# Membrane structure formation induced by two types of banana-shaped proteins

## TL;DR

This study combines analytical theory and simulations to explore how banana-shaped proteins induce membrane shape changes, revealing how different protein curvatures lead to various assembly structures and membrane morphologies.

## Contribution

It introduces a combined theoretical and simulation approach to understand membrane-mediated interactions of banana-shaped proteins and their role in membrane morphology.

## Key findings

- Same-type rods form linear assemblies causing tubulation.
- Opposite-type rods stabilize bump structures and form stripe patterns.
- Positive surface tension stabilizes stripe formations.

## Abstract

The assembly of banana-shaped rodlike proteins on membranes, and the associated membrane shape transformations, are investigated by analytical theory and coarse-grained simulations. The membrane-mediated interactions between two banana-shaped inclusions are derived theoretically using a point-like formalism based on fixed anisotropic curvatures, both for zero surface tension and for finite surface tension. On a larger scale, the interactions between assemblies of such rodlike inclusions are determined analytically. Meshless membrane simulations are performed in the presence of a large number of inclusions of two types, corresponding to curved rods of opposite curvatures, both for flat membranes and vesicles. Rods of the same type aggregate into linear assemblies perpendicular to the rod axis, leading to membrane tubulation. However, rods of the other type, those of opposite curvature, are attracted to the lateral sides of these assemblies, and stabilize a straight bump structure that prevents tubulation. When the two types of rods have almost opposite curvatures, the bumps attract one another, forming a stripe structure. Positive surface tension is found to stabilize the stripe formation. The simulation results agree well with the theoretical predictions provided the point-like curvatures of the model are scaled-down to account for the effective flexibility of the simulated rods.