Ionic permeation free energy in gramicidin: a semimicroscopic perspective

Abstract

Ion permeation through the gramicidin channel is studied using a model that circumvents two major difficulties inherent to standard simulational methods. It exploits the timescale separation between electronic and structural contributions to dielectric stabilization, accounting for the influence of electronic polarization by embedding the channel in a dielectric milieu that describes this polarization in a mean sense. The explicit mobile moieties are the ion, multipolar waters, and the carbonyls and amides of the peptide backbone. The model treats the influence of aromatic residues and the membrane dipole potential. A new electrical geometry is introduced that treats long-range electrostatics exactly and avoids problems related to periodic boundary conditions. It permits the translocating ion to make a seamless transition from nearby electrolyte to the channel interior. Other degrees of freedom (more distant bulk electrolyte and nonpolar lipid) are treated as dielectric continua. Reasonable permeation free energy profiles are obtained for potassium, rubidium, and cesium; binding wells are shallow and the central barrier is small. Estimated cationic single-channel conductances are smaller than experiment, but only by factors between 2 (rubidium) and 50 (potassium). When applied to chloride the internal barrier is large, with a corresponding miniscule single-channel conductance. The estimated relative single-channel conductances of gramicidin A, B, and C agree well with experiment.

FIGURE 1

(A) Modified electrical geometry of gramicidin, permitting continuous transition from single-file to bulk water. All explicit sources are in the low ɛ-region. The backbone is tethered, with mobile CO-Os and NH-Hs. Only 20 COs are shown. The dotted line is the physical boundary of the truncated system. The solid line is the electrical boundary. The Helmholtz layer is an electrical buffer region between the low ɛ-background and the high ɛ-bulk electrolyte. The coordinate arrows beneath the central water indicate the location of the channel midpoint. (B) For comparison, the full gramicidin dimer is sited relative to the water bubble with the regions encompassing the aromatic moieties indicated.

FIGURE 2

Confocal mapping of the bubble geometry of Fig. 1 A into a wedge. The point I, translated by x = −R_elec from the bubble center, is the center of the inversion sphere of radius 2R_elec. In the transformed geometry, points on the bubble surface lie on the plane at x = 2R_elec. The invariant point in the transformation is the intersection of the bubble and the inversion sphere.

FIGURE 3

Backbone contributions to the permeation free energy in gA for the three larger cations and chloride: Cs⁺, ▪; Rb⁺, ▴; K⁺, •; and Cl⁻, □.

FIGURE 4

Effect of structural relaxation and mean background electronic polarizability on backbone contributions to the permeation free energy for Cs⁺: ɛ_background = 2, mobile backbone ▪; ɛ_background = 1, mobile backbone, •; and ɛ_background = 2, rigid backbone, ▴.

FIGURE 5

Comparison of the cumulative contributions to the permeation free energy in gA for both cesium and chloride. Backbone only: Cs⁺ (+), Cl⁻ (−); full gA (backbone and tryptophan residues): Cs⁺, (•), Cl⁻ (○); all sources (backbone, tryptophan residues and membrane dipole potential): Cs⁺ (▪), Cl⁻ (□).

FIGURE 6

Total permeation free energy profiles for the three larger cations and chloride. Symbols are those of Fig. 3. Solid line is an experimental profile for K⁺ (Edwards et al., 2002); dashed line is the simulational profile for K⁺ based on the GROMOS force field (Allen et al., 2003b).

FIGURE 7

Effect of mean background electronic polarizability on the total permeation free energy for K⁺: ɛ_background = 2, mobile backbone ▪; ɛ_background = 1, mobile backbone, •. As in Fig. 6, solid and dashed lines are experimental and simulational profiles for K⁺.

FIGURE 8

Comparison of total permeation free energy profiles for Cs⁺ permeation through gA, ▴; gB, ▪; and gC, •.