{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T20:52:24Z","timestamp":1772052744091,"version":"3.50.1"},"reference-count":60,"publisher":"Springer Science and Business Media LLC","issue":"1","content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Syst Biol"],"published-print":{"date-parts":[[2012,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:sec>\n            <jats:title>Background<\/jats:title>\n            <jats:p>Experiments <jats:italic>in silico<\/jats:italic> using stochastic reaction-diffusion models have emerged as an important tool in molecular systems biology. Designing computational software for such applications poses several challenges. Firstly, realistic lattice-based modeling for biological applications requires a consistent way of handling complex geometries, including curved inner- and outer boundaries. Secondly, spatiotemporal stochastic simulations are computationally expensive due to the fast time scales of individual reaction- and diffusion events when compared to the biological phenomena of actual interest. We therefore argue that simulation software needs to be both computationally efficient, employing sophisticated algorithms, yet in the same time flexible in order to meet present and future needs of increasingly complex biological modeling.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Results<\/jats:title>\n            <jats:p>We have developed URDME, a flexible software framework for general stochastic reaction-transport modeling and simulation. URDME uses <jats:bold>U<\/jats:bold> nstructured triangular and tetrahedral meshes to resolve general geometries, and relies on the <jats:bold>R<\/jats:bold> eaction-<jats:bold>D<\/jats:bold> iffusion <jats:bold>M<\/jats:bold> aster <jats:bold>E<\/jats:bold> quation formalism to model the processes under study. An interface to a mature geometry and mesh handling external software (Comsol Multiphysics) provides for a stable and interactive environment for model construction. The core simulation routines are logically separated from the model building interface and written in a low-level language for computational efficiency. The connection to the geometry handling software is realized via a Matlab interface which facilitates script computing, data management, and post-processing. For practitioners, the software therefore behaves much as an interactive Matlab toolbox. At the same time, it is possible to modify and extend URDME with newly developed simulation routines. Since the overall design effectively hides the complexity of managing the geometry and meshes, this means that newly developed methods may be tested in a realistic setting already at an early stage of development.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Conclusions<\/jats:title>\n            <jats:p>In this paper we demonstrate, in a series of examples with high relevance to the molecular systems biology community, that the proposed software framework is a useful tool for both practitioners and developers of spatial stochastic simulation algorithms. Through the combined efforts of algorithm development and improved modeling accuracy, increasingly complex biological models become feasible to study through computational methods. URDME is freely available at <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"http:\/\/www.urdme.org\" ext-link-type=\"uri\">http:\/\/www.urdme.org<\/jats:ext-link>.<\/jats:p>\n          <\/jats:sec>","DOI":"10.1186\/1752-0509-6-76","type":"journal-article","created":{"date-parts":[[2012,9,12]],"date-time":"2012-09-12T00:36:11Z","timestamp":1347410171000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":119,"title":["URDME: a modular framework for stochastic simulation of reaction-transport processes in complex geometries"],"prefix":"10.1186","volume":"6","author":[{"given":"Brian","family":"Drawert","sequence":"first","affiliation":[]},{"given":"Stefan","family":"Engblom","sequence":"additional","affiliation":[]},{"given":"Andreas","family":"Hellander","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,6,22]]},"reference":[{"key":"918_CR1","doi-asserted-by":"publisher","first-page":"8614","DOI":"10.1073\/pnas.151588598","volume":"98","author":"M Thattai","year":"2001","unstructured":"Thattai M, van Oudenaarden A: Intrinsic noise in gene regulatory networks. Proc Natl Acad Sci USA 2001, 98: 8614-8619. 