Dielectric energy of orientation in dead and living cells of Schizosaccharomyces pombe. Fitting of experimental results to a theoretical model

Combined AC-electrokinetic effects: Theoretical considerations on a three-axial ellipsoidal model

AC fields induce charges at the structural interfaces of particles or biological cells. The interaction of these charges with the field generates frequency‐dependent forces that are the basis for AC‐electrokinetic effects such as dielectrophoresis (DEP), electrorotation (ROT), electro‐orientation, and electro‐deformation. The effects can be used for the manipulation or dielectric single‐particle spectroscopy. The observation of a particular effect depends on the spatial and temporal field distributions, as well as on the shape and the dielectric and viscoelastic properties of the object. Because the effects are not mutually independent, combined frequency spectra are obtained, for example, discontinuous DEP and ROT spectra with ranges separated by the reorientation of nonspherical objects in the linearly and circularly polarized DEP and ROT fields, respectively. As an example, the AC electrokinetic behavior of a three‐axial ellipsoidal single‐shell model with the geometry of chicken‐red blood cells is considered. The geometric and electric problems were separated using the influential‐radius approach. The obtained finite‐element model can be electrically interpreted by an RC model leading to an expression for the Clausius–Mossotti factor, which permits the derivation of force, torque, and orientation spectra, as well as of equations for the critical frequencies and force plateaus in DEP and of the characteristic frequencies and peak heights in ROT. Expressions for the orientation in linearly and circularly polarized fields, as well as for the reorientation frequencies were also derived. The considerations suggested that the simultaneous registration of various AC‐electrokinetic spectra is a step towards the dielectric fingerprinting of single objects.

Non-invasive, electro-orientation-based viability assay using optically transparent electrodes for individual fission yeast cells

A non-invasive assay of cylindrical yeast cell viability based on electro-orientation (EO) in an alternating electric field was developed, in which cell viability can be determined by each cell's EO direction without the need for reagents. A cell suspension of a few microliters was sandwiched between a pair of optically transparent indium-tin-oxide (ITO) plate electrodes. Observation under a light microscope enabled easy identification of EO based on cell shape, e.g., cells were standing upright and appeared perfectly circular when oriented parallel to the electric field direction (standing position), and they were lying flat and had an elongated shape when oriented perpendicular to the field (lain-down position). The alternative EO positions of living or dead cells were dependent on the applied frequency: opposite EO positions were obtained by applying an AC voltage of 1.5V at 10MHz; at which point, only living cells rapidly attained a standing position, whereas dead cells were lain-down within 10s. All the cell's EO positions agreed well with a viability assay by florescence staining. Therefore, at the single-cell level and fluorescently label-free, it was possible to simply and accurately determine whether individual cells were alive or dead based on their shape.

The Influence of Vesicle Shape and Medium Conductivity on Possible Electrofusion under a Pulsed Electric Field

The effects of electric field on lipid membrane and cells have been extensively studied in the last decades. The phenomena of electroporation and electrofusion are of particular interest due to their wide use in cell biology and biotechnology. However, numerical studies on the electrofusion of cells (or vesicles) with different deformed shapes are still rare. Vesicle, being of cell size, can be treated as a simple model of cell to investigate the behaviors of cell in electric field. Based on the finite element method, we investigate the effect of vesicle shape on electrofusion of contact vesicles in various medium conditions. The transmembrane voltage (TMV) and pore density induced by a pulsed field are examined to analyze the possibility of vesicle fusion. In two different medium conditions, the prolate shape is observed to have selective electroporation at the contact area of vesicles when the exterior conductivity is smaller than the interior one; selective electroporation is more inclined to be found at the poles of the oblate vesicles when the exterior conductivity is larger than the interior one. Furthermore, we find that when the exterior conductivity is lower than the internal conductivity, the pulse can induce a selective electroporation at the contact area between two vesicles regardless of the vesicle shape. Both of these two findings have important practical applications in guiding electrofusion experiments.

