Nuclear Coherence Research Articles

Analysis of Coherent Raman Beats from a Four-Level Electron–Nuclear-Spin-Coupled System

A linear analysis of the density-matrix equations for a four-level electron–nuclear-spin-coupled system predicts the onset of a coherent Raman beat signal. The signal appears during the application of a long, single, weak, continuous-wave EPR probe pulse which replaces the third pulse in the stimulated-echo experiment, and is identical to the three-pulse stimulated-echo envelope modulation calculated by Mims [Phys. Rev. B5,2409 (1972)]. The first two pulses prepare coherent superposition among coupled nuclear-spin states. During the EPR probe pulse, nuclear coherence is transfered to electron-spin coherence which exhibits beats as a measure of the splittings among the nuclear levels.

Pulse Schemes Free of Blind Spots and Dead Times for the Measurement of Nuclear Modulation Effects in EPR

A three-pulse and a four-pulse sequence for measuring nuclear modulation effects in pulsed EPR spectroscopy are proposed. The schemes make use of a combination of selective and nonselective microwave pulses to create and detect nuclear coherence. Both approaches are free of the suppression effect and are distinguished by an adjustable orientation selectivity for disordered systems. Phase problems do not exist in the four-pulse scheme, since the instrumental dead time is not relevant in this experiment. Qualitative descriptions of the experiments are given and analytical expressions are derived. The predicted features are verified experimentally.

Nuclear coherence-transfer echoes in pulsed EPR

Nuclear coherence-transfer echoes created in disordered electron–nuclear spin systems by microwave pulses are described. Once nuclear coherence is generated, a nonselective microwave π pulse inverts the electron spins thereby interchanging nuclear coherence between the two electron spin manifolds. This exchange refocuses the inhomogeneity of the secular part of the hyperfine interaction. The mechanisms of echo formation for weak and strong hyperfine couplings are explained by using simple vector diagrams. Various methods to create and detect nuclear coherence by microwave pulses are discussed with special attention directed to the sequence π/2–τ–π/2–t1–π–t2–π/2–τ. In this four-pulse experiment the nuclear coherence-transfer echo is observed as an amplitude modulation of the electron spin echo intensity. The nuclear coherence-transfer echo can be shifted to a time interval fully separated from the one covered by the instrumental deadtime. The time evolution of an S=1/2, I=1/2 model spin system during the four-pulse sequence is described using the density operator formalism. Several one- and two-dimensional four-pulse experiments are discussed on this basis and their spectra are analyzed in terms of nuclear coherence-transfer pathways. A new one-dimensional experiment based on nuclear coherence-transfer echoes, deadtime free ESEEM by nuclear coherence-transfer echoes (DEFENCE) is proposed to exploit undistorted electron spin echo envelope modulation (ESEEM) spectra. DEFENCE is a fast pulsed EPR technique that is unpretentious with respect to the required microwave equipment. The predicted features of the nuclear coherence-transfer echoes and of the DEFENCE approach are verified experimentally.

The High-resolution Structure of the Histidine-containing Phosphocarrier Protein HPr from Escherichia coli Determined by Restrained Molecular Dynamics from Nuclear Magnetic Resonance Nuclear Overhauser Effect Data

