{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T08:20:10Z","timestamp":1765268410810,"version":"3.37.3"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"S3","content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Syst Biol"],"published-print":{"date-parts":[[2017,3]]},"DOI":"10.1186\/s12918-017-0401-9","type":"journal-article","created":{"date-parts":[[2017,3,14]],"date-time":"2017-03-14T05:53:47Z","timestamp":1489470827000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics"],"prefix":"10.1186","volume":"11","author":[{"given":"Minghan","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fei","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuo","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Young","family":"Cao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,3,14]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"McAdams H, Arkin A. Stochastic mechanisms in gene expression. Proc Natl Acad Sci. 1997; 94(3):814\u20139. http:\/\/www.pnas.org\/content\/94\/3\/814 .","key":"401_CR1","DOI":"10.1073\/pnas.94.3.814"},{"doi-asserted-by":"crossref","unstructured":"Fedoroff N, Fontana W. Small numbers of big molecules. Science. 2002; 297(5584):1129\u201331. http:\/\/www.sciencemag.org\/content\/297\/5584\/1129 .","key":"401_CR2","DOI":"10.1126\/science.1075988"},{"doi-asserted-by":"crossref","unstructured":"Samoilov M, Plyasunov S, Arkin AP. Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations. Proc Natl Acad Sci U S A. 2005; 102(7):2310\u20135. http:\/\/www.pnas.org\/content\/102\/7\/2310 .","key":"401_CR3","DOI":"10.1073\/pnas.0406841102"},{"issue":"4","key":"401_CR4","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/0021-9991(76)90041-3","volume":"22","author":"DT Gillespie","year":"1976","unstructured":"Gillespie DT. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comput Phys. 1976; 22(4):403\u201334.","journal-title":"J Comput Phys"},{"issue":"25","key":"401_CR5","doi-asserted-by":"crossref","first-page":"2340","DOI":"10.1021\/j100540a008","volume":"81","author":"DT Gillespie","year":"1977","unstructured":"Gillespie DT. Exact stochastic simulation of coupled chemical reactions. J Phys Chem. 1977; 81(25):2340\u201361.","journal-title":"J Phys Chem"},{"key":"401_CR6","first-page":"333","volume":"49","author":"L Michaelis","year":"1913","unstructured":"Michaelis L, Menten ML. Die Kinetik der Invertinwirkung. Biochem Z. 1913; 49:333\u201369.","journal-title":"Biochem Z"},{"issue":"Suppl","key":"401_CR7","first-page":"iv","volume":"40","author":"AV Hill","year":"1910","unstructured":"Hill AV. The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J Physiol. 1910; 40(Suppl):iv\u2013vii.","journal-title":"J Physiol"},{"issue":"12","key":"401_CR8","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. Stochastic reaction-diffusion simulation with MesoRD. Bioinformatics. 2005; 21(12):2923\u20134.","journal-title":"Bioinformatics"},{"key":"401_CR9","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. Stochastic simulation of chemical reactions with spatial resolution and single molecule detail. Phys Biol. 2004; 1:137\u201351.","journal-title":"Phys Biol"},{"doi-asserted-by":"crossref","unstructured":"van Zon JS, ten Wolde PR. Green\u2019s-function reaction dynamics: A particle-based approach for simulating biochemical networks in time and space. J Chem Phys. 2005; 123(23):234910. http:\/\/scitation.aip.org\/content\/aip\/journal\/jcp\/123\/23\/10.1063\/1.2137716 .","key":"401_CR10","DOI":"10.1063\/1.2137716"},{"key":"401_CR11","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1093\/bioinformatics\/17.6.575","volume":"17","author":"NL Nov\u00e8re","year":"2001","unstructured":"Nov\u00e8re NL, Shimizu TS. StochSim: modelling of stochastic biomolecular processes. Bioinformatics. 