Modeling the Accumulation Kinetics of Anionic Photo-sensitizers in Tumor Cells with Different Trans-membrane Potentials

The accumulation of photo-sensitizer (PS) mainly in tumor cells (TC) is a necessary condition for the effectiveness of photodynamic therapy (PDT). The purpose of this work is the modeling of the accumulation kinetics of anionic PS in TC differing in energy metabolism and trans-membrane potentials (TMP). The kinetic model (KM) including a system of linear differential equations describing the accumulation of PS in some model system based on Nernst theory, is suggested. This system consists of four parallel-sequential compartments separated by permeable membranes with different electric field gradients. These potentials include negative plasma and the mitochondria' TMP as well as energy-dependent positive TMP of the nuclear membranes. The model in question accounts for the phenomenon of reduction of plasma and mitochondria' TMP in TC due to their more rapid division in comparison with normal cells. The KM is constructed for TC of tumor areas sites under hypoxic or oxygen conditions. We conclude that the accumulation kinetics of anionic PS (chlorin E6) in the tumor cells mainly depends on the relationship between the transfer rate constants through their plasma and mitochondria' membranes, these constants being functions of TMP.