Rotation of cells in an alternating electric field theory and experimental proof

Summary Protoplasts ofAvena sativa rotate in an alternating electric field provided that at least two cells are located close to each other. An optimum frequency range (20 to 30 kHz) exists where rotation of all cells exposed to the field is observed. Below and above this frequency range, rotation of some cells is only occasionally observed. The angular velocity of rotation depends on the square of the electric field strength. At field strengths above the value leading to electrical breakdown of the cell membrane, rotation is no longer observed due to deterioration of the cells. The absolute value of the angular velocity of rotation at a given field strength depends on the arrangement of the cells in the electric field. A maximum value is obtained if the angle between the field direction and the line connecting the two cells is 45^o. With increasing distance between the two cells the rotation speed decreases. Furthermore, if two cells of different radii are positioned close to each other the cell with the smaller radius will rotate with a higher speed than the larger one. Rotation of cells in an alternating electric field is described theoretically by interaction between induced dipoles is adjacent cells. The optimum frequency range for rotation is related to the relaxation of the polarization process in the cell. The quadratic dependence of the angular velocity of rotation on the field strength results from the fact that the torque is the product of the external field and the induced dipole moment which is itself proportional to the external field. The theoretical and experimental results may be relevant for cyclosis (rotational streaming of cytoplasm) in living cells.     

Electrorotation of colloidal particles and cells depends on surface charge.

The importance of surface conductivity to the frequency-dependent polarizability and the rotation of particles in circular electric fields (electrorotation) is emphasized by various theoretical and experimental investigations. Although surface conductivity seems to be naturally related to the ionic double layer, there is rare experimental evidence of a direct relationship. To highlight the role of surface charges in electrorotation, an apparatus was developed with a symmetrical three-electrode arrangement for field frequencies between 25 Hz and 80 MHz. The three-dimensional electrostatic field distribution between the electrodes was evaluated numerically. With this device, rotating, gradient, and homogeneous electric fields of defined precision and homogeneity could be applied to slightly conducting suspensions. Surface properties of monodisperse latex particles (O 9.67 microm), carrying weak acid groups, were characterized by suspension conductometric titration. This procedure determined the amount of carboxyl groups and showed that strong acid groups were missing on the surface of these particles. To obtain the electrophoretic mobility, the spheres were separated by free-flow electrophoresis, and the zeta-potential was calculated from these data. Single-particle rotation experiments on fractions of specified electrophoretic mobility were carried out at frequencies between 25 Hz and 20 MHz. By analyzing the pH dependence of the rotation velocity, it could be shown that the rotation rate is determined by surface charges, both at the peak in rotation rate near the Maxwell-Wagner frequency (MWF) and at low frequencies. The inversion of the rotation direction at the MWF peak for vanishing surface charges was demonstrated. An analytical model for the double layer and dissociation on a charged surface was developed that is valid for low and high zeta-potentials. This model could provide convincing evidence of the linear dependence of the MWF rotation velocity on surface charge.     

A new microsystem for automated electrorotation measurements using laser tweezers

We have developed a new microsystem for fast, automated studies of reactions and kinetics of single cells with biochemical or pharmacological agents. A cell spins in an external rotating electric field and the frequency dependence characterises the passive dielectric properties of membrane and cytoplasm. We use a planar microelectrode chip with microchannel (easily covered with a removable slip) for the application of frequencies exceeding 250 MHz to determine cytoplasmic properties in low and high conductivity electrolyte solutions. The laser tweezers serve as a bearing system, rotation is induced by microelectrodes and rotation speed is recorded automatically. This opens up new possibilities in biotechnology, e.g. for drug screening as demonstrated by measuring the influence of ionomycin on the passive dielectric properties of T-lymphoma cells. Additionally, a possible infrared-induced long-term cell damage could be observed by electrorotation and is discussed.     

Study of the torque of the bacterial flagellar motor using a rotating electric field.

