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

Vuk Milisic (LAGA, Université Paris 13)

Mathematical modelling of cell adhesion forces : from delay to friction, an instantaneous limit

vendredi 20 mars 2015, 11h00 - 12h00

Salle de réunion, espace Turing


Abstract:

Ce travail est effectué en collaboration avec Dietmar OELZ du Courant Institute, New York University.

In this talk we present the starting mechanical model of the lamellipodial actin-cytoskeleton meshwork.
The model is derived starting from the microscopic description of mechanical properties of laments and
cross-links and also of the life-cycle of cross-linker molecules [2, 5, 4].
We introduce a simplified system of equations that accounts for adhesions created
by a single point on which we apply a force. We present the adimensionalisation that led
to a singular limit that motivated our mathematical study. Then we explain the mathe-
matical setting and results already published [2, 3]. In the last part we present the latest
developments : we give results for the fully coupled system with unbounded non-linear
o-rates [1]. This leads to two possible regimes : under certain hypotheses on the data
there is global existence, out of this range we are able to prove blow-up in nite time.

References :

[1] V. Milisic and D. Oelz. Unbounded o-rates in the structured model for friction mediated by transient
elastic linkages. in preparation.

[2] V. Milisic and D. Oelz. On the asymptotic regime of a model for friction mediated by transient elastic
linkages. J. Math. Pures Appl. (9), 96(5):484{501, 2011.

[3] V. Milisic and D. Oelz. On a structured model for the load dependent reaction kinetics of transient
elastic linkages mediating nonlinear friction. 2015. accepted for publication in SIAM SIMA.

[4] D. Oelz and C. Schmeiser. Derivation of a model for symmetric lamellipodia with instantaneous cross-
link turnover. Arch. Ration. Mech. Anal., 198(3):963{980, 2010.

[5] D. Oelz, C. Schmeiser, and V. Small. Modelling of the actin-cytoskeleton in symmetric lamellipodial
fragments. Cell Adhesion and Migration, 2:117{126, 2008.