Zero-quantum Coherence Research Articles

The refocused INADEQUATE MAS NMR experiment in multiple spin-systems: Interpreting observed correlation peaks and optimising lineshapes

The robustness of the refocused INADEQUATE MAS NMR pulse sequence for probing through-bond connectivities has been demonstrated in a large range of solid-state applications. This pulse sequence nevertheless suffers from artifacts when applied to multispin systems, e.g. uniformly labeled 13C solids, which distort the lineshapes and can potentially result in misleading correlation peaks. In this paper, we present a detailed account that combines product-operator analysis, numerical simulations and experiments of the behavior of a three-spin system during the refocused INADEQUATE pulse sequence. The origin of undesired anti-phase contributions to the spectral lineshapes are described, and we show that they do not interfere with the observation of long-range correlations ( e.g. two-bond 13C– 13C correlations). The suppression of undesired contributions to the refocused INADEQUATE spectra is shown to require the removal of zero-quantum coherences within a z-filter. A method is proposed to eliminate zero-quantum coherences through dephasing by heteronuclear dipolar couplings, which leads to pure in-phase spectra.

High-resolution intermolecular zero-quantum coherence spectroscopy under inhomogeneous fields with effective solvent suppression

Intermolecular zero-quantum coherences (iZQCs) are not susceptible to magnetic field inhomogeneities significantly larger than the dipolar correlation distance and can be used to obtain 1D high-resolution spectra in an inhomogeneous field. However, with the iZQC methods proposed previously, residual conventional single-quantum coherences (SQCs) originating mainly from solvent resonance result in strong t(1) ridge noises. A modified HOMOGENIZED with an intermolecular double-quantum filter (iDQF), named iDQF-HOMOGENIZED, is presented in this work to suppress the residual conventional SQC signals as well as solvent iZQC signals. The solvent-suppression efficiency of the iDQF-HOMOGENIZED is analyzed and a thorough comparison of the new sequence with several relevant pulse sequences is made. Dramatic resolution enhancement and solvent suppression in the measurements of a piece of grape sarcocarp suggest potential applications of the method in in vivo spectroscopy.

Lifetimes of the singlet-states under coherent off-resonance irradiation in NMR spectroscopy

Singlet-states | S 〉 = ( | α β 〉 - | β α 〉 ) / 2 can be excited in pairs of coupled spins I and S, first by preparing either a non-vanishing zero-quantum coherence I + S − or a state of longitudinal two-spin order I z S z and then by applying a coherent radio-frequency (RF) irradiation with a carrier frequency ω rf = ( Ω I + Ω S )/2 that lies half-way between the chemical shifts of the two spins involved. The life-times T S can be much longer than the spin-lattice relaxation time T 1 of longitudinal magnetization, but singlet-states are ultimately relaxed, not only by dipolar interactions between the active spins or with the external spins, but also as a result of a non-vanishing offset Δ ω = ω rf − ( Ω I + Ω S )/2 or an insufficient amplitude of the RF irradiation that fails to fulfill the condition ω 1 ≫ Δ Ω = ( Ω I − Ω S ). In this work, the effect of off-resonance irradiation is explored and an approximate formula for the effective relaxation rate of the singlet population is provided on the basis of perturbation theory. The qualitative features of the dependence of the relaxation rate of the singlet population on the offset Δ ω and on the difference Δ Ω of the chemical shifts of the two spins are illustrated by comparison with numerical simulations.

Mixed Frequency/Time Domain Optical Analogues of Heteronuclear Multidimensional NMR

Ultrafast spectroscopy is dominated by time domain methods such as pump-probe and, more recently, 2D-IR spectroscopies. In this paper, we demonstrate that a mixed frequency/time domain ultrafast four wave mixing (FWM) approach not only provides similar capabilities, but it also provides optical analogues of multiple- and zero-quantum heteronuclear nuclear magnetic resonance (NMR). The method requires phase coherence between the excitation pulses only over the dephasing time of the coherences. It uses twelve coherence pathways that include four with populations, four with zero-quantum coherences, and four with double-quantum coherences. Each pathway provides different capabilities. The population pathways correspond to those of two-dimensional (2D) time domain spectroscopies, while the double- and zero-quantum coherence pathways access the coherent dynamics of coupled quantum states. The three spectral and two temporal dimensions enable the isolation and characterization of the spectral correlations between different vibrational and/or electronic states, coherence and population relaxation rates, and coupling strengths. Quantum-level interference between the direct and free-induction decay components gives a spectral resolution that exceeds that of the excitation pulses. Appropriate parameter choices allow isolation of individual coherence pathways. The mixed frequency/time domain approach allows one to access any set of quantum states with coherent multidimensional spectroscopy.