2001; 17:575\u20136.","journal-title":"Bioinformatics"},{"doi-asserted-by":"crossref","unstructured":"von Smoluchowski M. Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen. Annalen der Physik. 1906; 326(14):756\u201380. http:\/\/dx.doi.org\/10.1002\/andp.19063261405 .","key":"401_CR12","DOI":"10.1002\/andp.19063261405"},{"key":"401_CR13","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/BF01030197","volume":"14","author":"CW Gardiner","year":"1976","unstructured":"Gardiner CW, McNeil KJ, Walls DF, Matheson IS. Correlations in stochastic theories of chemical reactions. J Stat Phys. 1976; 14:307\u201331.","journal-title":"J Stat Phys"},{"key":"401_CR14","volume-title":"Self-organization in nonequilibrium systems : from dissipative structures to order through fluctuations","author":"G Nicolis","year":"1977","unstructured":"Nicolis G, Prigogine I. Self-organization in nonequilibrium systems : from dissipative structures to order through fluctuations. New York: A Wiley-Interscience Publication; 1977. http:\/\/opac.inria.fr\/record=b1078628 ."},{"doi-asserted-by":"crossref","unstructured":"doi M. Stochastic theory of diffusion-controlled reaction. J Phys A Math General. 1976; 9(9):1479. http:\/\/stacks.iop.org\/0305-4470\/9\/i=9\/a=009 .","key":"401_CR15","DOI":"10.1088\/0305-4470\/9\/9\/009"},{"doi-asserted-by":"crossref","unstructured":"Keizer J. Nonequilibrium statistical thermodynamics and the effect of diffusion on chemical reaction rates. J Phys Chem. 1982; 86(26):5052\u201367. http:\/\/dx.doi.org\/10.1021\/j100223a004 .","key":"401_CR16","DOI":"10.1021\/j100223a004"},{"doi-asserted-by":"crossref","unstructured":"Fange D, Berg OG, Sj\u00f6berg P, Elf J. Stochastic reaction-diffusion kinetics in the microscopic limit. Proc Natl Acad Sci. 2010; 107(46):19820\u20135. http:\/\/www.pnas.org\/content\/107\/46\/19820 .","key":"401_CR17","DOI":"10.1073\/pnas.1006565107"},{"doi-asserted-by":"crossref","unstructured":"McQuarrie DA. Stochastic approach to chemical kinetics. J Appl Probab. 1967; 4(3):413\u201378. http:\/\/www.jstor.org\/stable\/3212214 .","key":"401_CR18","DOI":"10.1017\/S002190020002547X"},{"issue":"1\u20133","key":"401_CR19","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. A rigorous derivation of the chemical master equation. Physica A: Stat Mech Appl. 1992; 188(1\u20133):404\u201325.","journal-title":"Physica A: Stat Mech Appl"},{"doi-asserted-by":"crossref","unstructured":"Baras F, Mansour MM. Reaction-diffusion master equation: a comparison with microscopic simulations. Phys Rev E. 1996; 54:6139\u201348. http:\/\/link.aps.org\/doi\/10.1103\/PhysRevE.54.6139 .","key":"401_CR20","DOI":"10.1103\/PhysRevE.54.6139"},{"issue":"1","key":"401_CR21","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1137\/070705039","volume":"70","author":"SA Isaacson","year":"2009","unstructured":"Isaacson SA. The reaction-diffusion master equation as an asymptotic approximation of diffusion to a small target. SIAM J Appl Math. 2009; 70(1):77\u2013111.","journal-title":"SIAM J Appl Math"},{"doi-asserted-by":"crossref","unstructured":"Erban R, Chapman SJ. Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions. Phys Biol. 2009; 6(4):046001. http:\/\/stacks.iop.org\/1478-3975\/6\/i=4\/a=046001 .","key":"401_CR22","DOI":"10.1088\/1478-3975\/6\/4\/046001"},{"doi-asserted-by":"crossref","unstructured":"Hellander S, Hellander A, Petzold L. Reaction-diffusion master equation in the microscopic limit. Phys Rev E. 2012; 85:042901. http:\/\/link.aps.org\/doi\/10.1103\/PhysRevE.85.042901 .","key":"401_CR23","DOI":"10.1103\/PhysRevE.85.042901"},{"doi-asserted-by":"crossref","unstructured":"Li S, Brazhnik P, Sobral B, Tyson JJ. A Quantitative Study of the Division Cycle of Caulobacter crescentus, Stalked Cells. PLoS Comput Biol. 2008; 4(1):e9. http:\/\/dx.plos.org\/10.1371%252Fjournal.pcbi.0040009 .","key":"401_CR24","DOI":"10.1371\/journal.pcbi.0040009"},{"doi-asserted-by":"crossref","unstructured":"Li S, Brazhnik P, Sobral B, Tyson JJ. Temporal controls of the asymmetric cell division cycle in Caulobacter crescentus. PLoS Comput Biol. 2009; 5(8):000463. http:\/\/dx.doi.org\/10.1371%252Fjournal.pcbi.1000463 .","key":"401_CR25","DOI":"10.1371\/journal.pcbi.1000463"},{"doi-asserted-by":"crossref","unstructured":"Subramanian K, Paul MR, Tyson JJ. Potential role of a bistable histidine kinase switch in the asymmetric division cycle of Caulobacter crescentus. PLoS Comput Biol. 2013; 9(9):003221. http:\/\/dx.doi.org\/10.1371%2Fjournal.pcbi.1003221 .","key":"401_CR26","DOI":"10.1371\/journal.pcbi.1003221"},{"issue":"7","key":"401_CR27","doi-asserted-by":"crossref","first-page":"004348","DOI":"10.1371\/journal.pcbi.1004348","volume":"11","author":"K Subramanian","year":"2015","unstructured":"Subramanian K, Paul MR, Tyson JJ. Dynamical localization of DivL and PleC in the asymmetric Division cycle of Caulobacter crescentus: a theoretical investigation of alternative models. PLoS Comput Biol. 2015; 11(7):004348.","journal-title":"PLoS Comput Biol"},{"issue":"2","key":"401_CR28","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1038\/sj.emboj.7600927","volume":"25","author":"J Collier","year":"2006","unstructured":"Collier J, Murray SR, Shapiro L. DnaA couples DNA replication and the expression of two cell cycle master regulators. EMBO J. 2006; 25(2):346\u201356.","journal-title":"EMBO J"},{"issue":"4","key":"401_CR29","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.copbio.2007.07.007","volume":"18","author":"J Collier","year":"2007","unstructured":"Collier J, Shapiro L. Spatial complexity and control of a bacterial cell cycle. Curr Opin Biotechnol. 2007; 18(4):333\u201340. http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0958166907000894 .","journal-title":"Curr Opin Biotechnol"},{"issue":"5673","key":"401_CR30","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1126\/science.1095191","volume":"304","author":"J Holtzendorff","year":"2004","unstructured":"Holtzendorff J, Hung D, Brende P, Reisenauer A, Viollier PH, McAdams HH, et al. Oscillating global regulators control the genetic circuit driving a bacterial cell cycle. Science. 2004; 304(5673):983\u20137. http:\/\/www.sciencemag.org\/content\/304\/5673\/983 .","journal-title":"Science"},{"issue":"1","key":"401_CR31","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1073\/pnas.95.1.120","volume":"95","author":"KC Quon","year":"1998","unstructured":"Quon KC, Yang B, Domian IJ, Shapiro L, Marczynski GT. Negative control of bacterial DNA replication by a cell cycle regulatory protein that binds at the chromosome origin. Proc Natl Acad Sci. 1998; 95(1):120\u20135. http:\/\/www.pnas.org\/content\/95\/1\/120 .","journal-title":"Proc Natl Acad Sci"},{"issue":"3","key":"401_CR32","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/j.cell.2005.12.033","volume":"124","author":"PT McGrath","year":"2006","unstructured":"McGrath PT, Iniesta AA, Ryan KR, Shapiro L, McAdams HH. A dynamically