Skip to main content
Log in

Cell traction models for generating pattern and form in morphogenesis

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

Abstract

During early development migratory mesenchymal cells navigate to distant sites where they aggregate to form a variety of embryonic organ rudiments. We present here a new model for mesenchymal cell morphogenesis based on the mechanical interaction between motile cells and their extracellular environment. The model is based on two properties of motile cells: (a) they are capable of generating large traction forces which can deform the extracellular matrix through which they move, and (b) the deformations they produce in their environment affect the direction of their movements. We derive field equations which describe the motion of cells in an elastic extracellular matrix and show that these equations can generate a variety of spatial patterns, such as the formations of skin organ primordia, especially feather germs, cartilage condensation patterns which presage bone formation in limb development, and melanocyte density patterns which form animal coat patterns.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bronner, M., Cohen, A.: Migratory patterns of cloned neural crest melanocytes injected into host chicken embryos. Proc. Natl. Acad. Sci. USA 76, 1843–47 (1979).

    Google Scholar 

  • Carter, S.: Principles of cell motility: the direction of cell movement and cancer invasion. Nature 208, 1183 (1965).

    Google Scholar 

  • Carter, S.: Haptotaxis and the mechanism of cell motility Nature 213, 256–60 (1967).

    Google Scholar 

  • Christiansen, R.: Mechanics of Composite Materials. New York: John Wiley 1979

    Google Scholar 

  • Cohen, D. S., Murray, J. D.: A generalized diffusion model for growth and dispersal in a population. J. Math. Biol. 12, 237–49 (1981)

    Google Scholar 

  • Dunn, G., Ebendahl, T.: Contact guidance on oriented collagen gels. Exp. Cell Res. 111, 475–79 (1978)

    Google Scholar 

  • Elsdale, T., Bard, J.: Cellular interactions in mass cultures of human diploid fibroblasts. Nature, 236 152–55 (1972)

    Google Scholar 

  • Folkman, J., Moscona, A.: Role of cell shape in growth control. Nature 273, 345–49 (1978)

    Google Scholar 

  • Gustafson, T., Wolpert, L.: Cellular movement and contact in sea urchin morphogenesis. Biol. Rev. 42, 442–498 (1967)

    Google Scholar 

  • Harris, A., Stopak, D., Wild, P.: Fibroblast traction as a mechanism for collagen morphogenesis. Nature 290, 249–51 (1981)

    Google Scholar 

  • Landau, L., Lifshitz, E.: Theory of Elasticity, 2nd ed. New York: Pergamon Press 1970

    Google Scholar 

  • Morse, P., Feshbach, H.: Methods of Theoretical Physics, Vol. 1, New York: McGraw-Hill 1953

    Google Scholar 

  • Murray, J. D.: Nonlinear Differential Equation Models in Biology. Oxford: Clarendon Press 1977.

    Google Scholar 

  • Murray, J. D., Oster, G. F., Harris, A. K.: A mechanical model for mesenchymal morphogenesis. J. Math. Biol. 17, 125–129 (1983)

    Google Scholar 

  • Murray, J. D.: A pre-pattern formation mechanism for animal coat patterns. J. Theoret. Biol. 88, 161–199 (1981a)

    Google Scholar 

  • Murray, J. D.: On pattern formation mechanisms for lepidopteran wing patterns and mammalian coat markings. Phil. Trans. Roy. Soc. London Ser. B 295 473–96 (1981b)

    Google Scholar 

  • Odell, G., Oster, G., Burnside, B. Alberch, P. The mechanical basis of morphogenesis I: Epithelial folding and invagination. Devel. Biol. 85, 446–62 (1981)

    Google Scholar 

  • Oster, G. F., Murray, J. D., Harris, A. K.: Mechanical aspects of mesenchymal morphogenesis. J. Embryol. exp. Morph. 78, 83–125 (1983)

    Google Scholar 

  • Othmer, H.: Interactions of reaction and diffusion in open systems. Ph.D. Dissertation. Chem. Engr. Dept., Univ. of Minnesota 1969

  • Perelson, A., Murray, J. D., Oster, G. F.: Nonlinear behavior of the cell traction model for mesenchymal morphogenesis (in preparation) (1983)

  • Purcell, E.: Life at low Reynolds number. Amer. J. Phys. 45, 1–11 (1977)

    Google Scholar 

  • Sengel, P.: Morphogenesis of Skin. Developmental and Cell Biology Series, vol. 3. Cambridge Univ. Press 1976

  • Turing, A. M.: The chemical basis of morphogenesis. Phil. Trans. R. Soc. Lond B237, 37–72 (1952)

    Google Scholar 

  • Weiss, P.: Erzwingung elementarer strukturverschiedenheiten am in vitro wachsenden gewebe. Wilhelm Roux Arch. 116, 438–554 (1929)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Support for this work was provided by NSF Grant # MCS-8110557 [GFO]

Rights and permissions

Reprints and permissions

About this article

Cite this article

Murray, J.D., Oster, G.F. Cell traction models for generating pattern and form in morphogenesis. J. Math. Biology 19, 265–279 (1984). https://doi.org/10.1007/BF00277099

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00277099

Key words

Navigation