Spectral Moments of the Edge-Adjacency Matrix of Molecular Graphs. 2. Molecules Containing Heteroatoms and QSAR Applications

Abstract

A novel substructural approach to structure-property and structure-activity relationships studies is proposed. The method is based on the computation of spectral moments of the edge-weighted adjacency matrix. In the present work, bond distances are used as bond weights in the diagonal entries of edge matrix. Spectral moments of the edge-weighted adjacency matrix are expressed in terms of structural fragments present in molecules via algebraic expressions. Boiling points of 58 alkyl halides were well described by the present approach, and this property was expressed as a linear combination of structural fragments of the studied molecules. QSAR applications of the novel approach are explored by studying the antifungal activity of benzyl alcohols. An equation expressing contributions of each substituent in benzyl alcohols to the antifungal activity is obtained. The methodology proposed here permits the rational design of novel compounds with improved activity, which is illustrated for benzyl alcohol derivatives.

Guidance Document on the Validation of (Quantitative) Structure-Activity Relationship [(Q)SAR] Models

“…Such parameters can be assigned as relevant in the context of skin sensitisation in that partition could be modelled by hydrophobicity, polar surface area, molar refractivity, van der Waals radii as bulk parameters and the reactivity accounted for by polarisability and charges. The Topological SubStructural Molecular Design (TOPS-MODE) approach used in this example is based on the method of moments (Estrada, 1996(Estrada, , 1997(Estrada, , 1998. The approach consists of using the topological bond matrix (edge adjacency matrix) of the molecular graph.…”

Structural Contributions of Substrates to their Binding to P-Glycoprotein. A TOPSMODE Approach

“…It is known as TOPS-MODE approach, which is the acronym for topological substructural molecular descriptors/design [57][58][59][60][61][62]. TOPS-MODE approach is based on the calculation of spectral moments of molecular bond matrices appropriately weighted to account for hydrophobic, electronic and steric molecular features.…”

“…Spectral moments are the trace of the kth power of a matrix, i.e., the sum of all entries in the main diagonal of such matrices. The reader is referred to [57][58][59] to obtain full details of this method.…”

“…An automatic knowledge generator is a methodology that will provide new structural alerts to the knowledge archive in a cyclic way keeping it updated. In previous works [54][55][56] we have shown that the so-called topological sub-structural molecular design (TOPS-MODE) approach [57][58][59][60][61][62] represents a useful platform for the automatic generation of toxicological structural alerts. In these works a general strategy for knowledge flow concerning skin sensitization and chromosome aberrations based on the combined use of TOPS-MODE and DEREK expert system was proposed [54][55][56].…”

TI2BioP — Topological Indices to BioPolymers. A Graphical– Numerical Approach for Bioinformatics

“…Later, several algorithms can be applied on the adjacency matrix to provide different TI types such as the Winner index (W) [24], first defined in a chemical context; and others like Randić invariant (χ) [25], Balaban index (J) [26], Broto-Moreau autocorrelation (ATSd) [27] and the spectral moments introduced by Estrada [28]. The spectral moments were defined as the sum of main diagonal entries of the different powers of the bond adjacency matrix [29]. Spectral moments were implemented in the TOPS-MODE (topological substructural molecular design) program [30] and have been widely validated by many authors to encode the structure of small molecules in QSAR studies [31][32][33].…”