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.