PITANSEMA, a low-power PISEMA solid-state NMR experiment

A low radio frequency power polarization inversion spin exchange at the magic angle (PISEMA) pulse sequence is described for the measurement of heteronuclear dipolar couplings from solids. The method employs a time averaged nutation concept to significantly reduce the rf power required to spin-lock low gamma nuclear spins in PISEMA experiments. The efficacy of the 2D method is demonstrated on a single crystal of n-acetyl-L-(15)N-valyl-L-(15)N-leucine dipeptide to measure (1)H-(15)N dipolar couplings and a liquid crystal sample to measure (1)H-(13)C dipolar couplings.     

PITANSEMA-MAS, a solid-state NMR method to measure heteronuclear dipolar couplings under MAS

A 2D NMR method is presented for the measurement of the dipole-dipole interaction between a proton and a low-frequency nuclear spin species in the solid state under the magic angle spinning. It employs the time averaged nutation concept to dramatically reduce the required radio frequency (rf) power on the low γ nuclear channel and spin exchange at the magic angle is used to suppress (1)H-(1)H dipolar interactions and chemical shifts. The flexibility in choosing the spinning speed, rf power and the scaling factor of the pulse sequence are of considerable importance for the structural studies of biological solids. The performance of the pulse sequence has been numerically and experimentally demonstrated on several solids.     

Theory of stochastic dipolar recoupling in solid-state nuclear magnetic resonance

Dipolar recoupling techniques in solid-state nuclear magnetic resonance (NMR) consist of radio frequency (rf) pulse sequences applied in synchrony with magic-angle spinning (MAS) that create nonzero average magnetic dipole-dipole couplings under MAS. Stochastic dipolar recoupling (SDR) is a variant in which randomly chosen rf carrier frequency offsets are introduced to cause random phase modulations of individual pairwise couplings in the dipolar spin Hamiltonian. Several aspects of SDR are investigated through analytical theory and numerical simulations: (1) An analytical expression for the evolution of nuclear spin polarization under SDR in a two-spin system is derived and verified through simulations, which show a continuous evolution from coherent, oscillatory polarization exchange to incoherent, exponential approach to equilibrium as the range of random carrier offsets (controlled by a parameter f(max)) increases; (2) in a many-spin system, polarization transfers under SDR are shown to be described accurately by a rate matrix in the limit of large f(max), with pairwise transfer rates that are proportional to the inverse sixth power of pairwise internuclear distances; (3) quantum mechanical interferences among noncommuting pairwise dipole-dipole couplings, which are a complicating factor in solid-state NMR studies of molecular structures by traditional dipolar recoupling methods, are shown to be absent from SDR data in the limit of large f(max), provided that coupled nuclei have distinct NMR chemical shifts.     

Magnetic exchange couplings in the single-molecule magnet of Mn(12)-Ac

Four types of isotropic exchange interactions of Mn(12)-Ac are obtained by using the classical Monte Carlo simulations. The equilibrium susceptibilities are well reproduced in the temperature range between 10 and 100 K. The calculated effective spin at 0.1 K coincides with the ground-state spin. Our results show that J(1) and J(2) are strong antiferromagnetic, but the magnitude of J(2) is much smaller than that of J(1). Both J(3) and J(4) favor weakly antiferromagnetic couplings. The effects of the exchange couplings on the magnetic properties and ground-state spin are investigated too. The magnetic susceptibilities below 100 K depend more on J(2) rather than on the stronger J(1). The weak exchange couplings J(3) and J(4) have significant frustration effects on the ground-state configuration.     

