Carr-Purcell-Meiboom-Gill Experiment Research Articles

A methyl-TROSY based 13C relaxation dispersion NMR experiment for studies of chemical exchange in proteins.

A methyl Transverse Relaxation Optimized Spectroscopy (methyl-TROSY) based, multiple quantum (MQ) 13C Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion NMR experiment is described. The experiment is derived from the previously developed MQ 13C-1H CPMG scheme (Korzhnev in J Am Chem Soc 126: 3964-73, 2004) supplemented with a CPMG train of refocusing 1H pulses applied with constant frequency and synchronized with the 13C CPMG pulse train. The optimal 1H 'decoupling' scheme that minimizes the amount of fast-relaxing methyl MQ magnetization present during CPMG intervals, makes use of an XY-4 phase cycling of the refocusing composite 1H pulses. For small-to-medium sized proteins, the MQ 13C CPMG experiment has the advantage over its single quantum (SQ) 13C counterpart of significantly reducing intrinsic, exchange-free relaxation rates of methyl coherences. For high molecular weight proteins, the MQ 13C CPMG experiment eliminates complications in the interpretation of MQ 13C-1H CPMG relaxation dispersion profiles arising from contributions to exchange from differences in methyl 1H chemical shifts between ground and excited states. The MQ 13C CPMG experiment is tested on two protein systems: (1) a triple mutant of the Fyn SH3 domain that interconverts slowly on the chemical shift time scale between the major folded state and an excited state folding intermediate; and (2) the 82-kDa enzyme Malate Synthase G (MSG), where chemical exchange at individual Ile δ1 methyl positions occurs on a much faster time-scale.

Algebraic expressions for Carr-Purcell-Meiboom-Gill relaxation dispersion for N-site chemical exchange

The Carr-Purcell-Meiboom-Gill (CPMG) NMR relaxation dispersion experiment measures the effective relaxation rate constant during a train of spin-echo pulse sequence elements as a function of the echo time. The CPMG experiment is a powerful method for characterizing chemical and conformational dynamic processes, termed chemical and conformational exchange, on μs-ms time scales, comparable to the experimentally accessible echo times. Approximate theoretical expressions for the effective relaxation rate constant for N-site chemical exchange have been reported (H. Koss, M. Rance, and A. G. Palmer, Biochemistry 57, 4753–4763 (2018)). Expressions for the effective relaxation rate constant have been improved by using the Cayley-Hamilton theorem to obtain simple and accurate approximations of the average Liouvillian for the CPMG experiment. The improved accuracy of the results allows efficient analyses of experimental data. In addition, the relationship is clarified between the approach of Koss and coworkers and that of Jen (1978).

A methyl 1H double quantum CPMG experiment to study protein conformational exchange.

Protein conformational changes play crucial roles in enabling function. The Carr-Purcell-Meiboom-Gill (CPMG) experiment forms the basis for studying such dynamics when they involve the interconversion between highly populated and sparsely formed states, the latter having lifetimes ranging from ~ 0.5 to ~ 5ms. Among the suite of experiments that have been developed are those that exploit methyl group probes by recording methyl 1H single quantum (Tugarinov and Kay in J Am Chem Soc 129:9514-9521, 2007) and triple quantum (Yuwen et al. in Angew Chem Int Ed Engl 55:11490-11494, 2016) relaxation dispersion profiles. Here we build upon these by developing a third experiment in which methyl 1H double quantum coherences evolve during a CPMG relaxation element. By fitting single, double, and triple quantum datasets, akin to recording the single quantum dataset at static magnetic fields of Bo, 2Bo and 3Bo, we show that accurate exchange values can be obtained even in cases where exchange rates exceed 10,000s-1. The utility of the double quantum experiment is demonstrated with a pair of cavity mutants of T4 lysozyme (T4L) with ground and excited states interchanged and with exchange rates differing by fourfold (~ 900s-1 and ~ 3600s-1), as well as with a fast-folding domain where the unfolded state lifetime is ~ 80µs.

Measuring the signs of the methyl 1H chemical shift differences between major and 'invisible' minor protein conformational states using methyl 1H multi-quantum spectroscopy.

