University of Sussex (UOS) - United Kingdom

Supervisor: Anotida Madzvamuse

Student: Victor Juma

12 - Life time models

Based on experimentally observed structures, we will develop and adapt current mathematical models of reaction-diffusion type (in 2D, 3D, on surfaces) to describe the spatio-temporal life cycles of actin and keratin filaments, their binding proteins, focal adhesions, hemidesmosomes and various regulatory molecules. We propose to adapt reaction models for actin and keratin filaments to describe biochemical processes such as nucleation, polymerisation and solubilisation, depolymerisation, annealing, disassembly and fragmentation and extend the models to take into account diffusion processes. To further understand migrating single cells, we will mathematically characterise the morphology and dynamics of FAs by modelling their size, number, localisation, velocity profiles and turnover. We will develop new mathematical models to describe hemidesmosome protein dynamics. The models derived will be solved efficiently, accurately and robustly by the use of moving and surface finite element methods in 2- and 3-D and on complex evolving topological surfaces. Ultimately, we will develop an integrated computational model to link the dependencies between the individual components of the life cycle.