A systematic strategy for design of optimum coherent experiments applied to efficient interconversion of double‐ and single‐quantum coherences in nuclear magnetic resonance

1H NMR with Partial Transition Selectivity

¹H NMR has unique strengths, owing, for one, to ¹H being the most sensitive NMR nucleus. However, the limited frequency range of ¹H chemical shifts implies spectral crowding, leading to difficulties in assignment and interpretation of the spectra. Homonuclear broadband decoupling has been developed as a means of simplifying ¹H NMR spectra but clearly leads to the inevitable and complete loss of precious information on homonuclear scalar couplings in solution state. A novel experiment is introduced in this work, which leads to partial ¹H multiplet selectivity, thereby reducing spectral crowding, while at the same time permitting couplings to be inferred. The present one-dimensional (1D) experiment relies on two-way coherence transfer starting from ¹H to coupled ¹³C carbons at natural abundance and ending finally with ¹H detection. The experiment may be termed CArbon Single transition EDited (CASED) ¹H NMR. The unusual spectral patterns that result are summarized, demonstrated, and rationalized for various molecular fragments. Artifacts in the present version of the CASED experiment are also described, and an application to the ¹H NMR of a disaccharide is demonstrated as a first practical example.

ADEQUATE CR: 13C connectivity mapping in indirect detection mode with composite refocusing

We report a novel rare spin correlation experiment termed ADEQUATE with composite refocusing (CR), which is the (1)H-detected version of 2D INADEQUATE CR. ADEQUATE CR begins with a polarization transfer from protons to the attached carbon, followed by (13)C-(13)C double-quantum (DQ) preparation. Unlike the ADEQUATE class of experiments, (13)C DQ coherence is converted after evolution to single-quantum single transitions (SQ-STs) by CR. (13)C SQ-ST is then transferred back to the coupled protons by a coherence order selective reconversion. The present sequence produces partial transition selectivity in the (1)H dimension as does (1)H Indirect detected (13)C Low-Abundance Single-transition correlation Spectroscopy (HICLASS), thereby mitigating the reduction in sensitivity enhancement because of the presence of homonuclear proton couplings. However, unlike HICLASS (which is an experiment that involves SQ-TS evolution), no homonuclear zero quantum mixing is required on the (13)C channel in the present experiment. Experimental results are demonstrated on a variety of samples, establishing the efficiency of the proposed method.

HCSE method for detection of small carbon-carbon couplings and their signs, comparison with SLAP pulse sequence

Performance of homonuclear coupling sign edited (HCSE) experiment applied to detection of signed carbon-carbon couplings is discussed using a set of already measured samples of nine monosubstituted benzenes. It is shown that coupling sign detection is insensitive to the settings of carbon-carbon polarization transfer delays. The HCSE spectra of ten from the total of 43 measured carbon-carbon couplings were considerably influenced by relaxations and proton-proton strong couplings. These effects are quantitatively discussed. The results of HCSE and SLAP experiments are compared. It is shown that the two methods may complement each other in detection of signed carbon-carbon couplings.

1H Indirect detected 13C Low-Abundance Single-transition correlation Spectroscopy (HICLASS)-13C homonuclear correlation at natural abundance

A novel proton-detected (13)C homonuclear correlation experiment is reported at natural abundance, viz., (1)H Indirect detected (13)C Low-Abundance Single-transition correlation Spectroscopy (HICLASS). HICLASS is based on the evolution of (13)C single-quantum single transitions, followed by their mixing, and (1)H detection subsequent to heteronuclear transfer. Reduced relaxation losses during the evolution time and partial selectivity in the (1)H multiplet structure result in enhanced sensitivity of HICLASS. The superior performance of HICLASS is demonstrated for (1)H-detected (13)C correlation work.

(119/117/115)Sn low-abundance single-transition correlation spectroscopy (LASSY): sensitivity-enhanced homonuclear correlation experiments for Sn NMR

We report the implementation of our novel rare-spin homonuclear correlation experiment, namely, Low-Abundance Single-transition correlation SpectroscopY (LASSY), for (119/117/115)Sn NMR at natural abundance. Our pulse sequence results in diagonal suppressed COSY-style display and outperforms the optimal homonuclear correlation experiment for rare spins, which involves double quantum evolution (INADEQUATE CR). The new experiment maximizes efficiency both in respect of pulse transformations as well as relaxation effects, and gives rise to a simplified two-dimensional (2D) spectrum with considerably reduced crowding, exhibiting only one transition in each cross peak, instead of four. Performance optimization of LASSY is carried out in light of the relatively 'large' line widths typical of Sn NMR in solution state. The superior performance of the sequence is demonstrated on dimeric tetraorganodistannoxane samples.

