Molecular descriptors, QSAR topological indices

MDL QSAR MDL Information Systems, Inc. www.mdl.com/products/predictive/qsar/index.jsp Molecular property descriptors, total topological descriptors, E-state indices... 

A molecular descriptor derived from the - H-depleted molecular graph and proposed to enhance the role of terminal vertices in QSAR and QSPR studies [Gupta et al, 1999]. It is calculated from the pendent matrix, which is a submatrix of the distance matrix D with A rows and a number m of columns corresponding to the number of terminal vertices. The superpendentic index is calculated as the square root of the sum of the products of the nonzero row elements (the topological distances d) in the pendent matrix ... 

Based on the use of chemical graph theory as described above, various indexes of molecular structure have been developed. These indexes may all be termed topological indexes. In the molecular connectivity method, indexes have been developed to characterize various aspects of molecular structure. The kappa shape indexes were developed so that shape measures could be directly entered in QSAR analyses. Each of these indexes characterizes the whole molecule with respect to one or more aspects of structure. In chemistry it is also of interest to characterize the skeletal atoms. In this final section we review briefly an investigation of the skeletal atoms as vertexes in the molecular graph as a basis for an atom descriptor. 

The third model (QSAR 25) developed using the hvdrogen bond descriptor FCPSA (a charge-weighted analog of FPSA [91]), first moment of inertia (J ) and the Balaban topological index (/, a measure of molecular... 

Bollobas and Erdos in one of their publications considered the upper bounds on the Randic index [5], which has been known in chemistry as the connectivity index (x) [6]. Undoubtedly, the work Bollobtis and Erdos attracted the interest of many mathematicians in graph theory to the study of the mathematical properties of the Randic index [7,8]. More recently, such woik extended toward the study of several additional topological indices. The Randic index or the connectivity index % is well known in QSAR. It is one of the most often used molecular descriptors in the structure-property-activity studies. As of the middle of 2014, the seminal publication of the connectivity index has passed 2500 citations, in part possibly also due to the continuing interest of mathematicians in the mathematical properties of molecular descriptors. 

Finally, there is one particular topological descriptor that should be mentioned because it has found considerable utility in a number of studies. This property, originally called a chemically intuitive molecular index by its inventor, Frank Burden, is based on a modified molecular adjacency matrix. The approach was extended by Pearlman " to take account of atomic charge, polarisability and hydrogen bonding ability, properties which are termed BCUT descriptors. BCUTs are available in a number of software packages and in addition to their utility in QSAR modelling, they have been shown to be useful measures of chemical similarity. 

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