Mojca Pavlin

Effect of electric field induced transmembrane potential on spheroidal cells: theory and experiment

The transmembrane potential on a cell exposed to an electric field is a critical parameter for successful cell permeabilization. In this study, the effect of cell shape and orientation on the induced transmembrane potential was analyzed. The transmembrane potential was calculated on prolate and oblate spheroidal cells for various orientations with respect to the electric field direction, both numerically and analytically. Changing the orientation of the cells decreases the induced transmembrane potential from its maximum value when the longest axis of the cell is parallel to the electric field, to its minimum value when the longest axis of the cell is perpendicular to the electric field. The dependency on orientation is more pronounced for elongated cells while it is negligible for spherical cells. The part of the cell membrane where a threshold transmembrane potential is exceeded represents the area of electropermeabilization, i.e. the membrane area through which the transport of molecules is established. Therefore the surface exposed to the transmembrane potential above the threshold value was calculated. The biological relevance of these theoretical results was confirmed with experimental results of the electropermeabilization of plated Chinese hamster ovary cells, which are elongated. Theoretical and experimental results show that permeabilization is not only a function of electric field intensity and cell size but also of cell shape and orientation.

Dependence of induced transmembrane potential on cell density, arrangement, and cell position inside a cell system

A nonuniform transmembrane potential (TMP) is induced on a cell membrane exposed to external electric field. If the induced TMP is above the threshold value, cell membrane becomes permeabilized in a reversible process called electropermeabilization. Studying electric potential distribution on the cell membrane gives us an insight into the effects of the electric field on cells and tissues. Since cells are always surrounded by other cells, we studied how their interactions influence the induced TMP. In the first part of our study, we studied dependence of potential distribution on cell arrangement and density in infinite cell suspensions where cells were organized into simple-cubic, body-centered cubic, and face-centered cubic lattices. In the second part of the study, we examined how induced TMP on a cell membrane is dependent on its position inside a three-dimensional cell cluster. Finally, the results for cells inside the cluster were compared to those in an infinite lattice. We used numerical analysis for the study, specifically the finite-element method (FEM). The results for infinite cell suspensions show that the induced TMP depends on both cell volume fraction and cell arrangement. We established from the results for finite volume cell clusters and layers, that there is no radial dependence of induced TMP for cells inside the cluster.

Mechanisms involved in gene electrotransfer using high- and low-voltage pulses — An in vitro study

Gene electrotransfer is an established method for gene delivery which uses high-voltage pulses to increase permeability of cell membrane and thus enables transfer of genes. Currently, majority of research is focused on improving in vivo transfection efficiency, while mechanisms involved in gene electrotransfer are not completely understood. In this paper we analyze the mechanisms of gene electrotransfer by using combinations of high-voltage (HV) and low-voltage pulses (LV) in vitro. We applied different combinations of HV and LV pulses to CHO cells and determined the transfection efficiency. We obtained that short HV pulses alone were sufficient to deliver DNA into cells for optimal plasmid concentrations and that LV pulse did not increase transfection efficiency, in contrast to reported studies in vivo. However, for sub-optimal plasmid concentrations combining HV and LV pulses increased transfection rate. Our results suggest that low-voltage pulses increase transfection in conditions where plasmid concentration is low, typically in vivo where mobility of DNA is limited by the extracellular matrix. LV pulses provide additional electrophoretic force which drags DNA toward the cell membrane and consequently increase transfection efficiency, while for sufficiently high concentrations of the plasmid (usually used in vitro) electrophoretic LV pulses do not have an important role.

