Semiempirical calculations of binding enthalpy for protein–ligand complexes

A systematic semiempirical quantum mechanical study of the interactions between proteins and ligands has been performed to determine the ability of this approach for the accurate estimation of the enthalpic contribution to the binding free energy of the protein–ligand systems. This approach has been applied for eight test protein–ligand complexes with experimentally known binding enthalpies. The calculations were performed using the semiempirical PM3 approach incorporated in the MOPAC 97, ZAVA originally elaborated in Algodign, and MOPAC 2002 with MOZYME facility packages. Special attention was paid to take into account structural water molecules, which were located in the protein–ligand binding site. It was shown that the results of binding enthalpy calculations fit experimental data within ～2 kcal/mol in the presented approach. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Prediction of trypsin/molecular fragment binding affinities by free energy decomposition and empirical scores

Two families of binding affinity estimation methodologies are described which were utilized in the SAMPL3 trypsin/fragment binding affinity challenge. The first is a free energy decomposition scheme based on a thermodynamic cycle, which included separate contributions from enthalpy and entropy of binding as well as a solvent contribution. Enthalpic contributions were estimated with PM6-DH2 semiempirical quantum mechanical interaction energies, which were modified with a statistical error correction procedure. Entropic contributions were estimated with the rigid-rotor harmonic approximation, and solvent contributions to the free energy were estimated with several different methods. The second general methodology is the empirical score LISA, which contains several physics-based terms trained with the large PDBBind database of protein/ligand complexes. Here we also introduce LISA+, an updated version of LISA which, prior to scoring, classifies systems into one of four classes based on a ligand's hydrophobicity and molecular weight. Each version of the two methodologies (a total of 11 methods) was trained against a compiled set of known trypsin binders available in the Protein Data Bank to yield scaling parameters for linear regression models. Both raw and scaled scores were submitted to SAMPL3. Variants of LISA showed relatively low absolute errors but also low correlation with experiment, while the free energy decomposition methods had modest success when scaling factors were included. Nonetheless, re-scaled LISA yielded the best predictions in the challenge in terms of RMS error, and six of these models placed in the top ten best predictions by RMS error. This work highlights some of the difficulties of predicting binding affinities of small molecular fragments to protein receptors as well as the benefit of using training data.     

胶束催化的假相理论模型

介绍并比较了胶束催化的理论模型：假阳离子交换（Ｐｓｅｕｄｏｐｈａｓｅ ｉｏｎ ｅｘｃｈａｎｇｅ,ＰＩＥ）模型和Ｐｏｉｓｓｏｎ－Ｂｏｌｔｚｅｍａｎｎ方程（ＰＢＥ）模型,ＰＩＥ模型通过计算各反应物在两相间的分配,成功地解释了总一级反应速率常数ｋ１随各参数的变化和胶束表面的反离子竞争结合。ＰＢＥ模型完善了ＰＩＥ模型,考虑了胶束的尺寸和分布,胶束与离子间的静电作用和其它特殊作用,可解释一些ＰＩＥ模型无法解释的实验现象。     

Receptor-independent 4D-QSAR analysis of a set of norstatine derived inhibitors of HIV-1 protease

A training set of 27 norstatine derived inhibitors of HIV-1 protease, based on the 3(S)-amino-2(S)-hydroxyl-4-phenylbutanoic acid core (AHPBA), for which the -log IC(50) values were measured, was used to construct 4D-QSAR models. Five unique RI-4D-QSAR models, from two different alignments, were identified (q(2) = 0.86-0.95). These five models were used to map the atom type morphology of the lining of the inhibitor binding site at the HIV protease receptor site as well as predict the inhibition potencies of seven test set compounds for model validation. The five models, overall, predict the -log IC(50) activity values for the test set compounds in a manner consistent with their q(2) values. The models also correctly identify the hydrophobic nature of the HIV protease receptor site, and inferences are made as to further structural modifications to improve the potency of the AHPBA inhibitors of HIV protease. The finding of five unique, and nearly statistically equivalent, RI-4D-QSAR models for the training set demonstrates that there can be more than one way to fit structure-activity data even within a given QSAR methodology. This set of unique, equally good individual models is referred to as the manifold model.     

POEM: Parameter Optimization using Ensemble Methods: application to target specific scoring functions

In computational biology processes such as docking, binding, and folding are often described by simplified, empirical models. These models are fitted to physical properties of the process by adjustable parameters. An appropriate choice of these parameters is crucial for the quality of the models. Locating the best choices for the parameters is often is a difficult task, depending on the complexity of the model. We describe a new method and program, POEM (Parameter Optimization using Ensemble Methods), for this task. In POEM we combine the DOE (Design Of Experiment) procedure with ensembles of different regression methods. We apply the method to the optimization of target specific scoring functions in molecular docking. The method consists of an iterative procedure that uses alternate evaluation and prediction steps. During each cycle of optimization we fit an approximate function to a defined loss function landscape and improve the quality of this fit from cycle to cycle by constantly augmenting our data set. As test applications we fitted the FlexX and Screenscore scoring functions to the kinase and ATPase protein classes. The results are promising: Starting from random parameters we are able to locate parameter sets which show superior performance compared to the original values. The POEM approach converges quickly and the approximated loss function landscapes are smooth, thus making the approach a suitable method for optimizations on rugged landscapes.     

