Topological transitions in fluid lipid membranes: activation energy and force fields

Topological transitions of fluid lipid membranes are fundamental processes for cell life. For example, they are required for endo- and exocytosis or to enable neurotransmitters to cross the neural synapses. They are also of strong interest in medicine and in the pharmaceutical industry, e.g. for the development of antivirals and drug delivery. Fluid lipid membranes can be treated not only from a biochemical perspective but also from a mechanical one, using the classical Canham-Helfrich elastic free energy which successfully describes many aspects of membrane dynamics but rules out the possibility of dealing with topological transitions. In this thesis, I develop, numerically demonstrate, and use a new Ginzburg-Landau type of free energy that treats the membrane as a diffuse interface, with the further ability to naturally handle topological changes, allowing the whole, full-scale topological transition to be simulated without interruption. The free energy functional approaches the Canham-Helfrich one in the limit of small width-to-vesicle-extension ratio, even accounting for the Gaussian energy term, which plays a crucial role during topology changes due to the celebrated Gauss-Bonnet theorem. Coupled with a rare event technique, the method is also capable of computing the force fields needed to overcome the elastic energy barriers involved in the topological transformation. Inspired by the idea that fusion and fission proteins could have evolved in nature in order to carry out a minimal work expenditure, I evaluate the minimal free energy pathway for the transition between two spherical large unilamellar vesicles and a dumbbell-shaped one. Results show merging intermediates reminiscent of those found in experiments and molecular dynamics simulations, while the obtained forces are in excellent agreement, in terms of intensity, scale, and spatial localization with experimental data on typical fission protein systems. As regards fusion, the obtained force field is extremely intense to be exerted by fusion proteins and its strong localization suggests that a local modification of the Gaussian modulus can substantially affect the pathway during the merging process. Therefore, I also investigate this scenario, showing that the energy barrier is drastically lowered and the pathway substantially changed by such a modification, and discuss biological examples in which it might be important. The case of vesicles with non-zero bilayer spontaneous curvature is considered as well. The ability of the diffuse interface to capture important features of the stalk-hemifusion pathway is revealed by considering the transition between a single oblate vesicle and a toroidal one, showing that a stabilization of the hemifusion-like intermediate occurs in accordance with the known fusogenic effect of lipids with negative (monolayer) spontaneous curvature. The same stabilization is obtained pushing the model toward its limits, namely dealing with small vesicles that start the merging process at closer distances. The lateral stress profile of the membrane diffuse interface is calculated as a function of the elastic rigidities, yielding a coarse-grained version of molecular model findings. Additionally, the diffuse-interface approach is used to study the fission of lipid tubules. The obtained elastic picture is compatible with many features of dynamin-driven constriction, and allows to speculate on the mechanism that couples the polymerization length to the fission site position. Finally, I discuss the extension of the model with a term that accounts for area-difference elasticity and introduce a possible way to deal with intermembrane interactions. Preliminary results on thermal fluctuations and coupling with macroscopic hydrodynamic motion are also shown.