Law of corresponding states for osmotic swelling of vesicles

TL;DR

This paper presents a universal scaling law for vesicle swelling due to osmotic permeation, revealing a phase transition-like behavior that allows precise measurement of membrane permeability and insights into vesicle mechanics.

Contribution

It introduces a universal curve for vesicle swelling across different solutes and vesicles, linking phase transition concepts to osmotic swelling behavior.

Findings

Swelling curves can be collapsed into a single universal curve.

Membrane permeability coefficients are measured, with urea showing concentration independence.

Transition width reveals the number of bending modes influencing vesicle thermodynamics.

Abstract

As solute molecules permeate into a vesicle due to a concentration difference across its membrane, the vesicle swells through osmosis. The swelling can be divided into two stages: (a) an "ironing" stage, where the volume-to-area ratio of the vesicle increases without a significant change in its area; (b) a stretching stage, where the vesicle grows while remaining essentially spherical, until it ruptures. We show that the crossover between these two stages can be represented as a broadened continuous phase transition. Consequently, the swelling curves for different vesicles and different permeating solutes can be rescaled into a single, theoretically predicted, universal curve. Such a data collapse is demonstrated for giant unilamellar POPC vesicles, osmotically swollen due to the permeation of urea, glycerol, or ethylene glycol. We thereby gain a sensitive measurement of the solutes' membrane permeability coefficients, finding a concentration-independent coefficient for urea, while those of glycerol and ethylene glycol are found to increase with solute concentration. In addition, we use the width of the transition, as extracted from the data collapse, to infer the number of independent bending modes that affect the thermodynamics of the vesicle in the transition region.