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.     

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.     

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.     

Conformational sampling by NMR solution structures calculated with the program DIANA evaluated by comparison with long-time molecular dynamics calculations in explicit water

The NMR solution structure of bovine pancreatic trypsin inhibitor (BPTI) obtained by distance geometry calculations with the program DIANA is compared with groups of conformers generated by molecular dynamics (MD) simulations in explicit water at ambient temperature and pressure. The MD simulations started from a single conformer and were free or restrained either by the experimental NOE distance restraints or by time-averaged restraints; the groups of conformers were collected either in 10 ps intervals during 200 ps periods of simulation, or in 50 ps intervals during a 1 ns period of simulation. Overall, these comparisons show that the standard protein structure determination protocol with the program DIANA provides a picture of the protein structure that is in agreement with MD simulations using “realistic” potential functions over a nanosecond timescale. For well-constrained molecular regions there is a trend in the free MD simulation of duration 1 ns that the sampling of the conformation space is slightly increased relative to the DIANA calculations. In contrast, for surface-exposed side-chains that are less extensively constrained by the NMR data, the DIANA conformers tend to sample larger regions of conformational space than conformers selected from any of the MD trajectories. Additional insights into the behavior of surface side-chains come from comparison of the MD runs of 200 ps or 1 ns duration. In this time range the sampling of conformation space by the protein surface depends strongly on the length of the simulation, which indicates that significant side-chain transitions occur on the nanosecond timescale and that much longer simulations will be needed to obtain statistically significant data on side-chain dynamics.     

Molecular dynamics simulations of Alzheimer's beta-amyloid protofilaments

Filamentous amyloid aggregates are central to the pathology of Alzheimer's disease. We use all-atom molecular dynamics (MD) simulations with explicit solvent and multiple force fields to probe the structural stability and the conformational dynamics of several models of Alzheimer's beta-amyloid fibril structures, for both wild-type and mutated amino acid sequences. The structural models are based on recent solid state NMR data. In these models, the peptides form in-register parallel beta-sheets along the fibril axis, with dimers of two U-shaped peptides located in layers normal to the fibril axis. Four different topologies are explored for stacking the beta-strand regions against each other to form a hydrophobic core. Our MD results suggest that all four NMR-based models are structurally stable, and we find good agreement with dihedral angles estimated from solid-state NMR experiments. Asp23 and Lys28 form buried salt-bridges, resulting in an alternating arrangement of the negatively and positively charged residues along the fibril axis that is reminiscent of a one-dimensional ionic crystal. Interior water molecules are solvating the buried salt-bridges. Based on data from NMR measurements and MD simulations of short amyloid fibrils, we constructed structural models of long fibrils. Calculated X-ray fiber diffraction patterns show the characteristics of packed beta-sheets seen in experiments, and suggest new experiments that could discriminate between various fibril topologies.     

Conformational properties of a cyclic peptide bradykinin B2 receptor antagonist using experimental and theoretical methods.

The solution conformation of the cyclic peptide J324 (cyclo0,6-[Lys0,Glu6,D-Phe7]BK), an antagonist targeted at the bradykinin (BK) B2 receptor, has been investigated using experimental and theoretical methods. In order to gain insight into the structural requirements essential for BK antagonism, we carried out molecular dynamics (MD) simulations using simulated annealing as the sampling protocol. Following a free MD simulation we performed simulations using nuclear Overhauser enhancement (NOE) distance constraints determined by NMR experiments. The low-energy structures obtained were compared with each other, grouped into families and analyzed with respect to the presence of secondary structural elements in their backbone. We also introduced new ways of plotting structural data for a more comprehensive analysis of large conformational sets. Finally, the relationship between characteristic backbone conformations and the spatial arrangement of specific pharmacophore centers was investigated.     

