NOE kinetics

Following the (assumed) instantaneous inversion of the S-spin resonance, the initial growth rate of the NOE at I depends linearly on the cross-relaxation rate between these two spins even in multispin systems, such that  

on the other hand, the goal is to qualitatively identify through-space correlations, as is more often the case in routine work, mixing periods comparable to T, provide maximum enhancements. Since transient NOEs develop in the absence of an external rf field they tend to be weaker than steady-state 

Assuming the initial rate approximation to be valid (the NOE growth linear), the magnitude of an enhancement between two spins, A and B, after a period t will be proportional to the cross-relaxation rate, which in turn depends on r  

The constants of proportionality here contain the molecular correlation time, Tc, in addition to a number of known physical constants, and B is now taken to signify inversion rather than saturation of B. In principle, if tc were known, this would directly provide a measure of rAB- Whilst it is possible to determine this (such as from relaxation time measurements) this is rarely done in practice, and it is more common to use a known internal distance as a reference and avoid the need for such laborious measurements. If the NOE between reference nuclei X and Y of internuclear separation rxy is also measured then  

A direct comparison of the two NOE intensities thus provides the unknown internuclear distance. This simple relationship has been extensively used to provide measurements of internuclear separations, particularly in biological macromolecules. From a single experiment, distances can be estimated assuming the initial rate approximation is valid for all interactions. This relies on all internuclear vectors in question possessing the same correlation time, which may not be the case where internal motion is present. A consideration of these matter lies beyond the scope of this work further details may be found in reference [1]. 

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