Some stable and closed-shell structures of anticancer drugs by graph theoretical parameters

Area of Science:

• Mathematical Chemistry
• Computational Chemistry
• Medicinal Chemistry

Background:

• Eigenvalues are crucial in mathematics and have applications in various scientific fields, including chemistry.
• In chemistry, eigenvalues represent energy levels and physicochemical properties of substances.
• Understanding the mathematical-chemical relationship is key to molecular analysis.

Purpose of the Study:

• To investigate the chemical properties of anticancer drug structures using mathematical concepts.
• To determine the stability and characteristics of specific anticancer drugs through eigenvalue analysis.

Main Methods:

• Calculated nullity, matching number, and eigenvalues of the adjacency matrix for drug structures.
• Analyzed characteristic polynomials to understand molecular properties.
• Correlated eigenvalue signs with bonding (negative), antibonding (positive), and nonbonding (zero) levels.

Main Results:

• The study analyzed the structures of Carmustine, Caulibugulone-E, and Aspidostomide-E.
• A nullity of zero was observed for these anticancer drug structures.
• This indicates stability and closed-shell characteristics for the analyzed molecules.

Conclusions:

• The mathematical analysis of eigenvalues and molecular descriptors provides insights into drug stability.
• Carmustine, Caulibugulone-E, and Aspidostomide-E exhibit stability, confirmed by their zero nullity.
• Eigenvalue analysis is a valuable tool for characterizing anticancer drug molecules.