The diffuse interface description of lipid membranes: hemifusion pathway and lateral stress profile

Fusion and fission of lipid membrane vesicles are at the basis of countless biological processes, ranging from neurotransmission to viral infections. Despite this, they are not well understood due to their multiscale character. Indeed, membrane fusion/fission simultaneously involves large-scale membrane deformations and a local rearrangement of lipids, a fact that limits the use of molecular models and calls for a mesoscopic approach such as the celebrated Canham–Helfrich one. However, this elastic model is not able to handle fusion/fission events, preventing access to the key Gaussian curvature forces at play during these processes. Moreover, it does not account for the membrane thickness scale, which is essential for capturing the hemifused intermediates observed in experiments. In order to overcome these limitations, we use a diffuse interface description of the membrane that contains both the large scale of the vesicle and the small scale of the membrane thickness. The method preserves the Canham-helfrich elasticity, while naturally handling fusion/fission events and providing access to the Gaussian curvature forces. We compute several minimal energy pathway for fusion/fission, also evaluating the involved elastic forces, and show that the diffuse interface captures key features of the hemifusion pathway, such as the fusogenic behavior of negative monolayer spontaneous curvatures and the presence of a (meta)stable hemifusion state, whose degree of stability is shown to depend on both the Gaussian curvature modulus and the vesicle curvature. Additionally, we show how the elastic parameters governing the large-scale affect the distribution of stresses within the membrane, which is employed by cells to regulate membrane proteins such as mechanosensitive channels. The lateral stress profile is calculated as a function of the Canham-Helfrich elastic rigidities, providing a coarse-grained version of molecular models findings, but with a top-down point of view.