S-Leaping: An Adaptive, Accelerated Stochastic Simulation Algorithm, Bridging τ-Leaping and R-Leaping

We propose the S -leaping algorithm for the acceleration of Gillespie’s stochastic simulation algorithm that combines the advantages of the two main accelerated methods; the τ -leaping and R -leaping algorithms. These algorithms are known to be efficient under different conditions; the τ -leaping is...

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Vydáno v:	Bulletin of mathematical biology Ročník 81; číslo 8; s. 3074 - 3096
Hlavní autoři:	Lipková, Jana, Arampatzis, Georgios, Chatelain, Philippe, Menze, Bjoern, Koumoutsakos, Petros
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.08.2019 Springer Nature B.V
Témata:	Acceleration Adaptive algorithms Algorithms Bacillus subtilis - genetics Bacillus subtilis - metabolism Biochemical Phenomena Cell Biology Computer Simulation Dimerization Escherichia coli - genetics Escherichia coli - metabolism Escherichia coli Proteins - genetics Escherichia coli Proteins - metabolism Kinetics Lac Operon Life Sciences Markov Chains Mathematical and Computational Biology Mathematical Concepts Mathematics Mathematics and Statistics Models, Biological Monosaccharide Transport Proteins - genetics Monosaccharide Transport Proteins - metabolism Sampling Special Issue: Gillespie and His Algorithms Stochastic Processes Symporters - genetics Symporters - metabolism Systems Biology Stochastic simulation algorithms Stiff systems Accelerated simulation
ISSN:	0092-8240, 1522-9602, 1522-9602
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Abstract	We propose the S -leaping algorithm for the acceleration of Gillespie’s stochastic simulation algorithm that combines the advantages of the two main accelerated methods; the τ -leaping and R -leaping algorithms. These algorithms are known to be efficient under different conditions; the τ -leaping is efficient for non-stiff systems or systems with partial equilibrium, while the R -leaping performs better in stiff system thanks to an efficient sampling procedure. However, even a small change in a system’s set up can critically affect the nature of the simulated system and thus reduce the efficiency of an accelerated algorithm. The proposed algorithm combines the efficient time step selection from the τ -leaping with the effective sampling procedure from the R -leaping algorithm. The S -leaping is shown to maintain its efficiency under different conditions and in the case of large and stiff systems or systems with fast dynamics, the S -leaping outperforms both methods. We demonstrate the performance and the accuracy of the S -leaping in comparison with the τ -leaping and R -leaping on a number of benchmark systems involving biological reaction networks.
AbstractList	We propose the S-leaping algorithm for the acceleration of Gillespie's stochastic simulation algorithm that combines the advantages of the two main accelerated methods; the -leaping and R-leaping algorithms. These algorithms are known to be efficient under different conditions; the -leaping is efficient for non-stiff systems or systems with partial equilibrium, while the R-leaping performs better in stiff system thanks to an efficient sampling procedure. However, even a small change in a system's set up can critically affect the nature of the simulated system and thus reduce the efficiency of an accelerated algorithm. The proposed algorithm combines the efficient time step selection from the -leaping with the effective sampling procedure from the R-leaping algorithm. The S-leaping is shown to maintain its efficiency under different conditions and in the case of large and stiff systems or systems with fast dynamics, the S-leaping outperforms both methods. We demonstrate the performance and the accuracy of the S-leaping in comparison with the -leaping and R-leaping on a number of benchmark systems involving biological reaction networks. We propose the S-leaping algorithm for the acceleration of Gillespie’s stochastic simulation algorithm that combines the advantages of the two main accelerated methods; the τ-leaping and R-leaping algorithms. These algorithms are known to be efficient under different conditions; the τ-leaping is efficient for non-stiff systems or systems with partial equilibrium, while the R-leaping performs better in stiff system thanks to an efficient sampling procedure. However, even a small change in a system’s set up can critically affect the nature of the simulated system and thus reduce the efficiency of an accelerated algorithm. The proposed algorithm combines the efficient time step selection from the τ-leaping with the effective sampling procedure from the R-leaping algorithm. The S-leaping is shown to maintain its efficiency