Free-energy analysis of enzyme-inhibitor binding: aspartic proteinase-pepstatin complexes

Expeditious in silico determinations of the free energies of binding of a series of inhibitors to an enzyme are of immense practical value in structure-based drug design efforts. Some recent advances in the field of computational chemistry have rendered a rigorous thermodynamic treatment of biologic molecules feasible, starting from a molecular description of the biomolecule, solvent, and salt. Pursuing the goal of developing and making available a software for assessing binding affinities, we present here a computationally rapid, albeit elaborate, methodology to estimate and analyze the molecular thermodynamics of enzyme-inhibitor binding with crystal structures as the point of departure. The complexes of aspartic proteinases with seven inhibitors have been adopted for this study. The standard free energy of complexation is considered in terms of a thermodynamic cycle of six distinct steps decomposed into a total of 18 well-defined components. The model we employed involves explicit all-atom accounts of the energetics of electrostatic interactions, solvent screening effects, van der Waals components, and cavitation effects of solvation combined with a Debye-Huckel treatment of salt effects. The magnitudes and signs of the various components are estimated using the AMBER parm94 force field, generalized Born theory, and solvent accessibility measures. Estimates of translational and rotational entropy losses on complexation as well as corresponding changes in the vibrational and configurational entropy are also included. The calculated standard free energies of binding at this stage are within an order of magnitude of the observed inhibition constants and necessitate further improvements in the computational protocols to enable quantitative predictions. Some areas such as inclusion of structural adaptation effects, incorporation of site-dependent amino acid pKa shifts, consideration of the dynamics of the active site for fine-tuning the methodology are easily envisioned. The present series of studies, nonetheless, creates potentially useful qualitative information for design purposes on what factors favor protein-drug binding. The net binding free energies are a result of several competing contributions with 6 of the 18 terms favoring complexation. The nonelectrostatic contributions (i.e., the net van der Waals interactions) and the differential cavitation effects favor binding. Electrostatic contributions show considerable diversity and turn out to be favorable in a consensus view for the seven aspartic proteinase-inhibitor complexes examined here. Implications of these observations to drug design are discussed.