Tomocomd-Cardd, a novel approach for computer-aided ? rational? drug design: I. Theoretical and experimental assessment of a promising method for computational screening and in silico design of new anthelmintic compounds

Omics and Remote Homology Integration to Decipher Protein Functionality

In the recent years, several "omics" technologies based on specific biomolecules (from DNA, RNA, proteins, or metabolites) have won growing importance in the scientific field. Despite each omics possess their own laboratorial protocols, they share a background of bioinformatic tools for data integration and analysis. A recent subset of bioinformatic tools, based on available templates or remote homology protocols, allow computational fast and high-accuracy prediction of protein structures. The quickly predict of actually unsolved protein structures, together with late omics findings allow a boost of scientific advances in multiple fields such as cancer, longevity, immunity, mitochondrial function, toxicology, drug design, biosensors, and recombinant protein engineering. In this chapter, we assessed methodological approaches for the integration of omics and remote homology inferences to decipher protein functionality, opening the door to the next era of biological knowledge.

Computational discovery of novel anthelmintic natural compounds from Agave Brittoniana trel. Spp. Brachypus

Helminth infections are a medical problem in the world nowadays. This report used bond-based 2D quadratic indices, a bond-level QuBiLs-MAS molecular descriptor family, and Linear Discriminant Analysis (LDA) to obtain a quantitative linear model that discriminates between anthelmintic and non-anthelmintic drug-like organic-compounds. The model obtained correctly classified 87.46% and 81.82% of the training and external data sets, respectively. The developed model was used in a virtual screening to predict the biological activity of all chemicals (19) previously obtained and chemically characterized by some authors of this report from Agave brittoniana Trel. spp. Brachypus. The model identified several metabolites (12) as possible anthelmintics, and a group of 5 novel natural products was tested in an in vitro assay against Fasciola hepatica (100% effectivity at 500 µg/mL). Finally, the two best hits were evaluated in vivo in bald/c mice and the same helminth parasite using a 25 mg/kg dose. Compound 8 (Karatavinoside A) showed an efficacy of 92.2% in vivo. It is important to remark that this natural compound exhibits similar-to-superior activity as triclabendazole, the best human fasciolicide available in the market against Fasciola hepatica, resulting in a novel lead scaffold with anti-helminthic activity. Keywords: TOMOCOMD-CARDD Software; QuBiLs-MAS, nonstochastic and stochastic bond-based quadratic indices; LDA-based QSAR model; Computational Screening, Anthelmintic Agent; Agave brittoniana Trel. spp. Brachypus, Fasciola hepatica.

Graph Theory-Based Sequence Descriptors as Remote Homology Predictors

Alignment-free (AF) methodologies have increased in popularity in the last decades as alternative tools to alignment-based (AB) algorithms for performing comparative sequence analyses. They have been especially useful to detect remote homologs within the twilight zone of highly diverse gene/protein families and superfamilies. The most popular alignment-free methodologies, as well as their applications to classification problems, have been described in previous reviews. Despite a new set of graph theory-derived sequence/structural descriptors that have been gaining relevance in the detection of remote homology, they have been omitted as AF predictors when the topic is addressed. Here, we first go over the most popular AF approaches used for detecting homology signals within the twilight zone and then bring out the state-of-the-art tools encoding graph theory-derived sequence/structure descriptors and their success for identifying remote homologs. We also highlight the tendency of integrating AF features/measures with the AB ones, either into the same prediction model or by assembling the predictions from different algorithms using voting/weighting strategies, for improving the detection of remote signals. Lastly, we briefly discuss the efforts made to scale up AB and AF features/measures for the comparison of multiple genomes and proteomes. Alongside the achieved experiences in remote homology detection by both the most popular AF tools and other less known ones, we provide our own using the graphical-numerical methodologies, MARCH-INSIDE, TI2BioP, and ProtDCal. We also present a new Python-based tool (SeqDivA) with a friendly graphical user interface (GUI) for delimiting the twilight zone by using several similar criteria.

Quantitative structure-activity relationship models for compounds with anticonvulsant activity

Introduction: Third-generation antiepileptic drugs have seemingly failed to improve the global figures of seizure control and can still be regarded as symptomatic treatments. Quantitative structure-activity relationships (QSAR) can be used to guide hit-to-lead and lead optimization projects and applied to the large-scale virtual screening of chemical libraries. Areas covered: In this review, the authors cover reports on QSAR models related to antiepileptic drugs and drug targets in epilepsy, analyzing whether they refer to classic or non-classic QSAR and if they apply QSAR as a descriptive or predictive approach, among other considerations. The article finally focuses on a more detailed discussion of those predictive studies which include some sort of experimental validation, i.e. papers in which the reported models have been used to identify novel active compounds which have been tested in vitro and/or in vivo. Expert opinion: There are significant opportunities to apply the QSAR methodology to assist the discovery of more efficacious antiepileptic drugs. Considering the intrinsic complexity of the disorder, such applications should focus on state-of-the-art approximations (e.g. systemic, multi-target and multi-scale QSAR as well as ensemble and deep learning) and modeling the effects on novel drug targets and modern screening tools.

