Three-dimensional multicomponent vesicles: dynamics and influence of material properties

Hydrodynamics of a multicomponent vesicle under strong confinement

We numerically investigate the hydrodynamics and membrane dynamics of a multicomponent vesicle in two strongly confined geometries. This serves as a simplified model for red blood cells undergoing large deformations while traversing narrow constrictions. We propose a new parameterization for the bending modulus that remains positive for all lipid phase parameter values. For a multicomponent vesicle passing through a stenosis, we establish connections between various properties: lipid phase coarsening, size and flow profile of the lubrication layers, excess pressure, and the tank-treading velocity of the membrane. For a multicomponent vesicle passing through a contracting channel, we find that the lipid always phase separates so that the vesicle is stiffer in the front as it passes through the constriction. For both cases of confinement we find that lipid coarsening is arrested under strong confinement, and resumes at a high rate upon relief from extreme confinement. The results may be useful for efficient sorting lipid domains using microfluidic flows by controlled release of vesicles passing through strong confinement.

Phase field modeling and computation of vesicle growth or shrinkage

We present a phase field model for vesicle growth or shrinkage induced by an osmotic pressure due to a chemical potential gradient. The model consists of an Allen-Cahn equation describing the evolution of the phase field parameter that describes the shape of the vesicle and a Cahn-Hilliard-type equation describing the evolution of the ionic fluid. We establish conditions for vesicle growth or shrinkage via a common tangent construction using free energy curves. During the membrane deformation, the model ensures total mass conservation of the ionic fluid, and we weakly enforce a surface area constraint of the vesicle. We develop a stable numerical scheme and an efficient nonlinear multigrid solver to evolve the phase and concentration fields, and we use this to evolve the fields to near equilibrium for 2D vesicles. Convergence tests confirm an [Formula: see text] accuracy for our scheme and near-optimal convergence for our multigrid solver. Numerical results reveal that the diffuse interface model captures the main features of cell shape dynamics: for a growing vesicle, there exist circle-like equilibrium shapes if the concentration difference across the membrane and the initial osmotic pressure are large enough; while for a shrinking vesicle, there exists a rich collection of finger-like equilibrium morphologies.

Curvature and shape relaxation in surface-viscous domains

The mechanics of curved, heterogeneous, surfactant-laden surfaces and interfaces are important to a variety of engineering and biological applications. To date, most models of rheologically complex interfaces have focused on homogeneous systems of planar or fixed curvature. In this study, we investigate a simple, dynamical model of a two-phase surface fluid on a curved interface: a condensed, surface-viscous domain embedded within a surface-inviscid, spherical interface of time-varying radius of curvature. Our aim is to understand how changes in surface curvature generate two-dimensional Stokes flows inside the domain, thereby resisting curvature deformation and distorting the domain shape. We model the surface stress within the domain using the classical Boussinesq-Scriven constitutive equation, simplified for a near-spherical cap undergoing a small-amplitude curvature deformation. We then analyze the frequency-dependent dynamics of the surface stress and curvature within the domain when the pressure difference across the surface is sinusoidally oscillated. We find that the curvature relaxes diffusively, and thus define a Peclet number (Pe) relating the rate of diffusion to the oscillation frequency. At small enough Pe, the surface deforms quasi-statically, whereas at high Pe, the curvature varies sharply within a thin boundary layer adjacent to the domain border. Consequently, the curvature of the domain appears discontinuous from the rest of the surface under rapid oscillation. We then examine the linear stability of the domain shape to small, non-axisymmetric perturbations when the surface is steadily compressed (i.e., the pressure difference across it is increased). While the line tension at the domain border tends to maintain circular symmetry, surface-viscous stresses generated by surface compression tend to destabilize the perimeter. A shape instability arises above a critical surface capillary number (Ca) relating surface-viscous stresses to line tension. Moreover, we show that the mechanism of instability is distinct from that of the famous Saffman-Taylor fingering instability. Various extensions of our model are discussed, including materials with finite dilatational surface viscosity, linear and nonlinear (visco)elasticity, and large-amplitude deformations.

Multicomponent Copolymer Planar Membranes with Nanoscale Domain Separation

Domain separation is crucial for proper cellular function and numerous biomedical technologies, especially artificial cells. While phase separation in hybrid membranes containing lipids and copolymers is well-known, the membranes' overall stability, limited by the lipid part, is hindering the technological applications. Here, we introduce a fully synthetic planar membrane undergoing phase separation into domains embedded within a continuous phase. The mono- and bilayer membranes are composed of two amphiphilic diblock copolymers (PEO₄₅-b-PEHOx₂₀ and PMOXA₁₀-b-PDMS₂₅) with distinct properties and mixed at various concentrations. The molar ratio of the copolymers in the mixture and the nature of the solid support were the key parameters inducing nanoscale phase separation of the planar membranes. The size of the domains and resulting morphology of the nanopatterned surfaces were tailored by adjusting the molar ratios of the copolymers and transfer conditions. Our approach opens new avenues for the development of biomimetic planar membranes with a nanoscale texture.

Curvature-driven feedback on aggregation-diffusion of proteins in lipid bilayers

Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be attributed to interactions between proteins and membranes. These interactions include protein diffusion and formation of aggregates due to protein-protein interactions in the plane of the membrane. Recently, we developed a model that couples the in-plane flow of lipids and diffusion of proteins with the out-of-plane bending of the membrane. Building on this work, here, we focus on the role of explicit aggregation of proteins on the surface of the membrane in the presence of membrane bending and diffusion. We develop a comprehensive framework that includes lipid flow, membrane bending, the entropy of protein distribution, along with an explicit aggregation potential and derive the governing equations for the coupled system. We compare this framework to the Cahn-Hillard formalism to predict the regimes in which the proteins form patterns on the membrane. We demonstrate the utility of this model using numerical simulations to predict how aggregation and diffusion, when coupled with curvature generation, can alter the landscape of membrane-protein interactions.