E-state modeling of corticosteroids binding affinity validation of model for small data set

Higher-Order and Mixed Discrete Derivatives such as a Novel Graph- Theoretical Invariant for Generating New Molecular Descriptors

BACKGROUND

Recently, some authors have defined new molecular descriptors (MDs) based on the use of the Graph Discrete Derivative, known as Graph Derivative Indices (GDI). This new approach about discrete derivatives over various elements from a graph takes as outset the formation of subgraphs. Previously, these definitions were extended into the chemical context (N-tuples) and interpreted in structural/physicalchemical terms as well as applied into the description of several endpoints, with good results.

OBJECTIVE

A generalization of GDIs using the definitions of Higher Order and Mixed Derivative for molecular graphs is proposed as a generalization of the previous works, allowing the generation of a new family of MDs.

METHODS

An extension of the previously defined GDIs is presented, and for this purpose, the concept of Higher Order Derivatives and Mixed Derivatives is introduced. These novel approaches to obtaining MDs based on the concepts of discrete derivatives (finite difference) of the molecular graphs use the elements of the hypermatrices conceived from 12 different ways (12 events) of fragmenting the molecular structures. The result of applying the higher order and mixed GDIs over any molecular structure allows finding Local Vertex Invariants (LOVIs) for atom-pairs, for atoms-pairs-pairs and so on. All new families of GDIs are implemented in a computational software denominated DIVATI (acronym for Discrete DeriVAtive Type Indices), a module of KeysFinder Framework in TOMOCOMD-CARDD system.

RESULTS

QSAR modeling of the biological activity (Log 1/K) of 31 steroids reveals that the GDIs obtained using the higher order and mixed GDIs approaches yield slightly higher performance compared to previously reported approaches based on the duplex, triplex and quadruplex matrix. In fact, the statistical parameters for models obtained with the higher-order and mixed GDI method are superior to those reported in the literature by using other 0-3D QSAR methods.

CONCLUSION

It can be suggested that the higher-order and mixed GDIs, appear as a promissory tool in QSAR/QSPRs, similarity/dissimilarity analysis and virtual screening studies.

QuBiLS-MAS, open source multi-platform software for atom- and bond-based topological (2D) and chiral (2.5D) algebraic molecular descriptors computations

BACKGROUND

In previous reports, Marrero-Ponce et al. proposed algebraic formalisms for characterizing topological (2D) and chiral (2.5D) molecular features through atom- and bond-based ToMoCoMD-CARDD (acronym for Topological Molecular Computational Design-Computer Aided Rational Drug Design) molecular descriptors. These MDs codify molecular information based on the bilinear, quadratic and linear algebraic forms and the graph-theoretical electronic-density and edge-adjacency matrices in order to consider atom- and bond-based relations, respectively. These MDs have been successfully applied in the screening of chemical compounds of different therapeutic applications ranging from antimalarials, antibacterials, tyrosinase inhibitors and so on. To compute these MDs, a computational program with the same name was initially developed. However, this in house software barely offered the functionalities required in contemporary molecular modeling tasks, in addition to the inherent limitations that made its usability impractical. Therefore, the present manuscript introduces the QuBiLS-MAS (acronym for Quadratic, Bilinear and N-Linear mapS based on graph-theoretic electronic-density Matrices and Atomic weightingS) software designed to compute topological (0-2.5D) molecular descriptors based on bilinear, quadratic and linear algebraic forms for atom- and bond-based relations.