NMR R1 rho rotating-frame relaxation with weak radio frequency fields

NMR spin relaxation in the rotating frame (R(1 rho)) is one of few methods available to characterize chemical exchange kinetic processes occurring on micros-ms time scales. R(1 rho) measurements for heteronuclei in biological macromolecules generally require decoupling of (1)H scalar coupling interactions and suppression of cross-relaxation processes. Korzhnev and co-workers demonstrated that applying conventional (1)H decoupling schemes while the heteronuclei are spin-locked by a radio frequency (rf) field results in imperfect decoupling [Korzhnev, Skrynnikov, Millet, Torchia, Kay. J. Am. Chem. Soc. 2002, 124, 10743-10753]. Experimental NMR pulse sequences were presented that provide accurate measurements of R(1 rho) rate constants for radio frequency field strengths > 1000 Hz. This paper presents new two-dimensional NMR experiments that allow the use of weak rf fields, between 150 and 1000 Hz, in R(1 rho) experiments. Fourier decomposition and average Hamiltonian theory are employed to analyze the spin-lock sequence and provide a guide for the development of improved experiments. The new pulse sequences are validated using ubiquitin and basic pancreatic trypsin inhibitor (BPTI). The use of weak spin-lock fields in R(1 rho) experiments allows the study of the chemical exchange process on a wider range of time scales, bridging the gap that currently exists between Carr-Purcell-Meiboom-Gill and conventional R(1 rho) experiments. The new experiments also extend the capability of the R(1 rho) technique to study exchange processes outside the fast exchange limit.     

Precision 1H-1H distance measurement via 13C NMR signals: utilization of 1H-1H double-quantum dipolar interactions recoupled under magic angle spinning conditions

We applied the POST-C7 DQ-dipolar recoupling pulse sequence to the measurement of (1)H-(1)H distances with high precision. The spectral resolution is enhanced by detecting the (1)H magnetization via (13)C signals. A least-squares fitting of the build-up curve of the transferred magnetization to the exact numerical simulations yielded a (1)H(alpha)-(1)H(beta) distance of 248 +/- 4 pm for fully (13)C-labeled L-valine. This distance agrees with the neutron diffraction study. The negative transferred magnetization clearly indicates that the direct DQ (1)H-(1)H dipolar couplings have the largest effect. The signal for the magnetization transfer builds up rapidly by the direct (1)H-(1)H dipolar coupling, and decreases to zero at longer mixing time when the relayed magnetization transfer becomes significant. This large intensity change of the signal leads to the high precision in the distance measurement. We inspected factors that limit the effective bandwidth of the POST-C7 recoupling for the (1)H and (13)C homonuclear spin systems. The spin interactions at times shorter than the cycle time of the C7 sequence were also evaluated to measure the distances. The carbon-detected 2D (1)H DQ mixing experiment was demonstrated for the measurement of multiple (1)H-(1)H distances.     

Spin dynamics in the modulation frame: application to homonuclear recoupling in magic angle spinning solid-state NMR

We introduce a family of solid-state NMR pulse sequences that generalizes the concept of second averaging in the modulation frame and therefore provides a new approach to perform magic angle spinning dipolar recoupling experiments. Here, we focus on two particular recoupling mechanisms-cosine modulated rotary resonance (CMpRR) and cosine modulated recoupling with isotropic chemical shift reintroduction (COMICS). The first technique, CMpRR, is based on a cosine modulation of the rf phase and yields broadband double-quantum (DQ) (13)C recoupling using >70 kHz omega(1,C)/2pi rf field for the spinning frequency omega(r)/2=10-30 kHz and (1)H Larmor frequency omega(0,H)/2pi up to 900 MHz. Importantly, for p>or=5, CMpRR recouples efficiently in the absence of (1)H decoupling. Extension to lower p values (3.5相似文献   

Two-dimensional (2D) pulsed electron paramagnetic resonance study of VO(2+)-triphosphate interactions: evidence for tridentate triphosphate coordination, and relevance to bone uptake and insulin enhancement by vanadium pharmaceuticals