Carr-Purcell-Meiboom-Gill (CPMG) type relaxation dispersion experiments are now routinely used to characterise protein conformational dynamics that occurs on the μs to millisecond (ms) timescale between a visible major state and 'invisible' minor states. The exchange rate(s) ([Formula: see text]), population(s) of the minor state(s) and the absolute value of the chemical shift difference [Formula: see text] (ppm) between different exchanging states can be extracted from the CPMG data. However the sign of [Formula: see text] that is required to reconstruct the spectrum of the 'invisible' minor state(s) cannot be obtained from CPMG data alone. Building upon the recently developed triple quantum (TQ) methyl [Formula: see text] CPMG experiment (Yuwen in Angew Chem 55:11490-11494, 2016) we have developed pulse sequences that use carbon detection to generate and evolve single quantum (SQ), double quantum (DQ) and TQ coherences from methyl protons in the indirect dimension to measure the chemical exchange-induced shifts of the SQ, DQ and TQ coherences from which the sign of [Formula: see text] is readily obtained for two state exchange. Further a combined analysis of the CPMG data and the difference in exchange induced shifts between the SQ and DQ resonances and between the SQ and TQ resonances improves the estimates of exchange parameters like the population of the minor state. We demonstrate the use of these experiments on two proteins undergoing exchange: (1) the ~18kDa cavity mutant of T4 Lysozyme ([Formula: see text]) and (2) the [Formula: see text]kDa Peripheral Sub-unit Binding Domain (PSBD) from the acetyl transferase of Bacillus stearothermophilus ([Formula: see text]).

Application of geometric approximation to the CPMG experiment: Two- and three-site exchange

The Carr–Purcell–Meiboom–Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C′, Cα, Hα, etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain.

A 15N CPMG relaxation dispersion experiment more resistant to resonance offset and pulse imperfection

Carr–Purcell–Meiboom–Gill (CPMG) relaxation dispersion is a powerful NMR method to study protein dynamics on the microsecond–millisecond time scale. J-coupling, resonance offset, radio frequency field inhomogeneity, and pulse imperfection often introduce systematic errors into the measured transverse relaxation rates. Here we proposed a modified continuous wave decoupling CPMG experiment, which is more unaffected by resonance offset and pulse imperfection. We found that it is unnecessary to match the decoupling field strength with the delay between CPMG refocusing pulses, provided that decoupling field is strong enough. The performance of the scheme proposed here was shown by simulations and further demonstrated experimentally on a fatty acid binding protein.

An ultra-low cost NMR device with arbitrary pulse programming

Ultra-low cost, general purpose electronics boards featuring microprocessors or field programmable gate arrays (FPGA) are reaching capabilities sufficient for direct implementation of NMR spectrometers. We demonstrate a spectrometer based on such a board, implemented with a minimal need for the addition of custom electronics and external components. This feature allows such a spectrometer to be readily implemented using typical knowledge present in an NMR laboratory. With FPGA technology, digital tasks are performed with precise timing, without the limitation of predetermined hardware function. In this case, the FPGA is used for programming of arbitrarily timed pulse sequence events, and to digitally generate required frequencies. Data acquired from a 0.53T permanent magnet serves as a demonstration of the flexibility of pulse programming for diverse experiments. Pulse sequences applied include a spin–lattice relaxation measurement using a pulse train with small-flip angle pulses, and a Carr–Purcell–Meiboom–Gill experiment with phase cycle. Mixing of NMR signals with a digitally generated, 4-step phase-cycled reference frequency is further implemented to achieve sequential quadrature detection. The flexibility in hardware implementation permits tailoring this type of spectrometer for applications such as relaxometry, polarimetry, diffusometry or NMR based magnetometry.

An exact solution for R2,eff in CPMG experiments in the case of two site chemical exchange

The Carr–Purcell–Meiboom–Gill (CPMG) experiment is widely used to quantitatively analyse the effects of chemical exchange on NMR spectra. In a CPMG experiment, the effective transverse relaxation rate, R2,eff, is typically measured as a function of the pulse frequency, νCPMG. Here, an exact expression for how R2,eff varies with νCPMG is derived for the commonly encountered scenario of two-site chemical exchange of in-phase magnetisation. This result, summarised in Appendix A, generalises a frequently used equation derived by Carver and Richards, published in 1972. The expression enables more rapid analysis of CPMG data by both speeding up calculation of R2,eff over numerical methods by a factor of ca. 130, and yields exact derivatives for use in data analysis. Moreover, the derivation provides insight into the physical principles behind the experiment.

