Direct Determination of Vibrational Density of States Change on Ligand Binding to a Protein

The change in the vibrational density of states of a protein (dihydrofolate reductase) on binding a ligand (methotrexate) is determined using inelastic neutron scattering. The vibrations of the complex soften significantly relative to the unbound protein. The resulting free-energy change, which is directly determined by the density of states change, is found to contribute significantly to the binding equilibrium.

Figure 1

Dynamic structure factor versus frequency for uncomplexed DHFR (black curve) and complexed with methotrexate form of DHFR (gray curve) at 120 K. Data from all scattering angles are summed. Both spectra are normalized to the elastic peak height. Inset: the low frequency region of the spectra.

Figure 2

Vibrational frequency distribution $g\left(\omega \right)$ for un­complexed (black) and complexed (gray) forms of DHFR. Inset: enlarged frequency region of the spectra.