Topological Editing of Cross‐Relaxation Networks

We have used the elements of graph theory to describe NMR cross‐relaxation networks in macromolecules and to analyze different experiments used for topological editing. We propose a new experiment, block decoupled NOESY (B.D. NOESY), that splits the cross‐relaxation network of a macromolecular system into two noninteracting subdomains. Splitting is achieved by arranging for the effective z‐components of the magnetization in one subdomain, as viewed from the other subdomain, to be zero. The B.D. NOESY experiment, in favorable cases, can usefully simplify the analysis of cross‐relaxation spectra by removing certain ambiguities. We demonstrate the method by separating the aromatic resonances from the rest of the cross‐relaxation network of a small globular protein: turkey ovomucoid third domain, M_r 6000. The resulting spectrum provides a clearer picture of cross‐relaxation pathways that involve only aromatic or only aliphatic spins. By comparing the B.D. NOESY spectrum with the normal NOESY spectrum, we were able to identify cross peaks that contain contributions from indirect magnetization transfer (spin diffusion) mediated by the aromatic side chains. In the terminology of graph theory, these experiments decompose topological networks of cross‐relaxation into two subgraphs, the join of which generates the original graph.