Analytical and numerical quantification and comparison of the local electric field in the tissue for different electrode configurations

BackgroundElectrochemotherapy and gene electrotransfer are novel promising treatments employing locally applied high electric pulses to introduce chemotherapeutic drugs into tumor cells or genes into target cells based on the cell membrane electroporation. The main focus of this paper was to calculate analytically and numerically local electric field distribution inside the treated tissue in two dimensional (2D) models for different plate and needle electrode configurations and to compare the local electric field distribution to parameter U/d, which is widely used in electrochemotherapy and gene electrotransfer studies. We demonstrate the importance of evaluating the local electric field distribution in electrochemotherapy and gene electrotransfer.MethodsWe analytically and numerically analyze electric field distribution based on 2D models for electrodes and electrode configurations which are most widely used in electrochemotherapy and gene electrotransfer. Analytical calculations were performed by solving the Laplace equation and numerical calculations by means of finite element method in two dimensions.ResultsWe determine the minimal and maximal E inside the target tissue as well as the maximal E over the entire treated tissue for the given electrode configurations. By comparing the local electric field distribution calculated for different electrode configurations to the ratio U/d, we show that the parameter U/d can differ significantly from the actual calculated values of the local electric field inside the treated tissue. By calculating the needed voltage to obtain E > U/d inside the target tissue, we showed that better electric field distribution can be obtained by increasing the number and changing the arrangement of the electrodes.ConclusionBased on our analytical and numerical models of the local electric field distribution we show that the applied voltage, configuration of the electrodes and electrode position need to be chosen specifically for each individual case, and that numerical modeling can be used to optimize the appropriate electrode configuration and adequate voltage. Using numerical models we further calculate the needed voltage for a specific electrode configuration to achieve adequate E inside the target tissue while minimizing damages of the surrounding tissue. We present also analytical solutions, which provide a convenient, rapid, but approximate method for a pre-analysis of electric field distribution in treated tissue.

Effective Conductivity of a Suspension of Permeabilized Cells: A Theoretical Analysis

During the electroporation cell membrane undergoes structural changes, which increase the membrane conductivity and consequently lead to a change in effective conductivity of a cell suspension. To correlate microscopic membrane changes to macroscopic changes in conductivity of a suspension, we analyzed the effective conductivity theoretically, using two different approaches: numerically, using the finite elements method; and analytically, by using the equivalence principle. We derived the equation, which connects membrane conductivity with effective conductivity of the cell suspension. The changes in effective conductivity were analyzed for different parameters: cell volume fraction, membrane and medium conductivity, critical transmembrane potential, and cell orientation. In our analysis we used a tensor form of the effective conductivity, thus taking into account the anisotropic nature of the cell electropermeabilization and rotation of the cells. To determine the effect of cell rotation, as questioned by some authors, the difference between conductivity of a cell suspension with normally distributed orientations and parallel orientation was also calculated, and determined to be <10%. The presented theory provides a theoretical basis for the analysis of measurements of the effective conductivity during electroporation.

Theoretical and experimental analysis of conductivity, ion diffusion and molecular transport during cell electroporation--relation between short-lived and long-lived pores.

Electroporation is usually described as a formation of transient pores in the cell membrane in the presence of a strong electric field, which enables transport of molecules and ions across the cell membrane. Several experimental studies of electroporation showed a complex dependence of the transport on pulse parameters. In only few studies, however, the actual transport across the membrane was quantified. Current theoretical studies can describe pore formation in artificial lipid membranes but still cannot explain mechanisms of formation and properties of long-lived pores which are formed during cell electroporation. The focus of our study is to connect theoretical description of pore formation during the electric pulses with experimental observation of increased transport after the pulses. By analyzing transient increase in conductivity during the pulses in parallel with ion efflux after the pulses the relation between short-lived and long-lived pores was investigated. We present a simple model that incorporates an increase in the fraction of long-lived pores with higher electric field due to larger area of the cell membrane exposed to above-critical voltage and due to higher energy which is available for pore formation. We also show that each consecutive pulse increases the probability for the formation of long-lived pores.

Effective conductivity of cell suspensions

Using finite-element method (FEM) effective conductivity of a cell suspension was calculated for different cell volume fractions and membrane conductivities. Cells were modeled as spheres having equivalent conductivity and were organized in cubic lattices, layers and clusters. The results were compared to different analytical expressions for effective conductivity and they showed that Maxwell theory is valid also for higher volume fractions.

Visualization of internalization of functionalized cobalt ferrite nanoparticles and their intracellular fate.

