An extended version of a novel method for the estimation of partition coefficients

Lipophilicity in drug design: an overview of lipophilicity descriptors in 3D-QSAR studies

The pharmacophore concept is a fundamental cornerstone in drug discovery, playing a critical role in determining the success of in silico techniques, such as virtual screening and 3D-QSAR studies. The reliability of these approaches is influenced by the quality of the physicochemical descriptors used to characterize the chemical entities. In this context, a pivotal role is exerted by lipophilicity, which is a major contribution to host-guest interaction and ligand binding affinity. Several approaches have been undertaken to account for the descriptive and predictive capabilities of lipophilicity in 3D-QSAR modeling. Recent efforts encode the use of quantum mechanical-based descriptors derived from continuum solvation models, which open novel avenues for gaining insight into structure-activity relationships studies.

A Simple, Robust and Efficient Computational Method for n-Octanol/Water Partition Coefficients of Substituted Aromatic Drugs

In this paper, multiple linear regression (MLR) was used to build quantitative structure property relationship (QSPR) of n-octanol-water partition coefficient (logP_o/w) of 195 substituted aromatic drugs. The molecular descriptors were calculated for each compound by the VLifeMDS. By applying genetic algorithm/multiple linear regressions (GA/MLR) the most relevant descriptors were selected to build a QSPR model. The robustness of the model was characterized by the statistical validation and applicability domain (AD). The prediction results from MLR are in good agreement with the experimental values. The R² and Q²_LOO for MLR are 0.9433, 0.9341. The AD of the model was analyzed based on the Williams plot. The effects of different selected descriptors are described.

Lipophilicity and biomimetic properties to support drug discovery

INTRODUCTION

Lipophilicity, expressed as the octanol-water partition coefficient, constitutes the most important property in drug action, influencing both pharmacokinetic and pharmacodynamics processes as well as drug toxicity. On the other hand, biomimetic properties defined as the retention outcome on HPLC columns containing a biological relevant agent, provide a considerable advance for rapid experimental - based estimation of ADME properties in early drug discovery stages. Areas covered: This review highlights the paramount importance of lipophilicity in almost all aspects of drug action and safety. It outlines problems brought about by high lipophilicity and provides an overview of the drug-like metrics which incorporate lower limits or ranges of logP. The fundamental factors governing lipophilicity are compared to those involved in phospholipophilicity, assessed by Immobilized Artificial Membrane Chromatography (IAM). Finally, the contribution of biomimetic properties to assess plasma protein binding is evaluated. Expert opinion: Lipophilicity and biomimetic properties have important distinct and overlapping roles in supporting the drug discovery process. Lipophilicity is unique in early drug design for library screening and for the identification of the most promising compounds to start with, while biomimetic properties are useful for the experimentally-based evaluation of ADME properties for the synthesized novel compounds, supporting the prioritization of drug candidates and guiding further synthesis.

Calculating Partition Coefficients of Small Molecules in Octanol/Water and Cyclohexane/Water

Partition coefficients describe how a solute is distributed between two immiscible solvents. They are used in drug design as a measure of a solute's hydrophobicity and a proxy for its membrane permeability. We calculate partition coefficients from transfer free energies using molecular dynamics simulations in explicit solvent. Setup is done by our new Solvation Toolkit which automates the process of creating input files for any combination of solutes and solvents for many popular molecular dynamics software packages. We calculate partition coefficients between octanol/water and cyclohexane/water with the Generalized AMBER Force Field (GAFF) and the Dielectric Corrected GAFF (GAFF-DC). With similar methods in the past we found a root-mean-squared error (RMSE) of 6.3 kJ/mol in hydration free energies which would correspond to an error of around 1.6 log units in partition coefficients if solvation free energies in both solvents were estimated with comparable accuracy. Here we find an overall RMSE of about 1.2 log units with both force fields. Results from GAFF and GAFF-DC seem to exhibit systematic biases in opposite directions for calculated cyclohexane/water partition coefficients.

