Electroporation from mitochondria to cell clusters: Model development toward analyzing electrically driven bioeffects over a large spatial range

Abstract

A general, self-consistent scheme for analyzing cellular electroporation for bio-medical applications is developed to probe realistic biological shapes and different length scales ranging from nanometers to hundreds of micrometers. The COMSOL Multiphysics suite is used with suitable embellishments to incorporate the details of the electroporation (EP) process and the inherent internal physics. The results are obtained for the voltage pulse driven electroporation for a Jurkat cell with mitochondria (as an example organelle) where spatial dimensions on the order of a few nanometers become important, to hundreds of cells (with Bacillus as an example) where collective effects and mutual interactions can dominate. Thus, scalable computing to generalized geometries with the ability to include complex organelles is made available. The results obtained for mitochondrial EP in Jurkat cells compare well with available data. In addition, quantitative predictions of field attenuation and shielding in Bacillus clusters are made, which point to highly nonuniform field distributions and a strong need to engineer novel electrode designs.

Electroporation Response in Mitochondria and the Endoplasmic Reticulum to Nanosecond Electric Pulses: Numerical Assessments of Geometry, Proximity and Multi- Electrode Effects

“…Their ow across the inner mitochondrial membrane (IMM) though, requires ion channels or transporters. However, it is quite likely that an external electric eld can porate the IMM 47 , as we recently predicted. Calcium entry could then follow, leading to ATP depletion, which can trigger a cell death pathway.…”

“…As in our previous study 47 , the self-consistent calculations of EP involved several repetitive steps. First, the spatial distribution of voltage values at a set of discrete nodes within the entire simulation volume was obtained from the eld solvers 47 . This then yielded a spatiotemporal electric eld distribution (and hence, the TMPs) that would drive EP.…”

“…Membrane poration was incorporated by using the Smoluchowski model for time-and angular-dependent changes in membrane conductivity. The membrane conductivity was then updated using the local pore density distributions with details given elsewhere 47,74,75 .…”

“…Intricate geometries involving curved surfaces, or double membranes separated by a few nanometers, require ne spatial resolution, which increases the number of grid points, making the full pore-radius dependent calculations through the Smoluchowski equation very time consuming. Consequently, we have applied an asymptotic model of electroporation 47,79,80 with a variable membrane tension 81,82 to reduce computational expense. The time domain simulations used a 0.1 ns step, with COMSOL's "Weak Form Boundary PDE" feature to solve the relevant partial differential equations 47 .…”

“…In biology, spherical shapes are uncommon with protoplasts, murine myeloma cells 58 , and Streptococcus 59 being rare examples of near-symmetric structures. A recent study modeled the buildup of TMPs at the mitochondrion with its two membranes, including geometric features of the cristae, within a spherical Jurkat 47 . This study showed that the buildup of TMP at the outer mitochondrial membrane (OMM) would most likely not be rapid, requiring either longer duration pulses (well beyond 500 ns), or a wavetrain of multiple pulses to induce poration.…”