An iterative fitting procedure for the determination of longitudinal NMR cross-correlation rates

We present a method to measure (15)N-(1)H dipolar/(15)N CSA longitudinal cross-correlation rates in protonated proteins. The method depends on the measurement of four observables: the cumulative proton-proton cross relaxation rates, the (15)N R(1) relaxation rate, the multiexponential decay of 2N(Z)H(N)(Z) spin-order, and multiexponential buildup of 2N(Z)H(N)(Z) spin-order. The (15)N-(1)H dipolar/(15)N CSA longitudinal cross-correlation rate is extracted from these measurements by an iterative fitting procedure to the solution of differential equations describing the coupled relaxation dynamics of the z-magnetization of the (15)N nucleus, the two-spin-order 2N(Z)H(N)(Z), and a two-spin-order term 2N(Z)H(Q)(Z) describing the interaction with remote protons. The method is applied to the microbial ribonuclease binase. The method can also extract longitudinal cross-correlation rates for those amide protons that are involved in rapid solvent exchange. The experiment that serves for extracting proton-proton cross-relaxation rates is a modification of 3D (15)N-resolved NOESY-HSQC. The experiment restores the solvent magnetization to its equilibrium state during data detection for all phase cycling steps and all values of NOE mixing times and is recommended for use in standard applications as well.     

Meson exchange interactions at low and intermediate energies: colour screening effects

We consider the colour screening effects of constituent quarks and the exchange of effective gluons in the interaction of hadrons. To this end we propose two different processes derived from fundamental properties of the underlying microscopic theory (QCD). Sum rules for diagrams providing colour screening are also given.     

Separation of cross-relaxation and exchange in two-site spin systems without resolved couplings

Variable temperature two-dimensional nuclear Overhauser enhancement experiment (2-D NOESY) is used to extract the rate constants and cross-relaxation rates that contribute to the same cross-peaks in NOESY spectra. Rate constants (k _AB) and cross-relaxation rates (R _AB) for two-site spin systems are related to the ratio between the cross-peak and diagonal peak integrals (F) by the expression:R _AB -k _AB = (1/2τ _m)ln[(1 -F)/(1 +F)], where τ_m is the mixing time. As a model, we investigated the exchange processes in a system of dimer calix[4]arenes of C_4v symmetrical configuration with guest inclusion (benzene or benzene-d₆), where the measurement of exchange processes is hindered by the presence of strong nuclear Overhauser enhancement between protons in adjacent aromatic rings in the cone conformation of the calix[4]arene.     

Separation of cross-relaxation and exchange in two-site spin systems with weak spin-spin couplings

A ratio relating the cross-relaxation rates, rate constants, and cross-peak and diagonal peak integrals is used for the analysis of exchanging two-site spin systems with weak scalar spin-spin couplings to extract the rate constants and cross-relaxation rates contributing to the same cross-peaks in two-dimensional nuclear Overhauser enhancement spectra (2-D NOESY). The method to separate contributions from cross-relaxation and chemical exchange into the cross-peaks in NOESY spectra was applied to investigate the intramolecular dynamics of trisulfide 4H, 8H-naphtho[1,8-ef]1,2,3-trithiocine in solutions.     

The shape of NMR absorption and cross-relaxation spectra in a heteronuclear spin system

A dynamic theory of heteronuclear spin systems in solids at high temperatures is developed. A system of nonlinear integral equations for the spin time correlation functions is derived in the self-consistent fluctuating local field approximation taking into account corrections for the correlated local field fluctuations in real crystal lattices. The theory is applied to interpretation of the experimental data available for a LiF crystal representing a system with the nuclei of two types. The signals of free precession for Li and F nuclei, as well as the spectra of harmonic cross-relaxation, cross-polarization of the ⁶Li isotope, and depolarization of the ⁸Li isotope, were calculated for the magnetic field oriented along the principal crystallographic axes of LiF. The results of calculations show good agreement with experiment.     

Proton residual dipolar couplings by NMR magnetization exchange in cross-linked elastomers: determination and imaging.

