Likely Mechanism of the Hydrophobic Sensitizer Accumulation in Tumor Cells: Mathematical Models

Abstract

Two mathematical models describing the accumulation kinetics of hydrophobic sensitizers in the cell membrane and cytoplasm and the influence of intra- and extracellular pH values on intracellular accumulation are suggested. Numerical calculations were done for hematoporphyrin (Hp) as an example. When compared with the experimental data, both models gave satisfactory results describing the accumulation time and level. A biphasic character of the sensitizer accumulation process was obtained as a result of the difference in the accumulation times characteristic for the plasma membrane and cytoplasm. The ratio of characteristic times was determined by the ratio of membrane and cytoplasm volumes and a "water-lipid" partition coefficient reflecting the height of the membrane barrier for the sensitizer penetration through the plasma membrane lipid bilayer. Generally, the enhanced uptake of Hp molecules by cells was obtained when both extracellular and intracellular pH (pHin) values were lower than the physiological ones. A "selectivity" of accumulation was achieved in "tumor" cells for reasonable pHin values (about 6.0). But when compared with the experimental data, the value of selectivity was not high enough, indicating that, though the pH value is an important factor in Hp intracellular accumulation, it might be less important as a factor for selectivity of Hp accumulation in tumors.