10.1073\/pnas.151588598","journal-title":"Proc Natl Acad Sci USA"},{"issue":"13","key":"918_CR2","doi-asserted-by":"publisher","first-page":"7148","DOI":"10.1073\/pnas.110057697","volume":"97","author":"J Paulsson","year":"2000","unstructured":"Paulsson J, Berg OG, Ehrenberg M: Stochastic focusing: Fluctuation-enhanced sensitivity of intracellular regulation. Proc Natl Acad Sci USA 2000,97(13):7148-7153. . [http:\/\/www.pnas.org\/cgi\/content\/abstract\/97\/13\/7148] []. 10.1073\/pnas.110057697","journal-title":"Proc Natl Acad Sci USA"},{"key":"918_CR3","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1038\/35002258","volume":"403","author":"N Barkai","year":"2000","unstructured":"Barkai N, Leibler S: Circadian clocks limited by noise. Nature 2000, 403: 267-268.","journal-title":"Nature"},{"issue":"20","key":"918_CR4","doi-asserted-by":"publisher","first-page":"12795","DOI":"10.1073\/pnas.162041399","volume":"99","author":"PS Swain","year":"2002","unstructured":"Swain PS, Elowitz MB, Siggia ED: Intrinsic and extrinsic contributions to stochasticity in gene expression. Proc Natl Acad Sci USA 2002,99(20):12795-12800. 10.1073\/pnas.162041399","journal-title":"Proc Natl Acad Sci USA"},{"issue":"5584","key":"918_CR5","doi-asserted-by":"publisher","first-page":"1183","DOI":"10.1126\/science.1070919","volume":"297","author":"MB Elowitz","year":"2002","unstructured":"Elowitz MB, Levine AJ, Siggia ED, Swain PS: Stochastic gene expression in a single cell. Science 2002,297(5584):1183-1186. . [http:\/\/www.sciencemag.org\/cgi\/content\/abstract\/297\/5584\/1183] []. 10.1126\/science.1070919","journal-title":"Science"},{"key":"918_CR6","doi-asserted-by":"publisher","first-page":"2010","DOI":"10.1126\/science.1105891","volume":"309","author":"JM Raser","year":"2005","unstructured":"Raser JM, O\u2019Shea EK: Noise in gene expression: Origins, consequences and control. Science 2005, 309: 2010-2013. 10.1126\/science.1105891","journal-title":"Science"},{"key":"918_CR7","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1016\/0021-9991(76)90041-3","volume":"22","author":"Gillespie DT","year":"1976","unstructured":"Gillespie DT: A general method for numerically simulating the stochastic time evolution of coupled chemical reacting systems. J Comput Phys 1976, 22: 403-434. 10.1016\/0021-9991(76)90041-3","journal-title":"J Comput Phys"},{"issue":"6","key":"918_CR8","doi-asserted-by":"crossref","first-page":"e80","DOI":"10.1371\/journal.pcbi.0020080","volume":"2","author":"D Fange","year":"2006","unstructured":"Fange D, Elf J: Noise induced Min phenotypes in E. coli. PLoS Comput Biol. 2006,2(6):e80.","journal-title":"Noise induced Min phenotypes in E. coli. PLoS Comput Biol"},{"issue":"6","key":"918_CR9","doi-asserted-by":"publisher","first-page":"2473","DOI":"10.1073\/pnas.0906885107","volume":"107","author":"K Takahashi","year":"2010","unstructured":"Takahashi K, T\u0103nase-Nicola S, ten Wolde PR: Spatio-temporal correlations can drastically change the response of a MAPK pathway. Proc Natl Acad Sci USA 2010,107(6):2473-2478. 10.1073\/pnas.0906885107","journal-title":"Proc Natl Acad Sci USA"},{"key":"918_CR10","volume-title":"Stochastic Processes in Physics and Chemistry. 3rd edition","author":"NG van Kampen","year":"2007","unstructured":"van Kampen NG: Stochastic Processes in Physics and Chemistry. 3rd edition. Amsterdam: Elsevier; 2007."},{"key":"918_CR11","volume-title":"Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences 3rd edition","author":"CW Gardiner","year":"2004","unstructured":"Gardiner CW: Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences 3rd edition. Berlin: Springer-Verlag; 2004."