Mixed implicit/explicit solvation models in quantum mechanical calculations of binding enthalpy for protein–ligand complexes

An approach to quantum mechanical investigation of interactions in protein–ligand complexes has been developed that treats the solvation effect in a mixed scheme combining implicit and explicit solvent models. In this approach, the first solvation shell of the solvent around the solute is modeled with a limited number of hydrogen bonded explicit solvent molecules. The influence of the remaining bulk solvent is treated as a surrounding continuum in the conductor‐like screening model (COSMO). The enthalpy term of the binding free energy for the protein–ligand complexes was calculated using the semiempirical PM3 method implemented in the MOPAC package, applied to a trimmed model of the protein–ligand complex constructed with special rules. The dependence of the accuracy of binding enthalpy calculations on size of the trimmed model and number of optimized parameters was evaluated. Testing of the approach was performed for 12 complexes of different ligands with trypsin, thrombin, and ribonuclease with experimentally known binding enthalpies. The root‐mean‐square deviation (RMSD) of the calculated binding enthalpies from experimental data was found as ～1 kcal/mol over a large range. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Prediction of properties from simulations: a re-examination with modern statistical methods

We discuss models fit to data collected by Duffy and Jorgensen to predict solvation free energies and partition equilibria of drugs, organic molecules, aromatic heterocycles, and other molecules. These data were originally examined using linear regression, but here more recently developed statistical models are applied. The data set is complicated due to the presence of discrepant observations and also curvature in the response. In some cases it is possible to discard a small number of the observations to get good fit to the data, but, in others, discarding an increasing proportion of the observations does not improve the fit. Our general preference is to use robust parameter estimation which downweights to reduce the influence of discrepant observations on the fitted models. Models are selected for four responses using linear or more complicated representations of the explanatory variables, such as cubic polynomials, B-splines, or smoothers via generalized additive models (GAMs). Variables are chosen using the traditional approach of formal tests to assess contribution to the fit of a model, and resampling methods including bootstrap are also considered to assess the prediction error for given models. Results of our analysis indicate that GAMs are an improvement on linear models for describing the data and making predictions. In general robust regression models and GAMs have the smallest conditional expected loss of prediction over the four responses. In addition, robust regression models offer the advantage of identifying molecules that perform poorly in the fit. In general, models were identified that yielded an improvement of approximately 50% in the conditional expected loss of prediction compared with the original parametrization of Duffy and Jorgensen. It was also found that the use of cross-validation to compare models was unreliable, and bootstrapping is preferred.     

应用机器学习方法构建药物分子解离速率常数的预测模型

越来越多的研究表明:药物分子与靶标分子的结合动力学性质与其在体内的药效有很强的相关性。因此,以改善结合动力学性质为导向的分子设计为药物研发提供了新的思路。本工作的研究目标在于得出预测药物分子解离速率常数(koff)的通用型定量结构-动力学关系(QSKR)模型。我们从文献中收集了406个配体分子的解离速率常数实验值,采用分子模拟方法构建了所有配体与靶蛋白复合物的三维结构模型。然后基于蛋白-配体原子对描述符,采用随机森林算法来构建预测配体分子解离速率常数的QSKR模型。通过探索不同条件(如距离区间,划分区间宽度和特征选择标准)下产生的描述符集合对模型预测精度的影响,确定当采用距离阈值为15?、划分区间宽度为3?、特征选择方差水平为2时得到的QSKR模型为最优,在两个独立测试集上获得良好的预测精度(相关系数为0.62)。本工作对预测药物分子解离速率常数这一关键科学问题进行了有益的探索,可为后续研究提供思路。     

3D QSAR and molecular docking studies of benzimidazole derivatives as hepatitis C virus NS5B polymerase inhibitors

The urgent need for novel HCV antiviral agents has provided an impetus for understanding the structural requisites of NS5B polymerase inhibitors at the molecular level. Toward this objective, comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA) of 67 HCV NS5B polymerase inhibitors were performed using two methods. First, ligand-based 3D QSAR studies were performed based on the lowest energy conformations employing the atom fit alignment method. Second, receptor-based 3D QSAR models were derived from the predicted binding conformations obtained by docking all NS5B inhibitors at the allosteric binding site of NS5B (PDB ID: 2dxs). Results generated from the ligand-based model were found superior (r2cv values of 0.630 for CoMFA and 0.668 for CoMSIA) to those obtained by the receptor-based model (r2cv values of 0.536 and 0.561 for CoMFA and CoMSIA, respectively). The predictive ability of the models was validated using a structurally diversified test set of 22 compounds that had not been included in a preliminary training set of 45 compounds. The predictive r2 values for the ligand-based CoMFA and CoMSIA models were 0.734 and 0.800, respectively, while the corresponding predictive r2 values for the receptor-based CoMFA and CoMSIA models were 0.538 and 0.639, respectively. The greater potency of the tryptophan derivatives over that of the tyrosine derivatives was interpreted based on CoMFA steric and electrostatic contour maps. The CoMSIA results revealed that for a NS5B inhibitor to have appreciable inhibitory activity it requires hydrogen bond donor and acceptor groups at the 5-position of the indole ring and an R substituent at the chiral carbon, respectively. Interpretation of the CoMFA and CoMSIA contour maps in context of the topology of the allosteric binding site of NS5B provided insight into NS5B-inhibitor interactions. Taken together, the present 3D QSAR models were found to accurately predict the HCV NS5B polymerase inhibitory activity of structurally diverse test set compounds and to yield reliable clues for further optimization of the benzimidazole derivatives in the data set.     

