K(+)/Na(+) selectivity of the KcsA potassium channel from microscopic free energy perturbation calculations

Microscopic molecular dynamics free energy perturbation calculations of the K(+)/Na(+) selectivity in the KcsA potassium channel, based on its experimental three-dimensional structure, are reported. The relative binding free energies for K(+) and Na(+) in the most relevant ion occupancy states of the four-site selectivity filter are calculated. The previously proposed mechanism for ion permeation through the KcsA channel is predicted, in agreement with available experimental data, to have a significant selectivity for K(+) over Na(+). The calculations also show that the individual 'binding site' selectivities are generally not additive and the doubly loaded states of the filter thus display cooperative effects. The only site that is not K(+) selective is that which is located at the entrance to the internal water cavity, suggesting the possibility that internal Na(+) could block outward currents.     

A computational study of ion binding and protonation states in the KcsA potassium channel

We report results from microscopic molecular dynamics and free energy perturbation simulations of the KcsA potassium channel based on its experimental atomic structure. Conformational properties of selected amino acid residues as well as equilibrium positions of K(+) ions inside the selectivity filter and the internal water cavity are examined. Positions three and four (counting from the extracellular site) in the experimental structure correspond to distinctly separate binding sites for K(+) ions inside the selectivity filter. The protonation states of Glu71 and Asp80, which are close to each other and to the selectivity filter, as well as K(+) binding energies are determined using free energy perturbation calculations. The Glu71 residue which is buried inside a protein cavity is found to be most stable in the neutral form while the solvent exposed Asp80 is ionized. The channel altogether exothermically binds up to three ions, where two of them are located inside the selectivity filter and one in the internal water cavity. Ion permeation mechanisms are discussed in relation to these results.     

Molecular dynamics study of the KcsA potassium channel

The structural, dynamical, and thermodynamic properties of a model potassium channel are studied using molecular dynamics simulations. We use the recently unveiled protein structure for the KcsA potassium channel from Streptomyces lividans. Total and free energy profiles of potassium and sodium ions reveal a considerable preference for the larger potassium ions. The selectivity of the channel arises from its ability to completely solvate the potassium ions, but not the smaller sodium ions. Self-diffusion of water within the narrow selectivity filter is found to be reduced by an order of magnitude from bulk levels, whereas the wider hydrophobic section of the pore maintains near-bulk self-diffusion. Simulations examining multiple ion configurations suggest a two-ion channel. Ion diffusion is found to be reduced to approximately (1)/(3) of bulk diffusion within the selectivity filter. The reduced ion mobility does not hinder the passage of ions, as permeation appears to be driven by Coulomb repulsion within this multiple ion channel.     

Accurate determination of the binding free energy for KcsA-charybdotoxin complex from the potential of mean force calculations with restraints

Free energy calculations for protein-ligand dissociation have been tested and validated for small ligands (50 atoms or less), but there has been a paucity of studies for larger, peptide-size ligands due to computational limitations. Previously we have studied the energetics of dissociation in a potassium channel-charybdotoxin complex by using umbrella sampling molecular-dynamics simulations, and established the need for carefully chosen coordinates and restraints to maintain the physiological ligand conformation. Here we address the ligand integrity problem further by constructing additional potential of mean forces for dissociation of charybdotoxin using restraints. We show that the large discrepancies in binding free energy arising from simulation artifacts can be avoided by using appropriate restraints on the ligand, which enables determination of the binding free energy within the chemical accuracy. We make several suggestions for optimal choices of harmonic potential parameters and restraints to be used in binding studies of large ligands.     

