Skip to main content
Log in

A moving boundary model of acrosomal elongation

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

Abstract

A sperm penetrates an egg by extending a long, actin-filled tube known as the acrosomal process. This simple example of biomotility is one of the most dramatic. In Thyone, a 90 μm process can extend in less than 10 s. Experiments have shown that actin monomers stored in the base of the sperm are transported to the growing tip of the acrosomal process where they add to the ends of the existing filaments.

The force that drives the elongation of the acrosomal process has not yet been identified although the most frequently discussed candidate is the actin polymerization reaction. Developing what we believe are realistic moving boundary models of diffusion limited actin fiber polymerization, we show that actin filament growth occurs too slowly to drive acrosomal elongation. We thus believe that other forces, such as osmotically driven water flow, must play an important role in causing the elongation. We conjecture that actin polymerization merely follows to give the appropriate shape to the growing structure and to stabilize the structure once water flow ceases.

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.

Similar content being viewed by others

References

  1. Abramowitz, M., Stegun, I. A.: Handbook of mathematical functions. Washington, D.C.: National Bureau of Standards 1964

    Google Scholar 

  2. Aebi, W., Fowler, W. E., Isenberg, G., Pollard, T. D., Smith, P. R.: Crystalline actin sheets: their structure and polymorphism. J. Cell Biol. 91, 340–351 (1981)

    Google Scholar 

  3. Bonder, E. M., Fishkind, D. J., Mooseker, M. S.: Direct measurement of critical concentrations and assembly rate constants at the two ends of an actin filament. Cell 34, 491–501 (1983)

    Google Scholar 

  4. Cannon, J. R.: The one-dimensional heat equation, Vol. 23. In: Encyclopeida of mathematics and its applications series. Addison-Wesley, Menlo Park, CA 1984

    Google Scholar 

  5. Coluccio, L. M., Tilney, L. G.: Phalloidin enhances assembly by preventing monomer dissociation. J. Cell Biol. 99, 529–535 (1984)

    Google Scholar 

  6. Crank, J.: Diffusion with rapid irreversible immobilization. Trans. Faraday Soc. 53, 1083–1091 (1957a)

    Google Scholar 

  7. Crank, J.: Two methods for the numerical solution of moving-boundary problems in diffusion and heat flow. Quart. J. Mech. Appl. Math 10 220–231 (1957b)

    Google Scholar 

  8. Dan, J. C., Hagiwara, Y.: Studies on the acrosome. IX. Course of acrosome reaction in the starfish. J. Ultrastruct. Res. 18, 562–579. (1967)

    Google Scholar 

  9. Dan, J. C., Ohori, Y., Kushida, H.: Studies on the acrosome. VII. Formation of the acrosomal process in sea urchin spermatoza. J. Ultrastruct. Res. 11, 508–524 (1964)

    Google Scholar 

  10. Hermans, J. J.: Diffusion with discontinuous boundary. J. Colloid Sci. 2, 387–398 (1947)

    Google Scholar 

  11. Hill, T. L.: Microfilament or microtubule assembly or disassembly against a force. Proc. Natl. Acad. Sci. USA 78, 5613–5617 (1981)

    Google Scholar 

  12. Hill, T. L., Kirschner, M. W.: Subunit treadmilling of microtubules or actin in the presence of cellular barriers: possible conversion of chemical free energy into mechanical work. Proc. Natl. Acad. Sci. USA 79, 490–494 (1982)

    Google Scholar 

  13. Inoué, S., Tilney, L. G.: The acrosomal reaction of Thyone sperm. I. Changes in the sperm head visualized by high resolution video microscopy. J. Cell Biol. 93, 812–819 (1982)

    Google Scholar 

  14. Kevorkian, J., Cole, J. D.: Perturbation Methods in Applied Mathematics. Springer, Berlin Heidelberg New York 1981

    Google Scholar 

  15. Markey, F., Larsson, H., Weber, K., Lindberg, U.: Nucleation of actin polymerization from profilactin opposite effects of different nuclei. Biochem. Biophys. Acta 704, 43–51 (1982)

    Google Scholar 

  16. Morse, P. M., Feshbach, H.: Methods of Theoretical Physics, Part II. McGraw-Hill, New York 1953

    Google Scholar 

  17. Murray, J. D.: Asymptotic Analysis. Springer, Berlin Heidelberg New York 1984

    Google Scholar 

  18. Oster, G. F., Perelson, A. S., Tilney, L. G.: A mechanical model for elongation of the acrosomal process in Thyone sperm. J. Math. Biol. 15, 259–265 (1982)

    Google Scholar 

  19. Pollard, T. D., Mooseker, M. S.: Direct measurement of actin polymerization rate constants by elecron microsopy of actin filaments nucleated by isolated microvillus cores. J. Cell Biol. 88, 654–659 (1981)

    Google Scholar 

  20. Tilney, L. G.: The role of actin in nonmuscle cell motility. In: Inoué, S., Stephens, R. E. (eds.) Molecules and cell movement, pp. 339–386. Raven Press, New York 1975

    Google Scholar 

  21. Tilney, L. G.: Actin, motility and membranes: In: Cone, R. A., Dowling, J. E. (eds.) Membrane transduction mechanisms, pp. 163–186. Raven Press, New York 1979

    Google Scholar 

  22. Tilney, L. G., Bonder, E. M., Coluccio, L. M., Mooseker, M. S.: Actin from Thyone sperm assembles on only one end of an actin filament: a behavior regulated by profilin. J. Cell Biol. 97, 112–124 (1983)

    Google Scholar 

  23. Tilney, L. G., Hatano, S., Ishikawa, H., Mooseker, M. S.: The polymerization of actin: its role in the generation of the acrosomal process of certain echinoderm sperm. J. Cell Biol. 59, 109–126 (1973)

    Google Scholar 

  24. Tilney, L. G., Kallenbach, N.: Polymerization of actin. VI. The polarity of the actin filaments in the acrosomal process and how it might be determined. J. Cell Biol. 81, 608–623 (1979)

    Google Scholar 

  25. Tilney, L. G., Inoué, S.: Acrosomal reaction of Thyone sperm. II. The kinetics and possible mechanism of acrosomal process elongation. J. Cell Biol. 93, 820–827 (1982)

    Google Scholar 

  26. Tobacman, L. S., Korn E. D.: The regulation of actin polymerization and the inhibition of monomeric actin ATPase activity by Acanthamoeba profilin. J. Biol. Chem. 257, 4166–4170 (1982)

    Google Scholar 

  27. Tseng, P. C.-H., Pollard, T. D.: Mechanism of a tin of Acanthamoeba profilin: demonstration of actin species specificity regulation by micromolar concentrations of MgCl2. J. Cell Biol. 94, 213–218 (1982)

    Google Scholar 

  28. Wegner, A.: Head to tail polymerization of actin. J. Mol. Biol. 108, 139–150 (1976)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Work partially supported by the United States Department of Energy

Rights and permissions

Reprints and permissions

About this article

Cite this article

Perelson, A.S., Coutsias, E.A. A moving boundary model of acrosomal elongation. J. Math. Biology 23, 361–379 (1986). https://doi.org/10.1007/BF00275254

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00275254

Key words

Navigation