RESULTS

The QuBiLS-MAS module was designed as standalone software, in which extensions and generalizations of the former ToMoCoMD-CARDD 2D-algebraic indices are implemented, considering the following aspects: (a) two new matrix normalization approaches based on double-stochastic and mutual probability formalisms; (b) topological constraints (cut-offs) to take into account particular inter-atomic relations; (c) six additional atomic properties to be used as weighting schemes in the calculation of the molecular vectors; (d) four new local-fragments to consider molecular regions of interest; (e) number of lone-pair electrons in chemical structure defined by diagonal coefficients in matrix representations; and (f) several aggregation operators (invariants) applied over atom/bond-level descriptors in order to compute global indices. This software permits the parallel computation of the indices, contains a batch processing module and data curation functionalities. This program was developed in Java v1.7 using the Chemistry Development Kit library (version 1.4.19). The QuBiLS-MAS software consists of two components: a desktop interface (GUI) and an API library allowing for the easy integration of the latter in chemoinformatics applications. The relevance of the novel extensions and generalizations implemented in this software is demonstrated through three studies. Firstly, a comparative Shannon's entropy based variability study for the proposed QuBiLS-MAS and the DRAGON indices demonstrates superior performance for the former. A principal component analysis reveals that the QuBiLS-MAS approach captures chemical information orthogonal to that codified by the DRAGON descriptors. Lastly, a QSAR study for the binding affinity to the corticosteroid-binding globulin using Cramer's steroid dataset is carried out.

CONCLUSIONS

From these analyses, it is revealed that the QuBiLS-MAS approach for atom-pair relations yields similar-to-superior performance with regard to other QSAR methodologies reported in the literature. Therefore, the QuBiLS-MAS approach constitutes a useful tool for the diversity analysis of chemical compound datasets and high-throughput screening of structure-activity data.

BCL::EMAS--enantioselective molecular asymmetry descriptor for 3D-QSAR

Stereochemistry is an important determinant of a molecule’s biological activity. Stereoisomers can have different degrees of efficacy or even opposing effects when interacting with a target protein. Stereochemistry is a molecular property difficult to represent in 2D-QSAR as it is an inherently three-dimensional phenomenon. A major drawback of most proposed descriptors for 3D-QSAR that encode stereochemistry is that they require a heuristic for defining all stereocenters and rank-ordering its substituents. Here we propose a novel 3D-QSAR descriptor termed Enantioselective Molecular ASymmetry (EMAS) that is capable of distinguishing between enantiomers in the absence of such heuristics. The descriptor aims to measure the deviation from an overall symmetric shape of the molecule. A radial-distribution function (RDF) determines a signed volume of tetrahedrons of all triplets of atoms and the molecule center. The descriptor can be enriched with atom-centric properties such as partial charge. This descriptor showed good predictability when tested with a dataset of thirty-one steroids commonly used to benchmark stereochemistry descriptors (r² = 0.89, q² = 0.78). Additionally, EMAS improved enrichment of 4.38 versus 3.94 without EMAS in a simulated virtual high-throughput screening (vHTS) for inhibitors and substrates of cytochrome P450 (PUBCHEM AID891).

Topological, hydrophobicity, and other descriptors on α-glucosidase inhibition: a QSAR study on xanthone derivatives

Quantitative structure activity relationship analysis was performed on a series of xanthone derivatives to establish the structural features required for α-glucosidase inhibitory activity. The computational and statistical analysis was performed with V life MDS (Molecular Design Suite) and Statistica software. The selected models show significant predictive power, stability, and reliability in terms of cross-validated correlation coefficient (Q(2)(cv) > 0.74 and Q(2)(test) > 0.5) and other validation parameters. The results show that the SaaaC count, MMFF_6 and dipole moment are mainly contributed for the activity along with the hydrophobicity descriptors. It describes that heteroatoms (oxygen atom connected with carbon atom) in the molecules are favourable for α-glucosidase inhibitory activity. The E-state count descriptor suggests that when carbon atoms connected with three aromatic bonds and hydrogen or other atoms are favourable for the activity. The SAHA and SAMH descriptors show that the hydrophilic area in the molecule is important for the activity while high hydrophilicity is unfavourable for the activity. This study concluded that hydrophilic, polar and/or electron negative groups, which are responsible for hydrogen bonding and interaction with the enzyme for favourable activity.

