{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T14:24:59Z","timestamp":1773239099785,"version":"3.50.1"},"publisher-location":"New York, NY","reference-count":212,"publisher":"Springer New York","isbn-type":[{"value":"9780387758886","type":"print"},{"value":"9780387304403","type":"electronic"}],"license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-0-387-30440-3_524","type":"book-chapter","created":{"date-parts":[[2009,6,17]],"date-time":"2009-06-17T16:22:15Z","timestamp":1245255735000},"page":"8730-8749","source":"Crossref","is-referenced-by-count":28,"title":["Stochastic Models of Biological Processes"],"prefix":"10.1007","author":[{"given":"Steven S.","family":"Andrews","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tuan","family":"Dinh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adam P.","family":"Arkin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"524_CR1_524","doi-asserted-by":"crossref","first-page":"413","DOI":"10.2307\/3212214","volume":"4","author":"DA McQuarrie","year":"1967","unstructured":"McQuarrie DA (1967) Stochastic approach to chemical kinetics. J\u00a0Appl Probab4:413\u2013478","journal-title":"J Appl Probab"},{"key":"524_CR2_524","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.compbiolchem.2004.05.001","volume":"28","author":"TE Turner","year":"2004","unstructured":"Turner TE, Schnell S, Burrage K (2004) Stochastic approaches for modelling invivo reactions. Comp Biol Chem 28:165\u2013178","journal-title":"Comp Biol Chem"},{"key":"524_CR3_524","doi-asserted-by":"crossref","first-page":"2010","DOI":"10.1126\/science.1105891","volume":"309","author":"JM Raser","year":"2005","unstructured":"Raser JM, O'Shea EK (2005) Noise in gene expression: Origins, consequences, andcontrol. Science 309:2010\u20132013","journal-title":"Science"},{"key":"524_CR4_524","doi-asserted-by":"crossref","first-page":"re17","DOI":"10.1126\/stke.3662006re17","volume":"2006","author":"MS Samoilov","year":"2006","unstructured":"Samoilov MS, Price G, Arkin AP (2006) From fluctuations to phenotypes: Thephysiology of noise. Sci STKE 2006:re17","journal-title":"Sci STKE"},{"key":"524_CR5_524","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1038\/nature01258","volume":"420","author":"CV Rao","year":"2002","unstructured":"Rao CV, Wolf DM, Arkin AP (2002) Control, exploitation, and tolerance ofintracellular noise. Nature 420:231\u2013237","journal-title":"Nature"},{"key":"524_CR6_524","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1146\/annurev.physchem.58.032806.104637","volume":"58","author":"DT Gillespie","year":"2007","unstructured":"Gillespie DT (2007) Stochastic simulation of chemical kinetics. Ann Rev PhysChem 58:35\u201355","journal-title":"Ann Rev Phys Chem"},{"key":"524_CR7_524","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/S1369-5274(03)00033-X","volume":"6","author":"DM Wolf","year":"2003","unstructured":"Wolf DM, Arkin AP (2003) Motifs, modules and games in bacteria. Curr OpinMicrobiol 6:125\u2013134","journal-title":"Curr Opin Microbiol"},{"key":"524_CR8_524","doi-asserted-by":"crossref","first-page":"R523","DOI":"10.1016\/j.cub.2006.06.048","volume":"16","author":"SS Andrews","year":"2006","unstructured":"Andrews SS, Arkin AP (2006) Simulating cell biology. Curr Biol16:R523\u2013R527","journal-title":"Curr Biol"},{"key":"524_CR9_524","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/S0168-9525(98)01659-X","volume":"15","author":"HH McAdams","year":"1999","unstructured":"McAdams HH, Arkin A (1999) It's a\u00a0noisy business! Genetic regulation at thenanomolar scale. Trends Genet 15:65\u201369","journal-title":"Trends Genet"},{"key":"524_CR10_524","doi-asserted-by":"crossref","first-page":"051406","DOI":"10.1117\/1.2103032","volume":"10","author":"RH Singer","year":"2005","unstructured":"Singer RH, Lawrence DS, Ovryn B, Condeelis J (2005) Imaging of gene expressionin living cells and tissues. Biomed J Optics 10:051406","journal-title":"Biomed J Optics"},{"key":"524_CR11_524","doi-asserted-by":"crossref","first-page":"836","DOI":"10.1126\/science.1072241","volume":"297","author":"JM Levsky","year":"2002","unstructured":"Levsky JM, Shenoy SM, Pezo RC, Singer RH (2002) Single\u2010cell geneexpression profiling. Science 297:836\u2013840","journal-title":"Science"},{"key":"524_CR12_524","doi-asserted-by":"crossref","first-page":"1183","DOI":"10.1126\/science.1070919","volume":"297","author":"MB Elowitz","year":"2002","unstructured":"Elowitz MB, Levine AJ, Siggia ED, Swain PS (2002) Stochastic gene expressionin a\u00a0single cell. Science 297:1183\u20131186","journal-title":"Science"},{"key":"524_CR13_524","doi-asserted-by":"crossref","first-page":"1811","DOI":"10.1126\/science.1098641","volume":"304","author":"JM Raser","year":"2004","unstructured":"Raser JM, O'Shea EK (2004) Control of stochasticity in eukaryotic geneexpression. Science 304:1811\u20131814","journal-title":"Science"},{"key":"524_CR14_524","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1038\/nature01546","volume":"422","author":"WJ Blake","year":"2003","unstructured":"Blake WJ, Kaern M, Cantor CR, Collins JJ (2003) Noise in eukaryotic geneexpression. Nature 422:633\u2013637","journal-title":"Nature"},{"key":"524_CR15_524","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1038\/ng869","volume":"31","author":"EM Ozbudak","year":"2002","unstructured":"Ozbudak EM, Thattai M, Kurtser I, Grossman AD, van Oudenaarden A (2002)Regulation of noise in the expression of a\u00a0single gene. Nature Genet 31:69\u201373","journal-title":"Nature Genet"},{"key":"524_CR16_524","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.cell.2005.06.006","volume":"122","author":"LS Weinberger","year":"2005","unstructured":"Weinberger LS, Burnett JC, Toettcher JE, Arkin AP, Schaffer DV (2005)Stochastic gene expression in a\u00a0lentiviral positive\u2010feedback loop: HIV-1 Tat fluctuations drive phenotypic diversity. Cell122:169\u2013182","journal-title":"Cell"},{"key":"524_CR17_524","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1038\/nature04599","volume":"440","author":"L Cai","year":"2006","unstructured":"Cai L, Friedman N, Xie XS (2006) Stochastic protein expression in individualcells at the single molecule level. Nature 440:358\u2013362","journal-title":"Nature"},{"key":"524_CR18_524","doi-asserted-by":"crossref","first-page":"1600","DOI":"10.1126\/science.1119623","volume":"311","author":"J Yu","year":"2006","unstructured":"Yu J, Xiao J, Ren X, Lao K, Xie XS (2006) Probing gene expression in livecells, one protein molecule at a\u00a0time. Science 311:1600\u20131603","journal-title":"Science"},{"key":"524_CR19_524","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1186\/gb-2006-7-6-212","volume":"7","author":"I Golding","year":"2006","unstructured":"Golding I, Cox EC (2006) Protein synthesis molecule by molecule. Genome Biol7:212","journal-title":"Genome Biol"},{"key":"524_CR20_524","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/S0960-9822(02)01436-7","volume":"13","author":"D Fusco","year":"2003","unstructured":"Fusco D, Accornero N, Lavoie B, Shenoy SM, Blanchard J-M, Singer RH, BertrandE (2003) Single mRNA molecules demonstrate probabilistic movement in living mammalian cells. Curr Biol 13:161\u2013167","journal-title":"Curr Biol"},{"key":"524_CR21_524","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1038\/35002125","volume":"403","author":"MB Elowitz","year":"2000","unstructured":"Elowitz MB, Leibler S (2000) A\u00a0synthetic oscillatory network oftranscriptional regulators. Nature 403:335\u2013338","journal-title":"Nature"},{"key":"524_CR22_524","volume-title":"Modern Quantum Mechanics","author":"JJ Sakurai","year":"1994","unstructured":"Sakurai JJ (1994) Modern Quantum Mechanics. Addison-Wesley, Boston"},{"key":"524_CR23_524","volume-title":"Nonlinear Dynamics and Chaos","author":"SH Strogatz","year":"1994","unstructured":"Strogatz SH (1994) Nonlinear Dynamics and Chaos. Westview Press,Cambridge"},{"key":"524_CR24_524","volume-title":"Physical Chemistry","author":"PW Atkins","year":"1986","unstructured":"Atkins PW (1986) Physical Chemistry. Freeman, NewYork"},{"key":"524_CR25_524","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/S0955-0674(03)00017-6","volume":"15","author":"JJ Tyson","year":"2003","unstructured":"Tyson JJ, Chen KC, Novak B (2003) Sniffers, buzzers, toggles, and blinkers:dynamics of regulatory and signaling pathways in the cell. Curr Opin Cell Biol 15:221\u2013231","journal-title":"Curr Opin Cell Biol"},{"key":"524_CR26_524","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/S0968-0004(00)01754-0","volume":"26","author":"MW Covert","year":"2001","unstructured":"Covert MW, Schilling CH, Famili I, Edwards JS, Goryanin II, Selkov E, PalssonBO (2001) Metabolic modeling of microbial strains in silico. Trends Biochem Sci 26:179\u2013186","journal-title":"Trends