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.     

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.     

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     

Determination of protein rotational correlation time from NMR relaxation data at various solvent viscosities

An accurate determination of the overall rotation of a protein plays a crucial role in the investigation of its internal motions by NMR. In the present work, an innovative approach to the determination of the protein rotational correlation time _R from the heteronuclear relaxation data is proposed. The approach is based on a joint fit of relaxation data acquired at several viscosities of a protein solution. The method has been tested on computer simulated relaxation data as compared to the traditional _R determination method from T₁/T₂ ratio. The approach has been applied to ribonuclease barnase from Bacillus amyloliquefaciens dissolved in an aqueous solution and deuterated glycerol as a viscous component. The resulting rotational correlation time of 5.56 ± 0.01 ns and other rotational diffusion tensor parameters are in good agreement with those determined from T₁/T₂ ratio.     

On the ability of molecular dynamics force fields to recapitulate NMR derived protein side chain order parameters

Molecular dynamics (MD) simulations have become a central tool for investigating various biophysical questions with atomistic detail. While many different proxies are used to qualify MD force fields, most are based on largely structural parameters such as the root mean square deviation from experimental coordinates or nuclear magnetic resonance (NMR) chemical shifts and residual dipolar couplings. NMR derived Lipari–Szabo squared generalized order parameter (O²) values of amide N? H bond vectors of the polypeptide chain were also often employed for refinement and validation. However, with a few exceptions, side chain methyl symmetry axis order parameters have not been incorporated into experimental reference sets. Using a test set of five diverse proteins, the performance of several force fields implemented in the NAMDD simulation package was examined. It was found that simulations employing explicit water implemented using the TIP3 model generally performed significantly better than those using implicit water in reproducing experimental methyl symmetry axis O² values. Overall the CHARMM27 force field performs nominally better than two implementations of the Amber force field. It appeared that recent quantum mechanics modifications to side chain torsional angles of leucine and isoleucine in the Amber force field have significantly hindered proper motional modeling for these residues. There remained significant room for improvement as even the best correlations of experimental and simulated methyl group Lipari–Szabo generalized order parameters fall below an R² of 0.8.     

Single-stranded DNA binding of the cold-shock protein CspB from Bacillus subtilis: NMR mapping and mutational characterization

Cold-shock proteins (CSPs) bind to single-stranded nucleic acids, thereby acting as a "RNA chaperone." To gain deeper insights into the rather unspecific nature of ssDNA/RNA binding, we characterized the binding interface of CspB from Bacillus subtilis to a 25-mer of ssDNA (Y-Box25) using heteronuclear 2D NMR spectroscopy. Seventeen residues, including eight out of nine aromatic amino acids, are directly involved in the Y-Box25 interaction and were identified by extreme line broadening of their cross-peaks. Eight residues belong to the earlier proposed RNP binding motifs. A second set of seven backbone amides becomes evident by major chemical shift perturbations reporting remote conformational rearrangements upon binding. These residues are located in loop beta3-beta4 and loopbeta4-beta5, and include Ile18. The individual contributions of the so-identified residues were examined by fluorescence titration experiments of 15 CspB variants. Phenylalanine substitutions in- and outside the RNP motifs significantly reduce the binding affinity. Unrestricted possible backbone conformations of loop beta3-beta4 also markedly contribute to binding. Stopped-flow fluorescence kinetics revealed that the different binding affinities of CspB variants are determined by the dissociation rate, whereas the association rate remains unchanged. This might be of importance for the "RNA chaperone" activity of CspB.     

