Quantitative Structure−Property Relationship Modeling of β-Cyclodextrin Complexation Free Energies

A Review of Machine Learning and QSAR/QSPR Predictions for Complexes of Organic Molecules with Cyclodextrins

Cyclodextrins are macrocyclic rings composed of glucose residues. Due to their remarkable structural properties, they can form host-guest inclusion complexes, which is why they are frequently used in the pharmaceutical, cosmetic, and food industries, as well as in environmental and analytical chemistry. This review presents the reports from 2011 to 2023 on the quantitative structure-activity/property relationship (QSAR/QSPR) approach, which is primarily employed to predict the thermodynamic stability of inclusion complexes. This article extensively discusses the significant developments related to the size of available experimental data, the available sets of descriptors, and the machine learning (ML) algorithms used, such as support vector machines, random forests, artificial neural networks, and gradient boosting. As QSAR/QPR analysis only requires molecular structures of guests and experimental values of stability constants, this approach may be particularly useful for predicting these values for complexes with randomly substituted cyclodextrins, as well as for estimating their dependence on pH. This work proposes solutions on how to effectively use this knowledge, which is especially important for researchers who will deal with this topic in the future. This review also presents other applications of ML in relation to CD complexes, including the prediction of physicochemical properties of CD complexes, the development of analytical methods based on complexation with CDs, and the optimisation of experimental conditions for the preparation of the complexes.

Development and Evaluation of Antimicrobial and Modulatory Activity of Inclusion Complex of Euterpe oleracea Mart Oil and β-Cyclodextrin or HP-β-Cyclodextrin

The development of inclusion complexes is used to encapsulate nonpolar compounds and improve their physicochemical characteristics. This study aims to develop complexes made up of Euterpe oleracea Mart oil (EOO) and β-cyclodextrin (β-CD) or hydroxypropyl-β-cyclodextrin (HP-β-CD) by either kneading (KND) or slurry (SL). Complexes were analyzed by molecular modeling, Fourier-transform infrared spectroscopy, scanning electron microscopy, powder X-ray diffraction, thermogravimetry analysis and differential scanning calorimetry. The antibacterial activity was expressed as Minimum Inhibitory Concentration (MIC), and the antibiotic resistance modulatory activity as subinhibitory concentration (MIC/8) against Escherichia coli, Streptomyces aureus, Pseudomonas aeruginosa and Enterococcus faecalis. Inclusion complexes with β-CD and HP-β-CD were confirmed, and efficiency was proven by an interaction energy between oleic acid and β-CD of -41.28 ± 0.57 kJ/mol. MIC values revealed higher antibacterial activity of complexes compared to the isolated oil. The modulatory response of EOO and EOO-β-CD prepared by KND as well as of EOO-β-CD and EOO-HP-β-CD prepared by SL showed a synergistic effect with ampicillin against E. coli, whereas it was not significant with the other drugs tested, maintaining the biological response of antibiotics. The antimicrobial response exhibited by the complexes is of great significance because it subsidizes studies for the development of new pharmaceutical forms.

Predicting complexation performance between cyclodextrins and guest molecules by integrated machine learning and molecular modeling techniques

Most pharmaceutical formulation developments are complex and ideal formulations are generally obtained after extensive experimentation. Machine learning is increasingly advancing many aspects in modern society and has achieved significant success in multiple subjects. Current research demonstrated that machine learning can be adopted to build up high-accurate predictive models in drugs/cyclodextrins (CDs) systems. Molecular descriptors of compounds and experimental conditions were employed as inputs, while complexation free energy as outputs. Results showed that the light gradient boosting machine provided significantly improved predictive performance over random forest and deep learning. The mean absolute error was 1.38 kJ/mol and squared correlation coefficient was 0.86. The evaluation of relative importance of molecular descriptors further demonstrated the key factors affecting molecular interactions in drugs/CD systems. In the specific ketoprofen-CD systems, machine learning model showed better predictive performance than molecular modeling calculation, while molecular simulation could provide structural, dynamic and energetic information. The integration of machine learning and molecular simulation could produce synergistic effect for interpreting and predicting pharmaceutical formulations. In conclusion, the developed predictive models were able to quickly and accurately predict the solubilizing capacity of CD systems. Current research has taken an important step toward the application of machine learning in pharmaceutical formulation design.

