Validation of NMR side-chain conformations by packing calculations

The precision and accuracy of protein structures determined by nuclear magnetic resonance (NMR) spectroscopy depend on the completeness of input experimental data set. Typically, rather than a single structure, an ensemble of up to 20 equally representative conformers is generated and routinely deposited in the Protein Database. There are substantially more experimentally derived restraints available to define the main-chain coordinates than those of the side chains. Consequently, the side-chain conformations among the conformers are more variable and less well defined than those of the backbone. Even when a side chain is determined with high precision and is found to adopt very similar orientations among all the conformers in the ensemble, it is possible that its orientation might still be incorrect. Thus, it would be helpful if there were a method to assess independently the side-chain orientations determined by NMR. Recently, homology modeling by side-chain packing algorithms has been shown to be successful in predicting the side-chain conformations of the buried residues for a protein when the main-chain coordinates and sequence information are given. Since the main-chain coordinates determined by NMR are consistently more reliable than those of the side-chains, we have applied the side-chain packing algorithms to predict side-chain conformations that are compatible with the NMR-derived backbone. Using four test cases where the NMR solution structures and the X-ray crystal structure of the same protein are available, we demonstrate that the side-chain packing method can provide independent validation for the side-chain conformations of NMR structures. Comparison of the side-chain conformations derived by side-chain packing prediction and by NMR spectroscopy demonstrates that when there is agreement between the NMR model and the predicted model, on average 78% of the time the X-ray structure also concurs. While the side-chain packing method can confirm the reliable residue conformations in NMR models, more importantly, it can also identify the questionable residue conformations with an accuracy of 60%. This validation method can serve to increase the confidence level for potential users of structural models determined by NMR.     

Improved efficiency of protein structure calculations from NMR data using the program DIANA with redundant dihedral angle constraints

Summary A new strategy for NMR structure calculations of proteins with the variable target function method (Braun, W. and Go, N. (1985)J. Mol. Biol.,186, 611) is described, which makes use of redundant dihedral angle constraints (REDAC) derived from preliminary calculations of the complete structure. The REDAC approach reduces the computation time for obtaining a group of acceptable conformers with the program DIANA 5-100-fold, depending on the complexity of the protein structure, and retains good sampling of conformation space.Dedicated to the memory of Professor V.F. Bystrov     

A comparison of the dynamic behavior of monomeric and dimeric insulin shows structural rearrangements in the active monomer

Molecular dynamics (MD) simulations (5-10ns in length) and normal mode analyses were performed for the monomer and dimer of native porcine insulin in aqueous solution; both starting structures were obtained from an insulin hexamer. Several simulations were done to confirm that the results obtained are meaningful. The insulin dimer is very stable during the simulation and remains very close to the starting X-ray structure; the RMS fluctuations calculated from the MD simulation agree with the experimental B-factors. Correlated motions were found within each of the two monomers; they can be explained by persistent non-bonded interactions and disulfide bridges. The correlated motions between residues B24 and B26 of the two monomers are due to non-bonded interactions between the side-chains and backbone atoms. For the isolated monomer in solution, the A chain and the helix of the B chain are found to be stable during 5ns and 10ns MD simulations. However, the N-terminal and the C-terminal parts of the B chain are very flexible. The C-terminal part of the B chain moves away from the X-ray conformation after 0.5-2.5ns and exposes the N-terminal residues of the A chain that are thought to be important for the binding of insulin to its receptor. Our results thus support the hypothesis that, when monomeric insulin is released from the hexamer (or the dimer in our study), the C-terminal end of the monomer (residues B25-B30) is rearranged to allow binding to the insulin receptor. The greater flexibility of the C-terminal part of the beta chain in the B24 (Phe-->Gly) mutant is in accord with the NMR results. The details of the backbone and side-chain motions are presented. The transition between the starting conformation and the more dynamic structure of the monomers is characterized by displacements of the backbone of Phe B25 and Tyr B26; of these, Phe B25 has been implicated in insulin activation.     