Bacterial flagella are driven by a rotary motor that is energized by an electrochemical ion gradient across the cell membrane. In this study the torque generated by the flagellar motor was measured in tethered cells of a smooth-swimming Escherichia coli strain by using rotating electric fields to determine the relationship between the torque and speed over a wide range. By measuring the electric current applied to the sample cell and combining the data obtained at different viscosities, the torque of the flagellar motor was estimated up to 55 Hz, and also at negative rotation rates. By this method we have found that the torque of the flagellar motor linearly decreases with rotation rate from negative through positive rate of rotation. In addition, the dependence of torque upon temperature was also investigated. We showed that torque at the high speeds encountered in swimming cells had a much steeper dependence on temperature that at the low speeds encountered in tethered cells. From these results, the activation energy of the proton transfer reaction in the torque-generating unit was calculated to be about 7.0 x 10(-20) J.     

MyDEP: A New Computational Tool for Dielectric Modeling of Particles and Cells

Dielectrophoresis (DEP) and electrorotation (ROT) are two electrokinetic phenomena exploiting nonuniform electric fields to exert a force or torque on biological particles suspended in liquid media. They are widely used in lab-on-chip devices for the manipulation, trapping, separation, and characterization of cells, microorganisms, and other particles. The DEP force and ROT torque depend on the respective polarizabilities of the particle and medium, which in turn depend on their dielectric properties and on the field frequency. In this work, we present a new software, MyDEP, which implements several particle models based on concentric shells with adjustable dielectric properties. This tool enables the study of the variation in DEP and ROT spectra according to different parameters, such as the field frequency and medium conductivity. Such predictions of particle behavior are very useful for choosing appropriate parameters in DEP experiments. The software also enables the study of the homogenized properties of spherical or ellipsoidal multishell particles and provides a database containing published cell properties. Equivalent electrical conductivity and relative permittivity of the cell alone and in suspension can be calculated. The software also offers the ability to create graphs of the evolution of the crossover frequencies with the electric field frequency. These graphs can be directly exported from the software.     

Plasmon Resonances in V-Shaped Gold Nanostructures

Using numerical simulations, we examine the change in plasmon resonance behavior in gold nanorod structures that have a V shape. The reduction in symmetry compared to linear rods causes two different longitudinal-type resonances to appear in a single structure, and the relative intensity and hybridization of these can be controlled by varying the angle of the arms of the ??V.?? The resonances may also be selectively excited by controlling the polarization of the incident light, thereby providing a convenient way to control a nanoscale optical electric field using far-field parameters. For example, the wavelength at which a strong resonance occurs in the V-shaped structures studied can be switched between 630 and 900?nm by a 90° rotation of the polarization of the incident light. Due to the symmetry of the targets, there will be three types of special near-field location; a location at which the electric field intensity is enhanced by either resonance, a location at which the electric field intensity is enhanced by the 630?nm resonance but not by the 890?nm resonance, and a location at which the electric field intensity is enhanced by the 890?nm resonance but not by the 630?nm one.     

Radial electric field and rotation of the ensemble of plasma particles in tokamak

The velocity of macroscopic rotation of an ensemble of charged particles in a tokamak in the presence of an electric field has been calculated in a collisionless approximation. It is shown that the velocity of toroidal rotation does not reduce to a local velocity of electric drift and has opposite directions on the inner and outer sides of the torus. This result is supplemented by an analysis of the trajectories of motion of individual particles in the ensemble, which shows that the passing and trapped particles of the ensemble acquire in the electric field, on the average, different toroidal velocities. For the trapped particles, this velocity is equal to that of electric drift in the poloidal magnetic field, while the velocity of passing particles is significantly different. It is shown that, although the electric-field-induced shift of the boundaries between trapped and passing particles in the phase space depends on the particle mass and charge and is, in the general case, asymmetric, this does not lead to current generation.     

Measurement of inherent particle properties by dynamic light scattering: introducing electrorotational light scattering.

