skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Reaction rates for mesoscopic reaction-diffusion kinetics

Journal Article · · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
 [1];  [2];  [1]
  1. Univ. of California, Santa Barbara, CA (United States)
  2. Uppsala Univ., Uppsala (Sweden)

The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. Finally, we show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.

Research Organization:
Univ. of California, Santa Barbara, CA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
SC0008975
OSTI ID:
1343614
Alternate ID(s):
OSTI ID: 1180098
Journal Information:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, Vol. 91, Issue 2; ISSN 1539-3755
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 31 works
Citation information provided by
Web of Science

References (38)

Coupled Mesoscopic and Microscopic Simulation of Stochastic Reaction-Diffusion Processes in Mixed Dimensions journal January 2012
A convergent reaction-diffusion master equation journal August 2013
Stochastic reaction-diffusion kinetics in the microscopic limit journal November 2010
Spatial stochastic modelling of the Hes1 gene regulatory network: intrinsic noise can explain heterogeneity in embryonic stem cell differentiation journal March 2013
A Comparison of Bimolecular Reaction Models for Stochastic Reaction–Diffusion Systems journal April 2013
Reaction-diffusion master equation in the microscopic limit journal April 2012
Stochastic modelling of reaction–diffusion processes: algorithms for bimolecular reactions journal August 2009
Correlations in stochastic theories of chemical reactions journal April 1976
Green’s-function reaction dynamics: A particle-based approach for simulating biochemical networks in time and space journal December 2005
A rigorous derivation of the chemical master equation journal September 1992
An adaptive algorithm for simulation of stochastic reaction–diffusion processes journal January 2010
Noise-Induced Min Phenotypes in E. coli journal January 2006
The Role of Dimerisation and Nuclear Transport in the Hes1 Gene Regulatory Network journal May 2013
Flexible single molecule simulation of reaction–diffusion processes journal May 2011
Fractional diffusion-reaction stochastic simulations journal March 2013
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
Incorporating Active Transport of Cellular Cargo in Stochastic Mesoscopic Models of Living Cells journal January 2010
Incorporating Diffusion in Complex Geometries into Stochastic Chemical Kinetics Simulations journal January 2006
Validity conditions for stochastic chemical kinetics in diffusion-limited systems journal February 2014
Spatial Stochastic Dynamics Enable Robust Cell Polarization journal July 2013
STEPS: efficient simulation of stochastic reaction–diffusion models in realistic morphologies journal January 2012
Relationship between the reaction–diffusion master equation and particle tracking models journal January 2008
Stochastic simulation of chemical reactions with spatial resolution and single molecule detail journal August 2004
Accelerated stochastic and hybrid methods for spatial simulations of reaction–diffusion systems journal January 2008
The multinomial simulation algorithm for discrete stochastic simulation of reaction-diffusion systems journal March 2009
Perspective: Stochastic algorithms for chemical kinetics journal May 2013
Stochastic reaction-diffusion simulation with MesoRD journal April 2005
The Reaction-Diffusion Master Equation as an Asymptotic Approximation of Diffusion to a Small Target journal January 2009
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
A general method for numerically simulating the stochastic time evolution of coupled chemical reactions journal December 1976
A diffusional bimolecular propensity function journal October 2009
Simulation of Stochastic Reaction-Diffusion Processes on Unstructured Meshes journal January 2009
Binomial tau-leap spatial stochastic simulation algorithm for applications in chemical kinetics journal September 2007
Pattern Formation inside Bacteria: Fluctuations due to the Low Copy Number of Proteins journal March 2003
Diffusion-controlled reaction rates journal August 1949
Detailed Simulations of Cell Biology with Smoldyn 2.1 journal March 2010

Cited By (8)

Fluctuating hydrodynamics of multi-species reactive mixtures journal June 2015
An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems journal March 2016
A framework for discrete stochastic simulation on 3D moving boundary domains journal November 2016
Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach journal March 2017
Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems journal September 2017
Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning journal December 2017
Stochastic self-tuning hybrid algorithm for reaction-diffusion systems journal December 2019
Reaction-diffusion kinetics on lattice at the microscopic scale journal September 2018

Similar Records

Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning
Journal Article · Fri Dec 15 00:00:00 EST 2017 · Journal of Chemical Physics · OSTI ID:1343614

Reaction rates for a generalized reaction-diffusion master equation
Journal Article · Tue Jan 19 00:00:00 EST 2016 · Physical Review E · OSTI ID:1343614

Reaction rates for reaction-diffusion kinetics on unstructured meshes
Journal Article · Wed Feb 08 00:00:00 EST 2017 · Journal of Chemical Physics · OSTI ID:1343614