Multiple-quantum J-resolved NMR spectroscopy (MQ-JRES): measurement of multiple-quantum relaxation rates and relative signs of spin coupling constants

The technique of multiple-quantum J-resolved NMR spectroscopy (MQ-JRES) is introduced and applied to the spin system SI(3)-M (such as in the example given here, the (13)CH(3)-(12)CH in alanine). The SI(3) spin system was excited to its highest quantum state (8S(y)I(x)I(y)I(y)), which consists of four coherences: quadruple quantum of (3I + S), double quantum of (3I - S), double quantum of (I + S), and zero quantum of (I - S). In the MQ spectrum generated from the projection onto the F(1) dimension, the resonances of the different multiple-quantum coherences are resolved by their coupling constants to the remote spin (M). The absorptive lineshapes in both F(1) and F(2) dimensions enable accurate measurements of transverse relaxation rates, and both amplitude and relative signs of the long-range coupling constants are to be derived from either frequency or time domain data. The selective detection of MQ-JRES spectra of the individual MQ coherences using either phase cycling or pulsed field gradients is presented.     

Simplified multiplet pattern HSQC-TOCSY experiment for accurate determination of long-range heteronuclear coupling constants

A new two-dimensional pulse sequence for accurately determining heteronuclear coupling constants is presented. It is derived from HSQC and HECADE techniques with B0 gradient coherence selection. The main feature of the proposed method is spectra with only one component of the IS doublet; i.e., the final result is equivalent to a selective broadband excitation of either Salpha or Sbeta spin states and a preservation of these states during the entire experiment. The effect is obtained by an appropriate combination of in- and antiphase coherences. It is demonstrated that heteronuclear single-bond as well as long-range coupling constants and their relative signs are readily evaluated. The proposed sequence is equally or less sensitive to a variation of heteronuclear one-bond couplings than previously published, closely related sequences. The new method is applied to a peptide sample for determination of 3JN, Hbeta.     

J pulses for multiplet-selective NMR

Exact product operator solutions have been obtained for the evolution of weakly coupled spin-(1/2) I(m)S(n) systems during arbitrary RF irradiation of one spin. These solutions, which completely characterize the nature of J-coupling modulation during RF pulses, show that significant exchange occurs between single-spin magnetization and two-spin product operator states when the RF field strength is comparable to the coupling. In particular, a long (t(p) = [2J](-1) s), low-power (B(1) = J/2 Hz), constant amplitude pulse applied on resonance to one spin in an IS system completely interconverts the spinstates S(z) <--> 2S(x)I(z) and S(x) <--> 2S(z)I(z) when the RF is applied to the S spins, and interconverts S(x) <--> 2S(y)I(y) in 100% yield when the RF is applied to the I spins. Thus, these "J pulses," which select a bandwidth approximately equal to J Hz, may replace any combination of a (2J)(-1) delay period and a consecutive hard 90 degrees pulse in any polarization transfer or multiple quantum sequence. Although these rectangular pulses are highly frequency selective, in general they increase the replaced (2J)(-1) period by only a modest 40%, a time saving of a factor of 5 compared to existing pulses exhibiting the same selectivity. In favorable cases, there is no increase in duration of a pulse sequence using a particular type of J pulse, the 90(J) variety, which accomplishes the third spin state transformation listed above. J pulses will be advantageous for systems subject to rapid signal loss from relaxation and more generally for the enhanced operation of pulse sequences via the use of J modulation during RF irradiation.     

Probing the validity of average Hamiltonian theory for spin I=1, 3/2 and 5/2 nuclei by analyzing a simple two-pulse sequence

In this work, we investigate the accuracy of controlling spin I=1, 3/2 and 5/2 spin systems by average Hamiltonian theory. By way of example, we consider a simple two-pulse echo sequence and compare this perturbation scheme to a numerical solution of the Von Neumann equation. For the different values of I, we examine this precision as a function of the quadrupolar coupling as well as various experimental parameters such as the pulse spacing and pulse width. Experiments and simulations on I=3/2 and I=5/2 spin systems are presented that highlight a spectral artifact introduced due to finite pulse widths as predicted by average Hamiltonian theory. The control of these spin systems by this perturbation scheme is considered by investigating a phase cycling scheme that suppresses these artifacts to zeroth-order of the Magnus expansion.     

