The Normal-Mode Entropy in the MM/GBSA Method: Effect of System Truncation, Buffer Region, and Dielectric Constant

Abstract

We have performed a systematic study of the entropy term in the MM/GBSA (molecular mechanics combined with generalised Born and surface-area solvation) approach to calculate ligand-binding affinities. The entropies are calculated by a normal-mode analysis of harmonic frequencies from minimised 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 and 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 minimisation 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.Keywords: MM/GBSA, entropy, ligand-binding affinities, dielectric constant, factor Xa, ferritin, HIV-1 protease.Introduction MM/GBSA is an approximate method to estimate the absolute binding free energy, ΔG bind , of a ligand L, to a biomacromolecule, e.g. a protein, P, forming a complex PL. It estimates ΔG bind as the difference in free energy between PL, P, and L, viz. ΔG bind = G(PL) -G(P) -G(L). Each of these three free energies are estimated from the following sum 1,2 G = E int + E vdW + E ele + G solv + G np − TS MM ( 1) where the brackets indicate an average over snapshots from a molecular dynamics (MD) simulation. The first three terms on the right-hand side are the molecular mechanics (MM) internal (i.e. bonds, angles, and dihedral), van der Waals, and electrostatic energies, G solv and G np are the polar and nonpolar solvation free energies, and the last term is the absolute temperature multiplied by an entropy estimate. The latter estimate is usually taken as a combination of translational, rotational, and vibrational terms. All the terms are calculated on a system where water molecules from the simulation have been stripped off. Moreover, typically only the complex (PL) is simulated and the free energies of P and L are obtained from the same simulation by simply deleting the coordinates of the other species. 3,4 Thereby, the E int term cancels exactly and the precision is improved by a factor of ~5. 5,6 The most common method to estimate the vibrational entropy in the MM/GBSA method is to use frequencies from a normal-mode analysis (NMA...

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