A Numerical Implementation to Calculate Elastic Properties of Biological Membrane Simulations

The elastic properties of biological membranes can be described by mechanical constants like the bending modulus at flexure (k_c) and the area compressibility modulus (K_A), which quantify the energy cost associated with bending, compression, and stretching of the membrane area. These properties provide a means to describe phenomena such as the shape variation of a vesicle in response to pressure or the strain energy of a membrane influenced by lipid composition, interactions with ions, small molecules, or biomolecules. The determination of elastic moduli provides a quantitative basis for describing deformation-related processes in cellular systems at the molecular and mesoscopic levels. However, measurements of elastic constants, such as the bending modulus, exhibit a wide dispersion of reported values, ranging from approximately 10 k_BT (4 × 10^-20 J) to 100 k_BT (4 × 10^-19 J) for liquid disordered phospholipid membranes. Computational protocols for estimating elastic constants of lipid membranes commonly rely on Fourier analysis of the membrane surface, where the upper integration limit is determined by lipid molecular dimensions, making results sensitive to lipid composition and complicating cross-system comparisons. We have implemented the s_comp tool in the SuAVE software to estimate area compressibility from the direct integration of membrane surface areas, circumventing the dependence on wavevector integration limits that arises when elastic constants are extracted from Fourier mode amplitude spectra. The calculation does not require prior knowledge of lipid molecular dimensions and is therefore applicable to membranes of arbitrary composition and morphology. The calculated elastic constants are in reasonable agreement with values reported in the literature, falling within the variability observed across computational protocols and experimental techniques. As with any fluctuation-derived property, fully converged trajectories and appropriate statistical sampling are prerequisites for reliable estimates. The SuAVE software is freely available from https://github.com/SuAVE-Software.