A New Computational Method for Membrane Compressibility: Bilayer Mechanical Thickness Revisited.

Because lipid bilayers can bend and stretch in ways similar to thin elastic sheets, physical models of bilayer deformation have utilized mechanical constants such as the moduli for bending rigidity (κ) and area compressibility (K). However, the use of these models to quantify the energetics of membrane deformation associated with protein-membrane interactions, and the membrane response to stress is often hampered by the shortage of experimental data suitable for the estimation of the mechanical constants of various lipid mixtures. Although computational tools such as molecular dynamics simulations can provide alternative means to estimate K values, current approaches suffer significant technical limitations. Here, we present a novel, to our knowledge, computational framework that allows for a direct estimation of K values for individual bilayer leaflets. The theory is based on the concept of elasticity and derives K from real-space analysis of local thickness fluctuations sampled in molecular dynamics simulations. We explore and validate the model on a large set of single and multicomponent bilayers of different lipid compositions and sizes, simulated at different temperatures. The calculated bilayer compressibility moduli agree with values estimated previously from experiments and those obtained from a standard computational method based on a series of constrained tension simulations. We further validate our framework in a comparison with an existing polymer brush model and confirm the polymer brush model's predicted linear relationship with proportionality coefficient of 24, using elastic parameters calculated from the simulation trajectories. The robustness of the results that emerge from the method allows us to revisit the origins of the bilayer mechanical (compressible) thickness and in particular its dependence on acyl-chain unsaturation and the presence of cholesterol.