Optimal control in NMR spectroscopy: numerical implementation in SIMPSON

We present the implementation of optimal control into the open source simulation package SIMPSON for development and optimization of nuclear magnetic resonance experiments for a wide range of applications, including liquid- and solid-state NMR, magnetic resonance imaging, quantum computation, and combinations between NMR and other spectroscopies. Optimal control enables efficient optimization of NMR experiments in terms of amplitudes, phases, offsets etc. for hundreds-to-thousands of pulses to fully exploit the experimentally available high degree of freedom in pulse sequences to combat variations/limitations in experimental or spin system parameters or design experiments with specific properties typically not covered as easily by standard design procedures. This facilitates straightforward optimization of experiments under consideration of rf and static field inhomogeneities, limitations in available or desired rf field strengths (e.g., for reduction of sample heating), spread in resonance offsets or coupling parameters, variations in spin systems etc. to meet the actual experimental conditions as close as possible. The paper provides a brief account on the relevant theory and in particular the computational interface relevant for optimization of state-to-state transfer (on the density operator level) and the effective Hamiltonian on the level of propagators along with several representative examples within liquid- and solid-state NMR spectroscopy.

Coherence Transfer in Spatially Resolved NMR

We present an overview of some applications of coherence transfer experiments in spatially resolved NMR, with examples from imaging and volume localized spectroscopy. While the major preoccupation of spatially resolved NMR experiments is normally with the dominant component (e.g. water) of heterogeneous multi-component systems, the interest in minor components (e.g. metabolites) of such systems is a strong motivation to develop and apply special techniques. Unlike water, these components typically involve scalar coupled spin systems. They lend themselves therefore to investigations based on the correlated evolution of coupled spins. Specifically, we briefly describe in this contribution the spatially resolved version of multiple quantum experiments, indirect detection experiments and spin correlation experiments.

Improved resolution in (13)C solid-state spectra through spin-state-selection

The application of a spin-state-selective coherence transfer experiment (INADEQUATE-SSS) to solid-state NMR spectroscopy is described. Two-dimensional (13)C double-quantum/single-quantum spectra without J splittings in both dimensions lead to enhanced spectral resolution. The method is demonstrated to significantly improve the spectral resolution of the crowded C'-C(alpha) region of two proteins.

Optimized 1D double quantum filter NMR experiments

We propose and demonstrate a 1D pulse sequence to convert double quantum coherence (DQC) of y phase with optimal efficiency, relying on single transition selection. Our sequence has a larger high-sensitivity bandwidth with respect to the coupling, compared to other reconversion strategies. A modified version of the new pulse sequence provides the missing chemical shift and coupling information, at minor cost in sensitivity. Application to 1D 13C INADEQUATE is demonstrated. Our new sequence is also applied to quadrupole coupled spin-1 systems, such as 2H in lyotropic phase. Performance of the sequence may be fine-tuned by pulse flip angle optimization, taking into account relaxation effects.

Double-quantum biased covariance spectroscopy: application to the 2D INADEQUATE experiment

A novel processing scheme is presented that converts a two-dimensional double-quantum NMR spectrum into a single-quantum correlation spectrum. The covariance-like spectrum is computed from the 2D Fourier transform spectrum by emphasizing contributions that fulfill the double-quantum condition resulting in a symmetric spectrum that is easier to analyze. The method is demonstrated for the 2D INADEQUATE experiment.

J-modulated ADEQUATE (JM-ADEQUATE) experiment for accurate measurement of carbon-carbon coupling constants

A new method for the accurate determination of carbon-carbon coupling constants is described. The method is based on a modified ADEQUATE experiment, where a J-modulated spin-echo sequence precedes the ADEQUATE pulse scheme. The J-modulation and scaling of carbon-carbon couplings is based on simultaneous incrementation of 13C chemical shift and coupling evolution periods. The time increment for the homonuclear carbon-carbon coupling evolution can be suitably scaled with respect to the corresponding increment for the chemical shift evolution. Typically a scaling factor of 2 to 3 is employed for the measurement of one-bond coupling constants, while multiplication by a factor of 10 to 15 is applied when small long-range couplings are determined. The same pulse scheme with coupling evolution period optimized for one-bond or long-range couplings allows the determination of the corresponding carbon-carbon coupling constants. The splittings of the ADEQUATE crosspeaks in the F1 dimension yield the appropriately multiplied coupling constants.

Closed solution to the Baker-Campbell-Hausdorff problem: exact effective Hamiltonian theory for analysis of nuclear-magnetic-resonance experiments

A closed solution to the Baker-Campbell-Hausdorff problem is described. The solution, which is based on the Cayley-Hamilton theorem, allows the entanglement between exponential operators to be described by an exact finite series expansion. Addressing specifically the special unitary Lie groups SU(2), SU(3), and SU(4), we derive expansion formulas for the entangled exponential operator as well as for the effective Hamiltonian describing the net evolution of the quantum system. The capability of our so-called exact effective Hamiltonian theory for analytical and numerical analysis is demonstrated by evaluation of multiple-pulse methods within liquid- and solid-state nuclear-magnetic-resonance spectroscopy. The examples include composite pulses for inversion, decoupling, and dipolar recoupling, as well as coherence-order- and spin-state-selective double- to single-quantum conversion, homonuclear dipolar decoupling, finite rf excitation for quadrupolar nuclei, heteronuclear coherence transfer, and gates for quantum computation.