Two- and four-pulse electron spin echo envelope modulation (ESEEM) and four-pulse two-dimensional hyperfine sublevel correlation (HYSCORE) spectroscopies have been used to determine the solution structure of a 3:1 triphosphate:vanadyl solution at pH 5.0. Limited quantitative data were extracted from the two pulse spectra; however, HYSCORE proved to be more useful in the detection and interpretation of the (31)P and (1)H couplings. Three sets of cross-peaks were observed for each nucleus. For the (31)P couplings, three sets of cross-peaks were observed in the HYSCORE spectrum, and contour line shape analysis yielded coupling constants of approximately 15, 9, and 1 MHz. HYSCORE cross-peaks in the proton region were partially overlapping; however, interpretation of the proton coupling was simplified through the use of one-dimensional four-pulse ESEEM and subsequent analysis of the sum combination peaks. Comparison of the derived isotropic and anisotropic coupling constants with results from earlier ESEEM and electron nuclear double resonance (ENDOR) studies was consistent with the presence of at least one, and most likely two, water molecules coordinated in the equatorial plane of the vanadyl cation. The vanadyl-triphosphate system was shown to be an accurate model of the in vivo vanadyl-phosphate coupling constants determined in an earlier study (Dikanov, S. A.; Liboiron, B. D.; Thompson, K. H.; Vera, E.; Yuen, V. G.; McNeill, J. H.; Orvig, C. J. Am. Chem. Soc. 1999, 121, 11004.) Comparison of these values to those found in previous spectroscopic studies of vanadyl-triphosphate interactions, along with a detailed structural interpretation, are presented. This work represents the first detection of tridentate polyphosphate coordination to the vanadyl ion, and the first observation of an axial phosphate interaction not previously reported in earlier ENDOR and pulsed electron paramagnetic resonance studies.     

PELDOR measurements on a nitroxide-labeled Cu(II) porphyrin: orientation selection, spin-density distribution, and conformational flexibility

Metal ions are functionally or structurally important centers in metalloproteins or RNAs, which makes them interesting targets for spectroscopic investigations. In combination with site-directed spin labeling, pulsed electron-electron double resonance (PELDOR or DEER) could be a well-suited method to characterize and localize them. Here, we report on the synthesis, full characterization, and PELDOR study of a copper(II) porphyrin/nitroxide model system. The X-band PELDOR time traces contain besides the distance information a convolution of orientational selectivity, conformational flexibility, exchange coupling, and spin density distribution, which can be deconvoluted by experiments with different frequency offsets and simulations. The simulations are based on the known experimental and spin Hamiltonian parameters and make use of a geometric model as employed for structurally similar bis-nitroxides and spin density parameters as obtained from density functional theory calculations. It is found that orientation selection with respect to dipolar angles is only weakly resolvable at X-band frequencies due to the large nitrogen hyperfine coupling of the copper porphyrin. On the other hand, the PELDOR time traces reveal a much faster oscillation damping than observed for structurally similar bis-nitroxides, which is mainly assigned to a small distribution in exchange couplings J. Taking the effects of orientation selectivity, distribution in J, and spin density distribution into account leads finally to a narrow distance distribution caused solely by the flexibility of the structure, which is in agreement with distributions from known bis-nitroxides of similar structure. Thus, X-band PELDOR measurements at different frequency offsets in combination with explicit time trace simulations allow for distinguishing between structural models and quantitative interpretation of copper-nitroxide PELDOR data gives access to localization of copper(II) ions.     

Heteronuclear proton assisted recoupling

We describe a theoretical framework for understanding the heteronuclear version of the third spin assisted recoupling polarization transfer mechanism and demonstrate its potential for detecting long-distance intramolecular and intermolecular (15)N-(13)C contacts in biomolecular systems. The pulse sequence, proton assisted insensitive nuclei cross polarization (PAIN-CP) relies on a cross term between (1)H-(15)N and (1)H-(13)C dipolar couplings to mediate zero- and∕or double-quantum (15)N-(13)C recoupling. In particular, using average Hamiltonian theory we derive effective Hamiltonians for PAIN-CP and show that the transfer is mediated by trilinear terms of the form N(±)C(?)H(z) (ZQ) or N(±)C(±)H(z) (DQ) depending on the rf field strengths employed. We use analytical and numerical simulations to explain the structure of the PAIN-CP optimization maps and to delineate the appropriate matching conditions. We also detail the dependence of the PAIN-CP polarization transfer with respect to local molecular geometry and explain the observed reduction in dipolar truncation. In addition, we demonstrate the utility of PAIN-CP in structural studies with (15)N-(13)C spectra of two uniformly (13)C,(15)N labeled model microcrystalline proteins-GB1, a 56 amino acid peptide, and Crh, a 85 amino acid domain swapped dimer (MW=2×10.4 kDa). The spectra acquired at high magic angle spinning frequencies (ω(r)∕2π>20 kHz) and magnetic fields (ω(0H)∕2π=700-900 MHz) using moderate rf fields, yield multiple long-distance intramonomer and intermonomer (15)N-(13)C contacts. We use these distance restraints, in combination with the available x-ray structure as a homology model, to perform a calculation of the monomer subunit of the Crh protein.     