under different conditions and in the case of large and stiff systems or systems with fast dynamics, the S-leaping outperforms both methods. We demonstrate the performance and the accuracy of the S-leaping in comparison with the τ-leaping and R-leaping on a number of benchmark systems involving biological reaction networks. We propose the S-leaping algorithm for the acceleration of Gillespie's stochastic simulation algorithm that combines the advantages of the two main accelerated methods; the τ -leaping and R-leaping algorithms. These algorithms are known to be efficient under different conditions; the τ -leaping is efficient for non-stiff systems or systems with partial equilibrium, while the R-leaping performs better in stiff system thanks to an efficient sampling procedure. However, even a small change in a system's set up can critically affect the nature of the simulated system and thus reduce the efficiency of an accelerated algorithm. The proposed algorithm combines the efficient time step selection from the τ -leaping with the effective sampling procedure from the R-leaping algorithm. The S-leaping is shown to maintain its efficiency under different conditions and in the case of large and stiff systems or systems with fast dynamics, the S-leaping outperforms both methods. We demonstrate the performance and the accuracy of the S-leaping in comparison with the τ -leaping and R-leaping on a number of benchmark systems involving biological reaction networks.We propose the S-leaping algorithm for the acceleration of Gillespie's stochastic simulation algorithm that combines the advantages of the two main accelerated methods; the τ -leaping and R-leaping algorithms. These algorithms are known to be efficient under different conditions; the τ -leaping is efficient for non-stiff systems or systems with partial equilibrium, while the R-leaping performs better in stiff system thanks to an efficient sampling procedure. However, even a small change in a system's set up can critically affect the nature of the simulated system and thus reduce the efficiency of an accelerated algorithm. The proposed algorithm combines the efficient time step selection from the τ -leaping with the effective sampling procedure from the R-leaping algorithm. The S-leaping is shown to maintain its efficiency under different conditions and in the case of large and stiff systems or systems with fast dynamics, the S-leaping outperforms both methods. We demonstrate the performance and the accuracy of the S-leaping in comparison with the τ -leaping and R-leaping on a number of benchmark systems involving biological reaction networks. We propose the S -leaping algorithm for the acceleration of Gillespie’s stochastic simulation algorithm that combines the advantages of the two main accelerated methods; the τ -leaping and R -leaping algorithms. These algorithms are known to be efficient under different conditions; the τ -leaping is efficient for non-stiff systems or systems with partial equilibrium, while the R -leaping performs better in stiff system thanks to an efficient sampling procedure. However, even a small change in a system’s set up can critically affect the nature of the simulated system and thus reduce the efficiency of an accelerated algorithm. The proposed algorithm combines the efficient time step selection from the τ -leaping with the effective sampling procedure from the R -leaping algorithm. The S -leaping is shown to maintain its efficiency under different conditions and in the case of large and stiff systems or systems with fast dynamics, the S -leaping outperforms both methods. We demonstrate the performance and the accuracy of the S -leaping in comparison with the τ -leaping and R -leaping on a number of benchmark systems involving biological reaction networks.
Author	Koumoutsakos, Petros Menze, Bjoern Lipková, Jana Arampatzis, Georgios Chatelain, Philippe
Author_xml	– sequence: 1 givenname: Jana surname: Lipková fullname: Lipková, Jana organization: Department of Informatics, Technical University of Munich – sequence: 2 givenname: Georgios surname: Arampatzis fullname: Arampatzis, Georgios organization: Computational Science and Engineering Laboratory, ETH Zurich – sequence: 3 givenname: Philippe surname: Chatelain fullname: Chatelain, Philippe organization: Institute of Mechanics, Materials and Civil Engineering, Université catholique de Louvain – sequence: 4 givenname: Bjoern surname: Menze fullname: Menze, Bjoern organization: Department of Informatics, Technical University of Munich – sequence: 5 givenname: Petros orcidid: 0000-0001-8337-2122 surname: Koumoutsakos fullname: Koumoutsakos, Petros email: petros@ethz.ch organization: Computational Science and Engineering Laboratory, ETH Zurich
