Neutron scattering experiments have demonstrated that binding of the cancer drug methotrexate softens the low-frequency vibrations of its target protein, dihydrofolate reductase (DHFR). Here, this softening is fully reproduced using atomic detail normal-mode analysis. Decomposition of the vibrational density of states demonstrates that the largest contributions arise from structural elements of DHFR critical to stability and function. Mode-projection analysis reveals an increase of the breathing-like character of the affected vibrational modes consistent with the experimentally observed increased adiabatic compressibility of the protein on complexation.