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

Abstract

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.

Exploring chemical reaction mechanisms through harmonic Fourier beads path optimization

“…30,31 Originally, the HFB method was used with molecular mechanical (MM) potentials that did not allow covalent bond breaking or forming. [25][26][27][32][33][34] The present work extends the applicability of the HFB method to chemical reactions involving covalent bond breaking and forming on quantum mechanical (QM) and hybrid QM/MM potentials.…”

“…The key ideas and features of the combined CG-HFB implementation and its differences from earlier HFB implementations [25][26][27][32][33][34] and other related methods 2,14,15,23,28,[43][44][45][46] are provided in the supplementary material. 64 In brief, CG-HFB performs optimization in Cartesian coordinates, which avoids costly transformations and complicated corrections associated with internal coordinates.…”

A Permeability Study of O2 and the Trace Amine p-Tyramine through Model Phosphatidylcholine Bilayers

“…Khavrutskii et al . [46] simulated the permeability of Na + , Cl − , and their ion pair, and found the pair to have a higher energetic barrier than either ion on its own. The generalized Born (GB) model [47, 48] describes an approximation for the difference in free-energy of n charges that have been transferred from medium w to medium b , Here, q i and q j represent a charge pair, ϵ w is the dielectric constant for water, ϵ b is the dielectric constant at the center of the bilayer, a i is the Born radius of each charge, and r ij is the distance between each charge pair.…”

“…The generalized Born (GB) model [47, 48] describes an approximation for the difference in free-energy of n charges that have been transferred from medium w to medium b , Here, q i and q j represent a charge pair, ϵ w is the dielectric constant for water, ϵ b is the dielectric constant at the center of the bilayer, a i is the Born radius of each charge, and r ij is the distance between each charge pair. From Eq 7, the following ratio can be derived for the free-energy of transferring a pair of opposite and equal charges, relative to the free-energy of transfering a single positive charge: The ratio of Δ G Na + Cl − /Δ G Na + in [46] is ≃ 1.26. Using Eq 7, with a for Na + and Cl − taken from [49] to be 1.80 Å and 1.91 Å, respectively, this gives an average interatomic spacing r +/− = 5.28 Å.…”

All-atom molecular dynamics simulations of an artificial sodium channel in a lipid bilayer: the effect of water solvation/desolvation of the sodium ion

“…Atomistic simulation enables the study of the effect of the explicit water molecules in the transport process. A number of simulation studies have investigated the free energy of unassisted ion transport through lipid bilayers (Khavrutskii, Gorfe, Lu, & McCammon, 2009;Tepper & Voth, 2006;Wilson & Pohorille, 1996) and have shown the importance of the solvation of the ions by water molecules as they pass through the lipid bilayer. Transport in biological ion channels has been effectively studied by simulation (Shi, Izvekov, & Voth, 2006).…”