In recent years, nanoparticles (NPs) and related applications have become an intensive area of research, especially in the biotechnological and biomedical fields, with magnetic NPs being one of the promising tools for tumor treatment and as MRI-contrast enhancers. Several internalization and cytotoxicity studies have been performed, but there are still many unanswered questions concerning NP interactions with cells and NP stability. In this study, we prepared functionalized magnetic NPs coated with polyacrylic acid, which were stable in physiological conditions and which were also nontoxic short-term. Using fluorescence, scanning, and transmission electron microscopy, we were able to observe and determine the internalization pathways of polyacrylic acid–coated NPs in Chinese hamster ovary cells. With scanning electron microscopy we captured what might be the first step of NPs internalization – an endocytic vesicle in the process of formation enclosing NPs bound to the membrane. With fluorescence microscopy we observed that NP aggregates were rapidly internalized, in a time-dependent manner, via macropinocytosis and clathrin-mediated endocytosis. Inside the cytoplasm, aggregated NPs were found enclosed in acidified vesicles accumulated in the perinuclear region 1 hour after exposure, where they stayed for up to 24 hours. High intracellular loading of NPs in the Chinese hamster ovary cells was obtained after 24 hours, with no observable toxic effects. Thus polyacrylic acid–coated NPs have potential for use in biotechnological and biomedical applications.

Effective-susceptibility tensor for a composite with ferromagnetic inclusions: Enhancement of effective-media theory and alternative ferromagnetic approach

For calculating magnetic properties of a composite usually effective-medium theories are used. However, we show that for a composite with ferromagnetic inclusions such theories, in particular, Maxwell-Garnett equation, give peculiar and unphysical results, such as significant shift of ferromagnetic-resonance frequency with diminishing volume fraction of ferromagnetic inclusions. Starting from ferromagnetic theory we derive a simple expression for the calculation of the effective magnetic susceptibility of a composite and follow with detailed magnetostatic derivation of tensor equivalent of Maxwell-Garnett equation. By demonstrating the equivalence of both derivations we confirm the validity of the expression which we obtained from the ferromagnetic theory. Furthermore, we identify errors leading to unphysical results of effective-medium theories and show the correct application of these theories.

Numerical optimization of gene electrotransfer into muscle tissue.

BackgroundElectroporation-based gene therapy and DNA vaccination are promising medical applications that depend on transfer of pDNA into target tissues with use of electric pulses. Gene electrotransfer efficiency depends on electrode configuration and electric pulse parameters, which determine the electric field distribution. Numerical modeling represents a fast and convenient method for optimization of gene electrotransfer parameters. We used numerical modeling, parameterization and numerical optimization to determine the optimum parameters for gene electrotransfer in muscle tissue.MethodsWe built a 3D geometry of muscle tissue with two or six needle electrodes (two rows of three needle electrodes) inserted. We performed a parametric study and optimization based on a genetic algorithm to analyze the effects of distances between the electrodes, depth of insertion, orientation of electrodes with respect to muscle fibers and applied voltage on the electric field distribution. The quality of solutions were evaluated in terms of volumes of reversibly (desired) and irreversibly (undesired) electroporated muscle tissue and total electric current through the tissue.ResultsLarge volumes of reversibly electroporated muscle with relatively little damage can be achieved by using large distances between electrodes and large electrode insertion depths. Orienting the electrodes perpendicular to muscle fibers is significantly better than the parallel orientation for six needle electrodes, while for two electrodes the effect of orientation is not so pronounced. For each set of geometrical parameters, the window of optimal voltages is quite narrow, with lower voltages resulting in low volumes of reversibly electroporated tissue and higher voltages in high volumes of irreversibly electroporated tissue. Furthermore, we determined which applied voltages are needed to achieve the optimal field distribution for different distances between electrodes.ConclusionThe presented numerical study of gene electrotransfer is the first that demonstrates optimization of parameters for gene electrotransfer on tissue level. Our method of modeling and optimization is generic and can be applied to different electrode configurations, pulsing protocols and different tissues. Such numerical models, together with knowledge of tissue properties can provide useful guidelines for researchers and physicians in selecting optimal parameters for in vivo gene electrotransfer, thus reducing the number of animals used in studies of gene therapy and DNA vaccination.