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.

Fragment-based in silico modeling of multi-target inhibitors against breast cancer-related proteins

Breast cancer is the most frequent cancer reported in women, being responsible for hundreds of thousands of deaths. Chemotherapy has proven to be effective against this malignant neoplasm depending on different biological factors such as the histopathology, grade, and stage, among others. However, breast cancer cells have become resistant to current chemotherapeutic regimens, urging the discovery of new anti-breast cancer drugs. Computational approaches have the potential to offer promising alternatives to accelerate the search for potent and versatile anti-breast cancer agents. In the present work, we introduce the first multitasking (mtk) computational model devoted to the in silico fragment-based design of new molecules with high inhibitory activity against 19 different proteins involved in breast cancer. The mtk-computational model was created from a dataset formed by 24,285 cases, and it exhibited accuracy around 93% in both training and prediction (test) sets. Several molecular fragments were extracted from the molecules present in the dataset, and their quantitative contributions to the inhibitory activities against all the proteins under study were calculated. The combined use of the fragment contributions and the physicochemical interpretations of the different molecular descriptors in the mtk-computational model allowed the design of eight new molecular entities not reported in our dataset. These molecules were predicted as potent multi-target inhibitors against all the proteins, and they exhibited a desirable druglikeness according to the Lipinski's rule of five and its variants.

QuBiLs-MAS method in early drug discovery and rational drug identification of antifungal agents

The QuBiLs-MAS approach is used for the in silico modelling of the antifungal activity of organic molecules. To this effect, non-stochastic (NS) and simple-stochastic (SS) atom-based quadratic indices are used to codify chemical information for a comprehensive dataset of 2478 compounds having a great structural variability, with 1087 of them being antifungal agents, covering the broadest antifungal mechanisms of action known so far. The NS and SS index-based antifungal activity classification models obtained using linear discriminant analysis (LDA) yield correct classification percentages of 90.73% and 92.47%, respectively, for the training set. Additionally, these models are able to correctly classify 92.16% and 87.56% of 706 compounds in an external test set. A comparison of the statistical parameters of the QuBiLs-MAS LDA-based models with those for models reported in the literature reveals comparable to superior performance, although the latter were built over much smaller and less diverse datasets, representing fewer mechanisms of action. It may therefore be inferred that the QuBiLs-MAS method constitutes a valuable tool useful in the design and/or selection of new and broad spectrum agents against life-threatening fungal infections.

Simultaneous virtual prediction of anti-Escherichia coli activities and ADMET profiles: A chemoinformatic complementary approach for high-throughput screening

Escherichia coli remains one of the principal pathogens that cause nosocomial infections, medical conditions that are increasingly common in healthcare facilities. E. coli is intrinsically resistant to many antibiotics, and multidrug-resistant strains have emerged recently. Chemoinformatics has been a great ally of experimental methodologies such as high-throughput screening, playing an important role in the discovery of effective antibacterial agents. However, there is no approach that can design safer anti-E. coli agents, because of the multifactorial nature and complexity of bacterial diseases and the lack of desirable ADMET (absorption, distribution, metabolism, elimination, and toxicity) profiles as a major cause of disapproval of drugs. In this work, we introduce the first multitasking model based on quantitative-structure biological effect relationships (mtk-QSBER) for simultaneous virtual prediction of anti-E. coli activities and ADMET properties of drugs and/or chemicals under many experimental conditions. The mtk-QSBER model was developed from a large and heterogeneous data set of more than 37800 cases, exhibiting overall accuracies of >95% in both training and prediction (validation) sets. The utility of our mtk-QSBER model was demonstrated by performing virtual prediction of properties for the investigational drug avarofloxacin (AVX) under 260 different experimental conditions. Results converged with the experimental evidence, confirming the remarkable anti-E. coli activities and safety of AVX. Predictions also showed that our mtk-QSBER model can be a promising computational tool for virtual screening of desirable anti-E. coli agents, and this chemoinformatic approach could be extended to the search for safer drugs with defined pharmacological activities.

Model for vaccine design by prediction of B-epitopes of IEDB given perturbations in peptide sequence, in vivo process, experimental techniques, and source or host organisms

Perturbation methods add variation terms to a known experimental solution of one problem to approach a solution for a related problem without known exact solution. One problem of this type in immunology is the prediction of the possible action of epitope of one peptide after a perturbation or variation in the structure of a known peptide and/or other boundary conditions (host organism, biological process, and experimental assay). However, to the best of our knowledge, there are no reports of general-purpose perturbation models to solve this problem. In a recent work, we introduced a new quantitative structure-property relationship theory for the study of perturbations in complex biomolecular systems. In this work, we developed the first model able to classify more than 200,000 cases of perturbations with accuracy, sensitivity, and specificity >90% both in training and validation series. The perturbations include structural changes in >50000 peptides determined in experimental assays with boundary conditions involving >500 source organisms, >50 host organisms, >10 biological process, and >30 experimental techniques. The model may be useful for the prediction of new epitopes or the optimization of known peptides towards computational vaccine design.

