Use of Mathematical Structural Invariants in Analyzing Combinatorial Libraries: A Case Study with Psoralen Derivatives

Abstract

In this paper, calculated topological indices have been used to cluster a large virtual library of 12⁵ psoralen derivatives into 25 clusters in an effort to select a subset of mutually dissimilar structures from a large collection of molecules. Inspection of the 25 structures, one closest to the respective centroid of each cluster, shows that the molecules are structurally more diverse as compared to a subset of 25 selected randomly. It is expected that such methods based on easily calculated descriptors may find applications in new drug discovery from the analysis of libraries of interesting lead compounds.

Characterization of Dihydrofolate Reductases from Multiple Strains of Plasmodium falciparum Using Mathematical Descriptors of Their Inhibitors

“…For each of the malarial strains, the RR models outperform the PCR and PLS models, with q 2 ranging from 0.648 to 0.920. This is in line with our earlier findings obtained for QSARs of physicochemical properties, bioactivities, and toxicities using the three modeling methods [35] [41] [42]. There is also significant improvement in the predictive ability of the models when the APs are added to the TIs as independent variables.…”

“…The interatomic separation is defined as the number of atoms traversed in the shortest bond-by-bond path containing both atoms. An example demonstrating the calculation of APs can be found in an earlier publication [23]. APProbe [24] was used to calculate the atom pairs for each molecule in the data set.…”

Use of Mathematical Chemodescriptors and Biodescriptors for New Drug Discovery, Environmental Protection, and Surveillance of Emerging Global Pathogens

“…In our research during the last four decades we have frequently used connectivity, valence connectivity, electrotopological, information theoretic, and Triplet indices calculated by the software POLLY [7], MolconnZ [8], and Triplet [9], The graph theoretic chemodescriptors fall into two major categories: …”

<strong>Two QSAR Paradigms- Congenericity Principle versus Diversity Begets Diversity Principle- analyzed using computed mathematical chemodescriptors of homogeneous and diverse sets of chemical mutagens</strong>

“…1 where P is any physical, biological, medicinal or toxicological property of interest and S represents the relevant aspect of the structure that determines the property. A look at the recently published literature would show that various classes of calculated properties, viz., topological, geometrical, quantum chemical, substructural, are used routinely in QSAR formulation [2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

“…But in many practical situations one has to develop models for the prediction of property/ bioactivity of sets of chemicals which are structurally diverse instead of being homogeneous [12]. In the course of carrying out principal components analysis (PCA) of homogeneous and diverse data sets, Basak et al [13,14] noted that a larger number of PCs are required to explain an analogous percentage of variance for diverse data sets as compared to homogeneous collection of molecules. From such QSAR studies Basak [15] formulated the "diversity begets diversity principle," which states that we need a diverse collection of descriptors independent variables) if we want to develop a QSAR for structurally diverse sets of chemicals.…”