Transverse Magnetization Decay Research Articles

23Na +-NMR studies of cation binding to multi-chain and single-chain glycosaminoglycan peptides

1. 1. 23Na + nuclear magnetic relaxation studies of cation binding to single-chain chondroitin 4-sulphate and dermatan sulphate and a multi-chain chondroitin 4-sulphate-polypeptide complex have been performed. Excess relaxation rates (longitudinal and transverse) for the bound sodium have been measured during titration experiments. The data were used to calculate the correlation time and the fraction of bound ions. This approach was also used to analyze the relative affinities of Na +, K + and Ca 2+. 2. 2. The excess transverse relaxation rates for 23Na + (obtained from line-width measurements or the decay of transverse magnetization) in solutions of single-chain and multi-chain chondroitin sulphate were recorded as a function of the degree of neutralization. There was a steep increase in transverse relaxation rate for the multi-chain preparation around pH 7 which was not seen with single chains. This could be ascribed to an increase in the correlation time for bound sodium. The alteration in binding properties observed with multi-chained material around pH 7 suggested a change in the quadropolar coupling constant for 23Na in this range. The behaviour of a multi-chained specimen (as expressed in excess line-width) during titration gradually changed to that of single chains upon prolonged exposure to alkali. 3. 3. Competition experiments using KCl additions to multi-chained sodium chondroitin sulphate at pH 12.3 and 3.3 indicated that Na + and K + have very similar affinities at high pH. However, at low pH there was an increased affinity for K + (expressed as a faster decrease in excess relaxation rate when KCl was added). 4. 4. Competition experiments using multi-chain chondroitin sulphate and Ca 2+ at pH 11.4 showed increasing excess relaxation rates during the initial phase. Above 4 mM Ca 2+ simple exchange of bound Na + with Ca 2+ was observed. The former behaviour was not seen at pH 3.3 nor with single-chain chondroitin sul[hate at pH 11.4. It is suggested that endogeneous Ca 2+ present in the multi-chain preparation is responsible for the pH dependence. The increased excess transverse relaxation rate seen with the multi-chained specimen upon Ca 2+ additions was referred to an increase in the correlation time for bound Na +. 5. 5. The most likely explanation for the abrupt increase in correlation time for Na + bound to multi-chain chondroitin sulphate around pH 7 is an aggregation between the side-chains. In the presence of Ca 2+, cross-linking of chains (clustered together on the protein core) was promoted and the local mobility of the Na + ions was further reduced. In addition to the formation of Ca 2+ bridges between chains, the results also imply increased binding of counter ions owing to a higher local charge density.

Zur Theorie der Kernspinrelaxation bei einem Austausch zwischen zwei Bereichen

AbstractUsing REDFIELD'S theory of relaxation and SILLESCU'S master equation treatment of molecular reorientation, the longitudinal and transverse nuclear spin relaxation functions have been calculated in a two phase system with different magnetic interaction energies. The interaction HAMILTONian represents the dipolar coupling amongst the nuclei in region (a, 1) and between a nucleus and a paramagnetic ion in region (b, 2). Assuming a strong electron spin relaxation which is statistically independent from the nuclear relaxation, a situation realized in paramagnetic solutions and adsorbate systems, the problem simplifies considerably.If some correlation, expressed by a correlation coefficient c, is lost in each transfer between the regions, a longitudinal relaxation time T(c)1m can be defined, as long as the life time Tb in the region with the lower mobility is not comparable with the correlation time T1 in the other phase. Without any restriction, however, one time constant T(c)2m should characterize the decay of transverse magnetization as a good approximation. The apparent correlation times, determined from experimental data without any knowledge of the coefficient c, differ only slightly from the effective correlation times (in general less than 10%), in contrast to the case of equal interaction energies in both regions. If the interaction HAMILTONian does not vary under the exchange (e. g. dipolar interaction between the nuclei in both regions) the results of the wellknown statistical treatment of BECKERT and PFEIFER are obtained.Neglecting any correlation at each transfer (i.e. c = 0) the relaxation rates are weighted averages, which correspond to the fast exchange case in the theory of ZIMMERMAN and BRITTIN with the effective correlation times magnified image.