Applications of pi-photon-induced transparency in two-frequency pulse electron paramagnetic resonance experiments

An approach to pulse electron paramagnetic resonance (EPR) experiments which are based on two different resonance fields is introduced. Instead of using two microwave (mw) sources or a magnetic field jump, bichromatic pulses consisting of a transverse microwave field with frequency omega(mw) and a longitudinal radio frequency field with frequency omega(rf) are employed. Such bichromatic pulses excite a number of multiple photon transitions at frequencies omega(mw)+komega(rf) (k in Z). The pi-photon-induced transparency phenomenon is used to select the required transitions. This approach is used in the stimulated soft electron spin echo envelope modulation and the four-pulse double electron-electron resonance experiments. The results obtained using the bichromatic pulse approach are in agreement with those obtained with the standard pulse EPR techniques. It is shown that applying bichromatic pulses is straightforward and advantageous in several respects.     

Frequency selective heteronuclear dipolar recoupling in rotating solids: accurate (13)C-(15)N distance measurements in uniformly (13)C,(15)N-labeled peptides

We describe a magic-angle spinning NMR experiment for selective (13)C-(15)N distance measurements in uniformly (13)C,(15)N-labeled solids, where multiple (13)C-(15)N and (13)C-(13)C interactions complicate the accurate measurement of structurally interesting, weak (13)C-(15)N dipolar couplings. The new experiment, termed FSR (frequency selective REDOR), combines the REDOR pulse sequence with a frequency selective spin-echo to recouple a single (13)C-(15)N dipolar interaction in a multiple spin system. Concurrently the remaining (13)C-(15)N dipolar couplings and all (13)C-(13)C scalar couplings to the selected (13)C are suppressed. The (13)C-(15)N coupling of interest is extracted by a least-squares fit of the experimentally observed modulation of the (13)C spin-echo intensity to the analytical expression describing the dipolar dephasing in an isolated heteronuclear spin pair under conventional REDOR. The experiment is demonstrated in three uniformly (13)C,(15)N-labeled model systems: asparagine, N-acetyl-L-Val-L-Leu and N-formyl-L-Met-L-Leu-L-Phe; in N-formyl-[U-(13)C,(15)N]L-Met-L-Leu-L-Phe we have determined a total of 16 internuclear distances in the 2.5-6 A range.     

Z-restored spin-echo 13C 1D spectrum of straight baseline free of hump, dip and roll

A pulse sequence of z-restored spin echo, -pi-beta-tau-pi-tau-, employing a pi pulse in the middle of the delay (2tau) to form a spin echo and the two pi pulses together to restore the residual longitudinal magnetization back to + z direction, is described. (13)C spectra of organic compounds provide a wealth of structural information; however, (13)C 1D spectra acquired using reverse geometry probes can have significant baseline humps or rolls because of pulse ring-down within the coil. The baseline distortions are especially apparent in spectra acquired using cryogenically enhanced probes. The baseline problem may be alleviated by extending the delay between the last pulse and the starting point of acquisition. However, uses of long delay times introduce large negative first-order phase corrections which themselves produce baseline roll. The prescribed experiment can be used to completely remove the hump, roll or dip in the baseline of the (13)C spectrum and at the same time obtain sensitivity similar to the experiment of a single beta pulse. We believe that this experiment will be of general applications in acquiring high-quality (13)C NMR data with reverse geometry probes and spectral interpretation.     

