Simulating Curved Lipid Membranes Using Anchored Frozen Patches

Lipid bilayers often form high-curvature configurations due to self-assembly conditions or certain biological processes. However, particle-based simulations of lipid membranes are predominantly of flat lipid membranes because planar membranes are easily connected over periodic boundary conditions. To simulate a curved lipid membrane, one can simulate an entire vesicle, a cylinder, or a bicelle (a disk-like bilayer aggregate). One can also use artificial methods to control curvature, such as applying virtual walls of beads, radial harmonic potentials, or "tape up the edges". These existing methods have limitations due to the method by which the curvature is imposed. Herein, we propose an alternative method of introducing arbitrary curvature by anchoring a curved lipid membrane with "frozen" equilibrated membrane patches. The method presented here is compatible with all particle-based lipid models and can be easily extended to many geometries. As an example, we simulate curved membranes with DPPC, DOPC, DLPC, and DOPE lipids as parametrized by the Martini 3 coarse-grained model. This method introduces limited finite-size artifacts, prevents lipid flip-flop at membrane edges, and allows fluctuations in the free membrane center. We provide verification of the method on flat membranes and discussion on extracting shape and per-leaflet quantities (thickness and order parameter) from curved membranes. Curvature produces asymmetric changes in the lipid leaflet properties. Finally, we explore the coupled effect of curvature and membrane asymmetry in both number and lipid type. We report the resulting unique morphologies (inducing gel phase and faceting) and behaviors (thickness-dependent on the adjacent leaflet type) that are accessible with this method.