Charge regulation in protein ion-exchange chromatography: development and experimental evaluation of a theory based on hydrogen ion Donnan equilibrium

An extension of the stoichiometric displacement (SD) model for the ion-exchange adsorption of dilute proteins is developed which accounts for the effects of hydrogen ion Donnan equilibrium on the protein charge. The ability of the new model to fit retention data when the fluid phase pH is near the protein pI and the effects of hydrogen ion Donnan equilibrium are important is examined using four different proteins and four different column packings. The results indicate that the model is able to fit retention data using values for the protein pI and the change in protein charge with pH at the pI, i.e., (dz/dpH)pI, that are significantly closer to the values of these parameters determined by isoelectric focusing and acid-base titrametry in free solution, respectively, as compared to the values obtained by determining the characteristic binding change as a function of pH using the traditional stoichiometric displacement model. This suggests that when the fluid phase pH is near the protein pI, charge regulation is an important cause of the discrepancy between the electrical charge of a protein in free solution and the characteristic binding charge from the stoichiometric displacement model. The results also indicate that for the case where the fluid phase pH is near the protein pI, the new model accounts for the effect of charge regulation during protein ion-exchange adsorption more accurately than previous models in the literature.     

Experimental versus predicted affinities for ligand binding to estrogen receptor: iterative selection and rescoring of docked poses systematically improves the correlation

The computational determination of binding modes for a ligand into a protein receptor is much more successful than the prediction of relative binding affinities (RBAs) for a set of ligands. Here we consider the binding of a set of 26 synthetic A-CD ligands into the estrogen receptor ERα. We show that the MOE default scoring function (London dG) used to rank the docked poses leads to a negligible correlation with experimental RBAs. However, switching to an energy-based scoring function, using a multiple linear regression to fit experimental RBAs, selecting top-ranked poses and then iteratively repeating this process leads to exponential convergence in 4–7 iterations and a very strong correlation. The method is robust, as shown by various validation tests. This approach may be of general use in improving the quality of predicted binding affinities.     

Formal Estimation of Errors in Computed Absolute Interaction Energies of Protein-ligand Complexes

A largely unsolved problem in computational biochemistry is the accurate prediction of binding affinities of small ligands to protein receptors. We present a detailed analysis of the systematic and random errors present in computational methods through the use of error probability density functions, specifically for computed interaction energies between chemical fragments comprising a protein-ligand complex. An HIV-II protease crystal structure with a bound ligand (indinavir) was chosen as a model protein-ligand complex. The complex was decomposed into twenty-one (21) interacting fragment pairs, which were studied using a number of computational methods. The chemically accurate complete basis set coupled cluster theory (CCSD(T)/CBS) interaction energies were used as reference values to generate our error estimates. In our analysis we observed significant systematic and random errors in most methods, which was surprising especially for parameterized classical and semiempirical quantum mechanical calculations. After propagating these fragment-based error estimates over the entire protein-ligand complex, our total error estimates for many methods are large compared to the experimentally determined free energy of binding. Thus, we conclude that statistical error analysis is a necessary addition to any scoring function attempting to produce reliable binding affinity predictions.     

On the use of semiempirical models of (solid + supercritical fluid) systems to determine solid sublimation properties

Experimental solubility data of solid–supercritical fluids have significantly increased in the last few years, and semiempirical models are emerging as one of the best choices to fit this type of data. This work establishes a methodology to calculate sublimation pressures using this type of equations. It requires the use of Bartle’s equation to model equilibria data solid–supercritical fluids with the aim of determining the vaporization enthalpy of the compound. Using this method, low deviations were obtained by calculating sublimation pressures and sublimation enthalpies. The values of the sublimation pressures were subsequently used to successfully model different multiphasic equilibria, as solid–supercritical fluids and solid–solvent–supercritical fluids with the Peng–Robinson equation of state (without considering the sublimation pressure as an adjustable parameter). On the other hand, the sublimation pressures were also used to calculate solid sublimation properties and acetaminophen solvation properties in some solvents. Also, solubility data solid–supercritical fluids from 62 pharmaceuticals were fitted with different semiempirical equations (Chrastil, Kumar-Johnston and Bartle models) in order to present the values of solvation enthalpies in sc-CO₂ and vaporization enthalpies for these compounds. All of these results highlight that semiempirical models can be used for any other purpose as well as modeling (solid + supercritical fluids) equilibria.