Cell membrane permeabilization by 12-ns electric pulses: Not a purely dielectric, but a charge-dependent phenomenon

Electric pulses of a few nanoseconds in duration can induce reversible permeabilization of cell membrane and cell death. Whether these effects are caused by ionic or purely dielectric phenomena is still discussed. We address this question by studying the impact of conductivity of the pulsing buffer on the effect of pulses of 12 ns and 3.2 MV/m on the DC-3F mammalian cell line. When pulses were applied in a high-conductivity medium (1.5 S/m), cells experienced both reversible electropermeabilization and cell death. On the contrary, no effect was observed in the low-conductivity medium (0.1 S/m). Possible artifacts due to differences in viscosity, temperature increase or electrochemical reactions were excluded. The influence of conductivity reported here suggests that charges still play a role, even for 12-ns pulses. All theoretical models agree with this experimental observation, since all suggest that only high-conductivity medium can induce a transmembrane voltage high enough to induce pore creation, in turn. However, most models fail to describe why pulse accumulation is experimentally required to observe biological effects. They mostly show no increase of permeabilization with accumulation of pulses. Currently, only one model properly describes pulse accumulation by modeling diffusion of the altered membrane regions

Mathematical model for transport of DNA plasmids from the external medium up to the nucleus by electroporation

We propose a mathematical model for the transport of DNA plasmids from the extracellular matrix up to the cell nucleus. The model couples two phenomena: the electroporation process, describing the cell membrane permeabilization to plasmids and the intracellular transport enhanced by the presence of microtubules. Numerical simulations of cells with arbitrary geometry, in 2D and 3D, and a network of microtubules show numerically the importance of the microtubules and the electroporation on the effectiveness of the DNA transfection, as observed by previous biological data. The paper proposes efficient numerical tools for forthcoming optimized procedures of cell transfection.Initiative d'excellence de l'Université de Bordeau

Nonlinear steady-state electrical current modeling for the electropermeabilization of biological tissue

We propose a steady-state electrical current equation with a nonlinear Ohm's law to model irreversible electropermeabilization in a biological tissue. The nonlinear problem is solved using Picard's method and the unknown parameters in Ohm's law are estimated from the observation of the tissue necrosis in experiences in which different voltages are applied to samples of potatoes

Impact of external medium conductivity on cell membrane electropermeabilization by microsecond and nanosecond electric pulses

The impact of external medium conductivity on the efficiency of the reversible permeabilisation caused by pulsed electric fields was investigated. Pulses of 12 ns, 102 ns or 100 μs were investigated. Whenever permeabilisation could be detected after the delivery of one single pulse, media of lower conductivity induced more efficient reversible permeabilisation and thus independently of the medium composition. Effect of medium conductivity can however be hidden by some saturation effects, for example when pulses are cumulated (use of trains of 8 pulses) or when the detection method is not sensitive enough. This explains the contradicting results that can be found in the literature. The new data are complementary to those of one of our previous study in which an opposite effect of the conductivity was highlighted. It stresses that the conductivity of the medium influences the reversible permeabilization by several ways. Moreover, these results clearly indicate that electropermeabilisation does not linearly depend on the energy delivered to the cells

Dependence of electroporation detection threshold on cell radius: an explanation to observations non compatible with Schwan’s equation model

It is widely accepted that electroporation occurs when the cell transmembrane voltage induced by an external applied electric field reaches a threshold. Under this assumption, in order to trigger electroporation in a spherical cell, Schwan’s equation leads to an inversely proportional relationship between the cell radius and the minimum magnitude of the applied electric field. And, indeed, several publications report experimental evidences of an inverse relationship between the cell size and the field required to achieve electroporation. However, this dependence is not always observed or is not as steep as predicted by Schwan’s equation. The present numerical study attempts to explain these observations that do not fit Schwan’s equation on the basis of the interplay between cell membrane conductivity, permeability, and transmembrane voltage. For that, a single cell in suspension was modeled and the electric field necessary to achieve electroporation with a single pulse was determined according to two effectiveness criteria: a specific permeabilization level, understood as the relative area occupied by the pores during the pulse, and a final intracellular concentration of a molecule due to uptake by diffusion after the pulse, during membrane resealing. The results indicate that plausible model parameters can lead to divergent dependencies of the electric field threshold on the cell radius. These divergent dependencies were obtained through both criteria and using two different permeabilization models. This suggests that the interplay between cell membrane conductivity, permeability, and transmembrane voltage might be the cause of results which are noncompatible with the Schwan’s equation model.This work was supported by the Ministry of Economy and Competitiveness of Spain through Grant TEC2014-52383-C3-2-R. PTV received support from the Old Dominion University Frank Reidy Research Center for Bioelectrics and the Air Force Office of Scientific Research (FA9550-15-1-0517, FA9550-14-1-0123)

A continuum mechanics model of enzyme-based tissue degradation in cancer therapies

We propose a mathematical model to describe enzyme-based tissue degradation in cancer therapies. The proposed model combines the poroelastic theory of mixtures with the transport of enzymes or drugs in the extracellular space. The effect of the matrix degrading enzymes on the tissue composition and its mechanical response are accounted for. Numerical simulations in 1D, 2D and ax-isymmetric (3D) configurations show how an injection of matrix degrading enzymes alters the porosity of a biological tissue. We eventually exhibit numerically the main consequences of a matrix degrading enzyme pretreatment in the framework of chemotherapy: the removal of the diffusive hindrance to the penetration of therapeutic molecules in tumors and the reduction of interstitial fluid pressure which improves transcapillary transport. Both effects are consistent with previous biological observations