Simulations of the Morphological Evolution of Lipid Bilayer Membranes Using a Phase-Field Method

Abstract

We present a continuum-level simulation method for modeling phase separation and morphological evolution of multicomponent lipid bilayer membranes. Our objective is to investigate how various physical parameters input into the model, such as spontaneous curvature, phase fraction, and interleaflet coupling strength, affect the dynamics and equilibrium morphological phases formed in two-phase lipid bilayer membrane systems. The model applies to membranes with planar and spherical background geometries, simulating a nearly planar portion of membrane or entire vesicle, respectively. The compositions and shape of the membrane are coupled through a modified Helfrich free energy. The planar model treats the composition of each leaflet, and thus includes a term coupling these compositions across the bilayer. The compositional evolution is modeled using a phase-field method and is described by a Cahn-Hilliard-type equation, while shape changes are described by relaxation dynamics. For nearly planar bilayer systems with each leaflet having the same phase fraction, we find that domains in both leaflets align to reduce the interaction energy, as expected. When the coupling effect is stronger, this alignment occurs more quickly and more precisely, showing that the coupling affects the dynamics. This leaflet coupling is found to heavily influence morphological evolution; in some cases the equilibrium morphological phase observed is very different from what was observed with our simpler monolayer model using similar conditions. We construct a phase diagram of equilibrium morphological phases in the composition space for a few values of the strength of the leaflet coupling. This model has been able to reproduce results found in lipid bilayer experiments probing interleaflet interactions, including the effect of domain registration across leaflets. For the vesicle model, we investigate how an ellipsoidal geometry imposed in the initial conditions affects the phase and morphological evolution.