Zur Theorie der Kernspinrelaxation bei einem Austausch zwischen zwei Bereichen

Using REDFIELD'S theory of relaxation and SILLESCU'S master equation treatment of molecular reorientation, the longitudinal and transverse nuclear spin relaxation functions have been calculated in a two phase system with different magnetic interaction energies. The interaction HAMILTONian represents the dipolar coupling amongst the nuclei in region (a, 1) and between a nucleus and a paramagnetic ion in region (b, 2). Assuming a strong electron spin relaxation which is statistically independent from the nuclear relaxation, a situation realized in paramagnetic solutions and adsorbate systems, the problem simplifies considerably. If some correlation, expressed by a correlation coefficient c, is lost in each transfer between the regions, a longitudinal relaxation time T(c)1m can be defined, as long as the life time Tb in the region with the lower mobility is not comparable with the correlation time T1 in the other phase. Without any restriction, however, one time constant T(c)2m should characterize the decay of transverse magnetization as a good approximation. The apparent correlation times, determined from experimental data without any knowledge of the coefficient c, differ only slightly from the effective correlation times (in general less than 10%), in contrast to the case of equal interaction energies in both regions. If the interaction HAMILTONian does not vary under the exchange (e. g. dipolar interaction between the nuclei in both regions) the results of the wellknown statistical treatment of BECKERT and PFEIFER are obtained. Neglecting any correlation at each transfer (i.e. c = 0) the relaxation rates are weighted averages, which correspond to the fast exchange case in the theory of ZIMMERMAN and BRITTIN with the effective correlation times .

Coherent Averaging Effects in Magnetic Resonance

A theory is developed to describe the slow component of the transient decay of transverse spin magnetization, and the central component of the slow-passage absorption spectrum, of a system of spins which is subjected to a periodic and cyclic perturbation. The theory is used to analyze and compare various schemes for high-resolution NMR of solids, including the spinning of the sample about an axis oriented at the "magic angle," the rotating-frame magic-angle experiment of Lee and Goldburg, pulsed versions of the latter, and a number of new pulsed-NMR experiments recently developed in this laboratory. Attention is focused on the factors, both theoretical and practical, which are important in obtaining optimal suppression of static dipole-dipole interactions and quadrupole splittings, and retention of chemical and Knight shifts and scalar spin-spin interactions. Several new experiments are proposed.

A time-dependent Dyson expansion - the nuclear resonance signal in a rotating single crystal

We generalize the usual Dyson expansion to incorporate a time-dependent unperturbed Hamiltonian. The formalism is then used to perform a non-stochastic calculation of the free induction nuclear magnetic resonance decay of transverse magnetization (i.e. the Bloch decay) in a rotating single-crystal sample. We assume the magnetic nuclei to have spin one-half, to be located on a simple cubic lattice and to interact with each other by the direct dipolar interaction only. We have computed our analytic expression for a case of possible experimental interest namely a single-crystal sample of CaF2 rotating about the [1, 1, 1] axis with the main field initially along the [1, 0, 0] axis of the crystal.

Multiple Spin Echoes in Dipolar Solids

The decay of transverse nuclear spin magnetization in a homogeneously broadened solid can be prolonged for a time ${{T}_{2}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\gg}{T}_{2}$ by applying a train of 90\ifmmode^\circ\else\textdegree\fi{} pulses in a modified Carr-Purcell sequence with pulse spacing $\ensuremath{\tau}<{T}_{2}$. A time-expansion theory which treats the problem from the viewpoint of spin echoes is used to explain an observed proportionality between ${{T}_{2}}^{\ifmmode\dagger\else\textdagger\fi{}}$ and ${\ensuremath{\tau}}^{\ensuremath{-}5}$, and predicts that ${{T}_{2}}^{\ifmmode\dagger\else\textdagger\fi{}}$ depends upon a modified sixth moment of the resonance. An alternative viewpoint, in which one considers the long-time development of the spin system in a periodically modulated rf field ${H}_{1}(t)$, shows that the experiment is closely related to spin locking and explains the fact that ${{T}_{2}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\rightarrow}{T}_{1\ensuremath{\rho}}({\overline{H}}_{1})$, the relaxation time parallel to the average rf field, as $\ensuremath{\tau}\ensuremath{\rightarrow}0$. The experiment offers some possibilities for the study of spin-lattice relaxation in weak fields and for double resonance in the rotating frame.