Prediction of HPLC retention index using artificial neural networks and IGroup E-state indices

A back-propagation artificial neural network (ANN) was used to create a 10-fold leave-10%-out cross-validated ensemble model of high performance liquid chromatography retention index (HPLC-RI) for a data set of 498 diverse druglike compounds. A 10-fold multiple linear regression (MLR) ensemble model of the same data was developed for comparison. Molecular structure was described using IGroup E-state indices, a novel set of structure-information representation (SIR) descriptors, along with molecular connectivity chi and kappa indices and other SIR descriptors previously reported. The same input descriptors were used to develop models by both learning algorithms. The MLR model yielded marginally acceptable statistics with training correlation r(2) = 0.65, mean absolute error (MAE) = 83 RI units. External validation of 104 compounds not used for model development yielded validation v(2) = 0.49 and MAE = 73 RI units. The distribution of residuals for the fit and validate data sets suggest a nonlinear relationship between retention index and molecular structure as described by the SIR indices. Not surprisingly, the ANN model was significantly more accurate for both training and validation with training set r(2) = 0.93, MAE = 30 RI units and validation v(2) = 0.84, MAE = 41 RI units. For the ANN model, a total of 91% of validation predictions were within 100 RI units of the experimental value.

Glucocorticoid receptor binding: a biphasic dependence on molecular size as revealed by the bilinear LinBiExp model

For corticosteroids, receptor-binding affinity (RBA) at the glucocorticoid receptor (GR) is a major determinant of therapeutic potential. Here, the results of a comprehensive quantitative analysis of relative RBA (rRBA) data obtained from more than a hundred active structures are reported. Because of a clear biphasic size-dependence, the recently introduced linearized biexponential (LinBiExp) model provided very good fit: for steroids that satisfy the main binding criteria at the GR, it accounts for close to 80% of the variability in the free energy of binding DeltaG0 (or logrRBA) data by using only two descriptors: calculated molecular volume and an indicator variable for the presence of 6alpha/9alpha-halogen or cyclic 16,17-acetal moieties. Accordingly, binding is strongest for corticosteroids close to an ideal size that is large enough to provide as large nonspecific (van der Waals-type) interactions as possible, but is not too large to have difficulty fitting due to size-limitations at the binding site. Binding affinity is dramatically increased by 6alpha- or 9alpha-halogenation or introduction of a cyclic 16,17-acetal moiety (in average, about 7-fold), but there is no significant increase after the first substitution. Known highly active glucocorticoids, such as betamethasone 17-monopropionate, fluticasone propionate, or mometasone furoate, indeed satisfy both of these criteria. For small-enough structures, the obtained size-dependency (slope) of the free energy of binding suggest that, as long as only nonspecific interactions are involved, addition of a methylene-sized non-hydrogen atom to the ligand structure increases DeltaG0 on average by about 1.5 kJ/mol, corresponding to an almost doubling of the binding affinity.

Atom-based stochastic and non-stochastic 3D-chiral bilinear indices and their applications to central chirality codification

Non-stochastic and stochastic 2D bilinear indices have been generalized to codify chemical structure information for chiral drugs, making use of a trigonometric 3D-chirality correction factor. In order to evaluate the effectiveness of this novel approach in drug design we have modeled the angiotensin-converting enzyme inhibitory activity of perindoprilate's sigma-stereoisomers combinatorial library. Two linear discriminant analysis models, using non-stochastic and stochastic linear indices, were obtained. The models had shown an accuracy of 95.65% for the training set and 100% for the external prediction set. Next the prediction of the sigma-receptor antagonists of chiral 3-(3-hydroxyphenyl)piperidines by multiple linear regression analysis was carried out. Two statistically significant QSAR models were obtained when non-stochastic (R(2)=0.953 and s=0.238) and stochastic (R(2)=0.961 and s=0.219) 3D-chiral bilinear indices were used. These models showed adequate predictive power (assessed by the leave-one-out cross-validation experiment) yielding values of q(2)=0.935 (s(cv)=0.259) and q(2)=0.946 (s(cv)=0.235), respectively. Finally, the prediction of the corticosteroid-binding globulin binding affinity of steroids set was performed. The obtained results are rather similar to most of the 3D-QSAR approaches reported so far. The validation of this method was achieved by comparison with previous reports applied to the same data set. The non-stochastic and stochastic 3D-chiral linear indices appear to provide a very interesting alternative to other more common 3D-QSAR descriptors.

