Accuracy and precision of NMR relaxation experiments and MD simulations for characterizing protein dynamics

Model-free parameters obtained from nuclear magnetic resonance (NMR) relaxation experiments and molecular dynamics (MD) simulations commonly are used to describe the intramolecular dynamical properties of proteins. To assess the relative accuracy and precision of experimental and simulated model-free parameters, three independent data sets derived from backbone ¹⁵N NMR relaxation experiments and two independent data sets derived from MD simulations of Escherichia coli ribonuclease HI are compared. The widths of the distributions of the differences between the order parameters for pairs of NMR data sets are congruent with the uncertainties derived from statistical analyses of individual data sets; thus, current protocols for analyzing NMR data encapsulate random uncertainties appropriately. Large differences in order parameters for certain residues are attributed to systematic differences between samples for intralaboratory comparisons and unknown, possibly magnetic field-dependent, experimental effects for interlaboratory comparisons. The widths of distributions of the differences between the order parameters for two NMR sets are similar to widths of distributions for an NMR and an MD set or for two MD sets. The linear correlations between the order parameters for an MD set and an NMR set are within the range of correlations observed between pairs of NMR sets. These comparisons suggest that the NMR and MD generalized order parameters for the backbone amide N—H bond vectors are of comparable accuracy for residues exhibiting motions on a fast time scale (<100 ps). Large discrepancies between NMR and MD order parameters for certain residues are attributed to the occurrence of “rare” motional events over the simulation trajectories, the disruption of an element of secondary structure in one of the simulations, and lack of consensus among the experimental data sets. Consequently, (easily detectable) severe distortions of local protein structure and infrequent motional events in MD simulations appear to be the most serious artifacts affecting the accuracy and precision, respectively, of MD order parameters relative to NMR values. In addition, MD order parameters for motions on a fast (<100 ps) timescale are more precisely determined than their NMR counterparts, thereby permitting more detailed dynamic characterization of biologically important residues by MD simulation than is sometimes possible by experimental methods. Proteins 28:481–493, 1997. © 1997 Wiley-Liss, Inc.     

NMR analysis of carbohydrates with model-free spectral densities: the dispersion range revisited

Over the past decade molecular mechanics and molecular dynamics studies have demonstrated considerable flexibility for carbohydrates. In order to interpret the corresponding NMR parameters, which correspond to a time-averaged or 'virtual' conformer, it is necessary to simulate the experimental data using the averaged geometrical representation obtained with molecular modelling methods. This structural information can be transformed into theoretical NMR data using empirical Karplus-type equations for the scalar coupling constants and the appropriate formalism for the relaxation parameters. In the case of relaxation data, the 'model-free' spectral densities have been widely used in order to account for the internal motions in sugars. Several studies have been conducted with truncated model-free spectral densities based on the assumption that internal motion is very fast with respect to overall tumbling. In this report we present experimental and theoretical evidence that suggests that this approach is not justified. Indeed, recent results show that even in the case of moderate-sized carbohydrates internal motions are occurring on the same timescale as molecular reorientation. Simulations of relaxation parameters (NOESY volumes, proton cross-relaxation rates, carbon T1 and nOe values) in the dispersion range (0.1<Tc<5 ns) show that rates of internal motion can be fairly precisely defined with respect to overall tumbling. Experimental data for a variety of oligosaccharides clearly indicate similar timescales for internal and overall motion. This revised version was published online in August 2006 with corrections to the Cover Date.     

Model-free model elimination: A new step in the model-free dynamic analysis of NMR relaxation data

Model-free analysis is a technique commonly used within the field of NMR spectroscopy to extract atomic resolution, interpretable dynamic information on multiple timescales from the R ₁, R ₂, and steady state NOE. Model-free approaches employ two disparate areas of data analysis, the discipline of mathematical optimisation, specifically the minimisation of a χ² function, and the statistical field of model selection. By searching through a large number of model-free minimisations, which were setup using synthetic relaxation data whereby the true underlying dynamics is known, certain model-free models have been identified to, at times, fail. This has been characterised as either the internal correlation times, τ _e , τ _f , or τ _s , or the global correlation time parameter, local τ _m , heading towards infinity, the result being that the final parameter values are far from the true values. In a number of cases the minimised χ² value of the failed model is significantly lower than that of all other models and, hence, will be the model which is chosen by model selection techniques. If these models are not removed prior to model selection the final model-free results could be far from the truth. By implementing a series of empirical rules involving inequalities these models can be specifically isolated and removed. Model-free analysis should therefore consist of three distinct steps: model-free minimisation, model-free model elimination, and finally model-free model selection. Failure has also been identified to affect the individual Monte Carlo simulations used within error analysis. Each simulation involves an independent randomised relaxation data set and model-free minimisation, thus simulations suffer from exactly the same types of failure as model-free models. Therefore, to prevent these outliers from causing a significant overestimation of the errors the failed Monte Carlo simulations need to be culled prior to calculating the parameter standard deviations.     

