Mathematical Modelling of Cell Adhesion Forces: From Delay to Friction, an Instantaneous Limit
Speaker: Vuk Milisic, Université Paris 13
Location: Warren Weaver Hall 1302
Date: Tuesday, April 21, 2015, 11 a.m.
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 that motivated 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.