Eur. Phys. J. E 3, 403-412
Vesicle propulsion in haptotaxis: A local model
I. Cantat1 - C. Misbah2 - Y. Saito3
1 GMCM, Université de Rennes (CNRS),
Campus de Beaulieu, Bât. 11A, CS 74205
263, av. du Général Leclerc, 35042 Rennes Cedex, France
2 Laboratoire de Spectrométrie Physique, Université Joseph Fourier (CNRS),
Grenoble I, B.P. 87, 38402 Saint-Martin d'Hères Cedex, France
3 Department of Physics, Keio University,
3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
icantat@univ-rennes1.fr
Received 10 February 2000
Abstract
We study theoretically vesicle locomotion due to haptotaxis.
Haptotaxis is referred to motion induced by an adhesion gradient
on a substrate. The problem is solved
within a local approximation where a Rayleigh-type dissipation
is adopted. The dynamical model is akin to the Rousse model
for polymers. An
invariant formulation
is used to solve a dynamical model which includes a kind
of dissipation due to bond breaking/restoring with the substrate.
For a stationary situation where the vesicle acquires
a constant drift velocity, we formulate the propulsion problem
in terms of a nonlinear eigenvalue (the a priori unknown drift velocity)
one of Barenblat-Zeldovitch type. A counting argument shows
that the velocity belongs to a discrete set. For a relatively tense
vesicle, we provide an analytical expression for the drift velocity
as a function of relevant parameters. We find good agreement
with the full numerical solution. Despite the oversimplification of the model
it allows the identification of a relevant quantity, namely the
adhesion length, which turns out to be crucial also in the nonlocal
model in the presence of hydrodynamics, a situation on which
we have recently
reported (I. Cantat and C. Misbah, Phys. Rev. Lett. 83, 235 (1999))
and which constitutes the subject of a forthcoming extensive study.
PACS
87.16.-b Subcellular structure and processes -
87.19.-j Properties of higher organisms -
47.55.Dz Drops and bubbles
Copyright EDP Sciences, Società Italiana di Fisica, Springer-Verlag