Hydrodynamic coupling for particle-based solvent-free membrane models

The great challenge with biological membrane systems is the wide range of scales involved, from nanometers and picoseconds for individual lipids, to the micrometers and beyond millisecond for cellular signalling processes. While solvent-free coarse-grained membrane models are convenient for large-scale simulations, and promising to provide insight into slow processes involving membranes, these models usually have unrealistic kinetics. One major obstacle is the lack of an equally convenient way of introducing hydrodynamic coupling without significantly increasing the computational cost of the model. To address this, we introduce a framework based on anisotropic Langevin dynamics, for which major in-plane and out-of-plane hydrodynamic effects are modeled via friction and diffusion tensors from analytical or semi-analytical solutions to Stokes hydrodynamic equations. Using this framework, we obtain accurate dispersion relations for planar membrane patches, both free-standing and in the vicinity of a wall. We also briefly discuss how non-equilibrium dynamics is affected by hydrodynamic interactions.