LEAST-SQUARES METHOD FOR QUANTITATIVE-DETERMINATION OF CHEMICAL-EXCHANGE AND CROSS-RELAXATION RATE CONSTANTS FROM A SERIES OF 2-DIMENSIONALEXCHANGE NMR-SPECTRA

We present a new method, the least-error matrix analysis (LEMA), to qu antify the dynamic matrix from a series of 2D NMR exchange spectra. Th e method is based on a weighted averaging of individual dynamic matric es. The matrices are obtained by full-matrix analysis (FMA) from a ser ies of 2D exchange spectra recorded at different mixing times. The wei ghts, calculated by error propagation analysis, are explicit functions of the mixing time. The principal advantage of LEMA in comparison to FMA is that it uses all the known relationships between the spectral p eaks: the peak correlations within 2D spectra, and the mixing time evo lution among the spectra. We tested LEMA by analyzing a series of 10 c ross-relaxation spectra (NOESY, tau(m) = 60 mu s-1.28 s) in a rigid 10 -spin system (cyclo(L-Pro-Gly) in 3:1 v/v H2O/DMSO). At 233 K the dipe ptide has a mobility like a small protein with a correlation time of 3 .8 ns. While FMA at tau(m) = 30 ms could extract only 14 distances in a range 1.75-3 Angstrom, LEMA provided 22 distances, of which the long est was 4 Angstrom. The extension of the available interproton distanc es from 3 to 4 Angstrom afforded by LEMA is caused by a 10-fold decrea se of the lower limit of measurable cross-relaxation rates, from -0.59 to -0.06 s(-1). The most important property of LEMA, provision of acc urate average values of magnetization exchange rates from a given set of peak volumes, is verified experimentally on a model system.