Proton nuclear magnetic resonance (NMR) magnetization exchange is used to investigate residual dipolar couplings in a series of cross-linked poly(styrene-cobutadiene) elastomers. A new model for the dipolar unit is used for the evaluation of the signal decay in magnetization exchange experiments. It takes into account an extended residual dipolar coupling network along the polymer chain. It is shown that in the regime of short mixing times, information about the residual dipolar coupling between methine and methylene protons can be obtained which is not affected by other inter- and intramolecular dipolar couplings. The dynamic order parameter of methine-methylene protons is measured and correlated with cross-link density. This study certifies the quality of a filter for magnetization from residual dipolar couplings which exploit magnetization exchange. The filter can be used to generate contrast in NMR images of heterogeneous elastomers. The first proton NMR parameter image of a dynamic order parameter is presented for a phantom made from poly(styrene-cobutadiene) samples with different cross-link densities.     

Time-domain calculation of chemical exchange effects in the NMR spectra of rotating solids.

A simple method is described for the calculation of magic-angle-spinning (MAS) spectra of solids in the presence of chemical exchange. The method converges quickly, allowing rapid calculation of the spectra. Calculated spectra are given for molecular motion involving 2 and 6 sites.     

Effects of off-resonance irradiation, cross-relaxation, and chemical exchange on steady-state magnetization and effective spin-lattice relaxation times

In the presence of an off-resonance radiofrequency field, recovery of longitudinal magnetization to a steady state is not purely monoexponential. Under reasonable conditions with zero initial magnetization, recovery is nearly exponential and an effective relaxation rate constant R_1eff = 1/T_1eff can be obtained. Exact and approximate formulas for R_1eff and steady-state magnetization are derived from the Bloch equations for spins undergoing cross-relaxation and chemical exchange between two sites in the presence of an off-resonance radiofrequency field. The relaxation formulas require that the magnetization of one spin is constant, but not necessarily zero, while the other spin relaxes. Extension to three sites with one radiofrequency field is explained. The special cases of off-resonance effects alone and with cross-relaxation or chemical exchange, cross-relaxation alone, and chemical exchange alone are compared. The inaccuracy in saturation transfer measurements of exchange rate constants by published formulas is discussed for the creatine kinase reaction.     

The effects of pre-equilibrium emission and secondary decay on the determination of freeze-out volume at intermediate energies

The effects of pre-equilibrium emission and secondary decay on the determination of the freeze-out volume are investigated using the isospin-dependent quantum molecular dynamics model accompanied by the statistical decay model GEMINI. Small-mass projectiles and large-mass targets with central collisions are studied at intermediate energies. It is revealed that the proton yields of pre-equilibrium emission are smaller than those of secondary decay. However, the determination of the freeze-out volume from the proton yields is more easily affected by pre-equilibrium emission. Moreover, the percentage of proton yields in the freeze-out stage is found to be approximately 50%.     

Two-dimensional NMR of velocity exchange: VEXSY and SERPENT

Two different multidimensional pulsed field gradient sequences are compared which have the purpose of correlating spin displacements in different time intervals with each other. The simplest possible sequence, three-pulse SERPENT, measures displacements in two interleaved time intervals, while in VEXSY, consisting of two independent pairs of gradient pulses separated by a mixing time, displacements during the two encoding intervals are compared to each other. The formalism for both sequences is discussed in q space and in displacement space and common features as well as differences between the two types of experiments are highlighted, employing the particular case of the concurrent VEXSY scheme which allows treatment according to both formalisms.     

Multidimensional NMR cross-correlation relaxation study of carrot phloem and xylem. Part I: Peak assignment

We report, for the first time, a detailed analysis of the complicated two-dimensional (2-D) nuclear magnetic resonance relaxation spectra of the xylem and phloem of carrots. By combining chemical extraction with different 2-D pulse sequences attempts are made to assign relaxation peaks to cell components, including compartmentalized water, pectins, starch, proteins and hemicelluloses. In a separate report, we use these assignments to interpret the effects of thermal and high-pressure processing (M. E. Furfaro, N. Marigheto, G. K. Moates, K. Cross, M. L. Parker, K. W. Waldron, B. P. Hills: Appl. Magn. Reson. 35, 537–547, 2009).     

