Electrical and ionic conductivity effects on magic-angle spinning nuclear magnetic resonance parameters of CuI

We investigate experimentally and theoretically the effects of two different types of conductivity, electrical and ionic, upon magic-angle spinning NMR spectra. The experimental demonstration of these effects involves (63)Cu, (65)Cu, and (127)I variable temperature MAS-NMR experiments on samples of γ-CuI, a Cu(+)-ion conductor at elevated temperatures as well as a wide bandgap semiconductor. We extend previous observations that the chemical shifts depend very strongly upon the square of the spinning-speed as well as the particular sample studied and the magnetic field strength. By using the (207)Pb resonance of lead nitrate mixed with the γ-CuI as an internal chemical shift thermometer we show that frictional heating effects of the rotor do not account for the observations. Instead, we find that spinning bulk CuI, a p-type semiconductor due to Cu(+) vacancies in nonstoichiometric samples, in a magnetic field generates induced AC electric currents from the Lorentz force that can resistively heat the sample by over 200 °C. These induced currents oscillate along the rotor spinning axis at the spinning speed. Their associated heating effects are disrupted in samples containing inert filler material, indicating the existence of macroscopic current pathways between micron-sized crystallites. Accurate measurements of the temperature-dependence of the (63)Cu and (127)I chemical shifts in such diluted samples reveal that they are of similar magnitude (ca. 0.27 ppm/K) but opposite sign (being negative for (63)Cu), and appear to depend slightly upon the particular sample. This relationship is identical to the corresponding slopes of the chemical shifts versus square of the spinning speed, again consistent with sample heating as the source of the observed large shift changes. Higher drive-gas pressures are required to spin samples that have higher effective electrical conductivities, indicating the presence of a braking effect arising from the induced currents produced by rotating a conductor in a homogeneous magnetic field. We present a theoretical analysis and finite-element simulations that account for the magnitude and rapid time-scale of the resistive heating effects and the quadratic spinning speed dependence of the chemical shift observed experimentally. Known thermophysical properties are used as inputs to the model, the sole adjustable parameter being a scaling of the bulk thermal conductivity of CuI in order to account for the effective thermal conductivity of the rotating powdered sample. In addition to the dramatic consequences of electrical conductivity in the sample, ionic conductivity also influences the spectra. All three nuclei exhibit quadrupolar satellite transitions extending over several hundred kilohertz that reflect defects perturbing the cubic symmetry of the zincblende lattice. Broadening of these satellite transitions with increasing temperature arises from the onset of Cu(+) ion jumps to sites with different electric field gradients, a process that interferes with the formation of rotational echoes. This broadening has been quantitatively analyzed for the (63)Cu and (65)Cu nuclei using a simple model in the literature to yield an activation barrier of 0.64 eV (61.7 kJ/mole) for the Cu(+) ion jumping motion responsible for the ionic conductivity that agrees with earlier results based on (63)Cu NMR relaxation times of static samples.     

Substrate affinities for membrane transport proteins determined by 13C cross-polarization magic-angle spinning nuclear magnetic resonance spectroscopy

We have devised methods in which cross-polarization magic-angle spinning (CP-MAS) solid-state NMR is exploited to measure rigorous parameters for binding of (13)C-labeled substrates to membrane transport proteins. The methods were applied to two proteins from Escherichia coli: a nucleoside transporter, NupC, and a glucuronide transporter, GusB. A substantial signal for the binding of methyl [1-(13)C]-beta-d-glucuronide to GusB overexpressed in native membranes was achieved with a sample that contained as little as 20 nmol of GusB protein. The data were fitted to yield a K(D) value of 4.17 mM for the labeled ligand and 0.42 mM for an unlabeled ligand, p-nitrophenyl beta-d-glucuronide, which displaced the labeled compound. CP-MAS was also used to measure binding of [1'-(13)C]uridine to overexpressed NupC. The spectrum of NupC-enriched membranes containing [1'-(13)C]uridine exhibited a large peak from substrate bound to undefined sites other than the transport site, which obscured the signal from substrate bound to NupC. In a novel application of a cross-polarization/polarization-inversion (CPPI) NMR experiment, the signal from undefined binding was eliminated by use of appropriate inversion pulse lengths. By use of CPPI in a titration experiment, a K(D) value of 2.6 mM was determined for uridine bound to NupC. These approaches are broadly applicable to quantifying binding of substrates, inhibitors, drugs, and antibiotics to numerous membrane proteins.     