Common dynamic light scattering (DLS) methods determine the size and zeta-potential of particles by analyzing the motion resulting from thermal noise or electrophoretic force. Dielectric particle spectroscopy by common microscopic electrorotation (ER) measures the frequency dependence of field-induced rotation of single particles to analyze their inherent dielectric structure. We propose a new technique, electrorotational light scattering (ERLS). It measures ER in a particle ensemble by a homodyne DLS setup. ER-induced particle rotation is extracted from the initial decorrelation of the intensity autocorrelation function (ACF) by a simple optical particle model. Human red blood cells were used as test particles, and changes of the characteristic frequency of membrane dispersion induced by the ionophore nystatin were monitored by ERLS. For untreated control cells, a rotation frequency of 2 s-1 was induced at the membrane peak frequency of 150 kHz and a field strength of 12 kV/m. This rotation led to a decorrelation of the ACF about 10 times steeper than that of the field free control. For deduction of ERLS frequency spectra, different criteria are discussed. Particle shape and additional field-induced motions like dielectrophoresis and particle-particle attraction do not significantly influence the criteria. For nystatin-treated cells, recalculation of dielectric cell properties revealed an ionophore-induced decrease in the internal conductivity. Although the absolute rotation speed and the rotation sense are not yet directly accessible, ERLS eliminates the tedious microscopic measurements. It offers computerized, statistically significant measurements of dielectric particle properties that are especially suitable for nonbiological applications, e.g., the study of colloidal particles.     

Configuration of an inviscid plasma in the field of a rotating magnetized central body

The problem is considered of configurations of a strongly magnetized inviscid plasma around a rotating magnetized central body. Strong plasma magnetization implies that the Hall conductivity is much lower than the transverse conductivity, which in turn is much lower than the longitudinal conductivity. For such conditions, a self-consistent set of equations is derived that describes the conduction current density, the magnetic and electric fields, and the angular frequency of the plasma rotation under the assumptions that the components of the dielectric tensor of the plasma envelope are known functions of height and that the plasma mass velocity has only the azimuthal component. Under the assumption that the transverse conductivity is constant over a magnetic surface, the nonlinear equations derived are solved in quadratures within the class of angular frequency distributions that are symmetric about the equatorial plane. A particular solution for the plasma configurations in a dipole magnetic field is considered that corresponds to a model exponential dependence of the transverse conductivity on the number of the L-envelope (or, equivalently, on the number of the unperturbed magnetic surface).     

Extremely low frequency pulsed DC electric fields promote neutrophil extension, metabolic resonance and DNA damage when phase-matched with metabolic oscillators

Application of extremely low frequency pulsed DC electric fields that are frequency- and phase-matched with endogenous metabolic oscillations leads to greatly exaggerated neutrophil extension and metabolic resonance wherein oscillatory NAD(P)H amplitudes are increased. In the presence of a resonant field, migrating cell length grows from 10 to approximately 40 microm, as does the overall length of microfilament assemblies. In contrast, cells stop locomotion and become spherical when exposed to phase-mismatched fields. Although cellular effects were not found to be dependent on electrode type and buffer, they were sensitive to temporal constraints (phase and pulse length) and cell surface charge. We suggest an electromechanical coupling hypothesis wherein applied electric fields and cytoskeletal polymerization forces act together to overcome the surface/cortical tension of neutrophils, thus promoting net cytoskeletal assembly and heightened metabolic amplitudes. Metabolic resonance enhances reactive oxygen metabolic production by neutrophils. Furthermore, cellular DNA damage was observed after prolonged metabolic resonance using both single cell gel electrophoresis ('comet' assay) and 3'-OH DNA labeling using terminal deoxynucleotidyl transferase. These results provide insights into transmembrane signal processing and cell interactions with weak electric fields.     

Absorption of electromagnetic surface waves by electrons in a transition layer between the plasma and dielectric

The effect of the Debye layer on the absorption of an electromagnetic surface wave propagating along the plasma-dielectric interface is considered. The electric field distribution in the Debye layer and the energy absorbed by the plasma electrons in this layer are determined. It is shown that the ratio of the rate at which surface waves are damped due to Cherenkov absorption by the electrons reflected from the electric field potential in the transition layer to their frequency is on the order of the ratio of the electron thermal velocity to the wave phase velocity.     

