A fuzzy ARTMAP based on quantitative structure-property relationships (QSPRs) for predicting aqueous solubility of organic compounds

Predicting aqueous solubility by QSPR modeling

The aqueous solubility is predicted here using quantitative structure property relationship (QSPR) models. In this study, we examine whether descriptors that individually yield favorable models for the prediction of the Gibbs energy of solvation and sublimation can be used in combination with octanol-water partition coefficient to produce QSPR models for the prediction of aqueous solubility. Based on this strategy, applied to seven distinct datasets, all models exhibited an R² greater than 0.7 and Q² greater than 0.6 for the estimation of aqueous solubility. We also determined how uncoupling the descriptors used to create QSPR models in the prediction of Gibbs energy of sublimation yielded an improved model. Model refinement using an artificial neural network applying the same descriptors generated significantly better models with improved R² and standard deviation.

The History and Development of Quantitative Structure-Activity Relationships (QSARs)

It is widely accepted that modern QSAR began in the early 1960s. However, as long ago as 1816 scientists were making predictions about physical and chemical properties. The first investigations into the correlation of biological activities with physicochemical properties such as molecular weight and aqueous solubility began in 1841, almost 60 years before the important work of Overton and Meyer linking aquatic toxicity to lipid-water partitioning. Throughout the 20th century QSAR progressed, though there were many lean years. In 1962 came the seminal work of Corwin Hansch and co-workers, which stimulated a huge interest in the prediction of biological activities. Initially that interest lay largely within medicinal chemistry and drug design, but in the 1970s and 1980s, with increasing ecotoxicological concerns, QSAR modelling of environmental toxicities began to grow, especially once regulatory authorities became involved. Since then QSAR has continued to expand, with over 1400 publications annually from 2011 onwards.

New Linear Partitioning Models Based on Experimental Water: Supercritical CO2 Partitioning Data of Selected Organic Compounds

Partitioning coefficients of organic compounds between water and supercritical CO2 (sc-CO2) are necessary to assess the risk of migration of these chemicals from subsurface CO2 storage sites. Despite the large number of potential organic contaminants, the current data set of published water-sc-CO2 partitioning coefficients is very limited. Here, the partitioning coefficients of thiophene, pyrrole, and anisole were measured in situ over a range of temperatures and pressures using a novel pressurized batch-reactor system with dual spectroscopic detectors: a near-infrared spectrometer for measuring the organic analyte in the CO2 phase and a UV detector for quantifying the analyte in the aqueous phase. Our measured partitioning coefficients followed expected trends based on volatility and aqueous solubility. The partitioning coefficients and literature data were then used to update a published poly parameter linear free-energy relationship and to develop five new linear free-energy relationships for predicting water-sc-CO2 partitioning coefficients. A total of four of the models targeted a single class of organic compounds. Unlike models that utilize Abraham solvation parameters, the new relationships use vapor pressure and aqueous solubility of the organic compound at 25 °C and CO2 density to predict partitioning coefficients over a range of temperature and pressure conditions. The compound class models provide better estimates of partitioning behavior for compounds in that class than does the model built for the entire data set.

QSAR modeling: where have you been? Where are you going to?

Quantitative structure-activity relationship modeling is one of the major computational tools employed in medicinal chemistry. However, throughout its entire history it has drawn both praise and criticism concerning its reliability, limitations, successes, and failures. In this paper, we discuss (i) the development and evolution of QSAR; (ii) the current trends, unsolved problems, and pressing challenges; and (iii) several novel and emerging applications of QSAR modeling. Throughout this discussion, we provide guidelines for QSAR development, validation, and application, which are summarized in best practices for building rigorously validated and externally predictive QSAR models. We hope that this Perspective will help communications between computational and experimental chemists toward collaborative development and use of QSAR models. We also believe that the guidelines presented here will help journal editors and reviewers apply more stringent scientific standards to manuscripts reporting new QSAR studies, as well as encourage the use of high quality, validated QSARs for regulatory decision making.

