{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T09:23:38Z","timestamp":1781947418523,"version":"3.54.5"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"S4","content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Syst Biol"],"published-print":{"date-parts":[[2013,10]]},"DOI":"10.1186\/1752-0509-7-s4-s14","type":"journal-article","created":{"date-parts":[[2013,10,24]],"date-time":"2013-10-24T09:05:29Z","timestamp":1382605529000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Stochastic modelling of biochemical systems of multi-step reactions using a simplified two-variable model"],"prefix":"10.1186","volume":"7","author":[{"given":"Qianqian","family":"Wu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kate","family":"Smith-Miles","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tianshou","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tianhai","family":"Tian","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2013,10,23]]},"reference":[{"issue":"5900","key":"1184_CR1","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1126\/science.1166154","volume":"322","author":"J Lewis","year":"2008","unstructured":"Lewis J: From Signals to Patterns: Space, Time, and Mathematics in Developmental Biology. Science. 2008, 322 (5900): 399-403. 10.1126\/science.1166154. [http:\/\/www.sciencemag.org\/content\/322\/5900\/399.abstract] 10.1126\/science.1166154","journal-title":"Science"},{"issue":"5","key":"1184_CR2","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1038\/nrg2098","volume":"8","author":"CJ Tomlin","year":"2007","unstructured":"Tomlin CJ, Axelrod JD: Biology by numbers: mathematical modelling in developmental biology. Nat Rev Genet. 2007, 8 (5): 331-340. 10.1038\/nrg2098. [http:\/\/dx.doi.org\/10.1038\/nrg2098] 10.1038\/nrg2098","journal-title":"Nat Rev Genet"},{"issue":"48","key":"1184_CR3","doi-asserted-by":"publisher","first-page":"13600","DOI":"10.1021\/jp073708+","volume":"111","author":"Y Zhou","year":"2007","unstructured":"Zhou Y, Zhuang X: Kinetic Analysis of Sequential Multistep Reactions. The Journal of Physical Chemistry B. 2007, 111 (48): 13600-13610. 10.1021\/jp073708+. [http:\/\/pubs.acs.org\/doi\/abs\/10.1021\/jp073708%2B] 10.1021\/jp073708+","journal-title":"The Journal of Physical Chemistry B"},{"issue":"12","key":"1184_CR4","doi-asserted-by":"publisher","first-page":"A313","DOI":"10.1021\/ed073pA313.2","volume":"73","author":"SE Branz","year":"1996","unstructured":"Branz SE: A Primer to Mechanism in Organic Chemistry (Sykes, Peter). Journal of Chemical Education. 1996, 73 (12): A313-[http:\/\/pubs.acs.org\/doi\/abs\/10.1021\/ed073pA313.2]","journal-title":"Journal of Chemical Education"},{"issue":"3","key":"1184_CR5","doi-asserted-by":"publisher","first-page":"1657","DOI":"10.1529\/biophysj.103.037531","volume":"87","author":"F Qin","year":"2004","unstructured":"Qin F, Li L: Model-Based Fitting of Single-Channel Dwell-Time Distributions. Biophysical Journal. 2004, 87 (3): 1657-1671. 10.1529\/biophysj.103.037531. [http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0006349504736474] 10.1529\/biophysj.103.037531","journal-title":"Biophysical Journal"},{"issue":"16","key":"1184_CR6","doi-asserted-by":"publisher","first-page":"1409","DOI":"10.1016\/S0960-9822(03)00494-9","volume":"13","author":"NA Monk","year":"2003","unstructured":"Monk NA: Oscillatory expression of Hes1, p53, and NF-kappaB driven by transcriptional time delays. Current Biology. 2003, 13 (16): 1409-1413. 10.1016\/S0960-9822(03)00494-9. [http:\/\/view.ncbi.nlm.nih.gov\/pubmed\/12932324] 10.1016\/S0960-9822(03)00494-9","journal-title":"Current Biology"},{"issue":"4","key":"1184_CR7","doi-asserted-by":"publisher","first-page":"725","DOI":"10.1016\/j.jtbi.2007.01.021","volume":"246","author":"R Zhu","year":"2007","unstructured":"Zhu R, Ribeiro AS, Salahub D, Kauffman SA: Studying genetic regulatory networks at the molecular level: Delayed reaction stochastic models. Journal of Theoretical Biology. 