Theoretical classification of exchange geometries from the perspective of NMR relaxation dispersion

NMR relaxation dispersion experiments have been widely applied to probe important conformational exchange of macro-molecules in many biological systems. The current improvements in computational techniques as well as the theoretical breakthroughs make the quantitative data analysis of complex exchange models possible. However, the topology of a given exchange model is also one of the main factors affecting the solution of Bloch-McConnell equation. The lack of a theoretical analysis of the exchange topologies at n-site exchange hinders further progress of such data analysis. Here, using graph theory, we reveal the topological complexity of n-site exchange and present all exchange models when n is less than 6. Furthermore, we introduce an alternative way, using machine learning, to select an exchange model based on a set of relaxation dispersion data without fitting them with every individual exchange model.