Bulletin of Mathematical Biology

, Volume 51, Issue 4, pp 485–500 | Cite as

A mathematical model for cell sorting, migration and shape in the slug stage ofDictyostelium discoideum

  • Tamiki Umeda
Article
  • 62 Downloads

Abstract

A mathematical model for cell sorting and migration in the slug stage of cellular slime moldsDictyostelium discoideum is proposed. Assuming that a slug is a “mixed fluid” of prespore and prestalk cells, a set of equations which describe the dynamics of cell distribution, internal pressure and velocity of hte slug are derived from the balance formula of individual cell movement. These equations are analyzed to obtain the spatial patterns of the two types of cells at dynamical equilibrium and the relationship between the migration velocity and the slug size. The body shape of the elongated slug at the migrating stage is also investigated, taking account of the law of surface tension. The stable shapes of slugs with different volumes are explicity obtaained and the existence of critical size of a slug is suggested.

Keywords

Motive Force Dictyostelium Discoideum Cellular Slime Mold Prespore Cell Prestalk Cell 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  1. Bonner, J. T., P. G. Koontz Jr. and D. Paton. 1953. “Size in Relation to the Rate of Migration in the Slime MoldDictyostelium discoideum.”Mycologia 45, 235–240.Google Scholar
  2. Farnsworth, P. A. and W. F. Loomis, 1975. “A Gradient in the Thickness of the Surface Sheath in Pseudoplasmodia ofDictyostelium discoideum.”Dev. Biol. 46, 349–357.CrossRefGoogle Scholar
  3. Goel, N. S. and N. Richter-Dyn. 1974.Stochastic Models in Biology. New York: Academic Press.Google Scholar
  4. Hohl, H. R. and K. B. Raper. 1964. “Control of Sorocarp Size in the Cellular Smile MoldDictyostelium discoideum.”Dev Biol. 9, 137–153.CrossRefGoogle Scholar
  5. Inouye, K. and I. Takeuchi. 1979. “Analytical Studies on Migrating Movement of the Pseudoplasmodium ofDictyostelium discoideum.”Protoplasma 99, 289–304.CrossRefGoogle Scholar
  6. —. 1980. “Motive Force of the Migrating Psuedoplasmodium of the Cellular Slime MouldDictyostelium discoideum.”J. Cell Sci. 41, 53–64.Google Scholar
  7. Kobuchi, Y. 1985. “A Density Dependent Model for Prestalk/Prespore Pattern Formation inDictyostelium discoideum I. Basic Mathematic Framework.” In:Mathematical Topics in Population Biology, Morphogenesis and Neurosciences E. Teramoto and M. Yamaguti (eds),Lecture Notes in Biomathematics, Vol. 71, pp. 234–243. Berlin: Springer-Verlag.Google Scholar
  8. Kopachik, W. 1982. “Size Regulation inDictyosteliumJ. Embryol. exp. Morph. 68, 23–35.Google Scholar
  9. Landau, L. D. and E. M. Lifshitz. 1959.Fluid Mechanics (translated by J. B. Sykes and W. H. Reid). Oxford: Pergamon Press.Google Scholar
  10. MacWilliams, H. K. and J. T. Bonner, 1979. “The Prestalk-Prespore Pattern in Cellular Slime Molds.”Differentiation 14 1–22.CrossRefGoogle Scholar
  11. Matsukuma, S. and A. J. Durston. 1979. “Chemotactic Cell Sorting inDictyostelium discoideum.”J. embruol. exp. Morph. 50, 243–251.Google Scholar
  12. Odell, G. M. and J. T. Bonner. 1986. “How theDictyostelium discoideum Grex Crawls.”Phil. Trans. R. Soc. 312, 487–525.Google Scholar
  13. Pate, E. F. and H. G. Othmer. 1986. “Differentiation, Cell Sorting and Proportion Regulation in the Slug Stage ofDictyostelium discoideum.”J. theor. Biol. 118, 301–319.MathSciNetCrossRefGoogle Scholar
  14. Rubinow, S. I., L. A. Segel and W. Ebel. 1981. “A Mathematical Framework for the Study of Morphogenetic Development in the Slime Mold.”J. theor. Biol. 91, 99–113.CrossRefGoogle Scholar
  15. Shaffer, B. M. 1965. “Cell Movement within Aggregates of the Slime MouldDictyostelium discoideum Revealed by Surface Markers.”J. Embryol. exp. Morph. 13, 97–117.Google Scholar
  16. Sternfeld, J. and C. N. David. 1981. “Cell Sorting during Pattern Formation inDictyostelium.”Differentiation 20, 10–21.CrossRefGoogle Scholar
  17. Takeuchi, I., M. Tasaka, M. Oyama, A. Yamamoto and A. Amagai. 1982. “Pattern Formation in the Development ofDictyostelium discoideum.” InEmbryonic Development, M. M. Burger and R. Weber (eds.), pp. 283–294. New York: Liss.Google Scholar
  18. Teramoto, E. 1985. “An equilibrium Theory of Cell Distribution inDictyostelium discoideum.” InMathematical Topics in Population Biology, Morphogenesis and Neurosciences, E. Teramoto and M. Yamaguti (eds),Lecture Notes in Biomathematics, Vol. 71, pp. 217–223. Berlin: Springer-Verlag.Google Scholar

Copyright information

© Society for Mathematical Biology 1989

Authors and Affiliations

  • Tamiki Umeda
    • 1
  1. 1.Department of Biophysics, Faculty of ScienceKyoto UniversityKyotoJapan

Personalised recommendations