Use of Graph Invariants in Quantitative Structure-Activity Relationship Studies

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 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.

Zagreb Connection Numbers for Cellular Neural Networks

“…A topological index (TI) defined with the help of the degrees of nodes of the (molecular) network is a class of indices which are used to find out and model the certain properties of the chemical compounds of the (molecular) networks (see [14][15][16]). In particular, the degree-based topological properties for the CNN are studied in [17].…”

On the extremal cactus graphs for variable sum exdeg index with a fixed number of cycles

“…In molecular graphs, vertices correspond to the atoms while edges represent the covalent bonds between atoms [9,12]. Among the various existing techniques for handling the issues of predicting physicochemical properties of chemical compounds and seeking combinatorial libraries to find molecular structures that are generally comparative to a target structure, the method involving topological indices is one of the simplest and most widely used such techniques [1,3,6,16,17]. Topological indices are actually those numerical quantities of (molecular) graph which remain same under graph isomorphism [8].…”

Alkanes with the First Three Maximal/Minimal Modified First Zagreb Connection Indices

“…Among the various available methods for predicting physicochemical properties of molecules and for seeking combinatorial libraries to find molecular structures that are generally comparative to a target structure, the technique involving molecular descriptors is one of the simplest and most widely used such methods. [1][2][3][4] According to Todeschini and Consonni, [5] "a molecular descriptor is the final result of a logical and mathematical procedure which transforms chemical information encoded within a symbolic representation of a molecule into an useful number or the result of some standardized experiment".…”