NMR study of the tetrameric KcsA potassium channel in detergent micelles

Nuclear magnetic resonance (NMR) studies of large membrane-associated proteins are limited by the difficulties in preparation of stable protein-detergent mixed micelles and by line broadening, which is typical of these macroassemblies. We have used the 68-kDa homotetrameric KcsA, a thermostable N-terminal deletion mutant of a bacterial potassium channel from Streptomyces lividans, as a model system for applying NMR methods to membrane proteins. Optimization of measurement conditions enabled us to perform the backbone assignment of KcsA in SDS micelles and establish its secondary structure, which was found to closely agree with the KcsA crystal structure. The C-terminal cytoplasmic domain, absent in the original structure, contains a 14-residue helix that could participate in tetramerization by forming an intersubunit four-helix bundle. A quantitative estimate of cross- relaxation between detergent and KcsA backbone amide protons, together with relaxation and light scattering data, suggests SDS-KcsA mixed micelles form an oblate spheroid with approximately 180 SDS molecules per channel. K(+) ions bind to the micelle-solubilized channel with a K(D) of 3 +/- 0.5 mM, resulting in chemical shift changes in the selectivity filter. Related pH-induced changes in chemical shift along the "outer" transmembrane helix and the cytoplasmic membrane interface hint at a possible structural explanation for the observed pH-gating of the potassium channel.     

Efficient membrane assembly of the KcsA potassium channel in Escherichia coli requires the protonmotive force

Very little is known about the biogenesis and assembly of oligomeric membrane proteins. In this study, the biogenesis of KcsA, a prokaryotic homotetrameric potassium channel, is investigated. Using in vivo pulse–chase experiments, both the monomeric and tetrameric form could be identified. The conversion of monomers into a tetramer is found to be a highly efficient process that occurs in the Escherichia coli inner membrane. KcsA does not require ATP hydrolysis by SecA for insertion or tetramerization. The presence of the protonmotive force (pmf) is not necessary for transmembrane insertion of KcsA; however, the pmf proved to be essential for the efficiency of oligomerization. From in vivo and in vitro experiments it is concluded that the electrical component, Δψ, is the main determinant for this effect. These results demonstrate a new role of the pmf in membrane protein biogenesis.     

Potential of mean force calculations on an L-type calcium channel model

To understand the mechanisms of Na(+)/Li(+) permeation at submicromolar Ca(2+) concentrations, Na(+)/Li(+) blocking at higher Ca(2+) concentrations (10(-6)-10(-4) M) and Ca(2+) permeation at millimolar Ca(2+) concentrations, we used our recently described L-type calcium channel model. For this purpose, we obtained potential of mean force (pmf) curves for the position change of one Na(+) and one Ca(2+) ion inside the channel and for the position change of a second Ca(2+) ion when the EEEE locus is coordinated to Ca(2+). The pmf curves suggest that (i) at submicromolar Ca(2+) concentrations, because of the low velocity of Ca(2+) entry in the channel, monovalent ion flux occurs; (ii) at Ca(2+) concentrations between 10(-6) and 10(-4) M, thermodynamic equilibrium between the channel and Ca(2+) is achieved; as the coordination of Ca(2+) with the locus is more favorable than the coordination of Na(+), the monovalent ion flux is blocked; and (iii) to put a second Ca(2+) ion inside the channel at an appropriate rate, the Ca(2+) concentration should reach millimolar levels. Nevertheless, the entry of a second Ca(2+) is thermodynamically unfavorable, indicating that the competition of two Ca(2+) ions for the locus leads to Ca(2+) permeation.     

Effect of external electric fields on the potential energy profile of K+ ions in selective filter of the KcsA potassium channel

In this study, the potential energy profile of potassium ions in the selective filter part of a KcsA channel was investigated via the application of the molecular simulation method. For this purpose, using the molecular dynamics simulation, the effect of an applied electric field, either constant or oscillating, was studied on the dynamics of K ions in the filter. It was found that when the channel is exposed to a constant electric field of strength 0.03 V/nm, the ions experience a hopping motion. Furthermore, it was shown that the application of oscillating electric fields of 1 and 2.5 GHz, can increase the rigidity of the filter atomic bonds. By computing the potential energy of K ion in the filter, it was shown that the depth of the potential wells, corresponding to the filter sites, increased when an alternative field was applied. Therefore, exposing the channel to the GHz oscillating electric field could disturb the passing rate of ions through the filter, which in turn may affect the operation of these kinds of channels.     