S. Cordeiro MN, Yañez M, González-Díaz H, García-Mera X. Model for high-throughput screening of multitarget drugs in chemical neurosciences: synthesis, assay, and theoretic study of rasagiline carbamates

The disappointing results obtained in recent clinical trials renew the interest in experimental/computational techniques for the discovery of neuroprotective drugs. In this context, multitarget or multiplexing QSAR models (mt-QSAR/mx-QSAR) may help to predict neurotoxicity/neuroprotective effects of drugs in multiple assays, on drug targets, and in model organisms. In this work, we study a data set downloaded from CHEMBL; each data point (>8000) contains the values of one out of 37 possible measures of activity, 493 assays, 169 molecular or cellular targets, and 11 different organisms (including human) for a given compound. In this work, we introduce the first mx-QSAR model for neurotoxicity/neuroprotective effects of drugs based on the MARCH-INSIDE (MI) method. First, we used MI to calculate the stochastic spectral moments (structural descriptors) of all compounds. Next, we found a model that classified correctly 2955 out of 3548 total cases in the training and validation series with Accuracy, Sensitivity, and Specificity values>80%. The model also showed excellent results in Computational-Chemistry simulations of High-Throughput Screening (CCHTS) experiments, with accuracy=90.6% for 4671 positive cases. Next, we reported the synthesis, characterization, and experimental assays of new rasagiline derivatives. We carried out three different experimental tests: assay (1) in the absence of neurotoxic agents, assay (2) in the presence of glutamate, and assay (3) in the presence of H2O2. Compounds 11 with 27.4%, 8 with 11.6%, and 9 with 15.4% showed the highest neuroprotective effects in assays (1), (2), and (3), respectively. After that, we used the mx-QSAR model to carry out a CCHTS of the new compounds in >400 unique pharmacological tests not carried out experimentally. Consequently, this model may become a promising auxiliary tool for the discovery of new drugs for the treatment of neurodegenerative diseases.

In vitro assessment of the acaricidal activity of computer-selected analogues of carvacrol and salicylic acid on Rhipicephalus (Boophilus) microplus

Rhipicephalus (Boophilus) microplus is a tick that causes huge economic losses in cattle. The indiscriminate use of acaricides has generated resistance to most compounds present on the market. This makes further investigation on other potential acaricides necessary, the in silico assay being an alternative to the design of new compounds. In the present study a biosilico assay was performed using TOMOCOMD-CARDD (TOpological MOlecular COMputer Design-Computer-Aided Rational Drug Design) and WEKA (Waikato Environment for Knowledge Analysis) software. Two carvacrol and four salicylic acid derivatives, synthesized by conventional methods and evaluated with the larval packet test on larvae of R. (B.) microplus were selected. All evaluated compounds presented acaricidal activity; however, ethyl 2-methoxybenzoate (91.8 ± 1.7 % mortality) and ethyl 2,5-dihydroxybenzoate (89.1 ± 1.6 % mortality) showed greater activity than salicylic acid. With regard to the carvacrol analogues, carvacrol acetate (67.8 ± 2.1 % mortality) and carvacrol methyl ether (71.7 ± 1.6 % mortality) also showed greater activity than carvacrol (35.9 ± 3.2 % mortality). TOMOCOMD-CARDD and WEKA software were helpful tools in the search for alternative structures with potential acaricidal activity on R. (B.) microplus.

Biological assay of a novel quinoxalinone with antimalarial efficacy on Plasmodium yoelii yoelii

Compound 1-methyl-7-nitro-4-(5-(piperidin-1-yl)pentyl)-3,4-dihydroquinoxalin-2(1H)-one (VAM2-6) was evaluated against a blood-induced infection with chloroquine-sensitive Plasmodium yoelii yoelii lethal strain in CD1 mice in a 4-day test scheme. LD50 of the compound was 56.51 mg/kg and LD10 was 20.58 mg/kg (taken as the highest dose). Animals were treated by oral gavage of 20, 10, and 5 mg/kg. Mice in the untreated control group showed a progressively increasing parasitemia leading to mouse death on 6 days post-infection; in this group, all mice showed parasites in the blood on the fifth day of sampling; the mean parasitemia on that day was 19.4%. A 4-day dosage of 20 mg/kg of VAM2-6 showed a 97% chemosuppression of total parasitemia on the fifth day, a 28 days survival time, and 20% of cured animals. A 4-day dosage of 10 and 5 mg/kg showed 85 and 37%, respectively, chemosuppression of total parasitemia on the fifth day; but all mice died from days 6 to 9 post-infection with increasing parasitemia. Mice treated with chloroquine at 5 mg/kg survived during the experiment. The results obtained in this study showed that the infection outcome of P. yoelii yoelii-infected mice is affected by VAM2-6 compound by slowing down the parasite replication, retarding the patency time, and increasing their survival time. Although compound VAM2-6 was active at higher doses than chloroquine, these results leaves a door open to the study of its structure in order to improve its antimalarial activity.

