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

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 C 60 fullerene. Mathematical expressions for the interaction energy between an atom and graphene, as well as between an atom and C 60 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 C 60 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.

Stable Configurations of DOXH Interacting with Graphene: Heuristic Algorithm Approach Using NSGA-II and U-NSGA-III.

Nanoparticles in drug delivery have been widely studied and have become a potential technique for cancer treatment. Doxorubicin (DOX) and carbon graphene are candidates as a drug and a nanocarrier, respectively, and they can be modified or decorated by other molecular functions to obtain more controllable and stable systems. A number of researchers focus on investigating the energy, atomic distance, bond length, system formation and their properties using density function theory and molecular dynamic simulation. In this study, we propose metaheuristic optimization algorithms, NSGA-II and U-NSGA-III, to find the interaction energy between DOXH molecules and pristine graphene in three systems: (i) interacting between two DOXHs, (ii) one DOXH interacting with graphene and (iii) two DOXHs interacting with graphene. The result shows that the position of the carbon ring plane of DOXH is noticeably a key factor of stability. In the first system, there are three possible, stable configurations where their carbon ring planes are oppositely parallel, overlapping and perpendicular. In the second system, the most stable configuration is the parallel form between the DOXH carbon ring plane and graphene, and the spacing distance from the closest atom on the DOXH to the graphene is 2.57 Å. In the last system, two stable configurations are formed, where carbon ring planes from the two DOXHs lie either in the opposite direction or in the same direction and are parallel to the graphene sheet. All numerical results show good agreement with other studies.

Three model shapes of Doxorubicin for liposome encapsulation.

Targeted drug delivery provides a possible method for the transfer of drug molecules into cancer cells. Liposomes together with a drug, such as Doxorubicin (DOX) inside the liposomes, can be formed as a nano-capsule. In this study, we are interested in finding a favorable size of liposome and an appropriate shape of DOX cluster: sphere, cylinder or ellipsoid. Using mathematical modeling, the interaction energy of the system is obtained from the Lennard-Jones potential and the continuum assumption which assumes that discrete atomic structure can be replaced by an average atomic density spread over a surface. The numerical results show that the spherical shape gives the lowest energy at the equilibrium configuration amongst the three shapes. In the case of equivalent surface areas, the spherical shape gives the energy lower than -4,000 kJ/mol at the equilibrium while the energies for the other cases do not come close to this level. Further in the case of a liposome of 50 nm in radius, the sphere of radius 49.726 nm, equivalent to 31,072 nm(2) surface area, gives the minimum energy at -6,642 kJ/mol. However, an equivalent cylindrical shape is not possible due to geometric constraints. The lowest minimum energy for the ellipsoid occurs for equal major and minor axes, namely for the spherical case. The results presented here are a first step in the design and implementation of a drug molecule for a targeted drug delivery system.