Validation of quantitative structure-activity relationship models to predict water-solubility of organic compounds

Water-solubility is an important physicochemical property in pharmaceutical and environmental studies. We assessed the performance of five predictive computer models: ACD/PhysChem History, ADMET Predictor, T.E.S.T., EPI Suite-WSKOWWIN and EPI Suite-WATERNT; two of them are commercial, the others are free. We used more than 4000 compounds with experimental values to evaluate the models, considering the chemicals inside and outside the applicability domain of the models, those used to build up the model (training set) and those not present in it (prediction set). We also evaluated their ability to predict continuous solubility values, and solubility classes. Overall, considering the whole data set, some models gave a good statistical performance, with R(2) up to 0.88.

Prediction of physicochemical properties

Physicochemical properties are key factors in controlling the interactions of xenobiotics with living organisms. Computational approaches to toxicity prediction therefore generally rely to a very large extent on the physicochemical properties of the query compounds. Consequently it is important that reliable in silico methods are available for the rapid calculation of physicochemical properties. The key properties are partition coefficient, aqueous solubility, and pKa and, to a lesser extent, melting point, boiling point, vapor pressure, and Henry's law constant (air-water partition coefficient). The calculation of each of these properties from quantitative structure-property relationships (QSPRs) and from available software is discussed in detail, and recommendations made. Finally, detailed consideration is given of guidelines for the development of QSPRs and QSARs.

Fragment descriptors in structure-property modeling and virtual screening

This chapter reviews the application of fragment descriptors at different stages of virtual screening: filtering, similarity search, and direct activity assessment using QSAR/QSPR models. Several case studies are considered. It is demonstrated that the power of fragment descriptors stems from their universality, very high computational efficiency, simplicity of interpretation, and versatility.

A review on molecular topology: applying graph theory to drug discovery and design

Molecular topology is an application of graph theory and statistics in fields like chemistry, biology, and pharmacology, in which the molecular structure matters. Its scope is the topological characterization of molecules by means of numerical invariants, called topological indices, which are the main ingredients of the molecular topological models. These are statistical models that are instrumental in the discovery of new applications of naturally occurring molecules, as well as in the design of synthetic molecules with specific chemical, biological, or pharmacological properties. In this review, we focus on pharmacology, which is a novel field of application of molecular topology. Besides summarizing some recent developments, we also seek to bring closer this interesting biomedical application of mathematics to an interdisciplinary readership.

How not to develop a quantitative structure-activity or structure-property relationship (QSAR/QSPR)

Although thousands of quantitative structure-activity and structure-property relationships (QSARs/QSPRs) have been published, as well as numerous papers on the correct procedures for QSAR/QSPR analysis, many analyses are still carried out incorrectly, or in a less than satisfactory manner. We have identified 21 types of error that continue to be perpetrated in the QSAR/QSPR literature, and each of these is discussed, with examples (including some of our own). Where appropriate, we make recommendations for avoiding errors and for improving and enhancing QSAR/QSPR analyses.

QSPR prediction of aqueous solubility of drug-like organic compounds

A quantitative structure property relationship (QSPR) study was performed to develop a model that relates the structures of 150 drug organic compounds to their aqueous solubility (log S(w)). Molecular descriptors derived solely from 3D structure were used to represent molecular structures. A subset of the calculated descriptors selected using stepwise regression that used in the QSPR model development. Multiple linear regression (MLR) is utilized to construct the linear QSPR model. The applied multiple linear regression is based on a variety of theoretical molecular descriptors selected by the stepwise variable subset selection procedure. Stepwise regression was employed to develop a regression equation based on 110 training compounds, and predictive ability was tested on 40 compounds reserved for that purpose. The final regression equation included three parameters that consisted of octanol/water partition coefficient (log P), molecular volume (MV) and hydrogen bond forming ability (HB), of the drug molecules, all of which could be related to solubility property. Application of the developed model to a testing set of 40 drug organic compounds demonstrates that the new model is reliable with good predictive accuracy and simple formulation. The use of descriptors calculated only from molecular structure eliminates the need for experimental determination of properties for use in the correlation and allows for the estimation of aqueous solubility for molecules not yet synthesized. The prediction results are in good agreement with the experimental values. The root mean square error of prediction (RMSEP) and square correlation coefficient (R(2)) of prediction of log S(w) were 0.0959 and 0.9954, respectively.

