On Calculating the Bending Modulus of Lipid Bilayer Membranes from Buckling Simulations

The bending modulus is an important physical constant characterizing lipid membranes. Different methods have been devised for calculating the bending modulus from simulations, and one of them, named the buckling method, is nowadays widely used due to its simplicity and numerical stability. However, questions remain on the reproducibility, finite size effects, and interpretation of results on lipid mixtures. Here we explore the dependence of simulation results on the system size and the strain. We find that the dimensions of the box have a negligible impact on the results when the system size is beyond a certain threshold. We then calculate the bending rigidity for of a series of common single-component lipid bilayers (PC, PS, PE, PG, and SM), as well as a number of binary and ternary lipid mixtures. We find that bending moduli of lipid mixtures can be predicted from the weighted average of the moduli of the individual components, as long as the mixture is homogeneous. For phase-separated mixtures, the apparent elastic modulus is closer to the value of the softer component. Predictions of the bending modulus based on the area compressibility modulus are found to be generally unreliable.