{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,20]],"date-time":"2026-07-20T18:41:17Z","timestamp":1784572877227,"version":"3.55.0"},"reference-count":50,"publisher":"Public Library of Science (PLoS)","issue":"9","license":[{"start":{"date-parts":[[2021,9,23]],"date-time":"2021-09-23T00:00:00Z","timestamp":1632355200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMR 2104294"],"award-info":[{"award-number":["DMR 2104294"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS ONE"],"abstract":"<jats:p>The formation of neuron networks is a complex phenomenon of fundamental importance for understanding the development of the nervous system, and for creating novel bioinspired materials for tissue engineering and neuronal repair. The basic process underlying the network formation is axonal growth, a process involving the extension of axons from the cell body towards target neurons. Axonal growth is guided by environmental stimuli that include intercellular interactions, biochemical cues, and the mechanical and geometrical features of the growth substrate. The dynamics of the growing axon and its biomechanical interactions with the growing substrate remains poorly understood. In this paper, we develop a model of axonal motility which incorporates mechanical interactions between the axon and the growth substrate. We combine experimental data with theoretical analysis to measure the parameters that describe axonal growth on surfaces with micropatterned periodic geometrical features: diffusion (cell motility) coefficients, speed and angular distributions, and axon bending rigidities. Experiments performed on neurons treated Taxol (inhibitor of microtubule dynamics) and Blebbistatin (disruptor of actin filaments) show that the dynamics of the cytoskeleton plays a critical role in the axon steering mechanism. Our results demonstrate that axons follow geometrical patterns through a contact-guidance mechanism, in which high-curvature geometrical features impart high traction forces to the growth cone. These results have important implications for our fundamental understanding of axonal growth as well as for bioengineering novel substrates that promote neuronal growth and nerve repair.<\/jats:p>","DOI":"10.1371\/journal.pone.0257659","type":"journal-article","created":{"date-parts":[[2021,9,23]],"date-time":"2021-09-23T17:59:56Z","timestamp":1632419996000},"page":"e0257659","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":14,"title":["Axonal growth on surfaces with periodic geometrical patterns"],"prefix":"10.1371","volume":"16","author":[{"given":"Jacob P.","family":"Sunnerberg","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8504-3429","authenticated-orcid":true,"given":"Marc","family":"Descoteaux","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David L.","family":"Kaplan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9771-8400","authenticated-orcid":true,"given":"Cristian","family":"Staii","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2021,9,23]]},"reference":[{"key":"pone.0257659.ref001","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1146\/annurev.neuro.26.010302.081139","article-title":"Signaling at the growth cone: ligand receptor complexes and the control of axon growth and guidance","volume":"26","author":"AB Huber","year":"2003","journal-title":"Annu Rev Neurosci"},{"key":"pone.0257659.ref002","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1038\/nrm2679","article-title":"The trip of the tip: understanding the growth cone machinery","volume":"10","author":"LA Lowery","year":"2009","journal-title":"Nat Rev Mol Cell Biol"},{"key":"pone.0257659.ref003","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1021\/la102331x","article-title":"Distance Dependence of Neuronal Growth on Nanopatterned Gold Surfaces","volume":"27","author":"C Staii","year":"2011","journal-title":"Langmuir"},{"key":"pone.0257659.ref004","doi-asserted-by":"crossref","first-page":"094601","DOI":"10.1088\/0034-4885\/73\/9\/094601","article-title":"The biophysics of neuronal growth","volume":"73","author":"K Franze","year":"2010","journal-title":"Rep Prog Phys"},{"key":"pone.0257659.ref005","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.conb.2005.12.005","article-title":"Directional guidance of nerve growth cones","volume":"16","author":"Z Wen","year":"2006","journal-title":"Curr Opin