Transverse relaxation rate constants

From the simpler resonance line-shape and H/D-exchange analysis to the more complex studies of inherent dynamics, occurring on various time scale of motion, NMR remains a good choice to investigate protein flexibility and plasticity. If linebroadening due to exchange and inhomogeneity is minimized (or completely eliminated), then half-width, Aom, of a line becomes proportional to R, the transverse relaxation rate constant. 

The mandibular salivary glands (ca. 0.25 g) were isolated and perfused arterially with a modified Krebs solution. Na NMR spectra were collected at 8.4, 4.7 and 2.34 T by using MSL-100, AM-200wb and AMX-360wb, respectively. The T2 double-quantum filter and Tj double-quantum filter were used. Results are summarized in brief 1) The transverse relaxation rate constants showed a slight Bq dependency, which promises a poor fitting by the single population model. 2) When temperature was decreased (37 - 5°C), the ratio of the relaxation... 

Where, 1/T2i and D are the observed values of 1/T2f0r IT2s 2nd diffusion coefficient, respectively, sj and Db are the transverse relaxation rate constants (S or S2) and the diffusion coefficient of Na ion under the slow-motion condition, respectively. S2 and Sj correspond to the I1/2X-1/2I coherence and the l-l/2x-3/2l, 13/2x1/21 coherences, respectively. Pb is the fraction of the Na ion under the slow-motion condition (1> Pb ), which is proportional to the fraction of agar. Sj g and 2re the relaxation rate constant and the diffusion coefficient of Na+ under the extreme narrowing condition, respectively. 

The observed relaxation time is time-averaged value of s e and Sj. The fraction of Na ion under the slow-motion condition is expected small, but the transverse relaxation rate constants (s ) are expected larger than Sfr j by 10 to 100 times. Therefore, we applied this equation to the observed relaxation rate constants to estimate the 2 compartments. One problem is accurate knowledge of the value of s for 23Na+ in the agar gel. 

Since the relaxation rate constant of 23Na+ depends strongly on the viscosity of the solution, we measured the self-diffusion coefficient of 23Na+ in glycerol/water solution, and found a relationship between the self-diffusion coefficient and the transverse relaxation rate constant on viscosity [Fig. 2-a]. Then, we have estimated the Sf g value of Na ion in the agar gel from the self-diffusion coefficient of Na ion in the agar gel using the observed relationship [Fig. 2-b]. 

Figure 2. Relationships of transverse relaxation rate constants (I/T2) and diffusion coefficient of 23Na ion in glycerol/water solution (a), and estimated I/T2 value for 23Na ion in the agar gel from the diffusion coefficient of Na ion (b).

Figure 3. The transverse relaxation rate constants of 33Na ion in agar gel at 2.34 T (x) and at 8.45 T (o) as a function of the fraction of Na ion. Solid lines are results of fitting data to the discrete- exchange model.

The plot below compares the behaviour of the longitudinal and transverse relaxation rate constants. As the correlation time increases the longitudinal rate constant goes through a maximum. However, the transverse rate constant carries on increasing and shows no such maximum. We can attribute this to the secular part of transverse relaxation which depends on 7(0) and which simply goes on increasing as the correlation time increases. Detailed calculations show that in the fast motion limit the two relaxation rate constants are equal. 

Comparison of the longitudinal and transverse relaxation rate constants as a function of the correlation time for the fixed Larmor frequency. The longitudinal rate constant shows a maximum, but the transverse rate constant simply goes on increasing. 

The n-site Bloch-McConnell equations describe the evolution of nuclear spin magnetization in the laboratory or rotating frames of reference for molecules subject to chemical or conformational interconversions between n species with distinct NMR chemical shifts. Trott and Palmer used perturbation theory to approximate the largest eigenvalue of the Bloch-McConnell equations and obtain analytical expressions for the rotating-frame relaxation rate constant and for the laboratory frame resonance frequency and transverse relaxation rate constant. The perturbation treatment is valid whenever the population of one site is dominant. The new results are generally applicable to investigations of kinetic processes by NMR spectroscopy. 

Here keg- describes the dynamic process (e.g. the transverse relaxation rate R2, or the diffusion coefficient D) and r describes a time constant typical for the experimental setup. By use of Eq.(l) the kegf can be written as follows ... 