Boosting the electron spin coherence in binuclear Mn complexes by multiple microwave pulses

We investigate a possibility to enhance the coherence time of electron spins in magnetic molecular complexes by application of the Carr-Purcell-Meiboom-Gill (CPMG) multiple microwave pulse sequence. Our theoretical analysis shows that the CPMG sequence can efficiently suppress the spin decoherence channel arising due to spectral diffusion induced by a random modulation of the hyperfine interaction which is an important source of the spin dephasing in molecular magnets. We confirm this by employing the CPMG protocol in pulse electron spin resonance experiments on model binuclear 1,2-diphosphacyclopentadienyl manganese complexes. We show that, compared to the standardly used two-pulse primary spin-echo technique, the CPMG experiment can boost the phase memory time up to one order of magnitude, bringing it to above 10 $\ensuremath{\mu}$s at low temperatures. This finding may be important for the implementation of quantum computation protocols on molecular magnets. We discuss a possible interesting analogy with the Zeno's paradox in quantum theory (the Zeno quantum effect), which could be implicit in the CPMG experiment.

Quantitative comparison of errors in 15N transverse relaxation rates measured using various CPMG phasing schemes

Nitrogen-15 Carr-Purcell-Meiboom-Gill (CPMG) transverse relaxation experiment are widely used to characterize protein backbone dynamics and chemical exchange parameters. Although an accurate value of the transverse relaxation rate, R(2), is needed for accurate characterization of dynamics, the uncertainty in the R(2) value depends on the experimental settings and the details of the data analysis itself. Here, we present an analysis of the impact of CPMG pulse phase alternation on the accuracy of the (15)N CPMG R(2). Our simulations show that R(2) can be obtained accurately for a relatively wide spectral width, either using the conventional phase cycle or using phase alternation when the r.f. pulse power is accurately calibrated. However, when the r.f. pulse is miscalibrated, the conventional CPMG experiment exhibits more significant uncertainties in R(2) caused by the off-resonance effect than does the phase alternation experiment. Our experiments show that this effect becomes manifest under the circumstance that the systematic error exceeds that arising from experimental noise. Furthermore, our results provide the means to estimate practical parameter settings that yield accurate values of (15)N transverse relaxation rates in the both CPMG experiments.

Measurement of Methyl Axis Orientations in Invisible, Excited States of Proteins by Relaxation Dispersion NMR Spectroscopy

Few detailed studies of transiently populated conformations of biological molecules have emerged despite the fact that such states are often important to processes such as protein folding, enzyme catalysis, molecular recognition and binding. A major limitation has been the lack of experimental tools to study these often invisible, short-lived conformers. Recent advances in relaxation dispersion NMR spectroscopy are changing this paradigm with the potential to generate high resolution structural information which is necessary for a rigorous characterization of these states. In this study, we present an experimental method for establishing the relative orientations of methyl groups in invisible, excited states of proteins by measuring methyl (1)H-(13)C residual dipolar couplings (RDCs). In our approach, four two-dimensional spectra are acquired at a pair of static magnetic fields. Each spectrum contains one of the four isolated multiplet components of a coupled methyl carbon, whose signal intensities, modulated by the pulsing frequency of a Carr-Purcell-Meiboom-Gill (CPMG) element, are sensitive to both chemical shift and RDC differences between exchanging states. In addition, data sets from a CPMG experiment which monitors the decay of in-phase methyl (13)C magnetization are recorded, that are sensitive only to the differences in chemical shifts between the states. Using our methodology, RDC values obtained from an invisible state in an exchanging system are shown to be in good agreement with the corresponding values measured under conditions where the invisible state is stabilized to become the highly populated ground state. The approach allows the measurement of anisotropic restraints at methyl positions in excited states and complements previously developed experiments focusing on the protein backbone.

Practical aspects of 15N CPMG transverse relaxation experiments for proteins in solution

AbstractThe 15N transverse relaxation as measured by the Carr‐Purcell‐Meiboom‐Gill (CPMG) sequence is often used to characterize protein backbone dynamics in solution. In the 15N CPMG experiment, the delay between 15N CPMG pulses typically is set sufficiently short to minimize the effects of relaxation by the 15N‐1H antiphase component. This limits the total relaxation duration of the CPMG experiment because frequent application of the high B1 field to the heteronucleus may cause probe damage. The resulting antiphase component can be minimized by using 1H composite decoupling or by applying 1H 180° pulses more frequently than the 15N CPMG pulses. In this study, we simulated 15N CPMG relaxation in the presence of either 1H composite decoupling or 1H 180° pulses and compared the results with the experimental transverse relaxation data acquired with [u‐15N]‐ or [u‐15N, u‐2H]‐ubiquitin samples. We explain systematic errors resulting from these CPMG experiments and describe a method for recording 15N transverse relaxation in a manner that minimizes probe problems. © 2009 Wiley Periodicals, Inc. Concepts Magn Reson Part A 34A: 63–75, 2009.

