Lipari–Szabo mapping: A graphical approach to Lipari–Szabo analysis of NMR relaxation data using reduced spectral density mapping

In this paper, we explore connections between the Lipari–Szabo formalism and reduced spectral density mapping, and show how spectral density estimates can be associated with Lipari–Szabo parameters via a simple geometric construction which we call Lipari–Szabo mapping. This relationship can be used to estimate Lipari–Szabo parameters from spectral density estimates without the need for nonlinear optimization, and to perform `model selection' in a graphical manner. The Lipari–Szabo map also provides insight into the Lipari–Szabo model, and allows us to determine when a given set of experimental spectral densities are inconsistent with the Lipari–Szabo formalism. Practical applications of Lipari–Szabo mapping in conjunction with more traditional analysis methods are discussed.     

Can enzyme engineering benefit from the modulation of protein motions? Lessons learned from NMR relaxation dispersion experiments

Despite impressive progress in protein engineering and design, our ability to create new and efficient enzyme activities remains a laborious and time-consuming endeavor. In the past few years, intricate combinations of rational mutagenesis, directed evolution and computational methods have paved the way to exciting engineering examples and are now offering a new perspective on the structural requirements of enzyme activity. However, these structure-function analyses are usually guided by the time-averaged static models offered by enzyme crystal structures, which often fail to describe the functionally relevant 'invisible states' adopted by proteins in space and time. To alleviate such limitations, NMR relaxation dispersion experiments coupled to mutagenesis studies have recently been applied to the study of enzyme catalysis, effectively complementing 'structure-function' analyses with 'flexibility-function' investigations. In addition to offering quantitative, site-specific information to help characterize residue motion, these NMR methods are now being applied to enzyme engineering purposes, providing a powerful tool to help characterize the effects of controlling long-range networks of flexible residues affecting enzyme function. Recent advancements in this emerging field are presented here, with particular attention to mutagenesis reports highlighting the relevance of NMR relaxation dispersion tools in enzyme engineering.     

NMR relaxation parameters of methyl groups as a tool to map the interfaces of helix–helix interactions in membrane proteins

A number of recent advances in the field of magic-angle-spinning (MAS) solid-state NMR have enabled its application to a range of biological systems of ever increasing complexity. To retain biological relevance, these samples are increasingly studied in a hydrated state. At the same time, experimental feasibility requires the sample preparation process to attain a high sample concentration within the final MAS rotor. We discuss these considerations, and how they have led to a number of different approaches to MAS NMR sample preparation. We describe our experience of how custom-made (or commercially available) ultracentrifugal devices can facilitate a simple, fast and reliable sample preparation process. A number of groups have since adopted such tools, in some cases to prepare samples for sedimentation-style MAS NMR experiments. Here we argue for a more widespread adoption of their use for routine MAS NMR sample preparation.     

Study of protein dynamics in solution by measurement of 13Cα-13CO NOE and 13CO longitudinal relaxation

Summary ¹³C-¹³CO homonuclear NOE and ¹³CO T₁ relaxation were measured for a 20 kDa protein using tripleresonance pulse sequences. The experiments were sufficiently sensitive to obtain statistically significant differences in relaxation parameters over the molecule. The ¹³C-¹³CO cross-relaxation rate, obtained from these data, is directly proportional to an order parameter describing local motion and it is largely independent of the local correlation time. It is therefore a relatively straightforward observable for the identification of local dynamics.     

Pairwise NMR experiments for the determination of protein backbone dihedral angle Φ based on cross-correlated spin relaxation

Novel cross-correlated spin relaxation (CCR) experiments are described, which measure pairwise CCR rates for obtaining peptide dihedral angles Φ. The experiments utilize intra-HNCA type coherence transfer to refocus 2-bond coupling evolution and generate the or multiple quantum coherences which are required for measuring the desired CCR rates. The contribution from other coherences is also discussed and an appropriate setting of the evolution delays is presented. These CCR experiments were applied to ¹⁵N- and ¹³C-labeled human ubiquitin. The relevant CCR rates showed a high degree of correlation with the Φ angles observed in the X-ray structure. By utilizing these CCR experiments in combination with those previously established for obtaining dihedral angle Ψ, we can determine high resolution structures of peptides that bind weakly to large target molecules.     