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References	CaoYGillespieDTPetzoldLRAvoiding negative populations in explicit poisson tau-leapingJ Chem Phys2005123505410410.1063/1.1992473 GillespieDTExact stochastic simulation of coupled chemical reactionsJ Phys Chem197781252340236110.1021/j100540a008 CaoYGillespieDTPetzoldLRAdaptive explicit–implicit tau-leaping method with automatic tau selectionJ Chem Phys20071262222410110.1063/1.2745299 KoumoutsakosPFeigelmanJMultiscale stochastic simulations of chemical reactions with regulated scale separationJ Comput Phys2013244290297306422010.1016/j.jcp.2012.11.0301377.80003 AndersonDFKurtzTGContinuous time Markov chain models for chemical reaction networks2011New YorkSpringer342 MaamarHRajADubnauDNoise in gene expression determines cell fate in Bacillus subtilisScience2007317583752652910.1126/science.1140818 GillespieDTApproximate accelerated stochastic simulation of chemically reacting systemsJ Chem Phys2001115171610.1063/1.1378322 Erban R, Chapman J, Maini P (2007) A practical guide to stochastic simulations of reaction-diffusion processes. arXiv:0704.1908 MjolsnessEOrendorffDChatelainPKoumoutsakosPAn exact accelerated stochastic simulation algorithmJ Chem Phys200913014411010.1063/1.3078490 LipkovaJZygalakisKCChapmanSJErbanRAnalysis of Brownian dynamics simulations of reversible bimolecular reactionsSIAM J Appl Math2011713714730279608610.1137/1007942131229.80023 GillespieDTPetzoldLRImproved leap-size selection for accelerated stochastic simulationJ Chem Phys2003119822910.1063/1.1613254 BayatiBOwhadiHKoumoutsakosPA cutoff phenomenon in accelerated stochastic simulations of chemical kinetics via flow averaging (FLAVOR-SSA)J Chem Phys2010133241710.1063/1.3518419 KierzekAMSTOCKS: STOChastic Kinetic Simulations of biochemical systems with Gillespie algorithmBioinformatics (Oxford, England)200218347048110.1093/bioinformatics/18.3.470 CaoYPetzoldLRAccuracy limitations and the measurement of errors in the stochastic simulation of chemically reacting systemsJ Comput Phys20062121624218360310.1016/j.jcp.2005.06.0121079.80003 Sandmann W (2009) Exposition and streamlined formulation of adaptive explicitimplicit tau-leaping. Technical report, Citeseer ErbanRChapmanSJStochastic modelling of reaction–diffusion processes: algorithms for bimolecular reactionsPhys Biology20096404600110.1088/1478-3975/6/4/046001 CaoYGillespieDPetzoldLMultiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systemsJ Comput Phys20052062395411214332410.1016/j.jcp.2004.12.0141088.80004 RathinamMPetzoldLRCaoYGillespieDTStiffness in stochastic chemically reacting systems: the implicit tau-leaping methodJ Chem Phys20031191278410.1063/1.1627296 SüelGMGarcia-OjalvoJLibermanLMElowitzMBAn excitable gene regulatory circuit induces transient cellular differentiationNature2006440708354555010.1038/nature04588 TianTBurrageKBinomial leap methods for simulating stochastic chemical kineticsJ Chem Phys20041211035610.1063/1.1810475 AugerAChatelainPKoumoutsakosPR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R$$\end{document}-leaping: accelerating the stochastic simulation algorithm by reaction leapsJ Chem Phys2006125808410310.1063/1.2218339 BayatiBChatelainPKoumoutsakosPAdaptive mesh refinement for stochastic reaction–diffusion processesJ Comput Phys201123011326273427910.1016/j.jcp.2010.08.0351205.65020 ChattopadhyayIKuchinaASüelGMLipsonHInverse gillespie for inferring stochastic reaction mechanisms from intermittent samplesProc Natl Acad Sci2013110321299012995310435710.1073/pnas.12145591101292.62142 CaoYGillespieDPetzoldLEfficient step size selection for the tau-leaping simulation methodJ Chem Phys2006124404410910.1063/1.2159468 GillespieDTA general method for numerically simulating the stochastic time evolution of coupled chemical reactionsJ Comput Phys197622440343450337010.1016/0021-9991(76)90041-3
References_xml	– reference: TianTBurrageKBinomial leap methods for simulating stochastic chemical kineticsJ Chem Phys20041211035610.1063/1.1810475 – reference: AndersonDFKurtzTGContinuous time Markov chain models for chemical reaction networks2011New YorkSpringer342 – reference: GillespieDTExact stochastic simulation of coupled chemical reactionsJ Phys Chem197781252340236110.1021/j100540a008 – reference: KierzekAMSTOCKS: STOChastic Kinetic Simulations of biochemical systems with Gillespie algorithmBioinformatics (Oxford, England)200218347048110.1093/bioinformatics/18.3.470 – reference: BayatiBOwhadiHKoumoutsakosPA cutoff phenomenon in accelerated stochastic simulations of chemical kinetics via flow averaging (FLAVOR-SSA)J Chem Phys2010133241710.1063/1.3518419 – reference: ErbanRChapmanSJStochastic modelling of reaction–diffusion processes: algorithms for bimolecular reactionsPhys