Bond-based linear indices of the non-stochastic and stochastic edge-adjacency matrix. 1. Theory and modeling of ChemPhys properties of organic molecules.

Novel bond-level molecular descriptors are proposed, based on linear maps similar to the ones defined in algebra theory. The kth edge-adjacency matrix (E(k)) denotes the matrix of bond linear indices (non-stochastic) with regard to canonical basis set. The kth stochastic edge-adjacency matrix, ES(k), is here proposed as a new molecular representation easily calculated from E(k). Then, the kth stochastic bond linear indices are calculated using ES(k) as operators of linear transformations. In both cases, the bond-type formalism is developed. The kth non-stochastic and stochastic total linear indices are calculated by adding the kth non-stochastic and stochastic bond linear indices, respectively, of all bonds in molecule. First, the new bond-based molecular descriptors (MDs) are tested for suitability, for the QSPRs, by analyzing regressions of novel indices for selected physicochemical properties of octane isomers (first round). General performance of the new descriptors in this QSPR studies is evaluated with regard to the well-known sets of 2D/3D MDs. From the analysis, we can conclude that the non-stochastic and stochastic bond-based linear indices have an overall good modeling capability proving their usefulness in QSPR studies. Later, the novel bond-level MDs are also used for the description and prediction of the boiling point of 28 alkyl-alcohols (second round), and to the modeling of the specific rate constant (log k), partition coefficient (log P), as well as the antibacterial activity of 34 derivatives of 2-furylethylenes (third round). The comparison with other approaches (edge- and vertices-based connectivity indices, total and local spectral moments, and quantum chemical descriptors as well as E-state/biomolecular encounter parameters) exposes a good behavior of our method in this QSPR studies. Finally, the approach described in this study appears to be a very promising structural invariant, useful not only for QSPR studies but also for similarity/diversity analysis and drug discovery protocols.

Non-stochastic and stochastic linear indices of the molecular pseudograph's atom-adjacency matrix: a novel approach for computational in silico screening and "rational" selection of new lead antibacterial agents.

A novel approach (TOMOCOMD-CARDD) to computer-aided "rational" drug design is illustrated. This approach is based on the calculation of the non-stochastic and stochastic linear indices of the molecular pseudograph's atom-adjacency matrix representing molecular structures. These TOMOCOMD-CARDD descriptors are introduced for the computational (virtual) screening and "rational" selection of new lead antibacterial agents using linear discrimination analysis. The two structure-based antibacterial-activity classification models, including non-stochastic and stochastic indices, classify correctly 91.61% and 90.75%, respectively, of 1525 chemicals in training sets. These models show high Matthews correlation coefficients (MCC=0.84 and 0.82). An external validation process was carried out to assess the robustness and predictive power of the model obtained. These QSAR models permit the correct classification of 91.49% and 89.31% of 505 compounds in an external test set, yielding MCCs of 0.84 and 0.79, respectively. The TOMOCOMD-CARDD approach compares satisfactorily with respect to nine of the most useful models for antimicrobial selection reported to date. Finally, an in silico screening of 87 new chemicals reported in the anti-infective field with antibacterial activities is developed showing the ability of the TOMOCOMD-CARDD models to identify new lead antibacterial compounds.

3D-chiral quadratic indices of the 'molecular pseudograph's atom adjacency matrix' and their application to central chirality codification: classification of ACE inhibitors and prediction of sigma-receptor antagonist activities.

Quadratic indices of the 'molecular pseudograph's atom adjacency matrix' have been generalized to codify chemical structure information for chiral drugs. These 3D-chiral quadratic indices make use of a trigonometric 3D-chirality correction factor. These indices are nonsymmetric and reduced to classical (2D) descriptors when symmetry is not codified. By this reason, it is expected that they will be useful to predict symmetry-dependent properties. 3D-Chirality quadratic indices are real numbers and thus, can be easily calculated in TOMOCOMD-CARDD software. These descriptors circumvent the inability of conventional 2D quadratic indices (Molecules 2003, 8, 687-726. http://www.mdpi.org) and other (chirality insensitive) topological indices to distinguish sigma-stereoisomers. In this paper, we extend our earlier work by applying 3D-chirality quadratic indices to two data sets containing chiral compounds. Consequently, in order to test the potential of this novel approach in drug design we have modelled the angiotesin-converting enzyme inhibitory activity of perindoprilate's sigma-stereoisomers combinatorial library. Two linear discriminant analysis (LDA) models were obtained. The first one model was performed considering all data set as training series and classifies correctly 88.89% of active compounds and 100.00% of nonactive one for a global good classification of 96.87%. The second one LDA-QSAR model classified correctly 83.33% of the active and 100.00% of the inactive compounds in a training set, result that represent a total of 95.65% accuracy in classification. On the other hand, the model classifies 100.00% of these compounds in the test set. Similar predictive behaviour was observed in a leave-one-out cross-validation procedure for both equations. Canonical regression analysis corroborated the statistical quality of these models (R(can) of 0.82 and of 0.76, respectively) and was also used to compute biology activity canonical scores for each compound. Finally, prediction of the biological activities of chiral 3-(3-hydroxyphenyl)piperidines, which are sigma-receptor antagonists, by linear multiple regression analysis was carried out. Two statistically significant QSAR models were obtained (R2=0.940, s=0.270 and R2=0.977, s=0.175). These models showed high stability to data variation in the leave-one-out cross-validation procedure (q2=0.912, scv=0.289 and q2=0.957, scv=0.211). The results of this study compare favourably with those obtained with other chirality descriptors applied to the same data set. The 3D-chiral TOMOCOMD-CARDD approach provides a powerful alternative to 3D-QSAR.