Structure and internal dynamics of the bovine pancreatic trypsin inhibitor in aqueous solution from long-time molecular dynamics simulations

Structural and dynamic properties of bovine pancreatic trypsin inhibitor (BPTI) in aqueous solution are investigated using two molecular dynamics (MD) simulations: one of 1.4 ns length and one of 0.8 ns length in which atom-atom distance bounds derived from NMR spectroscopy are included in the potential energy function to make the trajectory satisfy these experimental data more closely. The simulated properties of BPTI are compared with crystal and solution structures of BPTI, and found to be in agreement with the available experimental data. The best agreement with experiment was obtained when atom-atom distance restraints were applied in a time-averaged manner in the simulation. The polypeptide segments found to be most flexible in the MD simulations coincide closely with those showing differences between the crystal and solution structures of BPTI. © 1995 Wiley-Liss, Inc.     

The conformational properties of methyl alpha-(2,8)-di/trisialosides and their N-acyl analogues: implications for anti-Neisseria meningitidis B vaccine design

The conformational properties of di- and trisaccharide fragments of the polysialic acid O-antigen capsular polysaccharide (CPS) of Neisseria meningitidis B (NmB) have been investigated by a combination of solution phase NMR spectroscopy and explicit-solvent molecular dynamics (MD) simulations. Simulations employing 100 ns of conventional MD, as well as 160 ns of replica exchange MD (REMD), with the GLYCAM06 force field were shown to be in agreement with experimental NMR scalar J-coupling and NOE values. The presence of conformational families has been determined by monitoring interglycosidic torsion angles, by comparing structural superimpositions, as well as via a Bayesian statistical analysis of the torsional data. Attempts to augment the immunogenicity of NmB CPS often involve chemical modifications of the N-acetyl moiety. Here the effects of these chemical group modifications on the conformational properties of the trisialoside have been probed via REMD simulations of the N-glycolyl, N-propionyl, N-propyl and N-butanoyl analogues. Although there were conformational families unique to each non-native analogue, the chemical modifications resulted in largely equivalent overall conformational phase-spaces compared to the native trisialoside. On the basis of the conformational distributions, these shared conformational properties suggest that a recurrent global conformational epitope may be present in both the native and chemically modified CPS fragments. Explanations are therefore provided for monoclonal antibody cross-reactivity, in terms of recognition of a shared global CPS conformation, as well as for lack of cross-reactivity, in terms of fine structural differences associated with the N-acyl groups, which may be dominant in highly matured antibody responses.     

Backbone conformational flexibility of the lipid modified membrane anchor of the human N-Ras protein investigated by solid-state NMR and molecular dynamics simulation

The lipid modified human N-Ras protein, implicated in human cancer development, is of particular interest due to its membrane anchor that determines the activity and subcellular location of the protein. Previous solid-state NMR investigations indicated that this membrane anchor is highly dynamic, which may be indicative of backbone conformational flexibility. This article aims to address if a dynamic exchange between three structural models exist that had been determined previously. We applied a combination of solid-state nuclear magnetic resonance (NMR) methods and replica exchange molecular dynamics (MD) simulations using a Ras peptide that represents the terminal seven amino acids of the human N-Ras protein. Analysis of correlations between the conformations of individual amino acids revealed that Cys 181 and Met 182 undergo collective conformational exchange. Two major structures constituting about 60% of all conformations could be identified. The two conformations found in the simulation are in rapid exchange, which gives rise to low backbone order parameters and nuclear spin relaxation as measured by experimental NMR methods. These parameters were also determined from two 300 ns conventional MD simulations, providing very good agreement with the experimental data.     

Assessment of the molecular dynamics structure of DNA in solution based on calculated and observed NMR NOESY volumes and dihedral angles from scalar coupling constants

To assess the accuracy of the molecular dynamics (MD) models of nucleic acids, a detailed comparison between MD-calculated and NMR-observed indices of the dynamical structure of DNA in solution has been carried out. The specific focus of our comparison is the oligonucleotide duplex, d(CGCGAATTCGCG)(2), for which considerable structural data have been obtained from crystallography and NMR spectroscopy. An MD model for the structure of d(CGCGAATTCGCG)(2) in solution, based on the AMBER force field, has been extended with a 14 ns trajectory. New NMR data for this sequence have been obtained in order to allow a detailed and critical comparison between the calculated and observed parameters. Observable two-dimensional (2D) nuclear Overhauser effect spectroscopy (NOESY) volumes and scalar coupling constants were back-calculated from the MD trajectory and compared with the corresponding NMR data. The comparison of these results indicate that the MD model is in generally good agreement with the NMR data, and shows closer accord with experiment than back-calculations based on the crystal structure of d(CGCGAATTCGCG)(2) or the canonical A or B forms of the sequence. The NMR parameters are not particularly sensitive to the known deficiency in the AMBER MD model, which is a tendency toward undertwisting of the double helix when the parm.94 force field is used. The MD results are also compared with a new determination of the solution structure of d(CGCGAATTCGCG)(2) using NMR dipolar coupling data.     