Conformational flexibility and binding interactions of the G protein βγ heterodimer

Previous NMR experiments on unbound G protein βγ heterodimer suggested that particular residues in the binding interface are mobile on the nanosecond timescale. In this work we performed nanosecond‐timescale molecular dynamics simulations to investigate conformational changes and dynamics of Gβγ in the presence of several binding partners: a high‐affinity peptide (SIGK), phosducin, and the GDP‐bound α subunit. In these simulations, the high mobility of GβW99 was reduced by SIGK, and it appeared that a tyrosine might stabilize GβW99 by hydrophobic or aromatic stacking interactions in addition to hydrogen bonds. Simulations of the phosducin‐Gβγ complex showed that the mobility of GβW99 was restricted, consistent with inferences from NMR. However, large‐scale conformational changes of Gβγ due to binding, which were hypothesized in the NMR study, were not observed in the simulations, most likely due to their short (nanosecond) duration. A pocket consisting of hydrophobic amino acids on Gα appears to restrict GβW99 mobility in the crystal structure of the Gαβγ? heterotrimer. The simulation trajectories are consistent with this idea. However, local conformational changes of residues GβW63, GβW211, GβW297, GβW332, and GβW339 were detected during the MD simulations. As expected, the magnitude of atomic fluctuations observed in simulations was greater for α than for the βγ subunits, suggesting that α has greater flexibility. These observations support the notion that to maintain the high mobility of GβW99 observed by solution NMR requires that the Gβ–α interface must open up on time scale longer than can be observed in nanosecond scale simulations. Proteins 2011. © 2010 Wiley‐Liss, Inc.     

Outer membrane proteins: comparing X-ray and NMR structures by MD simulations in lipid bilayers

The structures of three bacterial outer membrane proteins (OmpA, OmpX and PagP) have been determined by both X-ray diffraction and NMR. We have used multiple (7 × 15 ns) MD simulations to compare the conformational dynamics resulting from the X-ray versus the NMR structures, each protein being simulated in a lipid (DMPC) bilayer. Conformational drift was assessed via calculation of the root mean square deviation as a function of time. On this basis the ‘quality’ of the starting structure seems mainly to influence the simulation stability of the transmembrane β-barrel domain. Root mean square fluctuations were used to compare simulation mobility as a function of residue number. The resultant residue mobility profiles were qualitatively similar for the corresponding X-ray and NMR structure-based simulations. However, all three proteins were generally more mobile in the NMR-based than in the X-ray simulations. Principal components analysis was used to identify the dominant motions within each simulation. The first two eigenvectors (which account for >50% of the protein motion) reveal that such motions are concentrated in the extracellular loops and, in the case of PagP, in the N-terminal α-helix. Residue profiles of the magnitude of motions corresponding to the first two eigenvectors are similar for the corresponding X-ray and NMR simulations, but the directions of these motions correlate poorly reflecting incomplete sampling on a ∼10 ns timescale.     

Simultaneous single-structure and bundle representation of protein NMR structures in torsion angle space

A method is introduced to represent an ensemble of conformers of a protein by a single structure in torsion angle space that lies closest to the averaged Cartesian coordinates while maintaining perfect covalent geometry and on average equal steric quality and an equally good fit to the experimental (e.g. NMR) data as the individual conformers of the ensemble. The single representative ‘regmean structure’ is obtained by simulated annealing in torsion angle space with the program CYANA using as input data the experimental restraints, restraints for the atom positions relative to the average Cartesian coordinates, and restraints for the torsion angles relative to the corresponding principal cluster average values of the ensemble. The method was applied to 11 proteins for which NMR structure ensembles are available, and compared to alternative, commonly used simple approaches for selecting a single representative structure, e.g. the structure from the ensemble that best fulfills the experimental and steric restraints, or the structure from the ensemble that has the lowest RMSD value to the average Cartesian coordinates. In all cases our method found a structure in torsion angle space that is significantly closer to the mean coordinates than the alternatives while maintaining the same quality as individual conformers. The method is thus suitable to generate representative single structure representations of protein structure ensembles in torsion angle space. Since in the case of NMR structure calculations with CYANA the single structure is calculated in the same way as the individual conformers except that weak positional and torsion angle restraints are added, we propose to represent new NMR structures by a ‘regmean bundle’ consisting of the single representative structure as the first conformer and all but one original individual conformers (the original conformer with the highest target function value is discarded in order to keep the number of conformers in the bundle constant). In this way, analyses that require a single structure can be carried out in the most meaningful way using the first model, while at the same time the additional information contained in the ensemble remains available.     

