Evaluation of the conformational free energies of loops in proteins

In this paper we discuss the problem of including solvation free energies in evaluating the relative stabilities of loops in proteins. A conformational search based on a gas-phase potential function is used to generate a large number of trial conformations. As has been found previously, the energy minimization step in this process tends to pack charged and polar side chains against the protein surface, resulting in conformations which are unstable in the aqueous phase. Various solvation models can easily identify such structures. In order to provide a more severe test of solvation models, gas phase conformations were generated in which side chains were kept extended so as to maximize their interaction with the solvent. The free energies of these conformations were compared to that calculated for the crystal structure in three loops of the protein E. coli RNase H, with lengths of 7, 8, and 9 residues. Free energies were evaluated with a finite difference Poisson-Boltzmann (FDPB) calculation for electrostatics and a surface area-based term for nonpolar contributions. These were added to a gas-phase potential function. A free energy function based on atomic solvation parameters was also tested. Both functions were quite successful in selecting, based on a free energy criterion, conformations quite close to the crystal structure for two of the three loops. For one loop, which is involved in crystal contacts, conformations that are quite different from the crystal structure were also selected. A method to avoid precision problems associated with using the FDPB method to evaluate conformational free energies in proteins is described. © 1994 John Wiley & Sons, Inc.     

Calculating proton uptake/release and binding free energy taking into account ionization and conformation changes induced by protein-inhibitor association: application to plasmepsin, cathepsin D and endothiapepsin-pepstatin complexes

The protein-inhibitor binding energies of enzymes are often pH dependent, and binding induces either proton uptake or proton release. The proton uptake/release and the binding energy for three complexes with available experimental data were numerically studied: pepstatin-cathepsin D, pepstatin-plasmepsin II and pepstatin-endothiapepsin. Very good agreement with the experimental data was achieved when conformational changes were taken into account. The role of the desolvation energy and the conformational changes was revealed by modeling the complex, the separated molecules in the complex conformation and the free molecules. It was shown that the conformational changes induced by the complex formation are as important for the proton transfer as the loss of solvation energy caused by the burial of interface residues. The residues responsible for the proton transfer were identified and their contribution to the proton uptake/release calculated. These residues were found to be scattered along the whole protein rather than being localized only at the active site. In the case of cathepsin D, these residues were found to be highly conserved among the cathepsin D sequences of other species. It was shown that conformation and ionization changes induced by the complex formation are critical for the correct calculation of the binding energy. Taking into account the electrostatics and the van der Waals (vdW) energies within the Boltzmann distribution of energies and allowing ionization and conformation changes to occur makes the calculated binding energy more realistic and closer to the experimental value. The interplay between electrostatic and vdW forces makes the pH dependence of the binding energy smoother, because the vdW force acts in reaction to the changes of the electrostatic energy. It was found that a small fraction of the ionizable groups remain uncharged in both the free and complexed molecules. The sequence and structural position of these groups aligns well within the three proteases, suggesting that these may have specific role.     

Role of the protein side-chain fluctuations on the strength of pair-wise electrostatic interactions: comparing experimental with computed pK(a)s

The effect of the protein side-chain fluctuations on the strength of electrostatic interactions was studied. The effect was modeled on 7 different crystal structures on the same enzyme as well as on 20 molecular dynamics snapshot structures. It was shown that the side-chain flexibility affects predominantly the magnitude of the strong pair-wise interactions, that is, the pair-wise interaction among ion pairs, and practically does not affect the interactions with the rest of the protein. This was used to suggest a correction function that should be applied to the original pair-wise electrostatic interaction to mimic the effects of the fluctuations. The procedure is applied on three ion pairs identified in lysozyme. It was shown that sampling different side-chain rotamers and modifying the strength of the pair-wise interaction energies makes calculated pK(a)s less sensitive to the fluctuations of the structure and improves the prediction accuracy.     

A strategy for theoretical binding constant,Ki, calculations for neuraminidase aromatic inhibitors designed on the basis of the active site structure of influenza virus neuraminidase

Neuraminidase (NA) is one of the two major surface antigens of influenza virus. It plays an indispensable role in the release and spread of progeny virus particles during infection. NA inhibitors reduce virus infection in animals. To improve the clinical efficacy of NA inhibitors, we have begun the design of non-carbohydrate inhibitors based on the active site structure of NA. The approach is an iterative process of ligand modeling and electrostatic calculations followed by chemical synthesis of compounds, biological testing, and NA-inhibitor complex structure determination by X-ray crystallography. A strategy has been developed to calculate K_i for newly designed inhibitors. The calculations using the DelPhi program were performed for carbohydrate inhibitors and three preliminary benzoic acid inhibitors of neuraminidase (BANA) that have been synthesized and shown to bind to the active site of NA in the crystal structure. The calculated K_is of these inhibitors have an enlightening agreement with their in vitro biological activities. This demonstrates that the calculations produce informative results on the affinity of modeled inhibitors. GRID maps were also calculated and several pockets were identified for accepting possible new ligands. The calculated K_is for newly designed ligands suggest that these potential compounds will have high inhibitory activities. © 1995 Wiley-Liss, Inc.