2007, 246 (4): 725-745. 10.1016\/j.jtbi.2007.01.021. [http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0022519307000513] 10.1016\/j.jtbi.2007.01.021","journal-title":"Journal of Theoretical Biology"},{"issue":"40","key":"1184_CR8","doi-asserted-by":"publisher","first-page":"14266","DOI":"10.1073\/pnas.0501352102","volume":"102","author":"L Ma","year":"2005","unstructured":"Ma L, Wagner J, Rice JJ, Hu W, Levine AJ, Stolovitzky GA: A plausible model for the digital response of p53 to DNA damage. Proc Natl Acad Sci USA. 2005, 102 (40): 14266-71. 10.1073\/pnas.0501352102. [http:\/\/www.biomedsearch.com\/nih\/plausible-model-digital-response-p53\/16186499.html] 10.1073\/pnas.0501352102","journal-title":"Proc Natl Acad Sci USA"},{"issue":"4","key":"1184_CR9","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1093\/bib\/bbm033","volume":"8","author":"K Burrage","year":"2007","unstructured":"Burrage K, Hancock J, Leier A, Jr DN: Modelling and simulation techniques for membrane biology. Briefings in Bioinformatics. 2007, 8 (4): 234-244. 10.1093\/bib\/bbm033. [http:\/\/eprints.qut.edu.au\/44378\/] 10.1093\/bib\/bbm033","journal-title":"Briefings in Bioinformatics"},{"issue":"6","key":"1184_CR10","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1038\/nrg1615","volume":"6","author":"M Kaern","year":"2005","unstructured":"Kaern M, Elston T, Blake W, Collins J: Stochasticity in gene expression: from theories to phenotypes. Nat Rev Genet. 2005, 6 (6): 451-64. 10.1038\/nrg1615.","journal-title":"Nat Rev Genet"},{"issue":"2","key":"1184_CR11","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1038\/nrg2509","volume":"10","author":"D Wilkinson","year":"2009","unstructured":"Wilkinson D: Stochastic modelling for quantitative description of heterogeneous biological systems. Nat Rev Genet. 2009, 10 (2): 122-33. 10.1038\/nrg2509.","journal-title":"Nat Rev Genet"},{"issue":"3","key":"1184_CR12","doi-asserted-by":"publisher","first-page":"413","DOI":"10.2307\/3212214","volume":"4","author":"DA McQuarrie","year":"1967","unstructured":"McQuarrie DA: Stochastic Approach to Chemical Kinetics. Journal of Applied Probability. 1967, 4 (3): 413-478. 10.2307\/3212214. [http:\/\/dx.doi.org\/10.2307\/3212214] 10.2307\/3212214","journal-title":"Journal of Applied Probability"},{"key":"1184_CR13","doi-asserted-by":"publisher","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 Statistical Mechanics and its Applications. 1992, 188: 404-425. 10.1016\/0378-4371(92)90283-V.","journal-title":"Physica A Statistical Mechanics and its Applications"},{"issue":"25","key":"1184_CR14","doi-asserted-by":"publisher","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): 2340-2361. 10.1021\/j100540a008. [http:\/\/pubs.acs.org\/doi\/abs\/10.1021\/j100540a008] 10.1021\/j100540a008","journal-title":"J Phys Chem"},{"issue":"41","key":"1184_CR15","doi-asserted-by":"publisher","first-page":"14593","DOI":"10.1073\/pnas.0503858102","volume":"102","author":"D Bratsun","year":"2005","unstructured":"Bratsun D, Volfson D, Tsimring LS, Hasty J: Delay-induced stochastic oscillations in gene regulation. Proceedings of the National Academy of Sciences of the United States of America. 2005, 102 (41): 14593-14598. 10.1073\/pnas.0503858102. [http:\/\/www.pnas.org\/content\/102\/41\/14593.abstract] 10.1073\/pnas.0503858102","journal-title":"Proceedings of the National Academy of Sciences of the United States of America"},{"key":"1184_CR16","volume-title":"Oscillatory Regulation of Hes1: Discrete Stochastic Delay Modelling and Simulation","author":"M Barrio","year":"2006","unstructured":"Barrio M, Burrage K, Leier A, Tian T: Oscillatory Regulation of Hes1: Discrete Stochastic Delay Modelling and Simulation. PLoS Computational Biology. 