Detour matrix-based adjacent path eccentric distance sum indices for QSAR/QSPR. Part I: development and evaluation

Area of Science:

• Chemical Graph Theory
• Computational Chemistry
• Drug Discovery

Background:

• Topological indices (TIs) are crucial for quantitative structure-activity relationship (QSAR) studies.
• Existing TIs may have limitations in discriminating complex molecular structures.

Purpose of the Study:

• To conceptualize and compute novel detour matrix-based topological indices.
• To evaluate the discriminating power, degeneracy, and sensitivity of these new TIs.
• To explore their potential applications in drug design and molecular characterization.

Main Methods:

• Development of three adjacent path eccentric distance sum indices (A)ξ(1)(PDS), (A)ξ(2)(PDS), (A)ξ(3)(PDS) and their topochemical versions.
• Computation of TI values for cyclic and acyclic structures up to five vertices using a custom computer program.
• Evaluation of TIs based on discriminating power, degeneracy, intercorrelation, and sensitivity to branching and substituent positions.

Main Results:

• The proposed TIs demonstrated exceptionally high discriminating power.
• High sensitivity towards branching and the relative positions of substituents in cyclic structures was observed.
• Negligible degeneracy was found for the proposed indices.
• Mathematical properties of one TI were investigated.

Conclusions:

• The novel topological indices possess significant potential for molecular characterization and similarity/dissimilarity studies.
• Their properties make them valuable tools for lead identification, optimization, and combinatorial library design.
• These indices can facilitate quantitative structure-activity/property/toxicity/pharmacokinetic relationship studies in drug design.