Modeling the Distribution Kinetics of Charged Drugs in Tumor Cells under Variable Electric Fields Gradients on Mitochondrial and Nuclear Membranes

The distribution of charged cytostatics or photosensitizers (PS) in tumor cells (TC) is an important factor in anticancer therapy effectiveness. The aim of our study was to build the mathematical model of the distribution kinetics of charged PSs, namely, chlorin e6 (E6‒) and its derivative dimethyl ether (DME+) in TC with variable electric transmembrane potentials (TMPs) on mitochondrial and nuclear membranes. A kinetic model is presented that includes a system of four nonlinear differential equations describing the accumulation of PS in a certain model system based on the Nernst theory. This system consists of compartments separated by membranes with different TMPs. The sum of these potentials includes negative plasma and mitochondrial TMPs, as well as an energy-dependent positive TMP on the inner nuclear membrane. Numerical solutions of the nonlinear system of equations with given modulation parameters of TMPs were obtained using a special computer program. The initial rates of PSs transfer and membrane permeability were determined using the curves of fluorescence intensity changes of E6‒ and DME+ in lymphoblast cells. Comparative analysis of the data showed that the effective accumulation of the charged drugs depended on the optimal TMPs ratio in tumor cells. These TMPs can be determined using voltage sensitive fluorescent cationic probe 4-(p-di-methylaminostyryl)-1-methylpyridinium (DSM+).