Biochem Sci"},{"key":"524_CR27_524","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1038\/nbt1094-994","volume":"12","author":"A Varma","year":"1994","unstructured":"Varma A, Palsson BO (1994) Metabolic flux balancing: Basic concepts,scientific and practical use. Nature Biotech 12:994\u2013998","journal-title":"Nature Biotech"},{"key":"524_CR28_524","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1016\/j.copbio.2003.08.001","volume":"14","author":"KJ Kauffman","year":"2003","unstructured":"Kauffman KJ, Prakash P, Edwards JS (2003) Advances in flux balanceanalysis. Curr Opin Biotech 14:491\u2013496","journal-title":"Curr Opin Biotech"},{"key":"524_CR29_524","volume-title":"Understanding the Control of Metabolism","author":"D Fell","year":"1997","unstructured":"Fell D (1997) Understanding the Control of Metabolism. Portland Press,London"},{"key":"524_CR30_524","doi-asserted-by":"crossref","first-page":"7328","DOI":"10.1073\/pnas.88.16.7328","volume":"88","author":"JJ Tyson","year":"1991","unstructured":"Tyson JJ (1991) Modeling the cell division cycle: cdc2 and cyclininteractions. Proc Natl Acad Sci USA 88:7328\u20137332","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR31_524","doi-asserted-by":"crossref","first-page":"3841","DOI":"10.1091\/mbc.e03-11-0794","volume":"15","author":"KC Chen","year":"2004","unstructured":"Chen KC, Calzone L, Csikasz-Nagy A, Cross FR, Novak B, Tyson JJ (2004)Integrative analysis of cell cycle control in budding yeast. Mol Biol Cell 15:3841\u20133862","journal-title":"Mol Biol Cell"},{"key":"524_CR32_524","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1038\/nature01259","volume":"420","author":"A Goldbeter","year":"2002","unstructured":"Goldbeter A (2002) Computational approaches to cellular rhythms. Nature420:238\u2013245","journal-title":"Nature"},{"key":"524_CR33_524","doi-asserted-by":"crossref","first-page":"7420","DOI":"10.1073\/pnas.0608665104","volume":"104","author":"JS van Zon","year":"2007","unstructured":"van Zon JS, Lubensky DK, Altena PRH, ten Wolde PR (2007) An allosteric modelof circadian KaiC phosphorylation. Proc Natl Acad Sci USA 104:7420\u20137425","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR34_524","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1002\/jez.1402710106","volume":"271","author":"J Reinitz","year":"1995","unstructured":"Reinitz J, Mjolsness E, Sharp DH (1995) Model for cooperative control ofpositional information in Drosophila by bicoid and maternal hunchback. Exp J Zool 271:47\u201356","journal-title":"Exp J Zool"},{"key":"524_CR35_524","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1038\/35018085","volume":"406","author":"G von Dassow","year":"2000","unstructured":"von Dassow G, Meir E, Munro EM, Odell GM (2000) The segment polarity networkis a\u00a0robust developmental module. Nature 406:188\u2013192","journal-title":"Nature"},{"key":"524_CR36_524","doi-asserted-by":"crossref","first-page":"2517","DOI":"10.1016\/S0006-3495(01)75897-3","volume":"81","author":"N Kellershohn","year":"2001","unstructured":"Kellershohn N, Laurent M (2001) Prion diseases: dynamics of the infection andproperties of the bistable transition. Biophys J 81:2517\u20132529","journal-title":"Biophys J"},{"key":"524_CR37_524","doi-asserted-by":"crossref","unstructured":"Ferrell JEJ, Machleder EM (1998) The biochemical basis of an all-or-none cell fateswitch in Xenopus oocytes. Science 280:895\u2013898","DOI":"10.1126\/science.280.5365.895"},{"key":"524_CR38_524","doi-asserted-by":"crossref","first-page":"10078","DOI":"10.1073\/pnas.93.19.10078","volume":"93","author":"C-YF Huang","year":"1996","unstructured":"Huang C-YF, Ferrell JEJ (1996) Ultrasensitivity in the mitogen\u2010activatedprotein kinase cascade. Proc Natl Acad Sci USA 93:10078\u201310083","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR39_524","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1016\/S0968-0004(99)01473-5","volume":"24","author":"M Laurent","year":"1999","unstructured":"Laurent M, Kellershohn N (1999) Multistability: a\u00a0major means ofdifferentiation and evolution in biochemical systems. Trends Biochem Sci 24:418\u2013422","journal-title":"Trends Biochem Sci"},{"key":"524_CR40_524","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1038\/nbt1253","volume":"24","author":"MS Samoilov","year":"2006","unstructured":"Samoilov MS, Arkin AP (2006) Deviant effects in molecular reactionpathways. Nature Biotech 24:1235\u20131240","journal-title":"Nature Biotech"},{"key":"524_CR41_524","volume-title":"Stochastic Processes in Physics and Chemistry","author":"NG van Kampen","year":"1992","unstructured":"van Kampen NG (1992) Stochastic Processes in Physics and Chemistry. Elsevier,Amsterdam"},{"key":"524_CR42_524","doi-asserted-by":"crossref","first-page":"164115","DOI":"10.1063\/1.2062048","volume":"123","author":"EL Haseltine","year":"2005","unstructured":"Haseltine EL, Rawlings JB (2005) On the origins of approximations forstochastic chemical kinetics. Chem J Phys 123:164115","journal-title":"Chem J Phys"},{"key":"524_CR43_524","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1016\/0378-4371(92)90283-V","volume":"188","author":"DT Gillespie","year":"1992","unstructured":"Gillespie DT (1992) A\u00a0rigorous derivation of the chemical masterequation. Physica A 188:404\u2013425","journal-title":"Physica A"},{"key":"524_CR44_524","doi-asserted-by":"crossref","first-page":"10547","DOI":"10.1073\/pnas.95.18.10547","volume":"95","author":"JM Rohwer","year":"1998","unstructured":"Rohwer JM, Postma PW, Kholodenko BN, Westerhoff HV (1998) Implications ofmacromolecular crowding for signal transduction and metabolite channeling. Proc Natl Acad Sci USA 95:10547\u201310552","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR45_524","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1088\/1478-3967\/1\/3\/001","volume":"1","author":"SS Andrews","year":"2004","unstructured":"Andrews SS, Bray D (2004) Stochastic simulation of chemical reactions withspatial resolution and single molecule detail. Phys Biol 1:137\u2013151","journal-title":"Phys Biol"},{"key":"524_CR46_524","doi-asserted-by":"crossref","first-page":"044104","DOI":"10.1063\/1.2145882","volume":"124","author":"B Munsky","year":"2006","unstructured":"Munsky B, Khammash M (2006) The finite state projection algorithm for thesolution of the chemical master equation. Chem J Phys 124:044104","journal-title":"Chem J Phys"},{"key":"524_CR47_524","doi-asserted-by":"crossref","first-page":"204104","DOI":"10.1063\/1.2397685","volume":"125","author":"S Peles","year":"2006","unstructured":"Peles S, Munsky B, Khammash M (2006) Reduction and solution of the chemicalmaster equation using time scale separation and finite state projection. Chem J Phys 125:204104","journal-title":"Chem J Phys"},{"key":"524_CR48_524","first-page":"150","volume":"6","author":"H Kuwahara","year":"2006","unstructured":"Kuwahara H, Myers CJ, Samoilov MS, Barker NA, Arkin AP (2006) Automatedabstraction methodology for genetic regulatory networks. Trans Comput Syst Biol 6:150\u2013175","journal-title":"Trans Comput Syst Biol"},{"key":"524_CR49_524","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1016\/j.cam.2006.02.053","volume":"205","author":"M Hegland","year":"2007","unstructured":"Hegland M, Burden C, Santoso L, MacNamara S, Booth H (2007) A\u00a0solver forthe stochastic master equation applied to gene regulatory networks. Comp J Appl Math 205:708\u2013724","journal-title":"Comp J Appl Math"},{"key":"524_CR50_524","doi-asserted-by":"crossref","first-page":"046707","DOI":"10.1103\/PhysRevE.67.046707","volume":"67","author":"SV Nedea","year":"2003","unstructured":"Nedea SV, Jansen APJ, Lukkien JJ, Hilbers PAJ (2003) Infinitely fast diffusionin single\u2010file systems. Phys Rev E 67:046707","journal-title":"Phys Rev E"},{"key":"524_CR51_524","doi-asserted-by":"crossref","first-page":"064110","DOI":"10.1063\/1.2166380","volume":"124","author":"A Chatterjee","year":"2006","unstructured":"Chatterjee A, Vlachos DG (2006) Multiscale spatial Monte Carlo simulations:Multigriding, computational singular perturbation, and hierarchical stochastic closures. Chem J Phys 124:064110","journal-title":"Chem J Phys"},{"key":"524_CR52_524","doi-asserted-by":"crossref","unstructured":"Ambj\u00f6rnsson T, Banik SK, Lomholt MA, Metzler R (2007) Master equation approachto DNA breathing in heteropolymer DNA. Phys Rev E 75:021908","DOI":"10.1103\/PhysRevE.75.021908"},{"key":"524_CR53_524","doi-asserted-by":"crossref","first-page":"138101","DOI":"10.1103\/PhysRevLett.90.138101","volume":"90","author":"G Altan-Bonnet","year":"2003","unstructured":"Altan-Bonnet G, Libchaber A, Krichevsky O (2003) Bubble dynamics indouble\u2010stranded DNA. Phys Rev Lett 90:138101","journal-title":"Phys Rev Lett"},{"key":"524_CR54_524","doi-asserted-by":"crossref","first-page":"061905","DOI":"10.1103\/PhysRevE.64.061905","volume":"64","author":"G