Mathematical models for cell polarization – MODPOL

We investigate various models for cell polarisation in various experimental contexts. The models mainly concern the budding yeast Saccharomyces cerevisiae and to a less extent the fission yeast Schizosaccharomyces pombe. Interestingly, the budding yeast may be subject to spontaneous polarisation (Wedlich-Soldner et al. Science 2003). This process involves some cytoplasmic molecular marker (Cdc42) which is transported through the actin network and get attached to the membrane. There is a nonlinear feedback since the binding enhances the growth of new actin filaments. Several models have been proposed based on the Turing instability acting on the membrane concentration of the marker.

In this project we follow a promising model introduced recently by Hawkins et al. (Phys. Rev. E 2009) which takes into account the trafficking of markers in the cytoplasm. Based on a fruitful analogy with the so-called Keller-Segel model we have obtained encouraging preliminary results from the mathematical viewpoint via entropy methods (global existence, blow-up, asymptotic behaviour). These results have clear interpretation in the biological context of polarisation since the high concentration of molecular markers coincide with the location of the polar cap.

Nevertheless the main questions addressed by Hawkins et al have yet to be resolved. What are the main differences between the trafficking through the actin network and along the microtubules? It is expected that the actin network favors fast and spontaneous polarisation whereas the microtubules guarantee robustness. However the mathematical results are not so clear at the present time, and the methods adapted from the Keller-Segel system have shown their limit. We need new ideas to progress in this task.

Besides this mathematical task, we will progress in the modeling of cell polarisation by coupling the model for transport of the molecular markers with cell wall deformation. There is a large amount of literature devoted to the biomechanics law for this type of membrane. Also the interactions between several cells (e.g. during the mating phase of S. cerevisiae) will be investigated.

To achieve these advances in the basic research of cell polarisation, we will join together complementary skills: three mathematicians specialised in the analysis of PDE and familiar with mathematical biology problems, one mathematician expert in numerics, one physicist expert in the modeling of biophysical problems (e.g. cellular trafficking) and one experimentalist specialised in yeast.

We need a post-doctoral fellow during one year to carry out several mathematical and modeling tasks, and to create a strong connection between the teams involved in this project. We also plan to organise a workshop at the end of the project on different aspects of cellular trafficking and cytoskeleton organisation from the modeling viewpoint.