Dynamics of coarsening in multicomponent lipid vesicles with non-uniform mechanical properties

Lipid domain coarsening and fluidity in multicomponent lipid vesicles: A continuum based model and its experimental validation

Liposomes that achieve a heterogeneous and spatially organized surface through phase separation have been recognized to be a promising platform for delivery purposes. However, their design and optimization through experimentation can be expensive and time-consuming. To assist with the design and reduce the associated cost, we propose a computational platform for modeling membrane coarsening dynamics based on the principles of continuum mechanics and thermodynamics. This model couples phase separation to lateral flow and accounts for different membrane fluidity within the different phases, which is known to affect the coarsening dynamics on lipid membranes. The simulation results are in agreement with the experimental data in terms of liquid ordered domains area fraction, total domains perimeter over time, and total number of domains over time for two different membrane compositions (DOPC:DPPC with a 1:1 M ratio with 15% Chol and DOPC:DPPC with a 1:2 M ratio with 25% Chol) that yield opposite and nearly inverse phase behavior. This quantitative validation shows that the developed platform can be a valuable tool in complementing experimental practice.

Experimental validation of a phase-field model to predict coarsening dynamics of lipid domains in multicomponent membranes

Membrane phase-separation is a mechanism that biological membranes often use to locally concentrate specific lipid species in order to organize diverse membrane processes. Phase separation has also been explored as a tool for the design of liposomes with heterogeneous and spatially organized surfaces. These "patchy" liposomes are promising platforms for delivery purposes, however their design and optimization through experimentation can be expensive and time-consuming. We developed a computationally efficient method based on the surface Cahn-Hilliard phase-field model to complement experimental investigations in the design of patchy liposomes. The method relies on thermodynamic considerations to set the initial state for numerical simulations. We show that our computational approach delivers not only qualitative pictures, but also accurate quantitative information about the dynamics of the membrane organization. In particular, the computational and experimental results are in excellent agreement in terms of lipid domain area fraction, total lipid domain perimeter over time and total number of lipid domains over time for two different membrane compositions (DOPC:DPPC with a 2:1 M ratio with 20% Chol and DOPC:DPPC with a 3:1 M ratio with 20% Chol). Thus, the computational phase-field model informed by experiments has a considerable potential to assist in the design of liposomes with spatially organized surfaces, thereby containing the cost and time required by the design process.

A computational study of lateral phase separation in biological membranes

Conservative and non-conservative phase-field models are considered for the numerical simulation of lateral phase separation and coarsening in biological membranes. An unfitted finite element method is proposed to allow for a flexible treatment of complex shapes in the absence of an explicit surface parametrization. For a set of biologically relevant shapes and parameter values, the paper compares the dynamic coarsening produced by conservative and non-conservative numerical models, its dependence on certain geometric characteristics and convergence to the final equilibrium.

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

In this work, the nonlinear hydrodynamics of a three-dimensional multicomponent vesicle in shear flow are explored. Using a volume- and area-conserving projection method coupled to a gradient-augmented level set and surface phase field method, the dynamics are systematically studied as a function of the membrane bending rigidity difference between the components, the speed of diffusion compared to the underlying shear flow, and the strength of the phase domain energy compared to the bending energy. Using a pre-segregated vesicle, three dynamics are observed: stationary phase, phase-treading, and a new dynamic called vertical banding. These regimes are very sensitive to the strength of the domain line energy, as the vertical banding regime is not observed when the line energy is larger than the bending energy. The findings demonstrate that a complete understanding of multicomponent vesicle dynamics requires that the full three-dimensional system be modeled, and show the complexity obtained when considering heterogeneous material properties.

Stochastic phase segregation on surfaces

Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. Often, thermal fluctuations, modelled as stochastic noise, are present in the system and the phase segregation process occurs on a surface. In this work, the segregation process is modelled via the Cahn-Hilliard-Cook model, which is a fourth-order parabolic stochastic system. Coarsening is analysed on two sample surfaces: a unit sphere and a dumbbell. On both surfaces, a statistical analysis of the growth rate is performed, and the influence of noise level and mobility is also investigated. For the spherical interface, it is also shown that a lognormal distribution fits the growth rate well.

Numerical simulation of endocytosis: Viscous flow driven by membranes with non-uniformly distributed curvature-inducing molecules

The formation of membrane vesicles from a larger membrane that occurs during endocytosis and other cell processes are typically orchestrated by curvature-inducing molecules attached to the membrane. Recent reports demonstrate that vesicles can form de novo in a few milliseconds. Membrane dynamics at these scales are strongly influenced by hydrodynamic interactions. To study this problem, we develop new diffuse interface models for the dynamics of inextensible vesicles in a viscous fluid with stiff, curvature-inducing molecules. The model couples the Navier-Stokes equations with membrane-induced bending forces that incorporate concentration-dependent bending stiffness coefficients and spontaneous curvatures, with equations for molecule transport and for a Lagrange multiplier to enforce local inextensibility. Two forms of surface transport equations are considered: Fickian surface diffusion and Cahn-Hilliard surface dynamics, with the former being more appropriate for small molecules and the latter being better for large molecules. The system is solved using adaptive finite element methods in 3D axisymmetric geometries. The results demonstrate that hydrodynamics can indeed enable the rapid formation of a small vesicle attached to the membrane by a narrow neck. When the Fickian model is used, this is a transient state with the steady state being a flat membrane with a uniformly distributed molecule concentration due to diffusion. When the Cahn-Hilliard model is used, molecule concentration gradients are sustained, the neck stabilizes and the system evolves to a steady-state with a small, compact vesicle attached to the membrane. By varying the membrane coverage of molecules in the Cahn-Hilliard model, we find that there is a critical (smallest) neck radius and a critical (fastest) budding time. These critical points are associated with changes in the vesicle morphology from spherical to mushroom-like as the molecule coverage on the membrane is increased.