},{"key":"918_CR12","doi-asserted-by":"publisher","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: 77-111. 10.1137\/070705039","journal-title":"SIAM J Appl Math"},{"key":"918_CR13","doi-asserted-by":"publisher","first-page":"046001","DOI":"10.1088\/1478-3975\/6\/4\/046001","volume":"6","author":"R Erban","year":"2009","unstructured":"Erban R, Chapman J: Stochastic modelling of reaction-diffusion processes: Algorithms for bimolecular reactions. Phys Biol 2009, 6: 046001. 10.1088\/1478-3975\/6\/4\/046001","journal-title":"Phys Biol"},{"key":"918_CR14","doi-asserted-by":"publisher","first-page":"041103","DOI":"10.1103\/PhysRevE.71.041103","volume":"71","author":"D Bernstein","year":"2005","unstructured":"Bernstein D: Simulating mesoscopic reaction-diffusion systems using the Gillespie algorithm. Phys Rev E 2005, 71: 041103.","journal-title":"Phys Rev E"},{"issue":"2","key":"918_CR15","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1049\/sb:20045021","volume":"1","author":"J Elf","year":"2004","unstructured":"Elf J, Ehrenberg M: Spontaneous Separation of bi-stable biochemical systems into spatial domains of opposite phases. Syst Biol 2004,1(2):230-236. 10.1049\/sb:20045021","journal-title":"Syst Biol"},{"key":"918_CR16","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1006\/jcph.1996.0168","volume":"127","author":"AB Stundzia","year":"1996","unstructured":"Stundzia AB, Lumsden CL: Stochastic simulation of coupled reaction-diffusion processes. J Comput Phys 1996, 127: 196-207. 10.1006\/jcph.1996.0168","journal-title":"J Comput Phys"},{"issue":"10","key":"918_CR17","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1038\/nmeth.1253","volume":"5","author":"A Raj","year":"2008","unstructured":"Raj A, van den Bogaard, Rifkin SA, van Oudenaarden A: Imaging individual mRNA molecules using multiple singly labeled probes. Nat Meth 2008,5(10):877-879. 10.1038\/nmeth.1253","journal-title":"Nat Meth"},{"issue":"5828","key":"918_CR18","doi-asserted-by":"publisher","first-page":"1191","DOI":"10.1126\/science.1141967","volume":"316","author":"J Elf","year":"2007","unstructured":"Elf J, Li GW, Xie XS: Probing Transcription factor dynamics at the single-molecule level in a living cell. Science 2007,316(5828):1191-1194. 10.1126\/science.1141967","journal-title":"Science"},{"issue":"12","key":"918_CR19","doi-asserted-by":"publisher","first-page":"128103","DOI":"10.1103\/PhysRevLett.94.128103","volume":"94","author":"JS van Zon","year":"2005","unstructured":"van Zon JS, ten Wolde RP: Simulating biochemical networks at the particle level and in time and space: green\u2019s function reaction dynamics. Phys Rev Lett 2005,94(12):128103.","journal-title":"Phys Rev Lett"},{"issue":"3","key":"918_CR20","doi-asserted-by":"publisher","first-page":"e1000705","DOI":"10.1371\/journal.pcbi.1000705","volume":"6","author":"SS Andrews","year":"2010","unstructured":"Andrews SS, Addy NJ, Brent R, Arkin AP: Detailed simulations of cell biology with Smoldyn 2.1. PLoS Comput Biol 2010,6(3):e1000705. 10.1371\/journal.pcbi.1000705","journal-title":"PLoS Comput Biol"},{"issue":"6","key":"918_CR21","doi-asserted-by":"publisher","first-page":"3126","DOI":"10.1137\/070692017","volume":"30","author":"RA Kerr","year":"2008","unstructured":"Kerr RA, Bartol TM, Kaminsky B, Dittrich M, Chang JCJ, Baden SB, Sejnowski TJ, Stiles JR: Fast Monte Carlo simulation methods for biological reaction-diffusion systems in solution and on surfaces. SIAM J Sci Comput 2008,30(6):3126-3149. 10.1137\/070692017","journal-title":"SIAM J Sci Comput"},{"key":"918_CR22","volume-title":"STEPS: efficient simulation of stochastic reaction-diffusion models in realistic morphologies","author":"I Hepburn","year":"2012","unstructured":"Hepburn I, Chen W, Wils S, Schutter ED: STEPS: efficient simulation of stochastic reaction-diffusion models in realistic morphologies. BMC Syst Biol 2012.,6(35): . [http:\/\/www.biomedcentral.com\/1752-0509\/6\/36\/abstract] []."