Molecular dynamics study of free energy profiles for organic cations in gramicidin A channels

The free energy profiles for four organic cations in right-handed single-helix gramicidin A dimers were computed by using umbrella sampling molecular dynamics with CHARMM. ion-water column translocations were facilitated by using a novel ''water-tunnel'' approach. The overlapping pieces of free energy profile for adjacent windows were selected from three trajectories that differed in initial ion rotation and were aligned by the method of umbrella potential differences. Neglected long-range electrostatic energies from the bulk water and the bilayer were computed with DelPhi and added to the profile. The approach was corroborated for the formamidinium-guanidinium pair by using perturbation dynamics at axial positions 0, 6, 12, and 15 Angstrom from the channel center. The barrier to ethylammonium entry was prohibitive at 21 kcal/mol, whereas for methylammonium it was 5.5 kcal/mol, and the profile was quite flat through the channel, roughly consistent with conductance measurements. The profile for formamidinium was very similar to that of methylammonium. Guanidinium had a high entry barrier (Delta F = +8.6 kcal/mol) and a narrow deep central well (Delta F = -2.6 kcal/mol), qualitatively consistent with predictions from voltage-dependent potassium current block measurements. Its deep central well, contrasting with the flat profile for formamidinium, was verified with perturbation dynamics and was correlated with its high propensity to form hydrogen bonds with the channel at the dimer junction (not shared by the other three cations). Analysis of the ensemble average radial forces on the ions demonstrates that all four ions undergo compressive forces in the channel that are at maximum at the center of the monomer and relieved at the dimer junction, illustrating increased flexibility of the channel walls in the center of the channel.