液体核磁共振 HSQC 实验的量子化学计算与模拟

核磁共振（NMR）异核单量子相干（HSQC）实验因具有较高的灵敏度和分辨率而被广泛用于液体大分子化合物的结构鉴定和研究．然而由于HSQC脉冲的复杂性,需要严格控制实验参数和实验条件才能得到高质量的谱图．本文基于量子力学原理对HSQC实验进行数学建模,通过理论推导、数值计算求解自旋1/2的IS双核体系在每个脉冲节点作用后的密度矩阵,然后结合二维NMR信号采样方法,使用计算机程序完成了该体系HSQC谱图的模拟,同时,还实现了乙醇分子的HSQC谱图模拟． HSQC实验的成功模拟基于对复杂演化过程的精确计算,可用于预测谱图以及实验参数改变对NMR谱图的影响,指导高质量HSQC实验谱图的采集．     

Spin-state-selective excitation in selective 1D inverse NMR experiments

A general and very simple strategy for achieving clean spin-state-selective excitation with full sensitivity in carbon-selective gradient-enhanced 1D HMQC and HSQC pulse schemes is presented. The incorporation of an additional hard 90 degrees (13)C pulse applied along a specific orthogonal axis just prior to acquisition into the conventional sequences allows us to select a simultaneous coherence transfer pathway which usually is not detected. The superimposition of this resulting antiphase magnetization to the conventional in-phase magnetization gives the exclusive excitation of the directly attached proton showing only the alpha or beta spin state of the passive (13)C nucleus. The propagation of this particular spin state to other protons can be accomplished by adding any homonuclear mixing process just after this supplementary pulse. Such an approach affords a suite of powerful selective 1D (13)C-edited NMR experiments which are helpful for resonance assignment purposes in overcrowded proton spin systems and also for the accurate determination of the magnitude and sign of long-range proton-carbon coupling constants in CH spin sytems for samples at natural abundance. Such measurements are performed by measuring the relative displacement of relayed signals in the corresponding alpha and beta 1D subspectra.     

13C natural abundance S3E and S3CT experiments for measurement of J coupling constants between 13Calpha or 1Halpha and other protons in a protein

It is demonstrated that the spin-state-selective pulse sequence elements, S3E and S3CT, previously introduced for measurement of J coupling constants in 15N-labeled proteins can be applied for work with peptides and proteins with 13C at the natural abundance level. In addition, a method is described for suppression of crosstalk caused by passive spin flips and pulse imperfections, which otherwise results in systematically underestimated J coupling constants and thereby inaccurate structural constraints. This method is also applicable for crosstalk suppression in applications of S3E and S3CT to 13C- or 15N-labeled samples. Experimental confirmation is obtained using a 10 mM BPTI sample focusing on 13C in the alpha position. The measured J coupling constants include 3J(HN-Halpha) and 3J(Halpha-Hbeta) related to the phi and chi1 angles, respectively.     

Hyperfine decoupling in electron paramagnetic resonance as a powerful tool for unraveling complicated ESEEM spectra of S=1/2, I> or =1/2 systems

Hyperfine decoupling in electron paramagnetic resonance after strong microwave radiation is studied for S=1/2, I=1/2 and S=1/2, I=1 spin systems. A new 2D pulse sequence based on the hyperfine-decoupled DEFENCE (deadtime-free ESEEM by nuclear coherence-transfer echoes) experiment is introduced, which is distinguished by a remarkable reduction of the residual hyperfine coupling. The efficiency of this new decoupling experiment in comparison to the old pulse sequence is studied by means of numerical simulations. The advantages of the new decoupling experiment and its ability to simplify ESEEM spectra are experimentally demonstrated on two disordered systems.     

Sensitivity enhancement in natural-abundance solid-state 33S MAS NMR spectroscopy employing adiabatic inversion pulses to the satellite transitions

The WURST (wideband uniform rate smooth truncation) and hyperbolic secant (HS) pulse elements have each been employed as pairs of inversion pulses to induce population transfer (PT) between the four energy levels in natural abundance solid-state (33)S (spin I=3/2) MAS NMR, thereby leading to a significant gain in intensity for the central transition (CT). The pair of inversion pulses are applied to the satellite transitions for a series of inorganic sulfates, the sulfate ions in the two cementitious materials ettringite and thaumasite, and the two tetrathiometallates (NH(4))(2)WS(4) and (NH(4))(2)MoS(4). These materials all exhibit (33)S quadrupole coupling constants (C(Q)) in the range 0.1-1.0 MHz, with precise C(Q) values being determined from analysis of the PT enhanced (33)S MAS NMR spectra. The enhancement factors for the WURST and HS elements are quite similar and are all in the range 1.74-2.25 for the studied samples, in excellent agreement with earlier reports on HS enhancement factors (1.6-2.4) observed for other spin I=3/2 nuclei with similar C(Q) values (0.3-1.2 MHz). Thus, a time saving in instrument time by a factor up to five has been achieved in natural abundance (33)S MAS NMR, a time saving which is extremely welcome for this important low-gamma nucleus.     

