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 sampling.     

Methods of NMR structure refinement: molecular dynamics simulations improve the agreement with measured NMR data of a C-terminal peptide of GCN4-p1

The C-terminal trigger sequence is essential in the coiled-coil formation of GCN4-p1; its conformational properties are thus of importance for understanding this process at the atomic level. A solution NMR model structure of a peptide, GCN4p16–31, encompassing the GCN4-p1 trigger sequence was proposed a few years ago. Derived using a standard single-structure refinement protocol based on 172 nuclear Overhauser effect (NOE) distance restraints, 14 hydrogen-bond and 11 ϕ torsional-angle restraints, the resulting set of 20 NMR model structures exhibits regular α-helical structure. However, the set slightly violates some measured NOE bounds and does not reproduce all 15 measured ³J(H_N-H_Cα)-coupling constants, indicating that different conformers of GCN4p16–31 might be present in solution. With the aim to resolve structures compatible with all NOE upper distance bounds and ³J-coupling constants, we executed several structure refinement protocols employing unrestrained and restrained molecular dynamics (MD) simulations with two force fields. We find that only configurational ensembles obtained by applying simultaneously time-averaged NOE distance and ³J-coupling constant restraining with either force field reproduce all the experimental data. Additionally, analyses of the simulated ensembles show that the conformational variability of GCN4p16–31 in solution admitted by the available set of 187 measured NMR data is larger than represented by the set of the NMR model structures. The conformations of GCN4p16–31 in solution differ in the orientation not only of the side-chains but also of the backbone. The inconsistencies between the NMR model structures and the measured NMR data are due to the neglect of averaging effects and the inclusion of hydrogen-bond and torsional-angle restraints that have little basis in the primary, i.e. measured NMR data.     

On the similarity of properties in solution or in the crystalline state: A molecular dynamics study of hen lysozyme

As protein crystals generally possess a high water content, it is assumed that the behaviour of a protein in solution and in crystal environment is very similar. This assumption can be investigated by molecular dynamics (MD) simulation of proteins in the different environments. Two 2ns simulations of hen egg white lysozyme (HEWL) in crystal and solution environment are compared to one another and to experimental data derived from both X-ray and NMR experiments, such as crystallographic B-factors, NOE atom–atom distance bounds, ³J_{H N}-coupling constants, and ¹H-¹⁵N bond vector order parameters. Both MD simulations give very similar results. The crystal simulation reproduces X-ray and NMR data slightly better than the solution simulation.     

An NMR investigation of putative interresidue H-bonding in methyl α-cellobioside in solution

Methyl α-cellobioside (methyl β-d-glucopyranosyl-(1→4)-α-d-glucopyranoside) was labeled with ¹³C at C4′ for use in NMR studies in DMSO-d₆ solvent to attempt the detection of a trans-H-bond J-coupling (^3hJ_CCOH) between C4′ and OH3. Analysis of the OH3 signal at 600 MHz revealed only the presence of two homonuclear J-couplings: ³J_H3,OH3 and a smaller, longer range J_HH. No evidence for ^3hJ_C4′,OH3 was found. The longer range J_HH was traced to ⁴J_H4,OH3 based on 2D ¹H–¹H COSY data and inspection of the H2 and H4 signal lineshapes. A limited set of DFT calculations was performed on a methyl cellobioside mimic to evaluate the structural dependencies of ⁴J_H2,O3H and ⁴J_H4,O3H on the H3–C3–O3–H torsion angle. Computed couplings range from about −0.7 to about +1.1 Hz, with maximal values observed when the C–H and O–H bonds are roughly diaxial.     

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 residues.     

Assessing the effect of conformational averaging on the measured values of observables

Experiment and computer simulation are two complementary tools to understand the dynamics and behavior of biopolymers in solution. One particular area of interest is the ensemble of conformations populated by a particular molecule in solution. For example, what fraction of a protein sample exists in its folded conformation? How often does a particular peptide form an alpha helix versus a beta hairpin? To address these questions, it is important to determine the sensitivity of a particular experiment to changes in the distribution of molecular conformations. Consequently, a general analytic formalism is proposed to determine the sensitivity of a spectroscopic observable to the underlying distribution of conformations. A particular strength of the approach is that it provides an expression for a weighted average across conformational substates that is independent of the averaging function used. The formalism is described and applied to experimental and simulated nuclear Overhauser enhancement (NOE) and ³ J-coupling data on peptides in solution.     

