Mechanics of Cellular Transport
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Lipid membranes are versatile structures that interact with various kinds of proteins to maintain the shape and functionality of cells and their organelles. For example, they are actively involved in the transport of various proteins and other nutrients in and out of cells. The transport of macromolecules, which cannot diffuse through these bilayer membranes occur through an extensive remodeling of plasma membrane. This is executed by a designated set of membrane-deforming proteins, which supply the energy and drive membrane remodeling leading to formation of cargo-carrying vesicles. In our study, we focus on the most commonly used transport pathway termed "Clathrin Mediated Endocytosis." We use continuum mechanics to study the equilibrium of lipid bilayers in the presence of three key membrane-deforming proteins, namely, clathrin, BAR and actin filaments.To the end, we generalize the theory of lipid membranes to incorporate the anisotropic curvatures generated by proteins. Our study reveals a protein-induced "Snap-through Instability" that offsets tension in the lipid membrane and drives vesicle growth. It disentangles the individual role of key proteins and provides mechanistic insights into fundamental debates in the field of cellular transport. Since these proteins (actin and BAR proteins) are involved in other interfacial rearrangements in cells, our work could provide new insights into biological processes in cells at-large. Motivated by the observed instability, we derive the generalized stability conditions for heterogeneous lipid membranes. These theories, in the future, can provide physical insights into the observed instability.