Victor B. Luzhkov

Ion permeation mechanism of the potassium channel

Ion-selective channels enable the specific permeation of ions through cell membranes and provide the basis of several important biological functions; for example, electric signalling in the nervous system. Although a large amount of electrophysiological data is available, the molecular mechanisms by which these channels can mediate ion transport remain a significant unsolved problem. With the recently determined crystal structure of the representative K+ channel (KcsA) from Streptomyces lividans, it becomes possible to examine ion conduction pathways on a microscopic level. K+ channels utilize multi-ion conduction mechanisms, and the three-dimensional structure also shows several ions present in the channel. Here we report results from molecular dynamics free energy perturbation calculations that both establish the nature of the multiple ion conduction mechanism and yield the correct ion selectivity of the channel. By evaluating the energetics of all relevant occupancy states of the selectivity filter, we find that the favoured conduction pathway involves transitions only between two main states with a free difference of about 5 kcal mol-1. Other putative permeation pathways can be excluded because they would involve states that are too high in energy.

Free Energy Calculations and Ligand Binding

Publisher Summary This chapter gives an overview of some different methods for calculating ligand binding free energies that are all based on force fields and conformational sampling. Many of these studies of protein–ligand binding in the mid-1980s showed a remarkable agreement between theory and experiment, which led to an explosion of activity in the field of free energy calculations. More recent investigations, however, have demonstrated that significantly longer simulations than those used in the original reports are often required obtaining reliable results in protein–ligand binding studies. The increasing number of applications of free energy calculations also showed that the use of these methods was not as straightforward as expected; therefore, much effort was spent on improving the methodology. The free energy perturbation (FEP)/thermodynamic integration (TI) type of method has not really fulfilled its promise of being able to open a major new avenue to structure-based drug design due to slow convergence and sampling difficulties. In particular, in this type of extrapolation process in which one may want to look at 20 or so new ligands, arriving at the correct end-points by long perturbation paths sometimes seems hopeless. It appears that a better solution to this problem can often be provided by automated docking of individual compounds, at least when they differ significantly from each other, and then to try to evaluate the binding energetic by a method that does not require the unphysical transformations involved in FEP/TI and related methods. The docking problem resembles the protein-folding one in many respects, and the only way to attack difficult cases seems to be by extensive conformational searching in combination with more reliable scoring methods.

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.

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.

Computational and NMR study of quaternary ammonium ion conformations in solution

Conformations around C–N bonds at the quaternary centre in tetraalkylammonium ions in water solution are investigated. Structures of Me4N+, Et4N+, n-Pr4N+, n-Bu4N+, and n-Pe4N+ are calculated using quantum mechanical HF and DFT methods together with the PCM solvent model. Relative solvation free energies of tetraalkylammonium ions are further estimated from microscopic molecular dynamics free energy perturbation simulations using the Gromos-87 and Amber-95 force fields. The predicted free energy difference in solution between two stable conformations of Et4N+, D2d and S4, is 0.6–1.0 kcal mol−1 (in favour of D2d), which is in quantitative agreement with the recent Raman spectroscopy results. The energies of the g+g− conformations of Et4N+ are 3.6–4.0 kcal mol−1 higher. The ions with longer hydrocarbon chains show quite similar energy gap between D2d and S4. The torsion barrier for a two-step interconversion between the D2d and S4 structures is 9.5 kcal mol−1 (HF/6-31G(d) calculations). The computational results are augmented by NMR measurements of the Et4N+–I− salt in aqueous solution, which predict a symmetric structure of Et4N+ in water. However, the D2d and S4 conformers are not discernible due to presumably high similarity of chemical shifts. The calculated conformational energetics in solution together with previously observed D2d, S4 and high-energy g+g−-type structures of Et4N+, n-Pr4N+, and n-Bu4N+ in the solid state indicate that the carbon chain conformations at the quaternary ammonium centre sensitively depend on the actual microenvironment.

Computer simulation of primary kinetic isotope effects in the proposed rate-limiting step of the glyoxalase I catalyzed reaction.

The proposed rate-limiting step of the glyoxalase I catalyzed reaction is the proton abstraction from the C1 carbon of the substrate by Glu172. Here we examine primary kinetic isotope effects and the influence of quantum dynamics on this process by computer simulations. The calculations utilize the empirical valence bond method in combination with the molecular dynamics free energy perturbation technique and path integral simulations. For the enzyme-catalyzed reaction a H/D kinetic isotope effect of 5.0 ± 1.3 is predicted in reasonable agreement with the experimental result of about 3. Furthermore, the magnitude of quantum mechanical effects is found to be very similar for the enzyme reaction and the corresponding uncatalyzed process in solution, in agreement with other studies. The problems associated with attaining the required accuracy in order for the present approach to be useful as a diagnostic tool for the study of enzyme reactions are also discussed.

Structure-activity relationship for extracellular block of K+ channels by tetraalkylammonium ions.

External tetraalkylammonium ion binding to potassium channels is studied using microscopic molecular modelling methods and the experimental structure of the KcsA channel. Relative binding free energies of the KcsA complexes with Me4N+, Et4N+, and n‐Pr4N+ are calculated with the molecular dynamics free energy perturbation approach together with automated ligand docking. The four‐fold symmetry of the entrance cavity formed by the Tyr82 residues is found to provide stronger binding for the D 2d than for the S 4 conformation of the ligands. In agreement with experiment the Et4N+ blocker shows several kcal/mol better binding than the other tetraalkylammonium ions.

Free-energy perturbation calculations of binding and transition-state energies: hydrolysis of phenyl esters by β-cyclodextrin

Abstract The use of free-energy perturbation simulations for calculating binding and transition-state energies is examined. Reactions of three phenyl esters with β-cyclodextrin are considered. The binding free energies are calculated using conventional mutation of the substrate force field from one chemical structure to another (two-state problem) in water and in the neutral inclusion complex. For calculation of activation free-energy differences between two substrates the transition states are represented by linear combinations of reactant (anionic inclusion complexes) and product (tetrahedral intermediate) force fields (four-state problem). The coefficients of this linear combination are obtained from empirical valence bond simulations of a reference substrate. The calculated relative binding and activation energies are in a good agreement with experimental data. The approximations underlying this procedure are discussed.

Empirical valence bond study of radical reactions: hydrogen atom transfer in peroxidation of phenol

The use of free energy perturbation empirical valence bond (FEP/EVB) molecular dynamics technique for microscopic modeling of atom exchange reactions is examined. In particular, the analytical Morse and anti-Morse potentials for unpaired electron interactions are incorporated in the framework of molecular mechanics force field. Peroxidation of phenol is studied as a test case. The corresponding free energy profiles of hydrogen atom transfer are calculated by the FEP/EVB method in gas phase and chloroform. The reaction potential energy profile is also determined using DFT calculations. The FEP/EVB simulations correctly predict linear approach of reactants, tight structure of the transition state, and lower activation barrier in gas phase compared to solution.

Evaluation of Adamantane Derivatives as Inhibitors of Dengue Virus mRNA Cap Methyltransferase by Docking and Molecular Dynamics Simulations

Binding of the Dengue virus S‐adenosyl‐L‐methionine (AdoMet)‐dependent mRNA cap methyltransferase (NS5MTaseDV) with adamantane derivatives was explored using molecular modeling methods and (nucleoside‐2′O)‐methyltransferase bioassay. The studied compounds include urea derivatives of adamantane and the antiviral drugs amantadine and rimantadine. The urea derivatives of adamantanes had previously been identified as inhibitors of NS5MTaseDV. The docking simulations using GOLD, Glide, and Dock give consistent binding modes and binding affinities of adamantanes in the AdoMet‐binding site of NS5MTaseDV and, in particular, yield similar positions for the previously found inhibitors. Combined, they perfectly correspond to the bioassay measurements of nucleoside‐2′O‐methyltransferase activity of NS5TaseDV, which confirmed inhibitory properties of the active urea adamantane but did not show inhibitory activity for amantadine and rimantadine. We also employed microscopic molecular dynamics (MD) simulations and a linear interaction energy (LIE) method to verify the docking results. The MD/LIE binding free energies of selected protein–inhibitor complexes agree overall with the binding affinities from docking and demonstrate that amantadine and rimantadine only weakly bind at the explored site. The MD simulations also demonstrated the flexible character of a protein loop that is located between the β2 and β3 strands and is part of the AdoMet‐binding pocket of NS5MTaseDV.