Prediction of aqueous solubility based on large datasets using several QSPR models utilizing topological structure representation

Several QSPR models were developed for predicting intrinsic aqueous solubility, S(o). A data set of 5,964 neutral compounds was sub-divided into two classes, aromatic and non-aromatic compounds. Three models were created with different methods on both data sets: two regression models (multiple linear regression and partial least squares) and an artificial neural network model. These models were based on 3343 aromatic and 1674 non-aromatic compounds for training sets; 938 compounds were used in external validation testing. The range in -log S(o) is -1.6 to 10. Topological structure descriptors were used with all models. A genetic algorithm was used for descriptor selection for regression models. For the artificial neural network (ANN) model, descriptor selection was done with a backward elimination process. All models performed well with r2 values ranging 0.72 to 0.84 in external validation testing. The mean absolute errors in validation ranged from 0.44 to 0.80 for the classes of compounds for all the models. These statistical results indicate a sound ANN model. Furthermore, in a comparison with eight other available models, based on predictions using a validation test set (442 compounds), the artificial neural network model presented in this work (CSLogWS) was clearly superior based on both the mean absolute error and the percentage of residuals less than one log unit. In the ANN model both E-State and hydrogen E-State descriptors were found to be important.

Quantitative Structure−Activity (Affinity) Relationship (QSAR) Study on Protonation and Cationization of α-Amino Acids

A quantitative structure-activity (affinity) relationship (QSAR) study is carried out to model the proton, sodium, copper, and silver cation affinities of alpha-amino acids (AA). Stepping multiple linear regression (MLR), partial least squares (PLS), and artificial neural network (ANN) approaches are applied to elucidate the multiple factors affecting these affinities. The MLR and PLS models reveal that the variation in proton affinity is attributed to the highest electrophilic superdelocalizability of nitrogen (major) and the number of rotatable bonds (minor) in AA. The noncovalent interactions, especially ion-dipole interactions, are responsible for the changes in Na+ affinity. The ionization potential, dipole moment of the side chain, and degree of linearity are the properties of AA that give the best correlation with the Cu+ and Ag+ affinities. The ANN models are developed to study the relationships (linear or nonlinear) between the molecular descriptors and binding affinities. The ANN models show higher predictive power. The QSAR models are used to study the binding forms of AA (neutral vs zwitterionic) upon protonation/cationization. To our knowledge, this is the first attempt to carry out a QSAR study on protonated/cationized AlphaAlpha to elucidate their binding properties. In virtue of the Na+ affinity ANN model, the Na+ affinities of dihydroxyphenylalanine (DOPA) were predicted. This work may pave the way for the success of applying similar approaches to peptides or proteins (with AA as the building blocks) in the future.

Atom-based 3D-chiral quadratic indices. Part 2: Prediction of the corticosteroid-binding globulinbinding affinity of the 31 benchmark steroids data set

A quantitative structure-activity relationship (QSAR) study to predict the relative affinities of the steroid 'benchmark' data set to the corticosteroid-binding globulin (CBG) is described. It is shown that the 3D-chiral quadratic indices closely correlate with the measured CBG affinity values for the 31 steroids. The calculated descriptors were correlated with biological data through multiple linear regressions. Two statistically significant models were obtained when non-stochastic (R = 0.924 and s = 0.46) as well as stochastic (R = 0.929 and s = 0.46) 3D-chiral quadratic indices were used. A leave-one-out (LOO) approach to model validation is used here; the best results obtained in the cross-validation procedure with non-stochastic (q2 = 0.781) and stochastic (q2 = 0.735) 3D-chiral quadratic indices are better or similar to most of the 3D-QSAR approaches reported so far. These results support the idea that the 3D-chiral quadratic indices may be helpful in prediction of the corticosteroid-binding affinity for new compounds.

