Mathematical modelling of cell adhesion forces : from delay to friction, from global to local existence

par Vuk Milisic (CNRS & Paris 13)

mardi 9 févr. 2016, 15:15 → 16:15 Europe/Paris

salle Fokko du Cloux (ICJ, UCBL - La Doua, Bât. Braconnier)

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 filaments and cross-links and also of the life-cycle of cross-linker molecules. 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 motivating our mathematical study. Then we explain the mathematical setting and results already published. In the last part we present the latest developments~: we give results for the fully coupled system with unbounded non-linear off-rates. 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 finite time. This is joint work with Dietmar Oelz.