Use of the Cadzow procedure in 2D NMR for the reduction of t1 noise

Summary A data processing approach is proposed for reducing the t₁ noise observed in multidimensional NMR spectra. This method is based on the use of the Cadzow procedure [Cadzow, J.A. (1988) IEEE Trans. Acous. Speech Signal Proc., 36, 49–62], and is demonstrated to be efficient for simulated cases as well as real experiments.     

Reconstruction of the three-dimensional NMR spectrum of a protein from a set of plane projections

Three-dimensional protein NMR spectra can be obtained significantly faster than by traditional methods by a projection-reconstruction procedure related to X-ray tomography. First, two orthogonal projections are acquired in quick two-dimensional experiments with the evolution parameters t₁ or t₂ set to zero. These projections define a three-dimensional lattice; all cross-peaks must lie on this lattice but not all lattice points are occupied. A third experiment with t₁ and t₂ incremented simultaneously and in a fixed ratio, generates a projection onto a tilted plane and thus establishes the positions of all the cross-peaks unambiguously. This projection-reconstruction technique has been tested on the 500 MHz three-dimensional HNCO spectrum of ubiquitin.     

Some practical aspects of B0 gradient pulses

Summary Pulsed field gradients used together with trim pulses may cause artifacts in NMR spectra that originate from partial refocusing of dephased magnetization. These effects can reduce the efficiency of solvent suppression. The duration of the trim and PFG pulses should be in the range in which refocusing is negligible. Background gradients due to bad shimming also interfere with the B₀ field gradient pulses, producing gradient-recalled echoes that reduce the receiver gain for NMR experiments. The shim settings can be optimized using simple experiments, as described in this paper. Eddy currents that cannot be completely compensated by adjustments of preemphasis induce phase shifts in NMR signals. The decay constants for a given spectrometer setup can easily be measured. If the experiment does not allow for proper compensation delays, the phase of the pulses must be adjusted to compensate for these phase shifts.     

Processing of ND NMR spectra sampled in polar coordinates: a simple Fourier transform instead of a reconstruction

In order to reduce the acquisition time of multidimensional NMR spectra of biological macromolecules, projected spectra (or in other words, spectra sampled in polar coordinates) can be used. Their standard processing involves a regular FFT of the projections followed by a reconstruction, i.e. a non-linear process. In this communication, we show that a 2D discrete Fourier transform can be implemented in polar coordinates to obtain directly a frequency domain spectrum. Aliasing due to local violations of the Nyquist sampling theorem gives rise to base line ridges but the peak line-shapes are not distorted as in most reconstruction methods. The sampling scheme is not linear and the data points in the time domain should thus be weighted accordingly in the polar FT; however, artifacts can be reduced by additional data weighting of the undersampled regions. This processing does not require any parameter tuning and is straightforward to use. The algorithm written for polar sampling can be adapted to any sampling scheme and will permit to investigate better compromises in terms of experimental time and lack of artifacts.     

Optimizing resolution in multidimensional NMR by three-way decomposition

Resolution depends on the number of points sampled in a FID; in indirectly detected dimensions it is an important determinant of the total experiment time. Based on the high redundancy present in NMR data, we propose the following timesaving scheme for three-dimensional spectra. An extensive grid of discrete t1- and t2-values is used, which increases resolution while preserving the spectral width. Total experiment time is reduced by avoiding the recording of t3-FIDs for selected pairs of t1 and t2; typically the recording is omitted for about 75% of the (t1,t2) combinations. These data sets are referred to as sparse, and post-experimental processing making optimal use of spectral redundancy provides the missing, non-recorded data. We have previously shown that three-way decomposition (TWD) within the MUNIN approach provides a practical way to process dense NMR data sets. Here, a novel TWD algorithm [Ibraghimov, (2002) Numer. Linear Algebra Appl. 9, 551–565] is used to complement a sparselyrecorded time-domain data set by providing the missing FIDs for all (t1,t2) combinations omitted in the experiment. A necessary condition is that for each t1-value at least a few FIDs are recorded, and similar for each t2-value. The method is demonstrated on non-uniformly sampled ¹⁵N-NOESY-HSQC data sets recorded for the 14 kD protein azurin. The spectra obtained by TWD, reconstruction and ordinary transform to frequency-domain are, in spite of the large number of signals and the high dynamic range typical for NOESYs, highly similar to a corresponding reference spectrum, for which all (t1,t2) combinations were recorded.     

