{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T18:07:50Z","timestamp":1777399670062,"version":"3.51.4"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,3,17]],"date-time":"2017-03-17T00:00:00Z","timestamp":1489708800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2017,3,17]],"date-time":"2017-03-17T00:00:00Z","timestamp":1489708800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Australian Research Countil","award":["DP170100474"],"award-info":[{"award-number":["DP170100474"]}]},{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"publisher","award":["DP140100249"],"award-info":[{"award-number":["DP140100249"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Syst Biol"],"published-print":{"date-parts":[[2017,12]]},"DOI":"10.1186\/s12918-017-0413-5","type":"journal-article","created":{"date-parts":[[2017,3,17]],"date-time":"2017-03-17T01:54:01Z","timestamp":1489715641000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Quantifying the roles of random motility and directed motility using advection-diffusion theory for a 3T3 fibroblast cell migration assay stimulated with an electric field"],"prefix":"10.1186","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6254-313X","authenticated-orcid":false,"given":"Matthew J.","family":"Simpson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai-Yin","family":"Lo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yung-Shin","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,3,17]]},"reference":[{"key":"413_CR1","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1098\/rspb.1990.0061","volume":"241","author":"JA Sherratt","year":"1990","unstructured":"Sherratt JA, Murray JD. Models of epidermal wound healing. Proc R Soc Lond B. 1990; 241:29\u201336.","journal-title":"Proc R Soc Lond B"},{"key":"413_CR2","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1089\/107632704323061834","volume":"10","author":"PK Maini","year":"2004","unstructured":"Maini PK, McElwain DLS, Leavesley DI. Traveling wave model to interpret a wound-healing cell migration assay for human peritoneal mesothelial cells. Tissue Eng. 2004; 10:475\u201382.","journal-title":"Tissue Eng"},{"key":"413_CR3","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.jtbi.2014.04.026","volume":"356","author":"KK Treloar","year":"2014","unstructured":"Treloar KK, Simpson MJ, McElwain DLS, Baker RE. Are in vitro estimates of cell diffusivity and cell proliferation rate sensitive to assay geometry?J Theor Biol. 2014; 356:71\u201384.","journal-title":"J Theor Biol"},{"key":"413_CR4","first-page":"5745","volume":"56","author":"RA Gatenby","year":"1996","unstructured":"Gatenby RA, Gawlinski ET. A reaction-diffusion model of cancer invasion. Cancer Res. 1996; 56:5745\u201353.","journal-title":"Cancer Res"},{"key":"413_CR5","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1186\/s12918-015-0182-y","volume":"9","author":"ST Johnston","year":"2015","unstructured":"Johnston ST, Shah ET, Chopin LK, McElwain DLS, Simpson MJ. Estimating cell diffusivity and cell proliferation rate by interpreting IncuCyte ZOOMTM assay data using the Fisher-Kolmogorov model. BMC Syst Biol. 2015; 9:38.","journal-title":"BMC Syst Biol"},{"key":"413_CR6","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/0022-5193(71)90050-6","volume":"30","author":"EF Keller","year":"1971","unstructured":"Keller EF, Segel LA. Model for chemotaxis. J Theor Biol. 1971; 30:225\u201334.","journal-title":"J Theor Biol"},{"key":"413_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/b98868","volume-title":"Mathematical biology: i an introduction","author":"JD Murray","year":"2002","unstructured":"Murray JD. Mathematical biology: i an introduction. Springer-Verlag Berlin Heidelberg: Springer; 2002."},{"key":"413_CR8","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1016\/S0022-5193(03)00258-3","volume":"225","author":"KJ Painter","year":"2003","unstructured":"Painter KJ, Sherratt JA. Modelling the movement of interacting cell populations. J Theor Biol. 2003; 225:327\u201339.","journal-title":"J Theor Biol"},{"key":"413_CR9","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s11538-005-9028-x","volume":"68","author":"AQ Cai","year":"2006","unstructured":"Cai AQ, Landman KA, Hughes BD. Modelling directional guidance and motility regulation in cell migration. Bull Math Biol. 2006; 68:25\u201352.","journal-title":"Bull Math Biol"},{"key":"413_CR10","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1016\/j.jtbi.2006.06.021","volume":"243","author":"MJ Simpson","year":"2007","unstructured":"Simpson