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Specifically, the chemotherapy drugs, fluorouracil, proflavine, and methylene blue, are non-covalently bonded with either a flat graphene sheet or a spherical <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\rm C}_{60}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>C<\/mml:mi>\n                    <mml:mn>60<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> fullerene. Mathematical expressions for the interaction energy between an atom and graphene, as well as between an atom and <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\rm C}_{60}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>C<\/mml:mi>\n                    <mml:mn>60<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> 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\u2019 three-dimensional architectures are presented, accompanied by numerical values for crucial parameters. The results indicate that the nanocarrier\u2019s structure effectively accommodates the atoms on the drug\u2019s carbon planes. The three drug types\u2019 molecules disperse across the graphene surface, whereas only fluorouracil spreads on the <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\rm C}_{60}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>C<\/mml:mi>\n                    <mml:mn>60<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> 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.<\/jats:p>","DOI":"10.1038\/s41598-024-62483-4","type":"journal-article","created":{"date-parts":[[2024,5,25]],"date-time":"2024-05-25T11:01:39Z","timestamp":1716634899000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Mathematical modeling and optimization technique of anticancer antibiotic adsorption onto carbon nanocarriers"],"prefix":"10.1038","volume":"14","author":[{"given":"Kanes","family":"Sumetpipat","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Duangkamon","family":"Baowan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Prangsai","family":"Tiangtrong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,5,25]]},"reference":[{"issue":"2","key":"62483_CR1","doi-asserted-by":"publisher","first-page":"133","DOI":"10.2147\/IJN.S596","volume":"3","author":"WH De Jong","year":"2008","unstructured":"De Jong, W. 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