Comprehensive analysis of compositional interface fluctuations in planar lipid bilayer membranes

Crawling and turning in a minimal reaction-diffusion cell motility model: Coupling cell shape and biochemistry

We study a minimal model of a crawling eukaryotic cell with a chemical polarity controlled by a reaction-diffusion mechanism describing Rho GTPase dynamics. The size, shape, and speed of the cell emerge from the combination of the chemical polarity, which controls the locations where actin polymerization occurs, and the physical properties of the cell, including its membrane tension. We find in our model both highly persistent trajectories, in which the cell crawls in a straight line, and turning trajectories, where the cell transitions from crawling in a line to crawling in a circle. We discuss the controlling variables for this turning instability and argue that turning arises from a coupling between the reaction-diffusion mechanism and the shape of the cell. This emphasizes the surprising features that can arise from simple links between cell mechanics and biochemistry. Our results suggest that similar instabilities may be present in a broad class of biochemical descriptions of cell polarity.

Transbilayer Colocalization of Lipid Domains Explained via Measurement of Strong Coupling Parameters

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/nm2.

Fluctuating hydrodynamics of multicomponent membranes with embedded proteins

A simulation method for the dynamics of inhomogeneous lipid bilayer membranes is presented. The membrane is treated using stochastic Saffman-Delbrück hydrodynamics, coupled to a phase-field description of lipid composition and discrete membrane proteins. Multiple applications are considered to validate and parameterize the model. The dynamics of membrane composition fluctuations above the critical point and phase separation dynamics below the critical point are studied in some detail, including the effects of adding proteins to the mixture.

Kinetics of domain registration in multicomponent lipid bilayer membranes

The kinetics of registration of lipid domains in the apposing leaflets of symmetric bilayer membranes is investigated via systematic dissipative particle dynamics simulations. The decay of the distance between the centres of mass of the domains in the apposing leaflets is almost linear during early stages, and then becomes exponential during late times. The time scales of both linear and exponential decays are found to increase with decreasing strength of interleaflet coupling. The ratio between the time scales of the exponential and linear regimes decreases with increasing domain size, implying that the decay of the distance between the domains' centres of mass is essentially linear for large domains. These numerical results are largely in agreement with the recent theoretical predictions of Han and Haataja [Soft Matter, 2013, 9, 2120-2124]. We also found that the domains become elongated during the registration process.

Hydrodynamic interaction between overlapping domains during recurrence of registration within planar lipid bilayer membranes

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.

Lateral Dynamics in Polymer-Supported Membranes

We investigate the lateral dynamics in a purely viscous lipid membrane which is supported by a thin polymer sheet (polymer-supported membrane). The generalized frequency-dependent mobility tensor of the polymer-supported membrane is obtained by taking into account the viscoelasticity of the polymer sheet. Due to its viscoelasticity, the cross-correlation functions of two particles embedded in the membrane exhibit an anomalous diffusion. A useful relation for two-point microrheology connecting the cross-correlation function and the modulus of the polymer sheet is provided.