Lattanzi","year":"2001","unstructured":"Lattanzi G, Maritan A (2001) Master equation approach to molecularmotors. Phys Rev E 64:061905","journal-title":"Phys Rev E"},{"key":"524_CR55_524","doi-asserted-by":"crossref","first-page":"1186","DOI":"10.1016\/S0006-3495(98)77834-8","volume":"74","author":"H-Y Wang","year":"1998","unstructured":"Wang H-Y, Elston T, Mogilner A, Oster G (1998) Force generation in RNApolymerase. Biophys J 74:1186\u20131202","journal-title":"Biophys J"},{"key":"524_CR56_524","doi-asserted-by":"crossref","unstructured":"Peskin CS, Odell GM, Oster GF (1993) Cellular motions and thermalfluctuations: the Brownian ratchet. Biophys J 65:316\u2013324","DOI":"10.1016\/S0006-3495(93)81035-X"},{"key":"524_CR57_524","doi-asserted-by":"crossref","first-page":"5447","DOI":"10.1103\/PhysRevLett.84.5447","volume":"84","author":"J Paulsson","year":"2000","unstructured":"Paulsson J, Ehrenberg M (2000) Random signal fluctuations can reduce randomfluctuations in regulated component of chemical regulatory networks. Phys Rev Lett 84:5447\u20135450","journal-title":"Phys Rev Lett"},{"key":"524_CR58_524","doi-asserted-by":"crossref","first-page":"7148","DOI":"10.1073\/pnas.110057697","volume":"97","author":"J Paulsson","year":"2000","unstructured":"Paulsson J, Berg OG, Ehrenberg M (2000) Stochastic focusing:fluctuation\u2010enhanced sensitivity of intracellular regulation. Proc Natl Acad Sci USA 97:7148\u20137153","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR59_524","doi-asserted-by":"crossref","first-page":"2944","DOI":"10.1016\/S0006-3495(00)76531-3","volume":"79","author":"OG Berg","year":"2000","unstructured":"Berg OG, Paulsson J, Ehrenberg M (2000) Fluctuations in repressor control:thermodynamic constraints on stochastic focusing. Biophys J 79:2944\u20132953","journal-title":"Biophys J"},{"key":"524_CR60_524","doi-asserted-by":"crossref","first-page":"061916","DOI":"10.1103\/PhysRevE.71.061916","volume":"71","author":"H Li","year":"2005","unstructured":"Li H, Hou Z, Xin H (2005) Internal noise stochastic resonance forintracellular calcium oscillations in a\u00a0cell system. Phys Rev E 71:061916","journal-title":"Phys Rev E"},{"key":"524_CR61_524","doi-asserted-by":"crossref","first-page":"2310","DOI":"10.1073\/pnas.0406841102","volume":"102","author":"M Samoilov","year":"2005","unstructured":"Samoilov M, Plyasunov S, Arkin AP (2005) Stochastic amplification andsignaling in enzymatic futile cycles through noise\u2010induced bistability with oscillations. Proc Natl Acad Sci USA102:2310\u20132315","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR62_524","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/0021-9991(76)90041-3","volume":"22","author":"DT Gillespie","year":"1976","unstructured":"Gillespie DT (1976) A\u00a0general method for numerically simulating thestochastic time evolution of coupled chemical reactions. Comp J Phys 22:435\u2013450","journal-title":"Comp J Phys"},{"key":"524_CR63_524","doi-asserted-by":"crossref","first-page":"2340","DOI":"10.1021\/j100540a008","volume":"81","author":"DT Gillespie","year":"1977","unstructured":"Gillespie DT (1977) Exact stochastic simulation of coupled chemicalreactions. Phys J Chem 81:2340\u20132361","journal-title":"Phys J Chem"},{"key":"524_CR64_524","doi-asserted-by":"crossref","first-page":"1876","DOI":"10.1021\/jp993732q","volume":"104","author":"MA Gibson","year":"2000","unstructured":"Gibson MA, Bruck J (2000) Efficient exact stochastic simulation of chemicalsystems with many species and many channels. Phys J Chem A 104:1876\u20131889","journal-title":"Phys J Chem A"},{"key":"524_CR65_524","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1038\/nbt1054","volume":"23","author":"L Lok","year":"2005","unstructured":"Lok L, Brent R (2005) Automatic generation of cellular reaction networks withMolecularizer 1.0. Nature Biotech 23:131\u2013136","journal-title":"Nature Biotech"},{"key":"524_CR66_524","doi-asserted-by":"crossref","first-page":"4059","DOI":"10.1063\/1.1778376","volume":"121","author":"Y Cao","year":"2004","unstructured":"Cao Y, Li H, Petzold L (2004) Efficient formulation of the stochasticsimulation algorithm for chemically reacting systems. Chem J Phys 121:4059\u20134067","journal-title":"Chem J Phys"},{"key":"524_CR67_524","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.compbiolchem.2005.10.007","volume":"30","author":"JM McCollum","year":"2006","unstructured":"McCollum JM, Peterson GD, Cox CD, Simpson ML, Samatova NF (2006) The sortingdirect method for stochastic simulation of biochemical systems with varying reaction execution behavior. Comp Biol Chem30:39\u201349","journal-title":"Comp Biol Chem"},{"key":"524_CR68_524","doi-asserted-by":"crossref","unstructured":"Plyasunov S, Arkin AP (2007) Efficient stochastic sensitivity analysis ofdiscrete event systems. Comput J Phys 221:724\u2013738","DOI":"10.1016\/j.jcp.2006.06.047"},{"key":"524_CR69_524","doi-asserted-by":"crossref","first-page":"1465","DOI":"10.1016\/j.peptides.2003.10.022","volume":"25","author":"L Bardwell","year":"2004","unstructured":"Bardwell L (2004) A\u00a0walk\u2010through of the yeast mating pheromoneresponse pathway. Peptides 25:1465\u20131476","journal-title":"Peptides"},{"key":"524_CR70_524","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1006\/jtbi.1997.0651","volume":"192","author":"CJ Morton-Firth","year":"1998","unstructured":"Morton-Firth CJ, Bray D (1998) Predicting temporal fluctuations in anintracellular signalling pathway. Theor J Biol 192:117\u2013128","journal-title":"Theor J Biol"},{"key":"524_CR71_524","doi-asserted-by":"crossref","unstructured":"LeNov\u00e8re N, Shimizu TS (2001) StochSim: modelling of stochastic biomolecularprocesses. Bioinformatics 17:575\u2013576","DOI":"10.1093\/bioinformatics\/17.6.575"},{"key":"524_CR72_524","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1049\/sb:20045016","volume":"1","author":"T Lu","year":"2004","unstructured":"Lu T, Volfson D, Tsimring L, Hasty J (2004) Cellular growth and division inthe Gillespie algorithm. Syst Biol 1:121\u2013128","journal-title":"Syst Biol"},{"key":"524_CR73_524","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1146\/annurev.biophys.27.1.199","volume":"27","author":"H McAdams","year":"1998","unstructured":"McAdams H, Arkin A (1998) Simulation of prokaryotic genetic circuits. Annu RevBiophys Biomol Struct 27:199\u2013224","journal-title":"Annu Rev Biophys Biomol Struct"},{"key":"524_CR74_524","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1038\/nature02257","volume":"427","author":"J Paulsson","year":"2004","unstructured":"Paulsson J (2004) Summing up the noise in gene networks. Nature427:415\u2013418","journal-title":"Nature"},{"key":"524_CR75_524","doi-asserted-by":"crossref","first-page":"814","DOI":"10.1073\/pnas.94.3.814","volume":"94","author":"HH McAdams","year":"1997","unstructured":"McAdams HH, Arkin A (1997) Stochastic mechanisms in gene expression. Proc NatlAcad Sci USA 94:814\u2013819","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR76_524","doi-asserted-by":"crossref","first-page":"1633","DOI":"10.1093\/genetics\/149.4.1633","volume":"149","author":"A Arkin","year":"1998","unstructured":"Arkin A, Ross J, McAdams HH (1998) Stochastic kinetic analysis ofdevelopmental pathway bifurcation in phage lambda\u2010infected Escherichia coli cells. Genetics 149:1633\u20131648","journal-title":"Genetics"},{"key":"524_CR77_524","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/j.jtbi.2004.11.020","volume":"234","author":"DM Wolf","year":"2005","unstructured":"Wolf DM, Vazirani VV, Arkin AP (2005) Diversity in times of adversity:probabilistic strategies in microbial survival games. Theor J Biol 234:227\u2013253","journal-title":"Theor J Biol"},{"key":"524_CR78_524","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1002\/(SICI)1521-1878(200004)22:4<381::AID-BIES8>3.0.CO;2-E","volume":"22","author":"S Fiering","year":"2000","unstructured":"Fiering S, Whitelaw E, Martin DIK (2000) To be or not to be active: thestochastic nature of enhancer action. BioEssays 22:381\u2013387","journal-title":"BioEssays"},{"key":"524_CR79_524","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1038\/35002258","volume":"403","author":"N Barkai","year":"2000","unstructured":"Barkai N, Leibler S (2000) Biological rhythms: Circadian clocks limited bynoise. Nature 403:267\u2013268","journal-title":"Nature"},{"key":"524_CR80_524","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1534\/genetics.167.1.523","volume":"167","author":"M Thattai","year":"2004","unstructured":"Thattai M, van Oudenaarden A (2004) Stochastic gene expression in fluctuatingenvironments. Genetics 167:523\u2013530","journal-title":"Genetics"},{"key":"524_CR81_524","doi-asserted-by":"crossref","first-page":"2075","DOI":"10.1126\/science.1114383","volume":"309","author":"E