},{"issue":"9","key":"918_CR23","doi-asserted-by":"publisher","first-page":"094104","DOI":"10.1063\/1.3074302","volume":"130","author":"S Lampoudi","year":"2009","unstructured":"Lampoudi S, Gillespie DT, Petzold LR: The multinomial simulation algorithm for discrete stochastic simulation of reaction-diffusion systems. J Chem Phys 2009,130(9):094104. . [http:\/\/link.aip.org\/link\/?JCP\/130\/094104\/1] []. 10.1063\/1.3074302","journal-title":"J Chem Phys"},{"key":"918_CR24","doi-asserted-by":"publisher","first-page":"136","DOI":"10.1016\/j.cplett.2007.11.055","volume":"451","author":"D Rossinelli","year":"2008","unstructured":"Rossinelli D, Bayati B, Koumoutsakos P: Accelerated stochastic and hybrid method for spatial simulations of reaction-diffusion systems. Chem Phys Lett 2008, 451: 136-140. 10.1016\/j.cplett.2007.11.055","journal-title":"Chem Phys Lett"},{"issue":"10","key":"918_CR25","doi-asserted-by":"publisher","first-page":"104101","DOI":"10.1063\/1.2771548","volume":"127","author":"TT Marquez-Lago","year":"2007","unstructured":"Marquez-Lago TT, Burrage K: Binomial tau-leap spatial stochastic simulation algorithm for applications in chemical kinetics. J Chem Phys 2007,127(10):104101. . [http:\/\/link.aip.org\/link\/?JCP\/127\/104101\/1] []. 10.1063\/1.2771548","journal-title":"J Chem Phys"},{"key":"918_CR26","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/j.jcp.2010.08.035","volume":"230","author":"B Bayati","year":"2011","unstructured":"Bayati B, Chatelin P, Koumoutsakos P: Adaptive mesh refinement for stochastic reaction-diffusion processes. J Comput Phys 2011, 230: 13-26. 10.1016\/j.jcp.2010.08.035","journal-title":"J Comput Phys"},{"issue":"2","key":"918_CR27","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1016\/j.jcp.2009.09.030","volume":"229","author":"L Ferm","year":"2010","unstructured":"Ferm L, Hellander A, L\u00f6tstedt P: An adaptive algorithm for simulation of stochastic reaction-diffusion processes. J Comput Phys 2010,229(2):343-360. 10.1016\/j.jcp.2009.09.030","journal-title":"J Comput Phys"},{"issue":"12","key":"918_CR28","doi-asserted-by":"publisher","first-page":"2923","DOI":"10.1093\/bioinformatics\/bti431","volume":"21","author":"J Hattne","year":"2005","unstructured":"Hattne J, Fange D, Elf J: Stochastic reaction\u2013diffusion simulation with MesoRD. Bioinformatics 2005,21(12):2923-2924. 10.1093\/bioinformatics\/bti431","journal-title":"Bioinformatics"},{"key":"918_CR29","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1049\/sb:20045017","volume":"1","author":"M Ander","year":"2004","unstructured":"Ander M, Beltrao P, Ventura BD, Ferkinghoff-Borg J, Foglierini M, Lemerle C, Tomas-Oliveira I, Serrano L: SmartCell, a framework to simulate cellular processes that combines stochastic approximation with diffusion and localisation: analysis of simple networks. Syst Biol 2004, 1: 129-138. 10.1049\/sb:20045017","journal-title":"Syst Biol"},{"key":"918_CR30","volume-title":"Tech. Rep. 2011-003, Department of Information Technology","author":"B Drawert","year":"2011","unstructured":"Drawert B, Engblom S, Hellander A: URDME 1.1: User\u2019s manual. In Tech. Rep. 2011-003, Department of Information Technology. Division of Scientific Computing; 2011."},{"key":"918_CR31","unstructured":"Geuzaine C, Remacle JF: Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. . [http:\/\/www.geuz.org\/gmsh\/] []."},{"issue":"7","key":"918_CR32","doi-asserted-by":"publisher","first-page":"074101","DOI":"10.1063\/1.3310809","volume":"132","author":"B Drawert","year":"2010","unstructured":"Drawert B, Lawson MJ, Petzold L, Khammash M: The diffusive finite state projection algorithm for efficient simulation of the stochastic reaction-diffusion master equation. J Chem Phys 2010,132(7):074101. 