Starting‐structure dependence of nanosecond timescale intersubstate transitions and reproducibility of MD‐derived order parameters

Factors affecting the accuracy of molecular dynamics (MD) simulations are investigated by comparing generalized order parameters for backbone NH vectors of the B3 immunoglobulin‐binding domain of streptococcal protein G (GB3) derived from simulations with values obtained from NMR spin relaxation (Yao L, Grishaev A, Cornilescu G, Bax A, J Am Chem Soc 2010;132:4295‐4309.). Choices for many parameters of the simulations, such as buffer volume, water model, or salt concentration, have only minor influences on the resulting order parameters. In contrast, seemingly minor conformational differences in starting structures, such as orientations of sidechain hydroxyl groups, resulting from applying different protonation algorithms to the same structure, have major effects on backbone dynamics. Some, but not all, of these effects are mitigated by increased sampling in simulations. Most discrepancies between simulated and experimental results occur for residues located at the ends of secondary structures and involve large amplitude nanosecond timescale transitions between distinct conformational substates. These transitions result in autocorrelation functions for bond vector reorientation that do not converge when calculated over individual simulation blocks, typically of length similar to the overall rotational diffusion time. A test for convergence before averaging the order parameters from different blocks results in better agreement between order parameters calculated from different sets of simulations and with NMR‐derived order parameters. Thus, MD‐derived order parameters are more strongly affected by transitions between conformational substates than by fluctuations within individual substates themselves, while conformational differences in the starting structures affect the frequency and scale of such transitions. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

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.     

A structure-based simulation approach for electron paramagnetic resonance spectra using molecular and stochastic dynamics simulations

Electron paramagnetic resonance (EPR) spectroscopy using site-directed spin-labeling is an appropriate technique to analyze the structure and dynamics of flexible protein regions as well as protein-protein interactions under native conditions. The analysis of a set of protein mutants with consecutive spin-label positions leads to the identification of secondary and tertiary structure elements. In the first place, continuous-wave EPR spectra reflect the motional freedom of the spin-label specifically linked to a desired site within the protein. EPR spectra calculations based on molecular dynamics (MD) and stochastic dynamics simulations facilitate verification or refinement of predicted computer-aided models of local protein conformations. The presented spectra simulation algorithm implies a specialized in vacuo MD simulation at 600 K with additional restrictions to sample the entire accessible space of the bound spin-label without large temporal effort. It is shown that the distribution of spin-label orientations obtained from such MD simulations at 600 K agrees well with the extrapolated motion behavior during a long timescale MD at 300 K with explicit water. The following potential-dependent stochastic dynamics simulation combines the MD data about the site-specific orientation probabilities of the spin-label with a realistic rotational diffusion coefficient yielding a set of trajectories, each more than 700 ns long, essential to calculate the EPR spectrum. Analyses of a structural model of the loop between helices E and F of bacteriorhodopsin are illustrated to demonstrate the applicability and potentials of the reported simulation approach. Furthermore, effects on the motional freedom of bound spin-labels induced by solubilization of bacteriorhodopsin with Triton X-100 are examined.     

Combination of Neutron Scattering and Molecular Dynamics to Determine Internal Motions in Biomolecules

Abstract

The forms and frequencies of atomic dynamics on the pico- and nanosecond timescales are accessible experimentally using incoherent neutron scattering. Molecular dynamics simulations cover the same space and time domains and neutron scattering intensities can be calculated from the simulations for direct comparison with experiment. To illustrate the complementarity of neutron scattering and molecular dynamics we examine measured and simulation-derived elastic incoherent scattering profiles from myoglobin and from the crystalline alanine dipeptide. Elastic incoherent scattering gives information on the geometry of the volume accessible to the atoms in the samples. The simulation-derived dipeptide elastic scattering profiles are in reasonable accord with experiment, deviations being due to the sampling limitations in the simulations and experimental detector normalisation procedures. The simulated dynamics is decomposed, revealing characteristic profiles due to rotational diffusional and translational vibrational motions of the methyl groups. In myoglobin, for which the timescale of the simulation matches more closely that accessible to the experiment, good agreement is seen for the elastic incoherent structure factor. This indicates that the space sampled by the hydrogen atoms in the protein on the timescale <100 ps is well represented by the simulation. Part of the helix atom fluctuations can be described in terms of rigid helix motions.     

Locally accessible conformations of proteins: multiple molecular dynamics simulations of crambin.

