General Non-axisymmetric Shapes of Biological Membranes and their Importance in Understanding Endocytosis

Abstract

Many important biological phenomena are mediated by cell membranes and the shapes accommodated by these membranes. For example, endocytosis involves bending to form a bud or a tube from a flat shaped membrane under the action of proteins such as clathrin or BAR and their coupling to actin pulling forces. Various morphological shapes of membranes are governed by thermodynamic parameters such as osmotic pressure drop across the membrane or membrane tension. Most theoretical studies focusing on understanding membrane bending involve either small deformations about a given configuration or axi-symmetric shape transitions. In this talk, using the recent advancements in theoretical and computational modeling of membranes, we show that axi-symmetric or small deformations are inadequate to understanding the morphological phase-diagrams of membranes governed by protein induced spontaneous curvature and membrane tension. In particular, we discuss how axi-symmetric analysis of membranes misguide our understanding and demonstrate that non-axisymmetric shape transitions are almost always energetically favorable to axi-symmetric ones. We apply these methods to understand the classical endocytosis phenomena in mammalian and yeast cells. With the newly found non-axisymmetric shapes, we discuss the physical principles governing endocytosis at varying levels of membrane tension.