The normal-mode entropy in the MM/GBSA method: effect of system truncation, buffer region, and dielectric constant

We have performed a systematic study of the entropy term in the MM/GBSA (molecular mechanics combined with generalized Born and surface-area solvation) approach to calculate ligand-binding affinities. The entropies are calculated by a normal-mode analysis of harmonic frequencies from minimized snapshots of molecular dynamics simulations. For computational reasons, these calculations have normally been performed on truncated systems. We have studied the binding of eight inhibitors of blood clotting factor Xa, nine ligands of ferritin, and two ligands of HIV-1 protease and show that removing protein residues with distances larger than 8-16 Å to the ligand, including a 4 Å shell of fixed protein residues and water molecules, change the absolute entropies by 1-5 kJ/mol on average. However, the change is systematic, so relative entropies for different ligands change by only 0.7-1.6 kJ/mol on average. Consequently, entropies from truncated systems give relative binding affinities that are identical to those obtained for the whole protein within statistical uncertainty (1-2 kJ/mol). We have also tested to use a distance-dependent dielectric constant in the minimization and frequency calculation (ε = 4r), but it typically gives slightly different entropies and poorer binding affinities. Therefore, we recommend entropies calculated with the smallest truncation radius (8 Å) and ε =1. Such an approach also gives an improved precision for the calculated binding free energies.