MJ, Landman KA, Hughes BD, Newgreen DF. Looking inside an invasion wave of cells using continuum models: proliferation is the key. J Theor Biol. 2007; 243:343\u201360.","journal-title":"J Theor Biol"},{"key":"413_CR11","doi-asserted-by":"publisher","first-page":"2023","DOI":"10.1083\/jcb.101.6.2023","volume":"101","author":"KR Robinson","year":"1985","unstructured":"Robinson KR. The responses of cells to electrical fields: a review. J Cell Biol. 1985; 101:2023\u20137.","journal-title":"J Cell Biol"},{"key":"413_CR12","doi-asserted-by":"publisher","first-page":"1631","DOI":"10.1242\/jcs.01125","volume":"117","author":"ME Mycielska","year":"2004","unstructured":"Mycielska ME, Djamgoz MBA. Cellular mechanisms of direct-current electric field effects: galvanotaxis and metastatis diseasse. J Cell Sci. 2004; 117:1631\u20139.","journal-title":"J Cell Sci"},{"key":"413_CR13","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1016\/j.bioelechem.2012.08.002","volume":"88","author":"JC Vanegas-Acosta","year":"2012","unstructured":"Vanegas-Acosta JC, Garzon-Alvarado DA, Zwamborn APM. Mathematical model of electrotaxis in osetoblastic cells. Bioelectrochemistry. 2012; 88:134\u201343.","journal-title":"Bioelectrochemistry"},{"key":"413_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0070-2153(03)58001-2","volume":"58","author":"R Nuccitelli","year":"2003","unstructured":"Nuccitelli R. A role for endogenous electric fields in wound healing. Curr Top Dev Biol. 2003; 58:1\u201326.","journal-title":"Curr Top Dev Biol"},{"key":"413_CR15","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1006\/exer.2000.0830","volume":"70","author":"B Farboud","year":"2000","unstructured":"Farboud B, Nuccitelli R, Schwab IR, Isseroff RR. DC electric fields induce rapid directional migration in cultured human corneal epithelial cells. Exp Eye Res. 2000; 70:667\u201373.","journal-title":"Exp Eye Res"},{"key":"413_CR16","doi-asserted-by":"publisher","first-page":"674","DOI":"10.1016\/j.semcdb.2008.12.009","volume":"20","author":"M Zhao","year":"2009","unstructured":"Zhao M. Electrical fields in wound healing - an overriding signal that directs cell migration. Semin Cell Dev Biol. 2009; 20:674\u201382.","journal-title":"Semin Cell Dev Biol"},{"key":"413_CR17","doi-asserted-by":"publisher","first-page":"136","DOI":"10.1016\/j.jtbi.2015.10.040","volume":"390","author":"W Jin","year":"2016","unstructured":"Jin W, Shah ET, Penington CJ, McCue SW, Chopin LK, Simpson MJ. Reproducibility of scratch assays is affected by the initial degree of confluence: experiments, modelling and model selection. J Theor Biol. 2016; 390:136\u201345.","journal-title":"J Theor Biol"},{"key":"413_CR18","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1016\/j.ceb.2012.01.001","volume":"24","author":"SK Hughes-Alford","year":"2012","unstructured":"Hughes-Alford SK, Lauffenburger DA. Quantitative analysis of gradient sensing: towards building predictive models of chemotaxis in cancer. Curr Opin Cell Biol. 2012; 24:284\u201391.","journal-title":"Curr Opin Cell Biol"},{"key":"413_CR19","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1083\/jcb.106.2.303","volume":"106","author":"RT Tranquillo","year":"1988","unstructured":"Tranquillo RT, Lauffenburger DA, Zigmond SH. A stochastic model for leukocyte random motility and chemotaxis based on receptor binding fluctuations. J Cell Biol. 1988; 106:303\u201309.","journal-title":"J Cell Biol"},{"key":"413_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/cm.970110102","volume":"11","author":"RT Tranquillo","year":"1988","unstructured":"Tranquillo RT, Zigmond SH, Lauffenberger DA. Measurement of the chemotaxis coefficient for human neutrophils in the under-agarose migration assay. Cell Motil Cytoskel. 1988; 11:1\u201315.","journal-title":"Cell Motil Cytoskel"},{"key":"413_CR21","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1093\/imammb\/dql007","volume":"23","author":"BP Marchant","year":"2006","unstructured":"Marchant BP, Norbury J, Byrne HM. Biphasic behaviour in malignant invasion. Math Med Biol. 2006; 23:173\u201396.","journal-title":"Math Med Biol"},{"key":"413_CR22","doi-asserted-by":"publisher","first-page":"678","DOI":"10.1016\/j.physd.2007.10.003","volume":"237","author":"KA Landman","year":"2008","unstructured":"Landman KA, Simpson MJ, Pettet GJ. Tactically-driven nonmonotone travelling waves. Physica D. 2008; 237:678\u201391.","journal-title":"Physica D"},{"key":"413_CR23","doi-asserted-by":"publisher","first-page":"695","DOI":"10.1016\/j.bbrc.2011.07.004","volume":"411","author":"D