Quantitative Determination of Magnetization Exchange Rate Constants from a Series of Two-Dimensional Exchange NMR Spectra

A method for quantitative determination of magnetization exchange rate constants (cross-relaxation and chemical exchange) from a series of two-dimensional exchange spectra is presented. The method, the least error matrix analysis (LEMA), combines a series of full matrix calculations at different mixing times in a least-squares manner. LEMA embodies the principal advantages of full-relaxation matrix analysis (FMA) and initial rate buildup (BU) analysis. Like FMA, it takes into account all the relations among the spectral matrix elements and in analogy to BU makes use of their time evolution. By means of calculations, simulations, and experiments, we have shown that LEMA provides the dynamic matrix from a given set of experimental data with errors that are smaller than in either FMA or BU calculations.