# Cup-to-vesicle transition of a fluid membrane with spontaneous curvature

## TL;DR

This paper investigates the shape transition of asymmetric fluid membranes with spontaneous curvature, combining theoretical analysis and meshless simulations to understand vesicle formation and membrane stability.

## Contribution

It introduces a combined theoretical and simulation approach to study membrane shape transitions with spontaneous curvature, extending understanding beyond symmetric membranes.

## Key findings

- Membrane shapes are well approximated by spherical caps.
- Gaussian modulus can be estimated from membrane shape and transition probability.
- Higher spontaneous curvature and edge tension promote smaller vesicle formation.

## Abstract

The disk-to-vesicle transition of a fluid membrane with no spontaneous curvature is well described by the competition between edge line and curvature energies. However, the transition of asymmetric membranes with spontaneous curvatures is not yet understood. In this study, the shape of the fluid membrane patch with a constant spontaneous curvature and its closing transition to a vesicle is investigated using theory and meshless membrane simulations. It is confirmed that the (meta)stable and transient membranes are well approximated by spherical caps. The membrane Gaussian modulus can be estimated from the cup shape of membrane patches as well as from the transition probability, although the latter estimate gives slightly smaller negative values. Furthermore, the self-assembly dynamics of membranes are presented, in which smaller vesicles are formed at higher spontaneous curvatures, higher edge line tension, and lower density.