Fig. 4: Reduced bending moduli across different membrane compositions and techniques show universal scaling with area per lipid.

a Collective data obtained by NSE (Fig. 2d), ²H NMR (Fig. 3c), and corresponding MD simulations (Figs. 2e and 3d) show a unified dependence of \({{\kappa }}/{{{\kappa }}}_{{{0}}}\) on \({{{A}}}_{{{\rm{L}}}}\). b The reduced bending moduli, \({{\kappa }}/{{{\kappa }}}_{{{0}}}\), show a similar scaling relation with the reduced area per lipid, \({{{A}}}_{{{\rm{L}}}}/{{{A}}}_{{{0}}}\). Notably, bending moduli of POPC membranes (denoted by †) from earlier studies by Henriksen et al.⁵⁹ with different sterol types show excellent agreement with the scaling laws obtained in this study, when plotted against area per lipid values obtained from our SAXS measurements. This convergence of results indicates unified structure property relations in PC lipid membranes regardless of lipid chain unsaturation, sterol type, or sterol content. All data are at 25 °C except for DMPC at 30 °C and 44 °C. Error bars represent ± SD from the mean value or as described in the SI for simulation results. Source data are provided as a Source Data file.