J-multiplied HSQC (MJ-HSQC): a new method for measuring 3J(HNHalpha) couplings in 15N-labeled proteins

A new method for the measurement of homonuclear 3J(HNHalpha) coupling constants in 15N-labeled small proteins is described. The method is based on a modified sensitivity enhanced HSQC experiment, where the 3J(HNHalpha) couplings are multiplied in the f1-dimension. The J-multiplication of homonuclear 3J(HNHalpha) couplings is based on simultaneous incrementation of 15N chemical shift and homonuclear coupling evolution periods. The time increment for the homonuclear coupling evolution period is chosen to be a suitable multiple (2N x t1) of the corresponding increment for 15N-shift evolution. This results in the splitting of the HSQC correlation in the f1-dimension by 2N x 3J(HNHalpha). Because the pulse sequence has good sensitivity and water suppression properties, it is particularly useful for natural abundance samples.     

Rotor-encoded heteronuclear MQ MAS NMR spectroscopy of half-integer quadrupolar and spin I=1/2 nuclei

A new two-dimensional heteronuclear multiple-quantum magic-angle spinning (MQ MAS) experiment is presented which combines high resolution for the half-integer quadrupolar nucleus with information about the dipolar coupling between the quadrupolar nucleus and a spin I=1/2 nucleus. Homonuclear MQ coherence is initially created for the half-integer quadrupolar nucleus by a single pulse as in a standard MQ MAS experiment. REDOR recoupling of the heteronuclear dipolar coupling then allows the creation of a heteronuclear multiple-quantum coherence comprising multiple- and single-quantum coherence of the quadrupolar and spin I=1/2 nucleus, respectively, which evolves during t1. Provided that the t1 increment is not rotor synchronized, rotor-encoded spinning-sideband patterns are observed in the indirect dimension. Simulated spectra for an isolated IS spin pair show that these patterns depend on the recoupling time, the magnitude of the dipolar coupling, the quadrupolar parameters, as well as the relative orientation of the quadrupolar and dipolar principal axes systems. Spectra are presented for Na2HPO4, with the heteronuclear 23Na-1HMQ MAS experiments beginning with the excitation of 23Na (spin I=3/2) three-quantum coherence. Coherence counting experiments demonstrate that four- and two-quantum coherences evolve during t1. The heteronuclear spinning-sideband patterns observed for the three-spin H-Na-H system associated with the Na(2) site are analyzed. For an IS2 system, simulated spectra show that, considering the free parameters, the spinning-sideband patterns are particularly sensitive to only, first, the angle between the two IS internuclear vectors and, second, the two heteronuclear dipolar couplings. It is demonstrated that the proton localization around the Na(2) site according to the literature crystal structure of Na2HPO4 is erroneous. Instead, the experimental data is consistent with two alternative different structural arrangements, whereby either there is a deviation of 10 degrees from linearity for the case of two identical Na-H distances, or there is a linear arrangement, but the two Na-H distances are different. Furthermore, the question of the origin of spinning-sidebands in the (homonuclear) MQ MAS experiment is revisited. It is shown that the asymmetric experimental MQ sideband pattern observed for the low-C(Q) Na(2) site in Na(2)HPO4 can only be explained by considering the 23Na chemical shift anisotropy.     

Measuring fast hydrogen exchange rates by NMR spectroscopy

We introduce a method to measure hydrogen exchange rates based on the observation of the coherence of a neighboring spin S such as (15)N that has a scalar coupling J(IS) to the exchanging proton I. The decay of S(x) coherence under a Carr-Purcell-Meiboom-Gill (CPMG) multiple echo train is recorded in the presence and absence of proton decoupling. This method allows one to extract proton exchange rates up to 10(5)s(-1). We could extend the pH range for the study of the indole proton in tryptophan, allowing the determination of the exchange constants of the cationic, zwitterionic, and anionic forms of tryptophan.     