Atom, atom-type, and total linear indices of the "molecular pseudograph's atom adjacency matrix": application to QSPR/QSAR studies of organic compounds.

In this paper we describe the application in QSPR/QSAR studies of a new group of molecular descriptors: atom, atom-type and total linear indices of the molecular pseudograph's atom adjacency matrix. These novel molecular descriptors were used for the prediction of boiling point and partition coefficient (log P), specific rate constant (log k), and antibacterial activity of 28 alkyl-alcohols and 34 derivatives of 2-furylethylenes,respectively. For this purpose two quantitative models were obtained to describe the alkyl-alcohols' boiling points. The first one includes only two total linear indices and showed a good behavior from a statistical point of view (R(2) = 0.984, s = 3.78, F = 748.57,q(2) = 0.981, and s(cv) = 3.91). The second one includes four variables [3 global and 1 local(heteroatom) linear indices] and it showed an improvement in the description of physical property (R(2) = 0.9934, s = 2.48, F = 871.96, q(2) = 0.990, and s(cv) = 2.79). Later, linear multiple regression analysis was also used to describe log P and log k of the 2-furyl-ethylenes derivatives. These models were statistically significant [(R(2) = 0.984, s = 0.143, and F = 113.38) and (R(2) = 0.973, s = 0.26 and F = 161.22), respectively] and showed very good stability to data variation in leave-one-out (LOO) cross-validation experiment [(q(2) = 0.93.8 and scv = 0.178) and (q(2) = 0.948 and s(cv) = 0.33), respectively]. Finally, a linear discriminant model for classifying antibacterial activity of these compounds was also achieved with the use of the atom and atom-type linear indices. The global percent of good classification in training and external test set obtained was of 94.12% and 100.0%, respectively. The comparison with other approaches (connectivity indices, total and local spectral moments, quantum chemical descriptors, topographic indices and E- state/biomolecular encounter parameters) reveals a good behavior of our method. The approach described in this paper appears to be a very promising structural invariant, useful for QSPR/QSAR studies and computer-aided "rational" drug design.

Protein quadratic indices of the "macromolecular pseudograph's alpha-carbon atom adjacency matrix". 1. Prediction of Arc repressor alanine-mutant's stability.

This report describes a new set of macromolecular descriptors of relevance to protein QSAR/QSPR studies, protein's quadratic indices. These descriptors are calculated from the macromolecular pseudograph's alpha-carbon atom adjacency matrix. A study of the protein stability effects for a complete set of alanine substitutions in Arc repressor illustrates this approach. Quantitative Structure-Stability Relationship (QSSR) models allow discriminating between near wild-type stability and reduced-stability A-mutants. A linear discriminant function gives rise to excellent discrimination between 85.4% (35/41)and 91.67% (11/12) of near wild-type stability/reduced stability mutants in training and test series, respectively. The model's overall predictability oscillates from 80.49 until 82.93, when n varies from 2 to 10 in leave-n-out cross validation procedures. This value stabilizes around 80.49% when n was > 6. Additionally, canonical regression analysis corroborates the statistical quality of the classification model (Rcanc = 0.72, p-level <0.0001). This analysis was also used to compute biological stability canonical scores for each Arc A-mutant. On the other hand, nonlinear piecewise regression model compares favorably with respect to linear regression one on predicting the melting temperature (tm)of the Arc A-mutants. The linear model explains almost 72% of the variance of the experimental tm (R = 0.85 and s = 5.64) and LOO press statistics evidenced its predictive ability (q2 = 0.55 and scv = 6.24). However, this linear regression model falls to resolve t(m) predictions of Arc A-mutants in external prediction series. Therefore, the use of nonlinear piecewise models was required. The tm values of A-mutants in training (R = 0.94) and test(R = 0.91) sets are calculated by piecewise model with a high degree of precision. A break-point value of 51.32 degrees C characterizes two mutants' clusters and coincides perfectly with the experimental scale. For this reason, we can use the linear discriminant analysis and piecewise models in combination to classify and predict the stability of the mutants' Arc homodimers. These models also permit the interpretation of the driving forces of such a folding process. The models include protein's quadratic indices accounting for hydrophobic (z1), bulk-steric (z2), and electronic (z3) features of the studied molecules. Preponderance of z1 and z3 over z2 indicates the higher importance of the hydrophobic and electronic side chain terms in the folding of the Arc dimer. In this sense, developed equations involve short-reaching (k < or = 3), middle- reaching (3 < k < or = 7) and far-reaching (k= 8 or greater) z1, 2, 3-protein's quadratic indices. This situation points to topologic/topographic protein's backbone interactions control of the stability profile of wild-type Arc and its A-mutants. Consequently, the present approach represents a novel and very promising way to mathematical research in biology sciences.