Kussell","year":"2005","unstructured":"Kussell E, Leibler S (2005) Phenotypic diversity, population growth, andinformation in fluctuating environments. Science 309:2075\u20132078","journal-title":"Science"},{"key":"524_CR82_524","doi-asserted-by":"crossref","first-page":"1965","DOI":"10.1126\/science.1109090","volume":"307","author":"JM Pedraza","year":"2005","unstructured":"Pedraza JM, van Oudenaarden A (2005) Noise propagation in genenetworks. Science 307:1965\u20131969","journal-title":"Science"},{"key":"524_CR83_524","doi-asserted-by":"crossref","first-page":"12795","DOI":"10.1073\/pnas.162041399","volume":"99","author":"PS Swain","year":"2002","unstructured":"Swain PS, Elowittz MB, Siggia ED (2002) Intrinsic and extrinsic contributionsto stochasticity in gene expression. Proc Natl Acad Sci USA 99:12795\u201312800","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR84_524","doi-asserted-by":"crossref","first-page":"7304","DOI":"10.1073\/pnas.0509874103","volume":"103","author":"JT Mettetal","year":"2006","unstructured":"Mettetal JT, Muzzey D, Pedraza JM, Ozbudak EM, van Oudenaarden A (2006)Predicting stochastic gene expression dynamics in single cells. Proc Natl Acad Sci USA 103:7304\u20137309","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR85_524","doi-asserted-by":"crossref","first-page":"8165","DOI":"10.1074\/jbc.M006264200","volume":"276","author":"AM Kierzek","year":"2001","unstructured":"Kierzek AM, Zaim J, Zielenkiewicz P (2001) The effect of transcription andtranslation initiation frequencies on the stochastic fluctuations in prokaryotic gene expression. Biol J Chem 276:8165\u20138172","journal-title":"Biol J Chem"},{"key":"524_CR86_524","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1006\/tpbi.1995.1027","volume":"48","author":"J Peccoud","year":"1995","unstructured":"Peccoud J, Ycart B (1995) Markovian modeling of gene\u2010productsynthesis. Theor Popul Biol 48:222\u2013234","journal-title":"Theor Popul Biol"},{"key":"524_CR87_524","doi-asserted-by":"crossref","unstructured":"Rosenfeld N, Young JW, Alon U, Swain PS, Elowittz MB (2005) Gene regulation atthe single\u2010cell level. Science 307:1962\u20131965","DOI":"10.1126\/science.1106914"},{"key":"524_CR88_524","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1038\/nrg1471","volume":"5","author":"H Kitano","year":"2004","unstructured":"Kitano H (2004) Biological robustness. Nature Rev Genet5:826\u2013837","journal-title":"Nature Rev Genet"},{"key":"524_CR89_524","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1038\/16483","volume":"397","author":"U Alon","year":"1999","unstructured":"Alon U, Surette MG, Barkai N, Leibler S (1999) Robustness in bacterialchemotaxis. Nature 397:168\u2013171","journal-title":"Nature"},{"key":"524_CR90_524","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1038\/43199","volume":"387","author":"N Barkai","year":"1997","unstructured":"Barkai N, Leibler S (1997) Robustness in simple biochemical networks. Nature387:913\u2013917","journal-title":"Nature"},{"key":"524_CR91_524","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1016\/j.cell.2004.09.008","volume":"118","author":"J Stelling","year":"2004","unstructured":"Stelling J, Sauer U, Szallasi Z, Doyle FJI, Doyle J (2004) Robustness ofcellular functions. Cell 118:675\u2013685","journal-title":"Cell"},{"key":"524_CR92_524","doi-asserted-by":"crossref","first-page":"5988","DOI":"10.1073\/pnas.092133899","volume":"99","author":"JMG Vilar","year":"2002","unstructured":"Vilar JMG, Kueh HY, Barkai N, Leibler S (2002) Mechanisms ofnoise\u2010resistance in genetic oscillators. Proc Natl Acad Sci USA 99:5988\u20135992","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR93_524","doi-asserted-by":"crossref","first-page":"8710","DOI":"10.1073\/pnas.1536783100","volume":"100","author":"M Aldana","year":"2003","unstructured":"Aldana M, Cluzel P (2003) A\u00a0natural class of robust networks. Proc NatlAcad Sci USA 100:8710\u20138714","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR94_524","doi-asserted-by":"crossref","first-page":"2943","DOI":"10.1016\/S0006-3495(02)75635-X","volume":"82","author":"M Thattai","year":"2002","unstructured":"Thattai M, van Oudenaarden A (2002) Attenuation of noise in ultrasensitivesignaling cascades. Biophys J 82:2943\u20132950","journal-title":"Biophys J"},{"key":"524_CR95_524","doi-asserted-by":"crossref","first-page":"4649","DOI":"10.1073\/pnas.97.9.4649","volume":"97","author":"T-M Yi","year":"2000","unstructured":"Yi T-M, Huang Y, Simon MI, Doyle J (2000) Robust perfect adaptation inbacterial chemotaxis through integral feedback control. Proc Natl Acad Sci USA 97:4649\u20134653","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR96_524","first-page":"1","volume":"2","author":"HB Fraser","year":"2004","unstructured":"Fraser HB, Hirsh AE, Giaever G, Kumm J, Eisen MB (2004) Noise minimization ineukaryotic gene expression. PLoBiol S 2:1\u20135","journal-title":"PLoBiol S"},{"key":"524_CR97_524","doi-asserted-by":"crossref","first-page":"1187","DOI":"10.1534\/genetics.104.031955","volume":"169","author":"CA Voigt","year":"2005","unstructured":"Voigt CA, Wolf DM, Arkin AP (2005) The Bacillus subtilis sin operon: anevolvable network motif. Genetics 169:1187\u20131202","journal-title":"Genetics"},{"key":"524_CR98_524","doi-asserted-by":"crossref","first-page":"044109","DOI":"10.1063\/1.2159468","volume":"124","author":"Y Cao","year":"2006","unstructured":"Cao Y, Gillespie DT, Petzold LR (2006) Efficient step size selection for thetau\u2010leaping simulation method. Chem J Phys 124:044109","journal-title":"Chem J Phys"},{"key":"524_CR99_524","doi-asserted-by":"crossref","unstructured":"Gillespie DT, Petzold LR (2003) Improved leap\u2010size selection foraccelerated stochastic simulation. Chem J Phys 119:8229\u20138234","DOI":"10.1063\/1.1613254"},{"key":"524_CR100_524","doi-asserted-by":"crossref","unstructured":"Gillespie DT (2001) Approximate accelerated stochastic simulation ofchemically reacting systems. Chem J Phys 115:1716\u20131733","DOI":"10.1063\/1.1378322"},{"key":"524_CR101_524","doi-asserted-by":"crossref","first-page":"054104","DOI":"10.1063\/1.1992473","volume":"123","author":"Y Cao","year":"2005","unstructured":"Cao Y, Gillespie DT, Petzold LR (2005) Avoiding negative populations inexplicit Poisson tau\u2010leaping. Chem J Phys 123:054104","journal-title":"Chem J Phys"},{"key":"524_CR102_524","doi-asserted-by":"crossref","first-page":"2136","DOI":"10.1093\/bioinformatics\/bti308","volume":"21","author":"A Chatterjee","year":"2005","unstructured":"Chatterjee A, Mayawala K, Edwards JS, Vlachos DG (2005) Time acceleratedMonte Carlo simulations of biological networks using the binomial tau\u2011leap method. Bioinformatics 21:2136\u20132137","journal-title":"Bioinformatics"},{"key":"524_CR103_524","doi-asserted-by":"crossref","first-page":"084101","DOI":"10.1063\/1.2432326","volume":"126","author":"MF Pettigrew","year":"2007","unstructured":"Pettigrew MF, Resat H (2007) Multinomial tau\u2010leaping method forstochastic kinetic simulations. Chem J Phys 126:084101","journal-title":"Chem J Phys"},{"key":"524_CR104_524","doi-asserted-by":"crossref","first-page":"6472","DOI":"10.1021\/jp0034630","volume":"105","author":"R Zwanzig","year":"2001","unstructured":"Zwanzig R (2001) A\u00a0chemical Langevin equation with non\u2010Gaussiannoise. Phys J Chem B 105:6472\u20136473","journal-title":"Phys J Chem B"},{"key":"524_CR105_524","doi-asserted-by":"crossref","first-page":"1246","DOI":"10.1119\/1.18387","volume":"64","author":"DT Gillespie","year":"1996","unstructured":"Gillespie DT (1996) The multivariate Langevin and Fokker\u2013Planckequations. Am Phys J 64:1246\u20131257","journal-title":"Am Phys J"},{"key":"524_CR106_524","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1063\/1.481811","volume":"113","author":"DT Gillespie","year":"2000","unstructured":"Gillespie DT (2000) The chemical Langevin equation. Chem J Phys113:297\u2013306","journal-title":"Chem J Phys"},{"key":"524_CR107_524","doi-asserted-by":"crossref","first-page":"5063","DOI":"10.1021\/jp0128832","volume":"106","author":"DT Gillespie","year":"2002","unstructured":"Gillespie DT (2002) The chemical Langevin and Fokker\u2013Planck equationsfor the reversible isomerization reaction. Phys J Chem A 106:5063\u20135071","journal-title":"Phys J Chem A"},{"key":"524_CR108_524","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1006\/jtbi.2003.3200","volume":"221","author":"H Wang","year":"2003","unstructured":"Wang H, Peskin CS, Elston TC (2003) A\u00a0robust numerical algorithm forstudying biomolecular transport processes. Theor J Biol 221:491\u2013511","journal-title":"Theor J Biol"},{"key":"524_CR109_524","doi-asserted-by":"crossref","unstructured":"Xing J, Wang H, Oster G (2005) From continuum