The current-voltage relation for electropores with conductivity gradients

Abstract

In electroporation, an electric field transiently permeabilizes the cell membrane to gain access to the cytoplasm, and to deliver active agents such as DNA, proteins, and drug molecules. Past work suggests that the permeabilization is caused by the formation of aqueous, conducting pores on the lipid membrane, which are also known as electropores. The current-voltage relation across the membrane-bound pores is critical for understanding and predicting electroporation. In this work, we solve the Nernst-Planck equations in a geometry encompassing an isolated electropore to investigate this relation. In particular, we study cases where the intra-and extracellular electrical conductivities differ. We first derive an analytical solution, which is subsequently validated with a direct numerical simulation using a finite volume method. The main result of the current work is a formula for the effective pore resistance as a function of the pore radius, the membrane thickness, and the intra-and extracellular conductivities. This formula can be incorporated into whole-cell or planar-membrane electroporation models for system-level prediction and understanding.

The current-voltage relation of a pore and its asymptotic behavior in a Nernst-Planck model

“…The current-voltage relation of a porous membrane is useful in understanding the way in which epithelia function, especially the skin's epidermal stratum corneum [7] or for describing and predicting electroporation [8,9]. Thus, an improved understanding of the current-voltage relationship of a pore in a membrane is of use to various research fields of biology, material science, bioengineering, and nanoelectronics.…”

Modelling the Bioelectronic Interface in Engineered Tethered Membranes: From Biosensing to Electroporation

“…8(a), the computed conductance approximately follows a relationship. A surprising result at first glance, however if we consider the literature on "spreading conductance" [15], [21], [46], [47], it must be the case that the spreading conductance caused in the tethering reservoir above the bioelectronic interface dominates the pore conductance. Fig.…”

“…The GPNP is equivalent to the Poisson-Nernst-Planck (PNP) system of equations if steric effects are neglected. Recent models for computing pore conductance in the literature use the (PNP), assuming symmetric electrolytes and electroneutrality [21]; and models for computing assuming symmetric electrolytes, electroneutrality, and negligible concentration gradients [18]. The evaluation of and using the GPNP accounts for the dynamics of electrolytes and the Stern and diffuse layers present in the EMP.…”

Preface to Special Topic: Papers from the 13th International Conference on Surface and Colloid Science (ICSCS) and the 83rd ACS Colloid and Surface Science Symposium, Columbia University, New York, 2009

“…In another fundamental paper, a direct numerical simulation model is presented to predict the current-voltage relationship across conducting pores along cell membranes, which is of fundamental importance in the electroporation process. 8 We hope that you will enjoy reading the contributions in this special topic and that it encourages you to participate in future Electrokinetics and Microfluidics meetings at the ACS Colloid and Surface Science Symposia, which we definitely hope will continue on a regular basis.…”