A probabilistic approach for estimating water permeability in pressure-driven membranes

A probabilistic approach is proposed to estimate water permeability in a cellulose triacetate (CTA) membrane. Water transport across the membrane is simulated in reverse osmosis mode by means of non-equilibrium molecular dynamics (MD) simulations. Different membrane configurations obtained by an annealing MD simulation are considered and simulation results are analyzed by using a hierarchical Bayesian model to obtain the permeability of the different membranes. The estimated membrane permeability is used to predict full-scale water flux by means of a process-level Monte Carlo simulation. Based on the results, the parameters of the model are observed to converge within 5-ns total simulation time. The results also indicate that the use of unique structural configurations in MD simulations is essential to capture realistic membrane properties at the molecular scale. Furthermore, the predicted full-scale water flux based on the estimated permeability is within the same order of magnitude of bench-scale experimental measurement of 1.72×10^?5 m/s.     

Catalytic mechanism of cyclophilin as observed in molecular dynamics simulations: pathway prediction and reconciliation of X-ray crystallographic and NMR solution data

Cyclophilins are proteins that catalyze X-proline cis-trans interconversion, where X represents any amino acid. Its mechanism of action has been investigated over the past years but still generates discussion, especially because until recently structures of the ligand in the cis and trans conformations for the same system were lacking. X-ray crystallographic structures for the complex cyclophilin A and HIV-1 capsid mutants with ligands in the cis and trans conformations suggest a mechanism where the N-terminal portion of the ligand rotates during the cis-trans isomerization. However, a few years before, a C-terminal rotating ligand was proposed to explain NMR solution data. In the present study we use molecular dynamics (MD) simulations to generate a trans structure starting from the cis structure. From simulations starting from the cis and trans structures obtained through the rotational pathways, the seeming contradiction between the two sets of experimental data could be resolved. The simulated N-terminal rotated trans structure shows good agreement with the equivalent crystal structure and, moreover, is consistent with the NMR data. These results illustrate the use of MD simulation at atomic resolution to model structural transitions and to interpret experimental data.     

2H-NMR study and molecular dynamics simulation of the location, alignment, and mobility of pyrene in POPC bilayers

The alignment of pyrene in a 1-palmitoyl-2-oleoyl-phosphatidylcholine bilayer was investigated using two different approaches, namely solid-state (2)H-NMR spectroscopy and molecular dynamics (MD) simulations. Quadrupolar splittings from (2)H-NMR spectra of deuterated pyrene-d(10) in an oriented lipid bilayer give information about the orientation of C-D bonds with respect to the membrane normal. From MD simulations, geometric information is accessible via trajectories. By defining molecular and bond order parameters, the data from MD trajectories and NMR spectra can be compared straightforwardly. To ensure that the results from both methods are comparable, parameters of the experimental and the simulation setup were chosen to be as similar as possible. From simulations, we saw that pyrene prefers a position inside the lipid membrane near the headgroups and has no tendency to diffuse from one monolayer of the membrane to the other. The results from simulation and NMR show that the normal of the molecular plane is aligned nearly perpendicular to the bilayer normal. The long axis of pyrene lies preferentially parallel to the bilayer normal within a range of +/-30 degrees . The results from the two different methods are remarkably consistent. The good agreement can be explained by the fact that the different kind of motions of a pyrene molecule are already averaged within a few nanoseconds, which is the timescale covered by the MD simulation.     