SESAME-HSQC for simultaneous measurement of NH and CH scalar and residual dipolar couplings

We present a novel pulse sequence, SESAME-HSQC, for the simultaneous measurement of several NH and CH scalar and residual dipolar couplings in double labeled proteins. The proposed Spin-statE Selective All Multiplicity Edited (SESAME)-HSQC combines gradient selected and sensitivity enhanced (15)N- and constant-time (13)C-HSQC experiments with the recently introduced spin-state selective method (Nolis et al., J. Magn. Reson. 180 (2006) 39-50) for measuring couplings simultaneously at amide and aliphatic regions. Excellent resolution and high sensitivity is warranted by removing all coupling interactions during the indirectly detected t(1) period, and by employing pulsed field gradients for coherence selection and utilizing coherence order selective spin-state selection. The scalar and residual dipolar couplings can be readily measured from a two-dimensional (15)N/(13)C-HSQC spectrum without additional spectral crowding. SESAME-HSQC can be used for epitope mapping by observing chemical shift changes in both amide and aliphatic regions. Simultaneously, potential conversion in protein conformation can be probed by analyzing changes in residual dipolar couplings induced by ligand binding. The pulse sequence is experimentally verified with a sample of (15)N/(13)C enriched human ubiquitin. The internuclear vector directions determined from the residual dipolar couplings are found to be in excellent correlation with those predicted from ubiquitin's refined solution structure.     

Frequency-selective measurement of heteronuclear scalar couplings in solid-state NMR

A new technique is proposed for selective measurement of heteronuclear scalar J couplings between spins in solids. The method, referred to as FS-J-RES (Frequency-Selective-J-RESolved) NMR, uses frequency-selective irradiation at the I (nonobserved) spin frequency to target a specific pair of spins in a multispin system. In addition, the technique provides direct information about the number of identical I spins chemically bonded to the observed S nucleus. A reference spectrum, recorded without irradiating the I spins, accounts for transverse relaxation, pulse imperfections and dephasing due to homonuclear J couplings between S nuclei, which can be simultaneously measured with this method.     

Quantitative 2D HSQC (Q-HSQC) via suppression of J-dependence of polarization transfer in NMR spectroscopy: application to wood lignin

A quantitative method to record (1)H-(13)C correlation NMR spectra (Q-HSQC) is presented. The suppression of (1)J(CH)-dependence is achieved by modulating the polarization transfer delays of HSQC. In addition, the effect of homonuclear couplings, as well as relaxation during the pulse sequence are discussed. We developed the Q-HSQC approach for the quantitative analysis of wood lignin, a complex polymer where it has been difficult to obtain reliable data on the relative amounts of different structural units. The current method is applicable to a variety of complex mixtures, where normal 1D (1)H- and (13)C-NMR methods fail.     

Heteronuclear dipolar recoupling in solid-state nuclear magnetic resonance by amplitude-, phase-, and frequency-modulated Lee-Goldburg cross-polarization

This paper presents a theoretical, numerical, and experimental study of phase- and frequency-switched Lee-Goldburg cross-polarization (FSLG-CP) under magic-angle spinning conditions. It is shown that a well-defined amplitude modulation of one of the two radio-frequency (rf) fields in the FSLG-CP sequence results in highly efficient heteronuclear dipolar recoupling. The recoupled dipolar interaction is gamma-encoded and, under ideal conditions, the effective spin Hamiltonian is equivalent to that in continuous-wave Lee-Goldburg CP. In practice, however, FSLG-CP is less susceptible to rf field mismatch and inhomogeneity, and provides better suppression of (1)H spin diffusion. The performance of FSLG-CP is experimentally demonstrated on liquid-crystalline samples exhibiting motionally averaged dipolar couplings.     