Quantum mechanical calculations of charge effects on gating the KcsA channel

A series of ab initio (density functional) calculations were carried out on side chains of a set of amino acids, plus water, from the (intracellular) gating region of the KcsA K(+) channel. Their atomic coordinates, except hydrogen, are known from X-ray structures [D.A. Doyle, J.M. Cabral, R.A. Pfuetzner, A. Kuo, J.M. Gulbis, S.L. Cohen, B.T. Chait, R. MacKinnon, The structure of the potassium channel: molecular basis of K(+) conduction and selectivity, Science 280 (1998) 69-77; R. MacKinnon, S.L. Cohen, A. Kuo, A. Lee, B.T. Chait, Structural conservation in prokaryotic and eukaryotic potassium channels, Science 280 (1998) 106-109; Y. Jiang, A. Lee, J. Chen, M. Cadene, B.T. Chait, R. MacKinnon, The open pore conformation of potassium channels. Nature 417 (2001) 523-526], as are the coordinates of some water oxygen atoms. The 1k4c structure is used for the starting coordinates. Quantum mechanical optimization, in spite of the starting configuration, places the atoms in positions much closer to the 1j95, more tightly closed, configuration. This state shows four water molecules forming a "basket" under the Q119 side chains, blocking the channel. When a hydrated K(+) approaches this "basket", the optimized system shows a strong set of hydrogen bonds with the K(+) at defined positions, preventing further approach of the K(+) to the basket. This optimized structure with hydrated K(+) added shows an ice-like 12 molecule nanocrystal of water. If the water molecules exchange, unless they do it as a group, the channel will remain blocked. The "basket" itself appears to be very stable, although it is possible that the K(+) with its hydrating water molecules may be more mobile, capable of withdrawing from the gate. It is also not surprising that water essentially freezes, or forms a kind of glue, in a nanometer space; this agrees with experimental results on a rather different, but similarly sized (nm dimensions) system [K.B. Jinesh, J.W.M. Frenken, Capillary condensation in atomic scale friction: how water acts like a glue, Phys. Rev. Lett. 96 (2006) 166103/1-4]. It also agrees qualitatively with simulations on channels [A. Anishkin, S. Sukharev, Water dynamics and dewetting transitions in the small mechanosensitive channel MscS, Biophys. J. 86 (2004) 2883-2895; O. Beckstein, M.S.P. Sansom, Liquid-vapor oscillations of water in hydrophobic nanopores, Proc. Natl Acad. Sci. U. S. A. 100 (2003) 7063-7068] and on featureless channel-like systems [J. Lu, M.E. Green, Simulation of water in a pore with charges: application to a gating mechanism for ion channels, Prog. Colloid Polym. Sci. 103 (1997) 121-129], in that it forms a boundary on water that is not obvious from the liquid state. The idea that a structure is stable, even if individual molecules exchange, is well known, for example from the hydration shell of ions. We show that when charges are added in the form of protons to the domains (one proton per domain), the optimized structure is open. No stable water hydrogen bonds hold it together; an opening of 11.0 A appears, measured diagonally between non-neighboring domains as glutamine 119 carbonyl O-O distance. This is comparable to the opening in the MthK potassium channel structure that is generally agreed to be open. The appearance of the opening is in rather good agreement with that found by Perozo and coworkers. In contrast, in the uncharged structure this diagonal distance is 6.5 A, and the water "basket" constricts the uncharged opening still further, with the ice-like structure that couples the K(+) ion to the gating region freezing the entrance to the channel. Comparison with our earlier model for voltage gated channels suggests that a similar mechanism may apply in those channels.     

