Trends in information theory-based chemical structure codification

Digitalizing Structure–Symmetry Relations at the Formation of Endofullerenes in Terms of Information Entropy Formalism

Information entropy indices are widely used for numerical descriptions of chemical structures, though their applications to the processes are scarce. We have applied our original information entropy approach to filling fullerenes with a guest atom. The approach takes into account both the topology and geometry of the fullerene structures. We have studied all possible types of such fillings and found that information entropy (ΔhR) and symmetry changes correlate. ΔhR is negative, positive or zero if symmetry is increased, reduced or does not change, respectively. The ΔhR value and structural reorganization entropy, a contribution to ΔhR, are efficient parameters for the digital classification of the fullerenes involved into the filling process. Based on the calculated values, we have shown that, as the symmetry of the fullerene cage becomes higher, the structural changes due to the filling it with a guest atom become larger. The corresponding analytical expressions and numerical data are discussed.

Molecular size and molecular structure: Discriminating their changes upon chemical reactions in terms of information entropy

Structural descriptors take the central place in the digitalization of chemical reactions. Information entropy is one of such descriptors that has been a seminal for numerous derivative indices. Previously, we have studied the rules of calculating information entropies of molecular ensembles based on the corresponding values of constituting molecules and found that the complexity of the ensemble has the contributions from the molecular structure and the size of the molecules. Considering chemical reaction as the conversion of one molecular ensemble to another allows calculating the change in information entropy as well as its components associated with molecular-structure and molecular-size changes. We demonstrate that both total information entropy change and its contributions are characteristic for the selected classes of chemical reactions and exemplify this approach with the cycloaddition and exchange reactions widespread in organic chemistry.

Water Activity Prediction in Sugar and Polyol Systems Using Theoretical Molecular Descriptors

Water activity is a key factor in the development of pharmaceutical, cosmetic, and food products. In aqueous solutions of nonelectrolytes, the Norrish model provides a simple and effective way to evaluate this quantity. However, it contains a parameter, known as the Norrish constant, that must be estimated from experimental data. In this study, a new strategy is proposed for the prediction of water activity in the absence of experimental information, based on the use of theoretical molecular descriptors for characterizing the effects of a solute. This approach was applied to the evaluation of water activity in the presence of sugars (glucose, fructose, xylose, sucrose) and polyols (sorbitol, xylitol, glycerol, erythritol). The use of two descriptors related to the constitutional and connectivity properties of the solutes was first investigated. Subsequently, a new theoretical descriptor, named the global information index (G), was developed. By using this index, the water activity curves in the binary systems were reconstructed. The positive results obtained support the proposed strategy, as well as the possibility of including, in a single information index, the main molecular features of a solute that determine its effects on water activity.

Information Entropy in Chemistry: An Overview

Basic applications of the information entropy concept to chemical objects are reviewed. These applications deal with quantifying chemical and electronic structures of molecules, signal processing, structural studies on crystals, and molecular ensembles. Recent advances in the mentioned areas make information entropy a central concept in interdisciplinary studies on digitalizing chemical reactions, chemico-information synthesis, crystal engineering, as well as digitally rethinking basic notions of structural chemistry in terms of informatics.

Partition and Colored Distances in Graphs Induced to Subsets of Vertices and Some of Its Applications

If G is a graph and P is a partition of V(G), then the partition distance of G is the sum of the distances between all pairs of vertices that lie in the same part of P. A colored distance is the dual concept of the partition distance. These notions are motivated by a problem in the facility location network and applied to several well-known distance-based graph invariants. In this paper, we apply an extended cut method to induce the partition and color distances to some subsets of vertices which are not necessary a partition of V(G). Then, we define a two-dimensional weighted graph and an operator to prove that the induced partition and colored distances of a graph can be obtained from the weighted Wiener index of a two-dimensional weighted quotient graph induced by the transitive closure of the Djoković–Winkler relation as well as by any partition that is coarser. Finally, we utilize our main results to find some upper bounds for the modified Wiener index and the number of orbits of partial cube graphs under the action of automorphism group of graphs.

Classification of isentropic molecules in terms of Shannon entropy

Shannon entropy is widely used as a descriptor of molecular structure. Isentropicity of the molecules in terms of Shannon approach emerges in specific problems of physical and organic chemistry. In the present work, we consider the main classes of isentropic molecules, exemplify them, and provide their hierarchy.

