Starting from fertilization, through tissue growth, hormone secretion, synaptic transmission, and sometimes morbid events of carcinogenesis and viral infections, membrane fusion regulates the whole life of high organisms. Despite that, a lot of fusion processes still lack well-established models and even a list of main actors. A merger of membranes requires their topological rearrangements controlled by elastic properties of a lipid bilayer. That is why continuum models based on theories of membrane elasticity are actively applied for the construction of physical models of membrane fusion. Started from the view on the membrane as a structureless film with postulated geometry of fusion intermediates, they developed along with experimental and computational techniques to a powerful tool for prediction of the whole process with molecular accuracy. In the present review, focusing on fusion processes occurring in eukaryotic cells, we scrutinize the history of these models, their evolution and complication, as well as open questions and remaining theoretical problems. We show that modern approaches in this field allow continuum models of membrane fusion to stand shoulder to shoulder with molecular dynamics simulations, and provide the deepest understanding of this process in multiple biological systems.

Sphingomyelin- and cholesterol- enriched membrane domains, commonly referred to as “rafts” play a crucial role in a large number of intra- and intercellular processes. Recent experiments suggest that not only the volumetric inhomogeneity of lipid distribution in rafts, but also the arrangement of the 1D boundary between the raft and the surrounding membrane is important for the membrane-associated processes. The reason is that the boundary preferentially recruits different peptides, such as HIV (human immunodeficiency virus) fusion peptide. In the present work, we report a theoretical investigation of mechanisms of influence of the raft boundary arrangement upon virus-induced membrane fusion. We theoretically predict that the raft boundary can act as an attractor for viral fusion peptides, which preferentially distribute into the vicinity of the boundary, playing the role of ‘line active components’ of the membrane (‘linactants’). We have calculated the height of the fusion energy barrier and demonstrated that, in the case of fusion between HIV membrane and the target cell, presence of the raft boundary in the vicinity of the fusion site facilitates fusion. The results we obtained can be further generalized to be applicable to other enveloped viruses.

Fusion of cellular membranes during normal biological processes, including proliferation, or synaptic transmission, is mediated and controlled by sophisticated protein machinery ensuring the preservation of the vital barrier function of the membrane throughout the process. Fusion of virus particles with host cell membranes is more sparingly arranged and often mediated by a single fusion protein, and the virus can afford to be less discriminative towards the possible different outcomes of fusion attempts. Formation of leaky intermediates was recently observed in some fusion processes, and an alternative trajectory of the process involving formation of π-shaped structures was suggested. In this study, we apply the methods of elasticity theory and Lagrangian formalism augmented by phenomenological and molecular geometry constraints and boundary conditions to investigate the traits of this trajectory and the drivers behind the choice of one of the possible scenarios depending on the properties of the system. The alternative pathway proved to be a dead end, and, depending on the parameters of the participating membranes and fusion proteins, the system can either reversibly enter the corresponding “leaky” configuration or be trapped in it. A parametric study in the biologically relevant range of variables emphasized the fusion protein properties crucial for the choice of the fusion scenario.

Signal transduction through cellular membranes requires the highly specific and coordinated work of specialized proteins. Proper functioning of these proteins is provided by an interplay between them and the lipid environment. Liquid-ordered lipid domains are believed to be important players here, however, it is still unclear whether conditions for a phase separation required for lipid domain formation exist in cellular membranes. Moreover, membrane leaflets are compositionally asymmetric, that could be an obstacle for the formation of symmetric domains spanning the lipid bilayer. We theoretically show that the presence of protein in the membrane leads to the formation of a stable liquid-ordered lipid phase around it by the mechanism of protein wetting by lipids, even in the absence of conditions necessary for the global phase separation in the membrane. Moreover, we show that protein shape plays a crucial role in this process, and protein conformational rearrangement can lead to changes in the size and characteristics of surrounding lipid domains.

Lipid droplets are unique organelles that store neutral lipids encapsulated by the lipid monolayer. In some processes of cellular metabolism, lipid droplets interact with peroxisomes resulting in the fusion of their envelopes and the formation of protrusions of the peroxisome monolayer, called pexopodia. The formation of pexopodia is facilitated by free fatty acids generated during lipolysis within lipid droplets. In this work, we studied the fusion of monolayer and bilayer membranes during the interaction between lipid droplets and peroxisomes. To this end, we built the energy trajectory of this process using the continuum elasticity theory and investigated the molecular details of the fusion structures utilizing molecular dynamics. We divided the fusion process into two stages: formation of a stalk and its consequent expansion into pexopodia. We found that in the considered system, the stalk was energetically more stable and had a lower energy barrier of formation compared to the case of bilayer fusion. The further evolution of the stalk depended on the value of the spontaneous curvature of the membrane in a threshold manner. We attributed the possible expansion of the stalk to the incorporation of free fatty acids into the stalk region. The developed model allowed describing quantitatively the process of monolayer–bilayer fusion.

The line tension of the edge of the lipid bilayer pore is calculated on the basis of the elastic theory of continuous liquid-crystal medium. Three types of deformations of the membrane were taken into