Statistical mechanics of cell membranes

Lateral heterogeneity on cell membranes, such as lipid rafts, has been implicated in many biological functions. We used a field theory to examine the thermodynamic forces underlying lipid raft formation on resting living cell membranes. We found that it is difficult to reconcile the observed size of rafts on living cell membranes (∼100 nm) with a mechanism that involves coupling between spontaneous curvature differences and concentration fluctuations. Such a mechanism seems to predict raft domain sizes that are larger and commensurate with that observed on synthetic membranes. Therefore, using a Poisson-Boltzmann approach, we explored whether electrostatic forces originating from transmembrane proteins and net negative charges on cell membranes could play a role in determining lipid raft size on living cell membranes. We found that a balance between the intrinsic tendency of raft components to segregate, line tension, and the effective dipolar interactions among membrane constituents leads to a stable phase with a characteristic length scale commensurate with the observed size of lipid rafts on living cell membranes. We calculated the phase diagram of such a system. In a certain region of parameter space, an interesting phase with a mosaic-like morphology consisting of an intertwined pattern of raft domains and non-raft domains is predicted. These patterns are much larger than individual rafts.; We also studied kinetic pathways of order-order transitions in lipid raft model systems using a time-dependent Ginzburg-Landau (TDGL) approach. During the stripe to hexagonal phase transition in an incompressible two-component system, the stripe phase first develops a pearling-like instability along the phase boundaries, which grows and drives the stripes to break up into droplets that arrange into a hexagonal pattern. These dynamic features are consistent with recent experimental observations. During the disorder to hexagonal phase transition in an incompressible three-component system, the disordered state first passes through a transient stripe-like structure, which breaks up into a hexagonal droplet phase by a similar pearling instability.; A closely-related problem concerns how the lateral heterogeneity on cell membranes affects the endocytosis process. Supported by recent in vivo and in vitro experiments, we constructed a theoretical model investigating the scission process of buds in living cells. (Abstract shortened by UMI.)...