Numerical Simulation of Molecular Delivery via Electroporation

A numerical simulation to study molecular delivery via electroporation is presented. The Nernst-Planck equations for species transport are solved in both the intra- and extra-cellular spaces, and are coupled at the cell membrane through an asymptotic Smoluchowski equation for membrane permeabilization. The delivery of calcium ions into a Chinese Hamster Ovary cell is simulated. To facilitate comparison with fluorescence measurement, the simulation includes three species (Ca2+, Fluo-3, and CaFluo) and their reactive kinetics. The results agree well with experimental data from the literature (Gabriel and Teissie, Biophys. J., 1999), and reveal that ion electrophoresis plays an important role in the process. Furthermore, the maximum achievable concentration within the cell is reciprocally correlated with the extracellular electrical conductivity. This observation corroborates well with both previous data (Djuzenova et al., Biochim. Biophys. Acta, 1996) and our own recent measurements. The root-cause of this behavior is an electrokinetic mechanism known as field-amplified sample stacking. Through this mechanism, the intracellular ion concentration can reach a level higher than the extracellular one provided that the intra-to-extra-cellular conductivity ratio is greater than unity. This work is a step toward the quantification of electroporation-mediated molecular delivery.