Interpretation of Solution X-Ray Scattering by Explicit-Solvent Molecular Dynamics

Small- and wide-angle x-ray scattering (SWAXS) and molecular dynamics (MD) simulations are complementary approaches that probe conformational transitions of biomolecules in solution, even in a time-resolved manner. However, the structural interpretation of the scattering signals is challenging, while MD simulations frequently suffer from incomplete sampling or from a force-field bias. To combine the advantages of both techniques, we present a method that incorporates solution scattering data as a differentiable energetic restraint into explicit-solvent MD simulations, termed SWAXS-driven MD, with the aim to direct the simulation into conformations satisfying the experimental data. Because the calculations fully rely on explicit solvent, no fitting parameters associated with the solvation layer or excluded solvent are required, and the calculations remain valid at wide angles. The complementarity of SWAXS and MD is illustrated using three biological examples, namely a periplasmic binding protein, aspartate carbamoyltransferase, and a nuclear exportin. The examples suggest that SWAXS-driven MD is capable of refining structures against SWAXS data without foreknowledge of possible reaction paths. In turn, the SWAXS data accelerates conformational transitions in MD simulations and reduces the force-field bias.     

Structure, dynamics and hydration of the nogalamycin-d(ATGCAT)2Complex determined by NMR and molecular dynamics simulations in solution.

The structure of the 1:1 nogalamycin:d(ATGCAT)2 complex has been determined in solution from high-resolution NMR data and restrained molecular dynamics (rMD) simulations using an explicit solvation model. The antibiotic intercalates at the 5'-TpG step with the nogalose lying along the minor groove towards the centre of the duplex. Many drug-DNA nuclear Overhauser enhancements (NOEs) in the minor groove are indicative of hydrophobic interactions over the TGCA sequence. Steric occlusion prevents a second nogalamycin molecule from binding at the symmetry-related 5'-CpA site, leading to the conclusion that the observed binding orientation in this complex is the preferred orientation free of the complication of end-effects (drug molecules occupy terminal intercalation sites in all X-ray structures) or steric interactions between drug molecules (other NMR structures have two drug molecules bound in close proximity), as previously suggested. Fluctuations in key structural parameters such as rise, helical twist, slide, shift, buckle and sugar pucker have been examined from an analysis of the final 500 ps of a 1 ns rMD simulation, and reveal that many sequence-dependent structural features previously identified by comparison of different X-ray structures lie within the range of dynamic fluctuations observed in the MD simulations. Water density calculations on MD simulation data reveal a time-averaged pattern of hydration in both the major and minor groove, in good agreement with the extensive hydration observed in two related X-ray structures in which nogalamycin is bound at terminal 5'-TpG sites. However, the pattern of hydration determined from the sign and magnitude of NOE and ROE cross-peaks to water identified in 2D NOESY and ROESY experiments identifies only a few "bound" water molecules with long residence times. These solvate the charged bicycloaminoglucose sugar ring, suggesting an important role for water molecules in mediating drug-DNA electrostatic interactions within the major groove. The high density of water molecules found in the minor groove in X-ray structures and MD simulations is found to be associated with only weakly bound solvent in solution.     

Folding study of an Aib-rich peptide in DMSO by molecular dynamics simulations.

To evaluate the ability of molecular dynamics (MD) simulations using atomic force-fields to correctly predict stable folded conformations of a peptide in solution, we show results from MD simulations of the reversible folding of an octapeptide rich in alpha-aminoisobutyric acid (2-amino-2-methyl-propanoic acid, Aib) solvated in di-methyl-sulfoxide (DMSO). This solvent generally prevents the formation of secondary structure, whereas Aib-rich peptides show a high propensity to form secondary structural elements, in particular 3(10)- and alpha-helical structures. Aib is, moreover, achiral, so that Aib-rich peptides can form left- or right-handed helices depending on the overall composition of the peptide, the temperature, and the solvation conditions. This makes the system an interesting case to study the ensembles of peptide conformations as a function of temperature by MD simulation. Simulations involving the folding and unfolding of the peptide were performed starting from two initial structures, a right-handed alpha-helical structure and an extended structure, at three temperatures, 298 K, 340 K, and 380 K, and the results are compared with experimental nuclear magnetic resonance (NMR) data measured at 298 K and 340 K. The simulations generally reproduce the available experimental nuclear Overhauser effect (NOE) data, even when a wide range of conformations is sampled at each temperature. The importance of adequate statistical sampling in order to reliably interpret the experimental data is discussed.