Molecular recognition of polycyclic aromatic hydrocarbons by pyrene-imprinted microspheres

Pyrene-imprinted microbeads that display molecular recognition towards polyaromatic hydrocarbons (PAHs) were obtained by the aqueous suspension thermopolymerization of a mixture of template, 4-vinylpyridine and divinylbenzene in the molar ratio of 1:8:40. The microbeads were packed into an HPLC column and the retention behaviour of pyrene in the presence of eluents of increasing polarity was investigated by measuring the binding capacity and the imprinting factor. Selectivity was evaluated by eluting pyrene and 22 other related PAHs in the HPLC column when equilibrated with acetonitrile-dichloromethane 4:1 (v/v). Twelve molecular descriptors were calculated for each PAH molecule: MW, the molecular weight; SAS, the solvent-accessible molecular surface area; Svdw, the van der Waals molecular surface area; Vol, the van der Waals molecular volume; MOv, the molecular ovality; RG, the radius of gyration; B/L, the breadth-to-length ratio; micro(2), the square of the total dipole moment; HOMO, the highest occupied molecular orbital; LUMO, the lowest unoccupied molecular orbital; Deltaorb, the absolute value of the difference between the HOMO and LUMO; log P, the logarithm of the n-octanol-water partition coefficient. Quantitative structure-retention relationships between the logarithm of the capacity factors and these descriptors were searched for using a multiple linear regression (MLR) method. The best regression models obtained showed that the capacity factor correlated well with those molecular descriptors which had structural character, such as logP, while the effect of the molecular descriptors with electronic character was negligible. The results obtained indicate that the molecular recognition of PAHs by the imprinted polymer is controlled by the shape and dimension of the binding sites through hydrophobic interactions.

Application of quantitative structure activity relationship (QSAR) models to predict ozone toxicity in the lung

The sequence of events leading to ozone-induced airway inflammation is not well known. To elucidate the molecular and cellular events underlying ozone toxicity in the lung, we hypothesized that lipid ozonation products (LOPs) generated by the reaction of ozone with unsaturated fatty acids in the epithelial lining fluid and cell membranes play a key role in mediating ozone-induced airway inflammation. To test our hypothesis, we ozonized 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC) and generated LOPs. Confluent human bronchial epithelial cells were exposed to the derivatives of ozonized POPC-9-oxononanoyl, 9-hydroxy-9-hydroperoxynonanoyl, and 8-(5-octyl-1,2,4-trioxolan-3-yl-)octanoyl-at a concentration of 10 muM, and the activity of phospholipases A2 (PLA2), C (PLC), and D (PLD) was measured (1, 0.5, and 1 h, respectively). Quantitative structure-activity relationship (QSAR) models were utilized to predict the biological activity of LOPs in airway epithelial cells. The QSAR results showed a strong correlation between experimental and computed activity (r = 0.97, 0.98, 0.99, for PLA2, PLC, and PLD, respectively). The results indicate that QSAR models can be utilized to predict the biological activity of the various ozone-derived LOP species in the lung.

QSPR modeling of pseudoternary microemulsions formulated employing lecithin surfactants: application of data mining, molecular and statistical modeling

Data mining, computer aided molecular modeling, descriptor calculation, genetic algorithm and multiple linear regression analysis techniques were combined together to generate predictive quantitative structure property relationship (QSPR) models explaining the formation of lecithin-based W/O microemulsions. Ninety-four microemulsion phase diagrams were collected from five different references published over the past few years. Computer-based molecular modeling techniques were then applied on the components of the collected microemulsion systems to generate corresponding plausible three-dimensional (3D) structures. The resulting 3D models were utilized to calculate a group of molecular physicochemical descriptors. Thereafter, genetic algorithm and backward stepwise regression analysis were separately assessed as means for selecting optimal descriptor sets for statistical modeling. The selected descriptors were correlated with microemulsion existence areas employing multiple linear regression analysis. The resulting W/O models were statistically validated and found to be of significant predictive power. The models allowed better understanding of the process of microemulsion formation. Unfortunately, all QSPR modeling efforts directed towards O/W microemulsions failed completely.

An application of the QM-QSAR method to predict and rationalize lipophilicity of simple monomers

OBJECTIVES

The goal of this study is to develop a model used to predict octanol/water partition coefficients (log P(o/w)) values for a variety of potential dental materials. In this way, a primary consideration for potential toxicity and a rough estimate of solubility in various environments can be obtained.

METHOD

The AM1 semiempirical quantum mechanical method (in AMPAC) was used to compute chemical data for all compounds in the study. CODESSA then imported the chemical information from AMPAC and computed a large set of informational descriptors. A quantitative structure activity relationship (QSAR) model was derived correlating experimental results from a training set of molecules with certain of the descriptors computed above.

