Determination of biomembrane bending moduli in fully atomistic simulations

Abstract

The bilayer bending modulus (Kc) is one of the most important physical constants characterizing lipid membranes, but precisely measuring it is a challenge, both experimentally and computationally. Experimental measurements on chemically identical bilayers often differ depending upon the techniques employed, and robust simulation results have previously been limited to coarse-grained models (at varying levels of resolution). This Communication demonstrates the extraction of Kc from fully atomistic molecular dynamics simulations for three different single-component lipid bilayers (DPPC, DOPC, and DOPE). The results agree quantitatively with experiments that measure thermal shape fluctuations in giant unilamellar vesicles. Lipid tilt, twist, and compression moduli are also reported.

Figure 1

Lipid orientation vectors are defined from the midpoint between lipid headgroup phosphorus and glycerol C2, to the midpoint between terminal methyl groups in the tail region. Atom positions are from a simulation snapshot, with carbon atoms colored blue, hydrogen white, oxygen red, and phosphorus yellow/orange. Surrounding lipids are represented by a blue, semitransparent surface that outlines the aqueous-membrane interface.

Figure 2

(A–C) Power spectra of longitudinal lipid orientation weighted by q². The horizontal black lines represent the best fit to eq 2 over the smallest four wave vectors in the simulations; the plateau region extends over at least the smallest four wave vectors for all three simulations, clearly indicating well-converged values of K_c with system size. (D–F) Power spectra of transverse lipid orientation and the associated best-fit curves to eq 2.