"Ersatz" and "hybrid" NMR spectral estimates using the filter diagonalization method.

The filter diagonalization method (FDM) is an efficient and elegant way to make a spectral estimate purely in terms of Lorentzian peaks. As NMR spectral peaks of liquids conform quite well to this model, the FDM spectral estimate can be accurate with far fewer time domain points than conventional discrete Fourier transform (DFT) processing. However, noise is not efficiently characterized by a finite number of Lorentzian peaks, or by any other analytical form, for that matter. As a result, noise can affect the FDM spectrum in different ways than it does the DFT spectrum, and the effect depends on the dimensionality of the spectrum. Regularization to suppress (or control) the influence of noise to give an "ersatz", or EFDM, spectrum is shown to sometimes miss weak features, prompting a more conservative implementation of filter diagonalization. The spectra obtained, called "hybrid" or HFDM spectra, are acquired by using regularized FDM to obtain an "infinite time" spectral estimate and then adding to it the difference between the DFT of the data and the finite time FDM estimate, over the same time interval. HFDM has a number of advantages compared to the EFDM spectra, where all features must be Lorentzian. They also show better resolution than DFT spectra. The HFDM spectrum is a reliable and robust way to try to extract more information from noisy, truncated data records and is less sensitive to the choice of regularization parameter. In multidimensional NMR of liquids, HFDM is a conservative way to handle the problems of noise, truncation, and spectral peaks that depart significantly from the model of a multidimensional Lorentzian peak.

Minimizing the overlap problem in protein NMR: a computational framework for precision amino acid labeling.

MOTIVATION: Recent advances in cell-free protein expression systems allow specific labeling of proteins with amino acids containing stable isotopes ((15)N, (13) C and (2)H), an important feature for protein structure determination by nuclear magnetic resonance (NMR) spectroscopy. Given this labeling ability, we present a mathematical optimization framework for designing a set of protein isotopomers, or labeling schedules, to reduce the congestion in the NMR spectra. The labeling schedules, which are derived by the optimization of a cost function, are tailored to a specific protein and NMR experiment. RESULTS: For 2D (15)N-(1)H HSQC experiments, we can produce an exact solution using a dynamic programming algorithm in under 2 h on a standard desktop machine. Applying the method to a standard benchmark protein, calmodulin, we are able to reduce the number of overlaps in the 500 MHz HSQC spectrum from 10 to 1 using four samples with a true cost function, and 10 to 4 if the cost function is derived from statistical estimates. On a set of 448 curated proteins from the BMRB database, we are able to reduce the relative percent congestion by 84.9% in their HSQC spectra using only four samples. Our method can be applied in a high-throughput manner on a proteomic scale using the server we developed. On a 100-node cluster, optimal schedules can be computed for every protein coded for in the human genome in less than a month. AVAILABILITY: A server for creating labeling schedules for (15)N-(1)H HSQC experiments as well as results for each of the individual 448 proteins used in the test set is available at http://nmr.proteomics.ics.uci.edu.

SOGGY: solvent-optimized double gradient spectroscopy for water suppression. A comparison with some existing techniques.

Excitation sculpting, a general method to suppress unwanted magnetization while controlling the phase of the retained signal [T.L. Hwang, A.J. Shaka, Water suppression that works. Excitation sculpting using arbitrary waveforms and pulsed field gradients, J. Magn. Reson. Ser. A 112 (1995) 275-279] is a highly effective method of water suppression for both biological and small molecule NMR spectroscopy. In excitation sculpting, a double pulsed field gradient spin echo forms the core of the sequence and pairing a low-power soft 180 degrees (-x) pulse with a high-power 180 degrees (x) all resonances except the water are flipped and retained, while the water peak is attenuated. By replacing the hard 180 degrees pulse in the double echo with a new phase-alternating composite pulse, broadband and adjustable excitation of large bandwidths with simultaneous high water suppression is obtained. This "Solvent-Optimized Gradient-Gradient Spectroscopy" (SOGGY) sequence is a reliable workhorse method for a wide range of practical situations in NMR spectroscopy, optimizing both solute sensitivity and water suppression.