RESULTS

A training set of 92 molecules was used to derive the QSAR model and three descriptors were obtained: the molecular surface area, the total dipole moment of the molecule, and FPSA-3 (fractional atom charge weighted partial positive surface area). Various quality indicators were also computed and all fell within acceptable ranges: R(2)=0.945; adjusted R(2)=0.943; R(cv)(2)=0.940; variance inflation factors (VIF) for the descriptors above are 1.116, 1.044, and 1.162, respectively.

SIGNIFICANCE

This QSAR model can be used to accurately and rapidly predict log P(o/w) values for a wide variety of small organic molecules, including potential dental monomers.

Prediction of physicochemical properties based on neural network modelling

The literature describing neural network modelling to predict physicochemical properties of organic compounds from the molecular structure is reviewed from the perspective of pharmaceutical research. The standard three-layer, feed-forward neural network is the technique most frequently used, although the use of other techniques is increasing. Various approaches to describe the molecular structure have been successfully used, including molecular fragments, topological indices, and descriptors calculated by semi-empirical quantum chemical methods. Some physicochemical properties, such as octanol-water partition coefficient, water solubility, boiling point and vapour pressure, have been modelled by several research groups over the years using different approaches and structurally diverse large training sets. The prediction accuracy of most models seems to be rather close to the performance of the experimental measurements, when the accuracy is assessed with a test set from the working database. Results with independent test sets have been less satisfactory. Implications of this problem are discussed.

Acute toxicity and quantitative structure-activity relationships of alpha-branched phenylsulfonyl acetates to Daphnia magna

The acute toxicity (48 h-EC50, microM) of 20 alpha-substituted phenylsulfonyl acetates was measured using Daphnia magna with a static method. On the basis of physicochemical parameters (octanol/water partition coefficient logK(ow) and aqueous solubility logS(w)), the theoretical linear solvation energy relationships (TLSER) and Charge model descriptors, QSARs were calculated for the immobilization of D. magna. For the models with the physicochemical parameters logK(ow) and logS(w), the low squared correlation coefficients indicate that hydrophobicity plays a dominant role on the toxicity and hydrophobicity is not the only factor that influences the activity of the compounds. For the TLSER model and the Charge model, the great squared correlation coefficients suggest that the models have good predictive capability. The higher activity of the compounds can be explained with the disruption of van der Waals interactions between lipid and/or protein compounds within the membrane and the possibility of the compounds to form hydrogen bonds with the receptor molecules. The models may more completely illustrate the toxicity mechanisms.

Development of quantitative structure-property relationship models for pseudoternary microemulsions formulated with nonionic surfactants and cosurfactants: application of data mining and molecular modeling

Data mining, computer-aided molecular modeling, descriptor calculation and multiple linear regression techniques were utilized to produce statistically significant and predictive models for O/W and W/O microemulsions. The literature was scanned over the last 20 years, subsequently, 68 phase diagrams from eight different references were collected. Molecular modeling techniques were then applied on the components of the microemulsion systems to generate plausible 3-D structures. Subsequently, various physicochemical descriptors were calculated based on the resulting 3-D structures. The generated descriptors were correlated with microemulsion existence areas utilizing multiple linear regression analysis (MLR). The generated models were statistically cross-validated and were found to be of significant predictive power. Furthermore, the resulting models allowed better understanding of the process of microemulsion formation.

Fuzzy ARTMAP and back-propagation neural networks based quantitative structure-property relationships (QSPRs) for octanol-water partition coefficient of organic compounds

Quantitative structure-property relationships (QSPRs) for estimating the logarithm octanol/water partition coefficients, logK(ow), at 25 degrees C were developed based on fuzzy ARTMAP and back-propagation neural networks using a heterogeneous set of 442 organic compounds. The set of molecular descriptors were derived from molecular connectivity indices and quantum chemical descriptors calculated from PM3 semiempirical MO-theory. Quantum chemical input descriptors include average polarizability, dipole moments, exchange energy, total electrostatic interaction energy, total two-center energy, and ionization potential. The fuzzy ARTMAP/QSPR performed, for a logK(ow) range of -1.6 to 7.9, with average absolute errors of 0.03 and 0.14 logK(ow) for the overall data and test sets, respectively. The optimal 12-11-1 back-propagation/QSPR model, for the same range of logK(ow), exhibited larger average absolute errors of 0.23 and 0.27 logK(ow) for the test and validation data sets, respectively, over the same range of logK(ow) values. The present results with the fuzzy ARTMAP-based QSPR are encouraging and suggest that high performance logK(ow) QSPR that encompasses a wider range of chemical groups could be developed, following the present approach, by training with a larger heterogeneous data set.