Pressure-dependent <Superscript>13</Superscript>C chemical shifts in proteins: origins and applications

Pressure-dependent ¹³C chemical shifts have been measured for aliphatic carbons in barnase and Protein G. Up to 200 MPa (2 kbar), most shift changes are linear, demonstrating pressure-independent compressibilities. CH₃, CH₂ and CH carbon shifts change on average by +0.23, −0.09 and −0.18 ppm, respectively, due to a combination of bond shortening and changes in bond angles, the latter matching one explanation for the γ-gauche effect. In addition, there is a residue-specific component, arising from both local compression and conformational change. To assess the relative magnitudes of these effects, residue-specific shift changes for protein G were converted into structural restraints and used to calculate the change in structure with pressure, using a genetic algorithm to convert shift changes into dihedral angle restraints. The results demonstrate that residual ¹³Cα shifts are dominated by dihedral angle changes and can be used to calculate structural change, whereas ¹³Cβ shifts retain significant dependence on local compression, making them less useful as structural restraints.     

Determination of the glycosidic torsion angles in uniformly 13C-labeled nucleic acids from vicinal coupling constants 3J(C2)/4-H1' and 3J(C6)/8-H1'

A two-dimensional, quantitative J-correlation NMR experiment for precise measurements of the proton-carbon vicinal coupling constants ³J_C2/4–H1 and ³J_C6/8–H1 in uniformly ¹³C-labeled nucleic acids is presented. To reduce loss of signal due to ¹H -¹³C dipole-dipole relaxation, a multiple-quantum constant time experiment with appropriately incorporated band selective ¹H and ¹³C pulses was applied. The experiment is used to obtain the ³J_C2/4–H1 and ³J_C6/8–H1 coupling constants in a uniformly ¹³C, ¹⁵N-labeled [d(G₄T₄G₄)]₂ quadruplex. The measured values and glycosidic torsion angles in the G-quadruplex, obtained by restrained molecular dynamics with explicit solvent using the previously published restraints, along with selected data from the literature are used to check and modify existing parameters of the Karplus equations. The parameterizations obtained using glycosidic torsion angles derived from the original solution and recently determined X-ray structures are also compared.     

Dynamic stereochemistry of rutin (vitamin P) in solution: theoretical approaches and experimental validation

Rutin, vitamin P, was extracted from Salvia macrosiphon and identified by ¹H, ¹³C, ¹H-¹H COSY, HMQC, and HMBC spectroscopy. In parallel, density functional theory (DFT) using B₃LYP functional and split-valance 6-311G∗∗ basis set has been used to optimize the structures and conformers of rutin. Also experimental and theoretical methods have been used to correlate the dependencies of ¹J, ²J, and ³J involving ¹H and ¹³C on the C5″-C6″ (ω), C6″-O6″ (θ), and C1?-O6″ (φ) torsion angles in the glycosidic moiety. New Karplus equations are proposed to assist in the structural interpretation of these couplings. ³J_HH depends mainly on the C-C (ω) torsion angle, as expected, and ²J_HH values depend on both C-C (ω) and C-O (θ) torsions. ¹J_CH values within hydroxymethyl fragments were also examined and found to depend on r_CH, which is modulated by specific bond orientation and stereoelectronic factors. In all calculations solvent effects were considered using a polarized continuum model (PCM).     

A molecular dynamics simulation investigation of the relative stability of the cyclic peptide octreotide and its deprotonated and its (CF3)-Trp substituted analogs in different solvents

The cyclic octa-peptide octreotide and its derivatives are used as diagnostics and therapeutics in relation to particular types of cancers. This led to investigations of their conformational properties using spectroscopic, NMR and CD, methods. A CF₃-substituted derivative, that was designed to stabilize the dominant octreotide conformer responsible for receptor binding, turned out to have a lower affinity. The obtained spectroscopic data were interpreted as to show an increased flexibility of the CF₃ derivative compared to the unsubstituted octreotide, which could then explain the lower affinity.In this article, we use MD simulation without and with time-averaged NOE distance and time-averaged local-elevation ³J-coupling restraining representing experimental NMR data to determine the conformational properties of the different peptides in the different solvents for which experimental data are available, that are compatible with the NOE atom–atom distance bounds and the ³J_HNHα-couplings as derived from the NMR measurements. The conformational ensembles show that the CF₃ substitution in combination with the change of solvent from water to methanol leads to a decrease in flexibility and a shift in the populations of the dominant conformers that are compatible with the experimental data.     

