Geometric Description of Dynamin Induced Membrane Fission

Abstract

The terminal step during the process of clathrin-mediated endocytosis is the scission of the connection between the nascent bud and the parent membrane. Narrowing of the neck is driven by proteins or their complexes, most prominently dynamin, which assembles into rings and spirals that constrict the connection and are believed to generate sufficient force onto the membrane to induce fission. To advance our undertanding of the underlying mechanism, in this work we present a geometric framework to study the conformation of a semi-flexible polymer adhering to, or confined by an axially symmetric membrane. The rotational symmetry of the membrane is exploited to obtain a first integral of the fourth order Euler-Lagrange equation describing the polymer equilibrium states. In particular, we examine and characterize closed and helix-like curves with right-hand chirality, lying on surfaces with the shape of a cylinder and a catenoid. For the cylindrical case, the additional translational symmetry allows to integrate the Euler-Lagrange equation once more, obtaining a quadrature. In this framework the stresses transmitted by the polymer onto the membrane are determined entirely in terms of the local geometry of the combined system of the helical-dynamin coat wrapping around the membrane neck,allowing us to analyze the force and torques involved during the constriction process.