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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.

Khavrutskii IV, Gorfe AA, Lu B, McCammon JA - J. Am. Chem. Soc. (2009)

Bottom Line: 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).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.This work establishes general computational methodology to address ion-pairing in fluid anisotropic media and details the ion permeation mechanism on atomic level.

View Article: PubMed Central - PubMed

Affiliation: Howard Hughes Medical Institute, University of CaliforniaSan Diego, La Jolla, California 92093-0365, USA. ikhavru@mccammon.ucsd.edu

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.

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Change in the binding free energy in kcal/mol between Na+ and Cl− ions relative to bulk water as a function of the bilayer permeation depth. Averaged positions of individual ions are shown on the right axis, whereas the change in binding free energy is shown on the left axis. The vertical and horizontal black lines pass through values of zero of the three axes.
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fig5: Change in the binding free energy in kcal/mol between Na+ and Cl− ions relative to bulk water as a function of the bilayer permeation depth. Averaged positions of individual ions are shown on the right axis, whereas the change in binding free energy is shown on the left axis. The vertical and horizontal black lines pass through values of zero of the three axes.

Mentions: The final estimate of the change in the binding free energy between Na+ and Cl− along the membrane normal with respect to bulk water is shown in Figure 5. Except for a rather broad, short hump at the headgroup region, the magnitude of the binding free energy increases gradually upon going toward the center of the bilayer. The observed hump is due to preferential Na+ binding at the headgroup region and indicates that the association of the two ions in that region is not as strong as in water. Thus, the headgroup region dissociates the ion-pair better than water. Going over the hump, the electrostatic interactions between the ions become stronger and the magnitude of the binding energy inside the nonpolar region of the bilayer increases rapidly. As inferred from Figure 5, at the center of the bilayer, the absolute change in the ion binding free energy reaches a maximum of 17.1 kcal/mol near the bilayer center. If, for simplicity, we estimate the change in the binding free energy from the maxima of the three PMFs, we get a 17.9 kcal/mol absolute value (27.6 − 21.9 − 23.6 kcal/mol). Evidently, ion-pairing in the bilayer reduces the barrier for the ion-pair permeation from the sum of the individual Na+ and Cl− permeation barriers of 45.5 kcal/mol (21.9 + 23.6 kcal/mol) to 27.6 kcal/mol (45.5 − 17.9 kcal/mol). Thus, ion-pairing could in principle facilitate permeation of ions. However, in the present case the ion-pair permeation barrier is still larger than the barrier for the individual ions.


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.

Khavrutskii IV, Gorfe AA, Lu B, McCammon JA - J. Am. Chem. Soc. (2009)

Change in the binding free energy in kcal/mol between Na+ and Cl− ions relative to bulk water as a function of the bilayer permeation depth. Averaged positions of individual ions are shown on the right axis, whereas the change in binding free energy is shown on the left axis. The vertical and horizontal black lines pass through values of zero of the three axes.
© Copyright Policy - open-access - ccc-price
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2651636&req=5

fig5: Change in the binding free energy in kcal/mol between Na+ and Cl− ions relative to bulk water as a function of the bilayer permeation depth. Averaged positions of individual ions are shown on the right axis, whereas the change in binding free energy is shown on the left axis. The vertical and horizontal black lines pass through values of zero of the three axes.
Mentions: The final estimate of the change in the binding free energy between Na+ and Cl− along the membrane normal with respect to bulk water is shown in Figure 5. Except for a rather broad, short hump at the headgroup region, the magnitude of the binding free energy increases gradually upon going toward the center of the bilayer. The observed hump is due to preferential Na+ binding at the headgroup region and indicates that the association of the two ions in that region is not as strong as in water. Thus, the headgroup region dissociates the ion-pair better than water. Going over the hump, the electrostatic interactions between the ions become stronger and the magnitude of the binding energy inside the nonpolar region of the bilayer increases rapidly. As inferred from Figure 5, at the center of the bilayer, the absolute change in the ion binding free energy reaches a maximum of 17.1 kcal/mol near the bilayer center. If, for simplicity, we estimate the change in the binding free energy from the maxima of the three PMFs, we get a 17.9 kcal/mol absolute value (27.6 − 21.9 − 23.6 kcal/mol). Evidently, ion-pairing in the bilayer reduces the barrier for the ion-pair permeation from the sum of the individual Na+ and Cl− permeation barriers of 45.5 kcal/mol (21.9 + 23.6 kcal/mol) to 27.6 kcal/mol (45.5 − 17.9 kcal/mol). Thus, ion-pairing could in principle facilitate permeation of ions. However, in the present case the ion-pair permeation barrier is still larger than the barrier for the individual ions.

Bottom Line: 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).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.This work establishes general computational methodology to address ion-pairing in fluid anisotropic media and details the ion permeation mechanism on atomic level.

View Article: PubMed Central - PubMed

Affiliation: Howard Hughes Medical Institute, University of CaliforniaSan Diego, La Jolla, California 92093-0365, USA. ikhavru@mccammon.ucsd.edu

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.

Show MeSH
Related in: MedlinePlus