Extending membrane pore lifetime with AC fields: A modeling study

Abstract

AC (sinusoidal) fields with frequencies from kilohertz to gigahertz have been used for gene delivery. To understand the impact of AC fields on electroporation dynamics, we couple a nondimensionalized Smoluchowski equation to an exact representation of the cell membrane voltage obtained solving the Laplace equation. The slope of the pore energy function, dφ/dr, with respect to pore radius is critical in predicting pore dynamics in AC fields because it can vary from positive, inducing pore shrinkage, to negative, driving pore growth. Specifically, the net sign of the integral of dφ/dr over time determines whether the average pore size grows (negative), shrinks (positive), or oscillates (zero) indefinitely about a steady-state radius, rss. A simple analytic relationship predicting the amplitude of the membrane voltage necessary for this behavior agrees well with simulation for frequencies from 500 kHz to 5 MHz for rss < 10 nm. For larger pore size (rss > 10 nm), dφ/dr oscillates about a negative value, suggesting that a net creation of pores may be necessary to maintain a constant pore size. In both scenarios, the magnitude of rss depends only upon the amplitude of the membrane voltage and not directly upon the applied field frequency other than the relationship between the amplitudes of the applied field and membrane voltage.