Fokker\u2013Planck models todiscrete kinetic models. Biophys J 89:1551\u20131563","DOI":"10.1529\/biophysj.104.055178"},{"key":"524_CR110_524","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1016\/j.jtbi.2004.07.012","volume":"231","author":"Y Tao","year":"2004","unstructured":"Tao Y (2004) Intrinsic noise, gene regulation and steady\u2010statestatistics in a\u00a0two-gene network. Theor J Biol 231:563\u2013568","journal-title":"Theor J Biol"},{"key":"524_CR111_524","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/BF00275888","volume":"25","author":"CVM van der Mee","year":"1987","unstructured":"van der Mee CVM, Zweifel PF (1987) A\u00a0Fokker\u2013Planck equation forgrowing cell populations. Math J Biol 25:61\u201372","journal-title":"Math J Biol"},{"key":"524_CR112_524","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1088\/1478-3975\/3\/1\/008","volume":"3","author":"K Sato","year":"2006","unstructured":"Sato K, Kaneko K (2006) On the distribution of state values of reproducingcells. Phys Biol 3:74\u201382","journal-title":"Phys Biol"},{"key":"524_CR113_524","doi-asserted-by":"crossref","unstructured":"Hill NA, H\u00e4der D-P (1997) A\u00a0biased random walk model for thetrajectories of swimming micro\u2010organisms. Theor J Biol 186:503\u2013526","DOI":"10.1006\/jtbi.1997.0421"},{"key":"524_CR114_524","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1016\/S0092-8240(05)80241-1","volume":"55","author":"M Schienbein","year":"1993","unstructured":"Schienbein M, Gruler H (1993) Langevin equation, Fokker\u2013Planckequation and cell migration. Bull Math Biol 55:585\u2013608","journal-title":"Bull Math Biol"},{"key":"524_CR115_524","doi-asserted-by":"crossref","first-page":"16539","DOI":"10.1073\/pnas.0507207102","volume":"102","author":"J Xing","year":"2005","unstructured":"Xing J, Liao J-C, Oster G (2005) Making ATP. Proc Natl Acad Sci USA102:16539\u201316546","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR116_524","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1016\/S0006-3495(97)78104-9","volume":"73","author":"TC Elston","year":"1997","unstructured":"Elston TC, Oster G (1997) Protein turbines I: the bacterial flagellarmotor. Biophys J 73:703\u2013721","journal-title":"Biophys J"},{"key":"524_CR117_524","doi-asserted-by":"crossref","first-page":"024102","DOI":"10.1063\/1.2140273","volume":"124","author":"RJ Allen","year":"2006","unstructured":"Allen RJ, Frenkel D, ten Wolde PR (2006) Simulating rare events inequilibrium or nonequilibrium stochastic systems. Chem J Phys 124:024102","journal-title":"Chem J Phys"},{"key":"524_CR118_524","doi-asserted-by":"crossref","first-page":"12784","DOI":"10.1063\/1.1627296","volume":"119","author":"M Rathinam","year":"2003","unstructured":"Rathinam M, Petzold LR, Cao Y, Gillespie DT (2003) Stiffness in stochasticchemically reacting systems: The implicit tau\u2010leaping method. Chem J Phys 119:12784","journal-title":"Chem J Phys"},{"key":"524_CR119_524","doi-asserted-by":"crossref","first-page":"014116","DOI":"10.1063\/1.1824902","volume":"122","author":"Y Cao","year":"2005","unstructured":"Cao Y, Gillespie DT, Petzold LR (2005) The slow-scale stochastic simulationalgorithm. Chem J Phys 122:014116","journal-title":"Chem J Phys"},{"key":"524_CR120_524","doi-asserted-by":"crossref","first-page":"144917","DOI":"10.1063\/1.2052596","volume":"123","author":"Y Cao","year":"2005","unstructured":"Cao Y, Gillespie DT, Petzold LR (2005) Accelerated stochastic simulation ofthe stiff enzyme\u2010substrate reaction. Chem J Phys 123:144917","journal-title":"Chem J Phys"},{"key":"524_CR121_524","doi-asserted-by":"crossref","first-page":"4999","DOI":"10.1063\/1.1545446","volume":"118","author":"CV Rao","year":"2003","unstructured":"Rao CV, Arkin AP (2003) Stochastic chemical kinetics and thequasi\u2010steady\u2010state assumption: Application to the Gillespie algorithm. Chem J Phys 118:4999\u20135010","journal-title":"Chem J Phys"},{"key":"524_CR122_524","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1186\/1471-2105-5-24","volume":"5","author":"D Adalsteinsson","year":"2004","unstructured":"Adalsteinsson D, McMillen D, Elston TC (2004) Biochemical network stochasticsimulator (BioNetS): software for stochastic modeling of biochemical networks. Bioinformatics BMC 5:24","journal-title":"Bioinformatics BMC"},{"key":"524_CR123_524","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1093\/bioinformatics\/btg376","volume":"20","author":"K Vasudeva","year":"2004","unstructured":"Vasudeva K, Bhalla US (2004) Adaptive stochastic\u2010deterministicchemical kinetic simulations. Bioinformatics 20:78\u201384","journal-title":"Bioinformatics"},{"key":"524_CR124_524","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1016\/S0959-440X(02)00378-0","volume":"12","author":"W Baumeister","year":"2002","unstructured":"Baumeister W (2002) Electron tomography: towards visualizing the molecularorganization of the cytoplasm. Curr Opin Struct Biol 12:679\u2013684","journal-title":"Curr Opin Struct Biol"},{"key":"524_CR125_524","first-page":"30","volume":"12","author":"A Gierer","year":"1972","unstructured":"Gierer A, Meinhardt H (1972) A\u00a0theory of biological patternformation. Biol Cyber 12:30\u201339","journal-title":"Biol Cyber"},{"key":"524_CR126_524","doi-asserted-by":"crossref","first-page":"3601","DOI":"10.1039\/a702602a","volume":"93","author":"PK Maini","year":"1997","unstructured":"Maini PK, Painter KJ, Chau HNP (1997) Spatial pattern formation in chemicaland biological systems. Chem J Soc Faraday Trans 93:3601\u20133610","journal-title":"Chem J Soc Faraday Trans"},{"key":"524_CR127_524","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1038\/35101500","volume":"413","author":"JB Gurdon","year":"2001","unstructured":"Gurdon JB, Bourillot P-Y (2001) Morphogen gradient interpretation. Nature413:797\u2013803","journal-title":"Nature"},{"key":"524_CR128_524","doi-asserted-by":"crossref","first-page":"14202","DOI":"10.1073\/pnas.251216598","volume":"98","author":"H Meinhardt","year":"2001","unstructured":"Meinhardt H, de Boer PAJ (2001) Pattern formation in Escherichia coli:A\u00a0model for the pole-to-pole oscillations of Min proteins and the localization of the division site. Proc Natl Acad Sci USA98:14202\u201314207","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR129_524","doi-asserted-by":"crossref","first-page":"128102","DOI":"10.1103\/PhysRevLett.90.128102","volume":"90","author":"M Howard","year":"2003","unstructured":"Howard M, Rutenberg AD (2003) Pattern formation inside bacteria:fluctuations due to the low copy number of proteins. Phys Rev Lett 90:128102","journal-title":"Phys Rev Lett"},{"key":"524_CR130_524","doi-asserted-by":"crossref","first-page":"12724","DOI":"10.1073\/pnas.2135445100","volume":"100","author":"KC Huang","year":"2003","unstructured":"Huang KC, Meir Y, Wingreen NS (2003) Dynamic structures in Escherichia coli:spontaneous formation of MinE rings and MinD polar zones. Proc Natl Acad Sci USA 100:12724\u201312728","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR131_524","doi-asserted-by":"crossref","first-page":"14.11","DOI":"10.1146\/annurev.biochem.75.103004.142652","volume":"76","author":"J Lutkenhaus","year":"2007","unstructured":"Lutkenhaus J (2007) Assembly and dynamics of the bacterial MinCDE system andspatial regulation of the Z ring. Ann Rev Biochem 76:14.11\u201314.24","journal-title":"Ann Rev Biochem"},{"key":"524_CR132_524","first-page":"637","volume":"2","author":"D Fange","year":"2006","unstructured":"Fange D, Elf J (2006) Noise\u2010induced Min phenotypes in E coli. PLoCompS Biol 2:637\u2013648","journal-title":"PLoComp S Biol"},{"key":"524_CR133_524","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1073\/pnas.0505825102","volume":"103","author":"RA Kerr","year":"2006","unstructured":"Kerr RA, Levine H, Sejnowski TJ, Rappel W-J (2006) Division accuracy ina\u00a0stochastic model of Min oscillations in Escherichia coli. Proc Natl Acad Sci USA 103:347\u2013352","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR134_524","doi-asserted-by":"crossref","first-page":"1134","DOI":"10.1529\/biophysj.106.097162","volume":"93","author":"E Cytrynbaum","year":"2007","unstructured":"Cytrynbaum E, Marshall BDL (2007) A\u00a0multi\u2010stranded polymer modelexplains MinDE dynamics in E coli cell division. Biophys J\u00a093:1134\u20131150","journal-title":"Biophys J"},{"key":"524_CR135_524","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1146\/annurev.biophys.27.1.59","volume":"27","author":"D Bray","year":"1998","unstructured":"Bray D (1998) Signaling complexes: biophysical constraints on intracellularcommunication. Annu Rev Biophys Biomol Struct 27:59\u201375","journal-title":"Annu Rev Biophys Biomol Struct"},{"key":"524_CR136_524","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1146\/annurev.biophys.31.101101.140930","volume":"31","author":"BM