Multiple molecular dynamics (MD) simulations of crambin with different initial atomic velocities are used to sample conformations in the vicinity of the native structure. Individual trajectories of length up to 5 ns sample only a fraction of the conformational distribution generated by ten independent 120 ps trajectories at 300 K. The backbone atom conformational space distribution is analyzed using principal components analysis (PCA). Four different major conformational regions are found. In general, a trajectory samples only one region and few transitions between the regions are observed. Consequently, the averages of structural and dynamic properties over the ten trajectories differ significantly from those obtained from individual trajectories. The nature of the conformational sampling has important consequences for the utilization of MD simulations for a wide range of problems, such as comparisons with X-ray or NMR data. The overall average structure is significantly closer to the X-ray structure than any of the individual trajectory average structures. The high frequency (less than 10 ps) atomic fluctuations from the ten trajectories tend to be similar, but the lower frequency (100 ps) motions are different. To improve conformational sampling in molecular dynamics simulations of proteins, as in nucleic acids, multiple trajectories with different initial conditions should be used rather than a single long trajectory.     

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.     

Molecular dynamics simulations of DNA and a protein-DNA complex including solvent

The results of a recent nanosecond (ns) molecular dynamics (MD) simulation of the d(CGCGAATTCGCG) double helix in water and a 100 ps MD study of the repressor-operator complex are described. The DNA simulations are analyzed in terms of the structural dynamics, fluctuations in the groove width and bending of the helical axis. The results indicate that the ns dynamical trajectory progresses through a series of three substates of B form DNA, with lifetimes of the order of hundreds of picoseconds (ps). An incipient dynamical equilibrium is evident. A comparison of the calculated axis bending with that observed in corresponding crystal structure data is presented. Simulation of the DNA in complex with the protein and that of the free DNA in solution, starting from the crystal conformation, reveal the dynamical changes that occur on complex formation.     

Exploring the dynamic information content of a protein NMR structure: Comparison of a molecular dynamics simulation with the NMR and X‐ray structures of Escherichia coli ribonuclease HI

The multiconformer nature of solution nuclear magnetic resonance (NMR) structures of proteins results from the effects of intramolecular dynamics, spin diffusion and an uneven distribution of structural restraints throughout the molecule. A delineation of the former from the latter two contributions is attempted in this work for an ensemble of 15 NMR structures of the protein Escherichia coli ribonuclease HI (RNase HI). Exploration of the dynamic information content of the NMR ensemble is carried out through correlation with data from two crystal structures and a 1.7‐ns molecular dynamics (MD) trajectory of RNase HI in explicit solvent. Assessment of the consistency of the crystal and mean MD structures with nuclear Overhauser effect (NOE) data showed that the NMR ensemble is overall more compatible with the high‐resolution (1.48 Å) crystal structure than with either the lower‐resolution (2.05 Å) crystal structure or the MD simulation. Furthermore, the NMR ensemble is found to span more conformational space than the MD simulation for both the backbone and the sidechains of RNase HI. Nonetheless, the backbone conformational variability of both the NMR ensemble and the simulation is especially consistent with NMR relaxation measurements of two loop regions that are putative sites of substrate recognition. Plausible side‐chain dynamic information is extracted from the NMR ensemble on the basis of (i) rotamericity and syn‐pentane character of variable torsion angles, (ii) comparison of the magnitude of atomic mean‐square fluctuations (msf) with those deduced from crystallographic thermal factors, and (iii) comparison of torsion angle conformational behavior in the NMR ensemble and the simulation. Several heterogeneous torsion angles, while adopting non‐rotameric/syn‐pentane conformations in the NMR ensemble, exist in a unique conformation in the simulation and display low X‐ray thermal factors. These torsions are identified as sites whose variability is likely to be an artifact of the NMR structure determination procedure. A number of other torsions show a close correspondence between the conformations sampled in the NMR and MD ensembles, as well as significant correlations among crystallographic thermal factors and atomic msf calculated from the NMR ensemble and the simulation. These results indicate that a significant amount of dynamic information is contained in the NMR ensemble. The relevance of the present findings for the biological function of RNase HI, protein recognition studies, and previous investigations of the motional content of protein NMR structures are discussed. Proteins 1999;36:87–110. © 1999 Wiley‐Liss, Inc.     