10.1063\/1.3310809","journal-title":"J Chem Phys"},{"issue":"3","key":"918_CR33","doi-asserted-by":"publisher","first-page":"1774","DOI":"10.1137\/080721388","volume":"31","author":"S Engblom","year":"2009","unstructured":"Engblom S, Ferm L, Hellander A, L\u00f6tstedt P: Simulation of stochastic reaction\u2013diffusion processes on unstructured meshes. SIAM J Sci Comput 2009,31(3):1774-1797. 10.1137\/080721388","journal-title":"SIAM J Sci Comput"},{"issue":"2","key":"918_CR34","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1137\/110832148","volume":"10","author":"A Hellander","year":"2012","unstructured":"Hellander A, Hellander S, L\u00f6tstedt P: Coupled mesoscopic and microscopic simulation of reaction-diffusion processes in mixed dimensions. Multiscale Model Simul 2012,10(2):585-611. 10.1137\/110832148","journal-title":"Multiscale Model Simul"},{"issue":"5","key":"918_CR35","doi-asserted-by":"publisher","first-page":"1691","DOI":"10.1137\/100784709","volume":"8","author":"A Hellander","year":"2010","unstructured":"Hellander A, L\u00f6tstedt P: Incorporating active transport in mesoscopic reaction-transport models inside living cells. Multiscale Model Simul 2010,8(5):1691-1714. 10.1137\/100784709","journal-title":"Multiscale Model Simul"},{"issue":"22","key":"918_CR36","doi-asserted-by":"publisher","first-page":"12724","DOI":"10.1073\/pnas.2135445100","volume":"100","author":"KC Huang","year":"2003","unstructured":"Huang KC, Meir Y, Wingreen NS: Dynamic structures in Escherichia coli: Spontaneous formation of MinE and MinD polar zones. Proc Natl Acad Sci USA 2003,100(22):12724-12728. 10.1073\/pnas.2135445100","journal-title":"Proc Natl Acad Sci USA"},{"issue":"24","key":"918_CR37","doi-asserted-by":"publisher","first-page":"12784","DOI":"10.1063\/1.1627296","volume":"119","author":"M Rathinam","year":"2003","unstructured":"Rathinam M, Petzold L, Cao Y, Gillespie D: Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method. J Chem Phys 2003,119(24):12784-12794. . http:\/\/link.aip.org\/link\/?JCP\/119\/12784\/1] ]. 10.1063\/1.1627296","journal-title":"J Chem Phys"},{"key":"918_CR38","doi-asserted-by":"publisher","first-page":"014116","DOI":"10.1063\/1.1824902","volume":"122","author":"Y Cao","year":"2005","unstructured":"Cao Y, Gillespie D, Petzold L: The slow-scale stochastic simulation algorithm. J Chem Phys 2005, 122: 014116. . http:\/\/link.aip.org\/link\/?JCP\/122\/014116\/1] ]. 10.1063\/1.1824902","journal-title":"J Chem Phys"},{"key":"918_CR39","doi-asserted-by":"publisher","first-page":"3472","DOI":"10.1016\/j.cma.2008.02.024","volume":"197","author":"Y Cao","year":"2008","unstructured":"Cao Y, Petzold L: Slow scale Tau-Leaping method. Comput Meth Appl Mech Eng 2008, 197: 3472-3479. [PCMID:PMC2753989] 10.1016\/j.cma.2008.02.024","journal-title":"Comput Meth Appl Mech Eng"},{"issue":"13","key":"918_CR40","doi-asserted-by":"publisher","first-page":"134112","DOI":"10.1063\/1.3576123","volume":"134","author":"S Wu","year":"2011","unstructured":"Wu S, Fu J, Cao Y, Petzold L: Michaelis\u2013Menten speeds up tau-leaping under a wide range of conditions. J Chem Phys 2011,134(13):134112. . [http:\/\/link.aip.org\/link\/?JCP\/134\/134112\/1] []. 10.1063\/1.3576123","journal-title":"J Chem Phys"},{"key":"918_CR41","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1146\/annurev.ph.58.030196.003415","volume":"58","author":"J Howard","year":"1996","unstructured":"Howard J: The movement of kinesin along microtubules. Annu Rev Physiol 1996, 58: 703-729. 10.1146\/annurev.ph.58.030196.003415","journal-title":"Annu Rev Physiol"},{"key":"918_CR42","doi-asserted-by":"publisher","first-page":"971","DOI":"10.1016\/j.cub.2004.10.046","volume":"14","author":"R Mallik","year":"2004","unstructured":"Mallik R, Gross SP: Molecular motors: strategies to get along. Curr Biol 2004, 14: 971-982. 10.1016\/j.cub.2004.10.046","journal-title":"Curr Biol"},{"key":"918_CR43","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1016\/S0092-8674(03)00111-9","volume":"112","author":"RD Vale","year":"2003","unstructured":"Vale RD: The molecular motor toolbox for intracellular transport. Cell 2003, 112: 467-480. 