Mapping of spectral density functions using heteronuclear NMR relaxation measurements

Abstract

A method is proposed for direct mapping of spectral density functions of the rotational motions of H-X bond vectors, such as 1H---15N, by measuring a set of NMR relaxation parameters. The well known and frequently measured relaxation parameters T1 and T2 probe the spectral density function J([omega]) at five frequencies: 0, [omega]N, [omega]H, [omega]H - [omega]N, and [omega]H + [omega]N. In this study, the longitudinal relaxation time T1(Nz), the transverse relaxation times of in-phase coherence, T2(Nx,y), and of antiphase coherence, T2(2HzNx,y), the relaxation time of longitudinal two-spin order, T1(2HzNz), and the heteronuclear cross-relaxation rate [sigma]HN are measured for the heteronucleus N. These five relaxation parameters sample the spectral density function J([omega]) at the same five points where each measurement samples a subset of these frequencies with different weights. The five measurements permit an analytical calculation of J([omega]) at these five frequencies. Since longitudinal proton relaxation plays a role in these relaxation parameters, a sixth measurement is necessary to determine this relaxation time. The theory and experimental techniques for measuring these relaxation parameters are discussed. Preliminary results of these techniques as applied to the 15N-enriched protein eglin c are described. The proposed approach has the advantage that it does not rely on any a priori model assumptions about the shape of J([omega]); i.e., measurement of J([omega]) and interpretation can be separated.