In silico approach to screen compounds active against parasitic nematodes of major socio-economic importance

Background

Infections due to parasitic nematodes are common causes of morbidity and fatality around the world especially in developing nations. At present however, there are only three major classes of drugs for treating human nematode infections. Additionally the scientific knowledge on the mechanism of action and the reason for the resistance to these drugs is poorly understood. Commercial incentives to design drugs that are endemic to developing countries are limited therefore, virtual screening in academic settings can play a vital role is discovering novel drugs useful against neglected diseases. In this study we propose to build robust machine learning model to classify and screen compounds active against parasitic nematodes.

Results

A set of compounds active against parasitic nematodes were collated from various literature sources including PubChem while the inactive set was derived from DrugBank database. The support vector machine (SVM) algorithm was used for model development, and stratified ten-fold cross validation was used to evaluate the performance of each classifier. The best results were obtained using the radial basis function kernel. The SVM method achieved an accuracy of 81.79% on an independent test set. Using the model developed above, we were able to indentify novel compounds with potential anthelmintic activity.

Conclusion

In this study, we successfully present the SVM approach for predicting compounds active against parasitic nematodes which suggests the effectiveness of computational approaches for antiparasitic drug discovery. Although, the accuracy obtained is lower than the previously reported in a similar study but we believe that our model is more robust because we intentionally employed stringent criteria to select inactive dataset thus making it difficult for the model to classify compounds. The method presents an alternative approach to the existing traditional methods and may be useful for predicting hitherto novel anthelmintic compounds.

Structural determinants of PERK inhibitor potency and selectivity

The unfolded protein response (UPR) is a coordinated program that promotes cell survival under conditions of endoplasmic reticulum stress and is required in tumor progression as well. To date, no specific small molecule inhibitor targeting this pathway has been identified. Pancreatic endoplasmic reticulum kinase (PERK), one of the UPR transducers, is an eIF2α kinase. Compromising PERK function inhibits tumor growth in mice, suggesting that PERK may be a cancer drug target, but identifying a specific inhibitor of any kinase is challenging. The goal of this study was to identify some pair-wise receptor-ligand atomic contacts that confer selective PERK inhibition. Compounds selectively inhibiting PERK-mediated phosphorylation in vitro were identified using an initial virtual library screen, followed by structure-activity hypothesis testing. The most potent PERK selective inhibitors utilize three specific kinase active site contacts that, when absent from chemically similar compounds, abrogates the inhibition: (i) a strong van der Waals contact with PERK residue Met7, (ii) interactions with the N-terminal portion of the activation loop, and (iii) groups providing electrostatic complementarity to Asp144. Interestingly, the activation loop contact is required for PERK selectivity to emerge. Understanding these structure-activity relationships may accelerate rational PERK inhibitor design.

Multi-target spectral moment: QSAR for antiviral drugs vs. different viral species

The antiviral QSAR models have an important limitation today. They predict the biological activity of drugs against only one viral species. This is determined by the fact that most of the current reported molecular descriptors encode only information about the molecular structure. As a result, predicting the probability with which a drug is active against different viral species with a single unifying model is a goal of major importance. In this work, we use Markov Chain theory to calculate new multi-target spectral moments to fit a QSAR model for drugs active against 40 viral species. The model is based on 500 drugs (including active and non-active compounds) tested as antiviral agents in the recent literature; not all drugs were predicted against all viruses, but only those with experimental values. The database also contains 207 well-known compounds (not as recent as the previous ones) reported in the Merck Index with other activities that do not include antiviral action against any virus species. We used Linear Discriminant Analysis (LDA) to classify all these drugs into two classes as active or non-active against the different viral species tested, whose data we processed. The model correctly classifies 5129 out of 5594 non-active compounds (91.69%) and 412 out of 422 active compounds (97.63%). Overall training predictability was 92.34%. The validation of the model was carried out by means of external predicting series, the model classifying, thus, 2568 out of 2779 non-active compounds and 224 out of 229 active compounds. Overall training predictability was 92.82%. The present work reports the first attempts to calculate within a unified framework the probabilities of antiviral drugs against different virus species based on a spectral moment analysis.

Nucleotide's bilinear indices: novel bio-macromolecular descriptors for bioinformatics studies of nucleic acids. I. Prediction of paromomycin's affinity constant with HIV-1 Psi-RNA packaging region

