A ROBUST METHOD FOR ESTIMATING CROSS-RELAXATION RATES FROM SIMULTANEOUS FITS TO BUILDUP AND DECAY CURVES

This paper introduces a novel computational method for estimating rela xation rates among pairs of spin orders. This method simultaneously es timates all the auto- and cross-relaxation rates from the same measure ments, and avoids the ill-conditioning problems associated with multie xponential fits, The method models the relaxation dynamics by a system of linear differential equations, and assumes that measurements of th e spin orders have been made at an equally spaced sequence of time poi nts. It computes a nonlinear least-squares fit of the exponential of t he rate matrix at the shortest time point to these measurements. Preli minary estimates of the exponential matrix and initial spin orders fro m which to start the computations are obtained by solving simpler line ar-least-squares problems. The performance of the method on simulated 2 x 2 test problems indicates that when measurements at eight or more equally spaced times spanning the maximum and inflection points of the build-up curves are available, the relative errors in the rates are u sually less than the relative errors in the measurements. The method i s further demonstrated by applying it to the problem of determining th e cross correlation-induced cross-relaxation rates between the in-phas e and antiphase coherence of the amide groups in the N-15-labeled prot ein oxidized flavodoxin. Finally, the possibility of extending the met hod to other kinds of relaxation measurements and larger spin systems is discussed. (C) 1997 Academic Press.