A J-multiplied HMQC (MJ-HMQC) experiment for measuring (3)J(HNHalpha) coupling constants

The J-multiplied HSQC experiment (MJ-HSQC: S. Heikkinen et al., J. Magn. Reson 137, 243 (1999)) amplifies J coupling constants m times and allows direct observation of the (3)J(HNHalpha) coupling constants of peptides and proteins (<10 kDa). The drawbacks to this method are line broadening in the f(1)-dimension and lower sensitivity. In the J-multiplied HMQC (MJ-HMQC) experiment described here, the PEP-HSQC pulse sequence is replaced by a sensitivity-enhanced HMQC section, and the total decay time for the J-coupling and the chemical shift evolution is shortened by a period of t(1). This experiment affords narrower linewidth and enhances the sensitivity by 34%, on an average of 105 well-isolated peaks, when compared with the MJ-HSQC experiment.     

Measurement of small one-bond proton-carbon residual dipolar coupling constants in partially oriented (13)C natural abundance oligosaccharide samples: analysis of heteronuclear (1)J(CH)-modulated spectra with the BIRD inversion pulse

Two 2D J-modulated HSQC-based experiments were designed for precise determination of small residual dipolar one-bond carbon-proton coupling constants in (13)C natural abundance carbohydrates. Crucial to the precision of a few hundredths of Hz achieved by these methods was the use of long modulation intervals and BIRD pulses, which acted as semiselective inversion pulses. The BIRD pulses eliminated effective evolution of all but (1)J(CH) couplings, resulting in signal modulation that can be described by simple modulation functions. A thorough analysis of such modulation functions for a typical four-spin carbohydrate spin system was performed for both experiments. The results showed that the evolution of the (1)H-(1)H and long-range (1)H-(13)C couplings during the BIRD pulses did not necessitate the introduction of more complicated modulation functions. The effects of pulse imperfections were also inspected. While weakly coupled spin systems can be analyzed by simple fitting of cross peak intensities, in strongly coupled spin systems the evolution of the density matrix needs to be considered in order to analyse data accurately. However, if strong coupling effects are modest the errors in coupling constants determined by the "weak coupling" analysis are of similar magnitudes in oriented and isotropic samples and are partially cancelled during dipolar coupling calculation. Simple criteria have been established as to when the strong coupling treatment needs to be invoked.     

Density Matrix Simulations of the Effects of J Coupling in Spin Echo and Fast Spin Echo Imaging

A computer simulation has been used to calculate the effects of J coupling on the amplitudes of echoes produced by CPMG sequences. The program computes the evolution of the density matrix for different pulse intervals and can predict the signals obtainable from spin systems of any size and complexity. Results from the simulation confirm the prediction that a decrease in the effects of J coupling is largely responsible for the bright fat signal seen in fast spin echo imaging at high pulse rates. The effects of J coupling on CPMG echotrains are examined for A3B2 and A3B2C2 spin systems over a wide range of J coupling and chemical shift values and pulse spacings. The effects of J coupling on the point spread function obtained with fast spin echo imaging are also discussed.     

Accurate measurements of small J coupling constants under inhomogeneous fields via intermolecular multiple-quantum coherences

Two new NMR pulse sequences, based on intermolecular multiple-quantum coherences (iMQCs), were developed to obtain apparent J coupling constants with a scaling factor from one to infinity relative to the conventional J coupling constants. Here the apparent J coupling constants were defined as apparent peak separations in unit of Hz in a reconstructed spectrum for a coupled spin system. Except for the adjustable scaling factor for apparent J coupling constants, the sequences hold the advantage of high acquisition efficiency, and retain the spectral information such as chemical shifts, multiplet patterns, and relative peak areas under inhomogeneous fields. For spin systems with small scalar coupling constants, well-resolved J-spectra can be achieved by selecting a proper scaling factor. Theoretical predictions are in good agreement with simulation results and experimental observations.     

Determination of quadrupole parameters with a composite pulse for spurious signal suppression

