Scaling relations of elastic and structural properties in cholesterol-rich lipid membranes

The elastic properties of cell membranes play a key role in cell functions. Cholesterol – an essential component of eukaryotic cell membranes– is known to cause lipid condensation or a decrease in the average area per lipid (A_L). However, the interplay between cholesterol-driven lipid packing and emergent elastic properties of lipid membranes remains largely unexplored. Theories based on mean field calculations have predicted different dependences of the membrane bending modulus, κ, and the area compressibility modulus, K_A, on A_L. Here, we examine these relations in cholesterol-rich lipid membranes with various degrees of acyl chain unsaturation using neutron spin-echo spectroscopy (NSE), solid-state ²H NMR relaxometry, and molecular dynamics simulations. We find that cholesterol stiffens all studied membranes irrespective of the degree of chain unsaturation over the accessible length and time scales, with an inverse dependence of κ and K_A on A_L. To generalize the molecular mechanisms driving this dependence, we consider normalized variables that eliminate experimental factors leading to different observed values of elastic membrane parameters. These structure-property relations inform design rules for engineered membranes and artificial cells with real-world functionalities.