Determination of Spin−Spin Couplings from Ultrahigh Resolution 3D NMR Spectra Obtained by Optimized Random Sampling and Multidimensional Fourier Transformation

Structural analysis of 25-hydroxycholesterol stereoisomers differing in configuration in position 17 and 20, by three-dimensional NMR spectra

The application of 3D NMR experiments and DFT calculations enabled the structure investigation of C-17 epimer of 3-(25-hydroxycholest-5-enyl) acetate is presented. The H-17 and H-20 protons features the same values of ¹H chemical shift, what causes that the structure elucidation require additional resolution enabled by 3D NMR experiments. The NMR experiments and theoretical calculations allowed for: the resonance assignment (3D COSY-HMBC and 3D TOCSY-HSQC techniques), the prediction of spatial structure (3D NOESY-HSQC and 3D ROESY-HSQC experiments), and the precise measurement of heteronuclear coupling constants (3D HSQC-TOCSY spectra with E.COSY-type multiplets).

Nuclear overhauser spectroscopy of chiral CHD methylene groups

Nuclear magnetic resonance spectroscopy (NMR) can provide a great deal of information about structure and dynamics of biomolecules. The quality of an NMR structure strongly depends on the number of experimental observables and on their accurate conversion into geometric restraints. When distance restraints are derived from nuclear Overhauser effect spectroscopy (NOESY), stereo-specific assignments of prochiral atoms can contribute significantly to the accuracy of NMR structures of proteins and nucleic acids. Here we introduce a series of NOESY-based pulse sequences that can assist in the assignment of chiral CHD methylene protons in random fractionally deuterated proteins. Partial deuteration suppresses spin-diffusion between the two protons of CH2 groups that normally impedes the distinction of cross-relaxation networks for these two protons in NOESY spectra. Three and four-dimensional spectra allow one to distinguish cross-relaxation pathways involving either of the two methylene protons so that one can obtain stereospecific assignments. In addition, the analysis provides a large number of stereospecific distance restraints. Non-uniform sampling was used to ensure optimal signal resolution in 4D spectra and reduce ambiguities of the assignments. Automatic assignment procedures were modified for efficient and accurate stereospecific assignments during automated structure calculations based on 3D spectra. The protocol was applied to calcium-loaded calbindin D9k. A large number of stereospecific assignments lead to a significant improvement of the accuracy of the structure.

Applications of high dimensionality experiments to biomolecular NMR

High dimensionality NMR experiments facilitate resonance assignment and precise determination of spectral parameters such as coupling constants. Sparse non-uniform sampling enables acquisition of experiments of high dimensionality with high resolution in acceptable time. In this review we present and compare some significant applications of NMR experiments of dimensionality higher than three in the field of biomolecular studies in solution.

Speeding up the measurement of one-bond scalar (1J) and residual dipolar couplings (1D) by using non-uniform sampling (NUS)

The accurate and precise measurement of one-bond scalar and residual dipolar coupling (RDC) constants is of prime importance to be able to use RDCs for structure determination. If coupling constants are to be extracted from the indirect dimension of HSQC spectra a significant saving of measurement time can be achieved by non-uniform sampling (NUS). Coupling constants can either be obtained with the same precision as in traditionally acquired spectra in a fraction of the measurement time or the precision can be significantly improved if the same amount of measurement time as for traditionally acquired spectra is invested. The application of NUS for the measurement of (1)J (scalar coupling constants) and (1)T (total couplings constants) from different kinds of ω(1)-coupled spectra (including also J-scaled ones) is examined in detail and the possible gains in time or resolution are discussed. When using the newly proposed compressed sensing (CS) algorithm for processing, the quality of the spectra is comparable to the traditionally sampled ones.

Parallel receivers and sparse sampling in multidimensional NMR

The recent introduction of NMR spectrometers with multiple receivers permits spectra from several different nuclear species to be recorded in parallel, and several standard pulse sequences to be combined into a single entity. It is shown how these improvements in the flow and quality of spectral information can be significantly augmented by compressive sensing techniques--controlled aliasing, Hadamard spectroscopy, single-point evaluation of evolution space (SPEED), random sampling, projection-reconstruction, and hyperdimensional NMR. Future developments of these techniques are confidently expected to mitigate one of the most serious limitations in multidimensional NMR--the excessive duration of the measurements.

