Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning

Hellander, Stefan; Hellander, Andreas; Petzold, Linda

doi:10.1063/1.5002773

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

Journal Article · Fri Dec 15 00:00:00 EST 2017 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.5002773· OSTI ID:1512930

Hellander, Stefan ^[1]; Hellander, Andreas ^[1];

^[2]

Uppsala Univ. (Sweden)
Univ. of California, Santa Barbara, CA (United States)

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.

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Research Organization:: Univ. of California, Santa Barbara, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0008975

OSTI ID:: 1512930

Alternate ID(s):: OSTI ID: 1413550

Journal Information:: Journal of Chemical Physics, Vol. 147, Issue 23; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 6 works

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References (51)

Coupled Mesoscopic and Microscopic Simulation of Stochastic Reaction-Diffusion Processes in Mixed Dimensions Hellander, Andreas; Hellander, Stefan; Lötstedt, Per Multiscale Modeling & Simulation, Vol. 10, Issue 2 https://doi.org/10.1137/110832148	journal	January 2012
Random Walks on Lattices. III. Calculation of First‐Passage Times with Application to Exciton Trapping on Photosynthetic Units Montroll, Elliott W. Journal of Mathematical Physics, Vol. 10, Issue 4 https://doi.org/10.1063/1.1664902	journal	April 1969
A general computational framework for modeling cellular structure and function Schaff, J.; Fink, C. C.; Slepchenko, B. Biophysical Journal, Vol. 73, Issue 3 https://doi.org/10.1016/s0006-3495(97)78146-3	journal	September 1997
A convergent reaction-diffusion master equation Isaacson, Samuel A. The Journal of Chemical Physics, Vol. 139, Issue 5 https://doi.org/10.1063/1.4816377	journal	August 2013
Stochastic reaction-diffusion kinetics in the microscopic limit Fange, D.; Berg, O. G.; Sjoberg, P. Proceedings of the National Academy of Sciences, Vol. 107, Issue 46 https://doi.org/10.1073/pnas.1006565107	journal	November 2010
Multiscale Reaction-Diffusion Algorithms: PDE-Assisted Brownian Dynamics Franz, Benjamin; Flegg, Mark B.; Chapman, S. Jonathan SIAM Journal on Applied Mathematics, Vol. 73, Issue 3 https://doi.org/10.1137/120882469	journal	January 2013
A hybrid continuous-discrete method for stochastic reaction–diffusion processes Lo, Wing-Cheong; Zheng, Likun; Nie, Qing Royal Society Open Science, Vol. 3, Issue 9 https://doi.org/10.1098/rsos.160485	journal	September 2016
Multiscale reaction-diffusion simulations with Smoldyn: Fig. 1. Robinson, Martin; Andrews, Steven S.; Erban, Radek Bioinformatics, Vol. 31, Issue 14 https://doi.org/10.1093/bioinformatics/btv149	journal	March 2015
Stochastic Simulation Service: Bridging the Gap between the Computational Expert and the Biologist Drawert, Brian; Hellander, Andreas; Bales, Ben PLOS Computational Biology, Vol. 12, Issue 12 https://doi.org/10.1371/journal.pcbi.1005220	journal	December 2016
Hybrid approaches for multiple-species stochastic reaction–diffusion models Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas Journal of Computational Physics, Vol. 299 https://doi.org/10.1016/j.jcp.2015.07.002	journal	October 2015
Stochastic modelling of reaction–diffusion processes: algorithms for bimolecular reactions Erban, Radek; Chapman, S. Jonathan Physical Biology, Vol. 6, Issue 4 https://doi.org/10.1088/1478-3975/6/4/046001	journal	August 2009
MOLNs: A Cloud Platform for Interactive, Reproducible, and Scalable Spatial Stochastic Computational Experiments in Systems Biology Using PyURDME Drawert, Brian; Trogdon, Michael; Toor, Salman SIAM Journal on Scientific Computing, Vol. 38, Issue 3 https://doi.org/10.1137/15M1014784	journal	January 2016
Lost in presumption: stochastic reactions in spatial models Mahmutovic, Anel; Fange, David; Berg, Otto G. Nature Methods, Vol. 9, Issue 12 https://doi.org/10.1038/nmeth.2253	journal	December 2012