Spatially encoded strategies in the execution of biomolecular-oriented 3D NMR experiments

Three-dimensional nuclear magnetic resonance (3D NMR) provides one of the foremost analytical tools available for the elucidation of biomolecular structure, function and dynamics. Executing a 3D NMR experiment generally involves scanning a series of time-domain signals S(t ₃), as a function of two time variables (t ₁, t ₂) which need to undergo parametric incrementations throughout independent experiments. Recent years have witnessed extensive efforts towards the acceleration of this kind of experiments. Among the different approaches that have been proposed counts an “ultrafast” scheme, which distinguishes itself from other propositions by enabling—at least in principle—the acquisition of the complete multidimensional NMR data set within a single transient. 2D protein NMR implementations of this single-scan method have been demonstrated, yet its potential for 3D acquisitions has only been exemplified on model organic compounds. This publication discusses a number of strategies that could make these spatial encoding protocols compatible with 3D biomolecular NMR applications. These include a merging of 2D ultrafast NMR principles with temporal 2D encoding schemes, which can yield 3D HNCO spectra from peptides and proteins within ≈100 s timescales. New processing issues that facilitate the collection of 3D NMR spectra by relying fully on spatial encoding principles are also assessed, and shown capable of delivering HNCO spectra within 1 s timescales. Limitations and prospects of these various schemes are briefly addressed.     

Optimization of <Superscript>1</Superscript>H decoupling eliminates sideband artifacts in 3D TROSY-based triple resonance experiments

TROSY-based triple resonance experiments are essential for protein backbone assignment of large biomolecular systems by solution NMR spectroscopy. In a survey of the current Bruker pulse sequence library for TROSY-based experiments we found that several sequences were plagued by artifacts that affect spectral quality and hamper data analysis. Specifically, these experiments produce sidebands in the ¹³C(t ₁) dimension with inverted phase corresponding to ¹H_N resonance frequencies, with approximately 5% intensity of the parent ¹³C crosspeaks. These artifacts originate from the modulation of the ¹H_N frequency onto the resonance frequency of ¹³Cα and/or ¹³Cβ and are due to 180° pulses imperfections used for ¹H decoupling during the ¹³C(t ₁) evolution period. These sidebands can become severe for CA_i, CA_i?1 and/or CB_i, CB_i?1 correlation experiments such as TROSY-HNCACB. Here, we implement three alternative decoupling strategies that suppress these artifacts and, depending on the scheme employed, boost the sensitivity up to 14% on Bruker spectrometers. A class of comparable Agilent/Varian pulse sequences that use WALTZ16 ¹H decoupling can also be improved by this method resulting in up to 60–80% increase in sensitivity.     

Improved quantification from 1H-NMR spectra using reduced repetition times

A method of choosing the correction factor based on Bloch equation for the quantitative estimation of metabolite from ¹H NMR spectra recorded with reduced recycle delay is prescribed. The procedure reduces the experimental time without substantially compromising the accuracy of quantitative estimation. It is based on choosing the correction factors, which depend on T₁ and T₂ of the metabolite and recycle delay used for recording the spectra. It is validated by studying a mixture of amino acids with known concentration of constituents and human serum sample and it provides accuracy of quantitative estimation to 95–96%.     

VirtualSpectrum,a tool for simulating peak list for multi-dimensional NMR spectra

NMR spectroscopy is a widely used technique for characterizing the structure and dynamics of macromolecules. Often large amounts of NMR data are required to characterize the structure of proteins. To save valuable time and resources on data acquisition, simulated data is useful in the developmental phase, for data analysis, and for comparison with experimental data. However, existing tools for this purpose can be difficult to use, are sometimes specialized for certain types of molecules or spectra, or produce too idealized data. Here we present a fast, flexible and robust tool, VirtualSpectrum, for generating peak lists for most multi-dimensional NMR experiments for both liquid and solid state NMR. It is possible to tune the quality of the generated peak lists to include sources of artifacts from peak overlap, noise and missing signals. VirtualSpectrum uses an analytic expression to represent the spectrum and derive the peak positions, seamlessly handling overlap between signals. We demonstrate our tool by comparing simulated and experimental spectra for different multi-dimensional NMR spectra and analyzing systematically three cases where overlap between peaks is particularly relevant; solid state NMR data, liquid state NMR homonuclear ¹H and ¹⁵N-edited spectra, and 2D/3D heteronuclear correlation spectra of unstructured proteins. We analyze the impact of protein size and secondary structure on peak overlap and on the accuracy of structure determination based on data of different qualities simulated by VirtualSpectrum.     