Determination of long-range distances and dynamic order parameters by dipolar recoupling in high-resolution magic-angle spinning NMR spectroscopy

By introducing dipolar recoupling methods to high-resolution magic-angle spinning (HRMAS) NMR spectroscopy, a class of experiments has been delevoped that allows the measurement of residual dipole-dipole couplings of approximately 1 Hz in weakly immobilized molecules. Using homonuclear 1H-1H recoupling, distances of up to approximately 8 A can be selectively determined, while heteronuclear 1H-13C recoupling provides access to dynamic order parameters of individual molecular segments on the order of approximately 10-3. The experiments are demonstrated on functionalized oligopeptides that are attached to polymer resins.     

Single crystal nuclear magnetic resonance in spinning powders

We present a method for selectively exciting nuclear magnetic resonances (NMRs) from well-defined subsets of crystallites from a powdered sample under magic angle spinning. Magic angle spinning induces a time dependence in the anisotropic interactions, which results in a time variation of the resonance frequencies which is different for different crystallite orientations. The proposed method exploits this by applying selective pulses, which we refer to as XS (for crystallite-selective) pulses, that follow the resonance frequencies of nuclear species within particular crystallites, resulting in the induced flip angle being orientation dependent. By selecting the radiofrequency field to deliver a 180° pulse for the target orientation and employing a train of such pulses combined with cogwheel phase cycling, we obtain a high degree of orientational selectivity with the resulting spectrum containing only contributions from orientations close to the target. Typically, this leads to the selection of between 0.1% and 10% of the crystallites, and in extreme cases to the excitation of a single orientation resulting in single crystal spectra of spinning powders. Two formulations of this method are described and demonstrated with experimental examples on [1-(13)C]-alanine and the paramagnetic compound Sm(2)Sn(2)O(7).     

Theory for cross effect dynamic nuclear polarization under magic-angle spinning in solid state nuclear magnetic resonance: The importance of level crossings

We present theoretical calculations of dynamic nuclear polarization (DNP) due to the cross effect in nuclear magnetic resonance under magic-angle spinning (MAS). Using a three-spin model (two electrons and one nucleus), cross effect DNP with MAS for electron spins with a large g-anisotropy can be seen as a series of spin transitions at avoided crossings of the energy levels, with varying degrees of adiabaticity. If the electron spin-lattice relaxation time T(1e) is large relative to the MAS rotation period, the cross effect can happen as two separate events: (i) partial saturation of one electron spin by the applied microwaves as one electron spin resonance (ESR) frequency crosses the microwave frequency and (ii) flip of all three spins, when the difference of the two ESR frequencies crosses the nuclear frequency, which transfers polarization to the nuclear spin if the two electron spins have different polarizations. In addition, adiabatic level crossings at which the two ESR frequencies become equal serve to maintain non-uniform saturation across the ESR line. We present analytical results based on the Landau-Zener theory of adiabatic transitions, as well as numerical quantum mechanical calculations for the evolution of the time-dependent three-spin system. These calculations provide insight into the dependence of cross effect DNP on various experimental parameters, including MAS frequency, microwave field strength, spin relaxation rates, hyperfine and electron-electron dipole coupling strengths, and the nature of the biradical dopants.     

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.     

Heteronuclear dipolar decoupling effects on multiple-quantum and satellite-transition magic-angle spinning NMR spectra

We here report on the influence of heteronuclear dipolar decoupling on the (27)Al 3QMAS, 5QMAS, and the double-quantum filter-satellite-transition magic-angle spinning (DQF-STMAS) spectra of a strongly dipolar-coupled system, gibbsite. The requirements for heteronuclear dipolar decoupling increase with the order of coherence evolving in the indirect dimension of a two-dimensional (2D) experiment. The isotropic line width of the high-resolution 2D spectra, in samples like gibbsite, is composed of four parts: the distribution of isotropic shifts (delta(ISO), delta(QIS)), the homogeneous broadening related to the proton-proton flip-flop terms, the (27)Al-(27)Al homonulcear dipolar couplings, and the (1)H-(27)Al heteronuclear dipolar couplings. It is shown that, even in the case of gibbsite, where a strong proton-proton bath exists, the main resolution limiting factor in these experiments resides in the (1)H-(27)Al dipolar interaction.     