Determination of the conformation and stability of simple homopolypeptides using solid-state NMR

15N CPMAS, 13C CPMAS and 1H CRAMPS spectra of several polypeptide samples were compared to determine the useful features of each technique. 13C CPMAS is the most well-established technique and is useful for quick determination of secondary structure. The 15N nucleus is more sensitive to exact hydrogen-bonding parameters, which complicates interpretation of the spectra. However, it is better for resolving end effects and structural types in short oligomers. 1H CRAMPS spectra are similar to 13C CPMAS in the information obtained, but the resolution is not as good. Using 13C CPMAS, the conformation of polyglycine was investigated in detail. Precipitation from solvents such as DCA or TFA resulted in the rippled beta-sheet structure (PG I), while 3(1)-helix (PG II) was formed by precipitation from aqueous solutions of LiBr. Grinding the sample resulted in an increase in the amount of PG I, indicating that this form is more stable in the solid state. These results agree with previous work on poly(L-alanine) showing that the beta-sheet form is more stable in the solid state. Homopolypeptides with larger side chains did not change conformation upon grinding due to the greater difficulty in disrupting van der Waals interactions and inertia of the large side chains.     

Restricted diffusion and exchange of water in porous media: average structure determination and size distribution resolved from the effect of local field gradients on the proton NMR spectrum

NMR Pulsed field gradient measurements of the restrained diffusion of confined fluids constitute an efficient method to probe the local geometry in porous media. In most practical cases, the diffusion decay, when limited to its principal part, can be considered as Gaussian leading to an apparent diffusion coefficient. The evolution of the latter as a function of the diffusion interval yields average information on the surface/volume ratio of porosities and on the tortuosity of the network. In this paper, we investigate porous model systems of packed spheres (polystyrene and glass) with known mean diameter and polydispersity, and, in addition, a real porous polystyrene material. Applying an Inverse Laplace Transformation in the second dimension reveals an evolution of the apparent diffusion coefficient as a function of the resonance frequency. This evolution is related to a similar evolution of the transverse relaxation time T2. These results clearly show that each resonance frequency in the water proton spectrum corresponds to a particular magnetic environment produced by a given pore geometry in the porous media. This is due to the presence of local field gradients induced by magnetic susceptibility differences at the liquid/solid interface and to slow exchange rates between different pores as compared to the frequency differences in the spectrum. This interpretation is nicely confirmed by a series of two-dimensional exchange experiments.     

Multidimensional NMR cross-correlation relaxation study of carrot phloem and xylem. Part II: Thermal and high-pressure processing

The effects of thermal and high-pressure processing on the phloem and xylem tissue of carrots are investigated with a combination of optical fluorescence microscopy and two-dimensional nuclear magnetic resonance relaxometry. It is shown that precooking at 60 °C or rapid pressurization to 600 MPa prevents the cell-wall separation and that the combination of these two treatments may provide a commercially viable method for tissue texture preservation.     

Field-cycling NMR investigations of (13)C-(1)H cross-relaxation and cross-polarisation: the nuclear solid effect and dynamic nuclear polarisation

A field-cycling NMR investigation of (1)H-(13)C polarisation transfer using cross-relaxation and the nuclear solid effect (NSE) is described. Dynamic nuclear polarisation (DNP) of the (13)C spins is observed when forbidden transitions are driven by r.f. irradiation at the sum and difference Larmor frequencies of the two nuclei. When the (1)H spins are pre-polarised, a significant transfer of polarisation to the (13)C nuclei is achieved in a time short compared with the spin-lattice relaxation time of (13)C. The cross-polarisation arising from the NSE is studied as a function of B-field and time. These results are compared with the solutions of the differential equations that govern the coupled system of (1)H-(13)C spins. The effects of cross-relaxation are incorporated into the model for the first time and good agreement between theory and experiment is obtained. The experiments have been conducted at 20K on a (13)C-enriched sample of benzoic acid.     

Interference of homonuclear decoupling and exchange in the solid-state NMR of perfluorocyclohexane

We observe an interference between RF irradiation used for homonuclear decoupling of 19F and conformational exchange in the 13C spectrum of perfluorocyclohexane. We show that these effects can be readily reproduced in simulation, and characterise their dependence on the various NMR and experimental parameters. Their application to observing exchange rates on the kHz timescale is evaluated with respect to T(1rho) measurements and the connections between the two approaches established. The implications for experiments that use homonuclear decoupling of 1H to resolve 1J(CH)couplings in the solid-state are also evaluated in detail.     

A new model for the ground-state spin determination in ferromagnetics: The influence of many-electron exchange effects on the ground-state total spin in titanium and nickel

A new approximate exchange interaction operator, derived from the exact atomic second quantization formalism, has been applied to the study of the magnetic properties of atoms with spin $\text{S =}\text{1}\text{2}$ and S = 1 which obey Hund's rule. The new operator involves the effects of one-pair and two-pair electron exchanges. The one-pair exchange effects are compared with the Heisenberg model. It is shown that our model comprises the symmetry properties of the atomic wavefunction and the interaction of all electrons in the unfilled shells of two atoms, which are not considered in the Heisenberg theory. The conditions under which the new one-pair exchange effect may be used to improve the old one are pointed out. The significance of the two-pair exchange effects is discussed. It is demonstrated that, owing to the simultaneous exchange of two electron pairs, the total ground-state spin of two atoms may have intermediate values in addition to those predicted by the Heisenberg model. The importance of the interrelation between the first- and second-order effects, with respect to both sign and magnitude, is pointed out. The existence of the intermediate values, even in the case where the first order exchange integral is negative, is taken as a conjecture by which one may explain the fact that the mean magnetic moment per atom in magnetic 3d metals is not equal to the spin magnetic moment of an individual atom and accounts for the existence of magnetic ordering when the first order exchange integral is negative.     

Microwave determination of the conformation and dipole moment of 1,3-difluoroacetone

The microwave spectra of the ground state and several low-lying vibrational modes of 1,3-difluoroacetone have been assigned and analyzed. The assigned form has a molecular conformation in which one fluorine atom lies cis and the other trans to the oxygen atom. The rotational constants of the ground state species were determined using a centrifugal distortion analysis: A = 6024.843 ± 0.006 MHz, B = 2454.414 ± 0.001 MHz, C = 1783.897 ± 0.001 MHz. The molecular dipole moment components of the ground state species lie along the a and b principal axes with μ_a = 2.38 ± 0.03 D, μ_b = 0.89 ± 0.03 D, and μ_T = 2.54 ± 0.03 D. Comparative intensity measurements with OCS microwave lines indicate that the assigned form constitutes only 20% to 30% of the total gas mixture, the remainder presumably consisting of one or more other conformers, perhaps the gauche-gauche form. The lowest vibrational frequency (82 ± 12 cm^?1) is attributed to the trans-CH₂F torsion, while the next-higher vibrational frequency (127 ± 15 cm^?1) is believed to be the cis-torsion. A low-frequency in-plane bending motion is found at 285 ± 25 cm^?1.     

Dipolar cross-relaxation modulates signal amplitudes in the (1)H NMR spectrum of hyperpolarized [(13)C]formate

The asymmetry in the doublet of a spin coupled to hyperpolarized (13)C has been used previously to measure the initial polarization of (13)C. We tested the hypothesis that a single observation of the (1)H NMR spectrum of hyperpolarized (13)C formate monitors (13)C polarization. Depending on the microwave frequency during the polarization process, in-phase or out-of-phase doublets were observed in the (1)H NMR spectrum. Even in this simple two-spin system, (13)C polarization was not reflected in the relative area of the J(CH) doublet components due to strong heteronuclear cross-relaxation. The Solomon equations were used to model the proton signal as a function of time after polarization and to estimate (13)C polarization from the (1)H NMR spectra.