Metropolis Monte Carlo calculations of DNA structure using internal coordinates and NMR distance restraints: An alternative method for generating a high-resolution solution structure

Summary A new method, a restrained Monte Carlo (rMC) calculation, is demonstrated for generating high-resolution structures of DNA oligonucleotides in solution from interproton distance restraints and bounds derived from complete relaxation matrix analysis of two-dimensional nuclear Overhauser effect (NOE) spectral peak intensities. As in the case of restrained molecular dynamics (rMD) refinement of structures, the experimental distance restraints and bounds are incorporated as a pseudo-energy term (or penalty function) into the mathematical expression for the molecular energy. However, the use of generalized helical parameters, rather than Cartesian coordinates, to define DNA conformation increases efficiency by decreasing by an order of magnitude the number of parameters needed to describe a conformation and by simplifying the potential energy profile. The Metropolis Monte Carlo method is employed to simulate an annealing process. The rMC method was applied to experimental 2D NOE data from the octamer duplex d(GTA-TAATG)·d(CATTATAC). Using starting structures from different locations in conformational space (e.g. A-DNA and B-DNA), the rMC calculations readily converged, with a root-mean-square deviation (RMSD) of <0.3 Å between structures generated using different protocols and starting structures. Theoretical 2D NOE peak intensities were calculated for the rMC-generated structures using the complete relaxation matrix program CORMA, enabling a comparison with experimental intensities via residual indices. Simulation of the vicinal proton coupling constants was carried out for the structures generated, enabling a comparison with the experimental deoxyribose ring coupling constants, which were not utilized in the structure determination in the case of the rMC simulations. Agreement with experimental 2D NOE and scalar coupling data was good in all cases. The rMC structures are quite similar to that refined by a traditional restrained MD approach (RMSD<0.5 Å) despite the different force fields used and despite the fact that MD refinement was conducted with additional restraints imposed on the endocyclic torsion angles of deoxyriboses. The computational time required for the rMC and rMD calculations is about the same. A comparison of structural parameters is made and some limitations of both methods are discussed with regard to the average nature of the experimental restraints used in the refinement.Abbreviations MC Monte Carlo - rMC restrained Monte Carlo - MD molecular dynamics - rMD restrained molecular dynamics - DG distance geometry - EM energy minimization - 2D NOE two-dimensional nuclear Overhauser effect - DQF-COSY double-quantum-filtered correlation spectroscopy - RMSD root-mean-square deviation To whom correspondence should be addressed.     

The J-coupling Restrained Molecular Mechanics (JrMM) Protocol - An Efficient Alternative for Deriving DNA Endocyclic Torsion Angle Constraints Part II: Experimental Application of the JrMM Protocol

Abstract

The J-coupling restrained molecular mechanics (JrMM) protocol, which correlates deoxyribose endocyclic torsion angles and vicinal proton-proton torsion angle φ_{1′ 2′} in Part I of this study, is demonstrated to be a viable alternative to efficiently derive the endocyclic torsion angle constraints for the determination of the solution structures of DNA molecules. Extensive testing demonstrating the validity of the JrMM-derived torsion angle constraints in the restrained molecular dynamics and energy minimization structural refinement processes is performed theoretically using an energy-minimized B-DNA model and experimentally using a DNA hexamer d(CGTACG)₂. The results show that only a 0.2 Å difference exists between the RMSD values of the refined structures using the ideal and the JrMM-derived endocyclic torsion angle constraints. The JrMM-derived torsion angles are also determined to be in good agreement with the torsion angles derived through the use of the vicinal J-derived torsion angles. These results show that through the use of reliably measured J_{1′ 2′} values and computer simulation method, the endocyclic torsion angle constraints can be derived reliably and efficiently. Thus the JrMM method serves as an alternative strategy to generate endocyclic torsion angle constraints for the determination of the solution structures of DNA molecules.     