Quantum mechanical calculations of charge effects on gating the KcsA channel

A series of ab initio (density functional) calculations were carried out on side chains of a set of amino acids, plus water, from the (intracellular) gating region of the KcsA K⁺ channel. Their atomic coordinates, except hydrogen, are known from X-ray structures [D.A. Doyle, J.M. Cabral, R.A. Pfuetzner, A. Kuo, J.M. Gulbis, S.L. Cohen, B.T. Chait, R. MacKinnon, The structure of the potassium channel: molecular basis of K⁺ conduction and selectivity, Science 280 (1998) 69-77; R. MacKinnon, S.L. Cohen, A. Kuo, A. Lee, B.T. Chait, Structural conservation in prokaryotic and eukaryotic potassium channels, Science 280 (1998) 106-109; Y. Jiang, A. Lee, J. Chen, M. Cadene, B.T. Chait, R. MacKinnon, The open pore conformation of potassium channels. Nature 417 (2001) 523-526], as are the coordinates of some water oxygen atoms. The 1k4c structure is used for the starting coordinates. Quantum mechanical optimization, in spite of the starting configuration, places the atoms in positions much closer to the 1j95, more tightly closed, configuration. This state shows four water molecules forming a “basket” under the Q119 side chains, blocking the channel. When a hydrated K⁺ approaches this “basket”, the optimized system shows a strong set of hydrogen bonds with the K⁺ at defined positions, preventing further approach of the K⁺ to the basket. This optimized structure with hydrated K⁺ added shows an ice-like 12 molecule nanocrystal of water. If the water molecules exchange, unless they do it as a group, the channel will remain blocked. The “basket” itself appears to be very stable, although it is possible that the K⁺ with its hydrating water molecules may be more mobile, capable of withdrawing from the gate. It is also not surprising that water essentially freezes, or forms a kind of glue, in a nanometer space; this agrees with experimental results on a rather different, but similarly sized (nm dimensions) system [K.B. Jinesh, J.W.M. Frenken, Capillary condensation in atomic scale friction: how water acts like a glue, Phys. Rev. Lett. 96 (2006) 166103/1-4]. It also agrees qualitatively with simulations on channels [A. Anishkin, S. Sukharev, Water dynamics and dewetting transitions in the small mechanosensitive channel MscS, Biophys. J. 86 (2004) 2883-2895; O. Beckstein, M.S.P. Sansom, Liquid-vapor oscillations of water in hydrophobic nanopores, Proc. Natl Acad. Sci. U. S. A. 100 (2003) 7063-7068] and on featureless channel-like systems [J. Lu, M.E. Green, Simulation of water in a pore with charges: application to a gating mechanism for ion channels, Prog. Colloid Polym. Sci. 103 (1997) 121-129], in that it forms a boundary on water that is not obvious from the liquid state. The idea that a structure is stable, even if individual molecules exchange, is well known, for example from the hydration shell of ions. We show that when charges are added in the form of protons to the domains (one proton per domain), the optimized structure is open. No stable water hydrogen bonds hold it together; an opening of 11.0 Å appears, measured diagonally between non-neighboring domains as glutamine 119 carbonyl O-O distance. This is comparable to the opening in the MthK potassium channel structure that is generally agreed to be open. The appearance of the opening is in rather good agreement with that found by Perozo and coworkers. In contrast, in the uncharged structure this diagonal distance is 6.5 Å, and the water “basket” constricts the uncharged opening still further, with the ice-like structure that couples the K⁺ ion to the gating region freezing the entrance to the channel. Comparison with our earlier model for voltage gated channels suggests that a similar mechanism may apply in those channels.     

Mechanisms of tetraethylammonium ion block in the KcsA potassium channel

We report results from automated docking and microscopic molecular dynamics simulations of the tetraethylammonium (TEA) complexes with KcsA. Binding modes and energies for TEA binding at the external and internal sides of the channel pore are examined utilising the linear interaction energy method. Effects of the channel ion occupancy (based on our previous results for the ion permeation mechanisms) on the binding energies are considered. Calculations show that TEA forms stable complexes at both the external and internal entrances of the selectivity filter. Furthermore, the effects of the Y82V mutation are evaluated and the results show, in agreement with experimental data, that the mutant has a significantly reduced binding affinity for TEA at the external binding site, which is attributed to stabilising hydrophobic interactions between the ligand and the tyrosines.     

Use of a potential of mean force to analyze free energy contributions in protein folding.

A method for calculation of the free energy of residues as a function of residue burial is proposed. The method is based on the potential of mean force, with a reaction coordinate expressed by residue burial. Residue burials are calculated from high-resolution protein structures. The largest individual contributions to the free energy of a residue are found to be due to the hydrophobic interactions of the nonpolar atoms, interactions of the main chain polar atoms, and interactions of the charged groups of residues Arg and Lys. The contribution to the free energy of folding due to the uncharged side chain polar atoms is small. The contribution to the free energy of folding due to the main chain polar atoms is favorable for partially buried residues and less favorable or unfavorable for fully buried residues. Comparison of the accessible surface areas of proteins and model spheres shows that proteins deviate considerably from a spherical shape and that the deviations increase with the size of a protein. The implications of these results for protein folding are also discussed.     

