurya, Mano Ram; Tartakovsky, Daniel M.
  • The Journal of Chemical Physics, Vol. 137, Issue 18
  • DOI: 10.1063/1.4764108

Asymptotic relaxation of reversible bimolecular chemical reactions
journal, November 2002

First-Passage Monte Carlo Algorithm: Diffusion without All the Hops
journal, December 2006

Stochastic Hard-Sphere Dynamics for Hydrodynamics of Nonideal Fluids
journal, August 2008

Analysis of Brownian Dynamics Simulations of Reversible Bimolecular Reactions
journal, January 2011

  • Lipková, Jana; Zygalakis, Konstantinos C.; Chapman, S. Jonathan
  • SIAM Journal on Applied Mathematics, Vol. 71, Issue 3
  • DOI: 10.1137/100794213

Microscopic simulation of chemical bistability in homogeneous systems
journal, November 1996

  • Baras, F.; Mansour, M. Malek; Pearson, J. E.
  • The Journal of Chemical Physics, Vol. 105, Issue 18
  • DOI: 10.1063/1.472679

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

Simulating Biochemical Networks at the Particle Level and in Time and Space: Green’s Function Reaction Dynamics
journal, April 2005

Violation of the mass-action law in dilute chemical systems
journal, November 2013

  • Brogioli, Doriano
  • The Journal of Chemical Physics, Vol. 139, Issue 18
  • DOI: 10.1063/1.4829146

Rapid sampling of stochastic displacements in Brownian dynamics simulations
journal, March 2017

  • Fiore, Andrew M.; Balboa Usabiaga, Florencio; Donev, Aleksandar
  • The Journal of Chemical Physics, Vol. 146, Issue 12
  • DOI: 10.1063/1.4978242

Stochastic theory of diffusion-controlled reaction
journal, September 1976

Kinetics of reversible diffusion influenced reactions: The self-consistent relaxation time approximation
journal, July 2002

  • Gopich, Irina V.; Szabo, Attila
  • The Journal of Chemical Physics, Vol. 117, Issue 2
  • DOI: 10.1063/1.1482701

Stochastic Turing Patterns: Analysis of Compartment-Based Approaches
journal, November 2014

Exact Green's function of the reversible diffusion-influenced reaction for an isolated pair in two dimensions
journal, August 2012

  • Prüstel, Thorsten; Meier-Schellersheim, Martin
  • The Journal of Chemical Physics, Vol. 137, Issue 5
  • DOI: 10.1063/1.4737662

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

A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick’s law
journal, April 2014

  • Donev, Aleksandar; Fai, Thomas G.; Vanden-Eijnden, Eric
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2014, Issue 4
  • DOI: 10.1088/1742-5468/2014/04/p04004

Nanoscale Turing structures
journal, September 2014

  • Dziekan, Piotr; Hansen, J. S.; Nowakowski, Bogdan
  • The Journal of Chemical Physics, Vol. 141, Issue 12
  • DOI: 10.1063/1.4895907

Diffusion-controlled reaction rates
journal, August 1949

Stochastic Simulation of Turing Patterns
journal, April 2008

Detailed Simulations of Cell Biology with Smoldyn 2.1
journal, March 2010

SPOCK: Exact Parallel Kinetic Monte-Carlo on 1.5 Million Tasks
conference, January 2016

  • Oppelstrup, Tomas; Jefferson, David R.; Bulatov, Vasily V.
  • Proceedings of the 2016 annual ACM Conference on SIGSIM Principles of Advanced Discrete Simulation - SIGSIM-PADS '16
  • DOI: 10.1145/2901378.2901403

Long-range and many-body effects in coagulation processes
journal, February 2013

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

Asynchronous Event-Driven Particle Algorithms
journal, April 2009

A discrete stochastic formulation for reversible bimolecular reactions via diffusion encounter
journal, January 2016

Microscopic simulation of chemical oscillations in homogeneous systems
journal, October 1990

  • Baras, F.; Pearson, J. E.; Mansour, M. Malek
  • The Journal of Chemical Physics, Vol. 93, Issue 8
  • DOI: 10.1063/1.459568

Marginally Stable Chemical Systems as Precursors of Life
journal, July 2010

First-passage kinetic Monte Carlo method
journal, December 2009

Reaction-diffusion approach to prevertebrae formation: Effect of a local source of morphogen
journal, September 2013

  • Dziekan, P.; Signon, L.; Nowakowski, B.
  • The Journal of Chemical Physics, Vol. 139, Issue 11
  • DOI: 10.1063/1.4820952

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

Computational methods for diffusion-influenced biochemical reactions
journal, May 2007

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

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

ReaDDyMM: Fast Interacting Particle Reaction-Diffusion Simulations Using Graphical Processing Units
journal, February 2015

  • Biedermann, Johann; Ullrich, Alexander; Schöneberg, Johannes
  • Biophysical Journal, Vol. 108, Issue 3
  • DOI: 10.1016/j.bpj.2014.12.025

