* Vuk Milisic (Institut Galilée, Université Paris 13) - MAP5-UMR 8145

Vuk Milisic (Institut Galilée, Université Paris 13)

On the asymptotic regime of a model framework for friction mediated by transient elastic linkages

vendredi 26 novembre 2010, 11h00 - 12h00

Salle de réunion, espace Turing


In this presentation we will briefly introduce motility due to actin
filaments in the lamellipodia of living cells. We present its
mathematical modelling and specify issues that the model can deal with
[Oelz, et al, 2008]. We will then insist more on the transient elastic
linkages from the cell to the substrate. We present a system of an
integral equation of Volterra type coupled to an original renewal
equation. The integral equation describes the trajectory of a binding
site which is connected via transiently
remodelling linkages to the substrate and which evolves driven by a
given force. The renewal model accounts for the remodelling process of
linkages which attach and break with given probabilities.

We give a framework for solutions of such a coupled
system and provide a rigorous justification of the asymptotic limit
of infinitesimally rapid turnover of linkages. We present a simple
example and comment some preliminary numerical simulations.