Detection of correlated dynamics on multiple timescales by measurement of the differential relaxation of zero- and double-quantum coherences involving sidechain methyl groups in proteins

Multiple effects may lead to significant differences between the relaxation rates of zero-quantum coherences (ZQC) and double-quantum coherences (DQC) generated between a pair of nuclei in solution. These include the interference between the anisotropic chemical shifts of the two nuclei participating in formation of the ZQC or DQC, the individual dipolar interactions of each of the two nuclei with the same proton, and the slow modulation of the isotropic chemical shifts of the two nuclei due to conformational exchange. Motional events that occur on a timescale much faster than the rotational correlation time (ps–ns) influence the first two effects, while the third results from processes that occur on a far slower timescale (μs–ms). An analysis of the differential relaxation of ZQC and DQC is thus informative about dynamics on the fast as well as the slow timescales. We present here an experiment that probes the differential relaxation of ZQC and DQC involving methyl groups in protein sidechains as an extension to our recently proposed experiments for the protein backbone. We have applied the methodology to 15N, 13C-labeled ubiquitin and used a detailed analysis of the measured relaxation rates using a simple single-axis diffusion model to probe the motional restriction of the C nextH next bond vector where C next is the carbon that is directly bonded to a sidechain methyl carbon (C methyl). Comparison of the present results with the motional restriction of the C nextC methyl bond ( S axis 2 ) reveals that the single-axis diffusion model, while valid in the fringes of the protein and for shorter chain amino acids, proves inadequate in the central protein core for long chain, asymmetrically branched amino acids where more complex motional models are necessary, as is the inclusion of the possibility of correlation between multiple motional modes. In addition, the present measurements report on the modulation of isotropic chemical shifts due to motion on the μs–ms timescale. Three Leu residues (8, 50, and 56) are found to display these effects. These residues lie in regions where chemical shift modulation had been detected previously both in the backbone and sidechain regions of ubiquitin.

Formation and identification of pure intermolecular zero-quantum coherence signal in liquid NMR

A new pulse sequence with three radio-frequency pulses was designed to detect NMR signals originating from pure intermolecular zero-quantum coherence (iZQC) in isolated spin-1/2 samples such as water. Analytical expressions were derived from the modified Bloch equations with dipolar fields. All the experimental observations and simulated results demonstrate that the iZQC signals can be selectively detected, mostly free of contamination of other coherences and conventional signals. Compared to the two-pulse CRAZED sequence, the new sequence is insensitive to the imperfection of flip angles.

Removal of zero-quantum peaks from 1D selective TOCSY and NOESY spectra

Selective 1D TOCSY and NOESY experiments are widely used for structure determination. However, they often give distorted peak shapes owing to coherence transfer though zero-quantum coherence (ZQ) which cannot be suppressed by conventional phase cycling or pulse-field gradients. This paper demonstrates that ZQ contributions can be removed from selective 1D spectra by introducing a ZQ evolution time, as previously demonstrated for 2D NOESY spectra by Wang et al. [A three-dimensional method for the separation of zero-quantum coherence and NOE in NOESY spectra, J. Magn. Reson. A 102 (1993) 116–121]. This approach is simple to implement and robust, and is not demanding of spectrometer hardware. Using a new approach to phase cycling described here, spectra can be acquired in a similar time to spectra without a ZQ evolution time.

Ultrafast Intermolecular Zero Quantum Spectroscopy

Clinical magnetic resonance spectroscopy is typically limited by magnetic inhomogeneities which destroy spectral resolution, but intermolecular zero quantum coherences (iZQCs) are insensitive to such inhomogeneities. iZQC resolution in vivo, however, has been hampered by physiological fluctuations over the time scale of the two-dimensional acquisition. A faster iZQC sequence will allow us to average away these fluctuations, and thus we present a new approach to ultrafast two-dimensional spectroscopy. This communication reports iZQC experiments acquiring up to 31 t1-points per scan, as well as extensions to a broad range of other 2D sequences.

