Abstract
We present a stochastic model which describes fronts of cells invading a wound. In the model cells can move, proliferate, and experience cell-cell adhesion. We find several qualitatively different regimes of front motion and analyze the transitions between them. Above a critical value of adhesion and for small proliferation large isolated clusters are formed ahead of the front. This is mapped onto the well-known ferromagnetic phase transition in the Ising model. For large adhesion, and larger proliferation the clusters become connected (at some fixed time). For adhesion below the critical value the results are similar to our previous work which neglected adhesion. The results are compared with experiments, and possible directions of future work are proposed.
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M. Bramson, P. Calderoni, A. Demasi, P. Ferrari, J. Lebowitz and R. H. Schonmann, Microscopic selection principle for a diffusion-reaction equation, J. Stat. Phys. 45(5–6): 905–920 (1986).
T. Callaghan, E. Khain, L. M. Sander and R. M. Ziff, A stochastic model for wound healing, J. Stat. Phys. 122(5): 909–924 (2006).
R. A. Fisher, The wave of advance of advantageous genes, Ann. Eugen. 7: 355–369 (1937).
J. S. Langer, in C. Godreche ed. Solids far from equilibrium, Cambridge, Cambridge University Press, New York, pp. 297–364 (1992).
J. F. Gouyet, M. Plapp, W. Dieterich, and P. Maass, Description of far-from-equilibrium processes by mean-field lattice gas models, Adv. Phys. 52: 523–638 (2003).
A. R. Kerstein, Computational study of propagating fronts in a lattice-gas model, J. Stat. Phys. 45(5–6): 921–931 (1986).
A. Kolmogorov, I. Petrovsky and N. Piscounov, Etude de liequation de la diffusion avec croissance de la quantite de matiere et son application a un probleme biologique, Moscow Univ. Bull. Math. 1: 1–25 (1937).
P. K. Maini, D. L. S. McElwain and D. Leavesley, Travelling waves in a wound healing assay, Appl. Math. Lett. 17(5): 575–580 (2004).
E. Moro, Internal fluctuations effects on Fisher waves, Phys. Rev. Lett. 87(23): 238303 (2001).
J. D. Murray, Mathematical Biology. (Springer, New York 2002).
L. Onsager, Crystal statistics. I. A two-dimensional model with an order-disorder transition, Phys. Rev. 65: 117–149 (1944).
M. Plapp and J. F. Gouyet, Interface dynamics in a mean-field lattice gas model: Solute trapping, kinetic coefficient, and interface mobility, Phys. Rev. E 55(5): 5321–5337 (1997).
H. Sheardown and Y. L. Cheng, Mechanisms of corneal epithelial wound healing, Chem. Eng. Sci. 51(19): 4517–4529 (1996).
J. A. Sherratt and J. D. Murray, Models of epidermal wound-healing, Proc. R. Soc. London Ser. B Biol. Sci. 241(1300): 29–36 (1990).
J. A. Sherratt and J. C. Dallon, Theoretical models of wound healing: past successes and future challenges, C.R. Biol. 325(5): 557–564 (2002).
D. C. Walker, G. Hill, S. M. Wood, R. H. Smallwood and J. Southgate, Agent-based computational modeling of wounded epithelial cell monolayers, IEEE Tran. Nanobiosci. 3(3): 153–163 (2004).
D. C. Walker, J. Southgate, G. Hill, A. Holcombe, D. R. Hose, S. M. Wood, S. Mac Neil and R. H. Smallwood, The epitheliome: agent-based modelling of the social behaviour of cells, Biosystems 76(1–3): 89–100 (2004).
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We consider as an example the experiment of Sheardown and Cheng(13) on the wounding of rabbit corneas. It was shown in Ref. 2 that the typical ratio of proliferation rate and basic diffusion rate is of the order of 3 × 10−4.
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Khain, E., Sander, L.M. & Schneider-Mizell, C.M. The Role of Cell-Cell Adhesion in Wound Healing. J Stat Phys 128, 209–218 (2007). https://doi.org/10.1007/s10955-006-9194-8
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DOI: https://doi.org/10.1007/s10955-006-9194-8