Intramolecular Dipolar Relaxation Research Articles

Computing the frequency-dependent NMR relaxation of 1H nuclei in liquid water.

We present a computational framework for reliably determining the frequency-dependent intermolecular and intramolecular nuclear magnetic resonance (NMR) dipole-dipole relaxation rates of spin 1/2 nuclei from Molecular Dynamics (MD) simulations. This approach avoids the alterations caused by the well-known finite-size effects of translational diffusion. Moreover, a procedure is derived to control and correct for effects caused by fixed distance-sampling cutoffs and periodic boundary conditions. By construction, this approach is capable of accurately predicting the correct low-frequency scaling behavior of the intermolecular NMR dipole-dipole relaxation rate and thus allows for the reliable calculation of the frequency-dependent relaxation rate over many orders of magnitude. Our approach is based on the utilization of the theory of Hwang and Freed for the intermolecular dipole-dipole correlation function and its corresponding spectral density [L.-P. Hwang and J. H. Freed, J. Chem. Phys. 63, 4017-4025 (1975)] and its combination with data from MD simulations. The deviations from the Hwang and Freed theory caused by periodic boundary conditions and sampling distance cutoffs are quantified by means of random walker Monte Carlo simulations. An expression based on the Hwang and Freed theory is also suggested for correcting those effects. As a proof of principle, our approach is demonstrated by computing the frequency-dependent intermolecular and intramolecular dipolar NMR relaxation rates of 1H nuclei in liquid water at 273 and 298K based on the simulations of the TIP4P/2005 model. Our calculations are suggesting that the intermolecular contribution to the 1H NMR relaxation rate of the TIP4P/2005 model in the extreme narrowing limit has previously been substantially underestimated.

Hyperpolarized long-lived states in solution NMR: Three-spin case study in low field

Recent work has shown that singlet states in two-spin systems can possess lifetimes exceeding the T 1 relaxation time, provided that the system is kept under conditions that minimize the effects of the chemical shift Hamiltonian (for instance under low magnetic field or RF irradiation). Similar observations have been made in hyperpolarized states of multi-spin systems prepared via parahydrogen-induced polarization (PHIP). However, lifetime prolongation mechanisms in multi-spin systems are still under investigation. Here we present experimental observations of a long-lived state in a three-spin system prepared by PHIP and stored at low field. The observed lifetime of the long-lived state is 144s, about twice as long as the longest T 1 measured in the system at high field. The results are analyzed using a recently proposed theory of lifetime prolongation in multi-spin systems in low field. It is shown that quantum mechanical selection rules governing intramolecular dipolar relaxation in low field account for the enhanced lifetime and spectral features of this state.

Long-lived states in solution NMR: Theoretical examples in three- and four-spin systems

Long-lived spin states have been observed in a variety of systems. Although the dynamics underlying the long lifetimes of these states are well understood in the case of two-spin systems, the corresponding dynamics in systems containing more spins appear to be more complex. Recently it has been shown that a selection rule for transitions mediated by intramolecular dipolar relaxation may play a role in determining the lifetimes of long-lived states in systems containing arbitrary numbers of spins. Here we present a theory of long-lived states in systems containing three and four spins and demonstrate how it can be used to identify states that have little or no intramolecular dipolar relaxation.

Long-lived states in solution NMR: Selection rules for intramolecular dipolar relaxation in low magnetic fields

Recent work has shown that singlet states of two-spin systems in low magnetic fields can have lifetimes up to an order of magnitude longer than the usual spin–lattice relaxation time. This result may enable new applications of NMR, and in particular hyperpolarized NMR via parahydrogen-induced polarization, to the study of slow processes that take place over previously inaccessible timescales. At present it is unclear whether similar results apply to multi-spin systems, or if these long lifetimes are a peculiarity of the two-spin case. Moderately long-lived states have been observed in systems containing more than two spins, although the mechanisms that prolong their lifetimes are not well understood. Here we present formalism for the study of relaxation in multi-spin systems in low magnetic fields. This approach is used to derive a family of quantum-mechanical selection rules governing intramolecular dipolar relaxation at low field that may account for the extended lifetimes observed in multi-spin systems.