Solvent-localized NMR spectroscopy using the distant dipolar field: A method for NMR separations with a single gradient

Solvent-localized NMR (SOLO) is a new method which allows the separation of NMR spectra of substances dissolved in different solvents. It uses the selective HOMOGENIZED pulse sequence to produce a two-dimensional NMR spectrum resulting from intermolecular zero-quantum coherences in one distinct solvent. The detected signal is locally refocused by the action of the distant dipolar field, which is created by a frequency selective pulse only in regions containing the selected solvent. The prerequisites are that the different solvents have sufficiently different chemical shifts to be excited separately and that compartments with different solvents are spatially separated by more than the typical diffusion distance. Here, the method is demonstrated for the solvents water and DMSO on a length scale of 0.5 mm. Because signal in the spectra is refocused locally, SOLO is insensitive to variations in the magnetic field which may result from inhomogeneities or structures in the sample. This makes applications in strongly structured samples possible. SOLO is the first method that achieves localization of NMR signal with a single gradient pulse. Therefore, it can be used in conventional NMR spectrometers with one-axis gradient systems and lends itself to a wide range of applications including in vivo NMR.

Slow motions in nondeuterated proteins: Concerted chemical shift modulations of backbone nuclei

A simple method designed to measure autorelaxation rates of double- and zero-quantum coherences DQC/ZQC{C′N} involving a carbonyl C′ and the neighboring amide N nucleus in protein backbones provides valuable insight into slow motions in spite of interference both from the attached amide proton HN and from remote protons such as Hα in nondeuterated proteins. The method has been applied to human ubiquitin.

Localized two‐dimensional 1H magnetic resonance exchange spectroscopy: A preliminary evaluation in human muscle

A localized two-dimensional (2D) (1)H MR chemical exchange spectroscopic (L-EXSY) sequence has been implemented on a whole-body 1.5-T MRI/MRS scanner. The second spectroscopic encoding to monitor the chemical exchange was an integral part of the single-volume localization using three slice-selective 90 degrees radiofrequency (RF) pulses, thereby eliminating the need for any additional RF pulses, off-resonance/continuous wave saturation, or selective inversion, which are essential in the one-dimensional (1)H MR exchange spectroscopy. Even though the TM-crusher dephased single- and higher-order multiple-quantum coherences, the zero-quantum coherences were indistinguishable from the longitudinal magnetization leading to J-coupled 2D cross peaks similar to COSY. With TM of 300 ms, two different exchange cross peaks were recorded in human calf muscle: a first peak, between the mobile tissue water and total creatine pools, and a second peak, possibly between the olefinic and magnetically equivalent poly methylene protons of unsaturated lipids. Our preliminary results demonstrate that the intermolecular and intramolecular chemical exchange mechanisms can be monitored noninvasively in human calf muscle using 2D L-EXSY.

Simplifying DOSY spectra with selective TOCSY edited preparation

Diffusion-ordered NMR spectroscopy, while quite powerful, is limited by its inability to resolve signals that are severely overlapped in the proton spectrum. We present here a DOSY experiment that uses selective TOCSY as an editing/preparation period. With this method, well-resolved signals of the analytes are selectively excited and the magnetization subsequently transferred by isotropic mixing to resonances buried in the matrix background, which are then resolved by the ensuing DOSY sequence. Key to the success of our proposed method is the incorporation of a highly effective zero-quantum filter into the selective TOCSY preparation period, which prevents zero-quantum coherence from being carried into the DOSY part of the pulse sequence. Further improvement in spectral resolution can be obtained by expanding the proposed experiment into a 3D sequence and utilizing the homonuclear decoupling feature of the BASHD-TOCSY technique. Both pulse sequences were found to greatly simplify the DOSY spectrum of a ‘dirty’ sucrose/raffinose mixture, as the complex matrix background is no longer present to obscure or overlap with the signals of interests. Furthermore, complete resolution of the relevant signals was achieved with the 3D sequence.

