Cross-relaxation steady state

We have implemented the principle of multiple selective excitation (pulse sequence II in fig. 1) thereby replacing the low-power CW irradiation in the preparation period of the basic ID experiment by a series of selective 180° pulses. The whole series of selective pulses at frequencies /i, /2, , / is applied for several times in the NOE build-up period to achieve sequential saturation of the selected protons. Compared with the basic heteronuclear ID experiment, in this new variant the sensitivity is improved by the combined application of sequential, selective pulses and the more efficient data accumulation scheme. Quantitation of NOEs is no longer straightforward since neither pure steady-state nor pure transient effects are measured and since cross-relaxation in a multi-spin system after perturbation of a single proton (as in the basic experiment) or of several protons (as in the proposed variant) differs. These attributes make this modified experiment most suitable for the qualitative recognition of heteronuclear dipole-dipole interactions rather than for a quantitative evaluation of the corresponding effects. 

The terms pc and py correspond to 1/Tic and 1/Tih, respectively, and CTCH is the cross-relaxation rate. It should be stressed that the simplicity of the above equation is a consequence of the rareness of the I spins and of the dominant strength of the dipolar interaction between directly bonded nuclei. The situation for homonuclear proton spin systems is often more complicated, since the protons usually constitute a much larger spin system, and a separation into distinct two-spin systems may be not valid in this case. The broadband irradiation of the protons yields, in a steady state, Mhz = 0 and M z = Mj (1 rj). The factor 1 + 77 is called, as introduced above, the nuclear Overhauser enhancement factor. The NOE factor is related in a simple way to the equilibrium magnetizations of the I- and S-spins (which are proportional to the magnetogyric ratios 71 and 7s), the cross-relaxation rate and the relaxation rate of the I-spin ... 

Up to now steady state NOEs have been considered, i.e. when one signal is saturated for a long time with respect to T of the nucleus on which NOE is going to be measured. Let s consider here what happens when the saturation time is short and variable. The resulting NOE is called truncated NOE [17] because not enough time is left for full polarization transfer. These experiments are of fundamental importance for the measurement of pi, for evaluating cross relaxation, and to avoid or to measure spin diffusion. 

In this type of experiment the NOE buildup tends to disappear with p/. In the steady state case, the saturation time is always long enough to allow spin / to cross-relax with other spins, even if pr is large. In transient experiments, the cross relaxation with spin / is by itself limited in time and, pj being the same, cross relaxation with other spins is drastically limited. In any case, spin diffusion is limited in that region of time in which NOE is growing (Fig. 7.6). Truncated and transient NOEs performed with short NOE buildup times are efficient in quenching spin diffusion. 

After extraction, the fluorescent indicator was in the unbound state and gave input to the radiative relaxation. Therefore, the fluorescence lifetime increased and, consequently, the intensity as well. After MIP contacting with the analyte, the non-radiative processes were again efficient compared to the radiative processes and, subsequently, fluorescence was quenched. With steady-state fluorescence spectroscopy the cross-reactivity test towards structurally similar biomolecules was performed that yielded selectivity factors for guanosine, cAMP and cCMP of 1.5, 2.5 and 5.1, respectively. 

The qualitative basis of the NOE can be readily appreciated from Fig. 8.3. If rf energy is applied at frequency cos, the S transitions thus induced alter the populations of the energy levels, and because of cross relaxation (i.e., transitions W0 and W2, which affect both I and S simultaneously), that change affects the intensities of the I transitions. Quantitatively, Eq. 8.4 shows what happens when the two S transitions are subjected to a continuous wave rf that is intense enough to cause saturation. At the steady state both dlz/dt and Sz are zero, so that Eq. 8.4 (after some rearrangement) gives... 

Under continuous uv irradiation, the observed steady-state polarization (whether by cw or by FT spectrometers) may be substantially modified by various nuclear relaxation processes. For example, Closs and Czeropski (35,36) have demonstrated that CIDNP can be transferred from a group of polarized nuclei to another group not originally polarized. Both the dipolar and the scalar relaxation mechanisms (of the nuclear Overhauser effects) can be operative. The extremely interesting case of intramolecular dipolar nuclear cross relaxation reported by Closs and Czeropski (35) involves the thermal reaction of... 

As free energy stress is unstable in the presence of cross-system coupling, some (generally complex) relaxation process must become the short-term steady state. The principle that stabilized relaxation processes arise where they can reduce the impact of a free energy bottleneck has been likened by Eschenmoser to a dynamic Le Chatelier principle [46]. 

Figure 8.10. Schematic illustration of the maximum homonuclear steady-state NOE in the presence (solid line) and absence (dotted line) of external relaxation sourees that compete with cross-relaxation.

It is important to realise that the value of the steady-state NOE enhancement depends on the ratio of cross-relaxation rate constant to the self relaxation rate constant for the spin which is receiving the enhancement. If this spin is relaxing quickly, for example as a result of interaction with many other spins, the size of the NOE enhancement will be reduced. So, although the size of the enhancement does depend on the cross-relaxation rate constant the size of the enhancement cannot be interpreted in terms of this rate constant alone. This point is illustrated by the example in the margin. 

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