Predicting Value of Binding Constants of Organic Ligands to Beta-Cyclodextrin: Application of MARSplines and Descriptors Encoded in SMILES String

The quantitative structure–activity relationship (QSPR) model was formulated to quantify values of the binding constant (lnK) of a series of ligands to beta–cyclodextrin (β-CD). For this purpose, the multivariate adaptive regression splines (MARSplines) methodology was adopted with molecular descriptors derived from the simplified molecular input line entry specification (SMILES) strings. This approach allows discovery of regression equations consisting of new non-linear components (basis functions) being combinations of molecular descriptors. The model was subjected to the standard internal and external validation procedures, which indicated its high predictive power. The appearance of polarity-related descriptors, such as XlogP, confirms the hydrophobic nature of the cyclodextrin cavity. The model can be used for predicting the affinity of new ligands to β-CD. However, a non-standard application was also proposed for classification into Biopharmaceutical Classification System (BCS) drug types. It was found that a single parameter, which is the estimated value of lnK, is sufficient to distinguish highly permeable drugs (BCS class I and II) from low permeable ones (BCS class II and IV). In general, it was found that drugs of the former group exhibit higher affinity to β-CD then the latter group (class III and IV).

Investigating the Association Mechanism between Rafoxanide and Povidone

The low aqueous solubility of most hydrophobic medications limits their oral absorption. An approach to solve this problem is to make a drug-polymer association. Herein, we investigated the association between rafoxanide (RAF), a surface-active, poorly water-soluble drug, with a commercial hydrophilic polymer povidone. We found that the association is a function of medium composition and could only take place in polar media, such as water. The association is favored by the hydrogen-bond formation between the amide group in RAF and the carbonyl group in povidone. In addition, the association is also favored by the self-association of RAF through π-π interaction between the benzene rings in adjacent RAF molecules. Two-dimensional nuclear magnetic resonance has been applied to investigate the interactions and has confirmed our hypotheses. Geometry optimization confirmed that RAF exists primarily in the antiparallel configuration in the RAF aggregates. This study provides critical information for designing suitable drug-vehicle complexes and engineering the interactions between them to maximize the oral absorption. Our results shed light on drug design and delivery, drug molecule structure-functionality relationship, as well as efficacy enhancement toward interaction engineering.

Maltodextrins as chiral selectors in CE: molecular structure effect of basic chiral compounds on the enantioseparation

Prediction of chiral separation for a compound using a chiral selector is an interesting and debatable work. For this purpose, in this study 23 chiral basic drugs with different chemical structures were selected as model solutes and the influence of their chemical structures on the enantioseparation in the presence of maltodextrin (MD) as chiral selector was investigated. For chiral separation, a 100-mM phosphate buffer solution (pH 3.0) containing 10% (w/v) MD with dextrose equivalent (DE) of 4-7 as chiral selector at the temperature of 25°C and voltage of 20 kV was used. Under this condition, baseline separation was achieved for nine chiral compounds and partial separation was obtained for another six chiral compounds while no enantioseparation was obtained for the remaining eight compounds. The results showed that the existence of at least two aromatic rings or cycloalkanes and an oxygen or nitrogen atom or -CN group directly bonded to the chiral center are necessary for baseline separation. With the obtained results in this study, chiral separation of a chiral compound can be estimated with MD-modified capillary electrophoresis before analysis. This prediction will minimize the number of preliminary experiments required to resolve enantiomers and will save time and cost.

Development of machine learning models of β-cyclodextrin and sulfobutylether-β-cyclodextrin complexation free energies

A new set of 142 experimentally determined complexation constants between sulfobutylether-β-cyclodextrin and diverse organic guest molecules, and 78 observations reported in literature, were used for the development of the QSPR models by the two machine learning regression methods - Cubist and Random Forest. Similar models were built for β-cyclodextrin using the 233-compound dataset available in the literature. These results demonstrate that the machine learning regression methods can successfully describe the complex formation between organic molecules and β-cyclodextrin or sulfobutylether-β-cyclodextrin. In particular, the root mean square errors for the test sets predictions by the best models are low, 1.9 and 2.7kJ/mol, respectively. The developed QSPR models can be used to predict the solubilizing effect of cyclodextrins and to help prioritizing experimental work in drug discovery.

