Lattice-Based Monte Carlo Simulations of Lipid Membranes: Correspondence between Triangular and Square Lattices

Abstract

We have recently demonstrated [1, 2] that lattice-based Monte Carlo (MC) allows one to study the structure and dynamics of membranes on experimentally relevant spatial scales and time intervals with moderate computational expenses. To date, most of lattice-based MC simulations of lipid membranes have been carried out on triangular lattices. Previously we have argued [1, 2] that the particular lattice geometry in MC simulations should not matter for reproducing the properties of the membrane at scales larger than the lattice unit, provided that the lipid-lipid interaction parameters are properly rescaled. Still, it remained an open question whether there exists a single conversion factor for all lipid-lipid interaction parameters to achieve identical results on triangular and square lattices, or the different interaction parameters have to be adjusted individually. Here, based on the properties of the Ising model, we demonstrate that one can indeed choose a single numerical coefficient to rescale all lipid-lipid interaction parameters depending on the lattice type, which provides one-to-one correspondence of thermodynamics properties of lipid membranes in lattice-based MC simulations on triangular and square lattices.[1] J. Ehrig, E. P. Petrov, and P. Schwille, Biophys. J.100 (2011) 80.[2] J. Ehrig, E. P. Petrov, and P. Schwille, New J. Phys.13 (2011) 045019.