Substructure and whole molecule approaches for calculating log P

Lipophilicity is a major determinant of pharmacokinetic and pharmacodynamic properties of drug molecules. Correspondingly, there is great interest in medicinal chemistry in developing methods of deriving the quantitative descriptor of lipophilicity, the partition coefficient P, from molecular structure. Roughly, methods for calculating log P can be divided into two major classes: Substructure approaches have in common that molecules are cut into atoms (atom contribution methods) or groups (fragmental methods); summing the single-atom or fragmental contributions (supplemented by applying correction rules in the latter case) results in the final log P. Whole molecule approaches inspect the entire molecule; they use for instance molecular lipophilicity potentials (MLP), topological indices or molecular properties to quantify log P. In this review, representative members of substructure and whole molecule approaches for calculating log P are described; their advantages and shortcomings are discussed. Finally, the predictive power of some calculation methods is compared and a scheme for classifying calculation methods is proposed.

Prediction of n-octanol/water partition coefficients from PHYSPROP database using artificial neural networks and E-state indices

A new method, ALOGPS v 2.0 (http://www.lnh.unil.ch/~itetko/logp/), for the assessment of n-octanol/water partition coefficient, log P, was developed on the basis of neural network ensemble analysis of 12 908 organic compounds available from PHYSPROP database of Syracuse Research Corporation. The atom and bond-type E-state indices as well as the number of hydrogen and non-hydrogen atoms were used to represent the molecular structures. A preliminary selection of indices was performed by multiple linear regression analysis, and 75 input parameters were chosen. Some of the parameters combined several atom-type or bond-type indices with similar physicochemical properties. The neural network ensemble training was performed by efficient partition algorithm developed by the authors. The ensemble contained 50 neural networks, and each neural network had 10 neurons in one hidden layer. The prediction ability of the developed approach was estimated using both leave-one-out (LOO) technique and training/test protocol. In case of interseries predictions, i.e., when molecules in the test and in the training subsets were selected by chance from the same set of compounds, both approaches provided similar results. ALOGPS performance was significantly better than the results obtained by other tested methods. For a subset of 12 777 molecules the LOO results, namely correlation coefficient r(2)= 0.95, root mean squared error, RMSE = 0.39, and an absolute mean error, MAE = 0.29, were calculated. For two cross-series predictions, i.e., when molecules in the training and in the test sets belong to different series of compounds, all analyzed methods performed less efficiently. The decrease in the performance could be explained by a different diversity of molecules in the training and in the test sets. However, even for such difficult cases the ALOGPS method provided better prediction ability than the other tested methods. We have shown that the diversity of the training sets rather than the design of the methods is the main factor determining their prediction ability for new data. A comparative performance of the methods as well as a dependence on the number of non-hydrogen atoms in a molecule is also presented.

Simultaneous prediction of aqueous solubility and octanol/water partition coefficient based on descriptors derived from molecular structure

It has been shown that water solubility and octanol/water partition coefficient for a large diverse set of compounds can be predicted simultaneously using molecular descriptors derived solely from a two dimensional representation of molecular structure. These properties have been modelled using multiple linear regression, artificial neural networks and a statistical method known as canonical correlation analysis. The neural networks give slightly better models both in terms of fitting and prediction presumably due to the fact that they include non-linear terms. The statistical methods, on the other hand, provide information concerning the explanation of variance and allow easy interrogation of the models. Models were fitted using a training set of 552 compounds, a validation set and test set each containing 68 molecules and two separate literature test sets for solubility and partition.