Self-assembly of cyclodextrins: the effect of the guest molecule

The principle action by which cyclodextrins solubilize compounds is via inclusion complex formation. However, data suggest that cyclodextrins and their complexes also aggregate in solution and this aggregation contributes to their ability to solubilize poorly water-soluble materials. The current effort aims at better understanding the role of guest molecule nature (i.e. its structural and functional peculiarities) in cyclodextrin complex aggregation as well as in the aggregate stability assessed using a cellophane membrane permeability assay. A test set of 11 acidic, basic and neutral drugs and antibacterial agents (i.e. guests) were examined with regard to their interaction with hydroxypropyl-β-cyclodextrin (HPβCD) and the resulting ability of the formed aggregates to move through a semi-permeable membrane of various molecular weight cut-off values. The data suggested that the interaction of HPβCD with certain guests resulted in the formation of structure large enough to poorly penetrate semi-permeable membrane. The aggregates appeared to be highly dynamic in that there were no qualitative differences between systems that were diluted immediately prior to permeation experiments and those allowed to equilibrate. Pharmaceutical polymers which have been shown to enhance solubilizing efficiency of cyclodextrins had little or no effect on the stability of the aggregates using the permeability paradigm as an endpoint with the exception of carboxymethylcellulose.

QSAR modeling of photosynthesis-inhibiting nostoclide derivatives

BACKGROUND

A statistical model, built using the CODESSA software package, was developed to describe the relationship between the structure of nostoclide derivatives and their ability to interfere with the electron transport chain in the Hill reaction.

RESULTS

A QSAR treatment was carried out on a series of compounds designed using the naturally occurring toxin nostoclides to correlate molecular descriptors with their in vitro biological activity (the ability to interfere with light-driven reduction of ferricyanide by isolated spinach chloroplast thylakoid membranes). The treatment using the CODESSA software package resulted in a three-parameter model with n = 19, R(2) = 0.83, F = 23.8 and R(2) (cv) = 0.72. In the proposed model, the Image of Onsager Kirkwood solvation energy, which gives a measure of the polarity of a given compound, is the most important descriptor. The model was internally validated.

CONCLUSIONS

The results obtained in this study indicate that polarity, as expressed by the dipole moment, is the most relevant molecular property determining efficiency of photosynthetic inhibitory activity.

Artificial neural network prediction of the psychometric activities of phenylalkylamines using DFT-calculated molecular descriptors

In the present work, a quantitative structure-activity relationship (QSAR) method was used to predict the psychometric activity values (as mescaline unit, log MU) of 48 phenylalkylamine derivatives from their density functional theory (DFT) calculated molecular descriptors and an artificial neural network (ANN). In the first step, the molecular descriptors were obtained by DFT calculation at the 6-311G

Binding mechanisms in supramolecular complexes

Supramolecular chemistry has expanded dramatically in recent years both in terms of potential applications and in its relevance to analogous biological systems. The formation and function of supramolecular complexes occur through a multiplicity of often difficult to differentiate noncovalent forces. The aim of this Review is to describe the crucial interaction mechanisms in context, and thus classify the entire subject. In most cases, organic host-guest complexes have been selected as examples, but biologically relevant problems are also considered. An understanding and quantification of intermolecular interactions is of importance both for the rational planning of new supramolecular systems, including intelligent materials, as well as for developing new biologically active agents.

Predicting complexation thermodynamic parameters of β-cyclodextrin with chiral guests by using swarm intelligence and support vector machines

The Particle Swarm Optimization (PSO) and Support Vector Machines (SVMs) approaches are used for predicting the thermodynamic parameters for the 1:1 inclusion complexation of chiral guests with beta-cyclodextrin. A PSO is adopted for descriptor selection in the quantitative structure-property relationships (QSPR) of a dataset of 74 chiral guests due to its simplicity, speed, and consistency. The modified PSO is then combined with SVMs for its good approximating properties, to generate a QSPR model with the selected features. Linear, polynomial, and Gaussian radial basis functions are used as kernels in SVMs. All models have demonstrated an impressive performance with R(2) higher than 0.8.

Development of improved empirical models for estimating the binding constant of a beta-cyclodextrin inclusion complex

PURPOSE

To develop empirical models for predicting the binding between a drug and beta-cyclodextrin. Specifically, the logarithm of the 1:1 binding constant is expressed as the function of various molecular descriptors of the drug. Many potential drugs exhibit poor aqueous solubility. Also, the amount available for solubility studies is limited early in drug development. Thus, models that show which excipients can increase a drug's solubility are useful because formulation scientists can focus on them experimentally.

METHODS

Twenty-five descriptors were considered based on molecular characteristics governing complexation. These include the drug's size and/or shape, the dispersion of its electron cloud, its lipophilicity, and its flexibility. The training set contains 258 ligands, ranging from drug-like molecules to small polar organic compounds.

