An in silico osmotic pressure approach allows characterization of pressure–area isotherms of lipid monolayers at low molecular areas

Surface pressure–area isotherms of lipid monolayers at the air–water interface provide essential information about the structure and mechanical behaviour of lipid membranes. These curves can be readily obtained through Langmuir trough measurements and, as such, have been collected for decades in the field of membrane biochemistry. However, it is still challenging to directly observe and understand nanoscopic features of monolayers through such experiments, and molecular dynamics (MD) simulations are generally used to provide a molecular view of such interfaces. In MD simulations, the surface pressure–area (Π–A) isotherms are generally computed using the Kirkwood–Irving formula, that relies on the evaluation of the pressure tensor. This approach, however, has intrinsic limitations when the molecular area in the monolayer is low (typically < 60 Å(2) per lipid). Recently, an alternative method to compute Π–A isotherms of surfactants, based on the calculation of the three-dimensional osmotic pressure via the implementation of semipermeable barriers was proposed. In this work, we investigate the feasibility of this approach for long-chain surfactants such as phospholipids. We identify some discrepancies between the computed values and experimental results, and we propose a semi-empirical correction based on the molecular structure of the surfactants at the monolayer interface. To validate the potential of this new approach, we simulate several phosphatidylcholine and phosphatidylethanolamine lipids at various temperatures using all-atom and coarse-grained force fields, and we compute the corresponding Π–A isotherms. Our results show that the Π–A isotherms obtained using the new method are in very good agreement with experiments and far superior to the canonical pressure tensor-based method at low molecular areas. This corrected osmotic pressure method allows for accurate characterization of the molecular packing in monolayers in various physical phases.