A new set of nucleotide-based bio-macromolecular descriptors are presented. This novel approach to bio-macromolecular design from a linear algebra point of view is relevant to nucleic acids quantitative structure-activity relationship (QSAR) studies. These bio-macromolecular indices are based on the calculus of bilinear maps on Re(n)[b(mk)(x (m),y (m)):Re(n) x Re(n)-->Re] in canonical basis. Nucleic acid's bilinear indices are calculated from kth power of non-stochastic and stochastic nucleotide's graph-theoretic electronic-contact matrices, M(m)(k) and (s)M(m)(k), respectively. That is to say, the kth non-stochastic and stochastic nucleic acid's bilinear indices are calculated using M(m)(k) and (s)M(m)(k) as matrix operators of bilinear transformations. Moreover, biochemical information is codified by using different pair combinations of nucleotide-base properties as weightings (experimental molar absorption coefficient epsilon(260) at 260 nm and pH=7.0, first (Delta E(1)) and second (Delta E(2)) single excitation energies in eV, and first (f(1)) and second (f(2)) oscillator strength values (of the first singlet excitation energies) of the nucleotide DNA-RNA bases. As example of this approach, an interaction study of the antibiotic paromomycin with the packaging region of the HIV-1 Psi-RNA have been performed and it have been obtained several linear models in order to predict the interaction strength. The best linear model obtained by using non-stochastic bilinear indices explains about 91% of the variance of the experimental Log K (R=0.95 and s=0.08 x 10(-4)M(-1)) as long as the best stochastic bilinear indices-based equation account for 93% of the Log K variance (R=0.97 and s=0.07 x 10(-4)M(-1)). The leave-one-out (LOO) press statistics, evidenced high predictive ability of both models (q(2)=0.86 and s(cv)=0.09 x 10(-4)M(-1) for non-stochastic and q(2)=0.91 and s(cv)=0.08 x 10(-4)M(-1) for stochastic bilinear indices). The nucleic acid's bilinear indices-based models compared favorably with other nucleic acid's indices-based approaches reported nowadays. These models also permit the interpretation of the driving forces of the interaction process. In this sense, developed equations involve short-reaching (k<or=3), middle-reaching (4<k<9), and far-reaching (k=10 or greater) nucleotide's bilinear indices. This situation points to electronic and topologic nucleotide's backbone interactions control of the stability profile of paromomycin-RNA complexes. Consequently, the present approach represents a novel and rather promising way to theoretical-biology studies.

Alignment-free prediction of mycobacterial DNA promoters based on pseudo-folding lattice network or star-graph topological indices

The importance of the promoter sequences in the function regulation of several important mycobacterial pathogens creates the necessity to design simple and fast theoretical models that can predict them. This work proposes two DNA promoter QSAR models based on pseudo-folding lattice network (LN) and star-graphs (SG) topological indices. In addition, a comparative study with the previous RNA electrostatic parameters of thermodynamically-driven secondary structure folding representations has been carried out. The best model of this work was obtained with only two LN stochastic electrostatic potentials and it is characterized by accuracy, selectivity and specificity of 90.87%, 82.96% and 92.95%, respectively. In addition, we pointed out the SG result dependence on the DNA sequence codification and we proposed a QSAR model based on codons and only three SG spectral moments.

A novel approach to predict aquatic toxicity from molecular structure

The main aim of the study was to develop quantitative structure-activity relationship (QSAR) models for the prediction of aquatic toxicity using atom-based non-stochastic and stochastic linear indices. The used dataset consist of 392 benzene derivatives, separated into training and test sets, for which toxicity data to the ciliate Tetrahymena pyriformis were available. Using multiple linear regression, two statistically significant QSAR models were obtained with non-stochastic (R2=0.791 and s=0.344) and stochastic (R2=0.799 and s=0.343) linear indices. A leave-one-out (LOO) cross-validation procedure was carried out achieving values of q2=0.781 (scv=0.348) and q2=0.786 (scv=0.350), respectively. In addition, a validation through an external test set was performed, which yields significant values of Rpred2 of 0.762 and 0.797. A brief study of the influence of the statistical outliers in QSAR's model development was also carried out. Finally, our method was compared with other approaches implemented in the Dragon software achieving better results. The non-stochastic and stochastic linear indices appear to provide an interesting alternative to costly and time-consuming experiments for determining toxicity.

Prediction of tyrosinase inhibition activity using atom-based bilinear indices

A set of novel atom-based molecular fingerprints is proposed based on a bilinear map similar to that defined in linear algebra. These molecular descriptors (MDs) are proposed as a new means of molecular parametrization easily calculated from 2D molecular information. The nonstochastic and stochastic molecular indices match molecular structure provided by molecular topology by using the kth nonstochastic and stochastic graph-theoretical electronic-density matrices, M(k) and S(k), respectively. Thus, the kth nonstochastic and stochastic bilinear indices are calculated using M(k) and S(k) as matrix operators of bilinear transformations. Chemical information is coded by using different pair combinations of atomic weightings (mass, polarizability, vdW volume, and electronegativity). The results of QSAR studies of tyrosinase inhibitors using the new MDs and linear discriminant analysis (LDA) demonstrate the ability of the bilinear indices in testing biological properties. A database of 246 structurally diverse tyrosinase inhibitors was assembled. An inactive set of 412 drugs with other clinical uses was used; both active and inactive sets were processed by hierarchical and partitional cluster analyses to design training and predicting sets. Twelve LDA-based QSAR models were obtained, the first six using the nonstochastic total and local bilinear indices and the last six with the stochastic MDs. The discriminant models were applied; globally good classifications of 99.58 and 89.96 % were observed for the best nonstochastic and stochastic bilinear indices models in the training set along with high Matthews correlation coefficients (C) of 0.99 and 0.79, respectively, in the learning set. External prediction sets used to validate the models obtained were correctly classified, with accuracies of 100 and 87.78 %, respectively, yielding C values of 1.00 and 0.73. This subset contains 180 active and inactive compounds not considered to fit the models. A simulated virtual screen demonstrated this approach in searching tyrosinase inhibitors from compounds never considered in either training or predicting series. These fitted models permitted the selection of new cycloartane compounds isolated from herbal plants as new tyrosinase inhibitors. A good correspondence between theoretical and experimental inhibitory effects on tyrosinase was observed; compound CA6 (IC(50)=1.32 microM) showed higher activity than the reference compounds kojic acid (IC(50)=16.67 microM) and L-mimosine (IC(50)=3.68 microM).

