# Pattern formation by curvature-inducing proteins on spherical membranes

## TL;DR

This study presents a continuum model demonstrating how curvature-inducing proteins organize into patterns on spherical membranes, influenced by energy, entropy, and geometric constraints, with implications for biological processes.

## Contribution

It introduces a novel continuum framework for understanding protein pattern formation on spherical membranes considering multiple biophysical factors.

## Key findings

- Pattern formation depends on protein density and membrane tension.
- Parameters can control size and number of protein-rich domains.
- Mechanism may explain biological phenomena like cell division and membrane rafts.

## Abstract

Spatial organisation is a hallmark of all living cells, and recreating it in model systems is a necessary step in the creation of synthetic cells. It is therefore of both fundamental and practical interest to better understand the basic mechanisms underlying spatial organisation in cells. In this work, we use a continuum model of membrane and protein dynamics to study the behaviour of curvature-inducing proteins on membranes of spherical shape, such as living cells or lipid vesicles. We show that the interplay between curvature energy, entropic forces, and the geometric constraints on the membrane can result in the formation of patterns of highly-curved/protein-rich and weakly-curved/protein-poor domains on the membrane. The spontaneous formation of such patterns can be triggered either by an increase in the average density of curvature-inducing proteins, or by a relaxation of the geometric constraints on the membrane imposed by the membrane tension or by the tethering of the membrane to a rigid cell wall or cortex. These parameters can also be tuned to select the size and number of the protein-rich domains that arise upon pattern formation. The very general mechanism presented here could be related to protein self-organisation in many biological processes, ranging from (proto)cell division to the formation of membrane rafts.