Ramanathan Natarajan

Quantitative structure-activity relationship modeling of juvenile hormone mimetic compounds for Culex pipiens larvae, with a discussion of descriptor-thinning methods.

Quantitative structure-activity relationship (QSAR) modelers often encounter the problem of multicollinearity owing to the availability of large numbers of computable molecular descriptors. Sparsity of the variables while using descriptors such as atom pairs increases the complexity. Three different predictor-thinning methods, namely, a modified Gram-Schmidt algorithm, a marginal soft thresholding algorithm, and LASSO (least absolute shrinkage and selection operator), were utilized to reduce the number of descriptors prior to developing linear models. Juvenile hormone (JH) activity of 304 compounds on Culex pipiens larvae was taken as the model data set, and predictor trimming of a large number of diverse descriptors comprising 268 global molecular descriptors (topostructural, topochemical, and geometrical), 13 quantum chemical descriptors, and 915 atom pairs (substructural counts) was applied prior to linear regression by the ridge regression method. The data set (N = 304) was split into five calibration data sets of random samples of sizes 60/110/160/210/260, and the remaining 244/194/144/94/44 compounds were used for validations. LASSO was not found to be a very effective method in handling a large set of descriptors because the number of predictors retained could not exceed the number of observations. The results indicated that the modified Gram-Schmidt algorithm could be used to trim the number of predictors in the global molecular descriptor set where collinearity of the descriptors was the major concern. On the contrary, the soft thresholding approach was found to be an effective tool in subset selection from a diverse set of descriptors having both sparsity and multicollinearity, as in the case of the combined set of atom pairs and global molecular descriptors. The final model developed after variable selection was dominated more by atom pairs, which indicated the important structural moieties that affect JH activity of the compounds. The success of the method reiterates the fact that QSAR or quantitative structure-property relationship (QSPR) models can be developed for a diverse set of compounds using properly parametrized and diverse sets of descriptors, of course, with the selection of the appropriate statistical tools.

Novel Approach for the Numerical Characterization of Molecular Chirality

The use of chiral compounds as pharmaceuticals and agrochemicals continues to increase, warranting numerical characterization of chirality in order to develop structure-activity relationship models involving these compounds. Enantiomers are identical in all scalar properties and, hence, are not differentiated by topological indices and 3-D descriptors. Three distinct measures of chirality were developed to discriminate diastereomers and enantiomers. The novel topological indices treat chirality as a continuous measure, and hence we prefer to call it the Relative Chirality Index (RCI). Application of RCI in developing SAR is illustrated with the repellency data for the diastereomers of picaridin and AI3-37220.

Numerical Descriptors for the Characterization of Chiral Compounds and their Applications in Modeling Biological and Toxicological Activities

Due to the advancement in chiral synthesis and separation technology and the new regulatory policies for chiral pharmaceuticals several manufacturers are replacing the previously marketed racemate chemicals with single enantiomeric products, the so called chiral switch. Though 25% of agrochemicals are chiral in nature, most of them are sold as racemates or enantiomer enriched products. Chiral pesticides and some of the pharmaceuticals reach the human food chain as pollutants. Stereoisomers (enantiomers and diastereoisomers) not only differ from one another in their medicinal effects, but also in their phramacokinectic (adsorption, distribution, biotransformation and excretion) profiles and toxicological properties. Several recent attempts have been reported in the literature on developing mathematical models to predict the properties of chiral molecules from structure and such methods utilized numerical characterization. A comparison of different mathematical approaches on the numerical characterization of molecules with chiral center(s) and a brief background on the importance of stereochemistry in pharmacology, agrochemistry and environmental toxicology is presented.

Three dimensional structure-activity relationships (3D-QSAR) for insect repellency of diastereoisomeric compounds: a hierarchical molecular overlay approach¶

2-(2-Hydroxyethyl)-1-piperidinecarboxylic acid 1-methylpropyl ester (Picaridin), and 1-(cyclohex-3-ene-1-ylcarbonyl)-2-methylpiperidine (AI3-37220; 220) are alternatives to DEET (N,N-diethyl-3-methylbenzamide), the most popular mosquito repellent. Picaridin and AI3-37220 exhibit polychiral diastereoisomerism and each has four diastereoisomers due to the presence of two asymmetric centers in their molecules. The diastereoisomers of these compounds have differing degrees of mosquito-repellent activity according to quantitative behavioral assays conducted at the United States Department of Agriculture. An insight into the stereochemical requirements for repellency is of great importance in the development of better repellents. Molecular overlay of the optimized geometries of the diastereoisomers was considered as a novel tool for Stereochemical Structure-Activity Relationship (SSAR) modeling. An earlier study using molecular mechanics (MM2) optimized geometries showed good promise. In continuation of this effort and to overcome certain defects in using MM2 geometries, a hierarchical overlay approach was developed. In this method geometry of the low energy conformer of each diastereoisomer was optimized using: the following quantum chemical methods in a graduated manner: (a) semiempirical AM1, (b) Hartree Fock (STO3G, 3-21G, 6-31G, and 6-311G), and (c) Density Functional Theory (B3LYP/6-31G, B3LYP/6-311G). The optimized geometries of different diastereoisomers were overlaid in various user defined combinations to calculate the root mean square distances (RMSD) of the overlaid structures. The RMSD with respect to the most active diastereoisomer (220SS) were found to have a strong relationship with biological potency. Common motifs in shapes and molecular surfaces that are probably critical for effective repellent activity were identified. The hierarchical approach gave valuable information on the quantum chemical level (basis set) at which optimization must be carried out to get the correct order of repellency of the diastereoisomers of Picaridin and 220. ¶Presented at the 12th International Workshop on Quantitative Structure-Activity Relationships in Environmental Toxicology (QSAR2006), 8–12 May 2006, Lyon, France.