Generative Adversarial Networks (GANs) Based Synthetic Sampling for Predictive Modeling

In the present report we evaluate the possible utility of the Generative Adversarial Networks (GANs) in mapping the chemical structural space for molecular property profiles, with the goal of subsequently yielding synthetic (artificial) samples for ligand-based molecular modeling. Two case studies are considered: BACE-1 (β-Secretase 1) and DENV (Dengue Virus) inhibitory activities, with the former focused on data populating and the latter on data balancing tasks. We train GANs using subsamples extracted from datasets for each bioactivity endpoint, and apply the trained networks in generating synthetic examples from the respective bioactivity chemical spaces. Original and synthetic samples are pooled together and employed to build BACE-1 and DENV inhibitory activity classifiers and their performance evaluated over tenfold external validation sets. In both case studies, the obtained classifiers demonstrate satisfactory predictivity with the former yielding accuracy (ACC) and Mathew's correlation coefficient (MCC) values of 0.80 and 0.59, while the latter produces balanced accuracy(BACC) and MCC values of 0.81 and 0.70, respectively. Moreover, the statistics of these classifiers are compared with those of other models in the literature demonstrating comparable to better performance. These results suggest that GANs may be useful in mapping the chemical space for molecular property profiles of interest, and thus allow for the extraction of synthetic examples for computational modeling.

Alignment-Free Method to Predict Enzyme Classes and Subclasses

The Enzyme Classification (EC) number is a numerical classification scheme for enzymes, established using the chemical reactions they catalyze. This classification is based on the recommendation of the Nomenclature Committee of the International Union of Biochemistry and Molecular Biology. Six enzyme classes were recognised in the first Enzyme Classification and Nomenclature List, reported by the International Union of Biochemistry in 1961. However, a new enzyme group was recently added as the six existing EC classes could not describe enzymes involved in the movement of ions or molecules across membranes. Such enzymes are now classified in the new EC class of translocases (EC 7). Several computational methods have been developed in order to predict the EC number. However, due to this new change, all such methods are now outdated and need updating. In this work, we developed a new multi-task quantitative structure-activity relationship (QSAR) method aimed at predicting all 7 EC classes and subclasses. In so doing, we developed an alignment-free model based on artificial neural networks that proved to be very successful.

Tensor Algebra-based Geometrical (3D) Biomacro-Molecular Descriptors for Protein Research: Theory, Applications and Comparison with other Methods

In this report, a new type of tridimensional (3D) biomacro-molecular descriptors for proteins are proposed. These descriptors make use of multi-linear algebra concepts based on the application of 3-linear forms (i.e., Canonical Trilinear (Tr), Trilinear Cubic (TrC), Trilinear-Quadratic-Bilinear (TrQB) and so on) as a specific case of the N-linear algebraic forms. The definition of the kth 3-tuple similarity-dissimilarity spatial matrices (Tensor's Form) are used for the transformation and for the representation of the existing chemical information available in the relationships between three amino acids of a protein. Several metrics (Minkowski-type, wave-edge, etc) and multi-metrics (Triangle area, Bond-angle, etc) are proposed for the interaction information extraction, as well as probabilistic transformations (e.g., simple stochastic and mutual probability) to achieve matrix normalization. A generalized procedure considering amino acid level-based indices that can be fused together by using aggregator operators for descriptors calculations is proposed. The obtained results demonstrated that the new proposed 3D biomacro-molecular indices perform better than other approaches in the SCOP-based discrimination and the prediction of folding rate of proteins by using simple linear parametrical models. It can be concluded that the proposed method allows the definition of 3D biomacro-molecular descriptors that contain orthogonal information capable of providing better models for applications in protein science.

Choquet integral-based fuzzy molecular characterizations: when global definitions are computed from the dependency among atom/bond contributions (LOVIs/LOEIs)

BACKGROUND

Several topological (2D) and geometric (3D) molecular descriptors (MDs) are calculated from local vertex/edge invariants (LOVIs/LOEIs) by performing an aggregation process. To this end, norm-, mean- and statistic-based (non-fuzzy) operators are used, under the assumption that LOVIs/LOEIs are independent (orthogonal) values of one another. These operators are based on additive and/or linear measures and, consequently, they cannot be used to encode information from interrelated criteria. Thus, as LOVIs/LOEIs are not orthogonal values, then non-additive (fuzzy) measures can be used to encode the interrelation among them.

RESULTS

General approaches to compute fuzzy 2D/3D-MDs from the contribution of each atom (LOVIs) or covalent bond (LOEIs) within a molecule are proposed, by using the Choquet integral as fuzzy aggregation operator. The Choquet integral-based operator is rather different from the other operators often used for the 2D/3D-MDs calculation. It performs a reordering step to fuse the LOVIs/LOEIs according to their magnitudes and, in addition, it considers the interrelation among them through a fuzzy measure. With this operator, fuzzy definitions can be derived from traditional or recent MDs; for instance, fuzzy Randic-like connectivity indices, fuzzy Balaban-like indices, fuzzy Kier-Hall connectivity indices, among others. To demonstrate the feasibility of using this operator, the QuBiLS-MIDAS 3D-MDs were used as study case and, as a result, a module was built into the corresponding software to compute them ( http://tomocomd.com/qubils-midas ). Thus, it is the only software reported in the literature that can be employed to determine Choquet integral-based fuzzy MDs. Moreover, regression models were created on eight chemical datasets. In this way, a comparison between the results achieved by the models based on the non-fuzzy QuBiLS-MIDAS 3D-MDs with regard to the ones achieved by the models based on the fuzzy QuBiLS-MIDAS 3D-MDs was made. As a result, the models built with the fuzzy QuBiLS-MIDAS 3D-MDs achieved the best performance, which was statistically corroborated through the Wilcoxon signed-rank test.

