Protein-ligand binding free energy estimation using molecular mechanics and continuum electrostatics. Application to HIV-1 protease inhibitors

A method is proposed for the estimation of absolute binding free energy of interaction between proteins and ligands. Conformational sampling of the protein-ligand complex is performed by molecular dynamics (MD) in vacuo and the solvent effect is calculated a posteriori by solving the Poisson or the Poisson-Boltzmann equation for selected frames of the trajectory. The binding free energy is written as a linear combination of the buried surface upon complexation, SASbur, the electrostatic interaction energy between the ligand and the protein, Eelec, and the difference of the solvation free energies of the complex and the isolated ligand and protein, deltaGsolv. The method uses the buried surface upon complexation to account for the non-polar contribution to the binding free energy because it is less sensitive to the details of the structure than the van der Waals interaction energy. The parameters of the method are developed for a training set of 16 HIV-1 protease-inhibitor complexes of known 3D structure. A correlation coefficient of 0.91 was obtained with an unsigned mean error of 0.8 kcal/mol. When applied to a set of 25 HIV-1 protease-inhibitor complexes of unknown 3D structures, the method provides a satisfactory correlation between the calculated binding free energy and the experimental pIC5o without reparametrization.     

Harmonic analysis of large systems. I. Methodology

Methods have been developed for the determination of vibrational frequencies and normal modes of large systems in the full conformational space (including all degrees of freedom) and in a reduced conformational space (reducing the number of degrees of freedom). The computational method, which includes Hessian generation and storage, full and iterative diagonalization techniques, and the refinement of the results, is presented. A method is given for the quasiharmonic analysis and the reduced basis quasiharmonic analysis. The underlying principle is that from the atomic fluctuations, an effective harmonic force field can be determined relative to the dynamic average structure. Normal mode analysis tools can be used to characterize quasiharmonic modes of vibration. These correspond to conventional normal modes except that anharmonic effects are included. Numerous techniques for the analyses of vibrational frequencies and normal modes are described. Criteria for the analysis of the similarity of low-frequency normal modes is presented. The approach to determining the natural frequencies and normal modes of vibration described here is general and applicable to any large system. © 1995 John Wiley & Sons, Inc.

1 This article is a U.S. Government work and, as such, is in the public domain in the United States of America.

     

Effective atom volumes for implicit solvent models: comparison between Voronoi volumes and minimum fluctuation volumes

An essential element of implicit solvent models, such as the generalized Born method, is a knowledge of the volume associated with the individual atoms of the solute. Two approaches for determining atomic volumes for the generalized Born model are described; one is based on Voronoi polyhedra and the other, on minimizing the fluctuations in the overall volume of the solute. Volumes to be used with various parameter sets for protein and nucleic acids in the CHARMM force field are determined from a large set of known structures. The volumes resulting from the two different approaches are compared with respect to various parameters, including the size and solvent accessibility of the structures from which they are determined. The question of whether to include hydrogens in the atomic representation of the solute volume is examined. Copyright 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1857-1879, 2001     

Spatially constrained minimization of macromolecules

A structural minimization procedure which converges rapidly and restricts the atomic shifts is outlined. It is implemented by adding a harmonic penalty term for the displacements of atomic positions and resetting the reference coordinates with respect to which the constraints are computed during the minimization. The resetting serves to reduce the constraint energy of the minimized structure to negligible levels.     

Conformational analysis of a stereochemically complete set of cis-enediol peptide analogues

A conformational analysis of a stereochemically complete set of peptide analogues based on a cis-enediol unit is presented. The cis-enediol unit, which can replace a two or a three amino acid segment of a peptide, contains two "side chains", four asymmetrical carbon atoms, and six free dihedral angles. To determine the accessible conformational space, the molecules are divided into three fragments, each containing two free dihedral angles. The energy surfaces are computed for all dihedral angle values, and the possible conformations of the cis-enediol unit analogues are built using all combinations of the surface minima. Such a "build-up" procedure, which is very fast, is able to reproduce 75% of the minima obtained from a full dihedral angle exploration of the conformational space. The cis-enediol unit minima are compared with the corresponding di- and tripeptide minima; all peptide minima can be closely matched by a cis-enediol unit minimum of low energy (less than 2.2 kcal/mol above the lowest energy conformer). However, there are low energy minima of the cis-enediol unit that have no corresponding minima in peptides. The results are shown to depend strongly on the chirality of the analogues. The ability of each of the stereoisomers to mimic natural peptides, evaluated by the present approach, is correlated with its experimental activity in a renin inhibition assay.     

Structure activity relationship by NMR and by computer: a comparative study

There has recently been considerable interest in using NMR spectroscopy to identify ligand binding sites of macromolecules. In particular, a modular approach has been put forward by Fesik et al. (Shuker, S. B.; Hajduk, P. J.; Meadows, R. P.; Fesik, S. W. Science 1996, 274, 1531-1534) in which small ligands that bind to a particular target are identified in a first round of screening and subsequently linked together to form ligands of higher affinity. Similar strategies have also been proposed for in silico drug design, where the binding sites of small chemical groups are identified, and complete ligands are subsequently assembled from different groups that have favorable interactions with the macromolecular target. In this paper, we compare experimental and computational results on a selected target (FKBP12). The binding sites of three small ligands ((2S)1-acetylprolinemethylester, 1-formylpiperidine, 1-piperidinecarboxamide) in FKBP12 were identified independently by NMR and by computational methods. The subsequent comparison of the experimental and computational data showed that the computational method identified and ranked favorably ligand positions that satisfy the experimental NOE constraints.     

Synthesis of periphery-functionalized dendritic molecules using polylithiated dendrimers as starting material

A general method for the functionalization of Si-Cl terminated carbosilane dendritic molecules via organolithium or organomagnesium reagents is described. Quantitative exchange of the bromine atoms of 4-bromophenyl-functionalized dendrimers affords polylithiated species that are valuable starting materials for further functionalization, e.g., into pyridyl alcohols. The latter were successfully applied as catalyst precursors in a ruthenium-mediated ring-closure metathesis reaction.     

Quantum mechanics/molecular mechanics studies of triosephosphate isomerase-catalyzed reactions: effect of geometry and tunneling on proton-transfer rate constants

The role of tunneling for two proton-transfer steps in the reactions catalyzed by triosephosphate isomerase (TIM) has been studied. One step is the rate-limiting proton transfer from Calpha in the substrate to Glu 165, and the other is an intrasubstrate proton transfer proposed for the isomerization of the enediolate intermediate. The latter, which is not important in the wild-type enzyme but is a useful model system because of its simplicity, has also been examined in the gas phase and in solution. Variational transition-state theory with semiclassical ground-state tunneling was used for the calculation with potential energy surface determined by an AM1 method specifically parametrized for the TIM system. The effect of tunneling on the reaction rate was found to be less than a factor of 10 at room temperature; the tunneling becomes more important at lower temperature, as expected. The imaginary frequency (barrier) mode and modes that have large contributions to the reaction path curvature are localized on the atoms in the active site, within 4 A of the substrate. This suggests that only a small number of atoms that are close to the substrate and their motions (e.g., donor-acceptor vibration) directly determine the magnitude of tunneling. Atoms that are farther away influence the effect of tunneling indirectly by modulating the energetics of the proton transfer. For the intramolecular proton transfer, tunneling was found to be most important in the gas phase, to be similar in the enzyme, and to be the smallest in water. The major reason for this trend is that the barrier frequency is substantially lower in solution than in the gas phase and enzyme; the broader solution barrier is caused by the strong electrostatic interaction between the highly charged solute and the polar solvent molecules. Analysis of isotope effects showed that the conventional Arrenhius parameters are more useful as experimental criteria for determining the magnitude of tunneling than the widely used Swain-Schaad exponent (SSE). For the primary SSE, although values larger than the transition-state theory limit (3.3) occur when tunneling is included, there is no clear relationship between the calculated magnitudes of tunneling and the SSE. Also, the temperature dependence of the primary SSE is rather complex; the value of SSE tends to decrease as the temperature is lowered (i.e., when tunneling becomes more significant). For the secondary SSE, the results suggest that it is more relevant for evaluating the "coupled motion" between the secondary hydrogen and the reaction coordinate than the magnitude of tunneling. Although tunneling makes a significant contribution to the rate of proton transfer, it appears not to be a major aspect of the catalysis by TIM at room temperature; i.e., the tunneling factor of 10 is "small" relative to the overall rate acceleration by 10(9). For the intramolecular proton transfer, the tunneling in the enzyme is larger by a factor of 5 than in solution.