A suite of Mathematica notebooks for the analysis of protein main chain 15N NMR relaxation data

A suite of Mathematica notebooks has been designed to ease the analysis of protein main chain ¹⁵N NMR relaxation data collected at a single magnetic field strength. Individual notebooks were developed to perform the following tasks: nonlinear fitting of ¹⁵N-T ₁ and -T ₂ relaxation decays to a two parameter exponential decay, calculation of the principal components of the inertia tensor from protein structural coordinates, nonlinear optimization of the principal components and orientation of the axially symmetric rotational diffusion tensor, model-free analysis of ¹⁵N-T ₁, -T ₂, and {¹H}–¹⁵N NOE data, and reduced spectral density analysis of the relaxation data. The principle features of the notebooks include use of a minimal number of input files, integrated notebook data management, ease of use, cross-platform compatibility, automatic visualization of results and generation of high-quality graphics, and output of analyses in text format.L. Spyracopoulos is an AHFMR Medical Research Senior Scholar     

Temperature-dependent dynamics of the villin headpiece helical subdomain,an unusually small thermostable protein

(15)N spin relaxation experiments were used to measure the temperature-dependence of protein backbone conformational fluctuations in the thermostable helical subdomain, HP36, of the F-actin-binding headpiece domain of chicken villin. HP36 is the smallest domain of a naturally occurring protein that folds cooperatively to a compact native state. Spin-lattice, spin-spin, and heteronuclear nuclear Overhauser effect relaxation data for backbone amide (15)N spins were collected at five temperatures in the range of 275-305 K. The data were analyzed using a model-free formalism to determine generalized order parameters, S, that describe the distribution of N-H bond vector orientations in a molecular reference frame. A novel parameter, Lambda=dln(1-S)/dln T is introduced to characterize the temperature-dependence of S. An average value of Lambda=4.5 is obtained for residues in helical conformations in HP36. This value of Lambda is not reproduced by model potential energy functions commonly used to parameterize S. The maximum entropy principle was used to derive a new model potential function that reproduces both S and Lambda. Contributions to the entropy, S(r), and heat capacity, C(r)(p), from reorientational conformational fluctuations were analyzed using this potential energy function. Values of S(r) show a qualitative dependence on S similar to that obtained for the diffusion-in-a-cone model; however, quantitative differences of up to 0.5k, in which k is the Boltzmann constant, are observed. Values of C(r)(p) approach zero for small values of S and approach k for large values of S; the largest values of C(r)(p) are predicted to occur for intermediate values of S. The results suggest that backbone dynamics, as probed by relaxation measurements, make very little contribution to the heat capacity difference between folded and unfolded states for HP36.     

Internal mobility of the ologonucleotide duplexes d(TCGCG)2 and d(CGCGCG)2 in aqueous solution from molecular dynamics simulations

Summary In this paper we present longitudinal relaxation times, order parameters and effective correlation times for the base and sugar carbons in both strands of the oligonucleotide duplexes d(TCGCG)₂ and d(CGCGCG)₂, as calculated from 400 ps molecular dynamics trajectories in aqueous solution. The model-free approach (Lipari and Szabo, 1982) was used to determine the amplitudes and time scales of the internal motion. Comparisons were made with NMR relaxation measurements (Borer et al., 1994). The order parameters could acceptably be reproduced, and the effective correlation times were found to be lower than the experimental estimates. Reasonable T₁ relaxation times were obtained in comparison with experiment for the nonterminal nucleosides. The T₁ relaxation times were found to depend mainly on the order parameters and overall rotational correlation time.Abbreviations MD molecular dynamics - CSA chemical shift anisotropy To whom correspondence should be addressed.     

