Binding free energy contributions of interfacial waters in HIV-1 protease/inhibitor complexes

Water molecules are commonly observed in crystal structures of protein-ligand complexes where they mediate protein-ligand binding. It is of considerable theoretical and practical importance to determine quantitatively the individual free energy contributions of these interfacial water molecules to protein-ligand binding and to elucidate factors that influence them. The double-decoupling free energy molecular dynamics simulation method has been used to calculate the binding free energy contribution for each of the four interfacial water molecules observed in the crystal structure of HIV-1 protease complexed with KNI-272, a potent inhibitor. While two of these water molecules contribute significantly to the binding free energy, the other two have close to zero contribution. It was further observed that the protonation states of two catalytic aspartate residues, Asp25 and Asp125, strongly influence the free energy contribution of a conserved water molecule Wat301 and that different inhibitors significantly influence the free energy contribution of Wat301. Our results have important implications on our understanding of the role of interfacial water molecules in protein-ligand binding and to structure-based drug design aimed at incorporating these interfacial water molecules into ligands.     

Molecular dynamics simulation, free energy calculation and structure-based 3D-QSAR studies of B-RAF kinase inhibitors

(V600E)B-RAF kinase is the most frequent onco-genic protein kinase mutation in melanoma and is a promising target to treat malignant melanoma. In this work, a molecular modeling study combining QM-polarized ligand docking, molecular dynamics, free energy calculation, and three-dimensional quantitative structure-activity relationships (3D-QSAR) was performed on a series of pyridoimidazolone compounds as the inhibitors of (V600E)B-RAF kinase to understand the binding mode between the inhibitors and (V600E)B-RAF kinase and the structural requirement for the inhibiting activity. 3D-QSAR models, including CoMFA and CoMSIA, were developed from the conformations obtained by QM-polarized ligand docking strategy. The obtained models have a good predictive ability in both internal and external validation. Furthermore, molecular dynamics simulation and free energy calculations were employed to determine the detailed binding process and to compare the binding mode of the inhibitors with different activities. The binding free energies calculated by MM/PBSA gave a good correlation with the experimental biological activity. The decomposition of free energies by MM/GBSA indicates the van der Waals interaction is the major driving force for the interaction between the inhibitors and (V600E)B-RAF kinase. The hydrogen bond interactions between the inhibitors with Glu501 and Asp594 of the (V600E)B-RAF kinase help to stabilize the DFG-out conformation. The results from this study can provide some insights into the development of novel potent (V600E)B-RAF kinase inhibitors.     

键能的分子轨道理论研究 1: 理论公式

从LCAO-MO出发, 给出了一个计算键能的近似方法, 即EAB(i)-∑∑CaiSabCbiεi为第i个占据分子轨道(MO)中的一对电子对A-B键键能的贡献。对所有分子轨道求和即为该键的键能: EAB=∑EAB(i)。按该方法, 不仅可以计算各种不同分子中每两个相键连原子间的键能, 还可以从MO及AO角度分析每一具体键, 如σ, π, δ键的键能以及各AO对键能的贡献。该方法虽有别于求键焓和平衡离解能De, 但计算结果和De的实验值甚相符合。通过对键能的分析研究, 能较好地揭示原子间的相互作用关系及化学键的强弱, 从而可进一步探讨化学反应活性, 反应速率等化学性质。     

Molecular orbital studies of some transition metal complexes

A set of molecular orbital calculations based on a particular semi-empirical method, has been undertaken on a homologue series of bis(-2-methylallyl)transition metal (Ni, Co, Fe, Cr) complexes (abbreviated as ML₂). Arguments are found for predicting the stability of the NiL₂ system, which is the only one that could be synthetized.

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Zusammenfassung Eine Reihe von semiempirischen MO-Rechnungen wurde für die homologe Reihe von bis(-2-methylallyl) Metallkomplexen (Ni, Co, Fe, Cr) durchgeführt. Gründe für die Stabilität der Ni-Verbindung, die als einzige synthetisiert wurde, werden angeführt.

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Résumé Un ensemble de calculs par une méthode semi-empirique particulière d'orbitales moléculaires a été effectué sur une série homologue de complexes bis (-2-méthylallyl)-métal de transition (Ni, Co, Fe, Cr): ML₂.Certains arguments sont trouvés en faveur de la stabilité du système NiL₂, le seul à avoir été synthétisé.

     

Structural and dynamic studies on amido-bridged rhodium and iridium complexes

Treatment of [[M(mu-Cl)(diolefin)](2)] with the lithium salts of primary and secondary amines (LiNRR') in diethyl ether affords the complexes [[M(mu-NRR')(diolefin)](2)] (M=Rh, Ir; diolefin=1,5-cyclooctadiene (cod), tetrafluorobenzobarrelene (tfb); R'=H, R=tBu, Ph, 4-MeC(6)H(4); R=R'=Ph, 4-MeC(6)H(4)). Mixed-bridged chloro/amido complexes are intermediates in these syntheses, two of which, [[Rh(cod)](2)(mu-NHR)(mu-Cl)] (R=tBu, 4-MeC(6)H(4)), have been isolated. Replacement of the diolefin ligands by carbon monoxide or tert-butyl isocyanide in selected compounds takes place with retention of the binuclear structure to give the corresponding complexes [[M(mu-4-HNC(6)H(4)Me)(CO)(2)](2)], [[Rh(mu-4-HNC(6)H(4)Me)(CNtBu)(2)](2)] (12), and [[Rh(mu-NPh(2))(CNtBu)(2)](2)] (13). Single-crystal X-ray diffraction analyses of the complexes [[Rh(mu-NRR')(cod)](2)] (R'=H, R=4-MeC(6)H(4) (3); R=R'=4-MeC(6)H(4) (5)), 12, and 13 have shown that the conformation of the "RhN(2)Rh" four-membered metallacycle is planar in 5 and folded in 3, 12, and 13. The complexes with primary amides, 3 and 12, were found to exist as the syn,endo stereoisomers. The fluxionality of the complexes with secondary amides is due to rotation of the aromatic substituents about the N-C(ipso) bond and, in the case of 13, to the inversion of the "RhN(2)Rh" metallacycle as well. The complexes [[M(mu-NHR)(cod)](2)] (R=Ph, 4-MeC(6)H(4)) were found to exist as isomeric mixtures in solution, the syn/anti ratio being 2:3 for the rhodium derivatives and 1:1 for their iridium counterparts. Again, the motion detected was due to rotation of the aromatic substituents, and could be frozen only in the case of the syn isomers. The complex [[Rh(mu-NHtBu)(cod)](2)] with aliphatic amido ligands was found to be the anti folded isomer and proved to be nonfluxional. The most common conformation of the "RhN(2)Rh" metallacycle in these compounds is folded, and the preferred configuration varies from syn for the less encumbered compounds to anti on increasing the bulkiness of the bridging and ancillary ligands.     

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.     

Self-optimizing charge-transfer energy phenomena in metallosupramolecular complexes by dynamic constitutional self-sorting

In this paper we report an extended series of 2,6-(iminoarene)pyridine-type ZnII complexes [(Lii)2Zn]II, which were surveyed for their ability to self-exchange both their ligands and their aromatic arms and to form different homoduplex and heteroduplex complexes in solution. The self-sorting of heteroduplex complexes is likely to be the result of geometric constraints. Whereas the imine-exchange process occurs quantitatively in 1:1 mixtures of [(Lii)2Zn]II complexes, the octahedral coordination process around the metal ion defines spatial-frustrated exchanges that involve the selective formation of heterocomplexes of two, by two different substituents; the bulkiest ones (pyrene in principle) specifically interact with the pseudoterpyridine core, sterically hindering the least bulky ones, which are intermolecularly stacked with similar ligands of neighboring molecules. Such a self-sorting process defined by the specific self-constitution of the ligands exchanging their aromatic substituents is self-optimized by a specific control over their spatial orientation around a metal center within the complex. They ultimately show an improved charge-transfer energy function by virtue of the dynamic amplification of self-optimized heteroduplex architectures. These systems therefore illustrate the convergence of the combinatorial self-sorting of the dynamic combinatorial libraries (DCLs) strategy and the constitutional self-optimized function.     

Cylindrical cell model for the electrostatic free energy of polyelectrolyte complexes

Associative phase separation (complex coacervation) in a mixture of oppositely charged polyelectrolytes can lead to different types of (inter-)polyelectrolyte complexes (soluble micelles, macroscopic precipitation). In a previous report [Langmuir 2004, 20, 2785-2791], we presented a model for the electrostatic free energy change when (weakly charged) polyelectrolyte forms a homogeneous complex phase. The influence of ionization of the polymer on the electrostatic free energy of the complex was incorporated but the influence of complex density neglected. In the present effort, cylindrical cells are assumed around each polyelectrolyte chain in the complex, and on the basis of the Poisson-Boltzmann equation, the electrostatic free energy is calculated as a function of the complex density. After combination with Flory-Huggins mixing free energy terms and minimization of the total free energy, the equilibrium complex density is obtained, for a given ratio of polycations to polyanions in the complex. The analysis is used in an example calculation ofpolyelectrolyte film formation by alternatingly applying a polycation and a polyanion solution. The calculation suggests that the often observed exponential growth of a polyelectrolyte film when the polymer is weakly charged has a thermodynamic origin: the polyelectrolyte complex shifts repeatedly between two equilibrium states of different densities and compositions. However, when the polyelectrolytes are strongly charged the difference in the compositions between the two equilibrium states is very small, and exponential growth by an absorption mechanism is no longer possible.     

Comparative evaluation of MMPBSA and XSCORE to compute binding free energy in XIAP-peptide complexes

Evaluation of binding free energy in receptor-ligand complexes is one of the most important challenges in theoretical drug design. Free energy is directly correlated to the thermodynamic affinity constant, and, as a first step in druglikeness, a lead compound must have this constant in the range of micro- to nanomolar activity. Many efforts have been made to calculate it by rigorous computational approaches, such as free energy perturbation or linear response approximation. However, these methods are still computationally expensive. We focus our work on XIAP, an antiapoptotic protein whose inhibition can lead to new drugs against cancer disease. We report here a comparative evaluation of two completely different methodologies to estimate binding free energy, MMPBSA (a force field based function) and XSCORE (an empirical scoring function), in seven XIAP-peptide complexes using a representative set of structures generated by previous molecular dynamics simulations. Both methods are able to predict the experimental binding free energy with acceptable errors, but if one needs to identify slight differences upon binding, MMPBSA performs better, although XSCORE is not a bad choice taking into account the low computational cost of this method.     

Reversed stereochemical preference in binding of Ro 31-8959 to HIV-1 proteinase: A free energy perturbation analysis

Ro 31-8959 is a highly potent inhibitor of HIV-1 proteinase in phase III clinical trials for treatment of AIDS. It is also the first subnanomolar inhibitor that demonstrated reversed stereochemical preference at the central hydroxyl group. Free energy perturbation calculations have been carried out to rationalize the preference for the R-diastereomer by consideration of two models of the (weaker) S-diastereomer. In the first model, the central hydroxyl group makes only one hydrogen bond with the active site aspartates, whereas the hydroxyl group in the second model makes at least three strong hydrogen bonds. Using the first model, the free energy difference in binding of Ro 31-8959 and its S-diastereomer is calculated to be 3.4 kcal/mol, which is in close agreement with the experimental value. Although the second model has a more favorable interaction with the active site aspartates compared to the first model, it has a higher energy N-axial conformation at the decahydroisoquinoline group in P. We show here that the two contributions cancel each other and the two models of S-diastereomer are predicted to have equivalent binding. The stereochemical preference in a hydroxyethylamine series of inhibitors appears to be affected by both intermolecular and intramolecular (conformational) energies. The binding data on the proline containing inhibitors are rationalized based on these results. © 1994 by John Wiley & Sons, Inc.     

Comparative molecular field analysis and energy interaction studies of thrombin-inhibitor complexes

A Comparative Molecular Field Analysis (CoMFA) and an interaction energy-based method were applied on a database holding the 3D structures of 29 thrombin-inhibitor complexes. Several parameters were optimized in both methods in order to obtain the best correlation between theoretical and experimentally determined binding (Ki) data. CoMFA, which only uses the information of the inhibitors, performed best (r = 0.99, q2 = 0.46, N = 29) when HF 6-31G charges were used in combination with a pharmacophore-based alignment. Inclusion of hydrophobic fields did not lead to improvements. The interaction energy-based approach uses the information of the whole thrombin-inhibitor complex. A statistically significant correlation (r = 0.74, N = 14) could only be obtained for a subset of the database containing the high resolution structures. Geometry optimization of the ligand only in combination with downscaled electrostatics performed best.     

Linear free energy relations and solvent effects for complexes ofm-cresol and various bases

The enthalpies, entropies, and equilibrium constants for the hydrogen bonded complexes of m-cresol with ten bases in cyclohexane solvent have been determined by calorimetric and spectroscopic methods. The logarithm of the equilibrium constant correlates well with the dipole moment of the base and the solvatochromic parameter which measures the electron donating ability of the base. The enthalpy and entropy data show that the dipole term does not enter into the log K correlation as a consequence of electrostatic interactions between acid and base in the complex. The free base-solvent interaction, which appears to be dipolar in origin, reduces the entropy of the free base and hence contributes to a favorable entropy change for complex formation. The present data are compared to previously reported data obtained in CCl₄ solvent. Solvent effects on the thermodynamic parameters in CCl₄ and cyclohexane appear to be related to dipolar interactions by m-cresol and the bases with the two solvents.     

Spectral studies and crystal structures of molybdenum(VI) complexes containing pyridine or picoline as auxiliary ligands: interaction energy calculations and free radical scavenging studies

Transition Metal Chemistry - Three cis-MoO2 complexes [MoO2(CAB)(py)] (1), [MoO2(CAB)(3-pic)] (2) and [MoO2(CAB)(4-pic)] (3) which vary in the nature of the heterocyclic bases in...     

Molecular recognition in cyclodextrin complexes of amino acid derivatives. 1. Crystallographic studies of beta-cyclodextrin complexes with N-acetyl-L-phenylalanine methyl ester and N-acetyl-L-phenylalanine amide pseudopeptides

Cyclodextrins (CDs) are widely utilized in studies of chiral and molecular recognition. By changing the functionality of the guest molecule, the effect of such changes on recognition by the host CD molecule can be examined. We report crystal structure determinations for two nearly isomorphous complexes of phenylalanine derivatives: beta-CD/N-acetyl-L-phenylalanine methyl ester and beta-CD/N-acetyl-L-phenylalanine amide. The complexes crystallize as hydrated head-to-head host dimers with two included guest molecules in space group P1. The crystal packing is such that it presents a nonconstraining hydrophobic pocket adjacent to a hydrophilic region, where potential hydrogen-bonding interactions with hydroxyl groups of neighboring cyclodextrin molecules and waters of hydration can occur. The two host molecules display very similar conformations; only a few of the primary hydroxyl groups are conformationally disordered. There are a number of changes in the location of water of hydration molecules, some of which are the result of different hydrogen-bonding interactions. For the different guest molecules, similar modes of penetration are observed in the CD torus; however, there is a 0.985-A shift in the position of the guest molecules in the host torus, which takes place without changing the hydrophobic interactions displayed by the phenyl side chains. This observation and the thermal motion of the guest molecules in the ester complex are taken as evidence that complex binding forces are weak. The pseudopeptides experience a significant degree of flexibility in the crystalline environment provided by CD dimers. Conformational differences of the pseudopeptide backbones and the presence of disordered water molecules in the host-guest interface provide examples of different hydrogen-bonding schemes of similar potential energy. The crystal system presents an opportunity to establish a database of molecular interactions for small peptides and peptide analogues with waters of hydration and functional groups in nonconstraining binding environments.     

Computational studies on pseudorotaxanes by molecular dynamics and free energy perturbation simulations

A computational scheme that comprises the utilization of the AMBER force field with RESP charges and an explicit solvent model for acetonitrile proved to be useful for studying the structures and energetics of pseudorotaxanes of benzidine and 4,4'-biphenol with cyclobis(paraquat-p-phenylene). The scheme can be further utilized for modeling [2]rotaxanes.     

Molecular complexes of ketaconazole and oxatomide with p-chloranil: spectroscopic and spectrofluorimetric studies

The molecular complexes of the donors ketaconazole (KTZ) and oxatomide (OXA) drugs with 2,3,5,6-tetrachloro-1,4-benzoquinone (p-chloranil, p-CHL) have been investigated spectroscopically (UV-vis, FT-IR and 1H NMR) and spectrofluorimetrically in different solvents and temperatures. The stoichiometry of the complexes was found to be 1:1. The data are discussed in terms of formation constant, molar extinction coefficient, oscillator strength, dipole moment, ionization potential, dissociation energy and thermodynamic parameters. The results indicated that the formation of molecular complex is spontaneous and endothermic. The fluorescence quenching studies indicated that the interaction of the donors is spontaneous and the fluorescence quenching increased with an increase in the intensity of complexation with the acceptor.