Attempts of ranking in a series of synthetic nonpsychotropic cannabinoids

Dexanabinol and other synthetic 6aS-trans cannabinoids are devoid of cannabimimetic activity, as they do not have affinity toward cannabinoid receptors. On the other hand, these compound bind to the NMDA receptor and possess neuroprotective properties. A ranking of 6aS-trans cannabinoids based on their NMDA receptor binding affinity and by using a variety of calculated properties included in a fully computerized expert system has been attempted. The results of the study indicate that either the present isosteric-isoelectronic-based ranking criteria is not adequate to reproduce NMDA receptor binding or that some other members of the series rather than dexanabinol are the true lead compounds of 6aS-trans cannabinoids.

Evaluation of hydrophobic/hydrophilic balance of bile acids by comparative molecular field analysis (CoMFA)

A comparative molecular field analysis (CoMFA) model, employing standard steric and electrostatic fields, is able to predict the hydrophobic/hydrophilic balance, expressed as reverse-phase HPLC capacity factor, for a series of both naturally occurring and semi-synthetic bile acids. The very high values of cross-validated R(2) (Q(2)) demonstrate that the CoMFA method can give useful information on the hydrophobic balance of newly synthesized bile acids.

The n-octanol and n-hexane/water partition coefficient of environmentally relevant chemicals predicted from the mobile order and disorder (MOD) thermodynamics

The quantitative thermodynamic development of the mobile order and disorder theory in H-bonded liquids is extended in order to predict the partition coefficient. With respect to the classical predictive methods, the great advantage of the present approach resides in the possibility of predicting partition coefficient not only in the reference n-octanol/water partitioning system, but also in any mutually saturated two-phase system made up of two largely immiscible solvents. Constructed from the various free energy contributions encoded in the distribution process, the model furthermore provides a useful tool to understand both the origin and the factors, like the solute molar volume, that determine the partitioning of non-electrolytes between two immiscible liquid phases. From the comparison of the relative magnitude of the terms which contribute to the overall log P value, much information can also be gained concerning the variation of the partition coefficients of the same substances in different distribution systems. For example, the model has successfully been applied to the log P prediction of a number of environmentally important chemicals of varying structure, size and chemical nature in the n-octanol/water and n-hexane/water systems. Whatever the complexing or non-complexing substances studied, the hydrophobic effect always represent the driving force that rules distribution processes in the aqueous environments. As the dominant contribution to the partition coefficient in any organic/aqueous binary system, it is evidenced why hydrophobicity is usually considered to be a good measure of lipophilicity.

Soft drug design: general principles and recent applications

Soft drug design represents a new approach aimed to design safer drugs with an increased therapeutic index by integrating metabolism considerations into the drug design process. Soft drugs are new therapeutic agents that undergo predictable metabolism to inactive metabolites after exerting their therapeutic effect. Hence, they are obtained by building into the molecule, in addition to the activity, the most desired way in which the molecule is to be deactivated and detoxified. In an attempt to systematize and summarize the related work done in a number of laboratories, including ours, the present review presents an overview of the general soft drug design principles and provides a variety of specific examples to illustrate the concepts. A number of already marketed drugs, such as esmolol, remifentanil, or loteprednol etabonate, resulted from the successful application of such design principles. Many other promising drug candidates are currently under investigation in a variety of fields including possible soft antimicrobials, anticholinergics, corticosteroids, beta-blockers, analgetics, ACE inhibitors, antiarrhythmics, and others. Whenever possible, pharmacokinetic and pharmacodynamic properties are briefly summarized and compared to those of other compounds used in the same field.

Measurement and prediction of hydrophobicity parameters for highly lipophilic compounds: application of the HPLC column-switching technique to measurement of log P of diarylpyrazines

In the preparatory stage of structure-activity relationship (QSAR) studies of anti-platelet aggregant pyrazine derivatives, log P values (P: 1-octanol/water partition coefficient) of diarylpyrazines were measured by a newly developed HPLC column-switching technique. The system consists of two processes: (1) adsorption of the sample at the top end of a short precolumn, and then (2) quantifying the enriched analyte by a conventional analytical column. By using the log P values thus obtained, the correction factor for the steric hindrance caused by the vicinal diphenyl groups was estimated. The log k values (k; retention factor) were also measured with methanol-buffer (pH 7.4) eluents and related to log P. The eluent of 50% methanol content (M50) gave a good linear relationship over a wide range of log P (-0.3< log P < 5.2), indicating that log k(M50) parameter is useful for predicting the log P value.

