2020 Impact factor 1.890
Soft Matter and Biological Physics

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

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