Slepchenko","year":"2002","unstructured":"Slepchenko BM, Schaff JC, Carson JH, Loew LM (2002) Computational cellbiology: Spatiotemporal simulation of cellular events. Annu Rev Biophys Biomol Struct 31:423\u2013441","journal-title":"Annu Rev Biophys Biomol Struct"},{"key":"524_CR137_524","doi-asserted-by":"crossref","unstructured":"Meyers J, Craig J, Odde DJ (2006) Potential for control of signalingpathways via cell size and shape. Curr Biol 16:1685\u20131693","DOI":"10.1016\/j.cub.2006.07.056"},{"key":"524_CR138_524","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1088\/1478-3975\/2\/3\/002","volume":"2","author":"CV Rao","year":"2005","unstructured":"Rao CV, Kirby JR, Arkin AP (2005) Phosphatase localization in bacterialchemotaxis: divergent mechanisms, convergent principles. Phys Biol 2:148\u2013158","journal-title":"Phys Biol"},{"key":"524_CR139_524","doi-asserted-by":"crossref","first-page":"1582","DOI":"10.1016\/S0006-3495(97)78805-2","volume":"72","author":"N Agmon","year":"1997","unstructured":"Agmon N, Edelstein AL (1997) Collective binding properties of receptorarrays. Biophys J 72:1582\u20131594","journal-title":"Biophys J"},{"key":"524_CR140_524","doi-asserted-by":"crossref","first-page":"1215","DOI":"10.1016\/S0006-3495(98)77836-1","volume":"74","author":"BC Lagerholm","year":"1998","unstructured":"Lagerholm BC, Thompson NL (1998) Theory for ligand rebinding at cellmembrane surfaces. Biophys J 74:1215\u20131228","journal-title":"Biophys J"},{"key":"524_CR141_524","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1088\/1478-3975\/2\/2\/004","volume":"2","author":"SS Andrews","year":"2005","unstructured":"Andrews SS (2005) Serial rebinding of ligands to clustered receptors asexemplified by bacterial chemotaxis. Phys Biol 2:111\u2013122","journal-title":"Phys Biol"},{"key":"524_CR142_524","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1049\/sb:20045021","volume":"1","author":"J Elf","year":"2004","unstructured":"Elf J, Ehrenberg M (2004) Spontaneous separation of bi\u2010stablebiochemical systems into spatial domains of opposite phases. Syst Biol 1:230\u2013236","journal-title":"Syst Biol"},{"key":"524_CR143_524","doi-asserted-by":"crossref","first-page":"234910","DOI":"10.1063\/1.2137716","volume":"123","author":"JS van Zon","year":"2005","unstructured":"van Zon JS, ten Wolde PR (2005) Green's function reaction dynamics:A\u00a0particle\u2010based approach for simulating biochemical networks in time and space. Chem J Phys 123:234910","journal-title":"Chem J Phys"},{"key":"524_CR144_524","volume-title":"Computational Neuroscience: Realistic Modeling for Experimentalists","author":"JR Stiles","year":"2001","unstructured":"Stiles JR, Bartol TM (2001) Monte Carlo methods for simulating realisticsynaptic microphysiology using MCell. In: De Schutter E (ed) Computational Neuroscience: Realistic Modeling for Experimentalists. Press CRC, BocaRaton"},{"key":"524_CR145_524","doi-asserted-by":"crossref","first-page":"2535","DOI":"10.1103\/PhysRevLett.66.2535","volume":"66","author":"D Dab","year":"1991","unstructured":"Dab D, Boon J-P, Li Y-X (1991) Lattice\u2010gas automata for coupledreaction\u2010diffusion equation. Phys Rev Lett 66:2535\u20132539","journal-title":"Phys Rev Lett"},{"key":"524_CR146_524","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1006\/jtbi.1993.1007","volume":"160","author":"GB Ermentrout","year":"1993","unstructured":"Ermentrout GB, Edelstein-Keshet L (1993) Cellular automata approaches tobiological modeling. Theor J Biol 160:97\u2013133","journal-title":"Theor J Biol"},{"key":"524_CR147_524","doi-asserted-by":"crossref","unstructured":"Duke TAJ, LeNov\u00e8re N, Bray D (2001) Conformational spread in a\u00a0ring ofproteins: a\u00a0stochastic approach to allostery. Mol J Biol 308:541\u2013553","DOI":"10.1006\/jmbi.2001.4610"},{"key":"524_CR148_524","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1007\/s00249-004-0391-6","volume":"33","author":"J Goldman","year":"2004","unstructured":"Goldman J, Andrews SS, Bray D (2004) Size and composition of membraneprotein clusters predicted by Monte Carlo analysis. Eur Biophys J 33:506\u2013512","journal-title":"Eur Biophys J"},{"key":"524_CR149_524","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.bpc.2006.04.019","volume":"124","author":"R Grima","year":"2006","unstructured":"Grima R, Schnell S (2006) A\u00a0systematic investigation of the rate lawsvalid in intracellular environments. Biophys Chem 124:1\u201310","journal-title":"Biophys Chem"},{"key":"524_CR150_524","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/S0092-8240(05)80008-4","volume":"52","author":"AM Turing","year":"1990","unstructured":"Turing AM (1990) The chemical basis of morphogenesis. Bull Math Biol52:153\u2013197","journal-title":"Bull Math Biol"},{"key":"524_CR151_524","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1103\/RevModPhys.65.851","volume":"65","author":"MC Cross","year":"1993","unstructured":"Cross MC, Hohenberg PC (1993) Pattern formation outside of equilibrium. RevMod Phys 65:851\u20131123","journal-title":"Rev Mod Phys"},{"key":"524_CR152_524","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1016\/j.tcb.2003.09.002","volume":"13","author":"B Slepchenko","year":"2003","unstructured":"Slepchenko B, Schaff J, Macara I, Loew LM (2003) Quantitative cell biologywith the Virtual Cell. Cell TRENDS Biol 13:570\u2013576","journal-title":"Cell TRENDS Biol"},{"key":"524_CR153_524","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/S0006-3495(00)76281-3","volume":"79","author":"CC Fink","year":"2000","unstructured":"Fink CC, Slepchenko B, Moraru II, Watras J, Schaff JC, Loew LM (2000) Animage-based model of calcium waves in differentiated neuroblastoma cells. Biophys J 79:163\u2013183","journal-title":"Biophys J"},{"key":"524_CR154_524","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1083\/jcb.147.5.929","volume":"147","author":"CC Fink","year":"1999","unstructured":"Fink CC, Slepchenko B, Moraru II, Schaff J, Watras J, Loew LM (1999)Morphological control of inositol-1,4,5-triphosphate\u2010dependent signals. Cell J Biol 147:929\u2013935","journal-title":"Cell J Biol"},{"key":"524_CR155_524","doi-asserted-by":"crossref","first-page":"3790","DOI":"10.1529\/biophysj.105.065771","volume":"89","author":"N Hernjak","year":"2005","unstructured":"Hernjak N, Slepchenko B, Fernald K, Fink CC, Fortin D, Moraru II, Watras J,Loew LM (2005) Modeling and analysis of calcium signaling events leading to long-term depression in cerebellar Purkinje cells. Biophys J89:3790\u20133806","journal-title":"Biophys J"},{"key":"524_CR156_524","doi-asserted-by":"crossref","first-page":"6139","DOI":"10.1103\/PhysRevE.54.6139","volume":"54","author":"F Baras","year":"1996","unstructured":"Baras F, Malek-Mansour M (1996) Reaction\u2010diffusion master equation:A\u00a0comparison with microscopic simulations. Phys Rev E 54:6139\u20136148","journal-title":"Phys Rev E"},{"key":"524_CR157_524","doi-asserted-by":"crossref","unstructured":"Stundzia AB, Lumsden CJ (1996) Stochastic simulation of coupledreaction\u2010diffusion processes. Comput J Phys 127:196\u2013207","DOI":"10.1006\/jcph.1996.0168"},{"key":"524_CR158_524","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1007\/BF01012869","volume":"22","author":"G Nicolis","year":"1980","unstructured":"Nicolis G, Malek-Mansour M (1980) Systematic analysis of the multivariatemaster equation for a\u00a0reaction\u2010diffusion system. Stat J Phys 22:495\u2013512","journal-title":"Stat J Phys"},{"key":"524_CR159_524","doi-asserted-by":"crossref","first-page":"177","DOI":"10.7551\/mitpress\/6604.003.0012","volume-title":"System Modeling in Cell Biology From Concepts to Nuts and Bolts","author":"K Kruse","year":"2006","unstructured":"Kruse K, Elf J (2006) Kinetics in spatially extended systems. In: SzallasiZ, Stelling J, Periwal V (eds) System Modeling in Cell Biology From Concepts to Nuts and Bolts. Press MIT, Cambridge, pp177\u2013198"},{"key":"524_CR160_524","first-page":"171","volume-title":"Theory of Chemical Reaction Dynamics","author":"JT Hynes","year":"1985","unstructured":"Hynes JT (1985) The theory of reactions in solution. In: Baer M (ed) Theoryof Chemical Reaction Dynamics. Press CRC, Boca Raton, pp 171\u2013234"},{"key":"524_CR161_524","doi-asserted-by":"crossref","first-page":"9838","DOI":"10.1021\/ja001572m","volume":"122","author":"B Cohen","year":"2000","unstructured":"Cohen B, Huppert D, Agmon N (2000) Non\u2010exponential Smoluchowskidynamics in fast acid-base reaction. Am J Chem Soc 122:9838\u20139839","journal-title":"Am J Chem Soc"},{"key":"524_CR162_524","doi-asserted-by":"crossref","first-page":"2042","DOI":"10.1021\/ja01613a003","volume":"77","author":"RM Noyes","year":"1955","unstructured":"Noyes RM (1955) Kinetics of competitive processes when reactive