On the history of the connectivity index: from the connectivity index to the exact solution of the protein alignment problem

^$Presented at the 8^th International Symposium on Computational Methods in Toxicology and Pharmacology Integrating Internet Resources, CMTPI-2015, June 21–25, 2015, Chios, Greece.

Abstract

We briefly review the history of the connectivity index from 1975 to date. We hope to throw some light on why this unique, by its design, graph theoretical molecular descriptor continues to be of interest in QSAR, having wide use in applications in structure–property and structure–activity studies. We will elaborate on its generalizations and the insights it offered on applications in Multiple Regression Analysis (MRA). Going beyond the connectivity index we will outline several related developments in the development of molecular descriptors used in MRA, including molecular ID numbers (1986), the variable connectivity index (1991), orthogonal regression (1991), irrelevance of co-linearity of descriptors (1997), anti-connectivity (2006), and high discriminatory descriptors characterizing molecular similarity (2015). We will comment on beauty in QSAR and recent progress in searching for similarity of DNA, proteins and the proteome. This review reports on several results which are little known to the structure–property–activity community, the significance of which may surprise those unfamiliar with the application of discrete mathematics to chemistry. It tells the reader many unknown stories about the connectivity index, which may help the reader to better understand the meaning of this index. Readers are not required to be familiar with graph theory.

Keywords:

• topological indices
• connectivity index
• history
• QSAR, QSPR
• orthogonal molecular descriptors
• protein alignment

Acknowledgements

I would like to thank Dr Marjana Novič, the head of the Laboratory of Chemometrics of the National Institute of Chemistry, for warm hospitality and continuing support during my repeated visits to the Institute. I also thank Professor A.T. Balaban (Texas A&M University at Galveston, TX) for interest in this work and very helpful comments on the manuscript, and M. Vračko of the National Institute of Chemistry for help with preparation of figures. Last but not least I would like to thank Athina Geronikaki (Thessaloniki, Greece) and James Devillers (Lyon, France), the organizers of the International Conference on Computational Methods in Toxicology and Pharmacology Integrating Internet Resources (CMTPI), for giving me the honour of presenting the inaugural lecture at the Conference in Chios, Greece, June 22–25, 2015.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

^$ Presented at the 8^th International Symposium on Computational Methods in Toxicology and Pharmacology Integrating Internet Resources, CMTPI-2015, June 21–25, 2015, Chios, Greece.