Modeling steric and electronic effects in 3D- and 4D-QSAR schemes: predicting benzoic pK(a) values and steroid CBG binding affinities

6D-QSAR for predicting biological activity of human aldose reductase inhibitors using quasar receptor surface modeling

The application of QSAR analysis dates back a half-century ago and is currently continuously employed in any rational drug design. The multi-dimensional QSAR modeling can be a promising tool for researchers to develop reliable predictive QSAR models for designing novel compounds. In the present work, we studied inhibitors of human aldose reductase (AR) to generate multi-dimensional QSAR models using 3D- and 6D-QSAR methods. For this purpose, Pentacle and Quasar's programs were used to produce the QSAR models using corresponding dissociation constant (K_d) values. By inspecting the performance metrics of the generated models, we achieved similar results with comparable internal validation statistics. However, considering the externally validated values, 6D-QSAR models provide significantly better prediction of endpoint values. The obtained results suggest that the higher the dimension of the QSAR model, the higher the performance of the generated model. However, more studies are required to verify these outcomes.

Chemistry towards Biology-Instruct: Snapshot

The knowledge of interactions between different molecules is undoubtedly the driving force of all contemporary biomedical and biological sciences. Chemical biology/biological chemistry has become an important multidisciplinary bridge connecting the perspectives of chemistry and biology to the study of small molecules/peptidomimetics and their interactions in biological systems. Advances in structural biology research, in particular linking atomic structure to molecular properties and cellular context, are essential for the sophisticated design of new medicines that exhibit a high degree of druggability and very importantly, druglikeness. The authors of this contribution are outstanding scientists in the field who provided a brief overview of their work, which is arranged from in silico investigation through the characterization of interactions of compounds with biomolecules to bioactive materials.

Unsupervised Learning in Drug Design from Self-Organization to Deep Chemistry

The availability of computers has brought novel prospects in drug design. Neural networks (NN) were an early tool that cheminformatics tested for converting data into drugs. However, the initial interest faded for almost two decades. The recent success of Deep Learning (DL) has inspired a renaissance of neural networks for their potential application in deep chemistry. DL targets direct data analysis without any human intervention. Although back-propagation NN is the main algorithm in the DL that is currently being used, unsupervised learning can be even more efficient. We review self-organizing maps (SOM) in mapping molecular representations from the 1990s to the current deep chemistry. We discovered the enormous efficiency of SOM not only for features that could be expected by humans, but also for those that are not trivial to human chemists. We reviewed the DL projects in the current literature, especially unsupervised architectures. DL appears to be efficient in pattern recognition (Deep Face) or chess (Deep Blue). However, an efficient deep chemistry is still a matter for the future. This is because the availability of measured property data in chemistry is still limited.

Multiple Conformer Descriptors for QSAR Modeling

The most widely used QSAR approaches are mainly based on 2D molecular representation which ignores stereoconfiguration and conformational flexibility of compounds. 3D QSAR uses a single conformer of each compound which is difficult to choose reasonably. 4D QSAR uses multiple conformers to overcome the issues of 2D and 3D methods. However, many of existing 4D QSAR models suffer from the necessity to pre-align conformers, while alignment-independent approaches often ignore stereoconfiguration of compounds. In this study we propose a QSAR modeling approach based on transforming chirality-aware 3D pharmacophore descriptors of individual conformers into a set of latent variables representing the whole conformer set of a molecule. This is achieved by clustering together all conformers of all training set compounds. The final representation of a compound is a bit string encoding cluster membership of its conformers. In our study we used Random Forest, but this representation can be used in combination with any machine learning method. We compared this approach with conventional 2D and 3D approaches using multiple data sets and investigated the sensitivity of the approach proposed to tuning parameters: number of conformers and clusters.

Two Decades of 4D-QSAR: A Dying Art or Staging a Comeback?

A key question confronting computational chemists concerns the preferable ligand geometry that fits complementarily into the receptor pocket. Typically, the postulated ‘bioactive’ 3D ligand conformation is constructed as a ‘sophisticated guess’ (unnecessarily geometry-optimized) mirroring the pharmacophore hypothesis—sometimes based on an erroneous prerequisite. Hence, 4D-QSAR scheme and its ‘dialects’ have been practically implemented as higher level of model abstraction that allows the examination of the multiple molecular conformation, orientation and protonation representation, respectively. Nearly a quarter of a century has passed since the eminent work of Hopfinger appeared on the stage; therefore the natural question occurs whether 4D-QSAR approach is still appealing to the scientific community? With no intention to be comprehensive, a review of the current state of art in the field of receptor-independent (RI) and receptor-dependent (RD) 4D-QSAR methodology is provided with a brief examination of the ‘mainstream’ algorithms. In fact, a myriad of 4D-QSAR methods have been implemented and applied practically for a diverse range of molecules. It seems that, 4D-QSAR approach has been experiencing a promising renaissance of interests that might be fuelled by the rising power of the graphics processing unit (GPU) clusters applied to full-atom MD-based simulations of the protein-ligand complexes.