The solution structure of the histidine-containing phosphocarrier protein HPr from Escherichia coli has been determined by NMR in combination with distance geometry and restrained molecular dynamics. The structure is based on 1520 experimental restraints identified from both three-dimensional 1 H- 1H- 13C and 1 H- 1H- 15N nuclear Overhauser effect multiple quantum coherence spectroscopy and two dimensional 1H- 1H nuclear Overhauser effect spectra. Thirty-two four-dimensional coordinate frames were produced by metric matrix distance geometry, subjected to distance bounds driven dynamics, projected into three-dimensional space and again subjected to distance-bounds driven dynamics. These 32 distance geometry structures were refined further by restrained molecular dynamics (40 ps) in the GROMOS in vacuo force field. All 32 structures reached acceptable energy minima while satisfying the imposed restraints. Two of these structures were subjected to a further 200 ps of molecular dynamics simulation in water, using time-dependent distance restraining, followed by a 200 ps free simulation without any distance restraining. The resulting structure is very similar to the X-ray structure of Bacillus subtilis HPr, but differs mainly in the position of the two loops containing the active site histidine residue 15 and residues 53 to 57 relative to the rest of the structure. The unfavorable φ torsion angle that was found for residue 16 in the active center of unphosphorylated Streptococcus faecalis HPr was proposed to play a role in the activity of the protein. Although present at the early stages of the structure calculations, this torsion-angle strain disappeared in the final model obtained from molecular dynamics simulations in water using time-averaged distance restraining and upon releasing the distance restraints. This suggests that the strain may be an artifact of crystallization conditions instead of an essential element in the phosphorylation/dephosphorylation process.

Detection of Two-Quantum Nuclear Coherence by Nuclear-Quadrupole-Induced Electric Polarization

The response of a spin72in solids, subject to a first-order quadrupolar interaction, to a spin lock pulse sequence is calculated. The results are valid for any ratio of quadrupolar coupling, ωQ, to the amplitude, ω1, of the RF pulse. It is shown here that the measurements of the central line intensity as a function of the second pulse length can be used for the determination of quadrupolar parameters using various phase cycling techniques. It is proven that the DQ coherences developed during the first pulse can be selectively detected.

Pion production: Where's the coherence?

Formal solutions to the \ensuremath{\Delta}-hole and particle-hole coefficients describing nuclear coherent states are presented using the degenerate schematic model. These solutions are used to analytically solve for the momentum-dependent nuclear form factors in which the target is excited to a transition-spin-isospin, \ensuremath{\Delta}-giant resonance through the creation of coherent \ensuremath{\Delta}-hole states, whereas the projectile is excited to an ordinary spin-isospin giant resonance. The target then decays to its ground state emitting a pion. A more general model operator is proposed that leads to complete coherence for all momenta. The magnitudes of the nuclear form factors are calculated theoretically and the results coming from the completely coherent model are compared to the low-momentum coherent model. The calculation is then completed by introducing these models into the pion triple-differential cross section and energy distributions are calculated and compared. The importance of how the nuclear structure and coherence affect the magnitudes and shapes of the form factors and the pion-energy distributions is assessed.

Suppression of sodium nuclear magnetic resonance double-quantum coherence by chemical shift and relaxation reagents

An investigation into the signal suppression behavior of the paramagnetic shift and relaxation reagents, Dy(P3O10)27− and Gd(P3O10)27−, with regard to their use in the nuclear magnetic resonance spectroscopic study of sodium has been performed. Measurements of T1 and T2 relaxation time constants of sodium in normal saline, Krebs–Henseleit buffer, and human blood serum, as a function of concentration of these reagents showed that, although closely coupled in the saline and K–H buffer environments, in plasma T1 and T2 become decoupled, transverse relaxation dominating in comparison to longitudinal relaxation. Linewidth measurements further suggest that relaxation in the plasma milieu is controlled primarily by inherent T2 relaxation, rather than by field inhomogeneity or diffusion effects. Quantitative single-quantum (1Q) and double-quantum (2Q) intensity measurements, biexponential T2 relaxation measurements, and parametric studies of the preparation time of the 2Q pulse sequence, were obtained in suspensions of bovine serum albumin and human erythrocytes. The observed suppression of sodium 2Q coherence by paramagnetic shift and relaxation reagents was found to exhibit a complex behavior in albumin solutions, involving the biexponential T2 decay to be expected during the preparation time of the 2Q filter pulse sequence, as well as the optimum preparation time for production of the double-quantum coherence itself. The controlling factor for both of these effects is the biexponential amplitude function in the expression for the transverse magnetization observed following application of the 2Q pulse sequence. This in turn is determined entirely by the values for the slow and fast components of biexponential relaxation in sodium, which themselves depend upon the concentration of the macromolecular binding sites for quadrupolar interaction. A similar behavior has been observed in suspensions of human erythrocytes.

