A Computational Model of Protein Induced Membrane Morphology with Geodesic Curvature Driven Protein-Membrane Interface

TL;DR

This paper introduces a novel computational approach to model protein-induced membrane morphology by identifying protein-membrane interfaces using geodesic curvature and conformal mapping, enabling detailed analysis of complex membrane deformations.

Contribution

It develops the first computationally feasible method for determining protein-membrane interfaces and coupling membrane surface morphologies through conformal mapping and geodesic curvature modeling.

Findings

Efficiently locates minimal geodesic curvature curves on complex protein surfaces.

Demonstrates membrane deformation modeling using identified interfaces.

Reveals diverse membrane morphologies based on different protein-membrane interfaces.

Abstract

Continuum or hybrid modeling of bilayer membrane morphological dynamics induced by embedded proteins necessitates the identification of protein-membrane interfaces and coupling of deformations of two surfaces. In this article we developed (i) a minimal total geodesic curvature model to describe these interfaces, and (ii) a numerical one-one mapping between two surface through a conformal mapping of each surface to the common middle annulus. Our work provides the first computational tractable approach for determining the interfaces between bilayer and embedded proteins. The one-one mapping allows a convenient coupling of the morphology of two surfaces. We integrated these two new developments into the energetic model of protein-membrane interactions, and developed the full set of numerical methods for the coupled system. Numerical examples are presented to demonstrate (1) the efficiency and robustness of our methods in locating the curves with minimal total geodesic curvature on highly complicated protein surfaces, (2) the usefulness of these interfaces as interior boundaries for membrane deformation, and (3) the rich morphology of bilayer surfaces for different protein-membrane interfaces.