Effective Floquet Hamiltonians for dipolar and quadrupolar coupled N-spin systems in solid state nuclear magnetic resonance under magic angle spinning

Spin dynamics under magic angle spinning has been studied using different theoretical approaches and also by extensive numerical simulation programs. In this article we present a general theoretical approach that leads to analytic forms for effective Hamiltonians for an N-spin dipolar and quadrupolar coupled system under magic angle spinning (MAS) conditions, using a combination of Floquet theory and van Vleck (contact) transformation. The analytic forms presented are shown to be useful for the study of MAS spin dynamics in solids with the help of a number of simulations in two, three, and four coupled, spin-1/2 systems as well as spins in which quadrupolar interactions are also present.     

H homonuclear dipolar decoupling at high magic-angle spinning frequencies with rotor-synchronised symmetry sequences

We demonstrate here application of symmetry-adapted sequences of the form to obtain high-resolution ¹H spectra in solid-state nuclear magnetic resonance under high-speed magic-angle spinning. Experimental results are shown for samples of alanine and glycine for spinning speeds up to 30 kHz with radio-frequency nutation rates of around 100 kHz.     

Bimodal Floquet description of heteronuclear dipolar decoupling in solid-state nuclear magnetic resonance

A theoretical treatment of heteronuclear dipolar decoupling in solid-state nuclear magnetic resonance is presented here based on bimodal Floquet theory. The conditions necessary for good heteronuclear decoupling are derived. An analysis of a few of the decoupling schemes implemented until date is presented with regard to satisfying such decoupling conditions and efficiency of decoupling. Resonance conditions for efficient heteronuclear dipolar decoupling are derived with and without the homonuclear (1)H-(1)H dipolar couplings and their influence on heteronuclear dipolar decoupling is pointed out. The analysis points to the superior efficiency of the newly introduced swept two-pulse phase-modulation (SW(f)-TPPM) sequence. It is shown that the experimental robustness of SW(f)-TPPM as compared to the original TPPM sequence results from an adiabatic sweeping of the modulation frequencies. Based on this finding alternative strategies are compared here. The theoretical findings are corroborated by both numerical simulations and representative experiments.     

Study of brønsted acidity of zeolites using high-resolution proton magnetic resonance with magic-angle spinning

By applying magic angle spinning to proton magnetic resonance of zeolites, two different lines were separated. Comparison of the corresponding resonance shifts with values of OH groups of other adsorbents and of organic compounds in solution showed that the signals must be due to hydroxyl groups of different acidity.     

Composite dipolar recoupling: anisotropy compensated coherence transfer in solid-state nuclear magnetic resonance

The efficiency of dipole-dipole coupling driven coherence transfer experiments in solid-state nuclear magnetic resonance (NMR) spectroscopy of powder samples is limited by dispersion of the orientation of the internuclear vectors relative to the external magnetic field. Here we introduce general design principles and resulting pulse sequences that approach full polarization transfer efficiency for all crystallite orientations in a powder in magic-angle-spinning experiments. The methods compensate for the defocusing of coherence due to orientation dependent dipolar coupling interactions and inhomogeneous radio-frequency fields. The compensation scheme is very simple to implement as a scaffold (comb) of compensating pulses in which the pulse sequence to be improved may be inserted. The degree of compensation can be adjusted and should be balanced as a compromise between efficiency and length of the overall pulse sequence. We show by numerical and experimental data that the presented compensation protocol significantly improves the efficiency of known dipolar recoupling solid-state NMR experiments.     

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.     

Determinations of 15N chemical shift anisotropy magnitudes in a uniformly 15N,13C-labeled microcrystalline protein by three-dimensional magic-angle spinning nuclear magnetic resonance spectroscopy

