Mathematical Modeling: Cisplatin Binding to Deoxyribonucleic Acid

The discovery of the cisplatin drug attracted considerable research attention as scientists strove to understand the drug’s mechanism in the human body that is responsible for destroying cancer cells, particularly the coordination between the cisplatin drug and deoxyribonucleic acid. Here, the binding energies of a cisplatin molecule relative to double-stranded deoxyribonucleic acid are obtained. The interactions of the system are determined by performing double integrals, and the analytical expressions are derived from the Lennard–Jones function and the continuum approximation; here, it is assumed that a discrete atomic structure might be replaced by surfaces with a constant average atomic density. The results observed that the cisplatin molecule is binding to the double-stranded deoxyribonucleic acid at either the minor or major grooves. By minimizing the interaction energies between the cisplatin molecule and the minor and major grooves, for arbitrary distances λ and arbitrary tilt angles φ from the axis of the helix of the double-stranded deoxyribonucleic acid, the binding energies are determined, and their values are ≈ − 6 and ≈ − 12.5 (kcal/mol), respectively. Thus, we may deduce that the major groove in double-stranded deoxyribonucleic acid is the most preferred groove for linking with the cisplatin molecule. The current analysis might help in the equivalent continuum modeling of deoxyribonucleic acids and nanocomposites.