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.

xMaP-An Interpretable Alignment-Free Four-Dimensional Quantitative Structure-Activity Relationship Technique Based on Molecular Surface Properties and Conformer Ensembles

A novel alignment-free molecular descriptor called xMaP (flexible MaP descriptor) is introduced. The descriptor is the advancement of the previously published translationally and rotationally invariant three-dimensional (3D) descriptor MaP (mapping property distributions onto the molecular surface) to the fourth dimension (4D). In addition to MaP, xMaP is independent of the chosen starting conformation of the encoded molecules and is therefore entirely alignment-free. This is achieved by using ensembles of conformers, which are generated by conformational searches. This step of the procedure is similar to Hopfinger's 4D quantitative structure-activity relationship (QSAR). A five-step procedure is used to compute the xMaP descriptor. First, a conformational search for each molecule is carried out. Next, for each of the conformers an approximation to the molecular surface with equally distributed surface points is computed. Third, molecular properties are projected onto this surface. Fourth, areas of identical properties are clustered to so-called patches. Fifth, the spatial distribution of the patches is converted into an alignment-free descriptor that is based on the entire conformer ensemble. The resulting descriptor can be interpreted by superimposing the most important descriptor variables and the molecules of the data set. The most important descriptor variables are identified with chemometric regression tools. The novel descriptor was applied to several benchmark data sets and was compared to other descriptors and QSAR techniques comprising a binary fingerprint, a topological pharmacophore descriptor (Cats2D), and the field-based 3D-QSAR technique GRID/PLS which is alignment-dependent. The use of conformer ensembles renders xMaP very robust. It turns out that xMaP performs very well on (almost) all data sets and that the statistical results are comparable to GRID/PLS. In addition to that, xMaP can also be used to efficiently visualize the derived quantitative structure-activity relationships.

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.

Multidimensional (3D/4D-QSAR) probability-guided pharmacophore mapping: investigation of activity profile for a series of drug absorption promoters

A hybrid approach that combines 3D and 4D-QSAR methods based on grid and neural paradigms with automated IVE-PLS procedure was examined to identify the pharmacophore pattern for cholic acid derivatives as potential drug absorption promoters.

Modeling robust QSAR. 1. Coding molecules in 3D-QSAR--from a point to surface sectors and molecular volumes

Shape analysis is a powerful tool in chemistry and drug design. In the current work, we compare the results of CoMFA and Comparative Molecular Surface Analysis (CoMSA), the 3D-QSAR method, for a series of hypolipidemic and antiplatelet asarones and antifungal N-myristoyltransferase inhibitors. In this publication we show that a sector CoMSA formalism enables an analysis of the biological activity that is more directly related to the molecular shape and individual molecular functionalities than the traditional uniform and directionless CoMFA field. Iterative Variable Elimination allowed us to identify the potential pharmacophoric sites. We modeled QSARs for both series and demonstrate that sector-based molecular descriptors give very predictive models and allow one to generate a spatial interpretation of the QSAR models. In particular, we identified the central aromatic ring and carbonyl functions as the moieties determining the activity of the asarones series, while the pattern of substitution of the aromatic ring determines the activity of N-myristoyltransferase inhibitors.

A 4D-QSAR study on anti-HIV HEPT analogues

We used the 4D-QSAR method coupled with the PLS analysis and uninformative variable elimination or its variants for the investigations of the antiviral activity of HEPT, a series of conformationally flexible molecules that bind HIV-1 reverse transcriptase. An analysis of several Hopfinger's and SOM-4D-QSAR models indicated that both methods yield comparable results. Generally, charge descriptors provide better modeling efficiency. We have shown that the method properly indicates the mode of interaction revealed by X-ray studies. It also allows us to calculate highly predictive QSAR models.

Prediction of pKa for Neutral and Basic Drugs Based on Radial Basis Function Neural Networks and the Heuristic Method

PURPOSES

Quantitative structure-property relationships (QSPR) were developed to predict the pK(a) values of a set of neutral and basic drugs via linear and nonlinear methods. The ability of the models to predict pK(a) was assessed and compared.

METHODS

The descriptors of 74 neutral and basic drugs in this study were calculated by the software CODESSA, which can calculate constitutional, topological, geometrical, electrostatic, and quantum chemical descriptors. Linear and nonlinear QSPR models were developed based on the heuristic method (HM) and radial basis function neural networks (RBFNN), respectively. The heuristic method was also used for the preselection of appropriate molecular descriptors.

RESULTS

The obtained linear model had a correlation coefficient of r=0.884, F=37.72 with a root-mean-squared (RMS) error of 0.482 for the training set, and r=0.693, F=11.99, nd RMS=0.987 for the test set. The RMS in predicting the overall data set is 0.619. The nonlinear model gave better results; for the training set, r=0.886, F=202.314, and RMS=0.458, and for the test set r=0.737, F=15.41, and RMS=0.613. The RMS error in prediction for overall data set is 0.493. Prediction results from nonlinear model are in good agreement with experimental values.

CONCLUSIONS

In present study, we developed a QSPR model to predict the important parameter (pK(a)) of neutral and basic drugs. The model is useful in predicting pK(a) during the discovery of new drugs when experimental data are unknown.

Self-organizing neural networks for modeling robust 3D and 4D QSAR: application to dihydrofolate reductase inhibitors

We have used SOM and grid 3D and 4D QSAR schemes for modeling the activity of a series of dihydrofolate reductase inhibitors. Careful analysis of the performance and external predictivities proves that this method can provide an efficient inhibition model.