Fast Monte Carlo Simulation Methods for Biological Reaction-Diffusion Systems in Solution and on Surfaces Kerr, Rex A.; Bartol, Thomas M.; Kaminsky, Boris SIAM Journal on Scientific Computing, Vol. 30, Issue 6 https://doi.org/10.1137/070692017	journal	January 2008
Reaction-diffusion master equation in the microscopic limit Hellander, Stefan; Hellander, Andreas; Petzold, Linda Physical Review E, Vol. 85, Issue 4 https://doi.org/10.1103/physreve.85.042901	journal	April 2012
Green’s-function reaction dynamics: A particle-based approach for simulating biochemical networks in time and space van Zon, Jeroen S.; ten Wolde, Pieter Rein The Journal of Chemical Physics, Vol. 123, Issue 23 https://doi.org/10.1063/1.2137716	journal	December 2005
An adaptive algorithm for simulation of stochastic reaction–diffusion processes Ferm, Lars; Hellander, Andreas; Lötstedt, Per Journal of Computational Physics, Vol. 229, Issue 2 https://doi.org/10.1016/j.jcp.2009.09.030	journal	January 2010
The pseudo-compartment method for coupling partial differential equation and compartment-based models of diffusion Yates, Christian A.; Flegg, Mark B. Journal of The Royal Society Interface, Vol. 12, Issue 106 https://doi.org/10.1098/rsif.2015.0141	journal	May 2015
The Role of Type 4 Phosphodiesterases in Generating Microdomains of cAMP: Large Scale Stochastic Simulations Oliveira, Rodrigo F.; Terrin, Anna; Di Benedetto, Giulietta PLoS ONE, Vol. 5, Issue 7 https://doi.org/10.1371/journal.pone.0011725	journal	July 2010
The Role of Dimerisation and Nuclear Transport in the Hes1 Gene Regulatory Network Sturrock, Marc; Hellander, Andreas; Aldakheel, Sahar Bulletin of Mathematical Biology, Vol. 76, Issue 4 https://doi.org/10.1007/s11538-013-9842-5	journal	May 2013
Noise-Induced Min Phenotypes in E. coli Fange, David; Elf, Johan PLoS Computational Biology, Vol. 2, Issue 6 https://doi.org/10.1371/journal.pcbi.0020080	journal	January 2006
Flexible single molecule simulation of reaction–diffusion processes Hellander, Stefan; Lötstedt, Per Journal of Computational Physics, Vol. 230, Issue 10 https://doi.org/10.1016/j.jcp.2011.02.020	journal	May 2011
Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases Elf, J.; Ehrenberg, M. Systems Biology, Vol. 1, Issue 2 https://doi.org/10.1049/sb:20045021	journal	December 2004
URDME: a modular framework for stochastic simulation of reaction-transport processes in complex geometries Drawert, Brian; Engblom, Stefan; Hellander, Andreas BMC Systems Biology, Vol. 6, Issue 1 https://doi.org/10.1186/1752-0509-6-76	journal	January 2012
Convergence of methods for coupling of microscopic and mesoscopic reaction–diffusion simulations Flegg, Mark B.; Hellander, Stefan; Erban, Radek Journal of Computational Physics, Vol. 289 https://doi.org/10.1016/j.jcp.2015.01.030	journal	May 2015
Spatial Stochastic Dynamics Enable Robust Cell Polarization Lawson, Michael J.; Drawert, Brian; Khammash, Mustafa PLoS Computational Biology, Vol. 9, Issue 7 https://doi.org/10.1371/journal.pcbi.1003139	journal	July 2013
STEPS: efficient simulation of stochastic reaction–diffusion models in realistic morphologies Hepburn, Iain; Chen, Weiliang; Wils, Stefan BMC Systems Biology, Vol. 6, Issue 1 https://doi.org/10.1186/1752-0509-6-36	journal	January 2012
Reaction rates for mesoscopic reaction-diffusion kinetics Hellander, Stefan; Hellander, Andreas; Petzold, Linda Physical Review E, Vol. 91, Issue 2 https://doi.org/10.1103/physreve.91.023312	journal	February 2015
Stochastic simulation of chemical reactions with spatial resolution and single molecule detail Andrews, Steven S.; Bray, Dennis Physical Biology, Vol. 1, Issue 3 https://doi.org/10.1088/1478-3967/1/3/001	journal	August 2004
Reaction rates for reaction-diffusion kinetics on unstructured meshes Hellander, Stefan; Petzold, Linda The Journal of Chemical Physics, Vol. 146, Issue 6 https://doi.org/10.1063/1.4975167	journal	February 2017
Stochastic reaction-diffusion simulation with MesoRD Hattne, J.; Fange, D.; Elf, J. Bioinformatics, Vol. 21, Issue 12 https://doi.org/10.1093/bioinformatics/bti431	journal	April 2005
