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Compositional asymmetry between the leaflets of bilayer membranes modifiestheir phase behaviour, and is thought to influence other important featuressuch as mechanical properties and protein activity. We address here how phasebehaviour is affected by passive phospholipid \textit{flip-flop}, such that thecompositional asymmetry is not fixed. We predict transitions from "preflip-flop" behaviour to a restricted set of phase equilibria that can persistin the presence of passive flip-flop. Surprisingly, such states are notnecessarily symmetric. We further account for external symmetry-breaking, suchas a preferential substrate interaction, and show how this can stabilisestrongly asymmetric equilibrium states. Our theory explains severalexperimental observations of flip-flop mediated changes in phase behaviour, andshows how domain formation and compositional asymmetry can be controlled inconcert, by manipulating passive flip-flop rates and applying external fields.

Effects of passive phospholipid flip-flop and asymmetric external fields on bilayer phase equilibria