Generalized ordering parameter S2 for N-H peptide bonding as measure of the conformational flexibility of proteins: comparison of algorithms of S2 calculation from molecular dynamics simulation data

NMR spectroscopy in combination with molecular dynamics (MD) simulation technique is a powerful tool for investigation of biomolecule conformations. In the present study we compare the two algorithms of calculation of the generalized order parameter S2 for the peptide N-H bond from MD simulation data. The program based on this algorithm has been written and the effect of an adjustible parameter on results of calculation was studied. HIV-1 protease MD simulation was performed during 7.36 ns using GROMACS 3.1.4. software package. The calculated order parameter values are in good agreement with those obtained by other authors using NMR.     

Backbone dynamics of the regulatory domain of calcium vector protein, studied by 15N relaxation at four fields, reveals unique mobility characteristics of the intermotif linker

CaVP is a calcium-binding protein from amphioxus. It has a modular composition with two domains, but only the two EF-hand motifs localized in the C-terminal domain are functional. We recently determined the solution structure of this regulatory half (C-CaVP) in the Ca(2+)-saturated form and characterized the stepwise ion binding. This paper reports the (15)N nuclear relaxation rates of the Ca(2+)-saturated C-CaVP, measured at four different NMR fields (9.39, 11.74, 14.1, and 18.7 T), which were used to map the spectral density function for the majority of the amide H(N)-N vectors. Fitting the spectral density values at eight frequencies by a model-free approach, we obtained the microdynamic parameters characterizing the global and internal movements of the polypeptide backbone. The two EF-hand motifs, including the ion binding loops, behave like compact structural units with restricted mobility as reflected in the quite uniform order parameter and short internal correlation time (< 20 nsec). Comparative analysis of the two Ca(2+) binding sites shows that site III, having a larger affinity for the metal ion, is generally more rigid, and the amide vector in the second residue of each loop is significantly less restricted. The linker fragment is animated simultaneously by a larger amplitude fast motion and a slow conformational exchange on a microsecond to millisecond time scale. The backbone dynamics of C-CaVP characterized here is discussed in relation with other well-characterized Ca(2+)-binding proteins. Supplemental material: See www.proteinscience.org     

Propagation of experimental uncertainties using the Lipari-Szabo model-free analysis of protein dynamics

In this paper we make use of the graphical procedure previously described [Jin, D. et al. (1997) J. Am. Chem. Soc., 119, 6923–6924] to analyze NMR relaxation data using the Lipari-Szabo model-free formalism. The graphical approach is advantageous in that it allows the direct visualization of the experimental uncertainties in the motional parameter space. Some general rules describing the relationship between the precision of the relaxation measurements and the precision of the model-free parameters and how this relationship changes with the overall tumbling time (m) are summarized. The effect of the precision in the relaxation measurements on the detection of internal motions not close to the extreme narrowing limit is analyzed. We also show that multiple timescale internal motions may be obscured by experimental uncertainty, and that the collection of relaxation data at very high field strength can improve the ability to detect such deviations from the simple Lipari-Szabo model.     

All-atom molecular dynamics simulations using orientational constraints from anisotropic NMR samples

Orientational constraints obtained from solid state NMR experiments on anisotropic samples are used here in molecular dynamics (MD) simulations for determining the structure and dynamics of several different membrane-bound molecules. The new MD technique is based on the inclusion of orientation dependent pseudo-forces in the COSMOS-NMR force field. These forces drive molecular rotations and re-orientations in the simulation, such that the motional time-averages of the tensorial NMR properties approach the experimentally measured parameters. The orientational-constraint-driven MD simulations are universally applicable to all NMR interaction tensors, such as chemical shifts, dipolar couplings and quadrupolar interactions. The strategy does not depend on the initial choice of coordinates, and is in principle suitable for any flexible molecule. To test the method on three systems of increasing complexity, we used as constraints some deuterium quadrupolar couplings from the literature on pyrene, cholesterol and an antimicrobial peptide embedded in oriented lipid bilayers. The MD simulations were able to reproduce the NMR parameters within experimental error. The alignment of the three membrane-bound molecules and some aspects of their conformation were thus derived from the NMR data, in good agreement with previous analyses. Furthermore, the new approach yielded for the first time the distribution of segmental orientations with respect to the membrane and the order parameter tensors of all three systems.     

