# Budding and vesiculation induced by conical membrane inclusions

## TL;DR

This paper presents an analytical model explaining how conical membrane inclusions induce budding and vesiculation in lipid bilayers, considering membrane energy and inclusion entropy, aligning well with recent simulations.

## Contribution

The study introduces a novel analytical model combining membrane bending energy and inclusion entropy to predict budding and vesiculation phenomena.

## Key findings

- High inclusion density leads to aggregation and vesiculation.
- The model predicts bud radii based on bending energy.
- Results agree with recent computer simulations.

## Abstract

Conical inclusions in a lipid bilayer generate an overall spontaneous curvature of the membrane that depends on concentration and geometry of the inclusions. Examples are integral and attached membrane proteins, viruses, and lipid domains. We propose an analytical model to study budding and vesiculation of the lipid bilayer membrane, which is based on the membrane bending energy and the translational entropy of the inclusions. If the inclusions are placed on a membrane with similar curvature radius, their repulsive membrane-mediated interaction is screened. Therefore, for high inclusion density the inclusions aggregate, induce bud formation, and finally vesiculation. Already with the bending energy alone our model allows the prediction of bud radii. However, in case the inclusions induce a single large vesicle to split into two smaller vesicles, bending energy alone predicts that the smaller vesicles have different sizes whereas the translational entropy favors the formation of equal-sized vesicles. Our results agree well with those of recent computer simulations.