Fourth generation detour matrix-based topological indices for QSAR/QSPR - Part-1: development and evaluation

Abstract

In the present study, four detour matrix-based Topological Indices (TIs) termed as augmented path eccentric connectivity indices 1-4 (denoted by (AP)ξ(1)(C), (AP)ξ(2)(C), (AP)ξ(3)(C) and (AP)ξ(4)(C)) as well as their topochemical versions (denoted by (AP)ξ(1c)(C), (AP)ξ(2c)(C), (AP)ξ(3c)(C) and (AP)ξ(4c)(C)) have been conceptualised. A modified detour matrix termed as chemical detour matrix (Δ(c)) has also been proposed so as to facilitate computation of index values of topochemical versions of the said TIs. Values of the proposed TIs were computed for all the possible structures containing three, four and five vertices using an in-house computer program. The said TIs exhibited exceptionally high discriminating power and high sensitivity towards branching/relative position of substituent(s) in cyclic structures amalgamated with negligible degeneracy. Due care was taken during the development of TIs so as to ensure that reduction in index values of complex chemical structures to be within reasonable limits without compromising discriminating power. The mathematical properties of one of the proposed TIs have also been studied. With exceptionally high discriminating power, high sensitivity towards branching as well as relative position(s) of substituents in cyclic structures and negligible degeneracy, the proposed indices offer a vast potential for use in characterisation of structures, similarity/dissimilarity studies, lead identification and optimisation, combinatorial library design and quantitative structure-activity/property/toxicity/pharmacokinetic relationship studies.

Relative Eccentric Distance Sum/Product Indices for QSAR/QSPR: Development, Evaluation, and Application

“…This method has a distinct edge as it reduces the index values of complex chemical structures to be within reasonable limits without compromising with the discriminating power. 31 Use of relative values of longest distance and shortest distance between various atoms also helps in keeping index values of complex organic structures to be within limits. Finally, the proposed MDs are easily interpretable because of their simplicity as compared to other MDs and hence can be easily utilized for development of lead molecules through reverse engineering as well as virtual screening.…”

“…To overcome this problem, a recently reported approach [i.e., dividing the index values by a constant factor ( k m )] has been used. This method has a distinct edge as it reduces the index values of complex chemical structures to be within reasonable limits without compromising with the discriminating power . Use of relative values of longest distance and shortest distance between various atoms also helps in keeping index values of complex organic structures to be within limits.…”

“…where σ ic is the maximum chemical path sum, η ic is chemical path eccentricity (both obtained through chemical detour matrix), 31 and S ic is chemical distance sum, E ic is the chemical eccentricity (both obtained through chemical distance matrix) of vertex i, m is equal to 1, 2, and 3 for R ξ 1 cSV , R ξ 2 cSV , and R ξ 3 cSV . The value of k m is equal to 1, 10, and 10 2 for k 1, k 2 , and k 3 , respectively, and n is the number of vertices in a hydrogen suppressed graph G.…”

“…Similarly, topochemical version of the aforementioned index termed as relative eccentric distance sum topochemical index, denoted by R ξ m cSV , may be defined as the summation of ratio of the product of the maximum chemical path sum and chemical path eccentricity and the product of chemical distance sum and chemical eccentricity of each vertex in a hydrogen suppressed molecular graph having n vertices. It can be expressed as per the following: ξ m cSV R = bold1 italick normalm ∑ italici = bold1 italicn ( σ i c × η i c S i c × E i c ) m where σ ic is the maximum chemical path sum, η ic is chemical path eccentricity (both obtained through chemical detour matrix), and S ic is chemical distance sum, E i c is the chemical eccentricity (both obtained through chemical distance matrix) of vertex i , m is equal to 1, 2, and 3 for R ξ 1 cSV , R ξ 2 cSV , and R ξ 3 cSV . The value of k m is equal to 1, 10, and 10 2 for k 1, k 2 , and k 3 , respectively, and n is the number of vertices in a hydrogen suppressed graph G.…”

Path Pendeccentric Connectivity Indices: Detour Matrix Based Molecular Descriptors for QSAR/QSPR Studies, Part 1

“…Chemical degree of vertex v i can be obtained utilizing chemical adjacency matrix (A c ) which is in turn is achieved by replacing the non-zero row entries of adjacency matrix related to heteroatoms like Br, I, O, N, Cl etc., with relative atomic weight compared to carbon atom while counting from carbon atom to any of heteroatom(s) and with one while counting from any of these heteroatom(s) to carbon atom (Goel, & Madan, 1995;Kumar, Sardana, & Madan, 2004;Bajaj, Sambi, & Madan, 2004). Chemical path eccentricity of vertex v i , may be calculated from chemical detour matrix (Δ c ) and may be simply obtained by replacing all the non-zero row entries of detour matrix with corresponding chemical paths (Marwaha, Jangra, Das, Bharatam, & Madan, 2012).…”