15N Nuclear Magnetic Resonance Spectroscopy. Changes in Nuclear Overhauser Effects and T1 with Viscosity

A procedure is described for probing changes in 15N T1 relaxation rates and nuclear Overhauser effects (NOE) with viscosity as a function of temperature. The large freezing-point depression and high viscosities of 8.8 M dimethyl sulfoxide (DMSO)−water solutions allowed study of the molecular motions of several ammonium salts, amides, and heterocycles on the pico- to nanosecond time scale. Dipole−dipole interactions provide the dominant form of relaxation for the ammonium salts, but chemical-shift anisotropy (CSA) also plays a significant role in the relaxation of amides and heterocycles. For pyridine, CSA is a particularly important mechanism and the shielding anisotropy of pyridine in 8.8 M DMSO−water is estimated to be on the order of 325 ppm. The 15N NOE of NH4Cl is greater than the theoretical maximum for intramolecular dipolar relaxation at high viscosities, and can be accounted for either by significant intermolecular contributions operating on a different time scale or by rapid motional averaging.

A study of protein-water exchange through the off-resonance ROESY experiment: application to the DNA-binding domain of AlcR.

In this communication a new NMR experiment for the safe observation and quantification of water-protein exchange phenomena is presented. It combines a water-selective pulse, offering chemical shift-based separation, and the off-resonance ROESY dynamic filter, which permits the elimination of the unwanted intramolecular dipolar cross relaxation of protein protons. Moreover, pulsed field gradients are used for the suppression of radiation damping and the solvent signal. The straightforward incorporation of this sequence in heteronuclear experiments is demonstrated for the case of the DNA-binding domain of the alcohol regulator protein.

Methods for the determination of molecular mobility of adsorbed molecules based on high resolution NMR

Based on the increased resolution achieved in NMR on adsorbed molecules, various methods are proposed to determine the mobility of adsorbed species. 1H NMR linewidths are shown to reflect intramolecular dipolar relaxation and can therefore be used for mobility estimates. This method is applicable to extremely low loadings. Thus we measured a significant decrease in molecular mobility for 1-butene adsorbed in zeolite NaX at loadings of approximately one molecule per ten supercages compared to that observed at four molecules per supercage. 1H NMR cross-relaxation rates of adsorbed allyl alcohol have been determined by 2D NOESY experiments and used to calculate the mean reorientation time of the allyl group. 1H 13C cross-relaxation rates, calculated using NOE factors and 13C longitudinal relaxation rates, allowed the calculation of mean reorientation times of the CH bond vector for adsorbed 1-butene. The same results are obtained from a comparison of longitudinal relaxation rates of protons attached to 13C and 12C atoms. Finally, the relaxation behavior of molecular groups, including cross-correlation effects and hence generation and decay of multiple spin order, is examined for 1-butene adsorbed on NaX.

Influence of conformational exchange on the 2D NOESY spectra of biomolecules existing in multiple conformations

The coupled recovery of the magnetizations of individual spins in a multispin system undergoing slow conformational exchange (on the chemical-shift scale) between different sites is considered within the context of the complete relaxation matrix analysis of the NOESY experiment. Explicit expressions have been derived for the peak intensities in the NOESY spectrum of a two-spin- 1 2 system. The general case where the populations and the intramolecular dipolar relaxation rates are different at the two sites is treated. This general case is appropriate for many practical situations normally encountered in biomolecular systems including that of a ligand undergoing exchange between free and enzyme-bound states. The expressions for the general case have been simplified for two limiting situations that also may be encountered in biomolecular NMR studies. The intensity variations of the different peaks in the spectrum (diagonal, exchange, direct NOESY, and exchange-mediated NOESY peaks) have been computed as a function of the mixing time for some typical examples. It is shown that, depending upon the conformational exchange rate in relation to dipolar cross-relaxation rates, the NOESY spectrum as a function of mixing time also exhibits significant dependence on the exchange rates. The implication of these results in extracting distance information is discussed. With minor modifications, the theoretical formalism presented here is readily applicable to situations where the conformational exchange is fast on the chemical-shift scale.

