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


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.