Rapid high-resolution four-dimensional NMR spectroscopy using the filter diagonalization method and its advantages for detailed structural elucidation of oligosaccharides.

Four-dimensional nuclear magnetic resonance spectroscopy with high resolution of signals in the indirect dimensions is reported as an implementation of the filter diagonalization method (FDM). Using an oligosaccharide derivatized with 13C-labeled acetyl isotags, a four-dimensional constant-time pulse sequence was tailored for conjoint use with the FDM. Results demonstrate that high resolution in all dimensions can be achieved using a relatively short experimental time period (19 h), even though the spectrum is highly congested in the direct and all three indirect dimensions. The combined use of isotags, constant-time pulse sequences, and FDM permits rapid isolation of sugar ring proton spin systems in multiple dimensions and enables all endocyclic J-couplings to be simply measured, the key goal to assigning sugar stereochemistry and anomeric configuration. A general method for rapid, unambiguous elucidation of spin systems in oligosaccharides has been a long-sought goal of carbohydrate NMR, and isotags combined with the FDM now enable this to be easily performed. Additional general advantages of the FDM program for generating high-resolution 2D slices in any dimension from a 4D spectrum are emphasized.

Improved cross peak detection in two-dimensional proton NMR spectra using excitation sculpting.

In two-dimensional homonuclear experiments, reliable detection of very small cross peaks is sometimes hampered by t1-noise from larger diagonal peaks which have the same F2 frequency. This t1-noise can be selectively removed by recording partial 2D spectra using the double pulsed field gradient spin echo (DPFGSE). Resonances not selected by the DPFGSE do not contribute any t1-noise to the resulting spectrum. The absence of t1-noise from the diagonal peaks render the small cross peaks at the same F2 frequency observable. The success of this technique is shown by partial 2D NOESY and TOCSY spectra.

Multiple-pulse mixing sequences that selectively enhance chemical exchange or cross-relaxation peaks in high-resolution NMR spectra.

Rotating-frame NMR experiments which either emphasize or suppress cross relaxation, and which simultaneously suppress TOCSY, COSY, and zero-quantum peaks in NMR spectra, are presented and analyzed. The new experiments rely on mixing sequences which follow naturally from the transverse-ROESY (Tr-ROESY) sequence of Hwang and Shaka, and which are applicable to larger molecules in solution (spin diffusion limit). In the first variant a modified Tr-ROESY sequence, called multiple-pulse ROESY (MP-ROESY), is used to enhance cross-relaxation peak intensity compared to Tr-ROESY; in the second, called phase-modulated CLEAN chemical exchange (CLEANEX-PM), cross-relaxation peaks are greatly attenuated. The two methods are thus complementary: MP-ROESY is used to observe Overhauser peaks, and CLEANEX-PM is used to eliminate them, permitting clear observation of chemical exchange peaks alone. The new techniques are examined by theory and experiment. Practical guidelines that will result in high-quality spectra are given, including the judicious use of continuous weak static magnetic field gradients.

Composite pulsed field gradients with refocused chemical shifts and short recovery time.

An improved self-compensating pulsed field gradient (PFG) technique that combines antiphase gradient pairs with broadband frequency-modulated 180 degrees pulses is proposed. The antiphase gradient pairs lead to superb system recovery. In addition, evolution under chemical shift and heteronuclear J coupling are refocused during the PFG, making it appear effectively instantaneous. This new approach makes it possible to obtain high-resolution phase-sensitive 2D spectra for the PFG version of many experiments such as COSY, DQF-COSY, and HSQC without adding extra compensating delays or pulses. While reasonable suppression of unwanted magnetization is achieved, this method also gives satisfactory retention of desired signals. As a bonus, the field-frequency lock is not perturbed during the experiments.

Pure absorption electron spin echo envelope modulation spectra by using the filter-diagonalization method for harmonic inversion.