RESULTS

Two models were developed. The first is derived by partial least squares regression and consists of all 25 descriptors. The r2 determined by cross-validation is 0.79. The second contains four variables and was constructed by multiple linear regression. Its cross-validated r2 is 0.65.

CONCLUSIONS

Due to its simplicity, the second model is recommended over the first. The most important descriptor in both models is the calculated log P, indicating that drugs with greater lipophilicity form stronger complexes with beta-cyclodextrin.

On the ease of predicting the thermodynamic properties of beta-cyclodextrin inclusion complexes

Background

In this study we investigated the predictability of three thermodynamic quantities related to complex formation. As a model system we chose the host-guest complexes of β-cyclodextrin (β-CD) with different guest molecules. A training dataset comprised of 176 β-CD guest molecules with experimentally determined thermodynamic quantities was taken from the literature. We compared the performance of three different statistical regression methods – principal component regression (PCR), partial least squares regression (PLSR), and support vector machine regression combined with forward feature selection (SVMR/FSS) – with respect to their ability to generate predictive quantitative structure property relationship (QSPR) models for ΔG°, ΔH° and ΔS° on the basis of computed molecular descriptors.

Results

We found that SVMR/FFS marginally outperforms PLSR and PCR in the prediction of ΔG°, with PLSR performing slightly better than PCR. PLSR and PCR proved to be more stable in a nested cross-validation protocol. Whereas ΔG° can be predicted in good agreement with experimental values, none of the methods led to comparably good predictive models for ΔH°. In using the methods outlined in this study, we found that ΔS° appears almost unpredictable. In order to understand the differences in the ease of predicting the quantities, we performed a detailed analysis. As a result we can show that free energies are less sensitive (than enthalpy or entropy) to the small structural variations of guest molecules. This property, as well as the lower sensitivity of ΔG° to experimental conditions, are possible explanations for its greater predictability.

Conclusion

This study shows that the ease of predicting ΔG° cannot be explained by the predictability of either ΔH° or ΔS°. Our analysis suggests that the poor predictability of TΔS° and, to a lesser extent, ΔH° has to do with a stronger dependence of these quantities on the structural details of the complex and only to a lesser extent on experimental error.

Improved Cyclodextrin-Based Receptors for Camptothecin by Inverse Virtual Screening

We report the computer-aided optimization of a synthetic receptor for a given guest molecule, based on inverse virtual screening of receptor libraries. As an example, a virtual set of beta-cyclodextrin (beta-CD) derivatives was generated as receptor candidates for the anticancer drug camptothecin. We applied the two docking tools AutoDock and GlamDock to generate camptothecin complexes of every candidate receptor. Scoring functions were used to rank all generated complexes. From the 10 % top-ranking candidates nine were selected for experimental validation. They were synthesized by reaction of heptakis-[6-deoxy-6-iodo]-beta-CD with a thiol compound to form the hepta-substituted beta-CDs. The stabilities of the camptothecin complexes obtained from solubility measurements of five of the nine CD derivatives were significantly higher than for any other CD derivative known from literature. The remaining four CD derivatives were insoluble in water. In addition, corresponding mono-substituted CD derivatives were synthesized that also showed improved binding constants. Among them the 9-H-purine derivative was the best, being comparable to the investigated hepta-substituted beta-CDs. Since the measured binding free energies correlated satisfactorily with the calculated scores, the applied scoring functions appeared to be appropriate for the selection of promising candidates for receptor synthesis.

Explaining cyclodextrin–mycotoxin interactions using a ‘natural’ force field

Docking techniques and the HINT (Hydropathic Interaction) program were used to explain interactions of aflatoxin B(1) and ochratoxin A with beta- and gamma-cyclodextrins. The work was aimed at designing a chemosensor to identify very low concentrations of these mycotoxins by exploiting the affinity of the cyclodextrin cavity for many small organic molecules. Actually, the inclusion of the fluorescent portion of these toxins into the cavity may lower the quenching effect of the solvent, thus enhancing the luminescence. HINT is a 'natural' force field, based on experimentally determined LogP(octanol/water) values, that is able to consider both enthalpic and entropic contributions to the binding free energy with an unified approach. HINT is normally applied to predict the DeltaG degrees of binding for protein-ligand, protein-protein, and protein-DNA interactions. The leading forces in biomolecular processes are the same as those involved in organic host-guest inclusion phenomena, therefore we applied this methodology for the first time to cyclodextrin complexes. The results allowed us to explain spectroscopic data in absence of available crystallographic or NMR structural data.