An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice
journal, January 2014

  • Bezzola, Andri; Bales, Benjamin B.; Alkire, Richard C.
  • Journal of Computational Physics, Vol. 256
  • DOI: 10.1016/j.jcp.2013.08.053

Long-Time Tails in the Kinetics of Reversible Bimolecular Reactions
journal, January 2001

  • Gopich, Irina V.; Ovchinnikov, Alexander A.; Szabo, Attila
  • Physical Review Letters, Vol. 86, Issue 5
  • DOI: 10.1103/physrevlett.86.922

A First-Passage Kinetic Monte Carlo method for reaction–drift–diffusion processes
journal, February 2014

  • Mauro, Ava J.; Sigurdsson, Jon Karl; Shrake, Justin
  • Journal of Computational Physics, Vol. 259
  • DOI: 10.1016/j.jcp.2013.12.023

Stochastic Simulation of Chemical Kinetics
journal, May 2007

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

MesoRD 1.0: Stochastic reaction-diffusion simulations in the microscopic limit
journal, October 2012

Marginal stability in chemical systems and its relevance in the origin of life
journal, September 2011

Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach
journal, March 2017

  • Kim, Changho; Nonaka, Andy; Bell, John B.
  • The Journal of Chemical Physics, Vol. 146, Issue 12
  • DOI: 10.1063/1.4978775

The multinomial simulation algorithm for discrete stochastic simulation of reaction-diffusion systems
journal, March 2009

  • Lampoudi, Sotiria; Gillespie, Dan T.; Petzold, Linda R.
  • The Journal of Chemical Physics, Vol. 130, Issue 9
  • DOI: 10.1063/1.3074302

Stochastic reaction-diffusion simulation with MesoRD
journal, April 2005

Reversible diffusion-limited reactions: “Chemical Equilibrium” state and the Law of Mass Action revisited
journal, January 2005

Scaling Approach for the Kinetics of Recombination Processes
journal, March 1984

Diffusion with back reaction
journal, September 1984

  • Agmon, Noam
  • The Journal of Chemical Physics, Vol. 81, Issue 6
  • DOI: 10.1063/1.447954

Multinomial diffusion equation
journal, June 2011

Large-scale simulations of diffusion-limited n -species annihilation
journal, April 2003

Adaptive two-regime method: Application to front propagation
journal, March 2014

  • Robinson, Martin; Flegg, Mark; Erban, Radek
  • The Journal of Chemical Physics, Vol. 140, Issue 12
  • DOI: 10.1063/1.4868652

A master equation description of local fluctuations
journal, September 1975

  • Malek-Mansour, M.; Nicolis, G.
  • Journal of Statistical Physics, Vol. 13, Issue 3
  • DOI: 10.1007/bf01012838

Reactive boundary conditions for stochastic simulations of reaction–diffusion processes
journal, February 2007

Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids
book, January 2009

  • Gompper, G.; Ihle, T.; Kroll, D. M.
  • Advanced Computer Simulation Approaches for Soft Matter Sciences III
  • DOI: 10.1007/978-3-540-87706-6_1
    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    Diffusion-influenced reaction rates in the presence of pair interactions
    text, January 2019

    Reactive SINDy: Discovering governing reactions from concentration data
    journal, January 2019

    • Hoffmann, Moritz; Fröhner, Christoph; Noé, Frank
    • The Journal of Chemical Physics, Vol. 150, Issue 2
    • DOI: 10.1063/1.5066099

    MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations
    journal, June 2018

    • Dibak, Manuel; del Razo, Mauricio J.; De Sancho, David
    • The Journal of Chemical Physics, Vol. 148, Issue 21
    • DOI: 10.1063/1.5020294

    ReaDDy 2: Fast and flexible software framework for interacting-particle reaction dynamics
    journal, February 2019

    ReaDDy 2: Fast and flexible software framework for interacting-particle reaction dynamics
    journal, February 2019

    Diffusion-influenced reaction rates in the presence of pair interactions
    journal, October 2019

    • Dibak, Manuel; Fröhner, Christoph; Noé, Frank
    • The Journal of Chemical Physics, Vol. 151, Issue 16
    • DOI: 10.1063/1.5124728

    Fluctuating hydrodynamics of reactive liquid mixtures
    journal, August 2018

    • Kim, Changho; Nonaka, Andy; Bell, John B.
    • The Journal of Chemical Physics, Vol. 149, Issue 8
    • DOI: 10.1063/1.5043428

    Fluctuating Hydrodynamics of Reactive Liquid Mixtures
    text, January 2018

    Reaction-diffusion kinetics on lattice at the microscopic scale
    journal, September 2018

      Sort by:
      [ × clear filter / sort ]

      Figures / Tables found in this record:

      Fig. 1 (p. 11)figure
      Fig. 2 (p. 12)figure
      Fig. 3 (p. 13)figure
      Fig. 4 (p. 14)figure
      Fig. 5 (p. 15)figure
      Fig. 6 (p. 15)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: