An improved structural characterisation of reduced French bean plastocyanin based on NMR data and local-elevation molecular dynamics simulation

Deriving structural information about a protein from NMR experimental data is still a non-trivial challenge to computational biochemistry. This is because of the low ratio of the number of independent observables to the number of molecular degrees of freedom, the approximations involved in the different relationships between particular observable quantities and molecular conformation, and the averaged character of the experimental data. For example, protein 3 J-coupling data are seldom used for structure refinement because of the multiple-valuedness and limited accuracy of the Karplus relationship linking a 3 J-coupling to a torsional angle. Moreover, sampling of the large conformational space is still problematic. Using the 99-residue protein plastocyanin as an example we investigated whether use of a thermodynamically calibrated force field, inclusion of solvent degrees of freedom, and application of adaptive local-elevation sampling that accounts for conformational averaging produces a more realistic representation of the ensemble of protein conformations than standard single-structure refinement in a non-explicit solvent using restraints that do not account for averaging and are partly based on non-observed data. Yielding better agreement with observed experimental data, the protein conformational ensemble is less restricted than when using standard single-structure refinement techniques, which are likely to yield a picture of the protein which is too rigi

Solvating atomic level fine-grained proteins in supra-molecular level coarse-grained water for molecular dynamics simulations

Simulation of the dynamics of a protein in aqueous solution using an atomic model for both the protein and the many water molecules is still computationally extremely demanding considering the time scale of protein motions. The use of supra-atomic or supra-molecular coarse-grained (CG) models may enhance the computational efficiency, but inevitably at the cost of reduced accuracy. Coarse-graining solvent degrees of freedom is likely to yield a favourable balance between reduced accuracy and enhanced computational speed. Here, the use of a supra-molecular coarse-grained water model that largely preserves the thermodynamic and dielectric properties of atomic level fine-grained (FG) water in molecular dynamics simulations of an atomic model for four proteins is investigated. The results of using an FG, a CG, an implicit, or a vacuum solvent environment of the four proteins are compared, and for hen egg-white lysozyme a comparison to NMR data is made. The mixed-grained simulations do not show large differences compared to the FG atomic level simulations, apart from an increased tendency to form hydrogen bonds between long side chains, which is due to the reduced ability of the supra-molecular CG beads that represent five FG water molecules to make solvent-protein hydrogen bonds. But, the mixed-grained simulations are at least an order of magnitude faster than the atomic level one

On using time-averaging restraints in molecular dynamics simulation

Introducing experimental values as restraints into molecular dynamics (MD) simulations to bias the values of particular molecular properties, such as nuclear Overhauser effect intensities or distances, 3J coupling constants, chemical shifts or crystallographic structure factors, towards experimental values is a widely used structure refinement method. To account for the averaging of experimentally derived quantities inherent in the experimental techniques, time-averaging restraining methods may be used. In the case of structure refinement using 3J coupling constants from NMR experiments, time-averaging methods previously proposed can suffer from large artificially induced structural fluctuations. A modified time-averaged restraining potential energy function is proposed which overcomes this problem. The different possible approaches are compared using stochastic dynamics simulations of antamanide, a cyclic peptide of ten residue

Biomolecular structure refinement based on adaptive restraints using local-elevation simulation

Introducing experimental values as restraints into molecular dynamics (MD) simulation to bias the values of particular molecular properties, such as nuclear Overhauser effect intensities or distances, dipolar couplings, 3 J-coupling constants, chemical shifts or crystallographic structure factors, towards experimental values is a widely used structure refinement method. Because multiple torsion angle values ϕ correspond to the same 3 J-coupling constant and high-energy barriers are separating those, restraining 3 J-coupling constants remains difficult. A method to adaptively enforce restraints using a local elevation (LE) potential energy function is presented and applied to 3 J-coupling constant restraining in an MD simulation of hen egg-white lysozyme (HEWL). The method succesfully enhances sampling of the restrained torsion angles until the 37 experimental 3 J-coupling constant values are reached, thereby also improving the agreement with the 1,630 experimental NOE atom-atom distance upper bounds. Afterwards the torsional angles ϕ are kept restrained by the built-up local-elevation potential energie

Structure of hen egg-white lysozyme solvated in TFE/water: a molecular dynamics simulation study based on NMR data

Various experimental studies of hen egg white lysozyme (HEWL) in water and TFE/water clearly indicate structural differences between the native state and TFE state of HEWL, e.g. the helical content of the protein in the TFE state is much higher than in the native state. However, the available detailed NMR studies were not sufficient to determine fully a structure of HEWL in the TFE state. Different molecular dynamics (MD) simulations, i.e. at room temperature, at increased temperature and using proton-proton distance restraints derived from NMR NOE data, have been used to generate configurational ensembles corresponding to the TFE state of HEWL. The configurational ensemble obtained at room temperature using atom-atom distance restraints measured for HEWL in TFE/water solution satisfies the experimental data and has the lowest protein energy. In this ensemble residues 50-58, which are part of the β-sheet in native HEWL, adopt fluctuating α-helical secondary structur

Calculation of NMR-relaxation parameters for flexible molecules from molecular dynamics simulations

Comparatively small molecules such as peptides can show a high internal mobility with transitions between several conformational minima and sometimes coupling between rotational and internal degrees of freedom. In those cases the interpretation of NMR relaxation data is difficult and the use of standard methods for structure determination is questionable. On the other hand, in the case of those system sizes, the timescale of both rotational and internal motions is accessible by molecular dynamics (MD) simulations using explicit solvent. Thus a comparison of distance averages (〈r −6〉−1/6 or 〈r −3〉1/3) over the MD trajectory with NOE (or ROE) derived distances is no longer necessary, the (back)calculation of the complete spectra becomes possible. In the present study we use two 200ns trajectories of a heptapeptide of β-amino acids in methanol at two different temperatures to obtain theoretical ROESY spectra by calculating the exact spectral densities for the interproton vectors and the full relaxation matrix. Those data are then compared with the experimental ones. This analysis permits to test some of the assumptions and approximations that generally have to be made to interpret NMR spectra, and to make a more reliable prediction of the conformational equilibrium that leads to the experimental spectru

On using oscillating time-dependent restraints in MD simulation

The use of time-dependent restraints in molecular simulation in order to generate a conformational ensemble for molecules that is in accordance with measured ensemble averages for particular observable quantities is investigated. Using a model system consisting of liquid butane and the cyclic peptide antamanide the reproduction of particular average 3 J-coupling constant values in a molecular dynamics simulation is analysed. It is shown that the multiple-valuedness and the sizeable gradients of the Karplus curve relating 3 J-coupling constants measured in NMR experiments to the corresponding torsional-angle values cause severe problems when trying to restrain a 3 J-coupling constant to a value close to the extrema of the Karplus curve. The introduction of a factor oscillating with time into the restraining penalty function alleviates this problem and enhances the restrained conformational samplin

Intramolecular hydrogen-bonding in aqueous carbohydrates as a cause or consequence of conformational preferences: a molecular dynamics study of cellobiose stereoisomers

It is often assumed that intramolecular hydrogen-bonding (H-bonding) exerts a significant influence on the conformational properties of aqueous (bio-)polymers. To discuss this statement, one should, however, distinguish between solvent-exposed and buried H-bonds, and between their respective roles in promoting stability (i.e., as a driving force) and specificity (for which the term steering force is introduced here). In this study, the role of solvent-exposed H-bonding in carbohydrates as a driving or steering force is probed using explicit-solvent molecular dynamics simulations with local elevation umbrella sampling in the simple context of cellobiose stereoisomers. More specifically, four β(1→4)-linked d-aldohexopyranose disaccharides are considered, which present a different stereochemisty of the potentially H-bonding groups neighboring the glycosidic linkage. Although the epimerization may largely alter the intramolecular trans-glycosidic H-bonding pattern, it is found to have only very limited influence on the Ramachandran free-energy map of the disaccharide, a loss of intramolecular H-bonding being merely compensated for by an enhancement of the interaction with the solvent molecules. This finding suggests that solvent-exposed trans-glycosidic H-bonding (and in particular the $$\hbox{HO}_3^{\prime}$$ →O5 H-bond) is not the cause of the 21-helical secondary structure characteristic of cellooligosaccharides, but rather the opportunistic consequence of a sterically and stereoelectronically dictated conformational preference. In other words, for these compounds, solvent-exposed H-bonding appears to represent a minor (possibly adverse) conformational driving as well as steering forc

On the calculation of 3 J αβ-coupling constants for side chains in proteins

Structural knowledge about proteins is mainly derived from values of observables, measurable in NMR spectroscopic or X-ray diffraction experiments, i.e. absorbed or scattered intensities, through theoretically derived relationships between structural quantities such as atom positions or torsional angles on the one hand and observable quantities such as squared structure factor amplitudes, NOE intensities or 3 J-coupling constants on the other. The standardly used relation connecting 3 J-couplings to torsional angles is the Karplus relation, which is used in protein structure refinement as well as in the evaluation of simulated properties of proteins. The accuracy of the simple and generalised Karplus relations is investigated using side-chain structural and 3 J αβ-coupling data for three different proteins, Plastocyanin, Lysozyme, and FKBP, for which such data are available. The results show that the widely used Karplus relations are only a rough estimate for the relation between 3 J αβ-couplings and the corresponding χ1-angle in protein