Neurobiol"},{"key":"pone.0257659.ref006","doi-asserted-by":"crossref","first-page":"1123","DOI":"10.1126\/science.274.5290.1123","article-title":"The molecular biology of axon guidance","volume":"274","author":"M Tessier-Lavigne","year":"1996","journal-title":"Science"},{"key":"pone.0257659.ref007","doi-asserted-by":"crossref","first-page":"1959","DOI":"10.1126\/science.1072165","article-title":"Molecular mechanisms of axon guidance","volume":"298","author":"BJ Dickson","year":"2002","journal-title":"Science"},{"key":"pone.0257659.ref008","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1038\/nn1259","article-title":"A new chemotaxis assay shows the extreme sensitivity of axons to molecular gradients","volume":"7","author":"WJ Rosoff","year":"2004","journal-title":"Nat Neurosci"},{"key":"pone.0257659.ref009","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1039\/C2LC41166K","article-title":"Adhesive micro-line periodicity determines guidance of axonal outgrowth","volume":"13","author":"SR Hart","year":"2013","journal-title":"Lab Chip"},{"key":"pone.0257659.ref010","doi-asserted-by":"crossref","first-page":"e106709","DOI":"10.1371\/journal.pone.0106709","article-title":"Effects of surface asymmetry on neuronal growth","volume":"9","author":"E Spedden","year":"2014","journal-title":"PLOS One"},{"key":"pone.0257659.ref011","doi-asserted-by":"crossref","first-page":"1251","DOI":"10.1016\/j.biomaterials.2005.07.047","article-title":"Axonal outgrowth on nano-imprinted patterns","volume":"27","author":"F Johansson","year":"2006","journal-title":"Biomaterials"},{"key":"pone.0257659.ref012","doi-asserted-by":"crossref","first-page":"1812","DOI":"10.1007\/s10439-007-9348-0","article-title":"Optimal micropattern dimensions enhance neurite outgrowth rates, lengths, and orientations","volume":"35","author":"M Song","year":"2007","journal-title":"Ann Biomed Eng"},{"key":"pone.0257659.ref013","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/S0165-0270(02)00181-4","article-title":"Culture of neural cells on silicon wafers with nano-scale surface topograph","volume":"120","author":"YW Fan","year":"2002","journal-title":"J Neurosci Methods"},{"key":"pone.0257659.ref014","doi-asserted-by":"crossref","first-page":"3070","DOI":"10.1039\/c3lc50174d","article-title":"Superimposed topographic and chemical cues synergistically guide neurite outgrowth","volume":"13","author":"A Kundu","year":"2013","journal-title":"Lab Chip"},{"key":"pone.0257659.ref015","doi-asserted-by":"crossref","first-page":"143701","DOI":"10.1063\/1.4755837","article-title":"Neuronal alignment on asymmetric textured surfaces","volume":"101","author":"R Beighley","year":"2012","journal-title":"Appl Phys Lett"},{"issue":"5","key":"pone.0257659.ref016","doi-asserted-by":"crossref","first-page":"e0216181","DOI":"10.1371\/journal.pone.0216181","article-title":"Anomalous diffusion for neuronal growth on surfaces with controlled geometries","volume":"14","author":"I Yurchenko","year":"2019","journal-title":"PLoS One"},{"key":"pone.0257659.ref017","doi-asserted-by":"crossref","first-page":"3398","DOI":"10.1016\/j.biomaterials.2007.04.015","article-title":"Regulation of axon guidance and extension by three-dimensional constraints","volume":"28","author":"H Francisco","year":"2007","journal-title":"Biomaterials"},{"key":"pone.0257659.ref018","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.yexcr.2005.10.007","article-title":"Integration of topographical and biochemical cues by axons during growth on microfabricated 3-D substrates","volume":"311","author":"N Li","year":"2005","journal-title":"Exp Cell Res"},{"key":"pone.0257659.ref019","doi-asserted-by":"crossref","first-page":"042707","DOI":"10.1103\/PhysRevE.88.042707","article-title":"Neuronal growth as diffusion in an effective potential","volume":"88","author":"DJ Rizzo","year":"2013","journal-title":"Phys Rev E"},{"key":"pone.0257659.ref020","doi-asserted-by":"crossref","first-page":"022408","DOI":"10.1103\/PhysRevE.99.022408","article-title":"Role of geometrical cues in neuronal growth","volume":"99","author":"JM Vensi Basso","year":"2019","journal-title":"Phys Rev E"},{"key":"pone.0257659.ref021","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1016\/j.bpj.2011.12.025","article-title":"Strength in the periphery: growth cone biomechanics and substrate rigidity response in peripheral and central nervous system neurons","volume":"102","author":"D Koch","year":"2012","journal-title":"Biophys