Numerical study of patterning in biomembranes : from bicomponent vesicles to virus receptors

Plasma membrane forms a selective barrier for the cell, yet its role goes far beyond a simple frontier. Indeed, it plays a crucial role in biological functions such as endo and exocytosis, cell communication or adhesion. It is now widely agreed that membrane lipid and protein spatial repartition is not homogeneous but that these components are organized into nanodomains, which have proven to be key players in the above-mentioned biological functions. Combining statistical physics analytical tools and numerical simulations, we propose in this work a physical mechanism for this membrane organization in a simple model bicomponent vesicle. At the mesoscale, we describe the membrane with a composition- curvature coupling mechanism. We perform extensive Monte Carlo simulations for different membrane parameters (concentration, spontaneous curvature, mixture affinity, surface tension) and study its equilibrium states. We characterize the range of parameters leading to phase modulations by drawing phase diagrams from the simulation results and compare them to the ones previously obtained by analytical field-theoretic techniques. Different observables are computed such as correlation functions and domain size distributions to extract information about the emerging membrane patterns, such as their typical shape, size or spacing. With respect to domain shape, we analyse experimental membrane protein (HIV receptors) trajectories to quantify domain shape and compare it to our simulations. In order to propose a valid rationale for membrane structuring at different scales, we also perform coarse-grained molecular dynamics simulations (MARTINI) of lipid bilayers including curvature-generating components from which we extract the physical membrane parameters that can be plugged into the mesoscale model. We extend our mesoscale model by studying the effect of applied forces to the vesicle, inspired by cell division process during which membrane components reorganize and such forces are at play.