To our knowledge , this is the first time such oscillations are observed for the Fisher-KPP classical system, and we consider as a positive byproduct the mathematical challenge posed by the understanding and justification of such behavior Traction forces exerted by epithelial cell sheets, Journal of Physics: Condensed Matter, p.22194119, 2010. ,
Signaling pathways and cell mechanics involved in wound closure by epithelial cell sheets, Current Biology, vol.10, issue.14, pp.831-838, 2000. ,
DOI : 10.1016/S0960-9822(00)00579-0
Galectin-3 and polarized growth within collagen gels of wild-type and ricin-resistant MDCK renal epithelial cells, Glycobiology, vol.9, issue.5, pp.489-495, 1999. ,
DOI : 10.1093/glycob/9.5.489
Is the Mechanical Activity of Epithelial Cells Controlled by Deformations or Forces?, Biophysical Journal, vol.89, issue.6, pp.52-54, 2005. ,
DOI : 10.1529/biophysj.105.071217
URL : https://hal.archives-ouvertes.fr/hal-00016455
Emerging modes of collective cell migration induced by geometrical constraints, Proceedings of the National Academy of Sciences, pp.12974-12979, 2012. ,
Hepatocyte Growth Factor Decreases Sensitivity to Chemotherapeutic Agents and Stimulates Cell Adhesion, Invasion, and Migration, Biochemical and Biophysical Research Communications, vol.274, issue.3, pp.772-779, 2000. ,
DOI : 10.1006/bbrc.2000.3199
Involvement of Focal Adhesion Kinase in Hepatocyte Growth Factor-induced Scatter of Madin-Darby Canine Kidney Cells, Journal of Biological Chemistry, vol.275, issue.11, pp.2757474-7480, 2000. ,
DOI : 10.1074/jbc.275.11.7474
Induction of Hepatocyte Growth Factor/Scatter Factor by Fibroblast Clustering Directly Promotes Tumor Cell Invasiveness, Cancer Research, vol.65, issue.21, pp.659914-659936, 2005. ,
DOI : 10.1158/0008-5472.CAN-05-1559
Hepatocyte growth factor/scatter factor stimulates migration of rat mammary fibroblasts through both mitogen-activated protein kinase and phosphatidylinositol 3-kinase/Akt pathways, European Journal of Biochemistry, vol.144, issue.16, pp.4423-4432, 2001. ,
DOI : 10.1046/j.1432-1327.2001.02363.x
Pak4 is activated via pi3k in hgfstimulated epithelial cells, J Cell Sci, vol.115, pp.3947-56, 2002. ,
Involvement of PI3K/Akt Signaling Pathway in Hepatocyte Growth Factor???Induced Migration of Uveal Melanoma Cells, Investigative Opthalmology & Visual Science, vol.49, issue.2, pp.497-504, 2008. ,
DOI : 10.1167/iovs.07-0975
Molecules in the ARF Orbit, Journal of Biological Chemistry, vol.273, issue.34, pp.21431-21435, 1998. ,
DOI : 10.1074/jbc.273.34.21431
Structure-based discovery of an inhibitor of Arf activation by Sec7 domains through targeting of protein-protein complexes, Proceedings of the National Academy of Sciences, pp.10370-10375, 2007. ,
DOI : 10.1073/pnas.0700773104
URL : https://hal.archives-ouvertes.fr/hal-00172003
Hepatocyte growth factor induces mdck cell morphogenesis without causing loss of tight junction functional integrity, Am J Physiol Cell Physiol, vol.286, issue.3, 2004. ,
A mathematical model for dorsal closure, Journal of Theoretical Biology, vol.268, issue.1, pp.105-119, 2011. ,
DOI : 10.1016/j.jtbi.2010.09.029
URL : https://hal.archives-ouvertes.fr/inria-00544350
Multiple rows of cells behind an epithelial wound edge extend cryptic lamellipodia to collectively drive cell-sheet movement, Journal of Cell Science, vol.118, issue.1, pp.51-63, 2005. ,
DOI : 10.1242/jcs.01577
Collective migration of an epithelial monolayer in response to a model wound, Proceedings of the National Academy of Sciences, pp.15988-15993, 2007. ,
