Quand une cellule est exposée à un champ électrique externe, la tension électrique transmembranaire (ITV) est modifiée. Pendant l'exposition, l' ITV se superimpose au potentiel de repos (RTV) et quand la somme des deux tensions excède une valeur critique, la perméabilité de la membrane cellulaire augmente transitoirement localement . Ce phénomène est désigné comme electropermeabilisation. Dans beaucoup d'applications de l'electropermeabilisation une permeabilisation efficace et en même temps réversible est essentielle. Ainsi, une prédiction de l'expérience, qui implique l'évaluation de l'amplitude de l'ITV pour déclencher la permeabilisation, est exigée. Le problème est critique dans des tissus, où la géométrie cellulaire est plus compliquée, les cellules sont assez proches pour affecter le champ électrique autour d'elles et elles sont souvent connectées entre elles. Dans tous ces cas, une description analytique de l'ITV n'est en général pas accessible et des méthodes numériques sont ainsi souvent la seule approche envisageable. En raison de la complexité de la structure tissulaire, les modèles sont macroscopiques, et on ne considère pas la structure cellulaire détaillée, ou en cas des modèles microscopiques, les modèles sont construits utilisant des formes géométriques simples (des semi-sphères, des cubes). Pour mieux comprendre comment le champ électrique interagit avec des tissus, nous avons construit les modèles microscopiques réalistes de cellules irrégulièrement formées, des groupes de telles cellules et des suspensions denses. Le travail a alors été développé sur le plan expérimental au niveau de la cellule isolée. Les mesures de cinétique de transport de membrane ont montré que l'electropermeabilisation avec des amplitudes d'impulsion ou des durées d'impulsion progressivement croissantes conduit à des transports accrus dans des cellules. Une large augmentation a été observée dans les milisecondes après le début d'une impulsion, suivie par une augmentation de fluorescence progressive. Les résultats mesurés sur un intervalle de temps de 400 µ S ont révélé que le transport à travers la membrane permeabilisée ne peut être détecté que 100 µ S après le début de l'impulsion. En plus, une dynamique différente d'augmentation de fluorescence pendant et après l'impulsion a été observée.When a biological cell is exposed to an external electric field, induced transmembrane voltage (ITV) forms on its membrane. During the exposure, ITV superimposes to the native or resting transmembrane voltage (RTV) and when the sum of both voltages exceeds some threshold value, the permeability of the cell membrane in these regions transiently increases. This phenomenon is termed electropermeabilization. In many applications of electropermeabilization an efficient and at the same time reversible permeabilization is essential (e.g. DNA electrotransfer). Thus, a careful planning of the experiment, which involves the estimation of the amplitude of ITV leading to cell permeabilization, is required. The problem arises in case of tissues, where cell geometry is more complicated, cells are close enough to affect the electric field around each other, and they are often connected with pathways between them. In all these cases, an analytical description of ITV is in general not attainable and numerical methods are often the only feasible approach. Due to the complexity of tissue structure, numerical models are either macroscopic, where detailed cell structure is notconsidered, or in case of microscopic models, the models are constructed using simple geometrical shapes (semi-spheres, cubes). To better understand how the electric field interacts with tissues on a microscopic (single cell) level, which in turn determines the macroscopic behavior of the tissue, we constructed realistic microscopic models of irregularly shaped cells, clusters of such cells, and dense suspensions. Regarding the shape, density and connections between cells, these cell assemblies are in their complexity close to tissues. First, the amplitude of resting transmembrane voltage of cells used in the study was determined. Next, calculations of ITV were performed on models of single spherical, single attached cells, and cell clusters and they were compared to measurements of ITV on the same cells, from which the models were constructed. The course of electropermeabilization of these cells was then monitored and the results were compared with measurements and calculations of ITV. In a separate experiment, a detailed investigation of kinetics of molecular transport into cells after permeabilization was performed. Similarly, for dense cell suspensions, the ITV calculated on a model of suspension was compared with the fraction of permeabilized cells measured in suspensions with increasing cell densities. Measurements of resting transmembrane voltage (RTV) were performed by means of a slow potentiometric fluorescent dye TMRM on different cell lines in culture media and media with progressively decreasing conductivities. ITV was measured on single spherical cells, single irregularly shaped cells, and cell clusters with a fast potentiometric fluorescent dye di-8- ANEPPS. The cross-section fluorescence images of the same cells on which the measurements of ITV were performed, were used to construct realistic numerical models of cells and the ITV on these models was then