On the dissolution of vapors and gases

The captive bubble technique in combination with axisymmetric drop shape analysis (ADSA-CB) and with micro gas chromatography is used to study the dynamics of dissolution of different gases and vapors in water in situ. The technique yields the changes in the interfacial tension and bubble volume and surface. As examples, the dissolution of methanol and hexane vapors, inhaled anesthetic vapors, and gases, that is, diethyl ether, chloroform, isoflurane, enflurane, sevoflurane, desflurane, N2O, and xenon, and as nonimmobilizers perfluoropentane and 1,1,2-trichloro-1,2,2-trifluoro-ethane (R113) were investigated. The examination of interfacial tension-time and bubble volume-time functions permits us to distinguish between water-soluble and -insoluble substances, gases, and vapors. Vapors and gases generally differ in terms of the strength of their intermolecular interactions. The main difference between dissolution processes of gases and vapors is that, during the entire process of gas dissolution, no surface tension change occurs. In contrast, during vapor dissolution the surface tension drops immediately and decreases continuously until it reaches the equilibrium surface tension of water at the end of dissolution. The results of this study show that it is possible to discriminate anesthetic vapors from anesthetic gases and nonimmobilizers by comparing their dissolution dynamics. The nonimmobilizers have extremely low or no solubility in water and change the surface tension only negligibly. By use of newly defined molecular dissolution/diffusion coefficients, a simple model for the determination of partition coefficients is developed.

Computational models to predict aqueous drug solubility, permeability and intestinal absorption

In the last decade, poor intestinal absorption of candidate drugs intended for oral administration has been identified as a major bottleneck in drug development. Poor intestinal absorption can often be related to poor aqueous solubility and/or poor permeability across the intestinal wall. Other factors, such as poor stability and the metabolism of the compounds, can also decrease the amount of compound absorbed. In an effort to design compounds with enhanced absorption profile, theoretical predictions of solubility and permeability, among other factors, have gained increased interest, and a large number of papers have been published. In this review, the databases and techniques used for the development of in silico absorption models will be discussed. The focus is on aqueous drug solubility, which has become a major problem in drug development.

Substructural fragments: an universal language to encode reactions, molecular and supramolecular structures

Substructural fragments are proposed as a simple and safe way to encode molecular structures in a matrix containing the occurrence of fragments of a given type. The knowledge retrieved from QSPR modelling can also be stored in that matrix in addition to the information about fragments. Complex supramolecular systems (using special bond types) and chemical reactions (represented as Condensed Graphs of Reactions, CGR) can be treated similarly. The efficiency of fragments as descriptors has been demonstrated in QSPR studies of aqueous solubility for a diverse set of organic compounds as well as in the analysis of thermodynamic parameters for hydrogen-bonding in some supramolecular complexes. It has also been shown that CGR may be an interesting opportunity to perform similarity searches for chemical reactions. The relationship between the density of information in descriptors/knowledge matrices and the robustness of QSPR models is discussed.

In silico predictions of drug solubility and permeability: two rate-limiting barriers to oral drug absorption

Aqueous drug solubility and intestinal drug permeability are two of the most important factors influencing drug absorption. If the developability of a drug is to be included in the lead optimization, new experimental and computational models of solubility and permeability are needed. These models must have the capacity to handle a large amount of data. Nowadays, epithelial cell culture models such as Caco-2 are routinely used to assess intestinal drug permeability and transport in drug discovery settings. The permeability values obtained from the Caco-2 cell monolayers have been traditionally used to devise in silico models for the prediction of drug absorption. In this paper, the use of molecular surface areas as descriptors of permeability and solubility will be reviewed. Moreover, a virtual filter for the prediction of oral drug developability based on the successful combination of in vitro and in silico models of drug permeability and aqueous drug solubility will be discussed.

