Phase-Field Simulations of Multicomponent Lipid Membranes Coupling Composition with Deformation.

Abstract

In this work, we have developed a model and simulation method to study the thermodynamics and kinetics of phase-separating multicomponent lipid bilayer membranes. A continuum-level phase-field method is applied to model the phase separation, and a Helfrich free energy is used to couple the composition with the mechanical properties of the two separated phases, accounting for their bending rigidities and spontaneous curvatures. Four specific models are presented: a planar background model for nearly planar portions of membranes, a spherical background model for vesicles, a cylindrical background model for tubules, and an extension of the planar background model that additionally accounts for interactions between the two leaflets of the bilayer.

The planar background model is used to investigate what types of initial compositional and geometric configurations lead to a stripe phase morphology. We observe that, while patterned rigid supports are able to reliably induce such a morphology, perturbations in composition produce stripes less reliably. With the vesicle model, we investigate the effects of initial vesicle shapes, phase fractions, spontaneous curvatures, and bending rigidities on vesicle dynamics. We find that (i) a phase with spontaneous curvature closer to the vesicle surface curvature is favored to form continuous domain morphologies, even when present at or slightly less than 50%; and (ii) mixtures with small amounts of a phase with extreme spontaneous curvature, as well as vesicles with elongated shapes, can have enhanced stability in configurations with multiple minority phase domains as a result of the bending energy. The tubule model is applied to investigate whether bending energy can stabilize the pearling instability observed experimentally. We find that appropriate spontaneous curvature and bending rigidity can indeed stabilize the tubule. Lastly, we use the planar bilayer model to investigate the effects of the interleaflet coupling strength, finding that strong coupling can cause phase compositions to shift, such that the effective phase fraction becomes closer to 50% and the stripe morphology is more favored. Overall, we find that composition and shape are closely related, where compositional morphologies can alter the membrane shape and vice versa.