J"},{"key":"pone.0257659.ref022","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1016\/S0092-8240(05)80241-1","article-title":"Langevin equation, Fokker-Planck equation and cell migration","volume":"55","author":"M Schienbein","year":"1993","journal-title":"Bull Math Biol"},{"key":"pone.0257659.ref023","doi-asserted-by":"crossref","first-page":"098103","DOI":"10.1103\/PhysRevLett.96.098103","article-title":"Neuronal growth: a bistable stochastic process","volume":"96","author":"T Betz","year":"2006","journal-title":"Phys Rev Lett"},{"key":"pone.0257659.ref024","doi-asserted-by":"crossref","first-page":"e372213","DOI":"10.1371\/journal.pone.0037213","article-title":"A stochastic description of dictyostelium chemotaxis","volume":"7","author":"G Amselem","year":"2012","journal-title":"PLOS One"},{"key":"pone.0257659.ref025","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1529\/biophysj.105.061150","article-title":"Cell motility as persistent random motion: theories and experiment","volume":"89","author":"D Selmeczi","year":"2005","journal-title":"Biophys J"},{"key":"pone.0257659.ref026","doi-asserted-by":"crossref","first-page":"046006","DOI":"10.1088\/1478-3975\/8\/4\/046006","article-title":"\"Dicty dynamics\u2019: Dictyostelium motility as persistent random motion","volume":"8","author":"L Li","year":"2011","journal-title":"Phys Biol"},{"key":"pone.0257659.ref027","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1242\/jcs.99.2.419","article-title":"Migration of individual microvessel endothelial cells: stochastic model and parameter measurement","volume":"99","author":"CL Stokes","year":"1991","journal-title":"J Cell Sci"},{"key":"pone.0257659.ref028","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1007\/978-3-642-61544-3","volume-title":"The Fokker-Planck Equation: Methods of Solution and Applications","author":"H Risken","year":"1996"},{"key":"pone.0257659.ref029","volume-title":"Stochastic Pocesses in Physics and Chemistry","author":"N van Kampen","year":"2007","edition":"3"},{"key":"pone.0257659.ref030","doi-asserted-by":"crossref","first-page":"056002","DOI":"10.1088\/1478-3975\/10\/5\/056002","article-title":"Temperature response of the neuronal cytoskeleton mapped via atomic force and fluorescence microscopy","volume":"10","author":"E Spedden","year":"2013","journal-title":"Phys Biol"},{"key":"pone.0257659.ref031","doi-asserted-by":"crossref","first-page":"056002","DOI":"10.1088\/1478-3975\/10\/5\/056002","article-title":"Temperature response of the neuronal cytoskeleton mapped via atomic force and fluorescence microscopy","volume":"10","author":"E Spedden","year":"2013","journal-title":"Phys Biol"},{"issue":"33","key":"pone.0257659.ref032","doi-asserted-by":"crossref","first-page":"10965","DOI":"10.1021\/acs.langmuir.9b01651","article-title":"Variations of elastic modulus and cell volume with temperature for cortical neurons","volume":"35","author":"JP Sunnerberg","year":"2019","journal-title":"Langmuir"},{"key":"pone.0257659.ref033","doi-asserted-by":"crossref","first-page":"9931","DOI":"10.1039\/C9SM01769K","article-title":"Neuron dynamics on directional surfaces","volume":"15","author":"JM Vensi Basso","year":"2019","journal-title":"Soft Matter"},{"key":"pone.0257659.ref034","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1242\/jcs.088302","article-title":"Force transduction and strain dynamics in actin stress fibres in response to nanoNewton forces J","volume":"125","author":"BM Guolla L","year":"2012","journal-title":"Cell Sci"},{"issue":"3","key":"pone.0257659.ref035","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1007\/s10439-005-1740-z","article-title":"Substrate Curvature Influences the Direction of Nerve Outgrowth","volume":"33","author":"RM Smeal","year":"2005","journal-title":"Annals of Biomedical Engineering"},{"issue":"2","key":"pone.0257659.ref036","doi-asserted-by":"crossref","first-page":"e1005407","DOI":"10.1371\/journal.pcbi.1005407","article-title":"Modeling of the axon membrane skeleton structure and implications for its mechanical properties","volume":"13","author":"Y Zhang","year":"2017","journal-title":"PLOS Computational Biology"},{"key":"pone.0257659.ref037","doi-asserted-by":"crossref","first-page":"R415","DOI":"10.1088\/0953-8984\/13\/24\/201","article-title":"Colloidal soft matter under external control","volume":"13","author":"H