Ion binding affinity in the cavity of the KcsA potassium channel

The hydrophobic cell membrane interior presents a large energy barrier for ions to permeate. Potassium channels reduce this barrier by creating a water-filled cavity at the middle of their ion conduction pore to allow ion hydration and by directing the C-terminal "end charge" of four alpha-helices toward the water-filled cavity. Here we have studied the interaction of monovalent cations with the cavity of the KcsA K(+) channel using X-ray crystallography. In these studies, Tl(+) was used as an analogue for K(+) and the total ion-stabilization energy for Tl(+) in the cavity was estimated by measuring its binding affinity. Binding affinity for the Na(+) ion was also measured, revealing a weak selectivity ( approximately 7-fold) favoring Tl(+) over Na(+). The structures of the cavity containing Na(+), K(+), Tl(+), Rb(+), and Cs(+) are compared. These results are consistent with a fairly large (more negative than -100 mV) electrostatic potential inside the cavity, and they also imply the presence of a weak nonelectrostatic component to a cation's interaction with the cavity.     

Valence selectivity of the gramicidin channel: a molecular dynamics free energy perturbation study.

The valence selectivity of the gramicidin channel is examined using computer simulations based on atomic models. The channel interior is modeled using a gramicidin-like periodic poly (L,D)-alanine beta-helix. Free energy perturbation calculations are performed to obtain the relative affinity of K+ and Cl- for the channel. It is observed that the interior of the gramicidin channel provides an energetically favorable interaction site for a cation but not for an anion. Relative to solvation in bulk water, the carbonyl CO oxygens can provide a favorable interaction to stabilize K+, whereas the amide NH hydrogens are much less effective in stabilizing Cl-. The results of the calculations demonstrate that, as a consequence of the structural asymmetry of the backbone charge distribution, a K+ cation can partition spontaneously from bulk water to the interior of the gramicidin channel, whereas a Cl- anion cannot.     

Solid-state NMR study and assignments of the KcsA potassium ion channel of S. lividans

The extraordinary efficiency and selectivity of potassium channels have made them ideal systems for biophysical and functional studies of ion conduction. We carried out solid-state NMR studies of the selectivity filter region of the protein. Partial site-specific assignments of the NMR signals were obtained based on high field multidimensional solid-state NMR spectra of uniformly (13)C, (15)N enriched KcsA potassium channel from Streptomyces lividans. Both backbone and sidechain atoms were assigned for residues V76-D80 and P83-L90, in and near the selectivity filter region of the protein; this region exhibits good dispersion and useful chemical shift fingerprints. This study will enable structure, dynamic and mechanistic studies of ion conduction by NMR.     

Influence of lipids on membrane assembly and stability of the potassium channel KcsA

A novel antibacterial peptide, moricin, isolated from the silkworm Bombyx mori, consists of 42 amino acids. It is highly basic and the amino acid sequence has no significant similarity to those of other antibacterial peptides. The 20 structures of moricin in methanol have been determined from two-dimensional 1H-nuclear magnetic resonance spectroscopic data. The solution structure reveals an unique structure comprising of a long alpha-helix containing eight turns along nearly the full length of the peptide except for four N-terminal residues and six C-terminal residues. The electrostatic surface map shows that the N-terminal segment of the alpha-helix, residues 5-22, is an amphipathic alpha-helix with a clear separation of hydrophobic and hydrophilic faces, and that the C-terminal segment of the alpha-helix, residues 23-36, is a hydrophobic alpha-helix except for the negatively charged surface at the position of Asp30. The results suggest that the amphipathic N-terminal segment of the alpha-helix is mainly responsible for the increase in permeability of the membrane to kill the bacteria.     

Interactions of anionic phospholipids and phosphatidylethanolamine with the potassium channel KcsA