Amide 15N chemical shift anisotropy (CSA) tensors provide quantitative insight into protein structure and dynamics. Experimental determinations of 15N CSA tensors in biologically relevant molecules have typically been performed by NMR relaxation studies in solution, goniometric analysis of single-crystal spectra, or slow magic-angle spinning (MAS) NMR experiments of microcrystalline samples. Here we present measurements of 15N CSA tensor magnitudes in a protein of known structure by three-dimensional MAS solid-state NMR. Isotropic 15N, 13C alpha, and 13C' chemical shifts in two dimensions resolve site-specific backbone amide recoupled CSA line shapes in the third dimension. Application of the experiments to the 56-residue beta1 immunoglobulin binding domain of protein G (GB1) enabled 91 independent determinations of 15N tensors at 51 of the 55 backbone amide sites, for which 15N-13C alpha and/or 15N-13C' cross-peaks were resolved in the two-dimensional experiment. For 37 15N signals, both intra- and interresidue correlations were resolved, enabling direct comparison of two experimental data sets to enhance measurement precision. Systematic variations between beta-sheet and alpha-helix residues are observed; the average value for the anisotropy parameter, delta (delta = delta(zz) - delta(iso)), for alpha-helical residues is 6 ppm greater than that for the beta-sheet residues. The results show a variation in delta of 15N amide backbone sites between -77 and -115 ppm, with an average value of -103.5 ppm. Some sites (e.g., G41) display smaller anisotropy due to backbone dynamics. In contrast, we observe an unusually large 15N tensor for K50, a residue that has an atypical, positive value for the backbone phi torsion angle. To our knowledge, this is the most complete experimental analysis of 15N CSA magnitude to date in a solid protein. The availability of previous high-resolution crystal and solution NMR structures, as well as detailed solid-state NMR studies, will enhance the value of these measurements as a benchmark for the development of ab initio calculations of amide 15N shielding tensor magnitudes.     

13C nuclear overhauser polarization-magic-angle spinning nuclear magnetic resonance spectroscopy in uniformly 13C-labeled solid proteins

A recently introduced (13)C polarization technique based on the nuclear Overhauser effect in rotating solid (nuclear Overhauser polarization-magic-angle spinning, NOP-MAS) (Takegoshi, K.; Terao, T. J. Chem. Phys. 2002, 117, 1700-1707) is applied to uniformly (13)C, (15)N-labeled proteins. NOP enhancement factors per scan of 1.5 approximately 2.0 are obtained, while that by cross polarization (CP) is less than 1.0. We show that uniform enhancement of all (13)C signals by CP is difficult to attain, while it is easily achieved by NOP, thus enabling quantitative comparison of signal intensities. NOP is easy to carry out under fast MAS and works well even for somewhat mobile molecules, for which CP does not work. Moreover, in labeled protein samples containing nonlabeled additives, NOP can eliminate the latter signals. For these features, NOP is superior to CP in many uniformly (13)C labeled proteins.     

Second order average Hamiltonian theory of symmetry-based pulse schemes in the nuclear magnetic resonance of rotating solids: application to triple-quantum dipolar recoupling

The average Hamiltonian theory (AHT) of several classes of symmetry-based radio-frequency pulse sequences is developed to second order, allowing quantitative analyses of a wide range of recoupling and decoupling applications in magic-angle-spinning solid state nuclear magnetic resonance. General closed analytical expressions are presented for a cross term between any two interactions recoupled to second order AHT. We classify them into different categories and show that some properties of the recoupling pulse sequence may be predicted directly from this classification. These results are applied to examine a novel homonuclear recoupling strategy, effecting a second order average dipolar Hamiltonian comprising trilinear triple quantum (3Q) spin operators. We discuss general features and design principles of such 3Q recoupling sequences and demonstrate by numerical simulations and experiments that they provide more efficient excitation of (13)C 3Q coherences compared to previous techniques. We passed up to 15% of the signal through a state of 3Q coherence in rotating powders of uniformly (13)C-labeled alanine and tyrosine. Second order recoupling-based (13)C homonuclear 3Q correlation spectroscopy is introduced and demonstrated on tyrosine.     

Nuclear magnetic resonance proton dipolar order relaxation in thermotropic liquid crystals: a quantum theoretical approach