ESOL: estimating aqueous solubility directly from molecular structure

This paper describes a simple method for estimating the aqueous solubility (ESOL--Estimated SOLubility) of a compound directly from its structure. The model was derived from a set of 2874 measured solubilities using linear regression against nine molecular properties. The most significant parameter was calculated logP(octanol), followed by molecular weight, proportion of heavy atoms in aromatic systems, and number of rotatable bonds. The model performed consistently well across three validation sets, predicting solubilities within a factor of 5-8 of their measured values, and was competitive with the well-established "General Solubility Equation" for medicinal/agrochemical sized molecules.

Prediction methods and databases within chemoinformatics: emphasis on drugs and drug candidates

MOTIVATION

To gather information about available databases and chemoinformatics methods for prediction of properties relevant to the drug discovery and optimization process.

RESULTS

We present an overview of the most important databases with 2-dimensional and 3-dimensional structural information about drugs and drug candidates, and of databases with relevant properties. Access to experimental data and numerical methods for selecting and utilizing these data is crucial for developing accurate predictive in silico models. Many interesting predictive methods for classifying the suitability of chemical compounds as potential drugs, as well as for predicting their physico-chemical and ADMET properties have been proposed in recent years. These methods are discussed, and some possible future directions in this rapidly developing field are described.

Prediction of the aqueous solubility of benzylamine salts using QSPR model

Models predicting aqueous solubility of benzylamine salts were developed using multivariate partial least squares (PLS) and artificial neural network (ANN). Molecular descriptors, including binding energy (BE) and surface area of salts (SA), were calculated by the use of Hyperchem and ChemPlus QSAR programs for Windows. Other physicochemical properties, such as hydrogen acceptor for oxygen atoms, hydrogen acceptor for nitrogen atoms, hydrogen bond donors, hydrogen bond forming ability, molecular weight (MW), and calculated log partition coefficient (clog P) of p-substituted benzoic acids, were also used as descriptors. In this study, the predictive ability of ANN, especially multilayer perceptron (MLP) architecture networks, was founded to be superior to PLS models. The best ANN model derived, a 6-1-1 architecture, had an overall R(2) of 0.850 and root mean square error (RMSE) for cross-verification and test set of 0.189 and 0.185 log units, respectively. Since all the utilized descriptors are readily obtained from calculation, these derived models offer the advantage of not requiring the experimental determination of some descriptors.

QSPR analysis of the partitioning of vaporous chemicals in a water-gas phase system and the water solubility of liquid and solid chemicals on the basis of fragment and physicochemical similarity and hybot descriptors

QSPR analyses of the solubility in water of 558 vapors, 786 liquids and 2045 solid organic neutral chemicals and drugs are presented. Simultaneous consideration of H-bond acceptor and donor factors leads to a good description of the solubility of vapors and liquids. A volume-related term was found to have an essential negative contribution to the solubility of liquids. Consideration of polarizability, H-bond acceptor and donor factors and indicators for a few functional groups, as well as the experimental solubility values of structurally nearest neighbors yielded good correlations for liquids. The application of Yalkowsky's "General Solubility Equation" to 1063 solid chemicals and drugs resulted in a correlation of experimental vs calculated log S values with only modest statistical criteria. Two approaches to derive predictive models for solubility of solid chemicals and drugs were tested. The first approach was based on the QSPR for liquids together with indicator variables for different functional groups. Furthermore, a calculation of enthalpies for intermolecular complexes in crystal lattices, based on new H-bond potentials, was carried out for the better consideration of essential solubility- decreasing effects in the solid state, as compared with the liquid state. The second approach was based on a combination of similarity considerations and traditional QSPR. Both approaches lead to high quality predictions with average absolute errors on the level of experimental log S determination.

Predicting aqueous solubility from structure

The aqueous solubility of a drug is one of the key physical properties that affect both its ADME profile and 'screenability' in HTS. This review critically surveys a range of methods that can be used to predict the solubility of a compound in water and presents some of the main issues that affect the applicability of different techniques. As ever, there are trade-offs to be made between the speed, accuracy and transparency of methods, but current programs can provide estimates to well within an order of magnitude in favourable cases. The need for new ways to predict solubility in more challenging systems (e.g. solvents such as DMSO and charged solutes) is discussed.