Fat and moisture content determination with unilateral NMR

Abstract Unilateral (one-sided) NMR, with easy sample access and rapid “through-package” measurement, is a promising new technology in food science. Here we investigated the applicability of two methods for fat and moisture content determination by unilateral NMR. One is a post-measurement decomposition of a Carr–Purcell–Meiboom–Gill (CPMG) signal using a classical least-squares (CLS) multivariate analysis. The other is based on a diffusion-weighted CPMG experiment, where the components are discriminated at the time of measurement through the diffusivity difference between fat and moisture. The experiments were carried out on model samples of cod liver oil emulsion in water and on commercial ground beef. The CLS analysis exhibits a good predictive performance provided the fat and moisture components conserve their characteristic relaxation times in different samples. The diffusion-weighted CPMG, although more complex experimentally, is free of this restriction. The methods will be of interest for online analysis of food materials and supplement laborious standard extraction methods.

Signal-to-noise enhancement of NMR spectra of solids using multiple-pulse spin-echo experiments

Three multiple-pulse spin-echo experiments that have been used to enhance the sensitivity of broad powder patterns obtained from NMR spectra of spin-1/2 and half-integer quadrupolar nuclei in polycrystalline solids are examined. Specifically, the Carr-Purcell Meiboom-Gill (CPMG), the Mansfield-Waugh (MW-4), and a modified version of the CPMG experiment (modified-CPMG) are described and compared. Use of these pulse sequences results in transforming the broad powder lineshapes into a series of narrow spikelets whose overall envelope mimics that obtained from the normal Hahn-echo experiment. The CPMG and modified-CPMG methods can result in a considerable saving in experiment time and are particularly powerful in studying the central transition of half-integer spin quadrupolar nuclei. Artifacts generated by the MW-4 sequence or caused by imperfections in the π pulses in the CPMG sequences are explained using a product operator analysis. © 2005 Wiley Periodicals, Inc. Concepts Magn Reson Part A 26A: 62–77, 2005

Exploring the separate NMR responses from crude oil and water in rock cores

In analysis of transverse relaxation time (T2) curves in a Carr-Purcell-Meiboom-Gill (CPMG) experiment in a multicomponent system originating from measurements of oil and water in rock cores, where internal magnetic field gradients broaden the line widths significantly, there is very little direct information to be extracted of the different components contributing to the totalT2 relaxation time curve. From the study of rock cores saturated with different amounts of crude oil and water, we show that with an optimised experimental setup it is possible to extract information from the nuclear magnetic resonance response that is not resolved by any other methods. This setup combines pulsed field gradient methods with the CPMG experiment utilizing data from both rock cores and bulk oil and water. Then it becomes feasible to separate the signals from oil and water where the two-dimensional inverse Laplace transform ordinarily seems to fail.

Application of Multiple-Pulse Experiments to Characterize Broad NMR Chemical-Shift Powder Patterns from Spin-1/2Nuclei in the Solid State

The utility of the Carr-Purcell Meiboom-Gill (CPMG) experiment and a modified-CPMG experiment in characterizing NMR chemical-shift powder patterns for spin-1/2 nuclei is demonstrated. Heavier NMR-active nuclei such as 195Pt, 199Hg, and 207Pb are known to be extremely sensitive to their local environment and as such have very large chemical-shift ranges. In the solid state, such nuclei commonly exhibit chemical shifts that range well over 1000 ppm, depending upon the orientation of the molecule within the applied magnetic field. Thus, acquiring NMR spectra of polycrystalline samples is often an experimental challenge because of these very broad powder patterns. In acquiring chemical-shift powder patterns of these nuclei, we provide several examples that demonstrate that a considerable saving in time is realized by using the CPMG experiment as opposed to the standard one-pulse or spin-echo experiment. In general, this time saving is even greater if a modified-CPMG experiment is used. Homonuclear dipolar interactions are considerably reduced in the CPMG experiment and are almost completely removed in the modified-CPMG experiment. For samples containing 1H, larger enhancements are realized by combining the CPMG experiment with cross polarization. By use of the CPMG and the modified-CPMG experiments, the principal components of the chemical-shift tensors are determined for each of the samples studied.

