Mathematical modelling of cell migration

Rhoda Hawkins
Department of Physics & Astronomy
University of Sheffield

The cell cytoskeleton can be successfully modelled mathematically as an 'active gel'. This is gel that is driven out of equilibrium by the consumption of biochemical energy. In particular myosin molecular motors exert forces on actin filaments resulting in contraction. I will present simple models of cell movement using active get theory. Movement of a droplet of active gel is generated by flows of the contractile active gel inside the droplet. I will show how this depends on the average direction of cytoskeleton filaments and the boundary conditions at the edge of the model cell, which are set by interactions with the external environment. I will consider the shape deformation and movement of such model cells.
I will then discuss models for the cell nucleus and present calculation of the forces required to deform a nucleus when a cell passes through a constriction. I will comment on the relevance of this for metastatic cancer cells.