<Emphasis Type="Italic">J</Emphasis>-Spectroscopy in the presence of residual dipolar couplings: determination of one-bond coupling constants and scalable resolution

The access to weak alignment media has fuelled the development of methods for efficiently and accurately measuring residual dipolar couplings (RDCs) in NMR-spectroscopy. Among the wealth of approaches for determining one-bond scalar and RDC constants only J-modulated and J-evolved techniques retain maximum resolution in the presence of differential relaxation. In this article, a number of J-evolved experiments are examined with respect to the achievable minimum linewidth in the J-dimension, using the peptide PA₄ and the 80-amino-acid-protein Saposin C as model systems. With the JE-N-BIRD ^d,X -HSQC experiment, the average full-width at half height could be reduced to approximately 5 Hz for the protein, which allows the additional resolution of otherwise unresolved peaks by the active (J+D)-coupling. Since RDCs generally can be scaled by the choice of alignment medium and alignment strength, the technique introduced here provides an effective resort in cases when chemical shift differences alone are insufficient for discriminating signals. In favorable cases even secondary structure elements can be distinguished.     

Asymmetric Karplus curves for the protein side-chain <Superscript>3</Superscript><Emphasis Type="Italic">J</Emphasis> couplings

The standard Karplus equation for calculating ³ J coupling constants from any given dihedral angle requires three empirical coefficients be determined that relate to the magnitudes of three modes of the angle dependency of ³ J. Considering cosine modes only (bimodal, unimodal and baseline component), Karplus curves are generally symmetric with respect to the sign of the angle argument. Typically, their primary and secondary maxima differ in amplitude, whereas the two minima are of equal depth. However, chiral molecular topologies, such as those surrounding the main-chain and side-chain torsions in amino-acid residues, preclude, as regards substituent positioning, exact mirror-image conformations from being formed—for any given torsion-angle value. It is therefore unlikely that ³ J couplings assume identical values for the corresponding positive and negative dihedral angles. This suggests that a better empirical fit of the torsion-angle dependency of ³ J could be obtained when removing the constraint of symmetrically identical coupling constants. A sine term added to the Karplus equation allows independent modelling of both curve minima typically located near dihedral-angle values of +90° and −90°. Revisiting an extensive ³ J coupling dataset previously recorded to determine the side-chain torsions χ₁ in the protein flavodoxin, the asymmetric Karplus model accomplishes a more accurate fit to the experimental data. Asymmetries revealed in the angle dependencies exceed the experimental precision in determining ³ J. Accounting for these effects helps improve molecular models. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Validation of the GROMOS force-field parameter set 45A3 against nuclear magnetic resonance data of hen egg lysozyme

The quality of molecular dynamics (MD) simulations of proteins depends critically on the biomolecular force field that is used. Such force fields are defined by force-field parameter sets, which are generally determined and improved through calibration of properties of small molecules against experimental or theoretical data. By application to large molecules such as proteins, a new force-field parameter set can be validated. We report two 3.5 ns molecular dynamics simulations of hen egg white lysozyme in water applying the widely used GROMOS force-field parameter set 43A1 and a new set 45A3. The two MD ensembles are evaluated against NMR spectroscopic data NOE atom–atom distance bounds, ³J_NH and ³J coupling constants, and ¹5N relaxation data. It is shown that the two sets reproduce structural properties about equally well. The 45A3 ensemble fulfills the atom–atom distance bounds derived from NMR spectroscopy slightly less well than the 43A1 ensemble, with most of the NOE distance violations in both ensembles involving residues located in loops or flexible regions of the protein. Convergence patterns are very similar in both simulations atom-positional root-mean-square differences (RMSD) with respect to the X-ray and NMR model structures and NOE inter-proton distances converge within 1.0–1.5 ns while backbone ³J_HN-coupling constants and ¹H– ¹5N order parameters take slightly longer, 1.0–2.0 ns. As expected, side-chain ³J-coupling constants and ¹H– ¹5N order parameters do not reach full convergence for all residues in the time period simulated. This is particularly noticeable for side chains which display rare structural transitions. When comparing each simulation trajectory with an older and a newer set of experimental NOE data on lysozyme, it is found that the newer, larger, set of experimental data agrees as well with each of the simulations. In other words, the experimental data converged towards the theoretical result.     