10.1016\/S0092-8674(03)00111-9","journal-title":"Cell"},{"issue":"27","key":"918_CR44","doi-asserted-by":"publisher","first-page":"7131","DOI":"10.1523\/JNEUROSCI.1801-06.2006","volume":"26","author":"KC Martin","year":"2006","unstructured":"Martin KC, Zukin RS: RNA trafficking and local protein synthesis in dendrites: an overview. J Neurosci 2006,26(27):7131-7134. 10.1523\/JNEUROSCI.1801-06.2006","journal-title":"J Neurosci"},{"key":"918_CR45","doi-asserted-by":"publisher","first-page":"525","DOI":"10.1016\/j.cub.2004.06.045","volume":"14","author":"MA Welte","year":"2004","unstructured":"Welte MA: Bidirectional transport along microtubules. Curr Biol 2004, 14: 525-537. 10.1016\/j.cub.2004.06.045","journal-title":"Curr Biol"},{"key":"918_CR46","first-page":"R478\u2014R486","volume":"17","author":"SP Gross","year":"2007","unstructured":"Gross SP, Vershinin M, Shubeita GT: Cargo transport: two motors are sometimes better than one. Curr Biol 2007, 17: R478\u2014R486.","journal-title":"Curr Biol"},{"issue":"4","key":"918_CR47","doi-asserted-by":"publisher","first-page":"551","DOI":"10.1016\/j.cell.2011.01.021","volume":"144","author":"SE Encalada","year":"2011","unstructured":"Encalada SE, Szpankowski L, Xia Ch, Goldstein LSB: Stable kinesin and dynein assemblies drive the axonal transport of mammalian prion protein vesicles. Cell 2011,144(4):551-565. . http:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0092867411000602] ]. 10.1016\/j.cell.2011.01.021","journal-title":"Cell"},{"key":"918_CR48","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1146\/annurev.neuro.23.1.39","volume":"23","author":"LSB Goldstein","year":"2000","unstructured":"Goldstein LSB, Yang Z: Microtubule-based transport systems in neurons: the roles of kinesins and dyneins. Ann Rev Neurosci 2000, 23: 39-71. . [http:\/\/www.annualreviews.org\/doi\/abs\/10.1146\/annurev.neuro.23.1.39] []. 10.1146\/annurev.neuro.23.1.39","journal-title":"Ann Rev Neurosci"},{"key":"918_CR49","volume-title":"Basic mechanisms for recognition and transport of synaptic cargos","author":"MA Schlager","year":"2009","unstructured":"Schlager MA, Hoogenraad CC: Basic mechanisms for recognition and transport of synaptic cargos. Mol Brain 2009.,2(25): . [http:\/\/www.molecularbrain.com\/content\/2\/1\/25] []."},{"issue":"5866","key":"918_CR50","doi-asserted-by":"publisher","first-page":"1086","DOI":"10.1126\/science.1152993","volume":"319","author":"R Dixit","year":"2008","unstructured":"Dixit R, Ross JL, Goldman YE, Holzbaur EF: Differential regulation of dynein and kinesin motor proteins by Tau. Science 2008,319(5866):1086-1089. 10.1126\/science.1152993","journal-title":"Science"},{"issue":"3","key":"918_CR51","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1038\/nrn1624","volume":"6","author":"N Hirokawa","year":"2005","unstructured":"Hirokawa N, Takemura R: Molecular motors and mechanisms of directional transport in neurons. Nat Rev Neurosci 2005,6(3):201-214. 10.1038\/nrn1624","journal-title":"Nat Rev Neurosci"},{"key":"918_CR52","doi-asserted-by":"publisher","first-page":"845","DOI":"10.1109\/CCGrid.2012.72","volume-title":"Proceedings of CCGrid 2012 - The 12th IEEE\/ACM International Symposium on Cluster, Cloud and Grid Computing","author":"PO \u00d6stberg","year":"2012","unstructured":"\u00d6stberg PO, Hellander A, Drawert B, Elmroth E, Holmgren S, Petzold L: Reducing complexity in management of scientific computations. Proceedings of CCGrid 2012 - The 12th IEEE\/ACM International Symposium on Cluster, Cloud and Grid Computing 2012, 845-852."