NMR structure of cysteinyl-phosphorylated enzyme IIB of the N,N'-diacetylchitobiose-specific phosphoenolpyruvate-dependent phosphotransferase system of Escherichia coli

The determination by NMR of the solution structure of the phosphorylated enzyme IIB (P-IIB(Chb)) of the N,N'-diacetylchitobiose-specific phosphoenolpyruvate-dependent phosphotransferase system of Escherichia coli is presented. Most of the backbone and side-chain resonances were assigned using a variety of mostly heteronuclear NMR experiments. The remaining resonances were assigned with the help of the structure calculations.NOE-derived distance restraints were used in distance geometry calculations followed by molecular dynamics and simulated annealing protocols. In addition, combinations of ambiguous restraints were used to resolve ambiguities in the NOE assignments. By combining sets of ambiguous and unambiguous restraints into new ambiguous restraints, an error function was constructed that was less sensitive to information loss caused by assignment uncertainties. The final set of structures had a pairwise rmsd of 0.59 A and 1.16 A for the heavy atoms of the backbone and side-chains, respectively.Comparing the P-IIB(Chb) solution structure with the previously determined NMR and X-ray structures of the wild-type and the Cys10Ser mutant shows that significant differences between the structures are limited to the active-site region. The phosphoryl group at the active-site cysteine residue is surrounded by a loop formed by residues 10 through 16. NOE and chemical shift data suggest that the phosphoryl group makes hydrogen bonds with the backbone amide protons of residues 12 and 15. The binding mode of the phosphoryl group is very similar to that of the protein tyrosine phosphatases. The differences observed are in accordance with the presumption that IIB(Chb) has to be more resistant to hydrolysis than the protein tyrosine phosphatases. We propose a proton relay network by which a transfer occurs between the cysteine SH proton and the solvent via the hydroxyl group of Thr16.     

Conformational interconversion in compstatin probed with molecular dynamics simulations

Compstatin is a 13-residue cyclic peptide that has the potential to become a therapeutic agent against unregulated complement activation. In our effort to understand the structural and dynamic characteristics of compstatin that form the basis for rational and combinatorial optimization of structure and activity, we performed 1-ns molecular dynamics (MD) simulations. We used as input in the MD simulations the ensemble of 21 lowest energy NMR structures, the average minimized structure, and a global optimization structure. At the end of the MD simulations we identified five conformations, with populations ranging between 9% and 44%. These conformations are as follows: 1) coil with alphaR-alphaR beta-turn, as was the conformation of the initial ensemble of NMR structures; 2) beta-hairpin with epsilon-alphaR beta-turn; 3) beta-hairpin with alphaR-alphaR beta-turn; 4) beta-hairpin with alphaR-beta beta-turn; and 5) alpha-helical. Conformational switch was possible with small amplitude backbone motions of the order of 0.1-0.4 A and free energy barrier crossing of 2-11 kcal/mol. All of the 21 MD structures corresponding to the NMR ensemble possessed a beta-turn, with 14 structures retaining the alphaR-alphaR beta-turn type, but the average minimized structure and the global optimization structures were converted to alpha-helical conformations. Overall, the MD simulations have aided to gain insight into the conformational space sampled by compstatin and have provided a measure of conformational interconversion. The calculated conformers will be useful as structural and possibly dynamic templates for optimization in the design of compstatin using structure-activity relations (SAR) or dynamics-activity relations (DAR).     

Ensemble MD simulations restrained via crystallographic data: Accurate structure leads to accurate dynamics

Currently, the best existing molecular dynamics (MD) force fields cannot accurately reproduce the global free‐energy minimum which realizes the experimental protein structure. As a result, long MD trajectories tend to drift away from the starting coordinates (e.g., crystallographic structures). To address this problem, we have devised a new simulation strategy aimed at protein crystals. An MD simulation of protein crystal is essentially an ensemble simulation involving multiple protein molecules in a crystal unit cell (or a block of unit cells). To ensure that average protein coordinates remain correct during the simulation, we introduced crystallography‐based restraints into the MD protocol. Because these restraints are aimed at the ensemble‐average structure, they have only minimal impact on conformational dynamics of the individual protein molecules. So long as the average structure remains reasonable, the proteins move in a native‐like fashion as dictated by the original force field. To validate this approach, we have used the data from solid‐state NMR spectroscopy, which is the orthogonal experimental technique uniquely sensitive to protein local dynamics. The new method has been tested on the well‐established model protein, ubiquitin. The ensemble‐restrained MD simulations produced lower crystallographic R factors than conventional simulations; they also led to more accurate predictions for crystallographic temperature factors, solid‐state chemical shifts, and backbone order parameters. The predictions for ¹⁵N relaxation rates are at least as accurate as those obtained from conventional simulations. Taken together, these results suggest that the presented trajectories may be among the most realistic protein MD simulations ever reported. In this context, the ensemble restraints based on high‐resolution crystallographic data can be viewed as protein‐specific empirical corrections to the standard force fields.