2006, 2 (9): [http:\/\/www.ploscompbiol.org\/article\/info%3Adoi%2F10.1371%2Fjournal.pcbi.0020117]"},{"issue":"4","key":"1184_CR17","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1088\/1478-3975\/3\/4\/005","volume":"3","author":"M Roussel","year":"2006","unstructured":"Roussel M, Zhu R: Validation of an algorithm for delay stochastic simulation of transcription and translation in prokaryotic gene expression. Phys Biol. 2006, 3 (4): 274-84. 10.1088\/1478-3975\/3\/4\/005.","journal-title":"Phys Biol"},{"issue":"2","key":"1184_CR18","doi-asserted-by":"publisher","first-page":"696","DOI":"10.1016\/j.cam.2006.02.063","volume":"205","author":"T Tian","year":"2007","unstructured":"Tian T, Burrage K, Burrage PM, Carletti M: Stochastic delay differential equations for genetic regulatory networks. Journal of Computational and Applied Mathematics. 2007, 205 (2): 696-707. 10.1016\/j.cam.2006.02.063. [http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0377042706003943] 10.1016\/j.cam.2006.02.063","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"1184_CR19","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1007\/s00285-008-0178-y","volume":"57","author":"R Schlicht","year":"2008","unstructured":"Schlicht R, Winkler G: A delay stochastic process with applications in molecular biology. Journal of Mathematical Biology. 2008, 57: 613-648. 10.1007\/s00285-008-0178-y. [http:\/\/dx.doi.org\/10.1007\/s00285-008-0178-y] 10.1007\/s00285-008-0178-y","journal-title":"Journal of Mathematical Biology"},{"issue":"5","key":"1184_CR20","doi-asserted-by":"publisher","first-page":"e1000390","DOI":"10.1371\/journal.pcbi.1000390","volume":"5","author":"S Agrawal","year":"2009","unstructured":"Agrawal S, Archer C, Schaffer DV: Computational Models of the Notch Network Elucidate Mechanisms of Context-dependent Signaling. PLoS Comput Biol. 2009, 5 (5): e1000390-10.1371\/journal.pcbi.1000390. [http:\/\/dx.doi.org\/10.1371%2Fjournal.pcbi.1000390] 10.1371\/journal.pcbi.1000390","journal-title":"PLoS Comput Biol"},{"key":"1184_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1752-0509-4-19","volume":"4","author":"T Marquez-Lago","year":"2010","unstructured":"Marquez-Lago T, Leier A, Burrage K: Probability distributed time delays: integrating spatial effects into temporal models. BMC Systems Biology. 2010, 4: 1-16. 10.1186\/1752-0509-4-1. [http:\/\/eprints.qut.edu.au\/42737\/] 10.1186\/1752-0509-4-1","journal-title":"BMC Systems Biology"},{"issue":"9","key":"1184_CR22","doi-asserted-by":"publisher","first-page":"1742","DOI":"10.1016\/j.bpj.2010.01.018","volume":"98","author":"T Marquez-Lago","year":"2010","unstructured":"Marquez-Lago T, Stelling J: Counter-intuitive stochastic behavior of simple gene circuits with negative feedback. Biophys J. 2010, 98 (9): 1742-50. 10.1016\/j.bpj.2010.01.018.","journal-title":"Biophys J"},{"issue":"20","key":"1184_CR23","doi-asserted-by":"publisher","first-page":"205107","DOI":"10.1063\/1.2919124","volume":"128","author":"A Leier","year":"2008","unstructured":"Leier A, Marquez-Lago T, Burrage K: Generalized binomial tau-leap method for biochemical kinetics incorporating both delay and intrinsic noise. J Chem Phys. 2008, 128 (20): 205107-10.1063\/1.2919124.","journal-title":"J Chem Phys"},{"key":"1184_CR24","volume-title":"Brief Bioinform","author":"J Pahle","year":"2009","unstructured":"Pahle J: Biochemical simulations: stochastic, approximate stochastic and hybrid approaches. Brief Bioinform. 2009"},{"issue":"16","key":"1184_CR25","doi-asserted-by":"publisher","first-page":"5908","DOI":"10.1016\/j.jcp.2009.05.004","volume":"228","author":"B Bayati","year":"2009","unstructured":"Bayati B, Chatelain P, Koumoutsakos P: D-leaping: Accelerating stochastic simulation algorithms for reactions with delays. Journal of Computational Physics. 