Mathematical modeling the disc diffusion test: Antibacterial activity of copper-doped SnO2

In this keynote talk, the traditional disc diffusion-test bioassay is revisited within the perspective of using a mathematical approach grounded on the standard as well as on the modified Hill model. Importantly, the Hill model was established in 1910 to account for the binding of oxygen molecules to hemoglobin and since then has been used as a standard model for evaluation of a wide plethora of experimental situations, including cell viability assays. As for the challenging material, Cu-doped tin oxide (SnO₂) spherical nanoparticles (mean size 8.3 nm) will be tested against two bacteria cultures, namely the Gram positive Staphylococcus aureus (S. aureus) and the Gram negative Escherichia coli (E. coli). Although limited in terms of variety of challenging materials and bacteria cultures, the success of the proposed mathematical approach while explaining the experimental data is quite impressive. The outcomes of the present analysis point quite favorably toward the general use of it in the very near future. New concepts, such as the biological size and the biological size dispersity, for instance, will emerge naturally from the data analysis reported in the talk.