Use of graph invariants in quantitative structure-activity relationship studies

Subhash C. Basak

Research output: Contribution to journalReview articlepeer-review

19 Scopus citations


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 threedimensional (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.

Original languageEnglish (US)
JournalCroatica Chemica Acta
Issue number4
StatePublished - Dec 2016


  • Anticancer activity
  • Applicability domain (AD)
  • Aryl hydrocarbon (Ah) receptor
  • Congenericity principle
  • Dibenzofurans
  • Diversity begets diversity principle
  • External validation
  • Graph invariant
  • Interrelated two way clustering (ITC)
  • K-fold cross-validation
  • Leave-oneout (LOO) cross-validation
  • Model object
  • Molecular structure
  • Mutagenicity
  • Naïve q2
  • Principal component analysis (PCA)
  • Quantitative structure-activity relationship (QSAR)
  • Quantum chemical descriptors
  • Rank-deficient
  • Theoretical model
  • Three dimensional (3-D) or geometrical descriptors
  • Topological indices (TIs)
  • True q2
  • Two-deep cross validation


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