DOI: 10.1140/epje/e2003-00022-1
Vesicles in haptotaxis with hydrodynamical dissipation
I. Cantat1, 2, K. Kassner3 and C. Misbah11 Laboratoire de Spectrométrie Physique, Université Joseph Fourier (CNRS), Grenoble I, BP 87, Saint-Martin d'Hères, 38402 Cedex, France
2 GMCM, Université de Rennes (CNRS), Campus de Beaulieu, bâtiment 11A CS 74205, 263 avenue du Général Leclerc, 35042 Rennes Cedex, France
3 Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, 39016 Magdeburg, Germany
isabelle.cantat@univ-rennes1.fr
(Received 24 June 2002 and Received in final form 4 February 2003 Published online: 16 April 2003 )
Abstract
We analyze the problem of vesicle migration in haptotaxis (a motion directed
by an adhesion gradient), though most of the reasoning applies to chemotaxis
as well as to a variety of driving forces.
A brief account has
been published on this topic [6]. We present an extensive analysis of this problem and
provide a basic discussion of most of the relevant processes of migration.
The problem allows for an arbitrary shape evolution which is compatible
with the full hydrodynamical flow in the Stokes limit. The problem
is solved within the boundary integral formulation based on the Oseen
tensor. For the sake of simplicity we confine ourselves to 2D flows in the
numerical analysis. There are basically two regimes (i) the tense
regime where the vesicle behaves as a "droplet" with an effective
contact angle. In that case the migration velocity is given by the Stokes
law. (ii) The flask regime where the vesicle has a significant (on the
scale of the vesicle size)
contact curvature. In that case we obtain a new migration law
which substantially differs from the Stokes law.
We develop general arguments
in order to extract analytical laws
of migration. These are in good agreement with the full numerical analysis.
Finally we mention several important future issues and open questions.
87.17.Jj - Cell locomotion; chemotaxis and related directed motion.
87.16.Dg - Membranes, bilayers, and vesicles.
47.55.Dz - Drops and bubbles.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2003