Preparation and characterization of oxochromium(IV) and nickel(II) complexes with 5,14-dihydro-7,16-diethyl-(E)- or -(Z)-dipyrido[b,i][1,4,8,11]tetraazacyclotetradecine

The reaction of 5,14-dihydro-7,16-diethyl-(E) or -(Z)-dipyrido[b,i][1,4,8,11]tetraazacyclotetradecine with chromium hexacarbonyl produced the corresponding oxochromium(IV) complexes. These compounds had intense bands in the infrared region at 985 cm⁻¹, which are attributed to the CrO stretching modes. The two complexes gave mass spectra with prominent parent and parent-O peaks. On the other hand the mass spectra for the nickel(II) complexes showed parent and parent-CH₃ peaks. The absorption bands appearing in the energy range greater than 19 000 cm⁻¹ were attributable to the π→π* and CT transitions. Consistent with their diamagnetism, the oxochromium complexes gave well-resolved proton NMR and carbon-13 NMR spectra. The magnitude of downfield shifts for the oxochromium(IV) complex is much larger than that observed for the corresponding nickel(II) complex. This is due to the fact that the positive charge provided by chromium(IV) is greater in magnitude than that by nickel(II).     

RESPIRATION AND PROTEIN SYNTHESIS IN ESCHERICHIA COLI MEMBRANE-ENVELOPE FRAGMENTS : III. Electron Microscopy and Analysis of the Cytochromes

The membranous nature of pellets obtained from broken Escherichia coli spheroplasts by successive centrifugation at 3500 g (P₁), 20,000 g (P₂), and 105,000 g (P₃), has been established by electron microscopy. Spectrophotometric analysis has shown that about 90% of the cytochromes are concentrated in the particulate fractions. The crude ribosomal pellet (P₃) contained as much of the total cytochromes as did the pellet obtained at 20,000 g (P₂). The high cytochrome content of P₃ is consistent with its high oxidative activity (1) and the presence of membrane vesicles in this fraction. Analysis at 77°K intensified the optical extinction of all the cytochrome absorption bands, but the degree of intensification was not uniform for each fraction nor for each band within a given fraction. Carbon monoxide had little or no inhibiting effect on NADH oxidation. Reduced plus carbon monoxide difference spectra yielded artifactual absorption bands in the wave length regions where reduced vs. oxidized absorption bands normally occur. Succinate and NADH, either together or separately, reduced nearly all of the cytochromes, indicating that the cytochrome portion of the electron-transport chain is shared by both substrates. A tentative formulation of the electron-transport chain is presented.     

A two-dimensional nuclear Overhauser enhancement (2D NOE) experiment for the elucidation of complete proton-proton cross-relaxation networks in biological macromolecules

The recently developed technique of two-dimensional (2D) cross-relaxation spectroscopy is utilized for systematic measurements of selective nuclear Overhauser enhancements (NOE) in the high resolution ¹H nuclear magnetic resonance (NMR) spectra of biological macromolecules in solution. Compared to conventional one-dimensional NOE studies, the 2D NOE experiment has the principal advantage that it avoids detrimental effects arising from the limited selectivity of preirradiation in crowded spectral regions. Furthermore, it yields with a single instrument setting a complete network of NOE's between all the protons in the macromolecule. The resulting information on intramolecular proton-proton distances provides a new avenue for studies of the spatial structures of biopolymers.     

Interpolating and extrapolating with hmsIST: seeking a t<Subscript>max</Subscript> for optimal sensitivity,resolution and frequency accuracy

Non-Uniform Sampling has the potential to exploit the optimal resolution of high-field NMR instruments. This is not possible in 3D and 4D NMR experiments when using traditional uniform sampling due to the long overall measurement time. Nominally, uniformly sampled time domain data acquired to a maximum evolution time t_max can be extended to high resolution via a virtual maximum evolution time t*_max while extrapolating with linear prediction or iterative soft thresholding (IST). At the high resolution obtainable with extrapolation of US data, however, the accuracy of peak positions is compromised as observed when comparing inter- and intra-residue peaks in a 3D HNCA experiment. However, the accuracy of peak positions is largely improved by spreading the same number of acquired time domain data points non-uniformly over a larger evolution time to an optimal t_max followed by extrapolation to a total t*_max and processing the data with an appropriate reconstruction method, such as hmsIST. To explore the optimum value of experimentally measured t_max to be reached non-uniformly with a given number of sampling points we have created test situations of time-equivalent experiments and evaluate sensitivity and accuracy of peak positions. Here we use signal-to-maximum-noise ratio as the decisive measure of sensitivity. We find that both sensitivity and resolution are optimal when PoissonGap sampling to a t_max of about ½*T₂ ^*. Digital resolution is further enhanced by extrapolating the range of acquired time domain data to 2*T₂ ^* but without measuring experimental points beyond ½*T₂ ^*.     