Residue Specific Ribose and Nucleobase Dynamics of the cUUCGg RNA Tetraloop Motif by MNMR 13C Relaxation

The dynamics of the nucleobase and the ribose moieties in a 14-nt RNA cUUCGg hairpin-loop uniformly labeled with ¹³C and ¹⁵N were studied by ¹³C spin relaxation experiments. R₁, R_1ρ and the ¹³C-{¹H} steady-state NOE of C₆ and C_1′ in pyrimidine and C₈ and C_1′ in purine residues were obtained at 298 K. The relaxation data were analyzed by the model-free formalism to yield dynamic information on timescales of pico-, nano- and milli-seconds. An axially symmetric diffusion tensor with an overall rotational correlation time τ_c of 2.31±0.13 ns and an axial ratio of 1.35±0.02 were determined. Both findings are in agreement with hydrodynamic calculations. For the nucleobase carbons, the validity of different reported ¹³C chemical shift anisotropy values (Stueber, D. and Grant, D. M., 2002 J. Am. Chem. Soc. 124, 10539–10551; Fiala et al., 2000 J. Biomol. NMR 16, 291–302; Sitkoff, D. and Case, D. A., 1998 Prog. NMR Spectroscopy 32, 165–190) is discussed. The resulting dynamics are in agreement with the structural features of the cUUCGg motif in that all residues are mostly rigid (0.82 < S² < 0.96) in both the nucleobase and the ribose moiety except for the nucleobase of U7, which is protruding into solution (S² = 0.76). In general, ribose mobility follows nucleobase dynamics, but is less pronounced. Nucleobase dynamics resulting from the analysis of ¹³C relaxation rates were found to be in agreement with ¹⁵N relaxation data derived dynamic information (Akke et al., 1997 RNA 3, 702–709). Electronic supplementary material Electronic supplementary material is available for this article at and accessible for authorised users.     

Prediction of methyl-side Chain Dynamics in Proteins

A simple analytical model is presented for the prediction of methyl-side chain dynamics in comparison with S(2) order parameters obtained by NMR relaxation spectroscopy. The model, which is an extension of the local contact model for backbone order parameter prediction, uses a static 3D protein structure as input. It expresses the methyl-group S(2) order parameters as a function of local contacts of the methyl carbon with respect to the neighboring atoms in combination with the number of consecutive mobile dihedral angles between the methyl group and the protein backbone. For six out of seven proteins the prediction results are good when compared with experimentally determined methyl-group S(2) values with an average correlation coefficient r = 0.65+/-0.14. For the unusually rigid cytochrome c(2) no significant correlation between prediction and experiment is found. The presented model provides independent support for the reliability of current side-chain relaxation methods along with their interpretation by the model-free formalism.     

Relating side-chain mobility in proteins to rotameric transitions: Insights from molecular dynamics simulations and NMR

The dynamic aspect of proteins is fundamental to understanding protein stability and function. One of the goals of NMR studies of side-chain dynamics in proteins is to relate spin relaxation rates to discrete conformational states and the timescales of interconversion between those states. Reported here is a physical analysis of side-chain dynamics that occur on a timescale commensurate with monitoring by ²H spin relaxation within methyl groups. Motivated by observations made from tens-of-nanoseconds long MD simulations on the small protein eglin c in explicit solvent, we propose a simple molecular mechanics-based model for the motions of side-chain methyl groups. By using a Boltzmann distribution within rotamers, and by considering the transitions between different rotamer states, the model semi-quantitatively correlates the population of rotamer states with ‘model-free’ order parameters typically fitted from NMR relaxation experiments. Two easy-to-use, analytical expressions are given for converting S²_axis’ values (order parameter for C–CH₃ bond) into side-chain rotamer populations. These predict that S²_axis’ values below 0.8 result from population of more than one rotameric state. The relations are shown to predict rotameric sampling with reasonable accuracy on the ps–ns timescale for eglin c and are validated for longer timescales on ubiquitin, for which side-chain residual dipolar coupling (RDC) data have been collected.     

Assigning stereodiversity of the 27-Me group of furostane-type steroidal saponins via NMR chemical shifts

Applicability of (13)C and (1)H NMR chemical shifts for the assignment of the 25R/25S configuration of the 27-methyl group in the case of furostane-type steroidal saponins has been investigated. A comparative study of (13)C NMR data suggest that chemical shift values for C-20, C-21, C-22, C-23, C-24, C-25, C-26 and C-27 resonances were not much influenced by R/S configuration of the 27-Me group, thus reflecting limited application of (13)C NMR chemical shifts for such stereochemical determinations. In contrast, (1)H NMR chemical shifts (delta(a), delta(b)) for geminal protons of glycosyloxy methylene (H(2)-26) exhibit pronounced dependence and the difference (Delta(ab)=delta(a)-delta(b)) among their chemical shifts [Delta(ab)= or <0.48 for 25R; Delta(ab)= or >0.57 for 25S] seems to be of general applicability for ascertaining 25R/25S orientation of the 27-methyl group of furostane-type steroidal saponins.     

