Spin-lattice Relaxation Rate Constants Research Articles

NMR studies of ordered structures and valence states in the successive valence-transition system EuPtP

We have studied EuPtP, which undergoes two successive valence transitions at ${T}_{\mathrm{A}}\ensuremath{\sim}240$ K and ${T}_{\mathrm{B}}\ensuremath{\sim}200$ K by $^{31}\mathrm{P}$-nuclear magnetic resonance (NMR) measurements. From the analysis of NMR spectra, we obtained plausible ordered structures and Eu valence states in three phases divided by ${T}_{\mathrm{A}}$ and ${T}_{\mathrm{B}}$. These ordered structures well explain observed inequivalent P sites and the intensity ratio of the NMR spectra arising from these P sites. The results are also in good accordance with mean Eu valence measured by the x-ray absorption spectroscopy. We also discuss Eu $4f$ states and the origin of the transitions from the measurements of nuclear spin lattice relaxation rate and hyperfine coupling constant.

Extreme-Values Statistics and Dynamics of Water at Protein Interfaces

Immobilized proteins present a unique interface with water. The water translational diffusive motions affect the high-frequency dynamics and the nuclear spin-lattice relaxation as with all surfaces; however, rare binding sites for water in protein systems add very low-frequency components to the dynamics spectrum. Water binding sites in protein systems are not identical, thus distributions of free energies and consequent dynamics are expected. (2)H(2)O spin-lattice relaxation rate measurements as a function of magnetic field strength characterize the local rotational fluctuations for protein-bound water molecules. The measurements are sensitive to dynamics down to the kilohertz range. To account for the data, we show that the extreme-values statistics of rare events, i.e., water dynamics in rare binding sites, implies an exponential distribution of activation energies for the strongest binding events. In turn, for an activated dynamical process, the exponential energy distribution leads to a Pareto distribution for the reorientational correlation times and a power law in the Larmor frequency for the (2)H(2)O spin-lattice relaxation rate constants at low field strengths. The most strongly held water molecules escape from rare binding sites in times on the order of microseconds, which interrupts the intramolecular correlations and causes a plateau in the spin-lattice relaxation rate at very low magnetic field strengths. We examine the magnetic relaxation dispersion (MRD) data using two simple but related models: a protein-bound environment for water characterized by a single potential well and a protein-bound environment characterized by a double potential well where the potential functions for the local motions of the bound-state water are of different depth. This analysis is applied to D(2)O deuterium spin-lattice relaxation on cross-linked albumin and lysozyme, which is dominated by the intramolecular relaxation driven by the dynamical modulation of the nuclear electric quadrupole coupling. We also separate the intramolecular from the intermolecular contribution to water proton spin-lattice relaxation by isotope dilution and show that the intramolecular proton data map onto the deuterium relaxation by a scale factor implied by the relative strength of the quadrupole and dipolar couplings. The temperature and pH dependence of the magnetic relaxation dispersion are complex and accounted for by changing only the weighting factors in a superposition of contributions from single-well and double-well contributions. These experiments show that the reorientational dynamics spectrum for water, in and on a protein, is characterized by a strongly asymmetric distribution with a long-time tail that extends at least to microseconds.

Paramagnetic Contributions to Nuclear Spin-Lattice Relaxation in Proteins

Paramagnetic contributions to spin-lattice relaxation rate constants are very useful in providing long-range distance constraints for structural determinations by NMR and also for controlling image contrast in clinical MRI protocols. When a radical with a long electron-spin-relaxation time is bound to a protein, the paramagnetic contribution to the water-proton-spin-lattice-relaxation rate is larger than predicted by usual theory. We show that this excess nuclear spin relaxation efficiency results from long-lived-bound water molecules for which the electron-nuclear coupling is correlated with the long rotational correlation time of the protein. Because the correlation time is so long compared with the relative translational correlation times, even distant water molecules make significant contributions and increase the relaxation efficiency of the paramagnetic center. If the rotational motion of the protein is stopped, as in a solid protein, a protein gel, or a tissue, the paramagnetic contributions to relaxation are both qualitatively and quantitatively changed from the solution limit. The spin-lattice relaxation for different paramagnetic systems may be understood in terms of the intrinsic dynamics of the protein and the spin dynamics of the paramagnetic center, which depends on the identity and magnetic characteristics of the paramagnetic center. These different effects are important for applications to magnetic imaging and structure determination by solid state NMR.