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.

Bond-based 2D TOMOCOMD-CARDD approach for drug discovery: aiding decision-making in 'in silico' selection of new lead tyrosinase inhibitors

In this paper, we present a new set of bond-level TOMOCOMD-CARDD molecular descriptors (MDs), the bond-based bilinear indices, based on a bilinear map similar to those defined in linear algebra. These novel MDs are used here in Quantitative Structure-Activity Relationship (QSAR) studies of tyrosinase inhibitors, for finding functions that discriminate between the tyrosinase inhibitor compounds and inactive ones. In total 14 models were obtained and the best two discriminant functions (Eqs. 32 and 33) shown globally good classification of 91.00% and 90.17%, respectively, in the training set. The test set had accuracies of 93.33% and 88.89% for the models 32 and 33, correspondingly. A simulated virtual screening was also carried out to prove the quality of the determined models. In a final step, the fitted models were used in the biosilico identification of new synthesized tetraketones, where a good agreement could be observed between the theoretical and experimental results. Four compounds of the novel bioactive chemicals discovered as tyrosinase inhibitors: TK10 (IC(50) = 2.09 microM), TK11 (IC(50) = 2.61 microM), TK21 (IC(50) = 2.06 microM), TK23 (IC(50) = 3.19 microM), showed more potent activity than L-mimose (IC(50) = 3.68 microM). Besides, for this study a heterogeneous database of tyrosinase inhibitors was collected, and could be a useful tool for the scientist in the domain of tyrosinase enzyme researches. The current report could help to shed some clues in the identification of new chemicals that inhibits enzyme tyrosinase, for entering in the pipeline of drug discovery development.

QSAR study of anticoccidial activity for diverse chemical compounds: Prediction and experimental assay of trans-2-(2-nitrovinyl)furan

In this work we report a QSAR model that discriminates between chemically heterogeneous classes of anticoccidial and non-anticoccidial compounds. For this purpose we used the Markovian Chemicals in silico Design (MARCH-INSIDE) approach J. Mol. Mod.2002, 8, 237-245; J. Mol. Mod.2003, 9, 395-407]. Linear discriminant analysis allowed us to fit the discriminant function. This function correctly classifies 86.67% of anticoccidial compounds and 96.23% of inactive compounds in the training series. Overall classification is 94.12%. We validated the model by means of an external predicting series, with 86.96% of global predictability. Remarkably, the present model is based on topological as well as configuration-dependent molecular descriptors. Therefore, the model performs timely calculations and allows discrimination between Z/E and chiral isomers. Finally, to exemplify the use of the model in practice we report the prediction and experimental assay of trans-2-(2-nitrovinyl)furan. It is notable that lesion control was 72.86% at mg/kg of body weight with respect to 60% at 125 mg/kg for amprolium (control drug). The back-projection map for this compound predicts a high level of importance for the double bond and for the nitro group in the trans position. We conclude that the MARCH-INSIDE approach enables the accurate fast track identification of anticoccidial hits. Moreover, trans-2-(2-nitrovinyl)furan seems to be a promising drug for the treatment of coccidiosis.

Enantiomeric separation and determination of absolute stereochemistry of asymmetric molecules in drug discovery—Building chiral technology toolboxes

The application of Chiral Technology, or the (extensive) use of techniques or tools for the determination of absolute stereochemistry and the enantiomeric or chiral separation of racemic small molecule potential lead compounds, has been critical to successfully discovering and developing chiral drugs in the pharmaceutical industry. This has been due to the rapid increase over the past 10-15 years in potential drug candidates containing one or more asymmetric centers. Based on the experiences of one pharmaceutical company, a summary of the establishment of a Chiral Technology toolbox, including the implementation of known tools as well as the design, development, and implementation of new Chiral Technology tools, is provided.

Bond-based global and local (bond, group and bond-type) quadratic indices and their applications to computer-aided molecular design. 1. QSPR studies of diverse sets of organic chemicals

The concept of atom-based quadratic indices is extended to a series of molecular descriptors (MDs) (both total and local) based on adjacency between edges. The kth edge-adjacency matrix (E ( k )) denotes the matrix of bond-based quadratic indices (non-stochastic) with respect to the 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-based quadratic indices are calculated using ES ( k ) as operators of quadratic transformations. The study of six representative physicochemical properties of octane isomers was used to compare the ability of both series of MDs to produce significant quantitative structure-property relationship (QSPR) models. Moreover, the general performance of the new MDs in this QSPR study has been evaluated with respect to other 2D/3D well-known sets of indices and the obtained results shown a quite satisfactory behavior of the present method. The novel bond-level MDs were also used for the description and prediction of the boiling point of 28 alkyl-alcohols and to the modeling of the specific rate constant (log k) of 34 derivatives of 2-furylethylenes. These models were statistically significant and showed very good stability to data variation in leave-one-out (LOO) cross-validation experiment. 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) expose a good behavior of our method in this QSPR studies. The approach described in this report appears to be a very promising structural invariant, useful for QSPR/QSAR studies, similarity/diversity analysis, and computer-aided "rational" molecular (drug) design.

