Stability of growing vesicles

TL;DR

This paper analyzes the stability of growing vesicles using nonequilibrium thermodynamics, identifying critical radii and conditions under which vesicles maintain or lose stability during growth.

Contribution

It introduces a thermodynamic framework to study vesicle stability, revealing critical radii and the influence of perturbation modes on stability, with potential for experimental validation.

Findings

Two critical radii determine vesicle stability.

Stability depends on the ratio of hydraulic conductivity to membrane area change coefficient.

Lower zonal harmonic modes are more unstable.

Abstract

We investigate the stability of growing vesicles using the formalism of nonequilibrium thermodynamics. The vesicles are growing due to the accretion of lipids to the bilayer which forms the vesicle membrane. The thermodynamic description is based on the hydrodynamics of a water{/}lipid mixture together with a model of the vesicle as a discontinuous system in the sense of linear nonequilibrium thermodynamics. This formulation allows the forces and fluxes relevant to the dynamic stability of the vesicle to be identified. The method is used to analyze the stability of a spherical vesicle against arbitrary axisymmetric perturbations. It is found that there are generically two critical radii at which changes of stability occur. In the case where the perturbation takes the form of a single zonal harmonic, only one of these radii is physical and is given by the ratio $2 L_p / L_\gamma$, where $L_p$ is the hydraulic conductivity and $L_\gamma$ is the Onsager coefficient related to changes in membrane area due to lipid accretion. The stability of such perturbations is related to the value of $l$ corresponding to the particular zonal harmonic: those with lower $l$ are more unstable than those with higher $l$. Possible extensions of the current work and the need for experimental input are discussed.