Harmonic inversion of electron spin echo envelope (ESEEM) time-domain signals by filter diagonalization is investigated as an alternative to Fourier transformation. It is demonstrated that this method features enhanced resolution compared to Fourier-transform magnitude spectra, since it can eliminate dispersive contributions to the line shape, even if no linear phase correction is possible. Furthermore, instrumental artifacts can be easily removed from the spectra if they are narrow either in time or frequency domain. This applies to echo crossings that are only incompletely eliminated by phase cycling and to spurious spectrometer frequencies, respectively. The method is computationally efficient and numerically stable and does not require extensive parameter adjustments or advance knowledge of the number of spectral lines. Experiments on gamma-irradiated methyl-alpha-d-glucopyranoside show that more information can be obtained from typical ESEEM time-domain signals by filter-diagonalization than by Fourier transformation.

Cascaded z-filters for efficient single-scan suppression of zero-quantum coherence.

A simple and robust method to suppress zero-quantum coherence (ZQC) in NMR experiments, in a single scan and with very high suppression ratio, is described. It is an appreciable improvement on a previous technique by Thrippleton and Keeler [Angew. Chem. Int. Ed. 42 (2003) 3938]. The method, called a z-filter cascade, preserves longitudinal, or z-magnetization, with high efficiency. Losses depend mostly on T1 relaxation but not T2 relaxation mechanisms. At the same time, suppression of ZQC can be essentially complete in a single scan. The time duration of the z-filter cascade scales inversely to representative chemical shift differences between the coupled spins, and is typically a few tens of milliseconds. The high efficiency of the zero-quantum suppression and excellent retention of the desired z-magnetization, in a single scan without resort to phase cycling or difference spectroscopy, makes the z-filter cascade a useful new pulse sequence building block for a whole range of NMR experiments. In cases where unwanted residual ZQC may have previously contributed to baseline " t1-noise" in two-dimensional NMR spectra, the z-filter cascade can deliver a noteworthy improvement in spectral quality.

Adjustable, broadband, selective excitation with uniform phase.

An advance in the problem of achieving broadband, selective, and uniform-phase excitation in NMR spectroscopy of liquids is outlined. Broadband means that, neglecting relaxation, any frequency bandwidth may be excited even when the available radiofrequency (RF) field strength is strictly limited. Selective means that sharp transition edges can be created between pure-phase excitation and no excitation at all. Uniform phase means that, neglecting spin-spin coupling, all resonance lines have nearly the same phase. Conventional uniform-phase excitation pulses (e.g., E-BURP), mostly based on amplitude modulation of the RF field, are not broadband: they have an achievable bandwidth that is strictly limited by the peak power available. Other compensated pulses based on adiabatic half-passage, like BIR-4, are not selective. By contrast, inversion pulses based on adiabatic fast passage can be broadband (and selective) in the sense above. The advance outlined is a way to reformulate these frequency modulated (FM) pulses for excitation, rather than just inversion.

Ultra-high resolution 3D NMR spectra from limited-size data sets.

The advantage of the filter diagonalization method (FDM) for analysis of triple-resonance NMR experiments is demonstrated by application to a 3D constant time (CT) HNCO experiment. With a 15N-,13C-labeled human ubiquitin sample (1.0 mM), high spectral resolution was obtained at 500 MHz in 25 min with only 6-8 increments in each of the CT dimensions. This data set size is about a factor of 50-100 smaller than typically required, yet FDM analysis results in a fully resolved spectrum with a sharp peak for each HNCO resonance. Unlike Fourier transform (FT) processing, in which spectral resolution in each dimension is inversely proportional to the acquisition time in this dimension, FDM is a true multi-dimensional method; the resolution in all dimensions is determined by the total information content of the entire signal. As the CT dimensions of the 3D HNCO signal have approximate time-reversal symmetry, they can each be doubled by combining the usual four hyper-complex data sets. This apparent quadrupling of the data is important to the success of the method. Thus, whenever raw sensitivity is not limiting, well-resolved n-dimensional spectra can now be obtained in a small fraction of the usual time. Alternatively, to maximize sensitivity, evolution periods of faster relaxing nuclei may be radically shortened, the total required resolution being obtained through chemical shift encoding of other, more slowly relaxing, spins. Improvements similar to those illustrated with a 3D HNCO spectrum are expected for other triple-resonance spectra, where CT evolution in the indirect dimensions is implemented.

