A formula for membrane mediated point particle interactions on near spherical biomembranes

TL;DR

This paper develops a mathematical model for protein interactions on near-spherical biomembranes, deriving formulas for energy derivatives to understand how proteins influence membrane shape and behavior.

Contribution

It introduces a novel approach to model membrane-protein interactions on near-spherical surfaces, extending previous flat-membrane models with a new derivative calculation for energy optimization.

Findings

Derived a formula for energy derivatives with respect to protein configurations.

Implemented numerical experiments demonstrating the model's applicability.

Extended membrane-protein interaction models to near-spherical geometries.

Abstract

We consider a model of a biomembrane with attached proteins. The membrane is represented by a near spherical continuous surface and attached proteins are described as discrete rigid structures which attach to the membrane at a finite number of points. The resulting surface minimises a quadratic elastic energy (obtained by a perturbation of the Canham-Helfrich energy) subject to the point constraints which are imposed by the attachment of the proteins. We calculate the derivative of the energy with respect to protein configurations. The proteins are constrained to move tangentially by translation and by rotation in the axis normal to a reference point. Previous studies have typically restricted themselves to a nearly flat membrane and circular inclusions. A numerically accessible representation of this derivative is derived and employed in some numerical experiments.