Dynamics of water in and around proteins characterized by 1H-spin-lattice relaxometry

Abstract Nuclear magnetic spin-lattice relaxation rate constants measured as a function of the magnetic field strength over wide ranges of Larmor frequency map the noise spectrum that drives spin relaxation. For water in and around protein systems, the spin relaxation reports on the average local translational mobility at the interface which is reduced by approximately factor of three from the bulk and there is anisotropy induced in the motions caused by the excluded volume created by the presence of the protein. Water also penetrates the protein and relatively few bound water sites provide a strong coupling between the protein dynamics and the water-proton-spin relaxation.

Spin-diffusion couples proton relaxation rates for proteins in exchange with a membrane interface

Changes in nuclear spin-lattice relaxation rates that are induced by a freely diffusing paramagnetic relaxation agent are examined for a protein in solution and compared to the case where the protein binds to a membrane. In the solution case, the intramolecular cross-relaxation rates are modest and large differences are observed in the oxygen induced protein–proton relaxation rates. In the case where a dynamic equilibrium between solution and membrane-bound environments is established, the intramolecular 1H cross-relaxation rates for the protein protons increase dramatically because of the slow reorientational motion in the membrane-bound environment. As a consequence, all protein protons relax with nearly the same spin-lattice relaxation rate constants when bound to the membrane, and site specific relaxation effects of the diffusing paramagnet are suppressed. Slowly reorienting sites or rotationally immobilized sites sampled by observable molecules in vivo will demonstrate similar relaxation leveling effects.

Study of the Adsorption of Organic Molecules on Transition Metal Exchanged Zeolites via Solid State NMR. Part 1: Theoretical Aspects

A theoretical study is performed of the (1)H relaxation behavior of an organic molecule that is adsorbed in a zeolite exchanged with transition metal ions. An expression is derived for the spin-lattice and spin-spin relaxation rate constant of a uniform proton ensemble, while the occurrence of molecular exchange is taken into account. The influence is analyzed of an approach of a uniform proton ensemble toward the nearest neighboring paramagnetic ion system. It is shown that there exists a signal extinction effect, for which the critical distance was estimated.

Estimation of free copper ion concentrations in blood serum using T1 relaxation rates

The water proton relaxation rate constant R 1 = 1/ T 1 (at 60 MHz) of blood serum is substantially increased by the presence of free Cu 2+ ions at concentrations above normal physiological levels. Addition of chelating agents to serum containing paramagnetic Cu 2+ nulls this effect. This was demonstrated by looking at the effect of adding a chelating agent—D-penicillamine (D-PEN) to CuSO 4 and CuCl 2 aqueous solutions as well as to rabbit blood serum. We propose that the measurement of water proton spin–lattice relaxation rate constants before and after chelation may be used as an alternative approach for monitoring the presence of free copper ions in blood serum. This method may be used in the diagnosis of some diseases (leukaemia, liver diseases and particularly Wilson’s disease) because, in contrast to conventional methods like spectrophotometry which records the total number of both bound and free ions, the proton relaxation technique is sensitive solely to free paramagnetic ions dissolved in blood serum. The change in R 1 upon chelation was found to be less than 0.06 s −1 for serum from healthy subjects but greater than 0.06 s −1 for serum from untreated Wilson’s patients.

Solvation and Intermolecular Exploration of Drug Molecule Fragments

The paramagnetic contributions from dioxygen to solute proton spin-lattice relaxation rate constants are reported for a series of aromatic hydrocarbons and drug molecule fragments, in order to examine the energetic factors for intermolecular exploration in solution. The measurements provide differences in local oxygen concentration at different sites on the solute molecule. The relaxation rate differences caused by steric factors are taken into account using a lattice model calculation to normalize the relaxation rates for intermolecular contact. The measurements reveal small differences in oxygen accessibility for aromatic solutes in aqueous acetone and for aliphatic drug fragments in chloroform. Larger differences are observed for aliphatic protons in dimethyl sulfoxide; however, the differences are generally small compared with previous measurements on amino acids in water. Concentration ratios between local oxygen concentrations and the solvent references are all smaller than 2.2 and high local concentrations are favored by bulky adjacent groups such as alkane chains.

Picosecond water dynamics adjacent to charged paramagnetic ions measured by magnetic relaxation dispersion

Measurements of water-proton spin-lattice relaxation rate constants as a function of magnetic field strength [magnetic relaxation dispersion (MRD)] in aqueous solutions of paramagnetic solutes reveal a peak in the MRD profile. These previously unobserved peaks require that the time correlation functions describing the water-proton-electron dipolar coupling have a periodic contribution. In aqueous solutions of iron(III) ion the peak corresponds to a frequency of 8.7 cm-1, which the authors ascribe to the motion of water participating in the second coordination sphere of the triply charged solute ion. Similar peaks of weaker intensity in the same time range are observed for aqueous solutions of chromium(III) chloride as well as for ion pairs formed by ammonium ion with trioxalatochromate(III) ion. The widths of the dispersion peaks are consistent with a lifetime for the periodic motion in the range of 5 ps or longer.

