Binding of phosphorus-containing inhibitors to thermolysin studied by the Poisson-Boltzmann method

Zinc endopeptidase thermolysin can be inhibited by a series of phosphorus-containing peptide analogues, Cbz-Gly-psi (PO2)-X-Leu-Y-R (ZGp(X)L(y)R), where X = NH, O, or CH2; Y = NH or O; R = Leu, Ala, Gly, Phe, H, or CH3. The affinity correlation as well as an X-ray crystallography study suggest that these inhibitors bind to thermolysin in an identical mode. In this work, we calculate the electrostatic binding free energies for a series of 13 phosphorus-containing inhibitors with modifications at X, Y, and R moieties using finite difference solution to the Poisson-Boltzmann equation. A method has been developed to include the solvation entropy changes due to binding different ligands to a macromolecule. We demonstrate that the electrostatic energy and empirically derived solvation entropy can account for most of the binding energy differences in this series. By analyzing the binding contribution from individual residues, we show that the energy of a hydrogen bond is not confined to the donor and acceptor. In particular, the positive charges on Zn and Arg 203, which are not the acceptors, contribute significantly to the hydrogen bonds between two amides of ZGpLL and the thermolysin.