A Robust Post-Processing Workflow for Datasets with Motion Artifacts in Diffusion Kurtosis Imaging

Purpose

The aim of this study was to develop a robust post-processing workflow for motion-corrupted datasets in diffusion kurtosis imaging (DKI).

Materials and methods

The proposed workflow consisted of brain extraction, rigid registration, distortion correction, artifacts rejection, spatial smoothing and tensor estimation. Rigid registration was utilized to correct misalignments. Motion artifacts were rejected by using local Pearson correlation coefficient (LPCC). The performance of LPCC in characterizing relative differences between artifacts and artifact-free images was compared with that of the conventional correlation coefficient in 10 randomly selected DKI datasets. The influence of rejected artifacts with information of gradient directions and b values for the parameter estimation was investigated by using mean square error (MSE). The variance of noise was used as the criterion for MSEs. The clinical practicality of the proposed workflow was evaluated by the image quality and measurements in regions of interest on 36 DKI datasets, including 18 artifact-free (18 pediatric subjects) and 18 motion-corrupted datasets (15 pediatric subjects and 3 essential tremor patients).

Results

The relative difference between artifacts and artifact-free images calculated by LPCC was larger than that of the conventional correlation coefficient (p<0.05). It indicated that LPCC was more sensitive in detecting motion artifacts. MSEs of all derived parameters from the reserved data after the artifacts rejection were smaller than the variance of the noise. It suggested that influence of rejected artifacts was less than influence of noise on the precision of derived parameters. The proposed workflow improved the image quality and reduced the measurement biases significantly on motion-corrupted datasets (p<0.05).

Conclusion

The proposed post-processing workflow was reliable to improve the image quality and the measurement precision of the derived parameters on motion-corrupted DKI datasets. The workflow provided an effective post-processing method for clinical applications of DKI in subjects with involuntary movements.     

A general Monte Carlo/simulated annealing algorithm for resonance assignment in NMR of uniformly labeled biopolymers

We describe a general computational approach to site-specific resonance assignments in multidimensional NMR studies of uniformly ¹⁵N,¹³C-labeled biopolymers, based on a simple Monte Carlo/simulated annealing (MCSA) algorithm contained in the program MCASSIGN2. Input to MCASSIGN2 includes lists of multidimensional signals in the NMR spectra with their possible residue-type assignments (which need not be unique), the biopolymer sequence, and a table that describes the connections that relate one signal list to another. As output, MCASSIGN2 produces a high-scoring sequential assignment of the multidimensional signals, using a score function that rewards good connections (i.e., agreement between relevant sets of chemical shifts in different signal lists) and penalizes bad connections, unassigned signals, and assignment gaps. Examination of a set of high-scoring assignments from a large number of independent runs allows one to determine whether a unique assignment exists for the entire sequence or parts thereof. We demonstrate the MCSA algorithm using two-dimensional (2D) and three-dimensional (3D) solid state NMR spectra of several model protein samples (α-spectrin SH3 domain and protein G/B1 microcrystals, HET-s_218–289 fibrils), obtained with magic-angle spinning and standard polarization transfer techniques. The MCSA algorithm and MCASSIGN2 program can accommodate arbitrary combinations of NMR spectra with arbitrary dimensionality, and can therefore be applied in many areas of solid state and solution NMR.     

Regression imputation of missing values in longitudinal data sets

A stand-alone, menu-driven PC program, written in GAUSS, which can be used to estimate missing observations in longitudinal data sets is described and made available to interested readers. The program is limited to the situation in which we have complete data on N cases at each of the planned times of measurement t₁, t₂,…, t_T; and we wish to use this information, together with the non-missing values for n additional cases, to estimate the missing values for those cases. The augmented data matrix may be saved in an ASCII file and subsequently imported into programs requiring complete data. The use of the program is illustrated. Ten percent of the observations in a data set consisting of mandibular ramus height measurements for N = 12 young male rhesus monkeys measured at T = 5 time points are randomly discarded. The augmented data matrix is used to determine the lowest degree polynomial adequate to fit the average growth curve (AGC); the regression coefficients are estimated and confidence intervals for them are determined; and confidence bands for the AGC are constructed. The results are compared with those obtained when the original complete data set is used.     