QSPR modeling of hyperpolarizabilities

The polarizabilities and the first and second hyperpolarizabilities of 219 conjugated organic compounds are modeled by QSPR (quantitative structure activity relationship) based on a large pool of constitutional, topological, electronic and quantum chemical descriptors calculated by CODESSA Pro (comprehensive descriptors for structural and statistical analysis) derived solely from molecular structure. Multilinear models were developed using the BMLR (best multilinear regression) algorithm to relate the experimental (hyper)polarizabilities to their predicted values. The regression equations include AM1 (Austin model 1) calculated (hyper)polarizabilities together with the size, electrostatic and quantum chemical descriptors to compensate for the imprecision of the AM1 computational method. The results emphasize the main factors that influence (hyper)polarizability. All models were validated by the "leave-one-out" method and internal validations that confirmed the stability and good predictive ability.

QSAR modeling of anti-invasive activity of organic compounds using structural descriptors

The anti-invasive activity of 139 compounds was correlated by an artificial neural network approach with descriptors calculated solely from the molecular structures using CODESSA Pro. The best multilinear regression method implemented in CODESSA Pro was used for a pre-selection of descriptors. The resulting nonlinear (artificial neural network) QSAR model predicted the exact class for 66 (71%) of the training set of 93 compounds and 32 (70%) of validation set of 46 compounds. The standard deviation ratios for the both training and validation sets are less than unity, indicating a satisfactory predictive capability for classification of the nature of the anti-invasive activity data. The proposed model can be used for the prediction of the anti-invasive activity of novel classes of compounds enabling a virtual screening of large databases of anticancer drugs.

Benchmarking of linear and nonlinear approaches for quantitative structure-property relationship studies of metal complexation with ionophores

A benchmark of several popular methods, Associative Neural Networks (ANN), Support Vector Machines (SVM), k Nearest Neighbors (kNN), Maximal Margin Linear Programming (MMLP), Radial Basis Function Neural Network (RBFNN), and Multiple Linear Regression (MLR), is reported for quantitative-structure property relationships (QSPR) of stability constants logK1 for the 1:1 (M:L) and logbeta2 for 1:2 complexes of metal cations Ag+ and Eu3+ with diverse sets of organic molecules in water at 298 K and ionic strength 0.1 M. The methods were tested on three types of descriptors: molecular descriptors including E-state values, counts of atoms determined for E-state atom types, and substructural molecular fragments (SMF). Comparison of the models was performed using a 5-fold external cross-validation procedure. Robust statistical tests (bootstrap and Kolmogorov-Smirnov statistics) were employed to evaluate the significance of calculated models. The Wilcoxon signed-rank test was used to compare the performance of methods. Individual structure-complexation property models obtained with nonlinear methods demonstrated a significantly better performance than the models built using multilinear regression analysis (MLRA). However, the averaging of several MLRA models based on SMF descriptors provided as good of a prediction as the most efficient nonlinear techniques. Support Vector Machines and Associative Neural Networks contributed in the largest number of significant models. Models based on fragments (SMF descriptors and E-state counts) had higher prediction ability than those based on E-state indices. The use of SMF descriptors and E-state counts provided similar results, whereas E-state indices lead to less significant models. The current study illustrates the difficulties of quantitative comparison of different methods: conclusions based only on one data set without appropriate statistical tests could be wrong.

QSAR study of antiplatelet agents

A QSAR methodology that involves multilinear (Hansch-type) and nonlinear (ANN backpropagation) approaches was developed to correlate the antiplatelet activity of 60 benzoxazinone derivatives against factor Xa. The statistical characteristics provided by multilinear model (R2 = 0.821) indicated satisfactory stability and predictive ability, while the ANN predictive ability is somewhat superior (R2 = 0.909). The multilinear model provided insight into the main factors that modulate the inhibitory activity of the investigated compounds.

Theoretical studies on the binding affinities of β-cyclodextrin to small molecules and monosaccharides

Equilibrium geometries and electronic structures of complexes between β-cyclodextrin (β-CD) and some small molecules as well as monosaccharides were investigated by Austin Model 1 (AM1) to obtain binding energy of the complexes. It was indicated that β-CD could bind the structurally similar solvent molecules and monosaccharides because of the negative binding energy of the complexes, and especially could show the chiral binding ability to monosaccharides with more hydroxyl groups, due to its chiral characteristics. The complexes were stabilized by the hydrogen bonding between β-CD and guests. Based on the AM1 optimized geometries, the IR spectra were calculated by AM1 method. Vibration frequencies of O-H bonds in the guests were red-shifted owing to the weakening of the O-H bonds with the formation of the complexes.

