- [Show abstract] [Hide abstract] ABSTRACT: When micron-scale compositional heterogeneity develops in membranes, the distribution of lipids on one face of the membrane strongly affects the distribution on the other. Specifically, when lipid membranes phase separate into coexisting liquid phases, domains in each monolayer leaflet of the membrane are colocalized with domains in the opposite leaflet. Colocalized domains have never been observed to spontaneously move out of registry. This result indicates that the lipid compositions in one leaflet are strongly coupled to compositions in the opposing leaflet. Predictions of the interleaflet coupling parameter, Λ, vary by a factor of 50. We measure the value of Λ by applying high shear forces to supported lipid bilayers. This causes the upper leaflet to slide over the lower leaflet, moving domains out of registry. We find that the threshold shear stress required to deregister domains in the upper and lower leaflets increases with the inverse length of domains. We derive a simple, closed-form expression relating the threshold shear to Λ, and find Λ = 0.016 ± 0.004 kBT/nm(2).
- [Show abstract] [Hide abstract] ABSTRACT: Due to a thermodynamic coupling between the two leaflets comprising a lipid bilayer, compositional lipid domains residing within opposing leaflets are often found in registry. If the system is perturbed by displacing one domain relative to the other, diffusive and advective lipid fluxes are established to restore equilibrium and reestablish domain overlap. In this work, we focus on the advective part of the process, and first derive an analytical expression for the hydrodynamic drag coefficient associated with the advective flow for the special case of perfect domain overlap. The resulting expression identifies parameter regions where sliding friction between the leaflets dominates over viscous dissipation within the leaflets or vice versa. It is shown that in all practically relevant cases, sliding friction between the leaflets is the dominant factor. Finally, we investigate the domain separation dependence of the hydrodynamic drag coefficient via direct simulations of a continuum diffuse interface model, and provide useful empirical expressions for its behavior.
- [Show abstract] [Hide abstract] ABSTRACT: Compositional domains within multicomponent lipid bilayer membranes are believed to facilitate many important cellular processes. In this work, we first derive the general equations that describe the dynamics of compositional domains within planar membranes with asymmetry in leaflet properties and in the presence of a thermodynamic coupling between the leaflets. These equations are then employed to develop analytical solutions for the dynamics of the recurrence of registration for circular domains in the case of weak coupling. In addition, a closed-form expression for the decay rate of interface fluctuations, when only one leaflet supports compositional domains, is derived.
- [Show abstract] [Hide abstract] ABSTRACT: In this paper we present a comprehensive analysis of line tension-driven compositional interface fluctuations in planar lipid bilayer membranes. Our starting point is the advective Cahn-Hilliard equation for the local lipid composition in symmetric membranes, which explicitly incorporates both advective and diffusive lipid transport processes, and which is coupled to the continuum hydrodynamic equations governing the flow behavior of the membrane and surrounding solvent with finite subphase thickness. In order to extract the interface dynamics from the continuum phase-field formalism, we first derive the appropriate sharp-interface limit equations. We then carry out a linear perturbation analysis for the relaxational dynamics of small-amplitude sinusoidal interface fluctuations to yield the general dispersion relation ω(k) as a function of perturbation wave number k. The resulting expression incorporates the effects of diffusive and advective lipid transport processes within the membrane, viscous or viscoelastic membrane properties, coupling between membrane and solvent, and inertial effects within the membrane and solvent. It is shown that previously considered scenarios naturally emerge as limiting cases of the general result. Furthermore, we discuss two additional scenarios amenable to analysis, one in which the inertia of the solvent is relevant, and another one in which the membrane displays significant viscoelastic properties. Finally, we numerically evaluate the general dispersion relation for three representative model membrane systems.
- [Show abstract] [Hide abstract] ABSTRACT: The formation and dynamics of spatially extended compositional domains in multicomponent lipid membranes lie at the heart of many important biological and biophysical phenomena. While the thermodynamic basis for domain formation has been explored extensively in the past, domain growth in the presence of hydrodynamic interactions both within the (effectively) two-dimensional membrane and in the three-dimensional solvent in which the membrane is immersed has received little attention. In this work, we explore the role of hydrodynamic effects on spinodal decomposition kinetics via continuum simulations of a convective Cahn-Hilliard equation for membrane composition coupled to the Stokes equation. Our approach explicitly includes hydrodynamics both within the planar membrane and in the three-dimensional solvent in the viscously dominated flow regime. Numerical simulations reveal that dynamical scaling breaks down for critical lipid mixtures due to distinct coarsening mechanisms for elongated versus more isotropic compositional lipid domains. The breakdown in scaling should be readily observable in experiments on model membrane systems.