Extending the limits of the selective 1D NOESY experiment with an improved selective TOCSY edited preparation function

Compared to its 2D counterpart, the selective 1D NOESY experiment offers greatly simplified spectral interpretation and is invaluable to the structure elucidation of small-to-medium sized molecules, although its application is limited to well-resolved resonances only. The doubly selective 1D TOCSY–NOESY experiment allows the 1D NOESY experiment to be extended to resonances within overlapped spectral regions. However, existing methods do not address the critical issue of zero-quantum interference, which leads to severe anti-phase distortions to the line shape of scalar coupled spins and often complicates the identification of weak NOE enhancements. In this communication, we describe an improved selective TOCSY edited preparation (STEP) function and its application to the selective 1D NOESY experiment. The STEP function incorporates a novel zero-quantum filter introduced by Thrippleton and Keeler [Angew. Chem. Int. Ed. 42 (2003) 3938], which permits essentially complete suppression of zero-quantum coherence in a single scan. Residual anti-phase distortions due to spin-state mixing are removed using the double difference methodology reported by Shaka et al. [45th Experimental NMR Conference, Pacific Grove, USA, 2004]. The combined use of these techniques ensures that the final spectra are free of distortions, which is crucial to the reliable detection of weak NOE enhancements. Although employed as an additional preparation period in the example demonstrated here, the STEP function affords a general editing tool for spectral simplification and can be applied to a range of experiments.

Side chain dynamics monitored by 13C-13C cross-relaxation.

A method to measure (13)C-(13)C cross-relaxation rates in a fully (13)C labeled protein has been developed that can give information about the mobility of side chains in proteins. The method makes use of the (H)CCH-NOESY pulse sequence and includes a suppression scheme for zero-quantum (ZQ) coherences that allows the extraction of initial rates from NOE buildup curves. The method has been used to measure (13)C-(13)C cross-relaxation rates in the 269-residue serine-protease PB92. We focused on C(alpha)-C(beta) cross-relaxation rates, which could be extracted for 64% of all residues, discarding serine residues because of imperfect ZQ suppression, and methyl (13)C-(13)C cross-relaxation rates, which could be extracted for 47% of the methyl containing C-C pairs. The C(alpha)-C(beta) cross-relaxation rates are on average larger in secondary structure elements as compared to loop regions, in agreement with the expected higher rigidity in these elements. The cross-relaxation rates for methyl containing C-C pairs show a general decrease of rates further into the side chain, indicating more flexibility with increasing separation from the main chain. In the case of leucine residues also long-range C(beta)-C(delta) cross-peaks are observed. Surprisingly, for most of the leucines a cross-peak with only one of the methyl C(delta) carbons is observed, which correlates well with the chi(2) torsion-angle and can be explained by a difference in mobility for the two methyl groups due to an anisotropic side chain motion.

Probing slow backbone dynamics in proteins using TROSY-based experiments to detect cross-correlated time-modulation of isotropic chemical shifts.

The difference in the relaxation rates of zero-quantum (ZQ) and double-quantum (DQ) coherences is the result of three principal mechanisms. These include the cross-correlation between the chemical shift anisotropies of the two participating nuclei, dipolar interactions with remote protons as well as interference effects due to the time-modulation of their isotropic chemical shifts as a consequence of slow micros-ms dynamics. The last effect when present, dominates the others resulting in large differences between the relaxation rates of ZQ and DQ coherences. We present here four sets of TROSY-based (Salzmann et al., 1998) experiments that measure this effect for several pairs of backbone nuclei including (15)N, (13)C(alpha) and (13)C'. These experiments allow the detection of the presence of slow dynamic processes in the protein backbone including correlated motion over two and three bonds. Further, we define a new parameter chi which represents the extent of correlated motion on the slow (micros-ms) timescale. This methodology has been applied to (15)N,(13)C,REDPRO-(2)H-labeled (Shekhtman et al., 2002) human ubiquitin. The ubiquitin backbone is seen to exhibit extensive dynamics on the slow timescale. This is most pronounced in several residues in the N-terminal region of the alpha-helix and in the loop connecting the strands beta(4) and beta(5). These residues which include Glu24, Asn25, Glu51 and Asp 52 form a continuous surface. As an additional benefit, the measured rates confirm the dependence of the (13)C(alpha) chemical shift tensor on local secondary structure of the protein backbone.

Selective intermolecular zero-quantum coherence in high-resolution NMR under inhomogeneous fields

A selective 2D intermolecular zero-quantum coherences pulse sequence, SEL-HOMOGENIZED sequence, was developed for high-resolution NMR spectra in inhomogeneous fields. The sequence designed to effectively suppress strong solvent signals and other trivial signals can greatly decrease the t 1 noise artifacts. In the homogeneous-like 1D spectrum extracted from the 2D data, chemical shifts, coupling constants, multiplicity patterns, and relative peak areas are almost independent of the magnetic field inhomogeneity. Compared to the HOMOGENIZED sequence, the new sequence provides a total sensitivity enhancement of two times. It was also demonstrated that the theoretical predictions were in excellent agreement with the experimental results.

