Stochastic-based descriptors studying biopolymers biological properties: extended MARCH-INSIDE methodology describing antibacterial activity of lactoferricin derivatives.

Lactoferricin are a number of related peptides derived from the enzymatic cleavage of lactoferrin, an iron-binding protein. These peptides, and other peptides derived from them by simple amino acid substitutions, have shown interesting antibacterial activity. In this paper we applied the MARCH-INSIDE methodology extended to peptide and proteins, to a QSAR study related to antibacterial activity of 31 derivatives of lactoffericin against E. Coli and S. Aureus by means of Linear Discriminant (LDA) and Multiple Linear Regression Analysis (MLR). In the case of LDA we obtained models that classify correctly more than 80% of all cases (85.7% for E. Coli antibacterial activity and 83.9 for S. Aureus). With the application of a Leave-One-Out Cross Validation Procedure, the percentage of good classification of both classification models remained near the above reported values (87.1% for E. Coli antibacterial activity and 83.9 for S. Aureus). We obtained several linear regression models taking into account total and local descriptors. The inclusion of those local descriptors improved the correlation parameters, the statistical quality, and the predictive power of the former model obtained only with total descriptors. The best models explained more than 80% of the experimental variance in the antimicrobial activity of those compounds. These results are comparable with those reported previously by Strom (Strom, M. B.; Rekdal, O.; Svendesen, J. S. J Peptide Res 2001, 57, 127-139.) and Tore-Lejon (Lejon, T.; Strom, M.; Svendsen, S. J Protein Sci 2001, 7, 74-78.; Lejon, T.; Svendsen J. S.; Haug, B. E. J Peptide Sci 2002, 8, 302-306.) in a smaller dataset applying Z-scales and volume-based descriptors and PLS as statistical techniques.

A topological sub-structural approach for predicting human intestinal absorption of drugs.

The human intestinal absorption (HIA) of drugs was studied using a topological sub-structural approach (TOPS-MODE). The drugs were divided into three classes according to reported cutoff values for HIA. "Poor" absorption was defined as HIA < or =30%, "high" absorption as HIA > or =80%, whereas "moderate" absorption was defined between these two values (30% < HIA < 79%). Two linear discriminant analyses were carried out on a training set of 82 compounds. The percentages of correct classification, for both models, were 89.02%. The predictive power of the models were validated by three test: a leave-one-out cross validation procedure (88.9% and 87.9%), an external prediction set of 127 drugs (92.9% and 80.31%) and a test set of 109 oral drugs with bioavailability values reported (93.58% and 91.84%). Finally, positive and negative sub-structural contributions to the HIA were identified and their possibilities in the lead generation and optimization process were evaluated.

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.

Simple stochastic fingerprints towards mathematical modelling in biology and medicine. 1. The treatment of coccidiosis.

We have developed a classification function that is capable of discriminating between anticoccidial and nonanticoccidial compounds with different structural patterns. For this purpose, we calculated the Markovian electron delocalization negentropies of several compounds. These molecular descriptors, which act as molecular fingerprints, are derived from an electronegativity-weighted stochastic matrix (1Pi). The method attempts to describe the delocalization of electrons with time during the process of molecule formation by considering the 3D environment of the atoms. Accordingly, the entropies of this random process are used as molecular descriptors. The present study involves a stochastic generalization of the original idea described by Kier, which concerned the use of molecular negentropies in QSAR. Linear discriminant analysis allowed us to fit the discriminant function. This function has given rise to a good classification of 82.35% (28 anticoccidials out of 34) and 91.8% of inactive compounds (56/61) in training series. An overall classification of 88.42% (84/95) was achieved. Validation of the model was carried out by means of an external predicting series and this gave a global predictability of 93.1%. Finally, we report the experimental assay (more than 95% of lesion control) of two compounds selected from a large data set through virtual screening. We conclude that the approach described here seems to be a promising 3D-QSAR tool based on the mathematical theory of stochastic processes.

TOPS-MODE based QSARs derived from heterogeneous series of compounds. Applications to the design of new anti-inflammatory compounds.