Nuclear magnetic relaxation dispersion study of the dynamics in solid homopolypeptides

The (1)H nuclear magnetic relaxation dispersion profiles were measured from 10 kHz to 30 MHz as a function of temperature for polyglycine, polyalanine, polyvaline, and polyphenylalanine to examine the contributions of different side chain motions to the polypeptide proton relaxation rate constants. The spin-fracton theory for (1)H relaxation is modified to account for high frequency motions of side chains that are dynamically connected to the linear polymer backbone. The (1)H relaxation is dominated by propagation of rare disturbances along the backbone of the polymer. The side-chain dynamics cause an off-set in the field dependence of the (1)H spin-lattice relaxation rate constants which obey a power law in the Larmor frequency in the limit of low and high magnetic field strength.

Relaxation of protons by radicals in rotationally immobilized proteins

Proton spin–lattice relaxation by paramagnetic centers may be dramatically enhanced if the paramagnetic center is rotationally immobilized in the magnetic field. The details of the relaxation mechanism are different from those appropriate to solutions of paramagnetic relaxation agents. We report here large enhancements in the proton spin–lattice relaxation rate constants associated with organic radicals when the radical system is rigidly connected with a rotationally immobilized macromolecular matrix such as a dry protein or a cross-linked protein gel. The paramagnetic contribution to the protein–proton population is direct and distributed internally among the protein protons by efficient spin diffusion. In the case of a cross-linked-protein gel, the paramagnetic effects are carried to the water spins indirectly by chemical exchange mechanisms involving water molecule exchange with rare long-lived water molecule binding sites on the immobilized protein and proton exchange. The dramatic increase in the efficiency of spin relaxation by organic radicals compared with metal systems at low magnetic field strengths results because the electron relaxation time of the radical is orders of magnitude larger than that for metal systems. This gain in relaxation efficiency provides completely new opportunities for the design of spin–lattice relaxation based contrast agents in magnetic imaging and also provides new ways to examine intramolecular protein dynamics.

Paramagnetic relaxation of protons in rotationally immobilized proteins

The proton magnetic relaxation dispersion profiles are reported over the proton Larmor frequency range from 0.01 to 30 MHz for cross-linked gels and for the dry lyophilized bovine serum albumin covalently labeled at lysine with diethylenetriaminepentaacetic acid chelates of either Gd(III) or Mn(II) ions. The proton spin-lattice relaxation dispersion for the cross-linked paramagnetic protein gel is accurately represented as a sum of two major relaxation contributions. The diamagnetic term is a power law from the magnetic field dependence of the protein protons. The paramagnetic term is approximately described by the Solomon-Bloembergen-Morgan class of models. However, the paramagnetic relaxation mechanism in the dry lyophilized protein is fundamentally different and we develop a new quantitative description of the dispersion profile. In the dry case, no peak in the proton relaxation dispersion profile is detected from the field dependence of the electron spin relaxation times. The high-field paramagnetic relaxation dispersion is a power law in the Larmor frequency with an exponent of -0.8, which results from modulation of the electron-nuclear coupling by the intramolecular dynamics of the protein which primarily propagates along the primary structure of the protein. The low-field plateau is caused by the interruption of the electron-nuclear spin correlation by electron spin relaxation. This new quantitative description provides a simple approach to the measurement of electron spin-lattice relaxation times in paramagnetic protein systems at room temperature based on the magnetic field dependence of the proton spin-lattice relaxation rate constant.

Spin relaxation measurements of electrostatic bias in intermolecular exploration

We utilize the paramagnetic contribution to proton spin–lattice relaxation rate constants induced by freely diffusing charged paramagnetic centers to investigate the effect of charge on the intermolecular exploration of a protein by the small molecule. The proton NMR spectrum provided 255 resolved resonances that report how the explorer molecule local concentration varies with position on the surface. The measurements integrate over local dielectric constant variations, and, in principle, provide an experimental characterization of the surface free energy sampling biases introduced by the charge distribution on the protein. The experimental results for ribonuclease A obtained using positive, neutral, and negatively charged small nitroxide radicals are qualitatively similar to those expected from electrostatic calculations. However, while systematic electrostatic trends are apparent, the three different combinations of the data sets do not yield internally consistent values for the electrostatic contribution to the intermolecular free energy. We attribute this failure to the weakness of the electrostatic sampling bias for charged nitroxides in water and local variations in effective translational diffusion constant at the water–protein interface, which enters the nuclear spin relaxation equations for the nitroxide–proton dipolar coupling.