CPMG relaxation dispersion NMR experiments measuring glycine 1Hα and 13Cα chemical shifts in the ‘invisible’ excited states of proteins

Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion NMR experiments are extremely powerful for characterizing millisecond time-scale conformational exchange processes in biomolecules. A large number of such CPMG experiments have now emerged for measuring protein backbone chemical shifts of sparsely populated (>0.5%), excited state conformers that cannot be directly detected in NMR spectra and that are invisible to most other biophysical methods as well. A notable deficiency is, however, the absence of CPMG experiments for measurement of ¹H^α and ¹³C^α chemical shifts of glycine residues in the excited state that reflects the fact that in this case the ¹H^α, ¹³C^α spins form a three-spin system that is more complex than the AX ¹H^α–¹³C^α spin systems in the other amino acids. Here pulse sequences for recording ¹H^α and ¹³C^α CPMG relaxation dispersion profiles derived from glycine residues are presented that provide information from which ¹H^α, ¹³C^α chemical shifts can be obtained. The utility of these experiments is demonstrated by an application to a mutant of T4 lysozyme that undergoes a millisecond time-scale exchange process facilitating the binding of hydrophobic ligands to an internal cavity in the protein.     

Determination of sugar conformation in large RNA oligonucleotides from analysis of dipole–dipole cross correlated relaxation by solution NMR spectroscopy

A new experiment, the forward directed quantitative -HCCH-TOCSY for the measurement of the conformation of the five-membered ribosyl unit in RNA oligonucleotides, is presented. The experiment relies on quantification of cross peak intensities caused by evolution of CH,CH-dipole–dipole cross correlated relaxation in non-evolution periods and the resolution enhancement obtainable in forward directed HCC-TOCSY transfer. Cross correlated relaxation rates are interpreted to reveal the sugar conformation of 22 out of 25 nucleotides in an isotopically labelled 25-mer RNA. The results obtained with this new method are in agreement with the conformational analysis derived from ³J(H,H) coupling constants.     

Reconstructing parameters of the FitzHugh–Nagumo system from boundary potential measurements

We consider distributed parameter identification problems for the FitzHugh–Nagumo model of electrocardiology. The model describes the evolution of electrical potentials in heart tissues. The mathematical problem is to reconstruct physical parameters of the system through partial knowledge of its solutions on the boundary of the domain. We present a parallel algorithm of Newton–Krylov type that combines Newton’s method for numerical optimization with Krylov subspace solvers for the resulting Karush–Kuhn–Tucker system. We show by numerical simulations that parameter reconstruction can be performed from measurements taken on the boundary of the domain only. We discuss the effects of various model parameters on the quality of reconstructions. Action Editor: David Terman     

Utilization of lysine 13C-methylation NMR for protein–protein interaction studies

Chemical modification is an easy way for stable isotope labeling of non-labeled proteins. The reductive ¹³C-methylation of the amino group of the lysine side-chain by ¹³C-formaldehyde is a post-modification and is applicable to most proteins since this chemical modification specifically and quickly proceeds under mild conditions such as 4 °C, pH 6.8, overnight. ¹³C-methylation has been used for NMR to study the interactions between the methylated proteins and various molecules, such as small ligands, nucleic acids and peptides. Here we applied lysine ¹³C-methylation NMR to monitor protein–protein interactions. The affinity and the intermolecular interaction sites of methylated ubiquitin with three ubiquitin-interacting proteins were successfully determined using chemical-shift perturbation experiments via the ¹H–¹³C HSQC spectra of the ¹³C-methylated-lysine methyl groups. The lysine ¹³C-methylation NMR results also emphasized the importance of the usage of side-chain signals to monitor the intermolecular interaction sites, and was applicable to studying samples with concentrations in the low sub-micromolar range.     

Solution structure of Fe(II)–azide–bleomycin derived from NMR data: transition from Fe(II)–bleomycin to Fe(II)–azide–bleomycin as derived from NMR data and structural calculations

The coordination cage of the metal center in Fe(II)-bleomycin has been proposed to consist of the secondary amines in β-aminoalanine, the pyrimidinylpropionamide and imidazole rings, and the amide nitrogen in β-hydroxyhistidine as equatorial ligands, and the primary amine in β-aminoalanine and either the carbamoyl group in mannose or a solvent molecule occupying the axial sites. With the aim of supporting or not supporting coordination of a water molecule to the metal center in Fe(II)-bleomycin, the solution structure of Fe(II)-azide-bleomycin has been derived from NMR data. The structural changes that occur in Fe(II)-bleomycin upon azide binding have been monitored by comparing the experimental results with those obtained from the calculated structures for both bleomycin adducts. The results of this investigation strongly support a model of Fe(II)-bleomycin with six endogenous ligands as the most likely structure held in solution by this metallobleomycin in the absence of DNA.     