A new application of TOPological Sub-structural MOlecular DEsign (TOPS-MODE) was carried out in anti-inflammatory compounds using computer-aided molecular design. Two series of compounds, one containing anti-inflammatory and the other containing nonanti-inflammatory compounds were processed by a k-means cluster analysis in order to design the training and prediction sets. A linear classification function to discriminate the anti-inflammatory from the inactive compounds was developed. The model correctly and clearly classified 88% of active and 91% of inactive compounds in the training set. More specifically, the model showed a good global classification of 90%, that is, (399 cases out of 441). While in the prediction set, they showed an overall predictability of 88% and 84% for active and inactive compounds, being the global percentage of good classification of 85%. Furthermore this paper describes a fragment analysis in order to determine the contribution of several fragments towards anti-inflammatory property, also the present of halogens in the selected fragments were analyzed. It seems that the present TOPS-MODE based QSAR is the first alternate general 'in silico' technique to experimentation in anti-inflammatory discovery.

Designing antibacterial compounds through a topological substructural approach.

A novel application of TOPological Substructural MOlecular DEsign (TOPS-MODE) was carried out in antibacterial drugs using computer-aided molecular design. Two series of compounds, one containing antibacterial and the other containing non-antibacterial compounds, were processed by a k-means cluster analysis in order to design training and predicting series. All clusters had a p-level < 0.005. Afterward, a linear classification function has been derived toward discrimination between antibacterial and non-antibacterial compounds. The model correctly classifies 94% of active and 86% of inactive compounds in the training series. More specifically, the model showed a global good classification of 91%, i.e., 263 cases out of 289. In predicting series, the model has shown overall predictabilities of 91 and 83% for active and inactive compounds, respectively. Thereby, the model has a global percentage of good classification of 89%. The TOPS-MODE approach, also, similarly compares with respect to one of the most useful models for antimicrobials selection reported to date.

A novel approach to predict a toxicological property of aromatic compounds in the Tetrahymena pyriformis.

The TOPological Substructural MOlecular DEsign (TOPS-MODE) has been successfully used in order to explain the toxicity in the Tetrahymena pyriformis on a large data set. The obtained models for the training set had good statistical parameters (R(2)=0.72-0.81, p<0.05) an also the prediction power of the models found was adequate (Q(2)=0.70-0.80). A detailed study of the influence of variable numbers in the equation and the statistical outliers was carried out; leading to a good final model with a better physicochemical interpretation than the rest of the published models. Only two molecular descriptors codifying dipolar and hydrophobic features were introduced. Finally, the fragment contributions to the toxicity prediction evidenced the powerful of this topological approach.

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.

Vibrational Markovian modelling of footprints after the interaction of antibiotics with the packaging region of HIV type 1.

The design of novel anti-HIV compounds has now become a crucial area for scientists working in numerous interrelated fields of science such as molecular biology, medicinal chemistry, mathematical biology, molecular modelling and bioinformatics. In this context, the development of simple but physically meaningful mathematical models to represent the interaction between anti-HIV drugs and their biological targets is of major interest. One such area currently under investigation involves the targets in the HIV-RNA-packaging region. In the work described here, we applied Markov chain theory in an attempt to describe the interaction between the antibiotic paromomycin and the packaging region of the RNA in Type-1 HIV. In this model, a nucleic acid squeezed graph is used. The vertices of the graph represent the nucleotides while the edges are the phosphodiester bonds. A stochastic (Markovian) matrix was subsequently defined on this graph, an operation that codifies the probabilities of interaction between specific nucleotides of HIV-RNA and the antibiotic. The strength of these local interactions can be calculated through an inelastic vibrational model. The successive power of this matrix codifies the probabilities with which the vibrations after drug-RNA interactions vanish along the polynucleotide main chain. The sums of self-return probabilities in the k-vicinity of each nucleotide represent physically meaningful descriptors. A linear discriminant function was developed and gave rise to excellent discrimination in 80.8% of interacting and footprinted nucleotides. The Jackknife method was employed to assess the stability and predictability of the model. On the other hand, a linear regression model predicted the local binding affinity constants between a specific nucleotide and the antibiotic (R(2)=0.91, Q(2)=0.86). These kinds of models could play an important role either in the discovery of new anti-HIV compounds or the study of their mode of action.

Markovian negentropies in bioinformatics. 1. A picture of footprints after the interaction of the HIV-1 Psi-RNA packaging region with drugs.