Wu","year":"2011","unstructured":"Wu D, Lin F. A receptor-electromigration-based model for cellular electrostatic sensing and migration. Biochem Bioph Res Co. 2011; 411:695\u2013701.","journal-title":"Biochem Bioph Res Co"},{"key":"413_CR24","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/S0167-2789(98)00272-3","volume":"126","author":"AJ Perumpanani","year":"1999","unstructured":"Perumpanani AJ, Sherratt JA, Norbury J, Byrne HM. A two parameter family of travelling waves with a singular barrier arising from the modelling of extracellular matrix mediated cellular invasion. Physica D. 1999; 126:145\u201359.","journal-title":"Physica D"},{"key":"413_CR25","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1002\/bit.260370707","volume":"37","author":"RM Ford","year":"1991","unstructured":"Ford RM, Phillips BR, Quinn JA, Lauffenburger DA. Measurement of bacterial random motility and chemotaxis coefficients: 1 stopped-flow diffusion chamber assay. Biotechnol Bioeng. 1991; 37:647\u201360.","journal-title":"Biotechnol Bioeng"},{"key":"413_CR26","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1002\/bit.260370708","volume":"37","author":"RM Ford","year":"1991","unstructured":"Ford RM, Lauffenburger DA. Measurement of bacterial random motility and chemotaxis coefficients: II application of single-cell-based mathematical model. Biotechnol Bioeng. 1991; 37:661\u201372.","journal-title":"Biotechnol Bioeng"},{"key":"413_CR27","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1242\/jcs.99.2.419","volume":"99","author":"CL Stokes","year":"1991","unstructured":"Stokes CL, Lauffenburger DA, Williams SK. Migration of individual microvessel enthothelial cells: stochastic model and parameter measurement. J Cell Sci. 1991; 99:419\u201330.","journal-title":"J Cell Sci"},{"key":"413_CR28","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1016\/S0022-5193(05)80201-2","volume":"152","author":"CL Stokes","year":"1991","unstructured":"Stokes CL, Lauffenburger DA. Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis. J Theor Biol. 1991; 152:377\u2013403.","journal-title":"J Theor Biol"},{"key":"413_CR29","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1093\/imammb\/17.4.395","volume":"17","author":"GJ Pettet","year":"2000","unstructured":"Pettet GJ, McElwain DLS, Norbury J. Lotka-Volterra equations with chemotaxis: walls barriers and travelling waves. Math Med Biol. 2000; 17:395\u2013413.","journal-title":"Math Med Biol"},{"key":"413_CR30","doi-asserted-by":"publisher","first-page":"1949","DOI":"10.1088\/0951-7715\/23\/8\/008","volume":"23","author":"M Wechselberger","year":"2010","unstructured":"Wechselberger M, Pettet GJ. Folds, canards and shocks in advection-reaction-diffusion models. Nonlinearity. 2010; 23:1949\u201369.","journal-title":"Nonlinearity"},{"key":"413_CR31","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1137\/130923129","volume":"13","author":"K Harley","year":"2014","unstructured":"Harley K, van Heijster P, Marangell R, Pettet GJ, Weschelberger M. Existence of traveling wave solutions for a model of tumour invasion. SIAM J Appl Dyn Syst. 2014; 13:366\u201396.","journal-title":"SIAM J Appl Dyn Syst"},{"key":"413_CR32","doi-asserted-by":"publisher","first-page":"025002","DOI":"10.1088\/1367-2630\/16\/2\/025002","volume":"16","author":"N Charteris","year":"2014","unstructured":"Charteris N, Khain E. Modeling chemotaxis of adhesive cells: stochastic lattice approach and continuum description. New J Phys. 2014; 16:025002.","journal-title":"New J Phys"},{"key":"413_CR33","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1016\/j.physa.2015.08.049","volume":"442","author":"C Irons","year":"2016","unstructured":"Irons C, Plank MJ, Simpson MJ. Lattice-free models of directed cell motility. Physica A. 2016; 442:110\u201321.","journal-title":"Physica A"},{"key":"413_CR34","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1083\/jcb.17.2.299","volume":"17","author":"GJ Todaro","year":"1963","unstructured":"Todaro GJ, Green H. Quantitative studies of the growth of mouse embryo cells in culture and their development into established lines. J Cell Biol. 1963; 17:299\u2013313.","journal-title":"J Cell Biol"},{"key":"413_CR35","doi-asserted-by":"publisher","first-page":"054120","DOI":"10.1063\/1.4932662","volume":"9","author":"SY Wu","year":"2015","unstructured":"Wu SY, Hou HS, Sun YS, Cheng JY, Lo KY. Correlation between cell migration and reactive oxygen species under electric field stimulation. Biomicrofluidics. 