Review article

https://doi.org/10.5562/cca3029

Use of Graph Invariants in Quantitative Structure-Activity Relationship Studies

Subhash C. Basak ; Natural Resources Research Institute & Department of Chemistry and Biochemistry, University of Minnesota Duluth, 5013 Miller Trunk Highway, Duluth, Minnesota 55811, USA

Abstract

This chapter reviews results of research carried out by Basak and collaborators during the past four decades or so in the development of novel mathematical chemodescriptors and their applications in quantitative structure-activity relationship (QSAR) studies related to the prediction of toxicities and bioactivities of chemicals. For chemodescriptors based QSAR studies, we have used graph theoretical, three dimensional (3-D), and quantum chemical indices. The graph theoretic chemodescriptors fall into two major categories: (a) Numerical invariants defined on simple molecular graphs representing only the adjacency and distance relationship of atoms and bonds; such invariants are called topostructural (TS) indices; (b) Topological indices derived from weighted molecular graphs, called topochemical (TC) indices. Collectively, the TS and TC descriptors are known as topological indices (TIs). The set of independent variables used for modeling also includes a group of three-dimensional (3-D) molecular descriptors. Semi-empirical and various levels of ab initio quantum chemical indices have also been used for hierarchical QSAR (HiQSAR) modeling. Results indicate that in many cases of property / activity / toxicity analyzed by us, a TS + TC combination explains most of the variance in the data.

This work is licensed under a Creative Commons Attribution 4.0 International License.

Keywords

molecular structure; model object; theoretical model; graph invariant; quantitative structure-activity relationship (QSAR); topological indices (TIs); three dimensional (3-D) or geometrical descriptors; quantum chemical descriptors; principal component analysis (PCA); leave-one-out (LOO) cross-validation; k-fold cross-validation; external validation; rank-deficient; two-deep cross validation; naïve q2; true q2; dibenzofurans; aryl hydrocarbon (Ah) receptor; Interrelated two way clustering (ITC); congenericity principle; diversity begets diversity principle; applicability domain (AD); mutagenicity; anticancer activity

Hrčak ID:

173872

URI

https://hrcak.srce.hr/173872

Publication date:

19.12.2016.

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