Energetics of ion conduction through the gramicidin channel
Proceedings of the National Academy of Sciences of the United States of America
The free energy governing K ؉ conduction through gramicidin A channels is characterized by using over 0.1 s of all-atom molecular dynamics simulations with explicit solvent and membrane. The results provide encouraging agreement with experiments and insights into the permeation mechanism. The free energy surface of K ؉ , as a function of both axial and radial coordinates, is calculated. Correcting for simulation artifacts due to periodicity and the lack of hydrocarbon polarizability, the
... ted singlechannel conductance for K ؉ ions is 0.8 pS, closer to experiment than any previous calculation. In addition, the estimated single ion dissociation constants are within the range of experimental determinations. The relatively small free energy barrier to ion translocation arises from a balance of large opposing contributions from protein, single-file water, bulk electrolyte, and membrane. Mean force decomposition reveals a remarkable ability of the single-file water molecules to stabilize K ؉ by ؊40 kcal͞mol, roughly half the bulk solvation free energy. The importance of the single-file water confirms the conjecture of Mackay et al. [Mackay, D. H. J., Berens, P. H., Wilson, K. R. & Hagler, A. T. (1984) Biophys. J. 46, 229 -248]. Ion association with the channel involves gradual dehydration from approximately six to seven water molecules in the first shell, to just two inside the narrow pore. Ion permeation is influenced by the orientation of the single-file water column, which can present a barrier to conduction and give rise to long-range coupling of ions on either side of the pore. Small changes in the potential function, including contributions from electronic polarization, are likely to be sufficient to obtain quantitative agreement with experiments. M olecular dynamics (MD) simulation has become an essential tool for investigating a wide range of chemical and biological systems. Greater computational resources, improvements in simulation methodologies, and refinement of interaction potentials have made it possible to model increasingly complex processes that previously were intractable (1). It is important that the approach be thoroughly tested on systems that are small and yet possess the same ingredients and challenges as much larger and more complex biomolecular systems. These benchmarks serve to set standards on which studies of more complex problems can find foundation. For example, a single key protein secondary structure, the ␤ hairpin, has been used as a benchmark test in protein-folding studies (2). In the present study, we tackle the problem of ion permeation with a similar mindset. Ion permeation involves a seemingly straightforward process of an ion passing across the membrane through a molecular pore. However, this process is difficult to model because it entails the accurate representation of intermolecular interactions in vastly different environments (aqueous solution and narrow protein pore) for which there is little direct experimental data (3). As a rigorous examination of an all-atom force field to model ion permeation, we combine free energy methods with fully atomistic, dynamical simulations on a benchmark system. Atomic structures have been reported for many ion channels, but none is structurally and functionally as well characterized (4), or as amenable to computer simulation, as the gramicidin A (gA) channel. gA channels form by transmembrane dimerization of single-stranded, right-handed ␤ 6.3 -helices (5) with the sequence (underlined residues are D-amino acids): formyl-Val-Gly-Ala-Leu-Ala-Val-Val-Val-Trp-Leu-Trp-Leu-Trp-Leu-Trp-ethanolamine (6). High resolution structures have been obtained for gA embedded in detergent micelles by using liquid-state NMR (7, 8) and oriented dimyristoylphosphatidylcholine bilayers by using solid-state NMR (9), and refined with MD simulation (10). The depth of experimental knowledge and the simplicity of this protein also have lent it to numerous computational models (11) and make it the system of choice for investigating ion conduction. Since the first MD simulations on a fully flexible atomic model of gA were carried out 20 yr ago (12), system sizes and simulation times have grown by orders of magnitude, yet quantitative agreement with ion-flux experimental measurements has remained a difficult task (11, 13) . A direct connection between the atomic structure and the observed conductance properties cannot easily be obtained via a "brute force" MD simulation approach because ionic fluxes correspond to transit times of 10-100 ns, such that statistically accurate conductance measurements are beyond the capabilities of present day computers. A better computational strategy is to first determine the equilibrium free energy landscape, as described by the potential of mean force (PMF), which governs the systematic forces acting on the permeating ions in the system, and then invoke an appropriate macroscopic or semimicroscopic formalism to calculate the ionic current. Successful application of this computational strategy in calculating ion conductances in the KcsA potassium channel (14, 15) prompts us to return to the problem of ion permeation through the gA channel and assess how close we are to obtaining quantitative agreement with experiment. Although the microscopic force field still requires further refinements to describe accurately the permeation of ions across the gA channel, the current model does a surprisingly good job of predicting experimental conductances. Theory and Methods To focus our computational effort on the calculation of the free energy landscape governing ion conduction, we separate the system into "pore' ' and "bulk" regions (16). The equilibrium properties of the system then can be reconstructed from a hierarchy of PMFs ᐃ(r 1 , . . . , r n ), representing the pore region occupied by n ions. In the case of the gA channel, at moderately low alkali metal cation concentration (Ͻ100 mM), ion conduction is governed primarily by the 1-ion PMF, ᐃ(r 1 ), which can be expressed in terms of the total potential energy U of the system as a function of ionic coordinates r i (i ϭ 1, N) and remaining degrees of freedom X (water, protein, lipids) e Ϫᐃ͑r1͒͞kBT ϰ ͵ Ј dr 2 ⅐ ⅐ ⅐ ͵ Ј dr N ͵ dX e ϪU͑r1, r2,⅐ ⅐ ⅐rN;X͒͞kBT ,  This paper was submitted directly (Track II) to the PNAS office.