The smaller contribution to solvent proton relaxation due to the slow exchanging regime also allows detection of second and outer sphere contributions (62). In fact outer-sphere and/or second sphere protons contribute less than 5% of proton relaxivity for the highest temperature profile, and to about 30% for the lowest temperature profile. The fact that they affect differently the profiles acquired at different temperature influences the best-fit values of all parameters with respect to the values obtained without including outer and second sphere contributions, and not only the value of the first sphere proton-metal ion distance (as it usually happens for the other metal aqua ions). A simultaneous fit of longitudinal and transverse relaxation rates provides the values of the distance of the 12 water protons from the metal ion (2.71 A), of the transient ZFS (0.11 cm ), of the correlation time for electron relaxation (about 2 x 10 s at room temperature), of the reorienta-tional time (about 70 x 10 s at room temperature), of the lifetime (about 7 x 10 s at room temperature), of the constant of contact interaction (2.1 MHz). A second coordination sphere was considered with 26 fast exchanging water protons at 4.5 A from the metal ion (99), and the distance of closest approach was fixed in the range between 5.5 and 6.5 A. 

To a good approximation, p is the transverse relaxation rate of spin 7 and p is the transverse relaxation rate of spin J. The two cross peaks are distinguished according to which of the two T [ or constants appears in each dimension. From Eq. (8.3), it appears that the maximum information is not contained in the first data points. In fact, considering that Eq. (8.3) represents the evolution of the signal, the derivative of 7 (t) with respect to t (or t2) provides the value of t (or t2) with maximum intensity of the signal ... 

It turns out that the secular part depends on the spectral density at zero frequency, 7(0). We can see that this makes sense as this part of transverse relaxation requires no transitions, just a field to cause a local variation in the magnetic field. Looking at the result from section 8.5.2 we see that 7(0) = 2tc, and so as the correlation time gets longer and longer, so too does the relaxation rate constant. Thus large molecules in the slow motion limit are characterised by very rapid transverse relaxation this is in contrast to longitudinal relaxation is most rapid for a particular value of the correlation time. 

MTip and 1/T2 are the paramagnetic contribution to longitudinal and transverse relaxation rates of F (1/Ti and I/T2), Tjm is the longitudinal relaxation time of F in the first coordination shell of the paramagnetic center, copper(II), Tm the residence time that is the time a F ion is bound to copper(II) before it exchanges and (M ) is the stability constant of the superoxide dismutase-F complex. 

In NMR experiments, n is typically a backbone N-H bond vector, and dioc(n,2) is computed as a function of R2(n)/Ri(n) (or related quantities, such as (2R2 — Ri)/Ri)/ where Ri and R2 are longitudinal and transverse relaxation rates [48,47]. In this way, the local diffusion constants become a key intermediate quantity that can be estimated from both NMR experiments and from simulations in this respect, they play much the same role here as the model-free parameters and Tg play in the analysis of internal motions by MD. 

Here, is an Al-dimensional vector containing the transverse relaxation rates along all indirect dimensions, with R 2 = 0 for constant-time evolution elements in the dimension i. Since the standard GAPRO analysis attaches equal weight to each projection spectrum, it is desirable to have similar sensitivities for all individual projection experiments. If the projection angle-dependence of t) is known, (7) provides a basis for producing similar sensitivities for all the projections used in a given APSY experiment, since the user-defined parameters n (p), M (p), hm (p, t), and fmax(0) can be individually adjusted for each projection experiment [5, 42]. 

Nuclear magnetic relaxation rates have been used to investigate the coordination number. In an investigation of the line-width broadening of La in various perchlorate solutions, Nakamura and Kawamura (1971) attributed the decreases in the values of (Av is the relaxation rate and is the relative viscosity) to a possible equilibrium between the nonahydrates and octahydrates for lanthanum ion. This conclusion was disputed by Reuben (1975) who proposed that this apparent anomaly reflected an erroneous estimate of the corrections of the linewidths for peaks due to the effect of the finite modulation amplitude and/or of partial saturation. Measurement of the transverse relaxation rates by the pulse method gave results consistent with a constant hydration number for lanthanum ion (Reuben 1975). 

Fig. 8.4 (A-N). The excess transverse relaxation rate, A(l/T2), of a halide nucleus in a hypothetical two-site system as a function of the total halide concentration [X ]. Site A represents "free halide ion in solution and site B represents a macromolecule binding site, [m] denotes the concentration of the macromolecule, Vq is the quadrupole coupling constant in the B-site, is the rotational correlation time characterizing the halide in the macromolecular binding site and Kb denotes the binding constant for halide ion to the B-site. The curves have been calculated using Eqs. (8.25) to (8.28) and Eq. (8.40). The results are shown for two different halide exchange mechanisms. Case I represents the "first order" mechanism of Eq. (8.31)...

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