Abstract
The stimuli for the increase in epidermal mitosis during wound healing are not fully known. We construct a mathematical model which suggests that biochemical regulation of mitosis is fundamental to the process, and that a single chemical with a simple regulatory effect can account for the healing of circular epidermal wounds. The numerical results of the model compare well with experimental data. We investigate the model analytically by making biologically relevant approximations. We then obtain travelling wave solutions which provide information about the accuracy of these approximations and clarify the roles of the various model parameters.
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Bereiter-Hahn, J.: Epidermal cell migration and wound repair. In: Bereiter-Hahn, J., Matoltsy, A. G., Richards, K. S. (eds.) Biology of the integument, vol. 2 Vertebrates pp. 443–471. Berlin Heidelberg New York: Springer 1986
Brugal, G., Pelmont, J.: Existence of two chalone-like substances in intestinal extract from the adult newt, inhibiting embryonic intestinal cell proliferation. Cell Tissue Kinet. 8, 171–187 (1975)
Clark, R. A. F.: Overview and general considerations of wound repair. In: Clark, R. A. F., Henson, P. M. (eds.) The molecular and cellular biology of wound repair, pp. 3–34. New York: Plenum Press 1988
Clark, R. A. F.: Wound repair. Curr. Op. Cell Biol. 1, 1000–1008 (1989)
Eisinger, M., Sadan, S., Soehnchen, R., Silver, I. A.: Wound healing by epidermal-derived factors: experimental and preliminary chemical studies. In: Barbul, A., Pines, E., Caldwell, M., Hunt, T. K. (eds.) Growth factors and other aspects of wound healing, pp. 291–302. New York: Liss 1988a
Eisinger, M., Sadan, S., Silver, I. A., Flick, R. B.: Growth regulation of skin cells by epidermal cell-derived factors: implications for wound healing. Proc. Natl. Acad. Sci. USA 85, 1937–1941 (1988b)
Engel, J., Taylor, W., Paulsson, M., Sage, H., Hogan, B.: Calcium binding domains and calcium-induced conformational transition of SPARC/BM-40/Osteonectin, an extracellular glycoprotein expressed in mineralized and nonmineralized tissues. Biochem. 26, 6958–6965 (1987)
Folkman, J., Moscona, A.: Role of cell shape in growth control. Nature 273, 345–349 (1978)
Fremuth, F.: Chalones and specific growth factors in normal and tumor growth. Acta Univ. Carol. Monogr. 110 (1984)
Hennings, H., Elgjo, K., Iversen, O. H.: Delayed inhibition of epidermal DNA synthesis after injection of an aqueous skin extract (chalone). Virchows Arch. Abt. B Zellpath 4, 45–53 (1969)
Hondius-Boldingh, W., Laurence, E. B.: Extraction, purification and preliminary characterisation of the epidermal chalone. J. Biochem. 5, 191–198 (1968)
Irvin, T. T.: The healing wound. In: Bucknall, T. E., Ellis, H. (eds.) Wound healing for surgeons, pp. 3–28. Eastbourne, England: Bailliere Tindall 1984
Iversen, O. H.: What's new in endogenous growth stimulators and inhibitors (chalones). Path. Res. Pract. 180, 77–80 (1985)
Iversen, O. H.: The chalones. In: Baserga, R. (ed.) Tissue growth factors, pp. 491–550. Berlin Heidelberg New York: Springer 1981
Iversen, O. H.: Epidermal chalones and squamous cell carcinomas. Virchows Arch. B Cell Path. 27, 229–235 (1978)
Krawczyk, W. S.: A pattern of epidermal cell migration during wound healing. J. Cell Biol. 49, 247–263 (1971)
Marks, F.: A tissue-specific factor inhibiting DNA synthesis in mouse epidermis. Natl. Cancer Inst. Monogr. 38, 79–90 (1973)
Mason, I. J., Taylor, A., Williams, J. G., Sage, H., Hogan, B. L. M.: Evidence from molecular cloning that SPARC, a major product of mouse embryo parietal endoderm, is related to an endothelial cell ‘culture shock’ glycoprotein of M r 43000. The EMBO J. 5, 1465–1472 (1986)
Murray, J. D.: Mathematical biology. Berlin Heidelberg New York: Springer 1989
Odland, G. F.: Structure of the skin. In: Goldsmith, L. A. (ed.) Biochemistry and physiology of the skin, pp. 3–63. Oxford: Oxford Univ. Press 1983
Ortonne, J. P., Loning, T., Schmitt, D., Thivolet, J.: Immunomorphological and ultrastructural aspects of keratinocyte migration in epidermal wound healing. Virchows Arch. A 392, 217–230 (1981)
Potten, C. S., Hume W. J., Parkinson E. K.: Migration and mitosis in the epidermis. Br. J. Dermatol. 111, 695–699 (1984)
Radice, G.: The spreading of epithelial cells during wound closure in xenopus larvae. Dev. Biol. 76, 26–46 (1980)
Rudolph, R.: Contraction and the control of contraction. World J. Surg. 4, 279–287 (1980)
Rytömaa, T., Kiviniemi, K.: Chloroma regression induced by the granulocytic chalone. Nature 222, 995–996 (1969)
Rytömaa, T., Kiviniemi, K.: Regression of generalised leukemia in rat induced by the granulocytic chalone. Eur. J. Cancer 6, 401–410 (1970)
Sage, H., Vernon, R. B., Funk, S. E., Everitt, E. A., Angello, J.: SPARC, a secreted protein associated with proliferation, inhibits cell spreading in vitro and exhibits Ca2+-dependent binding to the extracellular matrix. J. Cell Biol. 109, 341–356 (1989)
Sherratt, J. A., Murray, J. D.: Models of epidermal wound healing. Proc. R. Soc. Lond. B 241, 29–36 (1990)
Snowden, J. M.: Wound closure: an analysis of the relative contributions of contraction and epithelialization. J. Surg. Res. 37, 453–463 (1984)
Stenn, K. S., DePalma, L.: Re-epithelialization. In: Clark, R. A. F., Henson. P. M. (eds.) The molecular and cellular biology of wound repair, pp. 321–335. New York: Plenum Press 1988
Trinkaus, J. P.: Cells into organs. The forces that shape the embryo. Englewood Cliffs, New Jersey: Prentice-Hall 1984
Van den Brenk, H. A. S.: Studies in restorative growth processes in mammalian wound healing. Brit. J. Surg. 43, 525–550 (1956)
Winstanley, E. W.: The epithelial reaction of the healing of excised cutaneous wounds in the dog. J. Comp. Pathol. 85, 61–75 (1975)
Winter, G. D.: Epidermal regeneration studied in the domestic pig. In: Maibach, H. I., Rovee, D. T. (eds.) Epidermal wound healing, pp. 71–112. Chicago: Year Book Med. Publ. Inc. 1972
Wright, N., Alison, M.: Biology of epithelial cell populations. Oxford: Clarendon Press 1984
Wright, N. A.: Cell proliferation kinetics of the epidermis. In: Goldsmith, L. A. (ed.) Biochemistry and physiology of the skin, pp. 203–229. Oxford: Oxford Univ. Press 1983
Yamaguchi, T., Hirobe, T., Kinjo, Y., Manaka, K.: The effect of chalone on the cell cycle in the epidermis during wound healing. Exp. Cell Res. 89, 247–254 (1974)
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Sherratt, J.A., Murray, J.D. Mathematical analysis of a basic model for epidermal wound healing. J. Math. Biol. 29, 389–404 (1991). https://doi.org/10.1007/BF00160468
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DOI: https://doi.org/10.1007/BF00160468