Mathematical models of cell migration - mathematical and computational analysis

Dietmar Oelz (The University of Queensland) #

Note that this seminar will take place in room 2/104 (Seminarrau Statistik) in Mathematikon! Seminar will start at 11:15!!! #

In this talk I will touch upon three different projects on modelling the migration of biological cells: I will start by introducing a continuum model for collective cell migration in which cells are characterised by position and polarity in one spatial dimension. For this toy model of so-called scratch wound experiments, we study travelling wave solutions corresponding to either polarisation and depolarisation waves including their (linear) stability. The second part of the talk deals with an interdisciplinary project in which we use modelling and simulation to verify that during cellular transmigration through narrow pores, e.g. during extra-vasation, the microtubule network in the rear part of migrating melanoma cells acts as a mechanostat controlling the timely passage of the nucleus through the narrow constraint. In the third part of the talk I present a fluid type model for the cytoplasm of cells undergoing amoeboid cell motion. Through simulation we show that friction-less cell migration in rough tubes can be explained by the shear forces occurring in the viscous cytoplasm and that the resulting intra-cellular flows are predicted to follow a circular pattern.