CONCLUSIONS

All in all, it can be concluded that the Choquet integral constitutes a prominent alternative to compute fuzzy 2D/3D-MDs from LOVIs/LOEIs. In this way, better characterizations of the compounds can be obtained, which will be ultimately useful in enhancing the modelling ability of existing traditional 2D/3D-MDs.

Discrete Fourier Transform-Based Multivariate Image Analysis: Application to Modeling of Aromatase Inhibitory Activity

We recently generalized the formerly alignment-dependent multivariate image analysis applied to quantitative structure-activity relationships (MIA-QSAR) method through the application of the discrete Fourier transform (DFT), allowing for its application to noncongruent and structurally diverse chemical compound data sets. Here we report the first practical application of this method in the screening of molecular entities of therapeutic interest, with human aromatase inhibitory activity as the case study. We developed an ensemble classification model based on the two-dimensional (2D) DFT MIA-QSAR descriptors, with which we screened the NCI Diversity Set V (1593 compounds) and obtained 34 chemical compounds with possible aromatase inhibitory activity. These compounds were docked into the aromatase active site, and the 10 most promising compounds were selected for in vitro experimental validation. Of these compounds, 7419 (nonsteroidal) and 89 201 (steroidal) demonstrated satisfactory antiproliferative and aromatase inhibitory activities. The obtained results suggest that the 2D-DFT MIA-QSAR method may be useful in ligand-based virtual screening of new molecular entities of therapeutic utility.

N-tuple topological/geometric cutoffs for 3D N-linear algebraic molecular codifications: variability, linear independence and QSAR analysis

Novel N-tuple topological/geometric cutoffs to consider specific inter-atomic relations in the QuBiLS-MIDAS framework are introduced in this manuscript. These molecular cutoffs permit the taking into account of relations between more than two atoms by using (dis-)similarity multi-metrics and the concepts related with topological and Euclidean-geometric distances. To this end, the kth two-, three- and four-tuple topological and geometric neighbourhood quotient (NQ) total (or local-fragment) spatial-(dis)similarity matrices are defined, to represent 3D information corresponding to the relations between two, three and four atoms of the molecular structures that satisfy certain cutoff criteria. First, an analysis of a diverse chemical space for the most common values of topological/Euclidean-geometric distances, bond/dihedral angles, triangle/quadrilateral perimeters, triangle area and volume was performed in order to determine the intervals to take into account in the cutoff procedures. A variability analysis based on Shannon's entropy reveals that better distribution patterns are attained with the descriptors based on the cutoffs proposed (QuBiLS-MIDAS NQ-MDs) with regard to the results obtained when all inter-atomic relations are considered (QuBiLS-MIDAS KA-MDs - 'Keep All'). A principal component analysis shows that the novel molecular cutoffs codify chemical information captured by the respective QuBiLS-MIDAS KA-MDs, as well as information not captured by the latter. Lastly, a QSAR study to obtain deeper knowledge of the contribution of the proposed methods was carried out, using four molecular datasets (steroids (STER), angiotensin converting enzyme (ACE), thermolysin inhibitors (THER) and thrombin inhibitors (THR)) widely used as benchmarks in the evaluation of several methodologies. One to four variable QSAR models based on multiple linear regression were developed for each compound dataset following the original division into training and test sets. The results obtained reveal that the novel cutoff procedures yield superior performances relative to those of the QuBiLS-MIDAS KA-MDs in the prediction of the biological activities considered. From the results achieved, it can be suggested that the proposed N-tuple topological/geometric cutoffs constitute a relevant criteria for generating MDs codifying particular atomic relations, ultimately useful in enhancing the modelling capacity of the QuBiLS-MIDAS 3D-MDs.

Activation energies and information entropies of helium penetration through fullerene walls. Insights into the formation of endofullerenes nX@C60/70 (n = 1 and 2) from the information entropy approach

In the present study, we calculate the activation barriers and information entropies of helium penetration into the C₆₀ and C₇₀ fullerenes resulting in the singly and doubly filled endofullerenes He_n@C_60/70 (n = 1 and 2).