Hyperfine sublevel correlation spectroscopy (HYSCORE ) of disordered solids

In the study of small hyperfine interactions unresolved in the EPR spectrum, in diluted paramagnetic systems, electron spin-echo envelope modulation has proven to be a very useful technique ( 1). For example, in a three-pulse (stimulated-echo ) experiment (2, 3), the nuclear spin frequencies of the nuclei that are coupled to the unpaired electron will appear as a modulation on the electron spin-echo (ESE) intensity which is recorded as a function of the time T between the second and third microwave pulses. The first two microwave pulses, which are separated by time T, will create nuclear spin coherences in the two electron spin ms manifolds, while the last microwave pulse will transform these coherences into a detectable electron spin-echo signal. The stimulated-echo ESEEM experiment has also been demonstrated as a two-dimensional technique, i.e., recording the electron spin-echo amplitude as a function of both times T and T to show the correlation of the nuclear spin coherences of the two electron spin ms manifolds to each other (4). A serious drawback of this experiment is the limited time range available in the 7 direction due to the usually very short T2 relaxation time of the electron spin system. In the last decade many new ESEEM experiments have been introduced (5). In particular, the two-dimensional four-pulse stimulated-echo experiment introduced by P. Hofer et al. as HYSCORE (hyperline sublevel correlation spectroscopy) (6) provides a useful alternative to the classical two-dimensional three-pulse technique. The HYSCORE experiment is derived from the three-pulse experiment by the insertion during the second time interval (see Fig. 1) of a x pulse which exchanges the populations of the ms manifolds. In terms of two-dimensional correlation spectroscopy, this pulse serves as a mixing pulse which creates correlations between nuclear spin transitions associated with the two electron spin ms manifolds. The mixing pulse terminates the evolution interval t, and is followed by the detection interval t2. As in the three-pulse experiment, the nuclear coherences evolving during this time interval are sampled by the last microwave pulse creating an electron spin echo. Compared to the classical

Investigation of nuclear coherence effects in optical and nuclear radiation

Investigation of nuclear coherence effects in optical and nuclear radiation

Coherent Raman Beat Detection of Nuclear Coherences: An Alternative to Electron Spin Echo Envelope Modulation

AbstractThe use of coherent Raman beats for the detection of nuclear coherences in solids from nuclei with hyperfine couplings to unpaired electron spins is discussed. The coherent Raman beats do not require refocusing of the electron spins and therefore are not strongly affected by spectral diffusion of the electron spins. Several methods for generating nuclear coherences using a single microwave pulse, two microwave pulses, or a combination of microwave and radiofrequency pulses are discussed. One‐dimensional and two‐dimensional spectroscopies for the measurement of hyperfine interactions in solids are proposed.

Dihydrofolate reductase; sequential resonance assignments using 2D and 3D NMR and secondary structure determination in solution

