We present a new computational approach to quantify the area per lipid and the area compressibility modulus of biological membranes. Our method relies on the analysis of the membrane fluctuations using our recently introduced coupled undulatory (CU) mode [Tarazona et al., J. Chem. Phys. 139, 094902 (2013)], which provides excellent estimates of the bending modulus of model membranes. Unlike the projected area, widely used in computer simulations of membranes, the CU area is thermodynamically consistent. This new area definition makes it possible to accurately estimate the area of the undulating bilayer, and the area per lipid, by excluding any contributions related to the phospholipid protrusions. We find that the area per phospholipid and the area compressibility modulus features a negligible dependence with system size, making possible their computation using truly small bilayers, involving a few hundred lipids. The area compressibility modulus obtained from the analysis of the CU area fluctuations is fully consistent with the Hooke's law route. Unlike existing methods, our approach relies on a single simulation, and no a priori knowledge of the bending modulus is required. We illustrate our method by analyzing 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayers using the coarse grained MARTINI force-field. The area per lipid and area compressibility modulus obtained with our method and the MARTINI forcefield are consistent with previous studies of these bilayers
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