DOI : 10.1073/pnas.0705062104
URL : https://hal.archives-ouvertes.fr/hal-00175727
Wound healing in the corneal epithelium: Biological mechanisms and mathematical models, J. Theor. Med, vol.1, issue.1, pp.13-23, 1997. ,
Spatially varying equilibria of mechanical models: Application to dermal wound contraction, Mathematical Biosciences, vol.147, issue.1, pp.113-129, 1998. ,
DOI : 10.1016/S0025-5564(97)00075-8
MATHEMATICAL MODELS FOR CELL-MATRIX INTERACTIONS DURING DERMAL WOUND HEALING, International Journal of Bifurcation and Chaos, vol.12, issue.09, pp.2021-2029, 2002. ,
DOI : 10.1142/S0218127402005674
Complex pattern formation in reaction???diffusion systems with spatially varying parameters, Physica D: Nonlinear Phenomena, vol.202, issue.1-2, pp.95-115, 2005. ,
DOI : 10.1016/j.physd.2005.01.022
Crawling Cells Can Close Wounds without Purse Strings or Signaling, PLoS Computational Biology, vol.16, issue.3, p.1002007, 2011. ,
DOI : 10.1371/journal.pcbi.1002007.s001
Continuum approximations of individual-based models for epithelial monolayers, Mathematical Medicine and Biology, vol.27, issue.1, pp.39-74, 2010. ,
DOI : 10.1093/imammb/dqp015
Collective Cell Motion in an Epithelial Sheet Can Be Quantitatively Described by a Stochastic Interacting Particle Model, PLoS Computational Biology, vol.107, issue.Pt 5, p.2013 ,
DOI : 10.1371/journal.pcbi.1002944.s014
Collective cell migration: leadership, invasion and segregation, J R Soc Interface, vol.9, issue.77, pp.3268-78, 2012. ,
Travelling waves in a wound healing assay, Applied Mathematics Letters, vol.17, issue.5, pp.575-580, 2004. ,
DOI : 10.1016/S0893-9659(04)90128-0
Traveling Wave Model to Interpret a Wound-Healing Cell Migration Assay for Human Peritoneal Mesothelial Cells, Tissue Engineering, vol.10, issue.3-4 ,
DOI : 10.1089/107632704323061834
Continuum Model of Collective Cell Migration in Wound Healing and Colony Expansion, Biophysical Journal, vol.100, issue.3, pp.535-543, 2011. ,
DOI : 10.1016/j.bpj.2010.11.083
Multi-scale modeling of a wound-healing cell migration assay, Journal of Theoretical Biology, vol.245, issue.3, pp.576-594, 2007. ,
DOI : 10.1016/j.jtbi.2006.10.024
Experimental characterization and computational modelling of two-dimensional cell spreading for skeletal regeneration, Journal of The Royal Society Interface, vol.4, issue.17, pp.1107-1117, 2007. ,
Quantifying the roles of cell motility and cell proliferation in a circular barrier assay, Journal of The Royal Society Interface, vol.391, issue.4, pp.10-2013 ,
DOI : 10.1016/j.clon.2008.01.006
Intensity Compensation within Series of Images, Medical image computing and computer-assisted intervention, pp.41-49, 2003. ,
DOI : 10.1007/978-3-540-39903-2_6
URL : https://hal.archives-ouvertes.fr/inria-00615950
Image analysis and mathematical morphology, 1982. ,
Digital topology: introduction and survey, Computer Vision, Graphics, and Image Processing, pp.357-393, 1989. ,
THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES, Annals of Eugenics, vol.7, issue.4, pp.355-369, 1937. ,
DOI : 10.1111/j.1469-1809.1937.tb02153.x
´ Etude de l'´ equation de la diffusion avec croissance de la quantité dematì ere et son applicationàapplication`applicationà unprobì eme biologique, Bull. Univ. Etat Moscou, Ser. Int., Sect. A, Math. et Mecan. 1, Fasc, vol.6, pp.1-25, 1937. ,
Optimal control of systems governed by partial differential equations. Translated from the French by S. K. Mitter. Die Grundlehren der mathematischen Wissenschaften, Band, vol.170, 1971. ,