Observation of long-range small-molecule NOEs using a neoteric sensitivity enhancement scheme.

A new method to increase the sensitivity of the 1D transient NOE experiment for molecules in the positive NOE regime is presented. This method, the reverse NOE, simply replaces the conventional relaxation delay between scans. Transient positive NOE enhancements from all other spins are used to accelerate the recovery of the target resonance toward its equilibrium intensity. In favorable cases, the intensity of the target peak at the start of an experiment can actually be increased beyond its equilibrium value. There is also a sensitivity enhancement in the rapid pulsing regime, where recovery is always incomplete. This sensitivity enhancement is illustrated with the one-dimensional double pulsed field gradient spin echo NOE experiment to observe a "fourth-order" NOE. Sensitivity gains of 30% are demonstrated.

Reference deconvolution, phase correction, and line listing of NMR spectra by the 1D filter diagonalization method.

We describe a new way to attack the problem of identifying and quantifying the number of NMR transitions in a given NMR spectrum. The goal is to reduce the spectrum to a tabular line list of peak positions, widths, amplitudes, and phases, and to have this line list be of high fidelity. In this context "high fidelity" means that each true NMR transition is represented by a single entry, with no spurious entries and no missed peaks. A high fidelity line list allows the measurement of chemical shifts and coupling constants with good accuracy and precision and is the ultimate in data compression. There are two parts to the problem. The first is to overcome common imperfections: the non-Lorentzian lineshapes that can arise whenever the magnetic field inhomogeneity is less than perfect, and nonzero time delays that cause frequency-dependent phase errors. The second is to fit the spectral features to a model of Lorentzian lines. We use the recently developed filter diagonalization method (FDM) to accomplish the reference deconvolution, the phase correction, and the fitting, and show good progress toward the goal of obtaining a high fidelity line list.

Processing DOSY spectra using the regularized resolvent transform.

A new method for processing diffusion ordered spectroscopy (DOSY) data is presented. This method, the regularized resolvent transform (iRRT-the i denoting the adaptation of the method to evaluate the inverse Laplace transform), is better than conventional processing techniques for generating 2D DOSY spectra using data that has poor chemical shift resolution. From the same data, it is possible to use the iRRT to generate 1D subspectra corresponding to different components of the sample mixture; these subspectra compare favorably to 1D spectra of the pure substances. Both the 2D spectra and the 1D subspectra offer a vast improvement over results generated using a conventional processing technique (non-linear least-squares fitting). Consequently, we present the iRRT as a stable and reliable tool for solving the inverse Laplace transform problem present in experiments such as DOSY.

Progress on the two-dimensional filter diagonalization method. An efficient doubling scheme for two-dimensional constant-time NMR.

An efficient way to treat two-dimensional (2D) constant-time (CT) NMR data using the filter diagonalization method (FDM) is presented. In this scheme a pair of N- and P-type data sets from a 2D CT NMR experiment are processed jointly by FDM as a single data set, twice as large, in which the signal effectively evolves in time for twice as long. This scheme is related to "mirror-image" linear prediction, but with the distinction that the data are directly used, without any preprocessing such as Fourier transformation along one dimension, or point-by-point reflection. As the signal has nearly perfect Lorentzian line shape in the CT dimension, it can be efficiently handled by the FDM approach. Applied to model and experimental signals, the scheme shows significant resolution improvement, and appears to tolerate noise reasonably well. Other complex aspects of multidimensional FDM are discussed and illustrated.

Regularized resolvent transform for direct calculation of 45 degrees projections of 2D J spectra.

The regularized resolvent transform (RRT) has been applied in a novel way to J-resolved spectra. This involves the direct calculation of the 45 degrees projection without constructing the 2D spectrum. The results show a significant resolution enhancement over that obtained by the 45 degrees projection of a 2D Fourier spectrum, even for much larger signals. In particular, RRT is able to resolve peaks that belong to different overlapping multiplets in a very crowded spectral region, where the conventional technique fails for any signal size. The resolving power of this method along with the significantly shorter signals required, make this method a powerful tool in spectral assignment.