Evaluation of cyclodextrin solubilization of drugs

The most common stoichiometry of drug/cyclodextrin complexes is 1:1, i.e. one drug molecule forms a complex with one cyclodextrin molecule, and the most common method for stoichiometric determination during formulation studies is the phase-solubility method. However, in recent years it has becoming increasingly clear that solubilizing effects of cyclodextrins are frequently due to the formation of multiple inclusion and non-inclusion complexes. The aqueous solubility of 38 different drugs was determined in pure aqueous solution, aqueous buffer solutions and aqueous cyclodextrin solutions, and the apparent stability constant (K1:1) of the 1:1 drug/cyclodextrin complexes calculated by the phase-solubility method. For poorly soluble drugs (aqueous solubility <0.1mM) the intrinsic solubility (S0) is in general much larger than the intercept of the phase-solubility diagram (Sint) resulting in non-linearity of otherwise linear (AL-type) phase-solubility diagram. This can lead to erroneous K(1:1)-values. A more accurate method for determination of the solubilizing efficiency of cyclodextrins is to determine their complexation efficiency (CE), i.e. the concentration ratio between cyclodextrin in a complex and free cyclodextrin. CE is calculated from the slope of the phase-solubility diagrams, it is independent of both S0 and Sint, and more reliable when the influences of different pharmaceutical excipients on the solubilization are being investigated.

QSAR study of mosquito repellents using Codessa Pro

Protection times provided by 31 synthetic repellents against Aedes aegypti mosquitoes were correlated with the chemical structures of these repellents using Codessa Pro software. Two statistically significant quantitative models with R2 values of ca. 0.80 are presented and discussed.

The application of cyclodextrins in textile area

The application of Cyclodextrins for textiles was reviewed in this paper. Cyclodextrins are crystalline, water soluble, cyclic, non-reducing oligosaccharides consisting of six, seven, or eight glucopyranose units. Cyclodextrins are known as products which are able to form inclusion complexes. The ability of Cyclodextrins to form inclusion complexes can be used, e.g., to remove malodor from textile materials, etc. Furthermore, some modifications of the parent Cyclodextrins are possible. The derivatives can be reactive (e.g. cyclodextrin with a monochlorotriazinyl group), more hydrophilic (by means of hydrophilic side groups, such as hydroxypropyl and hydroxyethyl), less hydrophilic (by means of lipophilic side groups, such as ethylhexyl glycidyl) or ionic (by means of ionic side groups, such as hydroxypropyl trimethyl ammonium chloride).The methods for treating textiles are thus quite simple. The method using anchor-bearing Cyclodextrins is especially useful, since no fixation agent is needed, enabling they use of conventional textile treatment techniques and equipment. Furthermore, this method has virtually no limitations with respect to the textile materials that can be used.

QSAR modeling of blood:air and tissue:air partition coefficients using theoretical descriptors

Human blood:air, human and rat tissue (fat, brain, liver, muscle, and kidney):air partition coefficients of a diverse set of organic compounds were correlated and predicted using structural descriptors by employing CODESSA-PRO and ISIDA programs. Four and five descriptor regression models developed using CODESSA-PRO were validated on three different test sets. Overall, these models have reasonable values of correlation coefficients (R(2)) and leave-one-out correlation coefficients (R(cv)(2)): R(2) = 0.881-0.983; R(cv)(2) = 0.826-0.962. Calculations with ISIDA resulted in models based on atom/bond sequences involving two to three atoms with statistical parameters that were similar to those of models obtained with CODESSA-PRO (R(2) = 0.911-0.974; R(cv)(2) = 0.831-0.936). A mixed pool of molecular and fragment descriptors did not lead to significant improvement of the models.

QSAR studies on 1-phenylbenzimidazoles as inhibitors of the platelet-derived growth factor

This work is devoted to the development of quantitative structure-activity relationship (QSAR) models of the biological activity of 123 1-phenylbenzimidazoles as inhibitors of the PDGF receptor. The molecular features are represented by chemical descriptors that have been calculated on geometrical, topological, quantum mechanical, and electronic basis by using CODESSA PRO. The obtained models, linear (multilinear regression) and nonlinear (artificial neural network), are aimed to link the structures to their reported activity log 1/IC50. The former model can be used for physico-chemical interpretation, while the latter possesses a superior predictive ability.