Role of protein flexibility in ion permeation: a case study in gramicidin A

Abstract

Proteins have a flexible structure, and their atoms exhibit considerable fluctuations under normal operating conditions. However, apart from some enzyme reactions involving ligand binding, our understanding of the role of flexibility in protein function remains mostly incomplete. Here we investigate this question in the realm of membrane proteins that form ion channels. Specifically, we consider ion permeation in the gramicidin A channel, and study how the energetics of ion conduction changes as the channel structure is progressively changed from completely flexible to a fixed one. For each channel structure, the potential of mean force for a permeating potassium ion is determined from molecular dynamics (MD) simulations. Using the same molecular dynamics data for completely flexible gramicidin A, we also calculate the average densities and fluctuations of the peptide atoms and investigate the correlations between these fluctuations and the motion of a permeating ion. Our results show conclusively that peptide flexibility plays an important role in ion permeation in the gramicidin A channel, thus providing another reason--besides the well-known problem with the description of single file pore water--why this channel cannot be modeled using continuum electrostatics with a fixed structure. The new method developed here for studying the role of protein flexibility on its function clarifies the contributions of the fluctuations to energy and entropy, and places limits on the level of detail required in a coarse-grained model.

FIGURE 1

The model system: gA dimer (green helix) embedded in a dimyristoylphosphatidylcholine bilayer and solvated with ∼3200 water molecules and 12 pairs of KCl ions. K⁺ ions are indicated by blue balls and Cl⁻ ions by red balls. Only the phosphate head groups of lipids (purple balls) are shown for clarity.

FIGURE 2

PMF profiles of a K⁺ ion along the central axis of the gA channel. The three curves correspond to the fixed, backbone fixed, and flexible structures of gA as indicated on the graph.

FIGURE 3

Comparison of PMFs obtained from two different fixed structures: 1MAG from NMR versus a structure obtained after equilibration with water. The former is indicated on the graph as NMR.

FIGURE 4

Square of the Fourier transform of the mean mass density and its fluctuations in gA without an ion in the channel (A). The mean density is shown with three curves using different damping factors, α⁻¹ = 1 Å (solid line), α⁻¹ = 0.5 Å (dashed line), and no damping (dash-dotted line). Fluctuations (without damping) are indicated by the dotted line. In B, the mean densities smoothed with damping factors are transformed back to the real space. Here the solid and dashed curves have the same damping factors as those in A.

FIGURE 5

Mass distribution in gA along the z axis. Each set of distributions has been shifted vertically for clarity, and corresponds to a different simulation with the potassium ion tethered to a different position via a harmonic potential as indicated in the graph. The solid lines give the smoothed mass density of the peptide along the z axis. The sharply peaked, solid lines show the distribution of the potassium ion for each simulation.

FIGURE 6

Similar to Fig. 5 but for the charge distribution of the peptide atoms along the z axis.

FIGURE 7

Similar to Fig. 6 but for the charge distribution of the carbonyl atoms only.

FIGURE 8

Same as Fig. 4 A but for the ion at z = 20 Å (dotted line), z = 9.75 Å (dashed line), and z = 9 Å (solid line). Squares of the densities rapidly fall with increasing k while their fluctuations increase. No damping factors are used in here and the following figures, but the Gaussian damping function used in previous figures is indicated in the lower left-hand side.

FIGURE 9

Similar to Fig. 8 but for the fluctuations in the charge of the carbonyl atoms (A) and the mass of the backbone atoms (B) for three ion positions: z = 20 Å (dotted line), z = 9.75 Å (dashed line), and z = 9 Å (solid line).

FIGURE 10

Here we show the quantity |R(k)| for the correlations between the ion and peptide masses (A) and ion and carbonyl charges (B) for three ion positions: z = 20 Å (dotted line), z = 9.75 Å (dashed line), and z = 9 Å (solid line). Where R is small, correlation between the ion and the mass density is weak. If |R| = 1, they are perfectly correlated, i.e., one is slave to the other.

FIGURE 11

Similar to Fig. 10 but for the mass (A) and charge (B) correlations between the ion and channel water for three ion positions: z = 20 Å (dotted line), z = 9.75 Å (dashed line), and z = 9 Å (solid line). Only waters within 15 Å of the center of mass of gA are included in the calculations.