Cross-relaxation pathways

A single-quantum transition involves one spin only, whereas the zero- and doublequantum transitions involve two spins at the same time. The zero- and double-quantum transitions give rise to cross-relaxation pathways, which provide an efficient mechanism for dipole-dipole relaxation. 

The positive nOe observed in small molecules in nonviscous solution is mainly due to double-quantum relaxation, whereas the negative nOe observed for macromolecules in viscous solution is due to the predominance of the zero-quantum 1% cross-relaxation pathway. 

The overall equation is a simple first-order decay with rate constant 2W. This corresponds to the longitudinal relaxation rate for Ha in the absence of cross-relaxation R = /T. Looking at the other Ha transition, aa state to f3a state, gives the same result, and the Hb transitions yield the analogous result R = 1 / T = 2 W. These self-relaxation times, T and 7j will decrease when we introduce the cross-relaxation pathways (DQ and ZQ relaxation). 

Now let s look at the more interesting situation where the cross-relaxation pathways (single quantum and double quantum) are available. Spins in the pfi state can relax by any of three pathways they can drop down to the aft state (rate Wf), drop down to the Pa state (rate W ), or follow the double-quantum pathway down to the aa state (rate Wi)- All of these pathways will contribute to the change in population of the pp state as a function of time (Fig. 10.3). Considering all three pathways leading away from the pp state, we can... 

The nOe data may be obtained by either one- or two-dimensional methods. These through-space effects may be used to estimate intemuclear distances. However, nOe cross-peak volumes are inversely proportional to the sixth power of the distance between the correlated protons only in the case of rigid spherical molecules whose tumbling is isotropic. The simplest method that has been proposed for the interpretation of nOe-derived distance data is the isolated spin pair approximation. The matrix treatment is more rigorous, although rel5dng also on several approximations. A set of equations describing the cross-relaxation pathways of all the protons in the molecule is cast into a matrix form and solved. 

Overlap of peaks along the diagonal, as in the spectra of large biomolecules, prevents the use of such an equation, as does the presence of several mechanisms of exchange or cross-relaxation pathways. Alternatively, analysis of the t dependence of the... 

While the final magnitude of nOe depends, as indicated earlier, on the relaxation pathways Wi, W, and W), the initial rate of buildup of nOe (transient nOe) depends only on the rate of cross-relaxation between the nuclei, and this can provide valuable information about the distance between the nuclei (r). This rate of buildup can be proportional to r" , where r is the distance between the nuclei. Thus, if the proportionality constant is determined, we can calculate an approximate distance between the two nuclei. The best results are obtained in rigid molecules when the nuclei are less than 3 A apart. If only direct nOe s are involved in a two-spin... 

Transient nOe represents the rate of nOe buildup. The nOe effect (so-called equilibrium value) itself depends only on the competing balance between various complex relaxation pathways. But the initial rate at which the nOe grows (so-called transient nOe) depends only on the rate of cross-relaxation t, between the relevant dipolarly coupled nuclei, which in turn depends on their internuclear distance (r). 

If the intersystem crossing rate with diamagnetic iron porphyrins is slow then the observed correspondence in relaxation times between S=0 and S=2 iron(II) porphyrins may not necessarily indicate that the relaxation pathways are the same. 

Sildenafil is a selective inhibitor of cGMP-specific PD-5 and therefore inhibits the degradation of cGMP PD-5, the predominant type in the corpus cavernosum, also is present in other tissues (e.g., lungs, platelets, and eye). TTie selective inhibition of this enzyme facilitates the release of nitric oxide and smooth muscle relaxation of the corpus cavernosa. Sildenafil enhances erection by augmenting nitric oxide-mediated relaxation pathways. It has been suggested that sildenafil s mechanism of action is due to cross-talk between cGMP- and cAMP-dependent transduction pathways within the cavernous muscles. 

When the primary electron donation pathway in photosystem II is inhibited, chlorophyll and p-carotene are alternate electron donors and EPR signals for Chl+ and Car+ radicals are observed.102 At 130 GHz the signals from the two species are sufficiently resolved to permit relaxation time measurements to be performed individually. Samples were Mn-depleted to remove the relaxation effects of the Mn cluster. Echo-detected saturation-recovery experiments were performed with pump pulses up to 10 ms long to suppress contributions from cross relaxation and spin or spectral diffusion. The difference between relaxation curves in the absence of cyanide, where the Fe(II) is S = 0, and in the presence of cyanide, where the Fe(II) is S = 2, demonstrated that the relaxation enhancement is due to the Fe(II). The known distance of 37 A between Fe(ll) and Tyrz and the decrease of the relaxation enhancement in the order Tyrz > Car+ > Chl+ led to the proposal of 38 A and > 40A for the Fe(II)-Car+ and Fe(II)-Chl+ distances, respectively. Based on these distances, locations of the Car+ and Chl+ were proposed. 

In summary, our photophysical studies indicate that the thermally activated relaxation pathways of (2E)Cr(III) very likely involve 2E-to- (intermediate) surface crossing. These (intermediates) can be associated with some, not necessarily the lowest energy, transition state (or transition states) for ground state substitution. The Arrhenius activation barriers for thermally activated relaxation are remarkably similar from complex to complex, but they can be altered in systems with highly strained ligands. Some of this work indicates that the steric and electronic perturbations of the ligands dictate the choice among possible relaxation channels. 

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