QSAR Modeling of Flotation Collectors Using Principal Components Extracted from Topological Indices

Several topological indices were calculated for substituted-cupferrons that were tested as collectors for the froth flotation of uranium. The principal component analysis (PCA) was used for data reduction. Seven principal components (PC) were found to account for 98.6% of the variance among the computed indices. The principal components thus extracted were used in stepwise regression analyses to construct regression models for the prediction of separation efficiencies (Es) of the collectors. A two-parameter model with a correlation coefficient of 0.889 and a three-parameter model with a correlation coefficient of 0.913 were formed. PCs were found to be better than partition coefficient to form regression equations, and inclusion of an electronic parameter such as Hammett sigma or quantum mechanically derived electronic charges on the chelating atoms did not improve the correlation coefficient significantly. The method was extended to model the separation efficiencies of mercaptobenzothiazoles (MBT) and aminothiophenols (ATP) used in the flotation of lead and zinc ores, respectively. Five principal components were found to explain 99% of the data variability in each series. A three-parameter equation with correlation coefficient of 0.985 and a two-parameter equation with correlation coefficient of 0.926 were obtained for MBT and ATP, respectively. The amenability of separation efficiencies of chelating collectors to QSAR modeling using PCs based on topological indices might lead to the selection of collectors for synthesis and testing from a virtual database.

Numerical characterization of molecular chirality of organic compounds

In 2006, 80% of the small molecule drugs approved by Food and Drug Administration (FDA) of USA were chiral and 75% were single enantiomers. It is expected that 200 chiral compounds could enter the development process every year. In order to keep pace with the industry, computational chemists are trying to develop chirality measures to as- sist and direct asymmetric synthesis and chiral catalysis. Parameterization of chirality and development of chirality met- rics, are very important in QSAR approach to be applied to chiral molecules. There are several attempts in the develop- ment of chirality measurements and earlier reviews on chirality measures concentrated more on the mathematics involved in their calculations. This review presents in-depth discussions of various chirality measures from the perspective of a QSAR modeler.

Quantitative structure-activity relationship modeling of insect juvenile hormone activity of 2,4-dienoates using computed molecular descriptors.

Juvenile hormone (JH) activity of one hundred and eighty 2,4-dienoates reported for the larvae/pupae of six insect species was modeled using 915 atom pairs and 258 global molecular descriptors (topological and geometrical). Ridge regression, principal component regression and partial least square regression methods were used to model each of the JH activities. The use of all of the available parameters did not yield any good models, and extensive predictor trimming was necessary to improve the models. Ridge regression was found to give the best results among the three statistical tools used. The top ten molecular descriptors selected based on the t-statistic for each of the six models were found to be mostly atom pairs containing heteroatoms and topochemical descriptors. This suggests the importance of the chemical nature of the ligand rather than mere space-filling as the basis of the JH bioactivity. The residual plots indicate the existence of some non-linear relations, and recursive partitioning was used to capture any nonlinear relation between the bioassays and the molecular descriptors.

Alignment-free sequence comparison using N-dimensional similarity space.

Several alignment free sequence comparison methods are available and they use similarity, based on a particular numerical descriptor of biological sequences. Any loss of information incurred in the transformation of a sequence into a numerical descriptor affects the results. A pool of descriptors that use different algorithms in their computation is expected to suffer minimum loss of information and an attempt is made in this direction to study the similarity of DNA sequences that are homogenous or heterogeneous. Several numerical descriptors for the characterization of DNA sequences are described, based on information theoretic approach, connectivity of vertex weighted line-graphs and those derived from the matrices obtained from the graphs constructed by depicting DNA sequences as a random walk on a Euclidean plane. The information theoretic descriptors were obtained based on the L-tuple approach for the combination of different numbers of bases. The connectivity type descriptors were calculated by converting the DNA sequence into vertex weighted graphs in which vertices (nucleotide) were assigned weights based on the pKa of the bases. The graphical representations were converted into numerical descriptors by constructing matrices. Computer programs were developed to calculate seventy DNA descriptors; 560 sequences of different types of organisms were used. After initial data analysis to eliminate almost perfectly correlated descriptors, orthogonal descriptors were obtained by performing principal component analysis. Principal components (PCs) were used to construct an N-dimensional similarity space wherein the 560 sequences were clustered by k-means cluster algorithm. Five principal components (orthogonal descriptors) were extracted and found to explain 92% of data variance. The PCs were used to cluster the sequences in a five-dimensional similarity space. The similarity-based dissimilarity clustering procedure using numerical descriptors was found to be effective for studying similarity/ dissimilarity of large number of sequences.

Graph Theoretical Invariants of Chemical and Biological Systems: Development and Applications

Chemical graph theory has been extensively applied in the characterization of structure in many areas of science, chemistry and biology in particular. Numerical graph invariants of molecules or topological indices have been used in the characterization of structure, discrimination of pathological structures like isospectral graphs, prediction of property/ bioactivity of molecules for new drug discovery and environment protection as well as quantification of intermolecular similarity. More recently, methods of discrete mathematics have found applications in the characterization of complex biological objects like DNA/ RNA/ protein sequences and proteomics maps. This chapter reviews the latest results in applications of discrete mathematics, graph theory in particular, to chemical and biological systems.