The effects of MAPK activity on cell-cell adhesion during wound healing

The mechanisms underlying collective migration, or the coordinated movement of a population of cells, are not well understood despite its ubiquitous nature. As a means to investigate collective migration, we consider a wound healing scenario in which a population of cells fills in the empty space left from a scratch wound. Here we present a simplified mathematical model that uses reaction-diffusion equations to model collective migration during wound healing with an emphasis on cell movement and its response to both cell signaling and cell-cell adhesion. We use the model to investigate the effect of the MAPK signaling cascade on cell-cell adhesion during wound healing after EGF treatment. Our results suggest that activation of the MAPK signaling cascade stimulates collective migration through increases in the pulling strength of leader cells. We further use the model to suggest that treating a cell population with EGF converts the time to wound closure (as function of wound area) from parabolic to linear.

[1]  D. Montell,et al.  Myosin VI is required for E-cadherin-mediated border cell migration , 2002, Nature Cell Biology.

[2]  Matthew J Simpson,et al.  Mean-field descriptions of collective migration with strong adhesion. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  John D. Haley,et al.  EGFR signaling networks in cancer therapy , 2008 .

[4]  Ken Jacobson,et al.  MAP kinases and cell migration , 2004, Journal of Cell Science.

[5]  E. Shin,et al.  c-Jun N-terminal kinase is involved in motility of endothelial cell , 2001, Experimental & Molecular Medicine.

[6]  E. Tadmor,et al.  New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection—Diffusion Equations , 2000 .

[7]  Jonathan A. Sherratt,et al.  Models of epidermal wound healing , 1990, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[8]  Lionel Roques,et al.  Allee effect promotes diversity in traveling waves of colonization , 2012, Proceedings of the National Academy of Sciences.

[9]  Ruth E Baker,et al.  Modelling Cell Migration and Adhesion During Development , 2012, Bulletin of Mathematical Biology.

[10]  Cyril Andrieu,et al.  Collective Cell Migration in Neural Crest , 2015 .

[11]  David A. Cheresh,et al.  Regulation of Cell Motility by Mitogen-activated Protein Kinase , 1997, The Journal of cell biology.

[12]  David Swigon,et al.  Using a continuum model to predict closure time of gaps in intestinal epithelial cell layers , 2013, Wound repair and regeneration : official publication of the Wound Healing Society [and] the European Tissue Repair Society.

[13]  Douglas A. Chapnick,et al.  Leader cell positioning drives wound-directed collective migration in TGFβ-stimulated epithelial sheets , 2014, Molecular biology of the cell.

[14]  T. Gilman,et al.  Wound Outcomes: The Utility of Surface Measures , 2004, The international journal of lower extremity wounds.

[15]  R L Juliano,et al.  Signal transduction by cell adhesion receptors and the cytoskeleton: functions of integrins, cadherins, selectins, and immunoglobulin-superfamily members. , 2002, Annual review of pharmacology and toxicology.

[16]  Roy S Herbst,et al.  Review of epidermal growth factor receptor biology. , 2004, International journal of radiation oncology, biology, physics.

[17]  Stuart A. Aaronson,et al.  Exogenous Expression of N-Cadherin in Breast Cancer Cells Induces Cell Migration, Invasion, and Metastasis , 2000, The Journal of cell biology.

[18]  S. Hagen,et al.  Traveling waves in response to a diffusing quorum sensing signal in spatially-extended bacterial colonies. , 2014, Journal of theoretical biology.

[19]  P. Friedl,et al.  Plasticity of cell migration: a multiscale tuning model , 2010 .

[20]  D A Lauffenburger,et al.  Mathematical model for the effects of adhesion and mechanics on cell migration speed. , 1991, Biophysical journal.

[21]  Douglas A. Chapnick,et al.  Partners in crime: the TGFβ and MAPK pathways in cancer progression , 2011, Cell & Bioscience.

[22]  Ruth E. Baker,et al.  Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves , 2012 .

