Reaction diffusion model for understanding the drug-target interaction in single cell

Drug target interaction determines the drug efficacy. While drug-target binding/unbinding kinetics can inform the interaction, the kinetics have not been well characterized inside the cell. To better understand this, we study the binding/unbinding kinetics of benzimidazole-derivative DNA binding drugs (Hoechst 33342 dye) in E. coli cells. Simple reaction kinetic models cannot explain the slow binding/unbinding kinetics observed in our experiments as compared to the in vitro measurement. Hence, we develop a reaction diffusion model which incorporates the passive diffusion of Hoechst molecules through the membrane, active efflux, and intracellular diffusion of the Hoechst molecules. We test the model prediction by experimentally measuring Hoechst binding/unbinding to/from DNA. Our model can be a basis for understanding the effects of the intracellular diffusion and permeability of cell membrane of the cell on the in vivo drug target interaction.