Prediction of aqueous solubility of organic salts of diclofenac using PLS and molecular modeling

Organic salts of diclofenac were predicted by using computed molecular descriptors and multivariate partial least squares (PLS). The molecular descriptors including binding energy and surface area of salts were calculated by the use of Hyperchem and ChemPlus QSAR programs for Windows. Other physicochemical properties such as hydrogen acceptor for oxygen atoms, hydrogen acceptor for nitrogen atoms, hydrogen bond donors, hydrogen bond-forming ability, molecular weight, and log partition coefficient (logP) of bases were also used as descriptors. Good statistical models were derived that permit simple computational prediction of salt solubility of a same parent structure. The final models derived had R2 value = 0.96 and root mean square error for prediction (RMSEP) values ranging from 0.021 to 0.054 (log scale). Preferably all utilized descriptors in the final models can readily obtain from the chemical structure of salt and base. Molecular weight of base is one of the important factors associated with salt solubility. While increased molecular weight of base, surface area of salt and hydrogen bonding ability of base increase solubility, and increased binding energy and logP of base have negative effect on salt solubility.

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.

Modeling aqueous solubility

This paper describes the development of an aqueous solubility model based on solubility data from the Syracuse database, calculated octanol-water partition coefficient, and 51 2D molecular descriptors. Two different statistical packages, SIMCA and Cubist, were used and the results were compared. The Cubist model, which comprises a collection of rules, each of which has an associated Multiple Linear Regression model (MLR), gave better overall results on a test set of 640 compounds with an overall squared correlation coefficient of 0.74 and an absolute average error of 0.68 log units. Both training and independent test sets had similar distributions of structures in terms of the different functionalities present-60% neutral, 14% acidic, 8% phenolic, 11% monobasic, 4% polybasic, and 3% zwitterionic molecules. Sets were designed by random selection, with 2688 (81%) and 640 (19%) molecules, respectively, forming the training and the test sets.

Equilibrium partitioning of chlorinated solvents in the vadose zone: low f(oc) geomedia

A series of gas (vapor)-advecting water-unsaturated column experiments using a low organic content (f(oc)) silica sand was conducted to determine mass distributions of chlorinated-volatile hydrophobic organic compounds (C-VHOCs) in a natural sorbent system. C-VHOCs used were trichloroethene (TCE), tetrachloroethene (PCE), chlorobenzene (CB), and 1,3-dichlorobenzene (DCB). Four volumetric water contents (theta(w) = 0.07, 0.12, 0.17, 0.20) and several influent gas-phase C-VHOC (solute) concentrations were considered. The method of temporal first moments was applied to complete breakthrough curve data to determine total C-VHOC gas-phase retardation and associated gas-phase C-VHOC mass fraction. Results were compared to an equilibrium partitioning advective-dispersive formulation of total gas-phase retardation. Literature-derived values of Henry's law constants and independent measurements of gas/water interface areal extent and interface phase adsorption allowed quantification of C-VHOC mass fractions in the aqueous and gas/water interface phases. Unaccounted C-VHOC mass, derived from comparison of measured C-VHOC retardation to independent phase prediction, was attributed to solid-phase sorption. Results indicate that for all conditions tested, gas/water interfacial adsorption exhibited only a small effect on C-VHOC vapor retardation (accounting for < or = 10% of the total C-VHOC distributions). Solid-phase association was the dominant uptake mechanism, accounting for 46-91% of the total C-VHOC mass in the porous system. Evaluation of the solid-phase C-VHOC uptake results in terms of a modified form of the Dubinin-Radushkevich (DR) isotherm equation provided strong evidence supporting the mechanism of pore-filling in this natural, low f(oc) sorbent.

Prediction of drug solubility from structure

The aqueous solubility of a drug is an important factor affecting its bioavailability. Numerous computational methods have been developed for the prediction of aqueous solubility from a compound's structure. A review is provided of the methodology and quality of results for the most useful procedures including the model implemented in the QikProp program. Viable methods now exist for predictions with less than 1 log unit uncertainty, which is adequate for prescreening synthetic candidates or design of combinatorial libraries. Further progress with predictive methods would require an experimental database of highly accurate solubilities for a large, diverse collection of drug-like molecules.

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.