Improved accuracy in measuring one-bond and two-bond (15)N, (13)C (α) coupling constants in proteins by double-inphase/antiphase (DIPAP) spectroscopy

An extension to HN(CO-α/β-N,C(α)-J)-TROSY (Permi and Annila in J Biomol NMR 16:221-227, 2000) is proposed that permits the simultaneous determination of the four coupling constants (1) J (N'(i)Cα(i)), (2) J (HN(i)Cα(i)), (2) J (Cα(i-1)N'(i)), and (3) J (Cα(i-1)HN(i)) in (15)N,(13)C-labeled proteins. Contrasting the original scheme, in which two separate subspectra exhibit the (2) J (CαN') coupling as inphase and antiphase splitting (IPAP), we here record four subspectra that exhibit all combinations of inphase and antiphase splittings possible with respect to both (2) J (CαN') and (1) J (N'Cα) (DIPAP). Complementary sign patterns in the different spectrum constituents overdetermine the coupling constants which can thus be extracted at higher accuracy than is possible with the original experiment. Fully exploiting data redundance, simultaneous 2D lineshape fitting of the E.COSY multiplet tilts in all four subspectra provides all coupling constants at ultimate precision. Cross-correlation and differential-relaxation effects were taken into account in the evaluation procedure. By applying a four-point Fourier transform, the set of spectra is reversibly interconverted between DIPAP and spin-state representations. Methods are exemplified using proteins of various size.

One-bond and two-bond J couplings help annotate protein secondary-structure motifs: J-coupling indexing applied to human endoplasmic reticulum protein ERp18

NMR coupling constants, both direct one-bond ((1)J) and geminal two-bond ((2)J), are employed to analyze the protein secondary structure of human oxidized ERp18. Coupling constants collected and evaluated for the 18 kDa protein comprise 1268 values of (1)J(CαHα), (1)J(CαCβ), (1)J(CαC'), (1)J(C'N'), (1)J(N'Cα), (1)J(N') (HN), (2)J(CαN'), (2)J(HNCα), (2)J(C'HN), and (2)J(HαC'). Comparison with (1)J and (2)J data from reference proteins and pattern analysis on a per-residue basis permitted main-chain ϕ,ψ torsion-angle combinations of many of the 149 amino-acid residues in ERp18 to be narrowed to particular secondary-structure motifs. J-coupling indexing is here being developed on statistical criteria and used to devise a ternary grid for interpreting patterns of relative values of J. To account for the influence of the varying substituent pattern in different amino-acid sidechains, a table of residue-type specific threshold values was compiled for discriminating small, medium, and large categories of J. For the 15-residue insertion that distinguishes the ERp18 fold from that of thioredoxin, the J-coupling data hint at a succession of five isolated Type-I β turns at progressively shorter sequence intervals, in agreement with the crystal structure.

Structure and dynamics of the first archaeal parvulin reveal a new functionally important loop in parvulin-type prolyl isomerases

Parvulins are a group of peptidyl-prolyl isomerases (PPIases) responsible for important biological processes in all kingdoms of life. The PinA protein from the psychrophilic archaeon Cenarchaeum symbiosum is a parvulin-like PPIase. Due to its striking similarity to the human parvulins Pin1 and Par14, PinA constitutes an interesting subject for structural and functional studies. Here, we present the first high resolution NMR structure of an archaeal parvulin, PinA, based on 1798 conformational restraints. Structure calculation yields an ensemble of 20 convergent low energy structures with a backbone r.m.s.d. value of 0.6 Å within the secondary structure elements. The overall fold of PinA comprises the β-α(3)-β-α-β(2) fold typical for all parvulin structures known so far, but with helix III being a short 3(10)-helix. A detailed comparison of this high resolution structure of the first archaeal PinA protein with bacterial and eukaryotic parvulin PPIase structures reveals an atypically large catalytic binding site. This feature provides an explanation for cold-adapted protein function. Moreover, the residues in and around 3(10)-helix III exhibit strong intramolecular dynamics on a microsecond to millisecond timescale and display structural heterogeneity within the NMR ensemble. A putative peptide ligand was found for PinA by phage display and was used for (1)H-(15)N-HSQC titrations. Again, the flexible region around 3(10)-helix III as well as residues of the peptide binding pocket showed the strongest chemical shift perturbations upon peptide binding. The local flexibility of this region also was modulated by ligand binding. A glycine and two positively charged residues are conserved in most parvulin proteins in this flexible loop region, which may be of general functional importance for parvulin-type PPIases.