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 T 1 relaxation but not T 2 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 “ t 1-noise” in two-dimensional NMR spectra, the z-filter cascade can deliver a noteworthy improvement in spectral quality.

Evidence of slow motions by cross-correlated chemical shift modulation in deuterated and protonated proteins.

Cross-correlated fluctuations of isotropic chemical shifts can provide evidence for slow motions in biomolecules. Slow side-chain dynamics have been investigated in (15)N and (13)C enriched ubiquitin by monitoring the relaxation of C(alpha)-C(beta) two-spin coherences (Frueh et al., 2001). This method, which had hitherto been demonstrated only for protonated ubiquitin, has now been applied to both protonated and deuterated proteins. Deuteration reduces the dipole-dipole contributions to the DD/DD cross-correlation, thus facilitating the observation of subtle effects due to cross-correlation of the fluctuations of the isotropic (13)C chemical shifts. The decays of double- and zero-quantum coherences are significantly slower in the deuterated protein than in the protonated sample. Slow motions are found both in loops and in secondary structure elements.

Evidence for slow motion in proteins by multiple refocusing of heteronuclear nitrogen/proton multiple quantum coherences in NMR.

A novel NMR method characterizes slow motions in proteins by multiple refocusing of double- and zero-quantum coherences of amide protons and nitrogen-15 nuclei. If both nuclei experience changes in their isotropic chemical shifts because of internal motions on slow time scales (mus - ms), this leads to a difference in the relaxation rates of double- and zero-quantum coherences. This is due to CSM/CSM (chemical shift modulation) cross-correlation effects that are related to the well-known chemical exchange contribution Rex to the decay rate R2 = 1/T2 of nitrogen-15 nuclei. The CSM/CSM contributions can be distinguished from other mechanisms through their dependence on the repetition rate of a Carr-Purcell-Meiboom-Gill (CPMG) multiple refocusing sequence. In ubiquitin, motional processes can be identified that could hitherto not be observed by conventional CPMG nitrogen-15 NMR.

Elimination of zero-quantum interference in two-dimensional NMR spectra.

High-resolution NMR experiments often contain periods during which the magnetization is placed along the z-axis. For example, the magnetization must be along the z-axis during the mixing time in a NOESY experiment so that crossrelaxation can take place. Either phase cycling or field gradient pulses are used to ensure that only the wanted zmagnetization ends up contributing to the spectrum. However, neither of these methods can distinguish between zmagnetization and homonuclear zero-quantum coherence, which is invariably present. The zero-quantum coherence gives rise to anti-phase dispersive components in the spectra, thereby reducing the effective resolution, introducing misleading correlations, and obscuring wanted features. Over the years a number of methods have been devised to suppress these zero-quantum contributions, but it is fair to say that none of these methods have proved entirely satisfactory. Herein we present a new method for suppressing zeroquantum coherence; the method is widely applicable, does not extend the duration of the experiment significantly, and can be implemented easily on any modern spectrometer. Our new method of zero-quantum suppression involves applying simultaneously a swept-frequency 1808 pulse and a gradient. Figure 1a shows how this combination can be introduced into the NOESY pulse sequence. The way in which this swept-pulse/gradient pair works can be envisaged in the following way. The application of the gradient (along the z-axis) results in the Larmor frequency becoming a function of position in the NMR tube. The swept-frequency 1808 pulse will therefore flip the spins at different positions in the sample at different times. Thus, the top of the sample might experience the 1808 pulse at the start of the sweep, the middle of the sample at time tf/2, and the bottom at time tf, where tf is the duration of the sweep. In general, the 1808 pulse occurs at time atf, where a is 0 at the top of the sample and 1 at the bottom. The 1808 pulse forms a spin echo which refocuses the evolution of the zero-quantum coherence over a time 2atf ; however, for the remainder of the time, (1–2a)tf, the zeroquantum continues to evolve. The result is that in different parts of the sample the zero-quantum has evolved for different times, and so has acquired a different phase. If the range of these phases across the sample is large enough, the net result will be cancelation of the zero-quantum coherence. A simple calculation (see Supporting Information) shows that the degree of attenuation A of the zero-quantum depends on both its frequency, WZQ (in rad s ), and the length of the swept-pulse/gradient pair, tf, [Eq. (1)]: