Evaluation of protein-ligand binding free energy focused on its entropic components

The binding free energy for FK506-binding protein-ligand systems is evaluated as a sum of two entropic components, the water-entropy gain, and the configurational-entropy loss for the protein and ligand molecules upon the binding. The two entropic components are calculated using morphometric thermodynamics combined with a statistical-mechanical theory for molecular liquids and the normal mode analysis, respectively. We find that there is an excellent correlation between the calculated and experimental values of the binding free energy. This result is compared with those of several other binding-free energy calculation methods, including MM-PB/SA. The binding can well be elucidated by competition of the two entropic components. Upon the protein-ligand binding, the total volume available to the translational displacement of the coexisting water molecules increases, leading to an increase in the number of accessible configurations of the water. The water-entropy gain, by which the binding is driven, originates primarily from this effect. This study sheds new light on the theoretical prediction of the protein-ligand binding free energy.     

Further development and validation of empirical scoring functions for structure-based binding affinity prediction

New empirical scoring functions have been developed to estimate the binding affinity of a given protein-ligand complex with known three-dimensional structure. These scoring functions include terms accounting for van der Waals interaction, hydrogen bonding, deformation penalty, and hydrophobic effect. A special feature is that three different algorithms have been implemented to calculate the hydrophobic effect term, which results in three parallel scoring functions. All three scoring functions are calibrated through multivariate regression analysis of a set of 200 protein-ligand complexes and they reproduce the binding free energies of the entire training set with standard deviations of 2.2 kcal/mol, 2.1 kcal/mol, and 2.0 kcal/mol, respectively. These three scoring functions are further combined into a consensus scoring function, X-CSCORE. When tested on an independent set of 30 protein-ligand complexes, X-CSCORE is able to predict their binding free energies with a standard deviation of 2.2 kcal/mol. The potential application of X-CSCORE to molecular docking is also investigated. Our results show that this consensus scoring function improves the docking accuracy considerably when compared to the conventional force field computation used for molecular docking.     

Computational prediction of monosaccharide binding free energies to lectins with linear interaction energy models

The linear interaction energy (LIE) method to compute binding free energies is applied to lectin‐monosaccharide complexes. Here, we calculate the binding free energies of monosaccharides to the Ralstonia solanacearum lectin (RSL) and the Pseudomonas aeruginosa lectin‐II (PA‐IIL). The standard LIE model performs very well for RSL, whereas the PA‐IIL system, where ligand binding involves two calcium ions, presents a major challenge. To overcome this, we explore a new variant of the LIE model, where ligand–metal ion interactions are scaled separately. This model also predicts the saccharide binding preference of PA‐IIL on mutation of the receptor, which may be useful for protein engineering of lectins. © 2012 Wiley Periodicals, Inc.     

Methods for the prediction of protein-ligand binding sites for structure-based drug design and virtual ligand screening

Structure Based Drug Design (SBDD) is a computational approach to lead discovery that uses the three-dimensional structure of a protein to fit drug-like molecules into a ligand binding site to modulate function. Identifying the location of the binding site is therefore a vital first step in this process, restricting the search space for SBDD or virtual screening studies. The detection and characterisation of functional sites on proteins has increasingly become an area of interest. Structural genomics projects are increasingly yielding protein structures with unknown functions and binding sites. Binding site prediction was pioneered by pocket detection, since the binding site is often found in the largest pocket. More recent methods involve phylogenetic analysis, identifying structural similarity with proteins of known function and identifying regions on the protein surface with a potential for high binding affinity. Binding site prediction has been used in several SBDD projects and has been incorporated into several docking tools. We discuss different methods of ligand binding site prediction, their strengths and weaknesses, and how they have been used in SBDD.     

The influence of variations of ligand protonation and tautomerism on protein-ligand recognition and binding energy landscape

We investigate the influence of variations of ligand protonation and tautomeric states on the protein-ligand binding energy landscape by applying the concept of structural consensus. In docking simulations, allowing full flexibility of the ligand, we explore whether the native binding mode could be successfully recovered using a non-native ligand protonation state. Here, we consider three proteins, dihydrofolate reductase, transketolase, and alpha-trichosanthin, complexed with ligands having multiple tautomeric forms. We find that for the majority of protonation and tautomeric states the native binding mode can be recovered without a great loss of accuracy.     

Role of binding entropy in the refinement of protein-ligand docking predictions: analysis based on the use of 11 scoring functions

We present results of testing the ability of eleven popular scoring functions to predict native docked positions using a recently developed method (Ruvinsky and Kozintsev, J Comput Chem 2005, 26, 1089) for estimation the entropy contributions of relative motions to protein-ligand binding affinity. The method is based on the integration of the configurational integral over clusters obtained from multiple docked positions. We use a test set of 100 PDB protein-ligand complexes and ensembles of 101 docked positions generated by (Wang et al. J Med Chem 2003, 46, 2287) for each ligand in the test set. To test the suggested method we compared the averaged root-mean square deviations (RMSD) of the top-scored ligand docked positions, accounting and not accounting for entropy contributions, relative to the experimentally determined positions. We demonstrate that the method increases docking accuracy by 10-21% when used in conjunction with the AutoDock scoring function, by 2-25% with G-Score, by 7-41% with D-Score, by 0-8% with LigScore, by 1-6% with PLP, by 0-12% with LUDI, by 2-8% with F-Score, by 7-29% with ChemScore, by 0-9% with X-Score, by 2-19% with PMF, and by 1-7% with DrugScore. We also compared the performance of the suggested method with the method based on ranking by cluster occupancy only. We analyze how the choice of a clustering-RMSD and a low bound of dense clusters impacts on docking accuracy of the scoring methods. We derive optimal intervals of the clustering-RMSD for 11 scoring functions.     

Estimation of relative binding free energy based on a free energy variational principle for the FKBP-ligand system

Predicting an accurate binding free energy between a target protein and a ligand can be one of the most important steps in a drug discovery process. Often, many molecules must be screened to find probable high potency ones. Thus, a computational technique with low cost is highly desirable for the estimation of binding free energies of many molecules. Several techniques have thus far been developed for estimating binding free energies. Some techniques provide accurate predictions of binding free energies but high large computational cost. Other methods give good predictions but require tuning of some parameters to predict them with high accuracy. In this study, we propose a method to predict relative binding free energies with accuracy comparable to the results of prior methods but with lower computational cost and with no parameter needing to be carefully tuned. Our technique is based on the free energy variational principle. FK506 binding protein (FKBP) with 18 ligands is taken as a test system. Our results are compared to those from other widely used techniques. Our method provides a correlation coefficient (r ² ) of 0.80 between experimental and calculated relative binding free energies and yields an average absolute error of 0.70 kcal/mol compared to experimental values. These results are comparable to or better than results from other techniques. We also discuss the possibility to improve our method further.     

Empirical scoring functions. II. The testing of an empirical scoring function for the prediction of ligand-receptor binding affinities and the use of Bayesian regression to improve the quality of the model

This paper tests the performance of a simple empirical scoring function on a set of candidate designs produced by a de novo design package. The scoring function calculates approximate ligand-receptor binding affinities given a putative binding geometry. To our knowledge this is the first substantial test of an empirical scoring function of this type on a set of molecular designs which were then subsequently synthesised and assayed. The performance illustrates that the methods used to construct the scoring function and the reliance on plausible, yet potentially false, binding modes can lead to significant over-prediction of binding affinity in bad cases. This is anticipated on theoretical grounds and provides caveats on the reliance which can be placed when using the scoring function as a screen in the choice of molecular designs. To improve the predictability of the scoring function and to understand experimental results, it is important to perform subsequent Quantitative Structure-Activity Relationship (QSAR) studies. In this paper, Bayesian regression is performed to improve the predictability of the scoring function in the light of the assay results. Bayesian regression provides a rigorous mathematical framework for the incorporation of prior information, in this case information from the original training set, into a regression on the assay results of the candidate molecular designs. The results indicate that Bayesian regression is a useful and practical technique when relevant prior knowledge is available and that the constraints embodied in the prior information can be used to improve the robustness and accuracy of regression models. We believe this to be the first application of Bayesian regression to QSAR analysis in chemistry.     

VISCANA: visualized cluster analysis of protein-ligand interaction based on the ab initio fragment molecular orbital method for virtual ligand screening

We have developed a visualized cluster analysis of protein-ligand interaction (VISCANA) that analyzes the pattern of the interaction of the receptor and ligand on the basis of quantum theory for virtual ligand screening. Kitaura et al. (Chem. Phys. Lett. 1999, 312, 319-324.) have proposed an ab initio fragment molecular orbital (FMO) method by which large molecules such as proteins can be easily treated with chemical accuracy. In the FMO method, a total energy of the molecule is evaluated by summation of fragment energies and interfragment interaction energies (IFIEs). In this paper, we have proposed a cluster analysis using the dissimilarity that is defined as the squared Euclidean distance between IFIEs of two ligands. Although the result of an ordered table by clustering is still a massive collection of numbers, we combine a clustering method with a graphical representation of the IFIEs by representing each data point with colors that quantitatively and qualitatively reflect the IFIEs. We applied VISCANA to a docking study of pharmacophores of the human estrogen receptor alpha ligand-binding domain (57 amino acid residues). By using VISCANA, we could classify even structurally different ligands into functionally similar clusters according to the interaction pattern of a ligand and amino acid residues of the receptor protein. In addition, VISCANA could estimate the correct docking conformation by analyzing patterns of the receptor-ligand interactions of some conformations through the docking calculation.     

Quantum chemical study on the interaction of some bisphosphonates and Ca2+: The role of molecular electrostatic potentials in the prediction of binding geometry

Summary Molecular electrostatic potentials have been used to model the calcium binding properties of some bisphosphonate drugs, which are used to treat various bone diseases. The mechanism of action involves the binding of bisphosphonates to the bone surface, where calcium plays an important role. Electrostatic potential maps derived from ab initio partial charges have been compared with both the crystal structure and the fully optimized ab initio structure of (dichloro)methylenebisphosphonate-calcium ion complex. Molecular electrostatic potentials can correctly predict the calcium binding geometry of bisphosphonate-type compounds and this type of information can be used in the practical drug design work.     

Evaluation of effective core potentials and basis sets for the prediction of the geometries of alkyltin halides

A systematic comparison of the optimized geometries of five organotin compounds, Cl(n)Sn(CH(3))(4-n), n = 0-4, with the available gas-phase electron diffraction results is reported. All optimizations were carried out with the B3LYP density functional method. Comparison of 10 basis sets and three effective core potentials leads to the conclusion that the combination of the SDB-aug-cc-pVTZ basis set and the LANL2 effective core potential for tin, together with the 6-31G(d,p) basis set for the other atoms, is recommended for the prediction of the geometries of organotin compounds.     

Evaluation of binary QSAR models derived from LUDI and MOE scoring functions for structure based virtual screening

In today's world of high-throughput in silico screening, the development of virtual screening methodologies to prioritize small molecules as new chemical entities (NCEs) for synthesis is of current interest. Among several approaches to virtual screening, structure-based virtual screening has been considered the most effective. However the problems associated with the ranking of potential solutions in terms of scoring functions remains one of the major bottlenecks in structure-based virtual screening technology. It has been suggested that scoring functions may be used as filters for distinguishing binders from nonbinders instead of accurately predicting their binding free energies. Subsequently, several improvements have been made in this area, which include the use of multiple rather than single scoring functions and application of either consensus or multivariate statistical methods or both to improve the discrimination between binders and nonbinders. In view of it, the discriminative ability (distinguishing binders from nonbinders) of binary QSAR models derived using LUDI and MOE scoring functions has been compared with the models derived by Jacobbsson et al. on five data sets viz. estrogen receptor alphamimics (ERalpha_mimics), estrogen receptor alphatoxins (ERalpha_toxins), matrix metalloprotease 3 inhibitors (MMP-3), factor Xa inhibitors (fXa), and acetylcholine esterase inhibitors (AChE). The overall analyses reveal that binary QSAR is comparable to the PLS discriminant analysis, rule-based, and Bayesian classification methods used by Jacobsson et al. Further the scoring functions implemented in LUDI and MOE can score a wide range of protein-ligand interactions and are comparable to the scoring functions implemented in ICM and Cscore. Thus the binary QSAR models derived using LUDI and MOE scoring functions may be useful as a preliminary screening layer in a multilayered virtual screening paradigm.     

Evaluation of Gibbs free energy for the transfer of a highly hydrophilic ion from an acidic aqueous solution to an organic solution based on ion pair extraction

A method to determine the standard Gibbs free energy for the transfer, ΔG°_tr, of a highly hydrophilic metal ion from an aqueous solution, W, in the presence of high concentration of H⁺ to an organic solution, O, was proposed based on the theoretical consideration of the distribution process of ions between W and O. The usefulness of the proposed method was verified experimentally by comparing ΔG°_tr of Mg²⁺ determined by the method with that obtained by voltammetry for the ion transfer at the W|O interface. The O examined were nitrobenzene (NB) and 1,2-dichloroethane (DCE). By applying the proposed method, ΔG°_tr of NpO₂⁺, UO₂²⁺, NpO₂²⁺ and PuO₂²⁺ from an acidic W to NB were determined.     

Evaluation of PM3, AM1, and MNDO for calculation of higher energy ionization potentials

Higher ionization energies were calculated with PM3, AM1, and MNDO for three series of molecules, representative small molecules, molecules containing heteroatoms, and sterically congested alkenes. Values from PM3, AM1, and MNDO were compared to experimental values. In most instances, the semiempirical calculations correctly predict the ordering of higher ionization energies. In the absence of steric hindrance, MNDO is the method of choice. Within groups of molecules, AM1 performs better on hydrocarbons, especially twisted hydrocarbons, than PM3. PM3 commonly gives sigma orbitals which are too high in energy compared to related pi orbitals. PM3 performed better than AM1 with molecules containing oxygen, but failed to give the correct geometry for hydrogen peroxide.     

Influence of size,ellipticity and charge separation on the free energy of some aqueous bolaform electrolyte models

The free energy of some models of aqueous bolaform electrolytes have been calculated at the Debye-Hückel limiting law plus B ₂ level of approximation. The repulsive forces are modeled by hard spheres or hard ellipsoids. The charges are placed either at the center of the sphere or at the foci of the ellipsoid. Parameters were chosen to approximate the size and shape of sodium and calcium p-benzenedisufonate and sodium 4,4-biphenyldisulfonate. The results show that contrary to the standard explanations for the unusual properties of bolaform electrolytes, separating the charges has little effect on the excess free energy. It is also shown that changing from a sphere to an ellipse has little effect on the excess free energy. The most important determinates of the properties of these salts are the sizes of the ions. Agreement of the model calculations with experimental results is reasonable considering the simplicity of the models.