Mapping of the spectral density function of a Cα−Hα bond vector from NMR relaxation rates of a 13C-labelled α-carbon in motilin

Summary The peptide hormone motilin was synthesised with a ¹³C-enriched -carbon in the leucine at position 10. In aqueous solution, six different relaxation rates were measured for the ¹³C–H fragment as a function of temperature and with and without the addition of 30% (v/v) of the cosolvent d ₂-1,1,1,3,3,3-hexafluoro-2-propanol (HFP). The relaxation rates were analysed employing the spectral density mapping technique introduced by Peng and Wagner [(1992) J. Magn. Reson., 98, 308–322] and using the model-free approach by Lipari and Szabo [(1982) J. Am. Chem. Soc., 104, 4546–4570]. The fit to various models of dynamics was also considered. Different procedures to evaluate the overall rotational correlation time were compared. A single exponential time correlation function was found to give a good fit to the measured spectral densities only for motilin in 30% (v/v) HFP at low temperatures, whereas at high temperatures in this solvent, and in D₂O at all temperatures, none of the considered models gave an acceptable fit. A new empirical spectral density function was tested and found to accurately fit the experimental spectral density mapping points. The application of spectral density mapping based on NMR relaxation data for specific ¹³C–¹H vector is shown to be a highly useful method to study biomolecular dynamics. Advantages are high sensitivity, high precision and uniform sampling of the spectral density function over the frequency range.Abbreviations CD circular dichroism - NOE nuclear Overhauser enhancement - NOESY two-dimensional NOE spectroscopy - INEPT insensitive nuclei enhanced by polarisation transfer - DANTE delays alternating with nutations for tailored excitation - WALTZ-16 wideband, alternating phase, low-power technique for zero residual splitting - FID Free induction decay - ppm parts per million - TSPA 3-trimethylsilyl-(3,3,2,2-d)-propionic acid - HFP d ₂-1,1,1,3,3,3-hexafluoro-2-propanol - CPMG Carr-Purcell-Meiboom-Gill - TFD time-resolved fluorescence depolarisation - CSA chemical shift anisotropy Partly presented at the symposium Dynamics and Function of Biomolecules, Szeged, Hungary, July 31–August 2, 1993.     

Mapping protein–protein interaction by 13C′-detected heteronuclear NMR spectroscopy

The copper-mediated protein–protein interaction between yeast Atx1 and Ccc2 has been examined by protonless heteronuclear NMR and compared with the already available ¹H–¹⁵N HSQC information. The observed chemical shift variations are analyzed with respect to the actual solution structure, available through intermolecular NOEs. The advantage of using the CON-IPAP spectrum with respect to the ¹H–¹⁵N HSQC resides in the increased number of signals observed, including those of prolines. CBCACO-IPAP experiments allow us to focus on the interaction region and on side-chain carbonyls, while a newly designed CEN-IPAP experiment on side-chains of lysines. An attempt is made to rationalize the chemical shift variations on the basis of the structural data involving the interface between the proteins and the nearby regions. It is here proposed that protonless ¹³C direct-detection NMR is a useful complement to ¹H based NMR spectroscopy for monitoring protein–protein and protein–ligand interactions. Electronic Supplementary Material Supplementary material is available to authorised users in the online version of this article at     

Order parameters of unsaturated phospholipids in membranes and the effect of cholesterol: a 1H–13C solid-state NMR study at natural abundance

Most biological phospholipids contain at least one unsaturated alkyl chain. However, few order parameters of unsaturated lipids have been determined because of the difficulty associated with isotopic labeling of a double bond. Dipolar recoupling on axis with scaling and shape preservation (DROSS) is a solid-state nuclear magnetic resonance technique optimized for measuring ¹H–¹³C dipolar couplings and order parameters in lipid membranes in the fluid phase. It has been used to determine the order profile of 1,2-dimyristoyl-sn-glycero-3-phosphocholine hydrated membranes. Here, we show an application for the measurement of local order parameters in multilamellar vesicles containing unsaturated lipids. Taking advantage of the very good ¹³C chemical shift dispersion, one can easily follow the segmental order along the acyl chains and, particularly, around the double bonds where we have been able to determine the previously misassigned order parameters of each acyl chain of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). We have followed the variation of such order profiles with temperature, unsaturation content and cholesterol addition. We have found that the phase formed by DOPC with 30% cholesterol is analogous to the liquid-ordered (l_o) phase. Because these experiments do not require isotopic enrichment, this technique can, in principle, be applied to natural lipids and biomembranes.Electronic Supplementary Material Supplementary material is available for this article at .     

Comparison of NMR and MD N–H bond order parameters: example of HIV-1 protease

It has been suggested that the cause of disagreements between molecular dynamics (MD) and NMR N–H bond order parameters is the fact that the NMR order parameter is determined for different amino acid residues at different time intervals, while the MD one is derived for all residues from the same MD trajectory of the same time interval. Therefore, it has been proposed for correct comparison with NMR data to calculate the MD order parameter for different amino acid residues separately for trajectory ranges close to NMR correlation time. The MD simulation of the human immunodeficiency virus type-1 protease (HIV-1 PR) with monoprotonated active centre was performed for verification of the proposition. It has been shown that the protease in aqueous solution adopts a set of conformations, which are intermediate between semiopen and closed ones. The calculated MD N–H bond order parameters are in agreement with literature NMR data in confidence interval limits.     