Lowen","year":"2001","journal-title":"J. Phys. Cond. Mat"},{"key":"pone.0257659.ref038","doi-asserted-by":"crossref","first-page":"022132","DOI":"10.1103\/PhysRevE.92.022132","article-title":"Enhancement of mobility in an interacting colloidal system under feedback control","volume":"92","author":"R Gernert","year":"2015","journal-title":"Phys. Rev. E"},{"key":"pone.0257659.ref039","doi-asserted-by":"crossref","first-page":"3833","DOI":"10.1002\/adfm.201200400","article-title":"Feedback Controlled Colloidal Self-Assembly","volume":"22","author":"JJ Juarez","year":"2012","journal-title":"Adv. Func. Mater"},{"key":"pone.0257659.ref040","doi-asserted-by":"crossref","first-page":"085302","DOI":"10.1103\/PhysRevB.84.085302","article-title":"Feedback stabilization of pure states in quantum transport","volume":"84","author":"C Poltl","year":"2011","journal-title":"Phys. Rev. B"},{"key":"pone.0257659.ref041","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/s003390051103","article-title":"Photonic force microscope calibration by thermal noise analysis","volume":"66","author":"EL Florin","year":"1998","journal-title":"Appl. Phys. A"},{"key":"pone.0257659.ref042","doi-asserted-by":"crossref","first-page":"011020","DOI":"10.1115\/1.4004774","article-title":"Nonlinear Proportional Plus Integral Control of Optical Traps for Exogenous Force Estimation","volume":"134","author":"DG Cole","year":"2012","journal-title":"J. Dyn. Syst. Meas. Control"},{"key":"pone.0257659.ref043","doi-asserted-by":"crossref","first-page":"041907","DOI":"10.1103\/PhysRevE.78.041907","article-title":"Interplay of subthreshold activity, time-delayed feedback, and noise on neuronal firing patterns","volume":"78","author":"C Masoller","year":"2008","journal-title":"Phys. Rev. E"},{"key":"pone.0257659.ref044","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1038\/nphys1611","article-title":"Neural control: Chaos control sets the pace","volume":"6","author":"E Scholl","year":"2010","journal-title":"Nature Physics"},{"key":"pone.0257659.ref045","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1385\/CBB:33:1:33","article-title":"The galvanotaxis response mechanism of keratinocytes can be modeled as a proportional controller","volume":"33","author":"H Gruler","year":"2000","journal-title":"Cell Biochemistry and Biophysics"},{"key":"pone.0257659.ref046","first-page":"1241","article-title":"Automatic control and direceted cell movement. Novel approach for understanding chemotaxis, galvanotaxis, galvanotropism","volume":"45","author":"H Gruler","year":"1990","journal-title":"J. Biosci"},{"key":"pone.0257659.ref047","doi-asserted-by":"crossref","first-page":"4701","DOI":"10.1529\/biophysj.105.067967","article-title":"Cell orientation by a microgrooved substrate can be predicted by automatic control theory","volume":"90","author":"R Kemkemer","year":"2006","journal-title":"Biophys. J"},{"key":"pone.0257659.ref048","doi-asserted-by":"crossref","first-page":"1090","DOI":"10.1002\/dneu.20947","article-title":"Biophysics of substrate interaction: influence on neural motility, differentiation, and repair.","volume":"71","author":"SW Moore","year":"2011","journal-title":"Dev Neurobiol"},{"key":"pone.0257659.ref049","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.1083\/jcb.153.6.1175","article-title":"Focal contacts as mechanosensors: externally applied local mechanical force induces growth of focal contacts by an mDia1-dependent and ROCK-independent mechanism","volume":"153","author":"D Riveline","year":"2001","journal-title":"J Cell Biol"},{"key":"pone.0257659.ref050","first-page":"3061","article-title":"Mechanosensitive mechanisms in transcriptional regulation","volume":"125","author":"A Mammoto","year":"2012","journal-title":"J Cell Sci"}],"container-title":["PLOS ONE"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0257659","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,9]],"date-time":"2023-11-09T08:30:43Z","timestamp":1699518643000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0257659"}},"subtitle":[],"editor":[{"given":"Etienne","family":"Dague","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2021,9,23]]},"references-count":50,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2021,9,23]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0257659","relation":{},"ISSN":["1932-6203"],"issn-type":[{"value":"1932-6203","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,23]]}}}