This study develops a model for a single cell electroporated by an external electric field and uses it to investigate the effects of shock strength and rest potential on the transmembrane potential V(m) and pore density N around the cell. As compared to the induced potential predicted by resistive-capacitive theory, the model of electroporation predicts a smaller magnitude of V(m) throughout the cell. Both V(m) and N are symmetric about the equator with the same value at both poles of the cell. Larger shocks do not increase the maximum magnitude of V(m) because more pores form to shunt the excess stimulus current across the membrane. In addition, the value of the rest potential does not affect V(m) around the cell because the electroporation current is several orders of magnitude larger than the ionic current that supports the rest potential. Once the field is removed, the shock-induced V(m) discharges within 2 micros, but the pores persist in the membrane for several seconds. Complete resealing to preshock conditions requires approximately 20 s. These results agree qualitatively and quantitatively with the experimental data reported by Kinosita and coworkers for unfertilized sea urchin eggs exposed to large electric fields.
This study expands a previously developed model of a single cell electroporated by an external electric field by explicitly accounting for the ionic composition of the electroporation current. The previous model with non-specific electroporation current predicts that both the transmembrane potential V(m) and the pore density N are symmetric about the equator, with the same values at either end of the cell. The new, ion-specific case predicts that V(m) is symmetric and almost identical to the profile from the non-specific case, but N has a profound asymmetry with the pore density at the hyperpolarized end of the cell twice the value at the depolarized end. These modeling results agree with the experimentally observed preferential uptake of marker molecules at the hyperpolarized end of the cell as reported in the literature. This study also investigates the changes in intracellular ionic concentrations induced around an electroporated single cell. For all ion species, the concentrations near the membrane vary significantly, which may explain the electrical disturbances observed experimentally after large electric shocks are delivered to excitable cells and tissues.
Experimental studies have shown that the magnitude of the shock-induced transmembrane potential (Vm) saturates with increasing electric field strength. This study uses a mathematical model to investigate the effects of electroporation and membrane kinetics on Vm in a cardiac fiber. The model consists of the core conductor equation for a one-dimensional fiber, where excitability is represented by the Luo-Rudy dynamic model (1994-1995) and electroporation is described by a membrane conductance that increases exponentially with Vm squared. For shocks delivered during the plateau of an action potential, the model reproduces the experimentally observed saturation of Vm with a root mean square error of 4.27% and a correlation coefficient of 0.9992. For shocks delivered during diastole, the saturation of Vm is qualitatively reproduced even when the sodium and calcium channels are inactivated. Quantitative replication of the response to diastolic shocks is hindered by the choice of electroporation parameters (optimized for shocks delivered during the plateau) and differences in the membrane kinetics between model and experiment. The complex behavior of Vm during large shocks is due to a combination of electroporation, electrotonus, propagation, and active membrane kinetics. The modeling results imply that the experimentally observed saturation of Vm is due to electroporation of the lipid bilayer.
These results indicate that electroporation of the cardiac membrane plays an important role in the distribution of Vm induced by defibrillation strength shocks.
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