The multidimensional filter diagonalization method.

The theory of the multidimensional filter diagonalization method (FDM) described in the previous paper (V. A. Mandelshtam, 2000, J. Magn. Reson. 144, 343-356 (2000)) is applied to NMR time signals with up to four independent time variables. Direct projections of the multidimensional time signals produce new kinds of 2D spectra. The resolution obtained by FDM can be far superior to that obtained by conventional phase-sensitive FT processing, and correlation peaks in heteronuclear and homonuclear experiments can be condensed to sharp singlets, removing all spin-spin couplings. Examples of singlet-HSQC and singlet-TOCSY spectra show big gains in resolution. It is not necessary to have a finely digitized spectrum, in which the individual multiplet components are resolved, for the methods to work. Examples of FDM spectra, ranging from simple organic molecules and steroids to metalloproteins, are shown.

Rapid 3D NMR using the filter diagonalization method: application to oligosaccharides derivatized with 13C-labeled acetyl groups.

Rapid 3D NMR spectroscopy of oligosaccharides having isotopically labeled acetyl "isotags" was made possible with high resolution in the indirect dimensions using the filter diagonalization method (FDM). A pulse sequence was designed for the optimal correlation of acetyl methyl protons, methyl carbons, and carbonyl carbons. The multi-dimensional nature of the FDM, coupled with the advantages of constant-time evolution periods, resulted in marked improvements over Fourier transform (FT) and mirror-image linear prediction (MI-LP) processing methods. The three methods were directly compared using identical data sets. A highly resolved 3D spectrum was achieved with the FDM using a very short experimental time (28 min).

Application of the Tethered Biginelli Reaction for Enantioselective Synthesis of Batzelladine Alkaloids. Absolute Configuration of the Tricyclic Guanidine Portion of Batzelladine B.

Tethered Biginelli condensation of enantioenriched hexahydropyrrolopyrimidines 8 with beta-ketoesters provides efficient asymmetric access to tricyclic guanidines 9 having a syn relationship of the angular C2a and C8a hydrogens. This reaction was employed to realize the first practical enantioselective access to this fragment of batzelladine alkaloids B (2) and E (5). The efficiency of this strategy is illustrated in the synthesis of the dextrorotatory enantiomer of batzelladine B methanolysis product 10 in 10 steps and 25% overall yield from 2-nonanone and methyl acetoacetate. The asymmetric synthesis of 10 establishes that the absolute configuration of the tricyclic portion of batzelladine B (2) is 25aR,28S,30R. The 4-methyl-7-alkyl-1,2,2a,3,4,5,6,7,8,8a-decahydro-5,6,8b-triazaacenaphthalene-3-carboxylic acid subunit, e.g., 29, of batzelladine alkaloids A (1), D (4), F (6), and G was also prepared for the first time by catalytic hydrogenation of tricyclic guanidines 26 having the 2a,8a-anti stereochemistry.

Brief early-life non-specific incorporation of deuterium extends mean life span in Drosophila melanogaster without affecting fecundity.

We have investigated the effects of brief, non-specific deuteration of Drosophila melanogaster by including varying percentages of ²H (D) in the H2O used in the food mix consumed during initial development. Up to 22.5% deuterium oxide (D2O) in H2O was administered, with the result that a low percentage of D2O in the water increased mean life span, whereas the highest percentage used (22.5%) reduced life span. After the one-time treatment period, adult flies were maintained ad libitum with food of normal isotopic distribution. At low deuterium levels, where life span extension was observed, there was no observed change in fecundity. Dead flies were assayed for deuterium incorporation by complete hydrolysis in hot 12 N HCl solution followed by subsequent high-performance liquid chromatography/mass spectrometry (HPLC/MS). Isoleucine and leucine residues showed a small, linear dose-dependent incorporation of deuterium at non-exchangeable sites. Although high levels of D2O itself are toxic for other reasons, higher levels of deuterium incorporation, which can be achieved without toxicity by strategies that avoid direct use of D2O, are clearly worth exploring.