Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-19T12:33:26.792Z Has data issue: false hasContentIssue false
  • English
  • Français

On the viscous deformation of biological cells under anisotropic surface tension

Published online by Cambridge University Press:  21 April 2006

Daniel Zinemanas  and
Avinoam Nir
Daniel Zinemanas
Affiliation:
Department of Chemical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
Avinoam Nir
Affiliation:
Department of Chemical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

A fluid-mechanical approach for the cleavage of biological cells is presented. The equations of motion were combined with concentration and orientation distribution balances, for active contractile filaments on the cell surface, to provide a dynamic evolution of interfacial forces and deformation. The resulting flow and the simultaneously developing surface-tension anisotropy provided a mechanism that facilitates the generation of a contractile ring at the cell equator: a major organelle in the establishment of cell furrow and the ultimate cleavage. The moving-boundary problem was solved numerically using boundary-integral representation for the Stokes equations which was modified to incorporate the anisotropic interfacial tensions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 193 , August 1988 , pp. 217 - 241
Copyright
© 1988 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adin Mann, J. 1984 Surf. Colloid Sci. 13, 145.
Akkas, N. 1980 J. Biomech. 13, 977.
Akkas, N. 1981 J. Biomech. 14, 621.
Aris, R. 1962 Vector, Tensors and the Basic Equations of Fluid Mechanics. Prentice-Hall.
Barthes-Biesel, D. 1980 J. Fluid Mech. 100, 831.
Barthes-Biesel, D. & Sgaier, H. 1985 J. Fluid Mech. 160, 119.
Beams, H. W. & Evans, T. C. 1940 Biol. Bull. 79, 188.
Butschli, O. 1876 Abh. Senckenberg. naturf. Ges., Frankf. M. 10, 232.
Conrad, G. W. & Rappaport, R. 1981 In Mitosis/Cytokinesis (ed. A. M. Zimmerman & A. Forer), p. 365. Academic.
Cox, R. G. 1969 J. Fluid Mech. 37, 601.
Edidin, N. 1977 Ann. Rev. Biophys. Bioengng 3, 179.
Evans, E. A. & Skalak, R. 1979 Mechanics and Thermodynamics of Biomembranes. CRC.
Gallez, D. 1984 J. Theor. Biol. 111, 341.
Geller, A. S., Lee, A. S. & Leal, L. G. 1986 J. Fluid Mech. 169, 27.
Goody, R. S. & Holmes, K. C. 1983 Biochim Biophys Acta 726, 13.
Greenspan, H. P. 1977a J. Theor. Biol. 65, 79.
Greenspan, H. P. 1977b Stud. Appl. Maths 57, 45.
Greenspan, H. P. 1978 J. Theor. Biol. 70, 135.
Higdon, J. J. L. 1985 J. Fluid Mech. 159, 195.
Hiram, Y. & Nir, A. 1983 J. Colloid Interface Sci. 95, 462.
Hiramoto, Y. 1956 Expl Cell. Res. 11, 630.
Hiramoto, Y. 1968 22nd Symp. Soc. Expl Biol., p. 311.
Hiramoto, Y. 1978 Dev. Grow. Diff. 13, 191.
Karasiewicz, J. 1981 In Mitosis/Cytokinesis (ed. A. M. Zimmerman & A. Forer), p. 419. Academic.
Koppel, D. E., Oliver, J. M. & Berlin, R. D. 1982 J. Cell. Biol. 93, 950.
Ladyzhenskaya, D. A. 1969 The Mathematical Theory of Viscous Incompressible Flow, 2nd edn. Gordon and Breach.
Lanir, Y. 1983 J. Biomech. 16, 1.
Leal, L. G. & Hinch, E. J. 1971 J. Fluid Mech. 46, 685.
Lee, S. H. & Leal, L. G. 1982 J. Colloid Interface Sci. 87, 81.
Levich, V. G. & Krylov, V. S. 1969 Ann. Rev. Fluid Mech. 1, 293.
Pujara, P. & Lardner, T. J. 1979 J. Biomech. 12, 293.
Rallison, J. M. & Acrivos, A. 1978 J. Fluid Mech. 89, 191.
Rappaport, R. 1978 J. Exp. Zool. 206, 1.
Rappaport, R. & Ebstein, R. P. 1965 J. Exp. Zool. 158, 373.
Sapir, T. 1984 Surface tension driven motion of interfaces. M.Sc. thesis, Technion.
Sapir, T. & Nir, A. 1985 Physico. Hydrodyn. 6, 803.
Schroeder, T. E. 1973 Proc. Natn. Acad. Sci. USA 70, 1688.
Schroeder, T. E. 1975 In Molecules and Cell Movement (ed. S. Inoue & E. R. Stephens), p. 305. NY: Raven.
Schroeder, T. E. 1981a In Cytoskeletal Elements and Plasma Membrane Organization (ed G. Poste & G. K. Nicolson), p. 169. Elsevier.
Schroeder, T. E. 1981b Expl Cell. Res. 134, 231.
Schroeder, T. E. 1987 In The Biomechanics of Cell Division (ed. N. Akkas), p. 209. Plenum.
Spek, J. 1918 Arch. f. Entw. Mech. 44, 5.
Waxman, A. M. 1981 J. Non Newtonian Fluid Mech. 9, 235.
Waxman, A. M. 1984 Stud. Appl. Maths 66, 189.
White, J. G. & Borisy, G. G. 1983 J. Theor. Biol. 101, 289.
Youngren, G. K. & Acrivos, A. 1975 J. Fluid Mech. 69, 377.
Youngren, G. K. & Acrivos, A. 1976 J. Fluid Mech. 76, 433.
Zinemanas, D. & Nir, A. 1987 In The Biomechanics of Cell Division (ed. N. Akkas), p. 281. Plenum.