Test of the Gouy-Chapman Theory for a Charged Lipid Membrane against Explicit-Solvent Molecular Dynamics Simulations

A wealth of experimental data has verified the applicability of the Gouy-Chapman (GC) theory to charged lipid membranes. Surprisingly, a validation of GC by molecular dynamics (MD) simulations has been elusive. Here, we report a test of GC against extensive MD simulations of an anionic lipid bilayer solvated by water at different concentrations of NaCl or KCl. We demonstrate that the ion distributions from the simulations agree remarkably well with GC predictions when information on the adsorption of counterions to the bilayer is incorporated.

Figure 1

Ion distributions around the charged DOPG bilayer. (a) A snapshot of the 32Cl system at 79 ns of the MD simulations. Lipids are displayed with carbonyl and hydroxyl groups highlighted with thick bonds and phosphorus atoms as medium dark spheres. Adsorbed and diffuse ${\mathrm{Na}}^{+}$ ions are displayed as dark and light spheres, respectively, and ${\mathrm{Cl}}^{-}$ are displayed as dark spheres in the bulk water. The lower leaflet is only partially shown. (b) A close-up view of the interactions around a ${\mathrm{Na}}^{+}$ ion penetrated into the bilayer. Favorable interactions with three carbonyls and two hydroxyls are indicated by dotted lines.

Figure 2

Average density profiles of lipid and solvent atoms of the 32Cl system. All densities, obtained in bins with a 1-Å width, are normalized by the bulk concentration of the ions, which is $163\mathrm{m}M$, except for the density of water (calculated using the oxygen atom), which is scaled down by an additional factor of 10. The origin of the $z$ axis is chosen to coincide with the outer density peak of ${\mathrm{Na}}^{+}$.

Figure 3

Comparisons of MD results for ${\mathrm{Na}}^{+}$ and ${\mathrm{Cl}}^{-}$ distributions with GC predictions. Panels (a)–(c) display data for the 64Cl, 32Cl, and 16Cl systems, respectively. For each system, the ion densities are normalized by the bulk concentrations.

Figure 4

Comparisons of MD results for ${\mathrm{K}}^{+}$ and ${\mathrm{Cl}}^{-}$ distributions with GC predictions. Data in panels (a)–(c) are similar to the counterparts in Fig. 3, but with ${\mathrm{K}}^{+}$ replacing ${\mathrm{Na}}^{+}$. MD results were calculated on the last 40 ns of 70-ns trajectories.