Motivation Protein function is intrinsically linked to native dynamics, but the systematic characterization of functionally relevant dynamics remains elusive besides specific examples. Here we exhaustively characterize three types of dynamical couplings between protein residues: co-directionality (moving along collinear directions), coordination (small fluctuations of the interatomic distance) and deformation (the extent by which perturbations applied at one residue modify the local structure of the other one), which we analytically compute through the torsional network model. Results We find that ligand binding sites are characterized by large within-site coordination and co-directionality, much larger than expected for generic sets of residues with equivalent sequence distances. In addition, catalytic sites are characterized by high coordination couplings with other residues in the protein, supporting the view that the overall protein structure facilitates the catalytic dynamics. The binding sites of allosteric effectors are characterized by comparably smaller coordination and higher within-site deformation than other ligands, which supports their dynamic nature. Allosteric inhibitors are coupled to the active site more frequently through deformation than through coordination, while the contrary holds for activators. We characterize the dynamical couplings of the sodium-dependent Leucine transporter protein (LeuT). The couplings between and within sites progress consistently along the transport cycle, providing a mechanistic description of the coupling between the uptake and release of ions and substrate, and they highlight qualitative differences between the wild-type and a mutant for which chloride is necessary for transport. Availability and implementation The program tnm is freely available at https://github.com/ugobas/tnm Supplementary information Supplementary data are available at Bioinformatics online.