Novel distance-based atom-type topological indices DAI for QSPR/QSAR studies of alcohols

In this work, we propose a distance-based atom-type topological index (DAI) for quantitative structure-property/activity relationship (QSPR/QSAR) studies. The newly constructed index, which codes the structural environment of each atom type in a molecule, can be calculated simply. These atom-type topological indices, along with our recently proposed Lu index, were used to construct QSPR/QSAR models for several representative physical properties and biological activities of several data sets of alcohols with a range of non-hydrogen atoms by using multiple linear regression (MLR) analysis. The efficiency of these indices is verified by high quality QSPR models. The results indicate that the combined use of Lu and DAI indices promises to be a useful method for QSPR/QSAR analysis of complex compounds.

Quantitative structure-activity relationships of mutagenic activity from quantum topological descriptors: triazenes and halogenated hydroxyfuranones (mutagen-X) derivatives

The mutagenic activity of 23 triazenes and, in a different set, of 24 halogenated hydroxyfuranones (MX derivatives) is quantitatively related to new features of contemporary molecular wave functions. Nowadays affordable computers are powerful enough to rapidly generate geometry-optimised ab initio wave functions at HF/3-21G*, HF/6-31G* and B3LYP/6-311 + G(2d,p) level for all molecules. The bonds of a common molecular skeleton are described by their ab initio bond lengths and local properties provided by the theory of quantum chemical topology (QCT). The chemometric analysis involves two types: one to generate a statistically validated quantitative model, and one to isolate the active center. In the former a genetic algorithm (GA) selects bond descriptors in order to optimise the cross-validation error, q2, followed by a full partial least squares (PLS) analysis, which also yields randomisation statistics. In the latter type principal components (PCs) are constructed from the original bond descriptors and their variables important to the projection (VIPs) are plotted in a histogram. This analysis suggests a preferred mechanistic pathway for the initial hydroxylation of the triazenes, an issue that has remained ambiguous so far. In the case of the hydroxyfuranones the proposed method aids the elucidation of a mechanistic ambivalence.

QSAR modeling based on structure-information for properties of interest in human health

The development of QSAR models based on topological structure description is presented for problems in human health. These models are based on the structure-information approach to quantitative biological modeling and prediction, in contrast to the mechanism-based approach. The structure-information approach is outlined, starting with basic structure information developed from the chemical graph (connection table). Information explicit in the connection table (element identity and skeletal connections) leads to significant (implicit) structure information that is useful for establishing sound models of a wide range of properties of interest in drug design. Valence state definition leads to relationships for valence state electronegativity and atom/group molar volume. Based on these important aspects of molecules, together with skeletal branching patterns, both the electrotopological state (E-state) and molecular connectivity (chi indices) structure descriptors are developed and described. A summary of four QSAR models indicates the wide range of applicability of these structure descriptors and the predictive quality of QSAR models based on them: aqueous solubility (5535 chemically diverse compounds, 938 in external validation), percent oral absorption (%OA, 417 therapeutic drugs, 195 drugs in external validation testing), AMES mutagenicity (2963 compounds including 290 therapeutic drugs, 400 in external validation), fish toxicity (92 substituted phenols, anilines and substituted aromatics). These models are established independent of explicit three-dimensional (3-D) structure information and are directly interpretable in terms of the implicit structure information useful to the drug design process.

Quantitative structure-activity relationships from optimised ab initio bond lengths: steroid binding affinity and antibacterial activity of nitrofuran derivatives

The present day abundance of cheap computing power enables the use of quantum chemical ab initio data in Quantitative Structure-Activity Relationships (QSARs). Optimised bond lengths are a new such class of descriptors, which we have successfully used previously in representing electronic effects in medicinal and ecological QSARs (enzyme inhibitory activity, hydrolysis rate constants and pKas). Here we use AM1 and HF/3-21G* bond lengths in conjunction with Partial Least Squares (PLS) and a Genetic Algorithm (GA) to predict the Corticosteroid-Binding Globulin (CBG) binding activity of the classic steroid data set, and the antibacterial activity of nitrofuran derivatives. The current procedure, which does not require molecular alignment, produces good r2 and q2 values. Moreover, it highlights regions in the common steroid skeleton deemed relevant to the active regions of the steroids and nitrofuran derivatives.