Precise vicinal coupling constants3JHNα in proteins from nonlinear fits of J-modulated [15N,1H]-COSY experiments

Summary Improved experimental schemes for the recently introduced J-modulated [¹⁵N,¹H]-correlation experiment for measurements of the homonuclear amide proton-C proton vicinal coupling constants.³J_HN, in uniformly¹⁵N-labeled proteins are described, and a nonlinear fit procedure is presented for quantitative evaluation of³J_HN. The method was first tested with the N-terminal DNA-binding domain of the 434 repressor (M=7.3 kDa), where at 13 C precise values of³J_HN in the range 2.0–9.5 Hz were obtained for all residues with resolved¹⁵N-¹H cross peaks. It was then applied to theAntennapedia homeodomain complexed to a synthetic 14-base pair DNA fragment (molecular weight of the complex 18 kDa). The³J_HN values measured were found to be in excellent agreement with those predicted from the secondary structure of this protein in the complex.Abbreviations and symbols NOE nuclear Overhauser effect - COSY two-dimensional correlated spectroscopy - ³J_HN or J homonuclear vicinal amide proton-C proton coupling constant - 434 repressor(1–69) N-terminal DNA-binding domain of the 434 repressor comprising 69 residues     

The three-dimensional structure of acyl-coenzyme A binding protein from bovine liver: Structural refinement using heteronuclear multidimensional NMR spectroscopy

Summary The 3D structure of bovine recombinant acyl-coenzyme A binding protein has been determined using multidimensional heteronuclear magnetic resonance spectroscopy in a study that combines investigations of ¹⁵N-labeled and unlabeled protein. The present structure determination is a refinement of the structure previously determined (Andersen, K.V. and Poulsen, F.M. (1992) J. Mol. Biol., 226, 1131–1141). It is based on 1096 distance restraints and 124 dihedral angle restraints of which 69 are for -angles and 8 for chiral centers and 47 for prochiral centers. The new experimental input for the structure determination has provided an increase of 263 distance restraints, 5 -angle restraints, and 32 -angle restraints in 2 chiral centers, and 31 prochiral centers restraining an additional 23 ¹, 8 ², and 1 ³ angles. The increase of 300 distance and dihedral angle restraints representing an additional 30% of input parameters for the structure determination has been shown to be in agreement with the first structure. A set of 29 structures has been calculated and each of the structures has been compared to a mean structure to give an atomic root mean square deviation of 0.44±0.12 (1 is 0.1 nm) for the backbone atoms C, C, and N in the four -helices A1, residues 4–15, A2, residues 21–36, A3, residues 51–62 and A4, residues 65–84. The loop-region of residues Gly⁴⁵-Lys⁵⁰ could not be defined by the restraints obtained by NMR.The program PRONTO has been used for the spectrum analysis, assignment of the individual nuclear Overhauser effects, the integration of the cross peaks, and the measurement of the coupling constants. The programs DIANA, X-PLOR and INSIGHT have been used in the structure calculations and evaluations.     

Conformational dynamics in mixed α/β-oligonucleotides containing polarity reversals: A molecular dynamics study using time-averaged restraints*

Nucleic acid duplexes featuring a single alpha-anomeric thymidine inserted into each DNA strand via 3′-3′ and 5′-5′ phosphodiester linkages exhibit local conformational dynamics that are not adequately depicted by conventional restrained molecular dynamics (rMD) methods. We have used molecular dynamics with time-averaged NMR restraints (MDtar) to explore its applicability to describing the conformational dynamics of two α-containing duplexes – d(GCGAAT-3′-3′-αT-5′-5′-CGC)₂ and d(ATGG-3′-3′-αT-5′-5′-GCTC)?r(gagcaccau). In contrast to rMD, enforcing NOE-based distance restraints over a period of time in MDtar rather than instantaneously results in better agreement with the experimental NOE and J-data. This conclusion is based on the dramatic decreases in average distance and coupling constant violations (Δd _av, J _rms, and ΔJ _av) and improvements in sixth-root R-factors (R ^x). In both duplexes, the deoxyribose ring puckering behavior predicted independently by pseudorotation analysis is portrayed remarkably well using this approach compared to rMD. This indicates that the local dynamic behavior is encoded within the NOE data, although this is not obvious from the local R ^x values. In both systems, the backbone torsion angles comprising the 3′-3′ linkage as well as the (high S-) sugars of the α-nucleotide and preceding residue (α?1) are relatively static, while the conformations of the 5′-5′ linkage and the sugar in the neighboring β-nucleotide (α+1) show enhanced flexibility. To reduce the large ensembles generated by MDtar to more manageable clusters we utilized the PDQPRO program. The resulting PDQPRO clusters (in both cases, 13 structures and associated probabilities extracted from a pool of 300 structures) adequately represent the structural and dynamic characteristics predicted by the experimental data.