A Quantitative Model for Formation of Protein-Mediated Protrusions, Based on Continuum Elasticity Theory

Abstract

The close opposition of membranes needed for fusion is initiated by the formation of local protrusions. In viral fusion, the protrusions should be generated by several fusion proteins acting cooperatively within a cluster. We start with two parallel planar membranes and show that membrane elasticity alone can spontaneously cause several fusion proteins to self-organize into a cylindrically symmetric cluster that consists of three to six proteins cluster, independent of specific short-range protein-protein interactions. In essence, fusion proteins induce membrane bending which then brings the proteins together, creating more bending -- a positive feedback system. Calculations of energy minimization yield the following progression of protein arrangements: Three proteins initially arrange at the vertices of an equilateral triangle. Cluster formation continues by three additional proteins symmetrically arranging at the vertices of a more distal equilateral triangle that surrounds the three central proteins. These distal proteins move toward, and the central proteins away, from the center, yielding a cluster of six proteins arranged hexagonally on a circle. The energy needed to bend membranes into protrusions is supplied by the proteins in the cluster; continuum elasticity theory is used to calculate this energy. The total energy consists of the change in elastic energy of membrane deformation and the energy generated by an osmotic pressure difference that arises because the density of proteins outside the cluster is greater than the zero density inside cluster. The minimum energy is 75 kT for a cluster radius of 15 nm. The minimal energy per protein is 12 kT, which is a reasonable estimate.