Randic

More details can be found in the contributions from Randic [17] and Lucic Trinajstic [18]. 

Other quite frequently used indices are the Randic index and the information-topological indices such as the Bonchev index (see Chapter VIll, Section 1 in the Handbook), Up to now several hundred indices have been devised. 

The Randic connectivity index, X, is also called the connectivity index or branching index, and is defined by Eq. (18) [7], where b runs over the bonds i-j of the molecule, and and dj are the vertex degrees of the atoms incident with the considered bond. 

Weiner index Randic indices Kier and Hall indices Inforanation content Connectivity index Balaban index... 

Most of the 2D QSAR methods are based on graph theoretic indices, which have been extensively studied by Randic [29] and Kier and Hall [30,31]. Although these structural indices represent different aspects of molecular structures, their physicochemical meaning is unclear. Successful applications of these topological indices combined with multiple linear regression (MLR) analysis are summarized in Ref. 31. On the other hand, parameters derived from various experiments through chemometric methods have also been used in the study of peptide QSAR, where partial least square (PLS) [32] analysis has been employed [33]. 

M Randic. On characterization of molecular branching. J Am Chem Soc 97 6609-6615, 1975. LB Kier, LH Hall. Molecular Connectivity in Structure-Activity Analysis. Chichester, England Research Studies Press, 1986. 

The Randic-Kier-Hall Molecular Connectivity Indices... 

M. J. Randic, On the recognition of identical graphs representing molecular topology. J. Chem. Physics, 60 (1974) 3920-3928. 

Carstens, E., Klumpp, D., Randic, M., and Zimmerman, M. (1981) Effect of iontophoretically applied 5-hydroxytryptamine on the excitability of single primary afferent C- and A-fibers in the cat spinal cord. Brain Res., 220 151-158. 

Randic, M., and Yu, H. H. (1976) Effects of 5-hydroxytryptamine and bradykinin in cat dorsal horn neurones activated by noxious stimuli. Brain Res., 111 197-203. 

Randic, M. Graph theoretical descriptors of two-dimensional chirality with possible extension to three-dimensional chirality. J. Chem. Inf. Comput. Sci. 2001, 41, 639-649. 

Among many theoretical approaches, the quantitative structure-property/ activity relationships (QSPR/QSAR) methods in conjunction with experimental data pave the way to characterization of properties of new compounds. Properly calibrated such methods provide tools for the prediction of physicochemical parameters (QSPR) and/or biological activity (QS AR) for substances, which have not been yet examined in experiments (Wiener, 1947a, b, 1948a, b Randic and Basak, 1999, 2001 Randic and Pompe, 2001a, b Basak et al., 2001). 

Flexible optimal descriptors have been defined as specific modifications of adjacency matrix, by means of utilization of nonzero diagonal elements (Randic and Basak, 1999, 2001 Randic and Pompe, 2001a, b). These nonzero values of matrix elements change vertex degrees and consequently the values of molecular descriptors. As a rule, these modifications are aimed to change topological indices. The values of these diagonal elements must provide minimum standard error of estimation for predictive model (that is based on the flexible descriptor) of property/activity of interest. 

The concept of the molecular connectivity index (originally called branching index) was introduced by Randic [266]. The information used in the calculation of molecular connectivity indices is the number and type of atoms and bonds as well as the numbers of total and valence electrons [176,178,181,267,268]. These data are readily available for all compounds, synthetic or hypothetical, from their structural formulas. All molecular connectivity indices are calculated only for the non-hydrogen part of the molecule [269-271]. Each non-hydrogen atom is described by its atomic 6 value, which is equal to the number of adjacent nonhydrogen atoms. For example, the first-order Oy) molecular connectivity index is calculated from the atomic S values using Eq. (38) ... 

Burns and Weaver [6] developed an MLR-based BBB permeability model using two experimental measures of BBB penetrability (brain/plasma ratio and the brain-uptake index) and 14 theoretically derived biophysical predictors based on Stein s hydrogen-bonding number and Randic s topological properties of the molecules. The final model accurately predicted the ability of test molecules to cross the BBB. 

Burns and Weaver [6] Stein s hydrogen-bonding number and Randic s topological properties... 

P. Taylor, The Cholinesterases , J. Biol. Chem. 1991, 266, 4025-4028 P. Taylor, Z. Randic, The Cholinesterases From Genes to Proteins , Annu. Rev. Pharmacol. Toxicol. 

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