Three-dimensional (3D) heteronuclear NMR techniques have been used to make sequential 1H and 15N resonance assignments for most of the residues of Lactobacillus casei dihydrofolate reductase (DHFR), a monomeric protein of molecular mass 18,300 Da. A uniformly 15N-labeled sample of the protein was prepared and its complex with methotrexate (MTX) studied by 3D 15N/1H nuclear Overhauser-heteronuclear multiple quantum coherence (NOESY-HMQC), Hartmann-Hahn-heteronuclear multiple quantum coherence (HOHAHA-HMQC), and HMQC-NOESY-HMQC experiments. These experiments overcame most of the spectral overlap problems caused by chemical shift degeneracies in 2D spectra and allowed the 1H-1H through-space and through-bond connectivities to be identified unambiguously, leading to the resonance assignments. The novel HMQC-NOESY-HMQC experiment allows NOE cross peaks to be detected between NH protons even when their 1H chemical shifts are degenerate as long as the amide 15N chemical shifts are nondegenerate. The 3D experiments, in combination with conventional 2D NOESY, COSY, and HOHAHA experiments on unlabelled and selectively deuterated DHFR, provide backbone assignments for 146 of the 162 residues and side-chain assignments for 104 residues of the protein. Data from the NOE-based experiments and identification of the slowly exchanging amide protons provide detailed information about the secondary structure of the binary complex of the protein with methotrexate. Sequential NHi-NHi+1 NOEs define four regions with helical structure. Two of these regions, residues 44-49 and 79-89, correspond to within one amino acid to helices C and E in the crystal structure of the DHFR.methotrexate.NADPH complex [Bolin et al. (1982) J. Biol. Chem. 257, 13650-13662], while the NMR-determined helix formed by residues 26-35 is about one turn shorter at the N-terminus than helix B in the crystal structure, which spans residues 23-34. Similarly, the NMR-determined helical region comprising residues 102-110 is somewhat offset from the crystal structure's helix F, which encompasses residues 97-107. Regions of beta-sheet structure were characterized in the binary complex by strong alpha CHi-NHi+1 NOEs and by slowly exchanging amide protons. In addition, several long-range NOEs were identified linking together these stretches to form a beta-sheet. These elements align perfectly with corresponding elements in the crystal structure of the DHFR.methotrexate.NADPH complex, which contains an eight-stranded beta-sheet, indicating that the main body of the beta-sheet is preserved in the binary complex in solution.

Stimulated echo time domain electron nuclear double resonance

The observation of nuclear spin coherences in a pulsed electron nuclear double resonance (ENDOR) experiment is reported. The coherences are detected indirectly as time-dependent modulations of the electron spin stimulated echo envelope. A theoretical description of these double resonance coherence experiments for spin systems coupled by nonsecular interactions is developed, and is employed to calculate the expected time domain signals assuming indirect detection of the nuclear coherences. The resolution and sensitivity of this technique is compared with other, related ENDOR techniques, and the prospects for more sophisticated time domain experiments are briefly assessed.

Two dimensional 31P nuclear magnetic resonance coherence transfer experiments under magic-angle sample spinning

In this paper, we report on two dimensional (2D) 31P cross polarization (CP) magic angle spinning (MAS) nuclear magnetic resonance (NMR) experiments on the coupled two-spin systems, sodium pyrophosphate decahydrate, Na4P2O7, 1OH2O (SP) and tetraphenyldiphosphine-1-oxide, (C6H5)2PP(O) (C6H5)2 (TPPO), including antiecho (COSY), double-quantum NMR, and zero-quantum NMR experiments. These experiments are generalizations of the absolute mode 2D Fourier transform antiecho COSY performed under MAS condition by Kentgens, de Boer, and Veeman [J. Chem. Phys. 87, 6859 (1987)]. The 2D sideband intensities for these experiments on polycrystalline samples are shown theoretically to be real. There are two mechanisms of coherence transfer; homonuclear J coupling and dipolar coupling. Theory shows that the zero-quantum signal for the coupled two spins can not be observed by using a (CPx−τ−(π)x−τ−(π/2)x−t1−(π/2)−t2 pulse sequence, when the coherence transfer is due to J coupling. When, however, the coherence transfer is induced by the flip-flop term of the dipolar coupling Hamiltonian, the zero-quantum signal can be observed by that pulse sequence. The preparation time dependences of the double-quantum and the zero-quantum sideband patterns, are expected, when the coherence transfer is induced by dipolar coupling. The zero-quantum signal was very weak for TPPO, while it was strong for SP. The apparent preparation time dependence of the zero-quantum sideband pattern was observed for SP. These results suggest that the coherence transfer is mainly due to J coupling in TPPO, where the two 31P nuclei have different isotropic chemical shifts. While, on the other hand, the dipolar coupling is more important in SP, where the two 31P nuclei have the same isotropic chemical shifts but different orientations of the chemical shift tensors. The 2D sideband intensities of the antiecho COSY spectrum of TPPO were calculated, and the relative orientation of the two chemical shift tensors was determined.