Comparison of aqueous molecular dynamics with NMR relaxation and residual dipolar couplings favors internal motion in a mannose oligosaccharide

An investigation has been performed to assess how aqueous dynamical simulations of flexible molecules can be compared against NMR data. The methodology compares state-of-the-art NMR data (residual dipolar coupling, NOESY, and (13)C relaxation) to molecular dynamics simulations in water over several nanoseconds. In contrast to many previous applications of residual dipolar coupling in structure investigations of biomolecules, the approach described here uses molecular dynamics simulations to provide a dynamic representation of the molecule. A mannose pentasaccharide, alpha-D-Manp-(1-->3)-alpha-D-Manp-(1-->3)-alpha-D-Manp-(1-->3)-alpha-D-Manp-(1-->2)-D-Manp, was chosen as the model compound for this study. The presence of alpha-linked mannan is common to many glycopeptides, and therefore an understanding of the structure and the dynamics of this molecule is of both chemical and biological importance. This paper sets out to address the following questions. (1) Are the single structures which have been used to interpret residual dipolar couplings a useful representation of this molecule? (2) If dynamic flexibility is included in a representation of the molecule, can relaxation and residual dipolar coupling data then be simultaneously satisfied? (3) Do aqueous molecular dynamics simulations provide a reasonable representation of the dynamics present in the molecule and its interaction with water? In summary, two aqueous molecular dynamics simulations, each of 20 ns, were computed. They were started from two distant conformations and both converged to one flexible ensemble. The measured residual dipolar couplings were in agreement with predictions made by averaging the whole ensemble and from a specific single structure selected from the ensemble. However, the inclusion of internal motion was necessary to rationalize the relaxation data. Therefore, it is proposed that although residual dipolar couplings can be interpreted as a single-structure, this may not be a correct interpretation of molecular conformation in light of other experimental data. Second, the methodology described here shows that the ensembles from aqueous molecular dynamics can be effectively tested against experimental data sets. In the simulation, significant conformational motion was observed at each of the linkages, and no evidence for intramolecular hydrogen bonds at either alpha(1-->2) or alpha(1-->3) linkages was found. This is in contrast to simulations of other linkages, such as beta(1-->4), which are often predicted to maintain intramolecular hydrogen bonds and are coincidentally predicted to have less conformational freedom in solution.

INADEQUATE-CR experiments in the solid state

Through-bond connectivity can be probed by J couplings. For effective two-spin systems, the INADEQUATE experiment is highly valuable in liquid-state spectroscopy. It is the purpose of this Communication to show that in-phase INADEQUATE-CR spectra, where the intensity is concentrated in only one line of the J splitted doublet, can be obtained from solid-state samples. The problem of the cancellation of nonresolved multiplet lines, as experienced typically in INADEQUATE spectra in the solid, is resolved and the (13)C spectra become simpler because the number of resonance lines is reduced. Furthermore, a gain in signal intensity by 2 can, theoretically, be achieved. We limit the discussion to two-spin systems. In the present context, a two-spin system is defined considering the J coupling only. When the dipolar coupling is also taken into account, the two-spin system will usually become a many-spin system, but in the present context this is not relevant.

Pulse sequences for measurement of one-bond (15)N-(1)H coupling constants in the protein backbone

A set of three improved two-dimensional (2D) NMR methods for measuring one-bond (15)N-(1)H coupling constants in the protein backbone is presented. They are tailored to suit the size of the TROSY effect, i.e., the degree of interference between dipolar and chemical shift anisotropy relaxation mechanisms. The methods edit 2D spectra into two separate subspectra corresponding to the two possible spin states of the coupling partner. Cross talk between the two subspectra is a second order effect in the difference between the actual coupling constants and the one used in setting the pertinent delays of the pulse sequences. This relatively high degree of editing accuracy makes the methods useful for applications to molecules subjected to weak alignment where the one-bond coupling constants are linear combinations of a scalar J and a residual dipolar contribution containing important structural information. A demonstration of the new methods is shown for the (15)N-labeled protein chymotrypsin inhibitor 2 in a lipid bicelle mixture.

An alpha/beta-HSQC-alpha/beta experiment for spin-state selective editing of IS cross peaks

A generalized version of the TROSY experiment allows the spin-state selective editing of the four multiplet components of 15N-1H cross peaks of amide groups in proteins into four different subspectra, with no penalty in sensitivity. An improvement by <SGMLEXP TYPE="INLINE">2 in sensitivity results, if only two of the four multiplet components are selected. Use of the experiment for the measurement of 1JHN coupling constants is discussed. A water flip-back version of the experiment is demonstrated with a 45 kDa fragment of 15N/2H labeled Staphylococcus aureus gyrase B. Copyright 1998 Academic Press.