Calculation of Relative Binding Free Energies and Configurational Entropies: A Structural and Thermodynamic Analysis of the Nature of Non-polar Binding of Thrombin Inhibitors Based on Hirudin 55–65

Abstract

Free energy calculations were carried out on a series of exosite-binding inhibitors of thrombin. These inhibitors are based on the C-terminal fragment of hirudin and have the sequence Phe-Glu-Glu-Ile H59-Pro-Glu-Glu-Tyr-Leu, where the superscript over Ile indicates its relative position in the natural sequence of hirudin. In this study, the effect of replacing Ile H59with ten other non-polar amino acids was examined. Three preferred interaction sites for methyl/methylene groups for the various Xaa H59side-chains in the complex were identified from conformational search calculations. The corresponding thermodynamic changes were determined using combination of systematic search and energy minimization in a manner that locates the local minima in the system and in the process simultaneously builds up the partition function. The free energy, internal energy and entropic contributions are readily calculated from the partition function. Very good agreement in the resulting relative binding free energies was obtained between theory and experiment. The calculations allowed us to dissect out the enthalpic, entropic and solvation contributions to ΔΔ G. The contribution from desolvation was found to be relatively weak. The binding of these non-polar side-chains to thrombin is found to be driven mainly by favourable protein-ligand interactions rather than by the desire for non-polar groups to be desolvated. We also find that the configurational entropy contributes about 0.48 kcal/mol (0.81 kT) in average for each torsional angle “frozen” in binding.