Nuclear spin relaxation and dipolar interactions in malononitrile/dichloromethane solutions

A low-temperature (-20 o C) NMR relaxation study of malononitrile dissolved in dichloromethane or dichlorodideuteriomethane was performed. Using a multispin formalism, both intermolecular and intramolecular dipolar relaxation rate constants were determined. Cross-correlation between various intramolecular dipolar interactions yielded a very exacting microdynamical description of malononitrile in the solution state. The plausibility of the relative ratio of intermolecular dipolar relaxation rates in the protonated and deuterated solvents was demonstrated. It is suggested that multispin NMR relaxation may provide a very sensitive probe of liquid-state structures. Further extensions of this work are proposed

The dynamics of the CH3CN molecule in the isotropic phase and in a nematic solution

Abstract NMR lineshape studies of acelonitrile in the isotropic and the liquid-crystalline nematic phase of PCH have been performed. The scalar relaxation of the second kind due to the presence of the 14N quadrupolar nucleus has been confirmed as the most important relaxation mechanism for this molecule in both the isotropic and the anisotropic phase. It has been found largely responsible for the selective broadening on 13C and 1H transitions. A minor contribution arising from intramolecular dipolar relaxation mechanism has also been investigated. Linewidth analysis of the NMR spectra allowed us to determine the quadrupolar relaxation time T IN of the 14N nucleus. This is connected to the correlation time for rotational diffusion perpendicular to the molecular symmetry axis. A possible explanation of a residual selective broadeining which effects the 13C and 1H NMR transitions and is not taken into account by this mechanism, is also given.

Does arachidonic acid exist in a well defined tertiary structure ?

Abstract 2d n.O.e. experiments as well as 1 H and 13 C relaxation time measurements force one to assume that arachidonic acid in solution exists at least partially in a backfolded tightly packed structure. Thereby in CDCl 3 this packed structure is most favored, whereas in CD 3 OD it seems to be of no valuable importance. Force field calculations performed on the same subject end up with four minima on the potential energy surface. One of those minima is well suited to explain the nmr results solely on basis of the r −6 dependence of intramolecular dipolar relaxation.

Transport and relaxation properties of dimethyl sulfoxide-water mixtures at high pressure

The pressure dependence of the deuterium T/sub 1/ in Me/sub 2/SO-D/sub 2/O mixtures and the proton T/sub 1/ and H/sub 2/O self-diffusion coefficients in Me/sub 2/SO-d/sub 6/-H/sub 2/O mixtures has been measured at 25/sup 0/C. The observations of increased motional freedom of H/sub 2/O with the initial application of pressure in mixtures up to 30 wt % Me/sub 2/SO (chi/sub Me/sub 2/SO/ = 0.1) indicates that small amounts of Me/sub 2/SO do not perturb in a major way the overall hydrogen-bond network in H/sub 2/O. The Debye equation describes well the reorientation of water molecules at 1 bar, but it fails at high pressure due to changes in the coupling between rotational and translational motions. The decreased pressure dependence of the rotational-translational coupling in solutions for chi/sub Me/sub 2/SO/ less than or equal to 0.2, as compared to pure water indicates that Me/sub 2/SO enhances the water structure at low Me/sub 2/SO concentration. The pressure dependence of the intramolecular and intermolecular proton dipolar relaxation rates of H/sub 2/O in Me/sub 2/SO-d/sub 6/-H/sub 2/O is also reported. 49 references, 6 figures, 2 tables.