Gated electron transfers and electron pathways in azurin: a NMR dynamic study at multiple fields and temperatures

Dynamic properties of electron transfer pathways in a small blue copper cupredoxin are explored using an extensive 15N NMR relaxation study of reduced Pseudomonas aeruginosa azurin at four magnetic fields (500-900 MHz) and at two temperatures chosen well below the melting point of the protein. Following a careful model-free analysis, several protein regions with different dynamic regimes are identified. Nanosecond time-scale mobility characterizes various residues of the hydrophobic surface patch believed to mark the natural entry point for electrons, notably the surface-exposed copper-ligand His117. These findings are consistent with a gated electron transfer process according to the "dynamic docking" model. Residues 47-49 along intramolecular pathways of electrons show rigidity that is remarkably conserved when increasing the temperature. Three different conformational exchange processes were observed in the millisecond range, one near the only disulfide bridge in the molecule and two near the copper ion. The latter two processes are consistent with previous data such as crystal structures at various pH values and NMR relaxation dispersion experiments; they may indicate an additional gated electron transfer mechanism at slower time-scales.     

Unusual naphthoquinones, catechin and triterpene from Byrsonima microphylla

The new triterpene Delta1-lupenone (1), together with lupeol, beta-amyrin and betulin were isolated from the wood of Byrsonima microphylla (Malpighiaceae). The new compounds 3-hydroxy-2-methoxy-8,8,10-trimethyl-8H-antracen-1,4,5-trione (2), 3,7-dihydroxy-2-methoxy-8,8,10-trimethyl-7,8-dihydro-6H-antracen-1,4,5-trione (3), (2S*,10aR*)-2,8-dihydroxy-6-methoxy-1,1,7-trimethyl-2,3,10, 10a-tetrahydro-1H-fenantren-9-one (4) and (2S,3S)-3'-hydroxy-4',5,7-trimethoxy-flavan-3-ol (5) were also isolated through monitored TLC using the antioxidant beta-carotene reagent. The antioxidant potential of the compounds 2-5 was measured and none of them showed activity. The structures of these compounds were elucidated by chemical and spectroscopic analysis based on NMR techniques (1H, 13C NMR, COSY, nOe difference, HMQC and HMBC), UV and MS.     

Molecular dynamics simulation of hen egg white lysozyme: a test of the GROMOS96 force field against nuclear magnetic resonance data

Biomolecular force fields for use in molecular dynamics (MD) simulations of proteins, DNA, or membranes are generally parametrized against ab initio quantum-chemical and experimental data for small molecules. The application of a force field in a simulation of a biomolecular system, such as a protein in solution, may then serve as a test of the quality and transferability of the force field. Here, we compare various properties obtained from two MD simulations of the protein hen egg white lysozyme (HEWL) in aqueous solution using the latest version, GROMOS96, of the GROMOS force field and an earlier version, GROMOS87+, with data derived from nuclear magnetic resonance (NMR) experiments: NOE atom-atom distance bounds, (3)J(HNalpha)-coupling constants, and backbone and side-chain order parameters. The convergence of these quantities over a 2-ns period is considered, and converged values are compared to experimental ones. The GROMOS96 simulation shows better agreement with the NMR data and also with the X-ray crystal structure of HEWL than the GROMOS87+ simulation, which was based on an earlier version of the GROMOS force field.     

Evidence of two-step deprotonation of D-mannitol in aqueous solution

Deprotonation of D-mannitol was studied in aqueous basic solutions by means of potentiometry and (13)C NMR spectroscopy. Two-step dissociation in the pH range from 12 to 13.8 was shown, and successive dissociation constants K(a1) and K(a2) were determined. In a solution with ionic strength I = 1.0 M (NaOH + NaNO(3)) pK(a1) = 13.1 +/- 0.1 and pK(a2) = 13.8 +/- 0.2. With increasing ionic strength from 0.75 to 3.0 M, both pK(a1) and pK(a2) values decrease. Deprotonation-induced chemical shifts in pH-variable (13)C NMR spectra show that the OH-groups next to internal carbon atoms C-3 and C-4 dissociate to a greater extent compared to OH-groups next to external carbon atoms C-1 and C-6.