Mixed and active membranes

In this proposal I describe my plan to attack several important open problems facing our understanding of multi-component, non-equilibrium fluid membranes. In a biological context these often interact with the cytoskeleton of a living cell. I will study how membrane microphase separation is induced by applied forces, such as might arise from coupling to the active cytoskeleton. This model is desperately needed to understand recent data, e.g. for large variations in the local membrane diffusion constant.I also plan to study the regulation and transient adaptation of the membrane tension and pressure of a living cell. I will construct an appropriate non-equilibrium model for the creation of transient bonds between the membrane and the cytoskeleton and use this to establish a self-consistent theory for the steady state, and time variation, of these quantities. Forces generated by molecular motors anchored to the cytoskeleton act on these bonds. The lifetime of the bonds depends on the membrane compliance, which in turn depends on it tension and pressure in a way that can be computed self-consistently. The transient response of the cell following rapid changes in volume or membrane area, can be probed by modern micropipette or tether-pulling experiments. We thereby hope to construct a theory for the active mechanical properties of the cell membrane.I will also work to rigorously test the long standing but untested Saffman-Delbruck theory for membrane diffusion. I will analyse experimental data from Prof Bassereau's group at the Institut Curie. These ongoing experiments have been motivated by our recent theoretical analysis of flows on cylindrical membrane tubes in which we suggest that the controlled variation of tube radius in this geometry may provide the most discriminatory test of the Saffman-Delbruck theory yet proposedI will also study the assembly and dynamics of the FtsZ contractile ring. This protein, a bacterial analogue of tubulin, assembles into fibers that form a ring around dividing bacterial cells. This process involves molecular force generation, fibre self assembly, depolymerisation and membrane-mediated forces, all of which are fields in which I have significant expertise. Very recently model in vitro experiments have studied the role of FtsZ in generating membrane deformation. We plan to repeat similar experiments in membrane vesicles but with the addition of additional vital molecular components, such as FtsA, which plays an important role in associating the FtsZ ring with the membrane. A testable physical model for the action of these dividing rings in generating controlled membrane deformation would be most useful in a field which is of the very highest contemporary interest. There is the hope that this may also have pharmaceutical relevance, e.g. in new antibacterial treatments that target the cell division apparatus.There is an additional element to this proposal which is not included here for reasons of confidentiality.