Identification of Slow Motions in the Reduced Recombinant High-potential Iron Sulfur Protein I (HiPIP I) from Ectothiorhodospira Halophila via 15N Rotating-frame NMR Relaxation Measurements

Rotating-frame 15N relaxation rate (R1) NMR experiments have been performed in order to study the dynamic behavior of the reduced recombinant high-potential iron-sulfur protein iso I (HiPIP I) from Ectothiorhodospira halophila, in the s to ms time range. Measurements of R1 were performed as a function of the effective spin-lock magnetic field amplitude by using both on and off-resonance radio frequency irradiation. The two data sets provided consistent results and were fit globally in order to identify possible exchange processes in an external loop of the reduced HiPIP I. The loop consists of residues 43-45 and the correlation time of the exchange process was determined to be 50 ± 8 s for the backbone nitrogen of Gln 44.     

15N relaxation study of the cold shock protein CspB at various solvent viscosities

For a detailed NMR study of the dynamics of the cold shock protein CspB from Bacillus subtilis, we determined ¹⁵N transverse and longitudinal relaxation rates and heteronuclear nuclear Overhauser effects at different solvent viscosities. Up to a relative viscosity of 2, which is equivalent to 27% ethylene glycol (EG), the overall correlation time follows the linear Stokes-Einstein equation. At a relative viscosity of 6 (70% EG) the correlation time deviates from linearity by 30%, indicating that CspB tumbles at a higher rate as expected from the solvent viscosity probably due to a preferential binding of water molecules at the protein surface. The corresponding hydrodynamic radii, determined by NMR diffusion experiments, show no variation with viscosity. The amplitudes of intramolecular motions on a sub-nanosecond time scale revealed by an extended Lipari–Szabo analysis were mainly independent of the solvent viscosity. The lower limit of the NMR `observation window' for the internal correlation time shifts above 0.5 ns at 70% EG, which is directly reflected in the experimentally derived internal correlation times. Chemical exchange contributions to the transverse relaxation rates derived from the Lipari-Szabo approach coincide with the experimentally determined values from the transverse ¹H-¹⁵N dipolar/¹⁵N chemical shift anisotropy relaxation interference. These contributions originate from fast protein folding reactions on a millisecond timescale, which get retarded at increased solvent viscosities.     

Microsecond time scale dynamics in the RXR DNA-binding domain from a combination of spin-echo and off-resonance rotating frame relaxation measurements

Slow protein dynamics can be studied by 15N spin-echo (CPMG) and off-resonance rotating frame relaxation through the effective field dependence of the exchange-mediated relaxation contribution. It is shown that, by a combination of these complementary techniques, a more extended sampling of the microsecond time scale processes is achieved than by either method alone. 15N R2 and improved off-resonance R1 experiments [Mulder et al. (1998) J. Magn. Reson., 131, 351–357] were applied to the 9- cis-retinoic acid receptor DNA-binding domain and allowed the identification of 14 residues exhibiting microsecond time scale dynamics. Assuming exchange between two conformational substates, average lifetimes ranging from 37 to 416 s, and chemical shift differences of up to 3 ppm were obtained. The largest perturbation of tertiary structure was observed for the second zinc finger region, which was found to be disordered in the solution structure [Holmbeck et al. (1998) J. Mol. Biol., 281, 271–284]. Since this zinc-coordinating domain comprises the principal dimerization interface for RXR in a wide repertoire of complexes with different hormone receptors to their cognate response elements, this finding has important implications for our understanding of nuclear receptor assembly on DNA direct repeats. The flexibility observed for the dimerization domain may explain how RXR, through the ability to adaptively interact with a wide variety of highly homologous partner molecules, demonstrates such a versatile DNA-binding repertoire.     

Heteronuclear NMR assignments and secondary structure of the coiled coil trimerization domain from cartilage matrix protein in oxidized and reduced forms.