Reaction rates for a generalized reaction-diffusion master equation Hellander, Stefan; Petzold, Linda Physical Review E, Vol. 93, Issue 1 https://doi.org/10.1103/physreve.93.013307	journal	January 2016
The Reaction-Diffusion Master Equation as an Asymptotic Approximation of Diffusion to a Small Target Isaacson, Samuel A. SIAM Journal on Applied Mathematics, Vol. 70, Issue 1 https://doi.org/10.1137/070705039	journal	January 2009
E-CELL: software environment for whole-cell simulation Tomita, M.; Hashimoto, K.; Takahashi, K. Bioinformatics, Vol. 15, Issue 1 https://doi.org/10.1093/bioinformatics/15.1.72	journal	January 1999
Spatio-temporal correlations can drastically change the response of a MAPK pathway Takahashi, K.; Tanase-Nicola, S.; ten Wolde, P. R. Proceedings of the National Academy of Sciences, Vol. 107, Issue 6 https://doi.org/10.1073/pnas.0906885107	journal	January 2010
The two-regime method for optimizing stochastic reaction–diffusion simulations Flegg, Mark B.; Chapman, S. Jonathan; Erban, Radek Journal of The Royal Society Interface, Vol. 9, Issue 70 https://doi.org/10.1098/rsif.2011.0574	journal	September 2011
Second quantization representation for classical many-particle system Doi, M. Journal of Physics A: Mathematical and General, Vol. 9, Issue 9 https://doi.org/10.1088/0305-4470/9/9/008	journal	September 1976
Random Walks on Lattices. II Montroll, Elliott W.; Weiss, George H. Journal of Mathematical Physics, Vol. 6, Issue 2 https://doi.org/10.1063/1.1704269	journal	February 1965
ReaDDy - A Software for Particle-Based Reaction-Diffusion Dynamics in Crowded Cellular Environments Schöneberg, Johannes; Noé, Frank PLoS ONE, Vol. 8, Issue 9 https://doi.org/10.1371/journal.pone.0074261	journal	September 2013
A diffusional bimolecular propensity function Gillespie, Daniel T. The Journal of Chemical Physics, Vol. 131, Issue 16 https://doi.org/10.1063/1.3253798	journal	October 2009
Simulation of Stochastic Reaction-Diffusion Processes on Unstructured Meshes Engblom, Stefan; Ferm, Lars; Hellander, Andreas SIAM Journal on Scientific Computing, Vol. 31, Issue 3 https://doi.org/10.1137/080721388	journal	January 2009
Exact Solution of the Reversible Diffusion-Influenced Reaction for an Isolated Pair in Three Dimensions Kim, Hyojoon; Shin, Kook Joe Physical Review Letters, Vol. 82, Issue 7 https://doi.org/10.1103/physrevlett.82.1578	journal	February 1999
Diffusion-controlled reaction rates Collins, Frank C.; Kimball, George E. Journal of Colloid Science, Vol. 4, Issue 4 https://doi.org/10.1016/0095-8522(49)90023-9	journal	August 1949
Spatial Stochastic Dynamics Enable Robust Cell Polarization Lawson, Michael J.; Drawert, Brian; Khammash, Mustafa Hani ETH Zurich https://doi.org/10.3929/ethz-b-000071221	text	January 2013
Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions Erban, Radek; Chapman, S. Jonathan arXiv https://doi.org/10.48550/arxiv.0903.1298	text	January 2009
Multiscale reaction-diffusion algorithms: PDE-assisted Brownian dynamics Franz, Benjamin; Flegg, Mark B.; Chapman, S. Jonathan arXiv https://doi.org/10.48550/arxiv.1206.5860	preprint	January 2012
A Convergent Reaction-Diffusion Master Equation Isaacson, Samuel A. arXiv https://doi.org/10.48550/arxiv.1211.6772	text	January 2012
Convergence of methods for coupling of microscopic and mesoscopic reaction-diffusion simulations Flegg, Mark B.; Hellander, Stefan; Erban, Radek arXiv https://doi.org/10.48550/arxiv.1304.7393	preprint	January 2013
Reaction rates for a generalized reaction-diffusion master equation Hellander, Stefan; Petzold, Linda arXiv https://doi.org/10.48550/arxiv.1503.07279	text	January 2015
Hybrid approaches for multiple-species stochastic reaction-diffusion models Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas arXiv https://doi.org/10.48550/arxiv.1507.07992	text	January 2015
MOLNs: A cloud platform for interactive, reproducible and scalable spatial stochastic computational experiments in systems biology using PyURDME Drawert, Brian; Trogdon, Michael; Toor, Salman arXiv https://doi.org/10.48550/arxiv.1508.03604	preprint	January 2015

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