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.

New ligand-based approach for the discovery of antitrypanosomal compounds

The antitrypanosomal activity of 10 already synthesized compounds was in silico predicted as well as in vitro and in vivo explored against Trypanosoma cruzi. For the computational study, an approach based on non-stochastic linear fingerprints to the identification of potential antichagasic compounds is introduced. Molecular structures of 66 organic compounds, 28 with antitrypanosomal activity and 38 having other clinical uses, were parameterized by means of the TOMOCOMD-CARDD software. A linear classification function was derived allowing the discrimination between active and inactive compounds with a confidence of 95%. As predicted, seven compounds showed antitrypanosomal activity (%AE>70) against epimastigotic forms of T. cruzi at a concentration of 100mug/mL. After an unspecific cytotoxic assay, three compounds were evaluated against amastigote forms of the parasite. An in vivo test was carried out for one of the studied compounds.

A novel non-stochastic quadratic fingerprints-based approach for the 'in silico' discovery of new antitrypanosomal compounds

A non-stochastic quadratic fingerprints-based approach is introduced to classify and design, in a rational way, new antitrypanosomal compounds. A data set of 153 organic chemicals, 62 with antitrypanosomal activity and 91 having other clinical uses, was processed by a k-means cluster analysis to design training and predicting data sets. Afterwards, a linear classification function was derived allowing the discrimination between active and inactive compounds. The model classifies correctly more than 93% of chemicals in both training and external prediction groups. The predictability of this discriminant function was also assessed by a leave-group-out experiment, in which 10% of the compounds were removed at random at each time and their activity predicted a posteriori. In addition, a comparison with models generated using four well-known families of 2D molecular descriptors was carried out. As an experiment of virtual lead generation, the present TOMOCOMD approach was finally satisfactorily applied on the virtual evaluation of 10 already synthesized compounds. The in vitro antitrypanosomal activity of this series against epimastigotes forms of Trypanosomal cruzi was assayed. The model was able to predict correctly the behaviour of these compounds in 90% of the cases.

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.

Linear indices of the 'macromolecular graph's nucleotides adjacency matrix' as a promising approach for bioinformatics studies. Part 1: prediction of paromomycin's affinity constant with HIV-1 psi-RNA packaging region

The design of novel anti-HIV compounds has now become a crucial area for scientists around the world. In this paper a new set of macromolecular descriptors (that are calculated from the macromolecular graph's nucleotide adjacency matrix) of relevance to nucleic acid QSAR/QSPR studies, nucleic acids' linear indices. A study of the interaction of the antibiotic Paromomycin with the packaging region of the HIV-1 psi-RNA has been performed as example of this approach. A multiple linear regression model predicted the local binding affinity constants [Log K (10(-4) M(-1))] between a specific nucleotide and the aforementioned antibiotic. The linear model explains more than 87% of the variance of the experimental Log K (R = 0.93 and s = 0.102 x 10(-4) M(-1)) and leave-one-out press statistics evidenced its predictive ability (q2 = 0.82 and s(cv) = 0.108 x 10(-4) M(-1)). The comparison with other approaches (macromolecular quadratic indices, Markovian Negentropies and 'stochastic' spectral moments) reveals a good behavior of our method.

A linear discrimination analysis based virtual screening of trichomonacidal lead-like compounds: Outcomes of in silico studies supported by experimental results

A computational (virtual) screening test to identify potential trichomonacidals has been developed. Molecular structures of trichomonacidal and non-trichomonacidal drugs were represented using stochastic and non-stochastic atom-based quadratic indices and a linear discrimination analysis (LDA) was trained to classify molecules regarding their antiprotozoan activity. Validation tests revealed that our LDA-QSAR models recognize at least 88.24% of trichomonacidal lead-like compounds and suggest using this methodology in virtual screening protocols. These classification functions were then applied to find new lead antitrichomonal compounds. In this connection, the biological assays of eight compounds, selected by computational screening using the present models, give good results (87.50% of good classification). In general, most of the compounds showed high activity against Trichomonas vaginalis at the concentration of 100 microg/ml and low cytotoxicity to this concentration. In particular, two heterocyclic derivatives (VA7-67 and VA7-69) maintained their efficacy at 10 microg/ml with an important trichomonacidal activity (100.00% of reduction), but it is remarkable that the compound VA7-67 did not show cytotoxic effects in macrophage cultivations. This result opens a door to a virtual study considering a higher variability of the structural core already evaluated, as well as of other chemicals not included in this study.