2015; 9:054120.","journal-title":"Biomicrofluidics"},{"key":"413_CR36","doi-asserted-by":"publisher","first-page":"576","DOI":"10.1016\/j.jtbi.2006.10.024","volume":"245","author":"AQ Cai","year":"2007","unstructured":"Cai AQ, Landman KA, Hughes BD. Multi-scale modeling of a wound-healing cell migration assay. J Theor Biol. 2007; 245:576\u201394.","journal-title":"J Theor Biol"},{"key":"413_CR37","first-page":"871","volume":"75","author":"MJ Simpson","year":"2013","unstructured":"Simpson MJ, Binder BJ, Haridas P, Wood BK, Treloar KK, McElwain DLS, Baker RE. Experimental and modelling investigation of monolayer development with clustering. Bull Math Model. 2013; 75:871\u201389.","journal-title":"Bull Math Model"},{"key":"413_CR38","volume-title":"Transport phenomena","author":"RB Bird","year":"2005","unstructured":"Bird RB, Stewart WE, Lightfood EN. Transport phenomena. Wiley Singapore: Wiley; 2005."},{"key":"413_CR39","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1016\/j.snb.2003.10.022","volume":"99","author":"JY Cheng","year":"2004","unstructured":"Cheng JY, Wei CW, Hsu KH, Young TH. Direct-write laser micromachining and universal surface modification of PMMA for device development. Sensor Actuat B-Chem. 2004; 99:186\u201396.","journal-title":"Sensor Actuat B-Chem"},{"key":"413_CR40","doi-asserted-by":"publisher","first-page":"1147","DOI":"10.1088\/0960-1317\/15\/6\/005","volume":"15","author":"JY Cheng","year":"2005","unstructured":"Cheng JY, Yen MH, Wei CW, Chuang YC, Young TH. Crack-free direct-writing on glass using a low-power UV laser in the manufacture of a microfluidic chip. J Micromech Microeng. 2005; 15:1147\u201356.","journal-title":"J Micromech Microeng"},{"key":"413_CR41","doi-asserted-by":"publisher","first-page":"24105","DOI":"10.1063\/1.2952290","volume":"2","author":"JY Cheng","year":"2008","unstructured":"Cheng JY, Yen MH, Kuo CT, Young TH. A transparent cell-culture microchamber with a variably controlled concentration gradient generator and flow field rectifier. Biomicrofluidics. 2008; 2:24105.","journal-title":"Biomicrofluidics"},{"key":"413_CR42","doi-asserted-by":"publisher","first-page":"052007","DOI":"10.1063\/1.4896296","volume":"8","author":"HS Hou","year":"2014","unstructured":"Hou HS, Tsai HF, Chiu HT, Cheng JY. Simultaneous chemical and electrical stimulation on lung cancer cells using a multichannel-dual-electric-field chip. Biomicrofluidics. 2014; 8:052007.","journal-title":"Biomicrofluidics"},{"key":"413_CR43","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1098\/rsif.2008.0014","volume":"5","author":"EA Codling","year":"2008","unstructured":"Codling EA, Plank MJ, Benhamou S. Random walk models in biology. J R Soc Interface. 2008; 5:813\u201334.","journal-title":"J R Soc Interface"},{"key":"413_CR44","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/j.physa.2008.10.038","volume":"388","author":"MJ Simpson","year":"2009","unstructured":"Simpson MJ, Landman KA, Hughes BD. Multi-species simple exclusion processes. Physica A. 2009; 388:299\u2013406.","journal-title":"Physica A"},{"key":"413_CR45","doi-asserted-by":"publisher","first-page":"130007","DOI":"10.1098\/rsif.2013.0007","volume":"10","author":"MJ Simpson","year":"2013","unstructured":"Simpson MJ, Treloar KK, Binder BJ, Haridas P, Manton KJ, Leavesley DI, McElwain DLS, Baker RE. Quantifying the roles of cell motility and cell proliferation in a circular barrier assay. J R Soc Interface. 2013; 10:130007.","journal-title":"J R Soc Interface"}],"container-title":["BMC Systems Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s12918-017-0413-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1186\/s12918-017-0413-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s12918-017-0413-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,26]],"date-time":"2022-07-26T16:12:36Z","timestamp":1658851956000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcsystbiol.biomedcentral.com\/articles\/10.1186\/s12918-017-0413-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,17]]},"references-count":45,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["413"],"URL":"https:\/\/doi.org\/10.1186\/s12918-017-0413-5","relation":{},"ISSN":["1752-0509"],"issn-type":[{"value":"1752-0509","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,17]]},"assertion":[{"value":"19 January 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 February 2017","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 March 2017","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"39"}}