A unified model of electroporation and molecular transport

Abstract

Biological membranes form transient, conductive pores in response to elevated transmembrane voltage, a phenomenon termed electroporation. These pores facilitate electrical and molecular transport across cell membranes that are normally impermeable. By applying pulsed electric fields to cells, electroporation can be used to deliver nucleic acids, drugs, and other molecules into cells, making it a powerful research tool. Because of its widely demonstrated utility for in vitro applications, researchers are increasingly investigating related in vivo clinical applications of electroporation, such as gene delivery, drug delivery, and tissue ablation. In this thesis, we describe a quantitative, mechanistic model of electroporation and concomitant molecular transport that can be used for guiding and interpreting electroporation experiments and applications. The model comprises coupled mathematical descriptions of electrical transport, electrodiffusive molecular transport, and pore dynamics. Where possible, each of these components is independently validated against experimental results in the literature. We determine the response of a discretized cell system to an applied electric pulse by assembling the discretized transport relations into a large system of nonlinear differential equations that is efficiently solved and analyzed with MATLAB. We validate the model by replicating in silico two sets of experiments in the literature that measure electroporation-mediated transport of fluorescent probes. The model predictions of molecular uptake are in excellent agreement with these experimental measurements, for which the applied electric pulses collectively span nearly three orders of magnitude in pulse duration (50 ts -20 ms) and an order of magnitude in pulse magnitude (0.3 -3 kV/cm). The advantages of our theoretical approach are the ability to (1) analyze in silico the same quantities that are measured by experimental studies in vitro, (2) simulate electroporation dynamics that are difficult to assess experimentally, and (3) quickly screen a wide array of electric pulse waveforms for particular applications. We believe that our approach will contribute to a greater understanding of the mechanisms of electroporation and provide an in silico platform for guiding new experiments and applications.