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

Abstract

Zinc endopeptidase thermolysin can be inhibited by a series of phosphorus-containing peptide analogues, CbzGly-$(PO2)-X-Leu-Y-R (ZGP(X)L(Y)R), where X = NH, 0, or CH2; Y = NH or 0; and 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. Morgan et al., 1991). It has been shown that modifications on X or Y yield uniform binding constant changes for those inhibitors with identical R. In particular, the average binding energy change between phosphonamidates and phosphonates is 4.0 * 0.1 kcal/mol. These correlations, as well as an X-ray crystallography study Tronrud et al., 1987;Matthews, 1988), suggest that these inhibitors bind to thermolysin in an identical mode.Previous theoretical studies focused on the variation of the X moiety of these inhibitors. Bash et al. (1987) and Merz and Kollman (1989) carried out free energy perturbation (FEP) simulations for ZGP(X)LL with thermolysin. The good agreement between the calculations and experiments indicates that the solvation of the inhibitors and the interaction between the X moiety and a hydrogen bond (H-bond) acceptor of the enzyme are two primary determinants of the binding affinity difference. Through a qualitative analysis, Bartlett and Marlowe (1987) suggested that the intrinsic H-bond energy for phosphonamidates Reprint requests to: Jian Shen at his present address: Marion Merre11 Dow, lnc., 2110 East Galbraith Road, P.O. Box 156300, Cincinnati, is significantly higher than the observed binding energy change of 4 kcal/mol from the PI' NH to 0 substitution. However, the calculated solvation energies as well as the interpretation were challenged by partition coefficient and pK, measurements. Grohelny et al. (1989) proposed that the basicities of the inhibitors and a much smaller H-bond energy of 1.5 kcal/mol are responsible for the loss of binding affinity in going from phosphonamidates to phosphonates. Although Morgan et al. (1991) showed that the basicities of another series of phosphorus-containing inhibitors are not critical to the binding, a final conclusion has not been reached due to the lack of relevant ...

Towards Predictive Ligand Design With Free-Energy Based Computational Methods?

“…A broader range of affinities a priori lends itself to better correlations between calculations and experiment. The agreement in rank order between calculated and measured affinities ranged from impressive [191] [40, 60,95,150,152,186,190,216,261] to moderate [88,149,181,272] to poor [56,94,192]. The quality of the agreement does improve with a broader range of affinities, eg [40,150,152,186,216,261], and degrades with small differences in affinity [56,94,152].…”

“…This approach has its roots in the mid 90's when investigations of protein-ligand recognition using the PB equation started to appear [63]. These first studies considered only the electrostatic/polar component of the total free energy of binding ∆G bind , but subsequent work included additional contributions [64,191,192]. In the full MM-PBSA scheme ∆G bind can be partitioned as follows [68,[193][194][195][196]: ∆G bind = ∆G ele + ∆G np + ∆G conf -T∆S solutes (7) ∆G ele encapsulates both the electrostatic interactions between ligand and receptor (Coulombic interactions; ∆G ele_Coul ) and the interaction of the solute charges with the solvent (∆G ele_solv ).…”

“…These transfer free energies were empirically found to be proportional to the area of solute-solvent boundary, usually represented by the solvent accessible surface area (SASA) [178,198,199,241], although it has been suggested that the smaller molecular surface is more relevant [242]. A correlation between SASA and entropy of hydration has been reported for a set of polar and apolar compounds [191]. Also, a SASA term was needed to reproduce free energies of hydration of small organic solutes when calculated in combination with continuum electrostatics [178,243] or with the linear response approach [244].…”

“…These methods can be applied to chemically diverse compounds [40, 63,88,150,190,192,216,261,269,272] without a need to transform a reference ligand into others, a major advantage over the FEP and TI methods. However, many studies addressed congeneric compounds [56,60,94,95,149,152,181,191,221,252]. MM-PBSA has the potential to tackle absolute binding free energies in favourable cases [95], but most applications are only concerned with relative binding affinities.…”

“…Initial PB studies were performed directly with the X-ray coordinates, after energy minimisation of the added hydrogens [63,191,221]. It is however dangerous to calculate energies directly on experimental coordinates with a force-field, because energies are very sensitive to small coordinate displacements, and structural models consistent with the force-field parametrisation should be used (eg minute displacements can release unfavourable steric clashes due to van der Waals interactions).…”