Abstract
Membrane remodelling processes involving the formation and fission of small buds require the formation and closure of narrow membrane necks, both for biological membranes and for model membranes such as lipid bilayers. The conditions required for the stability of such necks are well understood in the context of budding of vesicles with bilayer asymmetry and/or intramembrane domains. In many cases, however, the necks form in the presence of an adhesive surface, such as a solid particle or substrate, or the cellular cortex itself. Examples of such processes in biological cells include endocytosis, exocytosis and phagocytosis of solid particles, the formation of extracellular and outer membrane vesicles by eukaryotic and prokaryotic cells, as well as the closure of the cleavage furrow in cytokinesis. Here, we study the interplay of curvature elasticity, membrane-substrate adhesion, and constriction forces to obtain generalized stability conditions for closed necks which we validate by numerical energy minimization. We then explore the consequences of these stability conditions in several experimentally accessible systems such as particle-filled membrane tubes, supported lipid bilayers, giant plasma membrane vesicles, bacterial outer membrane vesicles, and contractile rings around necks. At the end, we introduce an intrinsic engulfment force that directly describes the interplay between curvature elasticity and membrane-substrate adhesion.
Highlights
In the absence of external forces, liquid droplets attain spherical shapes that minimize their surface area and, their interfacial free energy for a given droplet volume
We explore the consequences of these stability conditions in several experimentally accessible systems such as particle-filled membrane tubes, supported lipid bilayers, giant plasma membrane vesicles, bacterial outer membrane vesicles, and contractile rings around necks
We have shown that the presence of an adhesive surface strongly affects the stability of closed membrane necks
Summary
In the absence of external forces, liquid droplets attain spherical shapes that minimize their surface area and, their interfacial free energy for a given droplet volume. Intriguing vesicle shapes are provided by two spheres connected by a narrow membrane neck that appears to be highly curved but does not contribute to the curvature energy of the vesicle membrane.[1,2,3,4] Such necks are formed by membranes with uniform composition,[1,5] by membranes with intramembrane domains,[6,7,8] and by membranes exposed to optical tweezers.[9] narrow membrane necks are ubiquitous in biological cells Such necks are observed prior to endo- and exocytosis,[10,11] phagocytosis,[12] cytokinesis,[13] as well as autophagosome formation.[14] In the latter processes, the neck formation is regulated by a complex network of proteins.[15,16]. We extend the application of the analytical model to particle-filled membrane tubes, budding of supported lipid bilayers from homogeneous and patterned substrates, giant plasma membrane and outer membrane vesicle formation, and narrow necks in the presence of externally applied constriction forces. The upper and lower signs of the Æ or 8 symbols will correspond to endocytic and exocytic engulfment, respectively
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