High Frequency Dynamics in Hemoglobin Measured by Magnetic Relaxation Dispersion

The magnetic relaxation dispersion profiles for formate, acetate, and water protons are reported for aqueous solutions of hemoglobin singly and doubly labeled with a nitroxide and mercury(II) ion at cysteines at β-93. Using two spin labels, one nuclear and one electron spin, a long intramolecular vector is defined between the two β-93 positions in the protein. The paramagnetic contributions to the observed 1H spin-lattice relaxation rate constant are isolated from the magnetic relaxation dispersion profiles obtained on a dual-magnet apparatus that provides spectral density functions characterizing fluctuations sensed by intermoment dipolar interactions in the time range from the tens of microseconds to ∼1 ps. Both formate and acetate ions are found to bind specifically within 5 Å of the β-93 spin-label position and the relaxation dispersion has inflection points corresponding to correlation times of 30 ps and 4 ns for both ions. The 4-ns motion is identified with exchange of the anions from the site, whereas the 30-ps correlation time is identified with relative motions of the spin label and the bound anion in the protein environment close to β-93. The magnetic field dependence of the paramagnetic contributions in both cases is well described by a simple Lorentzian spectral density function; no peaks in the spectral density function are observed. Therefore, the high frequency motions of the protein monitored by the intramolecular vector defined by the electron and nuclear spin are well characterized by a stationary random function of time. Attempts to examine long vector fluctuations by employing electron spin and nuclear spin double-labeling techniques did not yield unambiguous characterization of the high frequency motions of the vector between β-93 positions on different chains.

Magnetic relaxation dispersion of lithium ion in solutions of DNA.

The magnetic field dependence of the nuclear spin-lattice relaxation rate constant defines the magnetic relaxation dispersion (MRD) and provides a direct characterization of the molecular dynamics that cause fluctuations in the magnetic couplings in the system and may also indicate the dimensional constraints on the motion. The counterion cloud surrounding a linear polyelectrolyte ion, such as DNA in solution, provides an interesting opportunity for ion confinement that helps in understanding the thermodynamics and the dynamics of the interactions between the polyion and other solutes. The MRD profiles of lithium ion and tetramethylammonium ion were recorded in dilute aqueous solutions of native calf thymus DNA, which provides a long, charged rod that reorients slowly. The 7Li ion relaxes through the nuclear electric quadrupole coupling and the proton-lithium dipole-dipole coupling; the protons of the tetramethylammonium ion relax by dipole-dipole coupling. MRD profiles of the 7Li+ ion are dominated by transient interactions with the DNA that yield a linear dependence of the spin-lattice relaxation rate constant on the logarithm of the Larmor frequency. This magnetic field dependence is consistent with diffusive ion motions that modulate two spatial coordinates that characterize the relaxation couplings in the vicinity of the polyion. Motions around the rod and fluctuations in the ion distance from the rod are consistent with these constraints for lithium. The magnetic field dependence of the tetramethylammonium ion proton relaxation rate constant is weak, but also approximately a linear function of the logarithm of the Larmor frequency, which implies that the field dependence is caused in part by local order in the DNA solution.

Mapping Oxygen Accessibility to Ribonuclease A Using High-Resolution NMR Relaxation Spectroscopy

Paramagnetic contributions to nuclear magnetic spin-lattice relaxation rate constant induced by freely diffusing molecular oxygen measured at hundreds of different protein proton sites provide a direct means for characterizing the exploration of the protein by oxygen. This report focuses on regions of ribonuclease A where the rate constant enhancements are either quite large or quite small. We find that there are several regions of enhanced oxygen affinity for the protein both on the surface and in interior pockets where sufficient free volume permits. Oxygen has weak associative interactions with a number of surface crevices that are generally between secondary structural elements of the protein fold. Several regions near the surface have higher than expected accessibility to oxygen indicating that structural fluctuations in the protein provide intermolecular access. Oxygen penetrates part of the hydrophobic interior, but affinity does not correlate simply with hydrophobicity indices. Oxygen is excluded from regions of high interior packing density and a few surface sites where x-ray diffraction data have indicated the presence of specific hydration with high occupancy.