},{"issue":"4","key":"918_CR53","doi-asserted-by":"publisher","first-page":"524","DOI":"10.1093\/bioinformatics\/btg015","volume":"19","author":"M Hucka","year":"2003","unstructured":"Hucka M, Finney A, Sauro HM, Bolouri H, Doyle JC, H K, the rest of the SBML Forum:, Arkin AP, Bornstein BJ, Bray D, Cornish-Bowden A, Cuellar AA, Dronov S, Gilles ED, Ginkel M, Gor V, Goryanin II, Hedley WJ, Hodgman TC, Hofmeyr JH, Hunter PJ, Juty NS, Kasberger JL, Kremling A, Kummer U, Le Novere N, Loew LM, Lucio D, Mendes P, Minch E, Mjolsness ED, Nakayama Y, Nelson MR, Nielsen PF, Sakurada T, Schaff JC, Shapiro BE, Shimizu TS, Spence HD, Stelling J, Takahashi K, Tomita M, Wagner J, Wang J: The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics 2003,19(4):524-531. 10.1093\/bioinformatics\/btg015","journal-title":"Bioinformatics"},{"key":"918_CR54","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1137\/040605060","volume":"28","author":"SA Isaacson","year":"2006","unstructured":"Isaacson SA, Peskin CS: Incorporating diffusion in complex geometries into stochastic chemical kinetics simulations. SIAM J Sci Comput 2006, 28: 47-74. 10.1137\/040605060","journal-title":"SIAM J Sci Comput"},{"key":"918_CR55","volume-title":"Master\u2019s thesis","author":"E Kieri","year":"2010","unstructured":"Kieri E: Accuracy aspects of the reaction-diffusion master equation on unstructured meshes. In Master\u2019s thesis. Department of Information Technology, Uppsala University; 2010."},{"key":"918_CR56","volume-title":"Master\u2019s thesis","author":"D Elversson","year":"2010","unstructured":"Elversson D, Kieri E: Spatial stochastic simulation of Spatial stochastic simulation of Spatial stochastic simulation of cellular reaction networks: A comparison of discretizations of the Laplace operator for mesoscopic diffusion. In Master\u2019s thesis. Department of Information Technology, Uppsala University; 2010."},{"issue":"46","key":"918_CR57","doi-asserted-by":"publisher","first-page":"19820","DOI":"10.1073\/pnas.1006565107","volume":"107","author":"D Fange","year":"2010","unstructured":"Fange D, Berg OG, Sj\u00f6berg P, Elf J: Stochastic reaction-diffusion kinetics in the microscopic limit. Proc Natl Acad Sci USA 2010,107(46):19820-19825. 10.1073\/pnas.1006565107","journal-title":"Proc Natl Acad Sci USA"},{"issue":"4","key":"918_CR58","doi-asserted-by":"publisher","first-page":"042901","DOI":"10.1103\/PhysRevE.85.042901","volume":"85","author":"S Hellander","year":"2012","unstructured":"Hellander S, Hellander A, Petzold L: On the reaction-diffusion master equation in the microscopic limit. Phys Rev E 2012,85(4):042901.","journal-title":"Phys Rev E"},{"key":"918_CR59","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1016\/S0006-3495(79)85228-5","volume":"27","author":"VA Bloomfield","year":"1979","unstructured":"Bloomfield VA, Prager S: Diffusion-controlled reactions on spherical surfaces. Biophys J 1979, 27: 447-453. 10.1016\/S0006-3495(79)85228-5","journal-title":"Biophys J"},{"key":"918_CR60","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1016\/S0006-3495(86)83463-4","volume":"50","author":"J Lindermann","year":"1986","unstructured":"Lindermann J, Lauffenburger D: Analysis of intracellular receptor\/ligand sorting-calculation of mean surface and bulk diffusion times within a sphere. Biophys J 1986, 50: 295-305. 10.1016\/S0006-3495(86)83463-4","journal-title":"Biophys J"}],"container-title":["BMC Systems Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1752-0509-6-76.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T19:34:40Z","timestamp":1630524880000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcsystbiol.biomedcentral.com\/articles\/10.1186\/1752-0509-6-76"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,22]]},"references-count":60,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,12]]}},"alternative-id":["918"],"URL":"https:\/\/doi.org\/10.1186\/1752-0509-6-76","relation":{},"ISSN":["1752-0509"],"issn-type":[{"value":"1752-0509","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,22]]},"assertion":[{"value":"10 January 2012","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 June 2012","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 June 2012","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"76"}}