QSAR modeling of beta-lactam binding to human serum proteins

The binding of beta-lactams to human serum proteins was modeled with topological descriptors of molecular structure. Experimental data was the concentration of protein-bound drug expressed as a percent of the total plasma concentration (percent fraction bound, PFB) for 87 penicillins and for 115 beta-lactams. The electrotopological state indices (E-State) and the molecular connectivity chi indices were found to be the basis of two satisfactory models. A data set of 74 penicillins from a drug design series was successfully modeled with statistics: r2 = 0.80, s = 12.1, q2 = 0.76, spress = 13.4. This model was then used to predict protein binding (PFB) for 13 commercial penicillins, resulting in a very good mean absolute error, MAE = 12.7 and correlation coefficient, q2 = 0.84. A group of 28 cephalosporins were combined with the penicillin data to create a dataset of 115 beta-lactams that was successfully modeled: r2 = 0.82, s = 12.7, q2 = 0.78, spress = 13.7. A ten-fold 10% leave-group-out (LGO) cross-validation procedure was implemented, leading to very good statistics: MAE = 10.9, spress = 14.0, q2 (or r2press) = 0.78. The models indicate a combination of general and specific structure features that are important for estimating protein binding in this class of antibiotics. For the beta-lactams, significant factors that increase binding are presence and electron accessibility of aromatic rings, halogens, methylene groups, and =N- atoms. Significant negative influence on binding comes from amine groups and carbonyl oxygen atoms.

E-state modeling of fish toxicity independent of 3D structure information

Topological structure methods are used to model fish toxicity against three classes of organic chemicals. The models were obtained independent of 3D structure information. Further, no mechanism of partitioning was assumed, thus avoiding the problems associated with selection of partitioning system for computation of log P. QSAR models were developed for a set of 92 compounds, including phenols, anilines and substituted aromatic hydrocarbons, yielding excellent statistics: r2 = 0.87, s = 0.25 and q2 = 0.85 leave-one-out (LOO), that are better than those reported in the literature. The model is based on molecular connectivity valence chi-1 index [1chiv], the atom type E-State indices for chlorine [ST(-Cl)] and for ether oxygen [ST(-O-)], and the maximum hydrogen E-State atom value in a molecule [Hmax]. Each of the subgroups was also separately well modeled. The model for the full set is validated through use of external validation test sets and ten-fold cross-validation (repeated three times). The quality of the validation statistics supports the claim that the model may be used for estimation of pLC50 values for similar molecules. Detailed structure interpretation is given for the descriptors in the model. These four structure descriptors encode influence of molecular context of groups as well as counts of those groups, in addition to molecular skeletal structure.

E-state modeling of HIV-1 protease inhibitor binding independent of 3D information

Data for HIV-1 protease inhibitors (in vitro enzyme binding) were used as a training set to develop a QSAR model based on topological descriptors, including two hydrogen E-state indices, along with a molecular connectivity chi and a kappa shape index. A statistically satisfactory four-variable model was obtained for the 32 compounds in the training set, r2 = 0.86, s = 0.60, and q2 = 0.79, without the use of information from 3D geometries or detailed interaction energy calculations. The model was validated through the prediction of 15 compounds in the external test set, yielding a mean absolute error, MAE, = 0.82. Structure interpretation is given for each variable to assist in the design of new compounds. Structure features emphasized in the model include hydrogen bond donating ability, nonpolar groups, skeletal branching, and molecular globularity. On the basis of these statistical criteria, this E-state model may be considered useful for prediction of pIC50 values for new HIV-1 protease inhibitors.