Mathematical modeling and optimization technique of anticancer antibiotic adsorption onto carbon nanocarriers

Abstract

This study employs a combination of mathematical derivation and optimization technique to investigate the adsorption of drug molecules on nanocarriers. Specifically, the chemotherapy drugs, fluorouracil, proflavine, and methylene blue, are non-covalently bonded with either a flat graphene sheet or a spherical C60\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\rm C}_{60}$$\\end{document} fullerene. Mathematical expressions for the interaction energy between an atom and graphene, as well as between an atom and C60\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\rm C}_{60}$$\\end{document} fullerene, are derived. Subsequently, a discrete summation is evaluated for all atoms on the drug molecule utilizing the U-NSGA-III algorithm. The stable configurations’ three-dimensional architectures are presented, accompanied by numerical values for crucial parameters. The results indicate that the nanocarrier’s structure effectively accommodates the atoms on the drug’s carbon planes. The three drug types’ molecules disperse across the graphene surface, whereas only fluorouracil spreads on the C60\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\rm C}_{60}$$\\end{document} surface; proflavine and methylene blue stack vertically to form a layer. Furthermore, all atomic positions of equilibrium configurations for all systems are obtained. This hybrid method, integrating analytical expressions and an optimization process, significantly reduces computational time, representing an initial step in studying the binding of drug molecules on nanocarriers.