Assignment of the side-chain proton and carbon-13 resonances of interleukin-1.beta. using double- and triple-resonance heteronuclear three-dimensional NMR spectroscopy

The assignment of the aliphatic 1H and 13C resonances of IL-1 beta, a protein of 153 residues and molecular mass 17.4 kDa, is presented by use of a number of novel three-dimensional (3D) heteronuclear NMR experiments which rely on large heteronuclear one-bond J couplings to transfer magnetization and establish through-bond connectivities. These 3D NMR experiments circumvent problems traditionally associated with the application of conventional 2D 1H-1H correlation experiments to proteins of this size, in particular the extensive chemical shift overlap which precludes the interpretation of the spectra and the reduced sensitivity arising from 1H line widths that are often significantly larger than the 1H-1H J couplings. The assignment proceeds in two stages. In the first step the 13C alpha chemical shifts are correlated with the NH and 15N chemical shifts by a 3D triple-resonance NH-15N-13C alpha (HNCA) correlation experiment which reveals both intraresidue NH(i)-15N(i)-13C alpha (i) and some weaker interresidue NH(i)-15N(i)-C alpha (i-1) correlations, the former via intraresidue one-bond 1JNC alpha and the latter via interresidue two-bond 2JNC alpha couplings. As the NH, 15N, and C alpha H chemical shifts had previously been sequentially assigned by 3D 1H Hartmann-Hahn 15N-1H multiple quantum coherence (3D HOHAHA-HMQC) and 3D heteronuclear 1H nuclear Overhauser 15N-1H multiple quantum coherence (3D NOESY-HMQC) spectroscopy [Driscoll, P.C., Clore, G.M., Marion, D., Wingfield, P.T., & Gronenborn, A.M. (1990) Biochemistry 29, 3542-3556], the 3D triple-resonance HNCA correlation experiment permits the sequence-specific assignments of 13C alpha chemical shifts in a straightforward manner. The second step involves the identification of side-chain spin systems by 3D 1H-13C-13C-1H correlated (HCCH-COSY) and 3D 1H-13C-13C-1H total correlated (HCCH-TOCSY) spectroscopy, the latter making use of isotropic mixing of 13C magnetization to obtain relayed connectivities along the side chains. Extensive cross-checks are provided in the assignment procedure by examination of the connectivities between 1H resonances at all the corresponding 13C shifts of the directly bonded 13C nuclei. In this manner, we were able to obtain complete 1H and 13C side-chain assignments for all residues, with the exception of 4 (out of a total of 15) lysine residues for which partial assignments were obtained. The 3D heteronuclear correlation experiments described are highly sensitive, and the required set of three 3D spectra was recorded in only 1 week of measurement time on a single uniformly 15N/13C-labeled 1.7 mM sample of interleukin-1 beta.(ABSTRACT TRUNCATED AT 400 WORDS)

Complete resonance assignment for the polypeptide backbone of interleukin 1.beta. using three-dimensional heteronuclear NMR spectroscopy

