Dielectric permittivity of water confined in stacks of charged lipid layers: Extracting profiles from molecular dynamics simulations using a modified Poisson–Boltzmann equation

Abstract

Most organic and inorganic surfaces (e.g., glass or lipid membranes) become charged in aqueous solutions. The resulting ionic distribution induces effective interactions between the charged surfaces, which depend on the permittivity of the confined aqueous solution. To explore this phenomenon in very confined systems, we perform all-atom molecular dynamics (MD) simulations of charged lipid membranes separated by a salted water layer of varying thickness. To extract an effective permittivity from the atomistic model, we compare the ion distributions of these simulations with the ones of a continuous, mesoscopic model: a modified Poisson–Boltzmann (mPB) equation taking into account a spatially varying dielectric permittivity and an explicit Born solvation energy for ions. Such mPB/MD comparisons, applied to lipid membranes at various hydration levels, reveal a sharp decrease of the permittivity upon dehydration, converging to a plateau value that we attribute to lipid headgroups. We discuss the limitations of the mPB model in the dehydrated lipid membranes, in particular through the appearance of ion/ion correlations, and compare our results to alternative computational methods. In our tension-free simulations of the fluid membranes, an increase in the area per lipid indicates that the permittivity decrease is accompanied by intermembrane attraction. Our approach could be generalized to estimate a mesoscopic permittivity of liquids confined by other interfaces, provided ions follow Boltzmann statistics.