Non-uniform frequency domain for optimal exploitation of non-uniform sampling

Random sampling of NMR signal, not limited by Nyquist Theorem, yields up to thousands-fold gain in the experiment time required to obtain desired spectral resolution. Discrete Fourier transform (DFT), that can be used for processing of randomly sampled datasets, provides rarely exploited possibility to introduce irregular frequency domain. Here we demonstrate how this feature opens an avenue to NMR techniques of ultra-high resolution and dimensionality. We present the application of high resolution 5D experiments for protein backbone assignment and measurements of coupling constants from the 4D E.COSY multiplets. Spectral data acquired with the use of proposed techniques allow easy assignment of protein backbone resonances and precise determination of coupling constants.

Correlation of (2)J couplings with protein secondary structure

Geminal two-bond couplings ((2)J) in proteins were analyzed in terms of correlation with protein secondary structure. NMR coupling constants measured and evaluated for a total six proteins comprise 3999 values of (2)J(CalphaN'), (2)J(C'HN), (2)J(HNCalpha), (2)J(C'Calpha), (2)J(HalphaC'), (2)J(HalphaCalpha), (2)J(CbetaC'), (2)J(N'Halpha), (2)J(N'Cbeta), and (2)J(N'C'), encompassing an aggregate 969 amino-acid residues. A seamless chain of pattern comparisons across the spectrum datasets recorded allowed the absolute signs of all (2)J coupling constants studied to be retrieved. Grouped by their mediating nucleus, C', N' or C(alpha), (2)J couplings related to C' and N' depend significantly on phi,psi torsion-angle combinations. beta turn types I, I', II and II', especially, can be distinguished on the basis of relative-value patterns of (2)J(CalphaN'), (2)J(HNCalpha), (2)J(C'HN), and (2)J(HalphaC'). These coupling types also depend on planar or tetrahedral bond angles, whereas such dependences seem insignificant for other types. (2)J(HalphaCbeta) appears to depend on amino-acid type only, showing negligible correlation with torsion-angle geometry. Owing to its unusual properties, (2)J(CalphaN') can be considered a "one-bond" rather than two-bond interaction, the allylic analog of (1)J(N'Calpha), as it were. Of all protein J coupling types, (2)J(CalphaN') exhibits the strongest dependence on molecular conformation, and among the (2)J types, (2)J(HNCalpha) comes second in terms of significance, yet was hitherto barely attended to in protein structure work.

Iterative algorithm of discrete Fourier transform for processing randomly sampled NMR data sets

Spectra obtained by application of multidimensional Fourier Transformation (MFT) to sparsely sampled nD NMR signals are usually corrupted due to missing data. In the present paper this phenomenon is investigated on simulations and experiments. An effective iterative algorithm for artifact suppression for sparse on-grid NMR data sets is discussed in detail. It includes automated peak recognition based on statistical methods. The results enable one to study NMR spectra of high dynamic range of peak intensities preserving benefits of random sampling, namely the superior resolution in indirectly measured dimensions. Experimental examples include 3D (15)N- and (13)C-edited NOESY-HSQC spectra of human ubiquitin.

A non-uniformly sampled 4D HCC(CO)NH-TOCSY experiment processed using maximum entropy for rapid protein sidechain assignment

One of the stiffest challenges in structural studies of proteins using NMR is the assignment of sidechain resonances. Typically, a panel of lengthy 3D experiments are acquired in order to establish connectivities and resolve ambiguities due to overlap. We demonstrate that these experiments can be replaced by a single 4D experiment that is time-efficient, yields excellent resolution, and captures unique carbon-proton connectivity information. The approach is made practical by the use of non-uniform sampling in the three indirect time dimensions and maximum entropy reconstruction of the corresponding 3D frequency spectrum. This 4D method will facilitate automated resonance assignment procedures and it should be particularly beneficial for increasing throughput in NMR-based structural genomics initiatives.