Solvent and intramolecular proton dipolar relaxation of the three phosphates of ATP: a heteronuclear 2D NOE study

Solvent and intramolecular proton dipolar relaxation of the three phosphates of ATP: a heteronuclear 2D NOE study

On the intramolecular spin-lattice relaxation in reorienting three-spin [formula omitted] systems

For three-spin 1 2 systems like CF 3 groups reorienting about their C 3-axes which make an angle β with the magnetic field, theory predicts that under extreme narrowing condition the ratio of the intramolecular dipolar and Zeeman relaxation times ( T ID/ T IZ) intra = ( 2 3 ) (1 + 3 cos 3 β ). Experiments on a CF 3COOAg single crystal confirm this. Even wit h intermolecular contributions included their ratio is found to be greater than 1 2 , whereas for most dipolar solids it is ≤ 1 2 .

Internal rotation and intramolecular dipolar relaxation: Effect of modulation of internuclear separation

Expressions for the spin-lattice relaxation time for a nucleus experiencing intramolecular dipolar interactions which are modulated by internal motion and by overall molecular reorientation are given for the case when the internal motion modulates the internuclear distance. Rotational diffusion models are used to describe both internal and overall rotational dynamics, and results are given for spherical and symmetric top molecules. It is shown that modulation of the internuclear distance can give rise to substantial effects on the nuclear relaxation rate in certain molecular geometries.

Linewidth analysis of the proton resonance spectrum of benzene in a nematic solution

A nonaromatic nematic solvent consisting of an equimolar mixture of trans-4- n-butyl and trans-4- n-hexyl-cyclohexane-l-carboxylic acid was used to study the hydrogen NMR spectrum of partially oriented benzene. Variations in linewidths between 0.7 and 2.6 Hz could be observed but there was no strong correlation between splitting frequency and linewidth. The spectrum was analyzed using the Redfield theory considering intramolecular and intermolecular dipolar relaxation separately. Best agreement with the experiment is obtained by combining intermolecular relaxation effects with the zero frequency term of the intramolecular relaxation which gives contributions to the linewidths that are proportional to the square of the splitting frequency. The results indicate that the intermolecular interactions dominate and that intramolecular interactions become of importance only due to relatively slow director fluctuations.

Characterization of the histidine residues in alkaline phosphatase by carbon-13 nuclear magnetic resonance.

beta,beta-[gamma-13C]Dideuteriohistidine has been biosynthetically incorporated into alkaline phosphatase from Escherichia coli and utilized as a nonperturbing 13C nuclear magnetic resonance (NMR) probe of the environments of the histidine residues in this zinc metalloenzyme. The 13C NMR spectrum of the labeled enzyme exhibits 9 separate resonances arising from the 10 histidine residues located in each of the symmetrically disposed subunits of the dimer. The excellent resolution and large chemical shift range (14 ppm) displayed by these signals are direct consequences of the sensitivity of the histidine gamma-carbon chemical shift to the ionization state and tautomeric form of the imidazole side chains and the coordination of several of these to metal ion. The environments of the individual histidine residues were inferred by investigating the chemical shift responses of their 13C resonances to enzyme metal composition, pH, and inhibitor binding. Additional information concerning their motional freedom was obtained from spin relaxation measurements which were analyzed in terms of the contributions expected from intramolecular 13C-1H and 13C-14N dipolar relaxation and chemical shift anisotropy. The combined results indicate that 4 of the 10 histidines, the only ones that titrate with pH, are surface residues located relatively remote from the active site. Of the six nontitrating residues, one appears to be buried in a solvent-inaccessible region of the protein. Three others are almost certainly involved in metal ion ligation to active-site metal ion(s), two via their N pi nitrogen atoms and the other via N pi. The spectral characteristics of the remaining two histidine residues strongly suggest they are also located at or near the active site. One or both may also participate in metal ion coordination, although the current evidence for this is inconclusive.

