Unbiased clustering of residues undergoing synchronous motions in proteins using NMR spin relaxation data

Biological macromolecules are dynamic entities that transition between various conformational states, often playing a vital role in biological functions. Their inherent flexibility spans a broad range of timescales. Motions occurring within the microsecond to millisecond range are especially important, as they are integral to processes such as enzyme catalysis, folding, ligand binding, and allostery. NMR Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion measurements are the preferred method for characterizing macromolecular motions at atomic resolution. However, it is still uncertain whether the functional motions of multiple residues in macromolecules need to be coordinated and/or synchronized within the protein matrix in order to perform the desired function. Here, we illustrate an unbiased method to analyze NMR relaxation dispersion and identify dynamic clusters of residues that fluctuate on similar timescales within proteins. The method requires relaxation dispersion data for backbone amides or side-chain methyl groups, which are globally fitted using the Bloch-McConnell equations for each pair of residues. The goodness of the pairwise fitting serves as a metric to construct two-dimensional synchronous dynamics (SyncDyn) maps, allowing us to identify residue clusters whose dynamics are influenced by ligand binding. We applied our method to the catalytic subunit of the cAMP-dependent protein kinase A (PKAC) and the T17A mutant of ribonuclease A (RNAse A). The SyncDyn maps for PKA-C showed distinct clusters of residues located in critical allosteric sites. Nucleotide binding activates the movement of residues at the interface between the two lobes and also those distal to the active site. In the case of RNAse A, the SyncDyn maps show that residues fluctuating with the same time scale are interspersed in both lobes of the enzyme. Overall, our approach eliminates arbitrary manual selection of residues for dynamic clustering and objectively identifies all possible residue pairs that fluctuate synchronously, i.e. on the same timescale.