The complete sequence-specific assignment of the 15N and 1H backbone resonances of the NMR spectrum of recombinant human interleukin 1 beta (153 residues, Mr = 17,400) has been obtained by using primarily 15N-1H heteronuclear three-dimensional (3D) NMR techniques in combination with 15N-1H heteronuclear and 1H homonuclear two-dimensional NMR. The fingerprint region of the spectrum was analyzed by using a combination of 3D heteronuclear 1H Hartmann-Hahn 15N-1H multiple quantum coherence (3D HOHAHA-HMQC) and 3D heteronuclear 1H nuclear Overhauser 15N-1H multiple quantum coherence (3D NOESY-HMQC) spectroscopies. We show that the problems of amide NH and C alpha H chemical shift degeneracy that are prevalent for proteins of this size are readily overcome by using the 3D heteronuclear NMR technique. A doubling of some peaks in the spectrum was found to be due to N-terminal heterogeneity of the 15N-labeled protein, corresponding to a mixture of wild-type and des-Ala-1-interleukin 1 beta. The complete list of 15N and 1H assignments is given for all the amide NH and C alpha H resonances of all non-proline residues, as well as the 1H assignments for some of the amino acid side chains. This first example of the sequence-specific assignment of a protein using heteronuclear 3D NMR provides a basis for further conformational and dynamic studies of interleukin 1 beta.

Overcoming the overlap problem in the assignment of 1H NMR spectra of larger proteins by use of three-dimensional heteronuclear 1H-15N Hartmann-Hahn-multiple quantum coherence and nuclear Overhauser-multiple quantum coherence spectroscopy: application to interleukin 1 beta.

The application of three-dimensional (3D) heteronuclear NMR spectroscopy to the sequential assignment of the 1H NMR spectra of larger proteins is presented, using uniformly labeled (approximately 95%) [15N]interleukin 1 beta, a protein of 153 residues and molecular mass of 17.4 kDa, as an example. The two-dimensional (2D) 600-MHz spectra of interleukin 1 beta are too complex for complete analysis, owing to extensive cross-peak overlap and chemical shift degeneracy. We show that the combined use of 3D 1H-15N Hartmann-Hahn-multiple quantum coherence (HOHAHA-HMQC) and nuclear Overhauser-multiple quantum coherence (NOESY-HMQC) spectroscopy, designed to provide the necessary through-bond and through-space correlations for sequential assignment, provides a practical general-purpose method for resolving ambiguities which severely limit the analysis of conventional 2D NMR spectra. The absence of overlapping cross-peaks in these 3D spectra allows the unambiguous identification of C alpha H(i)-NH(i+1) and NH(i)-NH(i+1) through-space nuclear Overhauser connectivities necessary for connecting a particular C alpha H(i)-NH(i) through-bond correlation with its associated through-space sequential cross-peak The problem of amide NH chemical shift degeneracy in the 1H NMR spectrum is therefore effectively removed, and the assignment procedure simply involves inspecting a series of 2D 1H-1H slices edited by the chemical shift of the directly bonded 15N atom. Connections between residues can be identified almost without any knowledge of the spin system types involved, though this type of information is clearly required for the eventual placement of the connected residues within the primary sequence.

Spectrally ordered Zeeman coherences and optical pulse-shape storage

We have experimentally investigated the creation of spectrally ordered nuclear and electronic Zeeman coherences in a gas-phase sample. A Zeeman coherence is generated through the sequential excitation of two coupled optical transitions. In our experiment, one transition was excited by a data pulse and the other by a short reference pulse. Subsequent excitation of one of these transitions by a short reading pulse transforms the Zeeman coherence into an optical coherence and leads to the emission of a time-forward or time-reversed duplicate of the data pulse. Output signals up to 5% as intense as the original data pulse were observed. We present a general analysis that is applicable to both gases and solids and find that the solid-state analog of this process will exist only if the inhomogeneous broadening of the two optical transitions is highly correlated.

Multipole NMR. VI. application to coherence transfer and 2-D spectroscopy in a spin-1 system

Using the multipole formulation the recent experiments of H. Hatanaka and C. S. Yannoni ( J. Magn. Reson. 42, 330 (1981)) are interpreted. It is shown how transfer of nuclear coherence between levels in a spin- I system corresponds to a transfer of polarization between single quantum dipole character and single quantum quadrupole character. Also discussed in the multipole formulation are the recent experiments of L. Müller ( J. Magn. Reson. 42, 324 (1981)) in which 2-D spectroscopy is used to extract the double quantum spectrum. Some comments are made regarding a spin I = 3 2 .