By means of the Jeener-Broekaert nuclear magnetic resonance pulse sequence, the proton spin system of a liquid crystal can be prepared in quasiequilibrium states of high dipolar order, which relax to thermal equilibrium with the molecular environment with a characteristic time (T1D). Previous studies of the Larmor frequency and temperature dependence of T1D in thermotropic liquid crystals, that included field cycling and conventional high-field experiments, showed that the slow hydrodynamic modes dominate the behavior of T1D, even at high Larmor frequencies. This noticeable predominance of the cooperative fluctuations (known as order fluctuations of the director, OFD) could not be explained by standard models based on the spin-lattice relaxation theory in the limit of high temperature (weak order). This fact points out the necessity of investigating the role of the quantum terms neglected in the usual high temperature theory of dipolar order relaxation. In this work, we present a generalization of the proton dipolar order relaxation theory for highly correlated systems, which considers all the spins belonging to correlated domains as an open quantum system interacting with quantum bath. As starting point, we deduce a formulation of the Markovian master equation of relaxation for the statistical spin operator, valid for all temperatures, which is suitable for introducing a dipolar spin temperature in the quantum regime, without further assumptions about the form of the spin-lattice Hamiltonian. In order to reflect the slow dynamics occurring in correlated systems, we lift the usual short-correlation-time assumption by including the average over the motion of the dipolar Hamiltonian together with the Zeeman Hamiltonian into the time evolution operator. In this way, we calculate the time dependence of the spin operators in the interaction picture in a closed form, valid for high magnetic fields, bringing into play the spin-spin interactions within the microscopic time scale. Then, by adopting the spin-temperature density operator to represent the collective state of the spin system, and removing the traditional hypothesis of high temperature, we deduce an expression for the first order quantum contribution to T1D (-1), in terms of spectral densities, with coefficients in form of spin traces. The properties that distinguish our result from the high-temperature T1D (-1) are as follows. (a) It is exclusively associated to cooperative fluctuations. (b) Because of its quantum character, it relies on both considering the lattice degrees of freedom quantum mechanically and including the spin-spin interactions in the microscopic time scale. With regard to the average dipolar Hamiltonian, only the nonsecular part plays a relevant role. (c) Associated with the structure of the spin operator involved in the quantum contribution, a term arises which is proportional to the number of spins in the correlated molecular domains, showing that the quantum contribution may be of macroscopic size in highly correlated systems. When applied to nematic liquid crystals, the new term exhibits the typical nu(-1/2) Larmor frequency dependence through the spectral density of the OFD, in consistence with the experimental results.     

Observable effects of mechanical stress induced by sample spinning in solid state nuclear magnetic resonance

The stress-induced change in chemical shielding induced by sample spinning is measured and interpreted theoretically. By considering the rotating sample as an elastic body in the plane-strain approximation, the internal stress field as a function of sample size, rotation frequency, and elastic constants is determined. This stress field and the dependence of chemical shielding on strain, as determined by first-principles calculations, are combined to predict the shielding dependence on rotation frequency under isothermal conditions in single crystal gallium phosphide. The prediction is in good qualitative agreement with the experiment. Little to no effect is detected in powder samples of both gallium phosphide and copper iodide, and it is argued that this follows from the stress distribution in granular material, as opposed to bulk crystals. Finally, the temperature and pressure dependence of the chemical shielding is estimated from these considerations and found consistently to underestimate the experimental values, indicating the importance of finite-temperature anharmonic effects even in very simple solids.     

Intermolecular structure determination of amyloid fibrils with magic-angle spinning and dynamic nuclear polarization NMR

We describe magic-angle spinning NMR experiments designed to elucidate the interstrand architecture of amyloid fibrils. Three methods are introduced for this purpose, two being based on the analysis of long-range (13)C-(13)C correlation spectra and the third based on the identification of intermolecular interactions in (13)C-(15)N spectra. We show, in studies of fibrils formed by the 86-residue SH3 domain of PI3 kinase (PI3-SH3 or PI3K-SH3), that efficient (13)C-(13)C correlation spectra display a resonance degeneracy that establishes a parallel, in-register alignment of the proteins in the amyloid fibrils. In addition, this degeneracy can be circumvented to yield direct intermolecular constraints. The (13)C-(13)C experiments are corroborated by (15)N-(13)C correlation spectra obtained from a mixed [(15)N,(12)C]/[(14)N,(13)C] sample which directly quantify interstrand distances. Furthermore, when the spectra are recorded with signal enhancement provided by dynamic nuclear polarization (DNP) at 100 K, we demonstrate a dramatic increase (from 23 to 52) in the number of intermolecular (15)N-(13)C constraints detectable in the spectra. The increase in the information content is due to the enhanced signal intensities and to the fact that dynamic processes, leading to spectral intensity losses, are quenched at low temperatures. Thus, acquisition of low temperature spectra addresses a problem that is frequently encountered in MAS spectra of proteins. In total, the experiments provide 111 intermolecular (13)C-(13)C and (15)N-(13)C constraints that establish that the PI3-SH3 protein strands are aligned in a parallel, in-register arrangement within the amyloid fibril.