Combining PFG and CPMG NMR measurements for separate characterization of oil and water simultaneously present in a heterogeneous system

When analyzingT2 relaxation time curves from an ordinary Carr-Purcell-Meiboom-Gill (CPMG) experiment in a multicomponent system, where internal magnetic field gradients broaden the line widths significantly, there is very little direct information regarding the mobility of the components and on the type of environment experienced by each component. Compared to a standard CPMG experiment, a combination of pulsed field gradient (PFG) methods with the CPMG experiment will increase the amount of information that is obtainable from the nuclear magnetic resonance (NMR) experiment on a system of components differing significantly in molecular mobility. We propose a method for achieving separate measurements of theT2 attenuation of two components simultaneously present within a sample, and we believe it to be generally valid for any system in which the components differ significantly in molecular mobility. The two components could be oil and water in porous rock, or fat and water in a biological tissue, where a separation of theT2 attenuations for the two components will add insight to the study of the systems. In order to verify the method we made use of a sample containing a mixture of oil and water in two separate bulk phases, and compared the results with PFG-CPMG experiments performed on samples containing oil or water only, respectively. The method was applied to systems containing glass spheres immersed in water and oil, and it was possible to obtain information about the physical environment of the components which otherwise is not easily obtainable. The method presented here is therefore presumably applicable to whole rock cores or tissue samples.

Direct measurement of the distance between adjacent guest molecules in a disordered solid inclusion compound using solid-state [formula omitted] NMR spectroscopy

Three solid-state NMR techniques have been used to determine the effective average intermolecular 19 F, 19 F dipolar interaction, 〈 D ′〉, between fluorine nuclei in neighbouring guest molecules in the 1,10-difluorodecane/urea inclusion compound using a static sample. An MREV8 pulse sequence was used to isolate the shielding powder pattern. A Carr–Purcell–Meiboom–Gill experiment was employed to obtain the dipolar powder pattern. To confirm the results, the full powder pattern influenced by both interactions was obtained and simulated by computer. In all experiments efficient proton decoupling was used. The value of 〈 D ′〉 obtained is 1.01 kHz. This is discussed in relation to the conformations and mutual orientation of the end-groups of the guest molecules. The result is consistent with random distribution over all mutual orientations of the gauche–gauche and gauche–trans situations, with little or no population in the trans–trans form.

Sensitivity-Enhanced Quadrupolar-Echo NMR of Half-Integer Quadrupolar Nuclei. Magnitudes and Relative Orientation of Chemical Shielding and Quadrupolar Coupling Tensors

A novel approach to quadrupolar-echo (QE) NMR of half-integer quadrupolar nuclei in static powders is analyzed. By acquisition of the QE spectrum during a Carr−Purcell−Meiboom−Gill (CPMG) train of selective π pulses, the second-order quadrupolar line shape for the central transition is split into a comb of sidebands leading to a considerable increase in the sensitivity compared to a conventional QE spectrum. The applicability of the method for determination of magnitudes and relative orientation of chemical shielding and quadrupolar coupling tensors is examined. Through numerical simulation and iterative fitting of experimental 87Rb (RbClO4 and RbVO3) and 59Co spectra (Co(NH3)5 Cl3), it is demonstrated that the quadrupolar CPMG experiment represents a useful method for studying half-integer quadrupolar nuclei exhibiting large quadrupolar coupling combined with anisotropic chemical shielding interactions. Sensitivity enhancements by a factor of up to about 30 are observed for the samples studied.

Combined proton T1N and CPMG T2N studies of water saturated sandstone core plugs

Diffusion dynamics for water in a series of sandstone core plugs with a broad range of permeabilities was studied using both the Carr-Purcell-Meiboom-Gill (CPMG) and inversion recovery experiments. Both the transverse and longitudinal magnetization curves were found to fit well to stretched exponential relaxation kinetics. At short times, the transverse magnetization is well described by an expression for free diffusion averaged over a distribution of pore sizes. The stretch exponents for the transverse and longitudinal magnetization are shown to be simply related to the width of the pore size distribution. A cross over from free to restricted diffusion is evident in the dependence of T 2 with increasing diffusion time set by the interpulse spacing τ in the CPMG experiment. The T 2( τ) data is fit to a model which interpolates between the limits of free and restricted diffusion. A length derived from this model is shown to provide a simple estimate of the absolute fluid flow permeability.