Structure and dynamics of ammonia adsorbed on graphitized carbon black. Part 4.—Nuclear magnetic resonance spectra

Proton nuclear magnetic resonance experiments on ammonia adsorbed on Graphon are described. Proton chemical shifts, spin–lattice relaxation times and linewidths have been measured as a function of temperature and coverage.The variation of the signal from adsorbed fluid ammonia has been used to measure adsorption isotherms, the isosteric heat of adsorption and melting curves of solid ammonia in contact with Graphon. All these results agree well with gravimetric and neutron scattering experiments described in three earlier papers.The chemical shift of adsorbed ammonia is large (39 p.p.m. to high field) and can be attributed to the effects of anisotropy in the susceptibility of graphite on ammonia molecules adsorbed close to the graphite basal planes. A semi-quantitative model of the effect shows that, above ≈ 195 K (the melting point of bulk solid ammonia), there can only be limited multilayer formation. As the temperature increases, the chemical shift decreases because ammonia molecules are promoted to layers further from the surface. At low temperatures the chemical shift also decreases because ammonia starts to aggregate at heterogeneities on the surface where there is no susceptibility effect. This is correlated with neutron scattering results. The two experiments taken together show the gradual transition with decreasing temperature from anisotropic fluid, through aggregates of ammonia similar to the super-cooled liquid, to bulk solid, the whole process resembling heterogeneous nucleation.The linewidths are abnormally large at all temperatures and coverages. There are two sources of the broadening, diffusion through local magnetic field gradients in the sample, and the possible restriction of the motion of the adsorbate to two dimensions. Other mechanisms which have been considered by other authors are eliminated by considering the neutron scattering results.The spin–lattice relaxation time of adsorbed ammonia is abnormally small (≈ 20 ms) and shows some evidence of a minimum corresponding to a correlation time of 2 × 10–9 s. Partial deuteration shows that the mechanism is intramolecular dipolar relaxation. Consideration of the frequency spectrum of the diffusive motions of adsorbed ammonia, known from quasielastic neutron scattering, indicates that the slow correlation time may arise from a slow rate of jumping between the molecular layers of adsorbate.

Spin lattice relaxation in an AM{Xn} system: Application to 13C relaxation in enriched molecules

In 13C-enriched molecules, 13C–13C dipolar interactions can contribute significantly to the relaxation of 13C nuclei which are not directly bonded to protons. Comparison of the relaxation behavior of the 13C–13C multiplet lines with that of the singlet for which there are no 13C–13C dipolar interactions allows a quantitative analysis of this interaction. However, since 13C–13C dipolar interactions are necessarily weak, substantial contributions to the relaxation of nonprotonated carbon atoms are made by protons attached to adjacent atoms. The general features of the spin lattice relaxation behavior of an AM{X} system in which {X} represents the decoupled protons, A, the nonprotonated carbon, and M, the adjacent protonated carbon, have been derived. In general, the A relaxation will be nonexponential and dependent on the initial state of the Mz magnetization. A particularly useful application of these measurements on 13C-enriched systems is found in their sensitivity to internal and/or anisotropic motions. Such rotations affect the 13C–13C and 13C−1H dipolar interactions differently, depending on the particular geometry involved and the axis of rotation. These techniques have been applied to the observed relaxation behavior of 6-phosphogluconate enriched to the 79% level. In this case the contributions to the intramolecular dipolar relaxation of the carboxyl carbon consist primarily of the 13C–13C interaction with its adjacent carbon, the 13C−1H interaction with the proton on the adjacent carbon, and a significant contribution from the proton attached to the third carbon in the chain. For this case, it is found that the carboxyl relaxation will be, to a very good approximation, exponential and independent of the initial value of Mz. Furthermore, a significantly improved fit of the data results if anisotropic rotation effects are considered.

The computer calculation of relaxation matrices and NMR line shapes

A computer program has been written to calculate relaxation matrices and NMR line shapes. The use of the program in calculating the effects of external random field relaxation in AB, ABX, and AA′XX′ spin systems, intramolecular dipolar relaxation in AB, ABX, AB 2 and A 3 systems, mutual exchange, and random noise decoupling in AA′XX′ systems is discussed. New results are presented, literature results are reproduced, and some disagreement with previous work is reported.