[23]  Philip K Maini,et al.  Traveling wave model to interpret a wound-healing cell migration assay for human peritoneal mesothelial cells. , 2004, Tissue engineering.

[24]  D. L. Sean McElwain,et al.  How much information can be obtained from tracking the position of the leading edge in a scratch assay? , 2014, Journal of The Royal Society Interface.

[25]  M. Jo,et al.  Cooperativity between the Ras-ERK and Rho-Rho Kinase Pathways in Urokinase-type Plasminogen Activator-stimulated Cell Migration* , 2002, The Journal of Biological Chemistry.

[26]  Alexandra Jilkine,et al.  Wave-pinning and cell polarity from a bistable reaction-diffusion system. , 2008, Biophysical journal.

[27]  Stanislav Y Shvartsman,et al.  Role of boundary conditions in an experimental model of epithelial wound healing. , 2006, American journal of physiology. Cell physiology.

[28]  L Edelstein-Keshet,et al.  Regimes of wave type patterning driven by refractory actin feedback: transition from static polarization to dynamic wave behaviour , 2012, Physical biology.

[29]  David M. Bortz,et al.  Analytical solutions to Fisher's equation with time-variable coefficients , 2011, Appl. Math. Comput..

[30]  Sean P. Palecek,et al.  Erratum: Integrin–ligand binding properties govern cell migration speed through cell–substratum adhesiveness , 1997, Nature.

[31]  David Swigon,et al.  Continuum Model of Collective Cell Migration in Wound Healing and Colony Expansion , 2022 .

[32]  R. Fisher.  THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES , 1937 .

[33]  P. Rørth,et al.  Collective cell migration. , 2009, Annual review of cell and developmental biology.

[34]  D. Webb,et al.  Extracellular signal-regulated kinase functions in the urokinase receptor-dependent pathway by which neutralization of low density lipoprotein receptor-related protein promotes fibrosarcoma cell migration and matrigel invasion. , 2000, Journal of cell science.

[35]  D. Bortz,et al.  Propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Geoffrey W. Stevens,et al.  Cell migration and proliferation during monolayer formation and wound healing , 2009 .

[37]  Xuedong Liu,et al.  Decoding the quantitative nature of TGF-beta/Smad signaling. , 2008, Trends in cell biology.

[38]  J. Downward,et al.  Ras and TGFβ cooperatively regulate epithelial cell plasticity and metastasis , 2002, The Journal of Cell Biology.

[39]  C. Schmeiser,et al.  A one-dimensional model of cell diffusion and aggregation, incorporating volume filling and cell-to-cell adhesion , 2009, Journal of mathematical biology.

[40]  Matthew J Simpson,et al.  Lattice-Free Models of Cell Invasion: Discrete Simulations and Travelling Waves , 2013, Bulletin of mathematical biology.

[41]  A. Misra,et al.  Epidermal growth factor receptor targeting in cancer: a review of trends and strategies. , 2013, Biomaterials.

[42]  James D. Murray.  Mathematical Biology: I. An Introduction , 2007 .

[43]  T. Chou,et al.  A mathematical model of intercellular signaling during epithelial wound healing. , 2009, Journal of theoretical biology.

[44]  A. Hall,et al.  Myosin-IXA Regulates Collective Epithelial Cell Migration by Targeting RhoGAP Activity to Cell-Cell Junctions , 2012, Current Biology.

[45]  Aimin Li,et al.  A new method for calculation of flocculation kinetics combining Smoluchowski model with fractal theory , 2013 .

[46]  P. Friedl,et al.  Collective cell migration in morphogenesis, regeneration and cancer , 2009, Nature Reviews Molecular Cell Biology.

[47]  H. Banks,et al.  Mathematical and Experimental Modeling of Physical and Biological Processes , 2009 .

[48]  A. A. Samarskii,et al.  Examples of the numerical calculation of temperature waves , 1963 .

[49]  Miki Ebisuya,et al.  ERK Activation Propagates in Epithelial Cell Sheets and Regulates Their Migration during Wound Healing , 2004, Current Biology.