calculated with finite elements method. Finitethickness, nonzero conductivity cell membrane in the model was replaced by a boundary condition in which a specific surface conductivity was assigned to the interface between the cell interior and the exterior. Electropermeabilization of cells was followed by monitoring thechanges in intracellular fluorescence of membrane-impermeant fluorescent dye Propidium Iodide. Measurements of RTV showed that in physiological conditions (cells in culture medium) and in the presence of pulsing buffer, RTV on investigated cell lines is low (between -4 and -35 mV for suspended cells and between -18 and -27 mV for attached cells). Therefore, in experiments involving electropermeabilization ITV can be used as a rough approximate of the total voltage on the membrane, while RTV can be neglected. RTV in cells in media with decreasing conductivities gradually decreased, but less than expected from theoretical calculations. This was partly attributed to overestimated intracellular concentration of potassium. However, it is also possible that the method for measuring RTV, although reported as efficient, was not suitable for these experiments. Measurements of ITV on single spherical cells, single attached cells, and cell clusters were in qualitative agreement with results of numerical calculations, while in some cases discrepancies in measured and calculated amplitudes could be observed. This was attributed to variations of the slope of calibration curve, the differences between the actual and implemented parameters of the model, physiological state of cells, and experimental setup. In addition, we observed that at pulse parameters used in measurements of ITV, cells in clusters behaved as electrically connected, i.e. a cluster acted as one giant cell. Numerical calculations on models of cells where cell membrane was replaced with a boundary condition resulted in considerably lower number of mesh elements and consequently shorter time needed to solve the problem. We also demonstrated that calculations of ITV on simplified models of irregularly shaped cells can lead to considerable deviations from ITV calculated on a realistic model. Electric field orientation affects the amplitude and distribution of calculated ITV and consequently permeabilization. Namely, cells oriented with their longer axis parallel to the field are more likely to get permeabilized than the same cells oriented perpendicularly to the field. Comparison of measured and calculated ITVs with observations of electropermeabilization on single spherical and single attached cells confirmed that permeabilization occurs in those regions of the membrane, where the absolute value of ITV is the highest (the regions facing the electrodes). Additional experiments performed on single spherical cells showed that during and immediately after the pulse, the fluorescence from cells increases asymmetrically if unipolar pulses were delivered, while symmetrical fluorescence was observed for bipolar pulses. These observations were attributed to electrophoretical effect of the pulse. On a longer time scale, asymmetry in fluorescence was still observed, even for bipolar pulses, and we did not find any reasonable explanation for that. Critical value of ITV, at which permeabilization occurs, was calculated from the polar angle of permeabilization measured immediately after the pulse and was found to be approximately 450 mV, in agreement with reported critical thresholds. Permeabilization results obtained on cell clusters showed that cells in clusters, atpulse parameters used in these experiments, behaved as electrically insulated and were permeabilized individually. This is in contradiction to what we observed during measurements of ITV (i.e. with longer, low voltage pulses), where cells in clusters behaved as electrically connected, and was assumed to be the result of opening and closing of gap junctions at different pulse parameters. Measurements of kinetics of membrane transport showed that electropermeabilization with progressively increasing pulse amplitudes or pulse durations results in increased dye transport into cells. A sharp increase was observed miliseconds after the onset of a pulse, followed by a moderate additional fluorescence increase. Results measured on a time interval of 400 µs revealed that the transport across the permeabilized membrane can be detected within 100 µs after the onset of the pulse. Besides, different dynamics of fluorescence increase was observed during and immediately after the pulse. Experiments carried out on dense cell suspensions showed that with increasing cell density (from 10×106 cells/ml to 400×106 cells/ml) the fraction of permeabilized cells decreased by approximately 50%. We attributed this to the changes in the local electric field, which lead to a decrease in the amplitude of ITV. The uptake of Propidium Iodide also decreased with cell density, but by a larger amount than expected from permeabilization results. We supposed that the additional decrease in fluorescence was mainly due to cell swelling after permeabilization, which reduced extracellular dye availability to the permeabilized membrane and hindered the dye diffusion into the cells. Resealing of cells appeared to be slower in dense suspensions, which can also be attributed to cell swelling resulting from electropermeabilization