Spurious signals such as the piezoelectric signal from a ferroelectric crystal or the ringing signal from the NMR probe head tuned for low gyromagnetic ratio nuclei are often observed in pulsed NMR. Both signals are cancelled using the Hahn echo sequence with appropriate phase cyclings. The present paper applies a composite-pulse sequence to cancel the ringing signal. The main advantage of this sequence over the Hahn echo sequence is in the simplicity of optimizing the line intensity: the optimization of only one pulse duration for this sequence but of two pulse durations and the interpulse delay for the Hahn echo sequence. We are interested in half-integer quadrupole spins (I = 3/2, 5/2, 7/2, and 9/2), which means that we must consider the first-order quadrupole interaction during the pulses. For simplicity, we deal mainly with spin I = 3/2 nuclei. Since the central-line intensity depends on the ratio of the quadrupole coupling constant (QCC) to the amplitude of the RF pulse, we can determine the QCC from a featureless lineshape by fitting the variation of the experimental central-line intensity for increasing pulse duration with theoretical results. Contrary to the one-pulse sequence where the central-line intensity is proportional to the pulse duration if the latter is short, there is no such condition with the composite-pulse sequence. In other words, this sequence does not allow us to quantify the relative spin populations in powders. The size of the sample must be much smaller than that of the RF coil in order for the RF magnetic field to become homogeneous for the sample. We used (87)Rb (I = 3/2) in an aqueous solution of RbCl and in RbNb2O5F powder, (131)Xe (I = 3/2) of xenon gas physisorbed in Na-Y zeolite, and (23)Na (I = 3/2) in two well-known powders (NaNO3 and NaNO2) to support our theoretical result.     

Observing in-phase single-quantum 15N multiplets for NH2/NH3+ groups with two-dimensional heteronuclear correlation spectroscopy

Two-dimensional (2D) F1-(1)H-coupled HSQC experiments provide 3:1:1:3 and 1:0:1 multiplets for AX(3) and AX(2) spin systems, respectively. These multiplets occur because, in addition to the 2S(y)H(z)(a)-->2S(y)H(z)(a) process, the coherence transfers such as 2S(y)H(z)(a)-->2S(y)H(z)(b) occurring in t(1) period provide detectable magnetization during the t(2) period. Here, we present a 2D F1-(1)H-coupled (1)H-(15)N heteronuclear correlation experiment that provides a 1:3:3:1 quartet for AX(3) spin system and a 1:2:1 triplet for AX(2). The experiment is a derivative of 2D HISQC experiment [J. Iwahara, Y.S. Jung, G.M. Clore, Heteronuclear NMR spectroscopy for lysine NH(3) groups in proteins: unique effect of water exchange on (15)N transverse relaxation. J. Am. Chem. Soc. 129 (2007) 2971-2980] and contains a scheme that kills anti-phase single-quantum terms generated in the t(1) period. The purge scheme is essential to observe in-phase single-quantum multiplets. Applications to the NH(2) and NH(3)(+) groups in proteins are demonstrated.     

S(3)E-E.COSY methods for the measurement of (19)F associated scalar and dipolar coupling constants

A (1)H-(19)F spin state selective excitation (S(3)E) pulse sequence element has been applied in combination with (1)H homonuclear mixing to create E.COSY-type experiments designed to measure scalar J(HF2') and J(HH2') and residual dipolar D(HF2') and D(HH2') couplings in 2'-deoxy-2'-fluoro-sugars. The (1)H-(19)F S(3)E pulse sequence element, which resembles a simple INEPT sequence, achieves spin-state-selective correlation between geminal (1)H-(19)F spin pairs by linear combination of in-phase (19)F magnetization and anti-phase magnetization evolved from (1)H. Since the S(3)E sequence converts both (19)F and (1)H steady-state polarization into observable coherences, an approximately twofold signal increase is observed for fully relaxed (1)H-(19)F spin pairs with respect to a standard (1)H coupled (19)F 1D experiment. The improved sensitivity and resolution afforded by the use of (1)H-(19)F S(3)E E.COSY-type experiments for measuring couplings is demonstrated on the nucleoside 9-(2',3'-dideoxy-2'-fluoro-beta-D-threo-pentofuranosyl)adenine (beta-FddA) and on a selectively 2'-fluorine labeled 21mer RNA oligonucleotide.     

Product Operator Theory for Spin‐5/2 Nuclei: Application to 2D J‐Resolved NMR Spectroscopy

Product operator theory is a simple quantum mechanical method that has often been used to analytically describe multi‐pulse NMR experiments for weakly coupled spin systems. Considering the existence of 2D‐J resolved NMR spectra of aqueous solutions containing S = 5/2 nuclear spins, the product operator formalism has been extended to the weakly coupled IS (I = 1/2, S = 5/2) spin system. The evolution of I_x, I_y, I_xS_z and I_yS_z product operators under spin–spin coupling Hamiltonian are given here. The analytical results obtained are applied to the well‐known gated decoupler pulse sequence for heteronuclear 2D‐J resolved NMR spectroscopy.