Figure 6.

Square-law dependence yields an estimate of bilayer bending rigidity. (A) Simulation (green) and NMR (black) data and best square-law fits to the experimental data for DMPC (squares) and DMPC containing 50 mol % cholesterol (triangles) in the liquid-crystalline state. Experimental data were taken from (41), and simulation data are shown for carbons C4 through C14 for DMPC and C8 through C14 for DMPC/cholesterol. (B) Comparison between the apparent bilayer bending modulus ${\kappa }_{\mathrm{C}}$ calculated from the square-law relationship (green) or splay fluctuations (yellow) in the simulations. Shown also are experimental results for ${\kappa }_{\mathrm{C}}$ obtained from the square-law relationship of NMR data (gray) and from bilayer thickness fluctuations measured with NSE (purple). All ${\kappa }_{\mathrm{C}}$ values are in units of k_BT. (C) Changes in ${\kappa }_{\mathrm{C}}$ in the cholesterol-containing bilayers relative to the bilayers without cholesterol. Plotted is the ratio between the two for each of the four methods displayed in (B). Errors for the ${\kappa }_{\mathrm{C}}$ values obtained from the experimentally determined slope of the square-law relationship were calculated as the standard deviation resulting from the best fits to the data after excluding the last 0, 1, and 2 carbon atoms with largest order parameters. The corresponding errors from the square-law dependence in the simulations were calculated in a similar way (see materials and methods). All simulations were performed at 44°C. The functional dependence between relaxation rates and order parameters is directly related to the bilayer bending rigidity as validated for the full range of cholesterol concentrations. To see this figure in color, go online.