The mechanism responsible for domain registration in two membrane leaflets has thus far remained enigmatic. Using continuum elasticity theory, we show that minimum line tension is achieved along the rim between thicker (ordered) and thinner (disordered) domains by shifting the rims in opposing leaflets by a few nanometers relative to each other. Increasing surface tension yields an increase in line tension, resulting in larger domains. Because domain registration is driven by lipid deformation energy, it does not require special lipid components nor interactions at the membrane midplane.

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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.

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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.