Free Energy for the Permeation of Na+ and Cl− Ions and Their Ion-Pair through a Zwitterionic Dimyristoyl Phosphatidylcholine Lipid Bilayer by Umbrella Integration with Harmonic Fourier Beads

Understanding the mechanism of ion permeation across lipid bilayers is key to controlling osmotic pressure and developing new ways of delivering charged, drug-like molecules inside cells. Recent reports suggest ion-pairing as the mechanism to lower the free energy barrier for the ion permeation in disagreement with predictions from the simple electrostatic models. In this paper we quantify the effect of ion-pairing or charge quenching on the permeation of Na(+) and Cl(-) ions across DMPC lipid bilayer by computing the corresponding potentials of mean force (PMFs) using fully atomistic molecular dynamics simulations. We find that the free energy barrier to permeation reduces in the order Na(+)-Cl(-) ion-pair (27.6 kcal/mol) > Cl(-) (23.6 kcal/mol) > Na(+) (21.9 kcal/mol). Furthermore, with the help of these PMFs we derive the change in the binding free energy between the Na(+) and Cl(-) with respect to that in water as a function of the bilayer permeation depth. Despite the fact that the bilayer boosts the Na(+)-Cl(-) ion binding free energy by as high as 17.9 kcal/mol near its center, ion-pairing between such hydrophilic ions as Na(+) and Cl(-) does not assist their permeation. However, based on a simple thermodynamic cycle, we suggest that ion-pairing between ions of opposite charge and solvent philicity could enhance ion permeation. Comparison of the computed permeation barriers for Na(+) and Cl(-) ions with available experimental data supports this notion. This work establishes general computational methodology to address ion-pairing in fluid anisotropic media and details the ion permeation mechanism on atomic level.