Numerical assessments of geometry, proximity and multi-electrode effects on electroporation in mitochondria and the endoplasmic reticulum to nanosecond electric pulses

Abstract

Most simulations of electric field driven bioeffects have considered spherical cellular geometries or probed symmetrical structures for simplicity. This work assesses cellular transmembrane potential build-up and electroporation in a Jurkat cell that includes the endoplasmic reticulum (ER) and mitochondria, both of which have complex shapes, in response to external nanosecond electric pulses. The simulations are based on a time-domain nodal analysis that incorporates membrane poration utilizing the Smoluchowski model with angular-dependent changes in membrane conductivity. Consistent with prior experimental reports, the simulations show that the ER requires the largest electric field for electroporation, while the inner mitochondrial membrane (IMM) is the easiest membrane to porate. Our results suggest that the experimentally observed increase in intracellular calcium could be due to a calcium induced calcium release (CICR) process that is initiated by outer cell membrane breakdown. Repeated pulsing and/or using multiple electrodes are shown to create a stronger poration. The role of mutual coupling, screening, and proximity effects in bringing about electric field modifications is also probed. Finally, while including greater geometric details might refine predictions, the qualitative trends are expected to remain.Electroporation (EP) primarily involves the increased permeability of both the outer and the intracellular membranes of biological cells upon exposure to external electric pulses of sufficient duration and intensity 1-10 . Studies of electroporation in cells have a long history, and several reports of numerical simulations can be found in the literature [11][12][13][14] . Other more microscopic treatments that better include the inherent physics of the method have also been discussed [15][16][17] . The method is an effective non-viral approach for transfection that is independent of cell surface receptors. Other secondary EP induced influences pertain to transport of ions, macromolecules, and genes or drugs for chemotherapeutics [18][19][20] . Other downstream electric-field induced responses include increases in reactive oxygen species [21][22][23][24] , capacitive cellular entry of calcium that can disrupt intracellular calcium homeostasis and trigger a cascade of other events [25][26][27][28] , changes in the mitochondrial transmembrane potential (TMP), opening of the mitochondrial permeability transition pore (mPTP) 29,30 , and adverse effects on adenosine triphosphate (ATP) dynamics. A large influx of Ca 2+ after EP can also deplete intracellular ATP and/or inhibit ATP production in mitochondria 31 . Pulsed electric fields have also been used for cell fusion 32 , microorganism inactivation 33,34 , and triggering of immunogenic processes 35,36 .Reversible and irreversible EP are the two common modalities. Reversible EP is used to deliver impermeant molecules into cells 37,38 , and avoid permanent cell damage. Irreversible EP is an efficient ablation modality for treating tumors, especially those un...