2009, 228 (16): 5908-5916. 10.1016\/j.jcp.2009.05.004. [http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0021999109002435] 10.1016\/j.jcp.2009.05.004","journal-title":"Journal of Computational Physics"},{"key":"1184_CR26","volume-title":"Annu Rev Phys Chem","author":"D Gillespie","year":"2007","unstructured":"Gillespie D: Stochastic simulation of chemical kinetics. Annu Rev Phys Chem. 2007, 58:"},{"key":"1184_CR27","volume-title":"The Origins of Time-Delay in Template Biopolymerization Processes","author":"L Mier-y Ter\u00e1n-Romero","year":"2010","unstructured":"Mier-y Ter\u00e1n-Romero L, Silber M, Hatzimanikatis V: The Origins of Time-Delay in Template Biopolymerization Processes. PLoS Computational Biology. 2010, 6 (4): [http:\/\/www.ploscompbiol.org\/article\/info%3Adoi%2F10.1371%2Fjournal.pcbi.1000726]"},{"key":"1184_CR28","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1186\/1752-0509-6-39","volume":"6","author":"P Thomas","year":"2012","unstructured":"Thomas P, Straube A, Grima R: The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions. BMC Syst Biol. 2012, 6: 39-10.1186\/1752-0509-6-39.","journal-title":"BMC Syst Biol"},{"issue":"15","key":"1184_CR29","doi-asserted-by":"publisher","first-page":"154109","DOI":"10.1063\/1.3580292","volume":"134","author":"R Srivastava","year":"2011","unstructured":"Srivastava R, Haseltine EL, Mastny E, Rawlings JB: The stochastic quasi-steady-state assumption: reducing the model but not the noise. J Chem Phys. 2011, 134 (15): 154109-10.1063\/1.3580292. [http:\/\/www.biomedsearch.com\/nih\/stochasticquasi-steady-state-assumption\/21513377.html] 10.1063\/1.3580292","journal-title":"J Chem Phys"},{"key":"1184_CR30","doi-asserted-by":"publisher","first-page":"e52029","DOI":"10.1371\/journal.pone.0052029","volume":"8","author":"T Tian","year":"2013","unstructured":"Tian T: Chemical memory reactions induced bursting dynamics in gene expression. PLoS One. 2013, 8: e52029-10.1371\/journal.pone.0052029.","journal-title":"PLoS One"},{"issue":"3","key":"1184_CR31","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1016\/S0955-0674(00)00214-3","volume":"13","author":"P Mitchell","year":"2001","unstructured":"Mitchell P, Tollervey D: mRNA turnover. Current Opinion in Cell Biology. 2001, 13 (3): 320-325. 10.1016\/S0955-0674(00)00214-3. [http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0955067400002143] 10.1016\/S0955-0674(00)00214-3","journal-title":"Current Opinion in Cell Biology"},{"issue":"2","key":"1184_CR32","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1038\/nrm2104","volume":"8","author":"NL Garneau","year":"2007","unstructured":"Garneau NL, Wilusz J, Wilusz CJ: The highways and byways of mRNA decay. Nat Rev Mol Cell Biol. 2007, 8 (2): 113-126. 10.1038\/nrm2104. [http:\/\/dx.doi.org\/10.1038\/nrm2104] 10.1038\/nrm2104","journal-title":"Nat Rev Mol Cell Biol"},{"issue":"3","key":"1184_CR33","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1038\/sj.emboj.7601977","volume":"2","author":"AB Shyu","year":"2008","unstructured":"Shyu AB, Wilkinson MF, van Hoof A: Messenger RNA regulation: to translate or to degrade. EMBO J. 2008, 2 (3): 471-478. [http:\/\/www.nature.com\/emboj\/journal\/v27\/n3\/full\/7601977a.html]","journal-title":"EMBO J"},{"issue":"8","key":"1184_CR34","doi-asserted-by":"publisher","first-page":"R285","DOI":"10.1016\/S0960-9822(02)00802-3","volume":"12","author":"A van Hoof","year":"2002","unstructured":"van Hoof A, Parker R: Messenger RNA Degradation: Beginning at the End. Current Biology. 2002, 12 (8): R285-R287. 