Equilibrium electrodeformation of a spheroidal vesicle in an ac electric field

In this work, we develop a theoretical model to explain the equilibrium spheroidal deformation of a giant unilamellar vesicle (GUV) under an alternating (ac) electric field. Suspended in a leaky dielectric fluid, the vesicle membrane is modeled as a thin capacitive spheroidal shell. The equilibrium vesicle shape results from the balance between mechanical forces from the viscous fluid, the restoring elastic membrane forces, and the externally imposed electric forces. Our spheroidal model predicts a deformation-dependent transmembrane potential, and is able to capture large deformation of a vesicle under an electric field. A detailed comparison against both experiments and small-deformation (quasispherical) theory showed that the spheroidal model gives better agreement with experiments in terms of the dependence on fluid conductivity ratio, permittivity ratio, vesicle size, electric field strength, and frequency. The spheroidal model also allows for an asymptotic analysis on the crossover frequency where the equilibrium vesicle shape crosses over between prolate and oblate shapes. Comparisons show that the spheroidal model gives better agreement with experimental observations.

Transmembrane voltage analyses in spheroidal cells in response to an intense ultrashort electrical pulse

Self-consistent evaluations of both the transmembrane potential (TMP) and possible electroporation density across membrane of spheroidal cells in response to ultrashort, high-intensity pulses are reported and discussed. Most treatments in the literature have been based on spherical cells, and this represents a step towards more realistic analyses. The present study couples the Laplace equation with Smoluchowski theory of pore formation, to yield dynamic membrane conductivities that influence the TMP. It is shown that the TMP induced by pulsed external voltages can be substantial higher in oblate spheroids as compared to spherical or prolate spheroidal cells. Flattening of the surface area in oblate spheroids leads to both higher electric fields seen by the membrane, and allows a great fraction of the surface area to be porated. This suggests that biomedical applications such as drug delivery and electrochemotherapy could work best for flatter-shaped cells, and secondary field-enabled orienting would be beneficial. Results for arbitrary field orientations and different cell sizes have also been presented.

Electrically driven alignment and crystallization of unique anisotropic polymer particles

Micrometer-sized monodisperse anisotropic polymer particles, with disk, rod, fenestrated hexagon (hexnut), and boomerang shapes, were synthesized using the particle replication in nonwetting templates (PRINT) process, and investigations were conducted on aqueous suspensions of these particles when subjected to alternating electric fields. A coplanar electrode configuration, with 1 to 2 mm electrode gaps (20-50 V ac, 0.5-5.0 kHz) was used, and the experiments were monitored with fluorescence microscopy. For all particle suspensions, the field brought about significant changes in the packing and orientation. Extensive particle chaining and packing were observed for the disk, rod, and hexnut suspensions. Because of the size and geometry of the boomerang particles, limited chaining was observed; however, the field triggered a change from random to a more ordered packing arrangement.

A new electro-optical approach to rapid assay of cell viability

A new electro-optical (EO) approach was developed and applied to rapidly assay cell viability by using phage M13K07. Since phage M13K07 can replicate only in living bacteria and cannot replicate in the presence of inhibitors, the difference between the EO signals obtained in the presence and absence of the phage can be used as an important factor for evaluating cell viability. Variation in the electrophysical parameters of Escherichia coli XL-1 during its interaction with phage M13K07 was studied under exposure of the cells to various inhibitors of cellular metabolism. Significant changes in the EO signal were found during incubation of living E. coli cells with phage M13K07. At the same time, no changes were recorded during cell incubation with the phage after pretreatment of E. coli XL-1 cells with sodium azide, carbonyl cyanide 3-chlorophenyl hydrazone, chloramphenicol, and kanamycin. This finding can be explained by the decrease in the number of living cells in the culture after preliminary incubation with the chemical agents, and it was confirmed by colony counts by conventional plating onto solid LB medium before and after treatment of the cells with the inhibitors. The EO approach can be used as a rapid method for evaluation of the inhibitory effects of various chemical agents and drugs, and it has the potential for the study of the molecular mechanisms underlying cell death.

Orientation behavior of retinal photoreceptors in alternating electric fields

In alternating electric (AC) fields, particles experience polarizing effects that induce dipoles that orient elongated specimens either parallel or perpendicular to the field lines. In this work we studied the behavior of photoreceptor cells' rod outer segments (ROS) in AC fields of different frequencies. We showed that at low frequencies, ROS orient parallel to the field, whereas at higher frequencies they orient perpendicular to the field lines (in the frequency range from 100 Hz to 10 MHz). We found this behavior to be dependent on the physiological state of cells (due to modifications in their electrical properties). To simulate cell damage, the membrane conductivity was changed by treating the cell with gramicidin A, which resulted in a decrease of cytosol conductivity and, consequently, in a change of the orientation behavior of the treated cells. The change of cell orientation with cytosol conductivity is rather sharp, suggesting the potential of the method for accurate evaluation of the cell physiological status. We modeled the interaction between ROS and AC fields approximating the rod cell by a prolate spheroid with a very long axis. The internal compartment of the ellipsoid was considered to be filled with an inhomogeneous medium consisting of alternating layers of membrane and cytoplasm as media modeling the disks. This theoretical model proved to be in good agreement with the experimental results and enabled the derivation (by fitting with the experimental results) of the membrane and cytosol parameters for normal and damaged cells.