MOTIVATION: Many experts worldwide have highlighted the potential of RNA molecules as drug targets for the chemotherapeutic treatment of a range of diseases. In particular, the molecular pockets of RNA in the HIV-1 packaging region have been postulated as promising sites for antiviral action. The discovery of simpler methods to accurately represent drug-RNA interactions could therefore become an interesting and rapid way to generate models that are complementary to docking-based systems. RESULTS: The entropies of a vibrational Markov chain have been introduced here as physically meaningful descriptors for the local drug-nucleic acid complexes. A study of the interaction of the antibiotic Paromomycin with the packaging region of the RNA present in type-1 HIV has been carried out as an illustrative example of this approach. A linear discriminant function gave rise to excellent discrimination among 80.13% of interacting/non-interacting sites. More specifically, the model classified 36/45 nucleotides (80.0%) that interacted with paromomycin and, in addition, 85/106 (80.2%) footprinted (non-interacting) sites from the RNA viral sequence were recognized. The model showed a high Matthews' regression coefficient (C = 0.64). The Jackknife method was also used to assess the stability and predictability of the model by leaving out adenines, C, G, or U. Matthews' coefficients and overall accuracies for these approaches were between 0.55 and 0.68 and 75.8 and 82.7, respectively. On the other hand, a linear regression model predicted the local binding affinity constants between a specific nucleotide and the aforementioned antibiotic (R2 = 0.83,Q2 = 0.825). These kinds of models may play an important role either in the discovery of new anti-HIV compounds or in the elucidation of their mode of action. AVAILABILITY: On request from the corresponding author (humbertogd@cbq.uclv.edu.cu or humbertogd@navegalia.com).

3D-MEDNEs: an alternative "in silico" technique for chemical research in toxicology. 1. prediction of chemically induced agranulocytosis.

A novel approach to molecular negentropy from the point of view of Markov models is introduced. Stochastic negentropies (MEDNEs) are used to develop a linear discriminant analysis. The discriminant analysis produced a set of two discriminant functions, which gave rise to a very good separation of 93.38% of 151 chemicals (training series) into two groups. The total predictability (86.67%, i.e., 52 compounds out of 60) was tested by means of an external validation set. Randic's orthogonalization procedures allowed interpretation of the model while avoiding collinearity descriptors. On the other hand, factor analysis was used to suggest the relation of MEDNEs with other molecular descriptors and properties into a property space. Three principal factors (related to three orthogonal MEDNEs) can be used to explain approximately 90% of the variance of different molecular parameters of halobenzenes including bulk, energetic, dipolar, molecular surface-related, and hydrophobic parameters. Finally, preliminary experimental results coincide with a theoretical prediction when agranulocytosis induction by G-1, a novel microcidal that presents Z/E isomerism, is not detected.

Symmetry considerations in Markovian chemicals 'in silico' design (MARCH-INSIDE) I: central chirality codification, classification of ACE inhibitors and prediction of sigma-receptor antagonist activities.

The MARCH-INSIDE methodology has been generalized, by means of an exponential central symmetry factor, to codify chemical structure information for chiral drugs. In order to test the potential of this novel approach in drug design we have modeled the angiotensin-converting enzyme inhibitory activity of perindoprilate's sigma-stereoisomer combinatorial library. A linear discriminant analysis (LDA) model classifies correctly 83.33% of active compounds and 94.12% of non-active ones in a training set, results that represent a total of 91.3% accuracy in classification. On the other hand, the model classifies 83.33% of these compounds in the predicting series. Only three isomers (those with higher activity) were used in the predicting set and the model classified all three very well. Similar predictive behavior was observed in a leave-1-out cross validation experiment. Canonical regression analysis corroborated the statistical quality of the models (Rcanc=0.79, with a P-level<0.000) and was also used to compute biological 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 regression analysis was carried out. The model was statistically significant (R=0.963, S=0.29, P<0.00) and can be considered as a preliminary comparative study between MARCH-INSIDE and Chiral Topologic descriptors. Application of the Student test permits the detection of non-symmetric properties within the data set and justified the requirement of non-symmetric (for pairs of enantiomers) molecular descriptors. The MARCH-INSIDE model showed very good stability to data variation in the leave-1-out cross validation experiment (Scv=0.32).