Influence of conformational exchange on the 2D NOESY spectra of biomolecules existing in multiple conformations

The coupled recovery of the magnetizations of individual spins in a multispin system undergoing slow conformational exchange (on the chemical-shift scale) between different sites is considered within the context of the complete relaxation matrix analysis of the NOESY experiment. Explicit expressions have been derived for the peak intensities in the NOESY spectrum of a two-spin- 1 2 system. The general case where the populations and the intramolecular dipolar relaxation rates are different at the two sites is treated. This general case is appropriate for many practical situations normally encountered in biomolecular systems including that of a ligand undergoing exchange between free and enzyme-bound states. The expressions for the general case have been simplified for two limiting situations that also may be encountered in biomolecular NMR studies. The intensity variations of the different peaks in the spectrum (diagonal, exchange, direct NOESY, and exchange-mediated NOESY peaks) have been computed as a function of the mixing time for some typical examples. It is shown that, depending upon the conformational exchange rate in relation to dipolar cross-relaxation rates, the NOESY spectrum as a function of mixing time also exhibits significant dependence on the exchange rates. The implication of these results in extracting distance information is discussed. With minor modifications, the theoretical formalism presented here is readily applicable to situations where the conformational exchange is fast on the chemical-shift scale.