Boundary-element calculations for dielectric behavior of doublet-shaped cells

In order to simulate dielectric relaxation spectra (DRS) of budding yeast cells (Saccharomyces cerevisiae) in suspension, the complex polarization factor (Clausius-Mossotti factor) beta for a single cell and the complex permittivity of a cell suspension epsilon(sus)* were calculated with a doublet-shaped model (model RD), in which two spheres were connected with a part of a ring torus, using the boundary element method. The beta values were represented by a diagonal tensor consisting of components beta(z) parallel to the rotation axis (z axis) and beta(h) in a plane (h plane) perpendicular to the axis. The epsilon(sus)* values were calculated from the complex permittivity of the suspending medium epsilon(a)* and the components of beta. The calculation was compared with that of a conventional prolate spheroid model (model CP). It was found that model CP could be used as a first approximation to model RD. However, differences existed in beta(z) between models RD and CP; beta(z) showed three relaxation terms in the case of model RD in contrast with two terms in model CP. Narrowing the junction between the two spheres in model RD markedly decreased the characteristic frequency of one of the relaxation terms in beta(z). This suggests that the structure of the junction can be estimated from DRS. Effects of the shape change from model RD to a two-sphere model (model RD without the junction) were also examined. The behavior of beta(z) in the two-sphere model, the relaxation intensity of which was much lower than model RD, was quite similar to that in a single-sphere model. These simulations were consistent with the experimental observations of the dielectric behavior of the yeast cells during cell cycle progression.

Dielectric spectroscopy of Schizosaccharomyces pombe using electrorotation and electroorientation

Two complementary AC electrokinetic techniques electrorotation (ER) and electroorientation (EO) enabled the dielectric characterization of the rod-shaped fission yeast Schizosaccharomyces pombe. The use of microstructured electrodes allowed both ER and EO measurements to be performed over wide ranges of field frequency and medium conductivity. Due to their layered structure, living S. pombe cells exhibited up to three well resolved peaks in their ER spectra and also two distinct orientations, i.e., parallel or perpendicular to the imposed linear field. Heat treatment and enzymatic protoplast isolation led to dramatic changes in the electrokinetic behavior of fission yeast. Application of the theoretical models linking the ER and EO spectra yielded the dielectric parameters of the major structural units of S. pombe cells (cell wall, plasma membrane and cytosol). The dielectric characterization of yeasts has an enormous impact in biotechnology and biomedicine, because electric field pulse techniques (electrofusion and electropermeabilization) are widely used for production of transgenic yeast strains of economic importance. The present study also showed that combined ER and EO measurements can be employed as a powerful diagnostic tool for analyzing changes in yeast structure and physiology upon exposure to various stress conditions.

A comprehensive approach to electro-orientation, electrodeformation, dielectrophoresis, and electrorotation of ellipsoidal particles and biological cells

Suspended cells may respond to AC polarization by orienting, deforming, moving or rotating. For modeling of ellipsoidal cells, a new dipole approach is proposed. Along each of the principal axis of the model, three finite elements of arbitrary but equal cross-sectional area for the interior, low conductive membrane shell and exterior are assumed. The length of the external medium elements is defined by influential radii which are related to the depolarizing factors. The model predicts the potential at the ellipsoid's surface leading to the induced dipole moment. The moment obtained is identical to the Laplace approach for homogeneous ellipsoids; in the single-shell case, it is slightly different. The reason is the constant shell thickness which overcomes the confocal thickness necessary for the Laplace solution. Expressions for electro-orientation, deformation, dielectrophoresis, and electrorotation are derived. In linearly and circularly polarized fields, different orientation spectra are predicted to occur. While in linearly polarized AC fields, particles are oriented along their axis of highest polarizability, in circularly polarized fields, the axis of lowest polarizability is oriented perpendicular to the plane of field rotation. Based on this finding, a new electro-orientation method is proposed. In dielectrophoresis and electrorotation, reorientations are predicted which lead to discontinuous spectra.