End-to-end correlation for a C-12 hydrocarbon chain

The 19F nuclear spin-lattice relaxation rate constants were measured as a function of magnetic field strength for 1,12-diaminododecane labeled at one end with a nitroxide radical and at the other with a trifluoromethyl group. The magnetic relaxation dispersion profile (MRD) reports the spectral density function appropriate to the end-to-end correlation function for the doubly labeled molecule. After extrapolation to zero concentration to eliminate the intermolecular relaxation contribution to relaxation, the resulting intramolecular MRD profile was compared with several model approaches. The rotational model for the spectral density functions as included in the Solomon–Bloembergen–Morgan equations does not describe the data well. The earlier model of Freed for nuclear spin relaxation induced by a freely diffusing paramagnetic co-solute is not rigorous for this case because the paramagnet is tethered to the observed nuclear spin and only a restricted space in the immediate vicinity of the nuclear spin is accessible for pseudo-translational diffusion of one end of the molecule with respect to the other. A generalization of the Torrey model for magnetic relaxation by translational diffusion developed by Nevzorov and Freed, which includes the effect of restrictions imposed by the finite length of the chain, describes the experiment within experimental errors. A simple modification of the Hwang–Freed model that does not specifically include the dynamical effects of the finite tether also provides a good approximation to the data when the tether chain is sufficiently long.

Protein Reorientation and Bound Water Molecules Measured by 1H Magnetic Spin-Lattice Relaxation

The water-proton spin-lattice relaxation rate constant, 1 /T 1, was measured as a function of magnetic field strength for several dilute protein solutions. By separating the intermolecular contributions from the intramolecular contributions to the water-proton spin-lattice relaxation, the number of water molecules that bind to the protein for a time long compared with the rotational correlation time may be measured. We find a good correlation between the number of long-lived water molecules and the predictions based on available free volume in the proteins studied. The rotational correlation times of these proteins are larger than predicted by the Stokes-Einstein-Debye (SED) model for a sphere reorienting in a viscous liquid. The discrepancy between experiment and theory is usually attributed to hydration effects increasing the effective radius of the particle. However, the average lifetime of water molecules at the protein interface is far too short to justify such a picture. We suggest that surface roughness may be responsible for the retardation of rotational mobility and find that the SED model provides a reasonable representation of experiment if the radius assumed for the reorienting particle is the arithmetic mean of the crystallographic packing radius and the radius deduced from the effective surface area of the protein.

Spin−Lattice Relaxation of the Tryptophan Triplet State Varies with Its Protein Environment

Spin−lattice relaxation (SLR) has been studied at 1.2 K in the photoexcited triplet state of tryptophan (Trp) in a number of protein sites in zero applied magnetic field. We find that there is a distribution of SLR rate constants in every case that indicates the partitioning into two populations, ns0 and nf0, with differing behavior. ns0 undergoes slow SLR with rate constants in the range found in crystalline matrixes, while the SLR of nf0 is at least 1−2 orders of magnitude faster. The former population has considerable spin alignment during optical pumping, decays nonexponentially, and gives rise to optically detected magnetic resonance (ODMR) responses at 1.2 K. The latter has negligible spin alignment, decays largely as a single exponential, and is ODMR silent. The rapid SLR of nf0 is attributed to coupling with disorder (tunneling) modes that modulate the electron−electron dipolar coupling, and whose efficiency varies with protein site. The less efficient SLR of ns0 is the result of direct interactio...

Paramagnetic Effects on Solid State Carbon‐13 Nuclear Magnetic Resonance Spectra of Soil Organic Matter

The effects of paramagnetic species on solid state 13C nuclear magnetic resonance (NMR) spectra were quantified in a series of doping experiments. The degree of signal loss caused by paramagnetic metals was shown to depend not only on the quantity, but also on the nature of the paramagnetic species, as well as the intimacy of contact with the organic substrate and the type of NMR experiment. Two mechanisms of signal loss were distinguished--signal loss via loss of magnetic field homogeneity, which affects all 13C nuclei in a sample, and signal loss via interaction between electronic and nuclear spins, the effects of which were localized to the close environment of the paramagnetic species. Loss of field homogeneity is important for manganese species, but not for copper species, and is equally important for both cross polarization and Bloch decay experiments. The interaction between electronic and nuclear spins is highly dependent on the spin-lattice relaxation rate constant of the free electron (T1e), as cations with very short T1e values (e.g., Pr3+) cause less signal loss than cations with longer T1e values (e.g., Cu2+, Mn2+). Cross polarization spectra are shown to be more susceptible than Bloch decay spectra to this mechanism of signal loss. Signal loss and increased relaxation rates brought about by paramagnetic species can be used to provide information on soil organic matter (SOM) heterogeneity in the submicron range. This is demonstrated for SOM doped with paramagnetic cations where selective signal loss and increased relaxation rates are used to determine the nature of cation exchange sites.