fragmentsare produced in pairs. Am J Chem Soc 77:2042\u20132045","journal-title":"Am J Chem Soc"},{"key":"524_CR163_524","doi-asserted-by":"crossref","unstructured":"Pines E, Huppert D (1988) Geminate recombination in excited\u2010stateproton transfer reactions: Numerical solution of the Debye\u2013Smoluchowski equation with backreaction and comparison with experimental results. Chem JPhys 88:5620\u20135630","DOI":"10.1063\/1.454572"},{"key":"524_CR164_524","doi-asserted-by":"crossref","unstructured":"Verkman AS (2002) Solute and macromolecule diffusion in cellular aqueouscompartments. Trends Biochem Sci 27:27\u201333","DOI":"10.1016\/S0968-0004(01)02003-5"},{"key":"524_CR165_524","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.pbiomolbio.2004.01.012","volume":"85","author":"S Schnell","year":"2004","unstructured":"Schnell S, Turner TE (2004) Reaction kinetics in intracellular environmentswith macromolecular crowding: simulations and rate laws. Prog Biophys Mol Biol 85:235\u2013260","journal-title":"Prog Biophys Mol Biol"},{"key":"524_CR166_524","doi-asserted-by":"crossref","unstructured":"Fulton AB (1982) How crowded is the cytoplasm? Cell 30:345\u2013347","DOI":"10.1016\/0092-8674(82)90231-8"},{"key":"524_CR167_524","doi-asserted-by":"crossref","first-page":"041103","DOI":"10.1103\/PhysRevE.71.041103","volume":"71","author":"D Bernstein","year":"2005","unstructured":"Bernstein D (2005) Simulating mesoscopic reaction\u2010diffusion systemsusing the Gillespie algorithm. Phys Rev E 71:041103","journal-title":"Phys Rev E"},{"key":"524_CR168_524","doi-asserted-by":"crossref","unstructured":"Ander M, Beltrao P, Di Ventura B, Ferkinghoff-Borg J, Foglierini M, KaplanA, Lemerle C, Tom\u00e1s-Oliveira I, Serrano L (2004) SmartCell, a\u00a0framework to simulate cellular processes that combines stochastic approximation withdiffusion and localisation: analysis of simple networks. Syst Biol 1:129\u2013138","DOI":"10.1049\/sb:20045017"},{"key":"524_CR169_524","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/BF01309430","volume":"83","author":"T Fricke","year":"1990","unstructured":"Fricke T, Schnakenberg J (1990) Monte-Carlo simulation of an inhomogeneousreaction\u2010diffusion system in the biophysics of receptor cells. Z Phys B 83:277\u2013284","journal-title":"Z Phys B"},{"key":"524_CR170_524","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1137\/040605060","volume":"28","author":"SA Isaacson","year":"2006","unstructured":"Isaacson SA, Peskin CS (2006) Incorporating diffusion in complex geometriesinto stochastic chemical kinetics simulations. Sci SIAMJ Comput 28:47\u201374","journal-title":"Sci SIAMJ Comput"},{"key":"524_CR171_524","doi-asserted-by":"crossref","first-page":"2923","DOI":"10.1093\/bioinformatics\/bti431","volume":"21","author":"J Hattne","year":"2005","unstructured":"Hattne J, Fange D, Elf J (2005) Stochastic reaction\u2010diffusionsimulation with MesoRD. Bioinformatics 21:2923\u20132924","journal-title":"Bioinformatics"},{"key":"524_CR172_524","volume-title":"Understanding molecular simulation: from algorithms to applications","author":"D Frenkel","year":"2002","unstructured":"Frenkel D, Smit B (2002) Understanding molecular simulation: from algorithmsto applications. Academic, San Diego"},{"key":"524_CR173_524","volume-title":"Random Walks in Biology","author":"HC Berg","year":"1993","unstructured":"Berg HC (1993) Random Walks in Biology. Princeton Univ Press,Princeton"},{"key":"524_CR174_524","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1119\/1.18210","volume":"64","author":"DT Gillespie","year":"1996","unstructured":"Gillespie DT (1996) The mathematics of Brownian motion and Johnson noise. AmPhys J 64:225\u2013240","journal-title":"Am Phys J"},{"key":"524_CR175_524","unstructured":"Rice SA (1985) Diffusion Limited Reactions. Elsevier, Amsterdam"},{"key":"524_CR176_524","doi-asserted-by":"crossref","first-page":"1352","DOI":"10.1063\/1.436761","volume":"69","author":"DL Ermak","year":"1978","unstructured":"Ermak DL, McCammon JA (1978) Brownian dynamics with hydrodynamicinteractions. Chem J Phys 69:1352\u20131360","journal-title":"Chem J Phys"},{"key":"524_CR177_524","doi-asserted-by":"crossref","first-page":"1517","DOI":"10.1063\/1.446900","volume":"80","author":"SH Northrup","year":"1984","unstructured":"Northrup SH, Allison SA, McCammon JA (1984) Brownian dynamics simulation ofdiffusion\u2010influenced bimolecular reactions. Chem J Phys 80:1517\u20131524","journal-title":"Chem J Phys"},{"key":"524_CR178_524","doi-asserted-by":"crossref","first-page":"5847","DOI":"10.1021\/j100331a060","volume":"92","author":"SH Northrup","year":"1988","unstructured":"Northrup SH (1988) Diffusion\u2010controlled ligand binding to multiplecompeting cell-bound receptors. Phys J Chem 92:5847\u20135850","journal-title":"Phys J Chem"},{"key":"524_CR179_524","doi-asserted-by":"crossref","first-page":"3338","DOI":"10.1073\/pnas.89.8.3338","volume":"89","author":"SH Northrup","year":"1992","unstructured":"Northrup SH, Erickson HP (1992) Kinetics of protein\u2010proteinassociation explained by Brownian dynamics computer simulation. Proc Natl Acad Sci USA 89:3338\u20133342","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR180_524","doi-asserted-by":"crossref","first-page":"5396","DOI":"10.1063\/1.465983","volume":"99","author":"AL Edelstein","year":"1993","unstructured":"Edelstein AL, Agmon N (1993) Brownian dynamics simulations of reversiblereactions in one dimension. Chem J Phys 99:5396\u20135404","journal-title":"Chem J Phys"},{"key":"524_CR181_524","doi-asserted-by":"crossref","first-page":"3269","DOI":"10.1063\/1.1492282","volume":"117","author":"C Oh","year":"2002","unstructured":"Oh C, Kim H, Shin KJ (2002) Excited\u2010state diffusion\u2010influencedreversible association\u2010dissociation reaction: Brownian dynamics simulation in three dimensions. Chem J Phys117:3269\u20133277","journal-title":"Chem J Phys"},{"key":"524_CR182_524","doi-asserted-by":"crossref","first-page":"1068","DOI":"10.1063\/1.479297","volume":"111","author":"H Kim","year":"1999","unstructured":"Kim H, Yang M, Shin KJ (1999) Dynamic correlation effect in reversiblediffusion\u2010influenced reactions: Brownian dynamics simulation in three dimensions. Chem J Phys 111:1068\u20131075","journal-title":"Chem J Phys"},{"key":"524_CR183_524","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1016\/S0006-3495(95)80258-4","volume":"68","author":"N Agmon","year":"1995","unstructured":"Agmon N, Edelstein A (1995) Geometric and many\u2010particle aspects oftransmitter binding. Biophys J 68:815\u2013825","journal-title":"Biophys J"},{"key":"524_CR184_524","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1006\/jcph.1996.5617","volume":"132","author":"AL Edelstein","year":"1997","unstructured":"Edelstein AL, Agmon N (1997) Brownian simulation of many\u2010particlebinding to a\u00a0reversible receptor array. Comput J Phys 132:260\u2013275","journal-title":"Comput J Phys"},{"key":"524_CR185_524","doi-asserted-by":"crossref","first-page":"5270","DOI":"10.1063\/1.458533","volume":"92","author":"N Agmon","year":"1990","unstructured":"Agmon N, Szabo A (1990) Theory of reversible diffusion\u2010influencedreactions. Chem J Phys 92:5270\u20135284","journal-title":"Chem J Phys"},{"key":"524_CR186_524","doi-asserted-by":"crossref","first-page":"1578","DOI":"10.1103\/PhysRevLett.82.1578","volume":"82","author":"H Kim","year":"1999","unstructured":"Kim H, Shin KJ (1999) Exact solution of the reversiblediffusion\u2010influenced reaction for an isolated pair in three dimensions. Phys Rev Lett 82:1578\u20131581","journal-title":"Phys Rev Lett"},{"key":"524_CR187_524","doi-asserted-by":"crossref","first-page":"128103","DOI":"10.1103\/PhysRevLett.94.128103","volume":"94","author":"JS van Zon","year":"2005","unstructured":"van Zon JS, ten Wolde PR (2005) Simulating biochemical networks at theparticle level in time and space: Green's function reaction dynamics. Phys Rev Lett 94:128103","journal-title":"Phys Rev Lett"},{"key":"524_CR188_524","doi-asserted-by":"crossref","first-page":"4350","DOI":"10.1529\/biophysj.106.086157","volume":"91","author":"JS van Zon","year":"2006","unstructured":"van Zon JS, Morelli MJ, Tanase-Nicola S, ten Wolde PR (2006) Diffusion oftranscription factors can drastically enhance the noise in gene expression. Biophys J 91:4350\u20134367","journal-title":"Biophys J"},{"key":"524_CR189_524","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1371\/journal.pcbi.0020039","volume":"2","author":"K Lipkow","year":"2006","unstructured":"Lipkow K (2006) Changing cellular location of CheZ predicted by molecularsimulations. Comp PLOS Biol 2:301\u2013310","journal-title":"Comp PLOS Biol"},{"key":"524_CR190_524","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1128\/JB.187.1.45-53.2005","volume":"187","author":"K Lipkow","year":"2004","unstructured":"Lipkow