Not only enthalpy: large entropy contribution to ion permeation barriers in single-file channels

Abstract

The effect of channel length on the barrier for potassium ion permeation through single-file channels has been studied by means of all-atom molecular dynamics simulations. Using series of peptidic gramicidin-like and simplified ring-structured channels, both embedded in model membranes, we obtained two distinct types of behavior: saturation of the central free energy barriers for peptidic channels and a linear increase in simplified ring-structured channels with increasing channel length. The saturation of the central free energy barrier for the peptidic channels occurs at relatively short lengths, and it is correlated with the desolvation from the bulk water. Remarkably, decomposition of free energy barriers into enthalpic and entropic terms reveals an entropic cost for ion permeation. Furthermore, this entropic cost dominates the ion permeation free energy barrier, since the corresponding free energy contribution is higher than the enthalpic barrier. We conclude that the length dependence of the free energy is enthalpy-dominated, but the entropy is the major contribution to the permeation barrier. The decrease in rotational water motion and the reduction of channel mobility are putative origins for the overall entropic penalty.

FIGURE 1

Schematic representations of model channels used for the study. (a) Side view of polyalanine pores of increasing number of residues, p-11 to p-29. (a′) Top view of p-17 channel. (a″) Side view of a typical simulation box for polyalanine channels. Half of the octane layer has been omitted for clarity. (b) Side view of ring-structured channels of increasing number of rings. (b′) Top view of r-02. (b″) Simulation box for r-08; half the argon atoms were removed for clarity.

FIGURE 2

Potentials of mean force (PMF) for potassium ion permeation at 300 K for the series of polyalanine peptides (black). Underlying each PMF is a three-Gaussian fit to the main features of the channel (gray): the two entrance barriers (constant) and the central barrier that varies with channel length. Dashed black lines indicate the channel entrance and exit. Errors bars (not shown for clarity) are <±1.5 kJ/mol.

FIGURE 3

Free energy barriers (a) for ion permeation in polyalanine channels as a function of channel length. The black line in the upper panel indicates the central barrier ΔG, which is dominant in channels longer than p-17. The height of the central Gaussian function fit (see Theory and Methods for details) is displayed in gray. Dashed lines represent the free energy for the access barrier. The difference in ion-water interaction between the ion in the bulk and the ion inside the center of the channel (b) as a function of channel length correlates with the free energy barrier.

FIGURE 4

Decomposition of free energy barriers for potassium ion permeation through polyalanine (a) and ring-05 (b) selected channels. The entropy components are weighted with the temperature (300 K) and sign reversed (–TΔS). For the polyalanine channels, all thermodynamic quantities could be directly computed from the simulation. For the ring-structured channel with charges ±0.5 e, only the free energies and the entropies could be extracted independently from the umbrella simulations. The enthalpy contribution of the ring system was computed from ΔH = ΔG + TΔS.

FIGURE 5

PMFs, F(z), for potassium ion permeation through ring-structured channels. (a) PMFs for ring channels with charges of +0.5 e on the carbon and −0.5 e on the oxygen. (b) PMFs for ring channels with charges of +0.7 e on the carbon, −0.7 e on the oxygen, and increased flexibility along the z coordinate.

FIGURE 6

Free energy barriers, ΔF, (a) and ion-water potential energy difference between the bulk and the channel (b) for the ring-structured channels, as a function of channel length.

FIGURE 7

Projection of the average dipole moment, 〈μ_z〉, of water molecules inside the channel onto the pore axis for the polyalanine channels (upper panel), the ring-05 (center), and the ring-07 (lower panel) channels. The water dipole was normalized with respect to the total dipole of the TIP4P water model (2.177 debye). Different colors indicate different channels of increasing length. Profiles have been symmetrized. On the upper left, a typical simulation snapshot shows the water orientation when the ion (yellow sphere) occupies the central position. As seen from the 〈μ_z〉 curves, water molecules far from the ion lose their alignment with the pore axis in the polyalanine channels due to a decay of the electric field and interactions with the bulk water (not shown). The central and lower panels illustrate the long-ranging polarization induced by the potassium ion for the ring channels.