Longitudinal nuclear relaxation rate

Figure 1. Distances in established enzyme-metal-substrate bridge complexes from longitudinal nuclear relaxation rates...

Longitudinal and transverse nuclear relaxation profiles differ in the high field part. In fact, the equation for the transverse nuclear relaxation rates contains a non-dispersive term, depending only on Xd. Therefore the transverse relaxation does not go to zero at high fields, as longitudinal relaxation does, but increases because Tie increases (until it increases to the point where it becomes longer than x or Xm)-... 

Fig. 3.16. (A) Plot of the nuclear longitudinal dipolar relaxation rate in the presence of a field dependent electron relaxation time (5 = sh) for rl0 = 10-9 s and r = 1,5, 10,50 x 10 12 s. The amplitude of the peak that appears in the high field part of the profile increases with increasing r . (B) Plot of the longitudinal dipolar relaxation rate in the presence of a field dependent electron relaxation time (S = V2) for A, = 0.047 cm-1 and r = 2,5, 10, 20 x 10-12 s. (C) Plot of the longitudinal relaxation rate in the presence of a field dependent electron relaxation time with A/h = 0 and 1 MHz (dotted lines) and of the transverse relaxation rate with A/h = 0 (dashed line) and 1 MHz (solid line). Conditions 5 = %, A, = 0.047 cm-1, r = 2 x 10-12 s (r,o = 10-9 s) and tr = 10-9 s.

For any nucleus i of a paramagnetic lanthanide complex in the absence of significant chemical exchange, the experimental longitudinal (l/7 p) and transversal (1 /7 xp) nuclear relaxation rates are given by eqs. (4), (5) in which 7]dia corresponds to the characteristic relaxation times of the same nucleus i in the analogous diamagnetic complex (R = La, Y, Lu) and 7)para are... 

The binding of Gd3+ to Ca2+-ATPase was also examined using water proton nuclear relaxation rates. Figure 11 shows the behavior of the observed enhancement of the longitudinal water proton relaxation rate when Gd3+ is used to titrate a solution of the Ca2" "-ATPase. At the lower concentrations of Gd3" " the large observed enhancement of the water proton relaxation rate suggests the formation of a tight binary Gd3+-ATPase complex. 

Here 7 is the nuclear spin, is the quadrupolar coupling constant, tj is an asymmetry parameter, is the Gd- O distance, and r j is defined by Eq. 12. The difficulty of this technique is that both the quadrupolar coupling constant and the Gd - O distance can only be estimated. However, rotational correlation times obtained from longitudinal 2Q relaxation rates can provide a good comparison for similar Gd(III) complexes. One advantage is that the rotational correlation time is measured directly on the Gd(III) complex. Furthermore, the determined in this way corresponds to the rotation of the Gd(III) - coordinated water oxygen vector which is probably analogous to the rotation of the Gd(III) - coordinated water proton, which, itself determines proton relaxivity. 

Eqs. 3 and 4 show the electron-nuclear relaxation-rates for the spin-lattice (longitudinal) and spin-spin (transverse) relaxation-rates. In both of these equations, the first terms reflect the dipolar term, and the second part reflects the scalar interaction. The dipolar term contains a distinct r distance term between the electron of the metal atom and the respective carbon atom in contrast, the scalar term has none. 

Nuclear relaxation rates have been used in studies of CyD complexes for the determination of correlation times, thus giving insight into the dynamics of the host and/or guest in the complex. H selective and nonselective longitudinal relaxation rates enable us to characterize the dynamics of the acridine-yS-CyD complex [9]. Proton longitudinal, Ri( H), and transverse, R2( H), relaxation rates were used to determine the motion of (+)camphor guest molecules in both diastereomeric complexes with a-CyD [10]. The Ri( C) rates were used as early as 1976 to obtain correlation times for guest and host molecules in complexes formed by a-CyD with three aromatic compounds [llj. The Ri( C) rates were also used for the determination of correlation times of constituents and complexes of several CyDs with azo dyes [12]. 

As we shall see, all relaxation rates are expressed as linear combinations of spectral densities. We shall retain the two relaxation mechanisms which are involved in the present study the dipolar interaction and the so-called chemical shift anisotropy (csa) which can be important for carbon-13 relaxation. We shall disregard all other mechanisms because it is very likely that they will not affect carbon-13 relaxation. Let us denote by 1 the inverse of Tt. Rt governs the recovery of the longitudinal component of polarization, Iz, and, of course, the usual nuclear magnetization which is simply the nuclear polarization times the gyromagnetic constant A. The relevant evolution equation is one of the famous Bloch equations,1 valid, in principle, for a single spin but which, in many cases, can be used as a first approximation. 

Outer sphere relaxation arises from the dipolar intermolecular interaction between the water proton nuclear spins and the gadolinium electron spin whose fluctuations are governed by random translational motion of the molecules (106). The outer sphere relaxation rate depends on several parameters, such as the closest approach of the solvent water protons and the Gdm complex, their relative diffusion coefficient, and the electron spin relaxation rate (107-109). Freed and others (110-112) developed an analytical expression for the outer sphere longitudinal relaxation rate, (l/Ti)os, for the simplest case of a force-free model. The force-free model is only a rough approximation for the interaction of outer sphere water molecules with Gdm complexes. 

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