3D-chiral Atom, Atom-type, and Total Non-stochastic and Stochastic Molecular Linear Indices and their Applications to Central Chirality Codification

Non-stochastic and stochastic 2D linear indices have been generalized to codify chemical structure information for chiral drugs, making use of a trigonometric 3D-chirality correction factor. These descriptors circumvent the inability of conventional 2D non-stochastic [Y. Marrero-Ponce. J. Chem. Inf. Comp., Sci. l 44 (2004) 2010] and stochastic [Y. Marrero-Ponce, et al. Bioorg. Med. Chem., 13 (2005) 1293] linear indices to distinguish sigma-stereoisomers. In order to test the potential of this novel approach in drug design we have modelled 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 showed an accuracy of 100% and 96.65% for the training set; and 88.88% and 100% in the external test set, respectively. Canonical regression analysis corroborated the statistical quality of these models (R(can) of 0.78 and of 0.77) and was also used to compute biology activity canonical scores for each compound. After that, the prediction of the sigma-receptor antagonists of chiral 3-(3-hydroxyphenyl)piperidines by linear multiple regression analysis was carried out. Two statistically significant QSAR models were obtained when non-stochastic (R2 = 0.982 and s = 0.157) and stochastic (R2 = 0.941 and s = 0.267) 3D-chiral linear indices were used. The predictive power was assessed by the leave-one-out cross-validation experiment, yielding values of q2 = 0.982 (s(cv) = 0.186) and q2 = 0.90 (s(cv) = 0.319), respectively. Finally, the prediction of the corticosteroid-binding globulin binding affinity of steroids set was performed. The best results obtained in the cross-validation procedure with non-stochastic (q2 = 0.904) and stochastic (q2 = 0.88) 3D-chiral linear indices 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 an interesting alternative to other more common 3D-QSAR descriptors.

Protein linear indices of the ‘macromolecular pseudograph α-carbon atom adjacency matrix’ in bioinformatics. Part 1: Prediction of protein stability effects of a complete set of alanine substitutions in Arc repressor

A novel approach to bio-macromolecular design from a linear algebra point of view is introduced. A protein's total (whole protein) and local (one or more amino acid) linear indices are a new set of bio-macromolecular descriptors of relevance to protein QSAR/QSPR studies. These amino-acid level biochemical descriptors are based on the calculation of linear maps on Rn[f k(xmi):Rn-->Rn] in canonical basis. These bio-macromolecular indices are calculated from the kth power of the macromolecular pseudograph alpha-carbon atom adjacency matrix. Total linear indices are linear functional on Rn. That is, the kth total linear indices are linear maps from Rn to the scalar R[f k(xm):Rn-->R]. Thus, the kth total linear indices are calculated by summing the amino-acid linear indices of all amino acids in the protein molecule. A study of the protein stability effects for a complete set of alanine substitutions in the Arc repressor illustrates this approach. A quantitative model that discriminates near wild-type stability alanine mutants from the reduced-stability ones in a training series was obtained. This model permitted the correct classification of 97.56% (40/41) and 91.67% (11/12) of proteins in the training and test set, respectively. It shows a high Matthews correlation coefficient (MCC=0.952) for the training set and an MCC=0.837 for the external prediction set. Additionally, canonical regression analysis corroborated the statistical quality of the classification model (Rcanc=0.824). This analysis was also used to compute biological stability canonical scores for each Arc alanine mutant. On the other hand, the linear piecewise regression model compared favorably with respect to the linear regression one on predicting the melting temperature (tm) of the Arc alanine mutants. The linear model explains almost 81% of the variance of the experimental tm (R=0.90 and s=4.29) and the LOO press statistics evidenced its predictive ability (q2=0.72 and scv=4.79). Moreover, the TOMOCOMD-CAMPS method produced a linear piecewise regression (R=0.97) between protein backbone descriptors and tm values for alanine mutants of the Arc repressor. A break-point value of 51.87 degrees C characterized two mutant clusters and coincided 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 mutant Arc homodimers. These models also permitted the interpretation of the driving forces of such folding process, indicating that topologic/topographic protein backbone interactions control the stability profile of wild-type Arc and its alanine mutants.

Atom, atom-type, and total nonstochastic and stochastic quadratic fingerprints: a promising approach for modeling of antibacterial activity

The TOpological MOlecular COMputer Design (TOMOCOMD-CARDD) approach has been introduced for the classification and design of antimicrobial agents using computer-aided molecular design. For this propose, atom, atom-type, and total quadratic indices have been generalized to codify chemical structure information. In this sense, stochastic quadratic indices have been introduced for the description of the molecular structure. These stochastic fingerprints are based on a simple model for the intramolecular movement of all valence-bond electrons. In this work, a complete data set containing 1006 antimicrobial agents is collected and presented. Two structure-based antibacterial activity classification models have been generated. The models (including nonstochastic and stochastic indices) classify correctly more than 90% of 1525 compounds in training sets. These models permit the correct classification of 92.28% and 89.31% of 505 compounds in an external test sets. The TOMOCOMD-CARDD approach, also, satisfactorily compares with respect to nine of the most useful models for antimicrobial selection reported to date. Finally, a virtual screening of 87 new compounds reported in the antiinfective field with antibacterial activities is developed showing the ability of the TOMOCOMD-CARDD models to identify new leads as antibacterial.

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.