Estimating the pKa of phenols, carboxylic acids and alcohols from semi-empirical quantum chemical methods

Quantitative structure property relationships (QSPR) for the pKa of phenols, carboxylic acids and alcohols were developed from descriptors derived from semi-empirical molecular orbital theory quantum chemical calculations. A training set of compounds were used to refine the models and a validation set of appropriate chemicals were chosen to test the models. Correlation coefficients for the estimated versus observed pKa values were 0.96 for phenols, 0.84 for non-aromatic carboxylic acids, 0.89 for benzoic acids and 0.89 for alcohols. The results obtained by the quantum chemical method are compared to results obtained from linear free energy relationships (LFER) and the merits of each approach are discussed.

The hydrophobic effect. 3. A key ingredient in predicting n-octanol-water partition coefficients

The quantitative development of the mobile order theory in H-bonded liquids is extended to predict the n-octanol/water partition coefficient (P). The log P predictive equation strictly issued from a thermodynamic treatment reduces to a simple linear volume-log P relationship whose intercept and slope encode, respectively, the solvation and entropy effects. For noncomplexing substances, the partition coefficient values result from two volume-dependent entropic contributions reflecting (a) the difference in the exchange entropy between the solute and solvent molecules in the n-octanol and water phases, and (b) the propensity difference between the two H-bonded solvents to induce a hydrophobic effect toward the solute. Although both effects increase, although with opposite signs, compared with the growing molar volume of the partitioned compound, the hydrophobic contribution always predominates favoring the transfer of the solute into the organic phase and hence increasing its partition coefficient. When dealing with complexing chemicals, the hydrophobic effect-related term, though remaining the dominant factor in most cases, is more or less counterbalanced by the formation of H-bonds between the interacting sites of the solute and the n-octanol and water solvent molecules. The log P, corrected for the substantial content of water into n-octanol, is estimated for a number of compounds of environmental and pharmaceutical interest. The extent to which the entropic and enthalpic factors affect the overall partition coefficient value is analyzed.

Computer-assisted design of new drugs based on retrometabolic concepts

Retrometabolic drug design approaches incorporate metabolic and toxicological considerations into the drug design process and represent a novel, systematic methodology for the design of safe compounds. Two major design concepts aimed to increase the therapeutic index (the activity/toxicity ratio) of drugs were developed. Chemical delivery systems (CDS) are primarily used to allow targeting of the active biological molecules to specific target sites or organs based on predictable enzymatic activation. Soft drug approaches are used to design new drugs by building in the molecule, in addition to the activity, the most desired way in which the molecule is to be deactivated and detoxified subsequent to exerting its biological effects. Special computer programs were developed that starting from a lead compound generate complete libraries of possible soft analogs and then help ranking these candidates based on isosteric-isoelectronic comparisons, predicted solubility/partition properties, and estimated metabolic rates. The novel field of large peptide-CDSs imposes special challenges, but a new, remarkably simple model was developed to estimate partition properties for a wide range of compounds, including quite large peptide derivatives. A suggested change of about five order of magnitudes in the distribution coefficient can explain the "lock in" mechanism of brain-targeting delivery systems.

Modeling lipophilicity from the distribution of electrostatic potential on a molecular surface

Molecular lipophilicity L is represented as a function of four surface electrostatic potential descriptors: L = f(B+F, B-F, B+R, B-R). Each B descriptor is computed from the products of elements of molecular surface area, delta(si), and the molecular electrostatic potential (MEP), V(ri), at the center of an area element: B = sigma(i) delta(si) V(r(i)). Octanol-water partition coefficients (P(ow)) are correlated with these four surface-MEP descriptors: log P(ow) = c0 + c1B+F + c2B-F + c3B+R + c4B-R. Good correlations are obtained for homologous series of aliphatic alcohols, amines and acids, as well as for a set of aromatic compounds with various functional groups. Within this approach, we find that the molecular fragment contributions of surface-MEP descriptions to log P are approximately additive. We have computed the values for the following fragments: -CH2-, -CH3, _COOH, -OH and -NH2. These contributions can be used to estimate the molecular lipophilicity and partition coefficients of new compounds, without additional quantum-mechanical calculations. The proposed approach provides a reasonably accurate tool that can be useful in quantitative structure-activity relations for computer-aided rational drug design. More importantly, the correlation model is conceptually simpler than previous work in the literature and can be improved systematically.