10.1016\/S0960-9822(02)00802-3. [http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0960982202008023] 10.1016\/S0960-9822(02)00802-3","journal-title":"Current Biology"},{"issue":"9","key":"1184_CR35","doi-asserted-by":"publisher","first-page":"1192","DOI":"10.1017\/S1355838201010330","volume":"7","author":"D Cao","year":"2001","unstructured":"Cao D, Parker R: Computational modeling of eukaryotic mRNA turnover. RNA. 2001, 7 (9): 1192-1212. 10.1017\/S1355838201010330. [http:\/\/rnajournal.cshlp.org\/content\/7\/9\/1192.abstract] 10.1017\/S1355838201010330","journal-title":"RNA"},{"issue":"4","key":"1184_CR36","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1016\/S0092-8674(03)00353-2","volume":"113","author":"D Cao","year":"2003","unstructured":"Cao D, Parker R: Computational Modeling and Experimental Analysis of Nonsense-Mediated Decay in Yeast. Cell. 2003, 113 (4): 533-545. 10.1016\/S0092-8674(03)00353-2. [http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0092867403003532] 10.1016\/S0092-8674(03)00353-2","journal-title":"Cell"},{"key":"1184_CR37","volume-title":"International Journal of Data Mining and Bioinformatics","author":"T Tian","year":"2012","unstructured":"Tian T: Simplified stochastic models with time delay for studying the degradation process of mRNA molecules. International Journal of Data Mining and Bioinformatics. 2012,"},{"key":"1184_CR38","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/BIBM.2012.6392681","volume-title":"Bioinformatics and Biomedicine (BIBM), 2012 IEEE International Conference on","author":"Q Wu","year":"2012","unstructured":"Wu Q, Smith-Miles K, Tian T: A two-variable model for stochastic modelling of chemical events with multi-step reactions. Bioinformatics and Biomedicine (BIBM), 2012 IEEE International Conference on. 2012, 1-6. 10.1109\/BIBM.2012.6392681."},{"issue":"7","key":"1184_CR39","doi-asserted-by":"publisher","first-page":"1473","DOI":"10.1016\/j.cell.2011.12.005","volume":"147","author":"A Bregman","year":"2011","unstructured":"Bregman A, Avraham-Kelbert M, Barkai O, Duek L, Guterman A, Choder M: Promoter elements regulate cytoplasmic mRNA decay. Cell. 2011, 147 (7): 1473-83. 10.1016\/j.cell.2011.12.005.","journal-title":"Cell"},{"issue":"7","key":"1184_CR40","doi-asserted-by":"publisher","first-page":"1484","DOI":"10.1016\/j.cell.2011.11.051","volume":"147","author":"T Trcek","year":"2011","unstructured":"Trcek T, Larson DR, Mold\u00f3n A, Query CC, Singer RH: Single-Molecule mRNA Decay Measurements Reveal Promoter- Regulated mRNA Stability in Yeast. Cell. 2011, 147 (7): 1484-1497. 10.1016\/j.cell.2011.11.051. [http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0092867411014450] 10.1016\/j.cell.2011.11.051","journal-title":"Cell"},{"key":"1184_CR41","doi-asserted-by":"publisher","first-page":"1716","DOI":"10.1063\/1.1378322","volume":"115","author":"DT Gillespie","year":"2001","unstructured":"Gillespie DT: Approximate accelerated stochastic simulation of chemically reacting systems. J Chem Phys. 2001, 115: 1716-1733. 10.1063\/1.1378322.","journal-title":"J Chem Phys"}],"container-title":["BMC Systems Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1752-0509-7-S4-S14.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,2]],"date-time":"2021-09-02T01:52:47Z","timestamp":1630547567000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcsystbiol.biomedcentral.com\/articles\/10.1186\/1752-0509-7-S4-S14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10]]},"references-count":41,"journal-issue":{"issue":"S4","published-print":{"date-parts":[[2013,10]]}},"alternative-id":["1184"],"URL":"https:\/\/doi.org\/10.1186\/1752-0509-7-s4-s14","relation":{},"ISSN":["1752-0509"],"issn-type":[{"value":"1752-0509","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,10]]},"assertion":[{"value":"23 October 2013","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"S14"}}