A study of homonuclear dipolar recoupling pulse sequences in solid-state nuclear magnetic resonance

Dipolar recoupling pulse sequences are of great importance in magic angle spinning solid-state NMR. Recoupling sequences are used for excitation of double-quantum coherence, which, in turn, is employed in experiments to estimate internuclear distances and molecular torsion angles. Much effort is spent on the design of recoupling sequences that are able to produce double-quantum coherence with high efficiency in demanding spin systems, i.e., spin systems with small dipole-dipole couplings and large chemical-shift anisotropies (CSAs). The sequence should perform robustly under a variety of experimental conditions. This paper presents experiments and computer calculations that extend the theory of double-quantum coherence preparation from the strong coupling/small CSA limit to the weak coupling limit. The performance of several popular dipole-dipole recoupling sequences-DRAWS, POST-C7, SPC-5, R1, and R2-are compared. It is found that the optimum performance for several of these sequences, in the weak coupling/large CSA limit, varies dramatically, with respect to the sample spinning speed, the magnitude and orientation of the CSAs, and the magnitude of dipole-dipole couplings. It is found that the efficiency of double-quantum coherence preparation by gamma-encoded sequences departs from the predictions of first-order theory. The discussion is supported by density-matrix calculations.     

Hydroxymethyl group conformation in saccharides: structural dependencies of (2)J(HH), (3)J(HH), and (1)J(CH) spin-spin coupling constants

Experimental and theoretical methods have been used to correlate (2)J(HH) and (3)J(HH) values within the exocyclic hydroxymethyl groups (CH(2)OH) of saccharides with specific molecular parameters, and new equations are proposed to assist in the structural interpretation of these couplings. (3)J(HH) depends mainly on the C-C torsion angle (omega) as expected, and new Karplus equations derived from J-couplings computed from density functional theory (DFT) in a model aldopyranosyl ring are in excellent agreement with experimental values and with couplings predicted from a previously reported general Karplus equation. These results confirm the reliability of DFT-calculated (1)H-(1)H couplings in saccharides. (2)J(HH) values depend on both the C-C (omega) and C-O (theta) torsions. Knowledge of the former, which may be derived from other parameters (e.g., (3)J(HH)), allows theta to be evaluated indirectly from (2)J(HH). This latter approach complements more direct determinations of theta from (3)J(HCOH) and potentially extends these more conventional analyses to O-substituted systems lacking the hydroxyl proton. (1)J(CH) values within hydroxymethyl fragments were also examined and found to depend on r(CH), which is modulated by specific bond orientation and stereoelectronic factors. These latter factors could be largely, but not completely, accounted for by C-C and C-O torsional variables, leading to only semiquantitative treatments of these couplings (details discussed in the Supporting Information). New equations pertaining to (2)J(HH) and (3)J(HH) have been applied to the analysis of hydroxymethyl group J-couplings in several mono- and oligosaccharides, yielding information on C5-C6 and/or C6-O6 rotamer populations.     

Fast numerical design of spatial-selective rf pulses in MRI using Krotov and quasi-Newton based optimal control methods

The use of increasingly strong magnetic fields in magnetic resonance imaging (MRI) improves sensitivity, susceptibility contrast, and spatial or spectral resolution for functional and localized spectroscopic imaging applications. However, along with these benefits come the challenges of increasing static field (B(0)) and rf field (B(1)) inhomogeneities induced by radial field susceptibility differences and poorer dielectric properties of objects in the scanner. Increasing fields also impose the need for rf irradiation at higher frequencies which may lead to elevated patient energy absorption, eventually posing a safety risk. These reasons have motivated the use of multidimensional rf pulses and parallel rf transmission, and their combination with tailoring of rf pulses for fast and low-power rf performance. For the latter application, analytical and approximate solutions are well-established in linear regimes, however, with increasing nonlinearities and constraints on the rf pulses, numerical iterative methods become attractive. Among such procedures, optimal control methods have recently demonstrated great potential. Here, we present a Krotov-based optimal control approach which as compared to earlier approaches provides very fast, monotonic convergence even without educated initial guesses. This is essential for in vivo MRI applications. The method is compared to a second-order gradient ascent method relying on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method, and a hybrid scheme Krotov-BFGS is also introduced in this study. These optimal control approaches are demonstrated by the design of a 2D spatial selective rf pulse exciting the letters "JCP" in a water phantom.