RELAXATION-MATRIX ANALYSIS OF THE TRANSFERRED NUCLEAR OVERHAUSER EFFECT FOR FINITE EXCHANGE-RATES

A matrix formalism is developed for calculations of time-dependent nuclear Overhauser effects in systems undergoing chemical exchange, and the analysis is applied to the interpretation of data obtained in transferred-NOE experiments. Simulations have been performed for a wide variety of nuclear geometries, and preliminary data for the reversible binding of the inhibitor tubercidin to bacterial purine nucleoside phosphorylase have also been obtained. Although theoretically the initial buildup rate of the NOE interaction is independent of the exchange-rate constant k, this independence persists for such a short period of time that it is experimentally unobservable unless the exchange rate is extremely high. For the parameters used in the models, calculated buildup rates corresponding to mixing times of 10-100 ms exhibit a strong dependence on k. Of greatest interest is the observation that a lag in the development of the transferred NOE, generally believed to characterize indirect relaxation pathways, frequently is observable only at very high rates of chemical exchange and is so minimal as to be experimentally undetectable. Alternatively, a pronounced lag phase is predicted if the exchange rate is sufficiently slow that the observed NOE corresponds to only the free species. An apparent lag can also be predicted to result from the small negative NOEs of the uncomplexed species for some exchange parameters. The analysis has also been extended to include macromolecule (enzyme) protons, and several models for the effects of enzyme-mediated relaxation have been evaluated. These calculations, combined with the limited ability of the researcher to control most of the parameters involved in this type of study, suggest significant problems with interpretations based on initial rate measurements and strongly support the need for an independent determination of the rate of chemical exchange and for the use of model calculations such as those presented here in the interpretation of transferred-NOE studies. © 1992.