Thesis title: Mesoscale remodeling of fluid lipid membranes
Lipid membranes, along with their ability to deform and shape-remodel, play a key role in the vast majority of life-related workings, hence making them abundant as well as unique materials. Indeed, due to the innate fluid and multiscale nature of a lipid bilayer, the local -- few nanometers range -- interplay of lipids and curvature-inducing proteins crowding its surface, as well as the reaction to external flows, may result in a full-scale -- hundreds of nanometers -- response of the membrane. This might involve triggering proteins clustering, invagination formation, and, eventually, vesicle detachment. Extensive multidisciplinary efforts, ranging from experimental to theoretical and numerical approaches, have already paved the way for how the relevant actors drive such processes. Nevertheless, a quantitative picture following membrane remodeling across different scales is yet to be fully addressed, thus calling for a flexible, full-scale, and comprehensive model, able to reproduce individual protein specificity whereas coupling hydrodynamics effects and topological rearrangements.
In this Thesis, a continuum diffuse interface model for the lipid membrane is developed in order to meet, by means of purposely designed numerical simulations, the aforementioned needs. Starting from a Ginzburg-Landau type of free elastic energy inferred from the celebrated Canham-Helfrich Hamiltonian, a topologically-related energy term is proposed and deployed in the context of fusion and fission of full-scale vesicles. Therefore, the activation energies and optimal force fields involved in the processes are retrieved through a rare event technique. The model is further enriched with the capability of reproducing the bilayer's response to external actions together with the surface-mobility of embedded inclusions. Protein-induced remodeling is thence analyzed, ranging from the effects of caveolin oligomers to how dynamin severs lipid tubules, and eventually tackling the highly non-linear, long-range, curvature-mediated interactions between partially adhesive capsids floating on the membrane.