Biology20096404600110.1088/1478-3975/6/4/046001 – reference: CaoYPetzoldLRAccuracy limitations and the measurement of errors in the stochastic simulation of chemically reacting systemsJ Comput Phys20062121624218360310.1016/j.jcp.2005.06.0121079.80003 – reference: MaamarHRajADubnauDNoise in gene expression determines cell fate in Bacillus subtilisScience2007317583752652910.1126/science.1140818 – reference: LipkovaJZygalakisKCChapmanSJErbanRAnalysis of Brownian dynamics simulations of reversible bimolecular reactionsSIAM J Appl Math2011713714730279608610.1137/1007942131229.80023 – reference: RathinamMPetzoldLRCaoYGillespieDTStiffness in stochastic chemically reacting systems: the implicit tau-leaping methodJ Chem Phys20031191278410.1063/1.1627296 – reference: Erban R, Chapman J, Maini P (2007) A practical guide to stochastic simulations of reaction-diffusion processes. arXiv:0704.1908 – reference: Sandmann W (2009) Exposition and streamlined formulation of adaptive explicitimplicit tau-leaping. Technical report, Citeseer – reference: BayatiBChatelainPKoumoutsakosPAdaptive mesh refinement for stochastic reaction–diffusion processesJ Comput Phys201123011326273427910.1016/j.jcp.2010.08.0351205.65020 – reference: AugerAChatelainPKoumoutsakosPR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R$$\end{document}-leaping: accelerating the stochastic simulation algorithm by reaction leapsJ Chem Phys2006125808410310.1063/1.2218339 – reference: CaoYGillespieDTPetzoldLRAdaptive explicit–implicit tau-leaping method with automatic tau selectionJ Chem Phys20071262222410110.1063/1.2745299 – reference: SüelGMGarcia-OjalvoJLibermanLMElowitzMBAn excitable gene regulatory circuit induces transient cellular differentiationNature2006440708354555010.1038/nature04588 – reference: ChattopadhyayIKuchinaASüelGMLipsonHInverse gillespie for inferring stochastic reaction mechanisms from intermittent samplesProc Natl Acad Sci2013110321299012995310435710.1073/pnas.12145591101292.62142 – reference: KoumoutsakosPFeigelmanJMultiscale stochastic simulations of chemical reactions with regulated scale separationJ Comput Phys2013244290297306422010.1016/j.jcp.2012.11.0301377.80003 – reference: MjolsnessEOrendorffDChatelainPKoumoutsakosPAn exact accelerated stochastic simulation algorithmJ Chem Phys200913014411010.1063/1.3078490 – reference: GillespieDTApproximate accelerated stochastic simulation of chemically reacting systemsJ Chem Phys2001115171610.1063/1.1378322 – reference: GillespieDTPetzoldLRImproved leap-size selection for accelerated stochastic simulationJ Chem Phys2003119822910.1063/1.1613254 – reference: CaoYGillespieDTPetzoldLRAvoiding negative populations in explicit poisson tau-leapingJ Chem Phys2005123505410410.1063/1.1992473 – reference: CaoYGillespieDPetzoldLEfficient step size selection for the tau-leaping simulation methodJ Chem Phys2006124404410910.1063/1.2159468 – reference: CaoYGillespieDPetzoldLMultiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systemsJ Comput Phys20052062395411214332410.1016/j.jcp.2004.12.0141088.80004 – reference: GillespieDTA general method for numerically simulating the stochastic time evolution of coupled chemical reactionsJ Comput Phys197622440343450337010.1016/0021-9991(76)90041-3
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Snippet	We propose the S -leaping algorithm for the acceleration of Gillespie’s stochastic simulation algorithm that combines the advantages of the two main... We propose the S-leaping algorithm for the acceleration of Gillespie's stochastic simulation algorithm that combines the advantages of the two main accelerated... We propose the S-leaping algorithm for the acceleration of Gillespie’s stochastic simulation algorithm that combines the advantages of the two main accelerated...
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SubjectTerms	Acceleration Adaptive algorithms Algorithms Bacillus subtilis - genetics Bacillus subtilis - metabolism Biochemical Phenomena Cell Biology Computer Simulation Dimerization Escherichia coli - genetics Escherichia coli - metabolism Escherichia coli Proteins - genetics Escherichia coli Proteins - metabolism Kinetics Lac Operon Life Sciences Markov Chains Mathematical and Computational Biology Mathematical Concepts Mathematics Mathematics and Statistics Models, Biological Monosaccharide Transport Proteins - genetics Monosaccharide Transport Proteins - metabolism Sampling Special Issue: Gillespie and His Algorithms Stochastic Processes Symporters - genetics Symporters - metabolism Systems Biology
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Title	S-Leaping: An Adaptive, Accelerated Stochastic Simulation Algorithm, Bridging τ-Leaping and R-Leaping
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