Abstract A problem-based learning experience integrating mathematical concepts of linear and abstract algebra for undergraduate chemistry students is presented. The pedagogical framework was focused on the conceptual understanding of the vector space, graph theory and matrix algebra as a tool to obtain chemical information. The students were capable to solve a problem of physicochemical properties prediction through the calculation of molecular descriptors of the TOMOCOMD (acronym for TOpological MOlecular COMputational Design) approach. A “scientific congress” was organized by students to expose the results of the research. This evaluation strategy stimulated the self- and co-evaluation. The proposed experience demonstrated an enhanced learning compared to the traditional model.

Resumen En este trabajo se presenta una experiencia de de aprendizaje basado en problemas que integra conceptos matemáticos de algebra lineal y abstracta para estudiante de pregrado de química. El marco pedagógico se enfocó en el entendimiento conceptual de espacios vectoriales, teoría de grafos y álgebra matricial como una herramienta para obtener información química. Los estudiantes fueron capaces de resolver un problema de predicción de propiedades fisicoquímicas a través del cálculo de descriptores del esquema TOMOCOMD (siglas en inglés de TOpological MOlecular COMputational Design). Los estudiantes organizaron un “congreso científico” para exponer los resultados de la investigación. Esta evaluación estimuló el auto- y co-evaluación. La experiencia propuesta demostró un aprendizaje mayor al ser comparado con el modelo tradicional.

The QSAR studies defined in the literature are based on uni-modal approaches and do not consider datasets with different chemical information. Thus, this research has as objective to apply and analyze the behavior of multi-modal approaches when QSAR studies are carried out. To this end, a compound dataset with hepatotoxicity activity was employed and four modalities were built considering molecular descriptors based on different mathematical theories. Also, several predictive models were developed taking into account both uni-modal and multi-modal approaches by using classification algorithms reported in the literature and implemented in R language. The parameters of these algorithms with the procedure "parameter tuning with repeated grid-search cross-validation" were optimized, while the strategy 10-fold cross-validation with 10 repetitions was used to corroborate the predictive accuracy of the models. As result of this study it can be stated that the behavior of the models based on multi-modal approach present significant differences with to those models developed from uni-modal approaches.

Los estudios QSAR definidos en la literatura están basados en enfoques uni-modales, dejando de analizar conjuntos de datos que contienen distintas informaciones químicas. En esta investigación se propone aplicar por primera vez y analizar el comportamiento del enfoque multi-modal en el desarrollo de estudios QSAR. Para este fin se utilizó una base de compuestos con actividad hepatotóxica, a partir de la cual se construyeron cuatro modalidades considerando distintos descriptores moleculares basados en diversas teorías y enfoques. Se desarrollaron varios modelos usando los enfoques uni-modales y multi-modales utilizando algoritmos de clasificación reportados en la literatura e implementados en el lenguaje R. Los parámetros de cada uno de los algoritmos se optimizaron con el procedimiento "parametertuningwithrepeatedgrid-searchcross-validation", mientras la validación de dichos modelos se realizó mediante validación cruzada de 10 pliegues con 10 repeticiones. Estadísticamente se comprobó que el enfoque multimodal mejora el desempeño de los modelos predictivos comparado con algunos de los modelos derivados de los conjuntos de datos con modalidades individuales.

In the recent times, the race to cope with the increasing multidrug resistance of pathogenic bacteria has lost much of its momentum and health professionals are grasping for solutions to deal with the unprecedented resistance levels. As a result, there is an urgent need for a concerted effort towards the development of new antimicrobial drugs to stay ahead in the fight against the ever adapting bacteria. In the present report, antibacterial classification functions (models) based on the topological molecular computational design-computer aided ‘‘rational’’ drug design (TOMOCOMD-CARDD) atom-based non-stochastic and stochastic bilinear indices are presented. These models were built using the linear discriminant analysis (LDA) method over a balanced chemical compounds dataset of 2230 molecular structures, with a diverse range of structural and molecular mechanism modes. The results of this study indicated that the non-stochastic and stochastic bilinear indices provided excellent classification of the chemical compounds (with accuracies of 86.31% and 84.92%, respectively, in the training set). These models were further externally validated yielding correct classification percentages of 86.55% and 87.91% for the non-stochastic and stochastic bilinear models, respectively. Additionally, the obtained models were compared with those reported in the literature and demonstrated comparable results, although the latter were built over much smaller datasets and with much higher degrees of freedom. Finally, simulated ligand-based virtual screening of 116 compounds, recently identified as potential antibacterials, was performed yielding 86.21% and 83.62% of correct classification, respectively, and thus demonstrating the utility of the obtained TOMOCOMD-CARDD models in the search of novel compounds with desirable antibacterial activity.

The recently introduced, non-stochastic and stochastic quadratic indices (Marrero-Ponce et al. J. Comp. Aided Mol. Des. 2006, 20, 685-701) were applied to QSAR/QSPR studies of heteroatomic molecules. These novel bond-based molecular descriptors (MDs) were used for the prediction of the partition coefficient (log P), and the antibacterial activity of 34 derivatives of 2-furylethylenes. Two statistically significant QSPR models using non-stochastic and stochastic bond-based quadratic indices were obtained (R² = 0.971, s = 0.137 and R² = 0.986, s = 0.096). These models showed good stability to data variation in leave-one-out (LOO) cross-validation experiment (q² = 0.9975, sCV = 0.164 and q² = 0.947, sCV = 0.114). The best two discriminant models computed using the non-stochastic and stochastic molecular descriptors had globally good classification of 94.12% in the training set. The external prediction sets had accuracies of 100% in both cases. The comparison with other approaches (edge- and vertex-based connectivity indices, total and local spectral moments, quantum chemical descriptors as well as with other TOMOCOMD-CARDD MDs) revealed the good performance of our method in this QSPR study. The obtained results suggest that it is possible to obtain a good estimation of physical, chemical and physicochemical properties for organic compounds with the present approach.

En el presente reporte, se aplican los índices cuadráticos de relaciones de enlace introducidos recientemente (Marrero-Ponce et al. J. Comp. Aided Mol. Des. 2006, 20, 685-701) en estudios QSAR/QSPR de moléculas heteroatómicas. Estos descriptores moleculares de tipo enlace son usados en la predicción del coeficiente de partición (log P) y la actividad antibacterial de 34 derivados de los 2-furiletilenos. Dos modelos QSPR estadísticamente significativos fueron obtenidos usando índices no estocásticos y estocásticos (R² = 0.971, s = 0.137 y R² = 0.986, s = 0.096, respectivamente) en la modelación del Log P. Estos modelos mostraron una estabilidad adecuada en la validación interna LOO (q² = 0.9975, sCV = 0.164 and q² = 0.947, sCV = 0.114, respectivamente). Por otro lado, los dos mejores modelos discriminantes muestran un porcentaje de exactitud global de 94.12% en la serie de entrenamiento y de 100% en la data de predicción en la modelación de actividad bactericida. Finalmente, la comparación con otros enfoques computacionales (índices de conectividad de enlace y de átomo tanto 2D como 3D, momentos espectrales totales y locales, descriptores químicos cuánticos al igual que con otros índices implementados en el programa TOMOCOMD-CARDD) evidencia un buen comportamiento de nuestros nuevos índices. Los resultados obtenidos sugieren que el método propuesto permite obtener una adecuada estimación de propiedades fisicoquímicas y biológicas de moléculas orgánicas.