K, Andrews SS, Bray D (2004) Simulated diffusion of CheYp through thecytoplasm of E coli. J\u00a0Bact 187:45\u201353","journal-title":"J Bact"},{"key":"524_CR191_524","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1186\/1748-7188-1-25","volume":"1","author":"AL Tournier","year":"2006","unstructured":"Tournier AL, Fitzjohn PW, Bates PA (2006) Probability\u2010based model ofprotein\u2010protein interactions on biological timescales. Algorithms Molec Biol 1:25","journal-title":"Algorithms Molec Biol"},{"key":"524_CR192_524","doi-asserted-by":"crossref","unstructured":"Tolle DP, Le Nov\u00e8re N (2006) Particle\u2010based stochastic simulation insystems biology. Curr Bioinformatics 1:1\u20136","DOI":"10.2174\/157489306777827964"},{"key":"524_CR193_524","doi-asserted-by":"crossref","first-page":"2333","DOI":"10.1016\/S0006-3495(02)75248-X","volume":"83","author":"KM Franks","year":"2002","unstructured":"Franks KM, Bartol TM, Sejnowski TJ (2002) A\u00a0Monte Carlo model revealsindependent signaling at central glutametergic synapses. Biophys J 83:2333\u20132348","journal-title":"Biophys J"},{"key":"524_CR194_524","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1126\/science.1108239","volume":"309","author":"JS Coggan","year":"2005","unstructured":"Coggan JS, Bartol TM, Esquenazi E, Stiles JR, Lamont S, Martone ME, Berg DK,Ellisman MH, Sejnowski TJ (2005) Evidence for ectopic neurotransmission at a\u00a0neuronal synapse. Science 309:446\u2013451","journal-title":"Science"},{"key":"524_CR195_524","doi-asserted-by":"crossref","first-page":"1999","DOI":"10.1529\/biophysj.105.065466","volume":"90","author":"X Koh","year":"2006","unstructured":"Koh X, Srinivasan B, Ching HS, Levchenko A (2006) A\u00a03D Monte Carloanalysis of the role of dyadic space geometry in spark generation. Biophys J 90:1999\u20132014","journal-title":"Biophys J"},{"key":"524_CR196_524","doi-asserted-by":"crossref","first-page":"5747","DOI":"10.1073\/pnas.93.12.5747","volume":"93","author":"JR Stiles","year":"1996","unstructured":"Stiles JR, van Helden D, Thomas J, Bartol M, Salpeter EE, Salpeter MM (1996)Miniature endplate current rise times <\u00a0100\u00a0microseconds from improved dual recordings can be modeled with passive acetylcholine diffusion froma\u00a0synaptic vesicle. Proc Natl Acad Sci USA 93:5747\u20135752","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR197_524","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1016\/S0006-3495(99)76969-9","volume":"77","author":"JR Stiles","year":"1999","unstructured":"Stiles JR, Kovyazina IV, Salpeter EE, Salpeter MM (1999) The temperaturesensitivity of miniature endplate currents is mostly governed by channel gating: Evidence from optimized recordings and Monte Carlo simulations. Biophys J77:1177\u20131187","journal-title":"Biophys J"},{"key":"524_CR198_524","doi-asserted-by":"crossref","unstructured":"Bartol TMJ, Land BR, Salpeter EE, Salpeter MM (1991) Monte Carlo simulationof miniature endplate current generation in the vertebrate neuromuscular junction. Biophys J 59:1290\u20131307","DOI":"10.1016\/S0006-3495(91)82344-X"},{"key":"524_CR199_524","doi-asserted-by":"crossref","first-page":"278102","DOI":"10.1103\/PhysRevLett.87.278102","volume":"87","author":"M Howard","year":"2001","unstructured":"Howard M, Rutenberg AD, de Vet S (2001) Dynamic compartmentalization ofbacteria: accurate division in E coli. Phys Rev Lett 87:278102","journal-title":"Phys Rev Lett"},{"key":"524_CR200_524","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1016\/S0006-3495(02)75426-X","volume":"82","author":"K Kruse","year":"2002","unstructured":"Kruse K (2002) A\u00a0dynamic model for determining the middle ofEscherichia coli. Biophys J 82:618\u2013627","journal-title":"Biophys J"},{"key":"524_CR201_524","doi-asserted-by":"crossref","first-page":"R3075","DOI":"10.1103\/PhysRevE.54.R3075","volume":"54","author":"HS Wio","year":"1996","unstructured":"Wio HS (1996) Stochastic resonance in a\u00a0spatially extended system. PhysRev E 54:R3075\u2013R3078","journal-title":"Phys Rev E"},{"key":"524_CR202_524","doi-asserted-by":"crossref","first-page":"6761","DOI":"10.1073\/pnas.102059099","volume":"99","author":"Z Hu","year":"2002","unstructured":"Hu Z, Gogol EP, Lutkenhaus J (2002) Dynamic assembly of MinD on phospholipidvesicles regulated by ATP and MinE. Proc Natl Acad Sci USA 99:6761\u20136766","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR203_524","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1128\/JB.185.1.196-203.2003","volume":"185","author":"Z Hu","year":"2003","unstructured":"Hu Z, Saez C, Lutkenhaus J (2003) Recruitment of MinC, an\u00a0inhibitor ofZ-ring formation, to the membrane in Escherichia coli: role of MinD and MinE. J\u00a0Bact 185:196\u2013203","journal-title":"J Bact"},{"key":"524_CR204_524","doi-asserted-by":"crossref","first-page":"3347","DOI":"10.1093\/emboj\/cdf323","volume":"21","author":"Y-L Shih","year":"2002","unstructured":"Shih Y-L, Fu X, King GF, Le T, Rothfield L (2002) Division site placement inE coli: mutations that prevent formation of the MinE ring lead to loss of the normal midcell arrest of growth of polar MinD membrane domains. EMBOJ21:3347\u20133357","journal-title":"EMBOJ"},{"key":"524_CR205_524","doi-asserted-by":"crossref","first-page":"7865","DOI":"10.1073\/pnas.1232225100","volume":"100","author":"Y-L Shih","year":"2003","unstructured":"Shih Y-L, Le T, Rothfield L (2003) Division site selection in Escherichia coli involves dynamic redistribution of Min proteins within coiled structures that extend between the two cellpoles. Proc Natl Acad Sci USA 100:7865\u20137870","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR206_524","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1111\/j.1365-2958.2005.04841.x","volume":"58","author":"Y-L Shih","year":"2005","unstructured":"Shih Y-L, Kawagishi I, Rothfield L (2005) The MreB and Mincytoskeletal\u2010like systems play independent roles in prokaryotic polar differentiation. Mol Microbiol 58:917\u2013928","journal-title":"Mol Microbiol"},{"key":"524_CR207_524","doi-asserted-by":"crossref","first-page":"16776","DOI":"10.1073\/pnas.262671699","volume":"99","author":"K Suefuji","year":"2002","unstructured":"Suefuji K, Valluzzi R, RayChaudhuri D (2002) Dynamic assembly of MinD intofilament bundles modulated by ATP, phospholipids, and MinE. Proc Natl Acad Sci USA 99:16776\u201316781","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR208_524","doi-asserted-by":"crossref","first-page":"021904","DOI":"10.1103\/PhysRevE.73.021904","volume":"73","author":"N Pavin","year":"2006","unstructured":"Pavin N, Paljetak C, Krstic V (2006) Min\u2010protein oscillations inEscherichia coli with spontaneous formation of two\u2010stranded filaments in a\u00a0three\u2010dimensional stochastic reaction\u2010diffusionmodel. Phys Rev E 73:021904","journal-title":"Phys Rev E"},{"key":"524_CR209_524","unstructured":"Adelman JL, Andrews SS (2004) Intracellular pattern formation:A\u00a0spatial stochastic model of bacterial division site selection proteins MinProc CDE. Complex Systems Summer School Final Project Papers, Santa Fe Institute, Santa Fe"},{"key":"524_CR210_524","doi-asserted-by":"crossref","first-page":"6114","DOI":"10.1073\/pnas.0502037102","volume":"102","author":"DA Drew","year":"2005","unstructured":"Drew DA, Osborn MJ, Rothfield LI (2005)A\u00a0polymerization\u2010depolymerization model that accurately generates the self\u2010sustained oscillatory system involved in bacterial divisionsite placement. Proc Natl Acad Sci USA 102:6114\u20136118","journal-title":"Proc Natl Acad Sci USA"},{"key":"524_CR211_524","doi-asserted-by":"crossref","first-page":"1872","DOI":"10.1529\/biophysj.106.102343","volume":"93","author":"SS Andrews","year":"2007","unstructured":"Andrews SS, Arkin AP (2007) A\u00a0mechanical explanation for cytoskeletalrings and helices in bacteria. Biophys J\u00a093:1872\u20131884","journal-title":"Biophys J"},{"key":"524_CR212_524","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1038\/35073068","volume":"2","author":"J Lippincott-Schwartz","year":"2001","unstructured":"Lippincott-Schwartz J, Snapp E, Kenworthy A (2001) Studying protein dynamics in living cells. Nat Rev Mol Cell Biol 2:444\u2013456","journal-title":"Nat Rev Mol Cell Biol"}],"container-title":["Encyclopedia of Complexity and Systems Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-0-387-30440-3_524","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,22]],"date-time":"2024-08-22T05:30:22Z","timestamp":1724304622000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-0-387-30440-3_524"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9780387758886","9780387304403"],"references-count":212,"URL":"https:\/\/doi.org\/10.1007\/978-0-387-30440-3_524","relation":{},"subject":[],"published":{"date-parts":[[2009]]}}}