13C–13C NOESY spectra of a 480 kDa protein: solution NMR of ferritin

Molecular size has limited solution NMR analyses of proteins. We report ¹³C–¹³C NOESY experiments on a 480 kDa protein, the multi-subunit ferritin nanocage with gated pores. By exploiting ¹³C-resonance-specific chemical shifts and spin diffusion effects, we identified 75% of the amino acids, with intraresidue C–C connectivities between nuclei separated by 1–4 bonds. These results show the potential of ¹³C–¹³C NOESY for solution studies of molecular assemblies >100 kDa.     

NMR experiments for resonance assignments of 13C, 15N doubly-labeled flexible polypeptides: Application to the human prion protein hPrP(23–230)

A combination of three heteronuclear three-dimensional NMR experiments tailored for sequential resonance assignments in uniformly ¹⁵N, ¹³C-labeled flexible polypeptide chains is described. The 3D (H)N(CO-TOCSY)NH, 3D (H)CA(CO-TOCSY)NH and 3D (H)CBCA(CO-TOCSY)NH schemes make use of the favorable ¹⁵N chemical shift dispersion in unfolded polypeptides, exploit the slow transverse ¹⁵N relaxation rates of unfolded polypeptides in high resolution constant-time [¹H, ¹⁵N]-correlation experiments, and use carbonyl carbon homonuclear isotropic mixing to transfer magnetization sequentially along the amino acid sequence. Practical applications are demonstrated with the 100-residue flexible tail of the recombinant human prion protein, making use of spectral resolution up to 0.6 Hz in the ¹⁵N dimension, simultaneous correlation with the two adjacent amino acid residues to overcome problems associated with spectral overlap, and the potential of the presently described experiments to establish nearest-neighbor correlations across proline residues in the amino acid sequence.     

Off-resonance 13C–2H REDOR NMR for site-resolved studies of molecular motion

We introduce a ¹³C–²H Rotational Echo DOuble Resonance (REDOR) technique that uses the difference between on-resonance and off-resonance ²H irradiation to detect dynamic segments in deuterated molecules. By selectively inverting specific regions of the ²H magic-angle spinning (MAS) sideband manifold to recouple some of the deuterons to nearby carbons, we distinguish dynamic and rigid residues in 1D and 2D ¹³C spectra. We demonstrate this approach on deuterated GB1, H/D exchanged GB1, and perdeuterated bacterial cellulose. Numerical simulations reproduce the measured mixing-time and ²H carrier-frequency dependence of the REDOR dephasing of bacterial cellulose. Combining numerical simulations with experiments thus allow the extraction of motionally averaged quadrupolar couplings from REDOR dephasing values.

     

UDP-induced relaxation is enhanced in aorta from female obese Otsuka Long–Evans Tokushima Fatty rats

Uridine 5′-diphosphate (UDP) plays an important role in controlling vascular tone; however, UDP-mediated response in metabolic syndromes, including obesity and type 2 diabetes in females, remains unclear. In this study, we investigated UDP-mediated response in the aorta of female obese Otsuka Long–Evans Tokushima Fatty (OLETF) rats and control Long–Evans Tokushima Otsuka (LETO) rats. In OLETF rat aortas precontracted by phenylephrine (PE) (vs. LETO), (1) UDP-induced relaxation was increased, whereas acetylcholine (ACh)-induced relaxation was decreased; (2) no UDP- or ACh-induced relaxations were observed in endothelial denudation, whereas UDP-induced small contraction was observed; and (3) N^G-nitro-L-arginine [L-NNA, a nitric oxide (NO) synthase inhibitor] eliminated UDP-induced relaxation and small contraction, whereas caused contrasting responses by ACh, including slight relaxations (LETO) and contractions (OLETF). Indomethacin, a cyclooxygenase inhibitor, eliminated the difference in UDP- and ACh-induced relaxations between the groups by increased UDP-induced relaxation in the LETO group and increased ACh-induced relaxation in the OLETF group. MRS2578, a P2Y₆ receptor antagonist, eliminated the difference in UDP-induced relaxations between the groups by decreasing UDP-induced relaxation in the OLETF group. MRS2578 had no effect on UDP-induced contraction in endothelium-denuded aortas. Therefore, these findings demonstrate opposite trends of relaxations by UDP and ACh in OLETF and LETO rat aortas. These differences may be attributed to the imbalance between NO and vasoconstrictor prostanoids upon stimulations. Increased UDP-induced relaxation in OLETF rat aorta may be caused by the activation of endothelial MRS2578-sensitive P2Y₆ receptor.