A set of 4D NMR experiments of enhanced resolution for easy resonance assignment in proteins

This paper presents examples of techniques based on the principle of random sampling that allows acquisition of NMR spectra featuring extraordinary resolution. This is due to increased dimensionality and maximum evolution time reached. The acquired spectra of CsPin protein and maltose binding protein were analyzed statistically with the aim to evaluate each technique. The results presented include exemplary spectral cross-sections. The spectral data provided by the proposed techniques allow easy assignment of backbone and side-chain resonances.

Complete (1)H and (13)C signal assignment of prenol-10 with 3D NMR spectroscopy

The complete assignment of (1)H and (13)C chemical shifts of natural abundance prenol-10 is reported for the first time. It was achieved using 3D NMR experiments, which were based on random sampling of the evolution time space followed by multidimensional Fourier transform. This approach makes it possible to acquire 3D NMR spectra in a reasonable time and preserves high resolution in indirectly detected dimensions. It is shown that the interpretation of 3D COSY-HMBC and 3D TOCSY-HSQC spectra is crucial in the structural analysis of prenol-10.

Spectroscopy by integration of frequency and time domain information for fast acquisition of high-resolution dark spectra

A simple and effective method, SIFT (spectroscopy by integration of frequency and time domain information), is introduced for processing nonuniformly sampled multidimensional NMR data. Applying the computationally efficient Gerchberg-Papoulis (G-P) algorithm, used previously in picture processing and medical imaging, SIFT supplements data at nonuniform points in the time domain with the information carried by known "dark" points (i.e., empty regions) in the frequency domain. We demonstrate that this rapid integration not only removes the severe pseudonoise characteristic of the Fourier transforms of nonuniformly sampled data, but also provides a robust procedure for using frequency information to replace time measurements. The latter can be used to avoid unnecessary sampling in sampling-limited experiments, and the former can be used to take advantage of the ability of nonuniformly sampled data to minimize trade-offs between the signal-to-noise ratio and the resolution in sensitivity-limited experiments. Processing 2D and 3D data sets takes about 0.1 and 2 min, respectively, on a personal computer. With these several attractive features, SIFT offers a novel, model-independent, flexible, and user-friendly tool for efficient and accurate processing of multidimensional NMR data.

Narrow peaks and high dimensionalities: exploiting the advantages of random sampling

Level of artifacts in spectra obtained by Multidimensional Fourier Transform has been studied, considering randomly sampled signals of high dimensionality and long evolution times. It has been shown theoretically and experimentally, that this level is dependent on the number of time domain samples, but not on its relation to the number of points required in appropriate conventional experiment. Independence of the evolution time domain size (in the terms of both: dimensionality and evolution time reached), suggests that random sampling should be used rather to design new techniques with large time domain than to accelerate standard experiments. 5D HC(CC-TOCSY)CONH has been presented as the example of such approach. The feature of Multidimensional Fourier Transform, namely the possibility of calculating spectral values at arbitrary chosen frequency points, allowed easy examination of resulting spectrum. We present the example of such approach, referred to as Sparse Multidimensional Fourier Transform.

Determination of heteronuclear coupling constants from 3D HSQC-TOCSY experiment with optimized random sampling of evolution time space

An application of 3D version of HSQC-TOCSY experiment for the measurement of heteronuclear coupling constants of organic compounds yielding complex spectra is proposed. The approach presented here is based on the optimized random sampling of the evolution time space followed by Multidimensional Fourier Transform (MFT). In this study, we show that the interpretation of omega(3)-(13)C coupled (1)H-(13)C 3D HSQC-TOCSY spectra with E.COSY-type multiplets allows one to evaluate heteronuclear coupling constants of strychnine with high accuracy, whereas the employment of 2D methods is associated with signal overlap and use of conventionally recorded 3D NMR spectra cannot provide accurate results in an overnight experiment.