title: Perspective: Stochastic algorithms for chemical kinetics.
abstract: We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discrete-stochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-deterministic description. We next take note of some of the more promising strategies for dealing stochastically with stiff systems, rare events, and sensitivity analysis. Finally, we review some recent efforts to adapt and extend the discrete-stochastic approach to systems that are not well-mixed. In that currently developing area, we focus mainly on the strategy of subdividing the system into well-mixed subvolumes, and then simulating diffusional transfers of reactant molecules between adjacent subvolumes together with chemical reactions inside the subvolumes.
authors: Dan T Gillespie Consulting, 30504 Cordoba Pl., Castaic, California 91384, USA. gillespiedt@mailaps.org
authors: Daniel T
authors: DT
authors: Gillespie
authors: Andreas
authors: A
authors: Hellander
authors: Linda R
authors: LR
authors: Petzold
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004058:Diffusion; D007700:Kinetics; D008956:Models, Chemical; D013269:Stochastic Processes
references: J Phys Chem B. 2009 Feb 12;113(6):1640-4
references: 19159264
references: J Chem Phys. 2006 Jan 28;124(4):044109
references: 16460151
references: Proc Natl Acad Sci U S A. 2011 Mar 1;108(9):3815-20
references: 21300894
references: J R Soc Interface. 2013 Jan 16;10(80):20120988
references: 23325756
references: Cell. 2005 Jul 29;122(2):169-82
references: 16051143
references: Proc Natl Acad Sci U S A. 2005 Jul 12;102(28):9808-13
references: 15998739
references: Proc Natl Acad Sci U S A. 1997 Feb 4;94(3):814-9
references: 9023339
references: J Math Biol. 2012 Dec;65(6-7):1017-99
references: 22071651
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Dec;80(6 Pt 2):066106
references: 20365230
references: IET Syst Biol. 2012 Aug;6(4):102-15
references: 23039691
references: J Chem Phys. 2010 Feb 21;132(7):074101
references: 20170209
references: Bioinformatics. 2011 Sep 1;27(17):2457-8
references: 21727139
references: Phys Biol. 2009 Aug 21;6(4):046001
references: 19700812
references: IEEE/ACM Trans Comput Biol Bioinform. 2011 Jan-Mar;8(1):27-35
references: 21071794
references: PLoS Comput Biol. 2006 Jun 30;2(6):e80
references: 16846247
references: J Chem Phys. 2007 Jan 21;126(3):034302
references: 17249866
references: Annu Rev Phys Chem. 2007;58:35-55
references: 17037977
references: IET Syst Biol. 2011 Jan;5(1):58
references: 21261403
references: J Comput Phys. 2009;228(10):3656-3668
references: 19360139
references: BMC Syst Biol. 2012 Jun 22;6:76
references: 22727185
references: Multiscale Model Simul. 2016;14(2):668-707
references: 29046618
references: J Chem Phys. 2011 Aug 28;135(8):084103
references: 21895155
references: SIAM J Sci Comput. 2016;38(1):A55-A83
references: 28611531
references: J Chem Phys. 2008 Feb 7;128(5):054103
references: 18266441
references: J Chem Phys. 2004 Sep 1;121(9):4059-67
references: 15332951
references: J Chem Phys. 2013 Aug 7;139(5):054101
references: 23927237
references: J Chem Phys. 2010 Nov 7;133(17):174106
references: 21054005
references: J Chem Phys. 2009 Oct 28;131(16):164109
references: 19894929
references: J R Soc Interface. 2012 May 7;9(70):859-68
references: 22012973
references: Proc Natl Acad Sci U S A. 2010 Feb 9;107(6):2473-8
references: 20133748
references: J Chem Phys. 2005 Nov 15;123(19):194107
references: 16321076
references: J Chem Phys. 2011 Apr 21;134(15):154103
references: 21513371
references: J Chem Phys. 2005 Jan 1;122(1):14116
references: 15638651
references: J Chem Phys. 2008 Oct 28;129(16):165101
references: 19045316
references: J Chem Phys. 2006 Aug 28;125(8):084103
references: 16964997
references: Proc Natl Acad Sci U S A. 2010 Nov 16;107(46):19820-5
references: 21041672
references: J Chem Phys. 2011 Dec 21;135(23):234108
references: 22191865
references: J Chem Phys. 2010 Mar 7;132(9):094101
references: 20210383
references: Science. 2002 Aug 16;297(5584):1183-6
references: 12183631
references: J Chem Phys. 2008 May 28;128(20):205101
references: 18513044
references: Phys Rev Lett. 2005 Apr 1;94(12):128103
references: 15903966
references: J Chem Phys. 2009 Mar 7;130(9):094104
references: 19275393
references: J Chem Phys. 2005 Oct 8;123(14):144917
references: 16238434
references: J Chem Phys. 2004 Dec 22;121(24):12169-78
references: 15606235
references: Phys Rev Lett. 2001 Aug 6;87(6):068103
references: 11497866
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Apr;85(4 Pt 1):042901
references: 22680526
references: J Chem Phys. 2007 Dec 7;127(21):214107
references: 18067349
references: J Chem Phys. 2009 May 7;130(17):174103
references: 19425765
references: Genetics. 1998 Aug;149(4):1633-48
references: 9691025
references: Comput Biol Chem. 2006 Feb;30(1):39-49
references: 16321569
references: J Chem Phys. 2011 Jan 28;134(4):044110
references: 21280690
references: J Chem Phys. 2010 Jan 21;132(3):034103
references: 20095724
references: Syst Biol (Stevenage). 2004 Dec;1(2):230-6
references: 17051695
references: J Chem Phys. 2007 Apr 7;126(13):137101; discussion 137102
references: 17430072
references: J Chem Phys. 2007 Sep 14;127(10):104101
references: 17867731