# Theoretical study of vesicle shapes driven by coupling curved proteins and active cytoskeletal forces

## TL;DR

This study uses Monte Carlo simulations to explore how active curved membrane proteins and cytoskeletal forces influence vesicle shapes in three dimensions, revealing new shape transitions relevant to cell motility.

## Contribution

It extends previous linear models by analyzing unrestricted 3D vesicle shapes with active proteins, uncovering novel shape transitions driven by activity and curvature coupling.

## Key findings

- Active forces promote protein aggregation and membrane protrusions.
- Transition from deformed spheres with necklace-like protein aggregates.
- Formation of flat, pancake-shaped vesicles with rim-lined proteins.

## Abstract

Eukaryote cells have a flexible shape, which dynamically changes according to the function performed by the cell. One mechanism for deforming the cell membrane into the desired shape is through the expression of curved membrane proteins. Furthermore, these curved membrane proteins are often associated with the recruitment of the cytoskeleton, which then applies active forces that deform the membrane. This coupling between curvature and activity was previously explored theoretically in the linear limit of small deformations, and low dimensionality. Here we explore the unrestricted shapes of vesicles that contain active curved membrane proteins, in three-dimensions, using Monte-Carlo numerical simulations. The activity of the proteins is in the form of protrusive forces that push the membrane outwards, as may arise from the cytoskeleton of the cell due to actin or microtubule polymerization occurring near the membrane. For proteins that have an isotropic convex shape, the additional protrusive force enhances their tendency to aggregate and form membrane protrusions (buds). In addition, we find another transition from deformed spheres with necklace type aggregates, to flat pancake-shaped vesicles, where the curved proteins line the outer rim. This second transition is driven by the active forces, coupled to the spontaneous curvature, and the resulting configurations may shed light on the organization of the lamellipodia of adhered and motile cells.