Energetics of ion conduction through the gramicidin channel

Abstract

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 calculated 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. 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-AlaLeu-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 dimyristoyl...

Diffusion constant of K+ inside Gramicidin A: A comparative study of four computational methods

“…In contrast to this conclusion, it was found in Ref. [26] that the diffusion constant of K + inside the GA channel is not much different from the bulk. These authors used MD simulations of K + restrained with a harmonic potential and mapped this microscopic dynamics to the generalized Langevin equation (GLE).…”

“…The last method [26,33,34] is based on an analysis of the GLE for a harmonic oscillator (GLE-HO). In Eq.…”

“…The maximum barrier for a K + ion inside the channel is 7.5 kcal/mol. The PMF of K + inside GA has been calculated previously using the CHARMM PARAM27 force field and TIP3P water model [26]. Both PMFs exhibit similar features such as periodicity and a maximum barrier of approximately 7 kcal/mol.…”

“…Calculation of the diffusion constant of K + in bulk TIP3P water and inside GA channel has been carried out by other researchers [26]. In their work a 10 kcal/mol/Å 2 harmonic restraint was used for K + and the function D̂ (s) was extrapolated to s=0 from the 15<s<35 range.…”

“…They are widely used for calculating diffusion properties of ions and molecules in bulk phases [20][21][22], but the applicability of some of these methods to narrow ion channels (e.g., Gramicidin A) is questionable. Currently, there is no consensus in the biophysics literature about the magnitude of diffusion constants of ions inside narrow channels [6,[23][24][25][26][27][28]. Different methods and authors have predicted a wide range of diffusion constants.…”