Fluorescence quenching methods have been used to study interactions of anionic phospholipids with the potassium channel KcsA from Streptomyces lividans. Quenching of the Trp fluorescence of KcsA reconstituted into mixtures of dioleoylphosphatidylcholine (DOPC) and an anionic phospholipid with dibromostearoyl chains is more marked at low mole fractions of the brominated anionic phospholipid than is quenching in mixtures of dibromostearoylphosphatidylcholine and nonbrominated anionic lipid. The quenching data are consistent with two classes of binding site for lipid on KcsA, one set corresponding to annular binding sites around KcsA to which DOPC and two-chain anionic phospholipids bind with similar affinities, the other set (non-annular sites) corresponding to sites at which anionic phospholipids can bind but from which DOPC is either excluded or binds with very low affinity. The binding constant for tetraoleoylcardiolipin at the annular sites is significantly less than that for DOPC, being comparable to that for dioleoylphosphatidylethanolamine. Tetraoleoylcardiolipin binds with highest affinity to the non-annular sites, the affinity for dioleoylphosphatidylglycerol being the lowest. The affinity for dioleoylphosphatidylserine decreases at high ionic strength, suggesting that electrostatic interactions between the anionic phospholipid headgroup and positively charged residues on KcsA are important for binding at the non-annular site. The effect of ionic strength on the binding of phosphatidic acid is less marked than on phosphatidylserine. The value of the binding constant for the non-annular site depends on the extent of Trp fluorescence quenching following from binding at the non-annular site. It is suggested that the non-annular site to which binding is detected in the fluorescence quenching experiments corresponds to the binding site for phosphatidylglycerol detected at monomer-monomer interfaces in x-ray diffraction studies.     

Protein self-assembly and lipid binding in the folding of the potassium channel KcsA

Moderate concentrations of the alcohol 2,2,2-trifluoroethanol (TFE) cause the coupled unfolding and dissociation into subunits of the homotetrameric potassium channel KcsA, in a process that is partially irreversible when the protein is solubilized in plain dodecyl beta-d-maltoside (DDM) micelles [Barrera et al. (2005) Biochemistry 44, 14344-52]. Here we report that the transition from the folded tetramer to the unfolded monomer becomes completely reversible when KcsA is solubilized in mixed micelles composed of the detergent DDM and the lipids DOPE (1,2-dioleoyl-sn-glycero-3-phosphoethanolamine) and DOPG (1,2-dioleoyl-sn-glycero-3-[phospho-rac-(1-glycerol)]). This result suggests that lipids may act as effectors in the tetramerization of KcsA. The observed reversibility allowed the determination of the standard free energy of the folding reaction of KcsA: DeltaG = 30.5 +/- 3.1 kcal x mol-1. We also observed that, prior to the unfolding of the tetramer, the presence of lower TFE concentrations causes the disassembly of supramolecular clusters of KcsA into the individual tetrameric molecules. Within the limits of experimental resolution, this is also a reversible process, but unlike the tetramer to monomer transition from above, the level of clustering is not influenced by the presence of solubilized lipids. These observations suggest a distinct role of the lipids in the different in vitro assembly steps (folding/tetramerization and clustering) of KcsA.     

Quantum calculations on water in the KcsA channel cavity with permeant and non-permeant ions

Different ions in the pore of the KcsA channel behave differently, and we relate this to their solvation. We show that the selectivity is dependent, in part, on the solvation in the cavity (sometimes referred to as the vestibule, it is the region containing water molecules between the intracellular gate and the selectivity filter at the extracellular end of the pore). We have shown earlier that potassium is more dependent at the upper end of the cavity region on solvation by the threonines there, while sodium ion has more water molecules as ligands. In addition, sodium ion is placed asymmetrically, while potassium is nearly exactly symmetric with respect to the four-fold symmetry of the channel. We have now extended these calculations to rubidium and cesium ions, and find that rubidium solvation resembles that of potassium (and both are permeant ions), while cesium resembles sodium (and both are non-permeant), in terms of the geometry of up to eight hydrating, and four non-hydrating, water molecules. In each case, a maximum of 12 water molecules are relevant to the calculation. The placement of the water molecules in the two cases is essentially the same as found from the electron density in the X-ray structure of Zhou and MacKinnon. For Na⁺ and K⁺, we show that energy decreases from bulk to the cavity to the lowest position in the selectivity filter (accurate energy could not be calculated for the heavier ions). A separate calculation shows that fixing the Na⁺ ion at the position of the K⁺ minimum, followed by re-optimization produced a significantly modified system, not something that could be produced by thermal fluctuations. Moving the K⁺ into the Na⁺ position in the upper cavity led to a small increase in energy, ≈ 3 k_BT, but was accompanied by large shifts in the positions of hydrating waters, which would create a major kinetic barrier. Therefore, thermal fluctuations could not invalidate the conclusions of the main calculations.