Magnetization exchange network editing: mathematical principles and experimental demonstration

We have examined analytically the effects of different NMR magnetization exchange network editing (MENE) procedures, starting from equilibrium or nonequilibrium conditions, on generalized systems that undergo magnetization exchange (cross-relaxation and/or chemical exchange). Larger errors in derived exchange rate constants are found in experiments that start from nonequilibrium states than in those that start from equilibrium. On the other hand, editing experiments that decompose the dynamic matrix into two or more block diagonal submatrices generally yield more accurate exchange rate constants. Theoretical arguments, backed up by experimental results, demonstrate that MENE experiments lead to increased rates of relaxation for the edited cross and diagonal peaks. We describe a new class of heteronuclear editing experiment in which the system starts from a nonequilibrium state and is edited during the mixing period. In an experimental application of this approach to the spectral analysis of a small protein, recombinant human ubiquitin (M_r 8565) labeled uniformly with ¹⁵N and ¹³C, we demonstrate how the cross-relaxation network of the protein can be decomposed simultaneously into subnetworks of ¹⁵N-bound protons, aliphatic ¹³C-bound protons, aromatic ¹³C-bound protons, and (¹²C/¹⁴N/O)-bound protons. Such a decomposition permits the measurement of slower magnetization exchange rates, including those that are masked in conventional cross-relaxation experiments.