localized protease complex and a polar specificity factor control a cell cycle master regulator. Cell. 2006; 124(3):535\u201347. http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0092867406000663 .","journal-title":"Cell"},{"issue":"19","key":"401_CR33","doi-asserted-by":"crossref","first-page":"5658","DOI":"10.1093\/emboj\/17.19.5658","volume":"17","author":"U Jenal","year":"1998","unstructured":"Jenal U, Fuchs T. An essential protease involved in bacterial cell-cycle control. EMBO J. 1998; 17(19):5658\u201369.","journal-title":"EMBO J"},{"issue":"29","key":"401_CR34","doi-asserted-by":"crossref","first-page":"10935","DOI":"10.1073\/pnas.0604554103","volume":"103","author":"AA Iniesta","year":"2006","unstructured":"Iniesta AA, McGrath PT, Reisenauer A, McAdams HH, Shapiro L. A phospho-signaling pathway controls the localization and activity of a protease complex critical for bacterial cell cycle progression. Proc Natl Acad Sci. 2006; 103(29):10935\u201340. http:\/\/www.pnas.org\/content\/103\/29\/10935 .","journal-title":"Proc Natl Acad Sci"},{"issue":"3","key":"401_CR35","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/j.devcel.2011.01.007","volume":"20","author":"C Tsokos","year":"2011","unstructured":"Tsokos C, Perchuk B, Laub M. A dynamic complex of signaling proteins uses polar localization to regulate cell-fate asymmetry in Caulobacter crescentus. Developmental Cell. 2011; 20(3):329\u201341.","journal-title":"Developmental Cell"},{"issue":"5","key":"401_CR36","doi-asserted-by":"crossref","first-page":"054101","DOI":"10.1063\/1.4816377","volume":"139","author":"SA Isaacson","year":"2013","unstructured":"Isaacson SA. A convergent reaction-diffusion master equation. J Chem Phys. 2013; 139(5):054101. http:\/\/scitation.aip.org\/content\/aip\/journal\/jcp\/139\/5\/10.1063\/1.4816377 .","journal-title":"J Chem Phys"},{"issue":"1","key":"401_CR37","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. The slow-scale stochastic simulation algorithm. J Chem Phys. 2005; 122(1):014116.","journal-title":"J Chem Phys"},{"issue":"15","key":"401_CR38","doi-asserted-by":"crossref","first-page":"6959","DOI":"10.1063\/1.1505860","volume":"117","author":"EL Haseltine","year":"2002","unstructured":"Haseltine EL, Rawlings JB. Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics. J Chem Phys. 2002; 117(15):6959\u201369.","journal-title":"J Chem Phys"},{"key":"401_CR39","first-page":"55","volume":"1","author":"AC Hindmarsh","year":"1983","unstructured":"Hindmarsh AC. ODEPACK, a systematized collection of ODE solvers. IMACS Trans Sci Comput Amsterdam. 1983; 1:55\u201364.","journal-title":"IMACS Trans Sci Comput Amsterdam"},{"unstructured":"Petzold LR. A Description of DASSL: a differential\/algebraic system solver, proceeding of the 1st IMACS World Congress. Montreal. 1982;1:65-68.","key":"401_CR40"}],"container-title":["BMC Systems Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s12918-017-0401-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,25]],"date-time":"2017-06-25T08:34:47Z","timestamp":1498379687000},"score":1,"resource":{"primary":{"URL":"http:\/\/bmcsystbiol.biomedcentral.com\/articles\/10.1186\/s12918-017-0401-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3]]},"references-count":40,"journal-issue":{"issue":"S3","published-print":{"date-parts":[[2017,3]]}},"alternative-id":["401"],"URL":"https:\/\/doi.org\/10.1186\/s12918-017-0401-9","relation":{},"ISSN":["1752-0509"],"issn-type":[{"type":"electronic","value":"1752-0509"}],"subject":[],"published":{"date-parts":[[2017,3]]},"article-number":"21"}}