The C-terminal oligomerization domain of chicken cartilage matrix protein is a trimeric coiled coil comprised of three identical 43-residue chains. NMR spectra of the protein show equivalent magnetic environments for each monomer, indicating a parallel coiled coil structure with complete threefold symmetry. Sequence-specific assignments for 1H-, 15N-, and 13C-NMR resonances have been obtained from 2D 1H NOESY and TOCSY spectra, and from 3D HNCA, 15N NOESY-HSQC, and HCCH-TOCSY spectra. A stretch of alpha-helix encompassing five heptad repeats (35 residues) has been identified from intra-chain HN-HN and HN-H alpha NOE connectivities. 3JHNH alpha coupling constants, and chemical shift indices. The alpha-helix begins immediately downstream of inter-chain disulfide bonds between residues Cys 5 and Cys 7, and extends to near the C-terminus of the molecule. The threefold symmetry of the molecule is maintained when the inter-chain disulfide bonds that flank the N-terminus of the coiled coil are reduced. Residues Ile 21 through Glu 36 show conserved chemical shifts and NOE connectivities, as well as strong protection from solvent exchange in the oxidized and reduced forms of the protein. By contrast, residues Ile 10 through Val 17 show pronounced chemical shift differences between the oxidized and reduced protein. Strong chemical exchange NOEs between HN resonances and water indicate solvent exchange on time scales faster than 10 s, and suggests a dynamic fraying of the N-terminus of the coiled coil upon reduction of the disulfide bonds. Possible roles for the disulfide crosslinks of the oligomerization domain in the function of cartilage matrix protein are proposed.     

NMR solution structure and characterization of substrate binding site of the PPIase domain of PrsA protein from Bacillus subtilis

PrsA is a peptidyl-prolyl isomerase (PPIase) from Bacillus subtilis belonging to the parvulin family of PPIases. It is a membrane bound lipoprotein at the membrane-wall interface, involved in folding of exported proteins. We present the NMR solution structure of the PPIase domain of PrsA, the first from a Gram-positive bacterium. In addition we mapped out the active site with NMR titration experiments. A high degree of conservation with other members of the parvulin family was revealed in the structure and binding site. Interactions with substrate peptides were also characterized by mutated domains revealing that H122 is indispensable for overall correct folding.     

Structural Reorganization of α-Synuclein at Low pH Observed by NMR and REMD Simulations

α-Synuclein is an intrinsically disordered protein that appears in aggregated forms in the brains of patients with Parkinson's disease. The conversion from monomer to aggregate is complex, and aggregation rates are sensitive to changes in amino acid sequence and environmental conditions. It has previously been observed that α-synuclein aggregates faster at low pH than at neutral pH. Here, we combine NMR spectroscopy and molecular simulations to characterize α-synuclein conformational ensembles at both neutral and low pH in order to understand how the altered charge distribution at low pH changes the structural properties of these ensembles and leads to an increase in aggregation rate. The N-terminus, which has a small positive charge at neutral pH due to a balance of positively and negatively charged amino acid residues, is very positively charged at low pH. Conversely, the acidic C-terminus is highly negatively charged at neutral pH and becomes essentially neutral and hydrophobic at low pH. Our NMR experiments and replica exchange molecular dynamics simulations indicate that there is a significant structural reorganization within the low-pH ensemble relative to that at neutral pH in terms of long-range contacts, hydrodynamic radius, and the amount of heterogeneity within the conformational ensembles. At neutral pH, there is a very heterogeneous ensemble with transient contacts between the N-terminus and the non-amyloid β component (NAC); however, at low pH, there is a more homogeneous ensemble that exhibits strong contacts between the NAC and the C-terminus. At both pH values, transient contacts between the N- and C-termini are observed, the NAC region shows similar exposure to solvent, and the entire protein shows similar propensities to secondary structure. Based on the comparison of the neutral- and low-pH conformational ensembles, we propose that exposure of the NAC region to solvent and the secondary-structure propensity are not factors that account for differences in propensity to aggregate in this context. Instead, the comparison of the neutral- and low-pH ensembles suggests that the change in long-range interactions between the low- and neutral-pH ensembles, the compaction of the C-terminal region at low pH, and the uneven distribution of charges across the sequence are key to faster aggregation.