Characterization of cryptomonad phycoerythrin and phycocyanin

Phycoerythrin, a chromoprotein, from the cryptomonad alga Rhodomonas lens is composed of two pairs of nonidentical polypeptides (α₂β₂). This structure is indicated by a molecular weight of 54,300, calculated from osmotic pressure measurements and by sodium dodecyl sulfate (SDS) gel electrophoresis, which showed bands with molecular weights of 9800 and 17,700 in a 1:1 molar ratio. The s_20,w⁰ of 4.3S is consistent with a protein of this molecular weight. Similar results were obtained with another cryptomonad phycoerythrin and a cryptomonad phycocyanin. Electrophoresis after partial cross-linking by dimethyl suberimidate revealed seven bands for the cryptomonad phycocyanin and six bands for cryptomonad phycoerythrin and confirmed the proposed structure. Spectroscopic studies on α and β subunits of cryptomonad phycocyanin and phycoerythrin were carried out on the separated bands in SDS gels. The individual polypeptides possessed a single absorption band with the following maxima: phycoerythrin (R. lens), α at 565 nm, β at 531 nm; phycocyanin (Chroomonas sp.), α at 644 nm, β at 566 nm. Fluorescence polarization was not constant across the visible absorption band regions of phycoerythrin (R. lens and C. ovata) with higher polarizations located at higher wavelengths, as had also been previously shown for cryptomonad phycocyanin (Chroomonas sp.). Combining the absorption spectra and the polarization results indicates that in each case the β subunit contains sensitizing chromophores and the α subunit fluorescing chromophores. The CD spectra of cryptomonad phycocyanin and both phycoerythrins were similar and were related to the spectra of the individual subunits. In Ouchterlony double-diffusion experiments the cryptomonad phycoerythrins and phycocyanins cross-reacted, with spurring, with phycoerythrin isolated from a red alga. The cryptomonad phycoerythrins were immunochemically very similar to each other and to cryptomonad phycocyanin, with little spurring detected.     

FTIR Emission Spectra of Bacteriorhodopsin in a Vibrational Excited-State

Vibrational IR-emission spectra of bacteriorhodopsin (bR) were recorded under continuous illumination with visible light at room temperature. They contain selective information about the chromophore, Schiff base, and opsin. The spectral bands were identified by comparing the data with resonance Raman and IR absorption data. The IR-emission spectra were shown to contain a set of bands characteristic for both all-trans (bR₅₆₈) and 13-cis conformations (K₆₁₀-like intermediate) simultaneously. Variation of spectral composition and the intensity of visible light illumination influenced the spectral traces and intensity distribution between them. Greater intensity of deformational vibrations suggests distorted retinal structure in the vibrationally excited ground electronic state. The origin of the emitting species of bR is discussed.     

Polarized Raman scattering from oriented single microcrystals of d(A5T5)2 and d(pTpT)

Polarized Raman spectra have been obtained from single microcrystals of the duplex of the decamer d(A₅T₅)₂ using a Raman microscope. This is the first report of Raman spectra from a crystal of a deoxyoligomer that contains only long, nonalternating sequences of adenine and thymine. Sequences containing d(A)_n and d(T)_n are of interest in view of recent suggestions that they induce bends in DNA and that they might exist in a nonstandard B-conformation. Polarized Raman spectra of a crystal of d(pTpT) have also been obtained. Both crystals display Raman bands whose intensities are very sensitive to the orientation of the crystal with respect to the direction of polarization of the incident laser beam. These spectra indicate that the helical axes of the oligonucleotides are parallel to the long axes of the crystals and that the d(A₅T₅)₂ is not appreciably bent in the crystal. The Raman spectrum from the d(pTpT) crystal indicates that all of the furanose ring puckers are in a C2′-endo configuration since only the C2′-endo marker band at 835 ± 5 cm^?1 is present. Crystals of d(A₅T₅)₂ show measurable Raman intensities in both the 838- and 816-cm^?1 bands. This indicates the presence of both the C2′-endo and C3′-endo, or possibly other non-C2′-endo, furanose conformations. The 816-cm^?1 band is weak so that only a small fraction of the residues are estimated to be in the non-C2′-endo conformation. In both the d(pTpT) and d(A₅T₅)₂ crystals the intensity of the bands due to vibrations of the backbone show only a small dependence on orientation of the crystals. This result is explained by the low symmetry of the puckered sugar rings. It is concluded that Raman spectra obtained from oligonucleotide crystals in which the orientation of the crystal axes to the laser polarization is not carefully controlled may contain intensity artifacts that are due to polarization effects.