This study focuses on how the low-frequency end of the vibrational spectrum related to the functional motions changes as a protein binds to a small ligand(s). Our recently proposed residue-specific (RESPEC) elastic network model provides a natural laboratory for this aim due to its systematic mixed coarse-graining approach and parametrization. Current analysis on a large data set of protein-ligand complexes reveals a universal curve enclosing the frequency distributions, which bears the features of previous computational and experimental studies. We mostly observe positive frequency shifts in the collective modes of the protein upon ligand binding. This observation, conforming to the Rayleigh-Courant-Fisher theorem, points to a constraining effect imposed by ligands on protein dynamics, which may be accompanied by a negative vibrational entropy difference. Positive frequency shifts in the global modes can thus be linked to the harmonic well getting steeper, because of interactions with the ligand(s).