Influence of a transverse magnetic field on the characteristics of a dc gas discharge

The influence of a transverse magnetic field and the working-gas pressure on the rotation frequency of the current channel, as well as on the electric field in the positive column and the cathode voltage drop in a dc gas discharge, was studied experimentally. The working gases were pure hydrogen and hydrogen-methane, hydrogen-argon, and hydrogen-argon-methane mixtures. It is shown that a transverse (with respect to the discharge current) magnetic field stabilizes a normal glow discharge against a transition to an arc discharge at specific absorbed powers above 300 W/cm³. The cathode voltage drop and the electric field in the positive column are measured. It is shown that the electric field does not depend on the magnetic field strength, whereas the cathode voltage drop increases with increasing magnetic field. It is found that the rotation frequency of the current channel is a complicated function of the discharge parameters and attains 400 Hz.     

Cell shape-dependent rectification of surface receptor transport in a sinusoidal electric field.

In the presence of an extracellular electric field, transport dynamics of cell surface receptors represent a balance between electromigration and mutual diffusion. Because mutual diffusion is highly dependent on surface geometry, certain asymmetrical cell shapes effectively create an anisotropic resistance to receptor electromigration. If the resistance to receptor transport along a single axis is anisotropic, then an applied sinusoidal electric field will drive a net time-average receptor displacement, effectively rectifying receptor transport. To quantify the importance of this effect, a finite difference mathematical model was formulated and used to describe charged receptor transport in the plane of a plasma membrane. Representative values for receptor electromigration mobility and diffusivity were used. Model responses were examined for low frequency (10(-4)-10 Hz) 10-V/cm fields and compared with experimental measurements of receptor back-diffusion in human fibroblasts. It was found that receptor transport rectification behaved as a low-pass filter; at the tapered ends of cells, sinusoidal electric fields in the 10(-3) Hz frequency range caused a time-averaged accumulation of receptors as great as 2.5 times the initial uniform concentration. The extent of effective rectification of receptor transport was dependent on the rate of geometrical taper. Model studies also demonstrated that receptor crowding could alter transmembrane potential by an order of magnitude more than the transmembrane potential directly induced by the field. These studies suggest that cell shape is important in governing interactions between alternating current (ac) electric fields and cell surface receptors.     

Light scattering of aqueous solutions of DNA, poly(acrylic acid), and tobacco mosaic virus under alternating electric field

Two new techniques, amplitude modulation (AM) and frequency modulation (FM) of an electric field, are developed for the light-scattering study of polymer solutions under ac electric fields. The AM technique makes it possible to observe accurately the frequency dependence of the intensity changes of scattered light due to the electric field. The FM one allows us to obtain directly the frequency derivative of the intensity change. The techniques are applied to DNA, poly(acrylic acid), and tobacco mosaic virus in the frequency range from 10 Hz to 100 kHz. A low-frequency relaxation is found for both DNA and poly(acrylic acid). The obsersved relaxation time of DNA agrees with that in the dielectric relaxation of DNA, which has been attributed to the rotation of the molecule with a quasipermanent dipole. In the case of poly(acrylic acid), the relaxation strength increases with increasing degree of neutralization. TMV at a concentration of 0.1% exhibits a negative relaxation at low frequencies, which indicates the rotation of TMV aggregate with a permanent dipole along its minor axis.     

Attraction, deformation and contact of membranes induced by low frequency electric fields

The force of attraction between erythrocyte ghosts induced by low frequency electric fields (60 Hz) was measured as a function of the intermembrane separation. It varied from 10(-14) N for separation of the order of the cell diameter to 10(-12) N for close approach and contact in 20 mM sodium phosphate buffers (conductivity 260 mS/m, pH 8.5). For large separations the interaction force followed a dependence on separation as predicted for dipole-dipole interactions. For small separation an empirical formula was obtained. The membranes deformed at close approach (less than 1 microns) before making contact. The contact area increased with time until reaching the final equilibrium state. The ghosts separated reversibly after switching off the electric field. The membrane tension induced by the ghost interaction at contact was estimated to be of the order of 0.1 mN/m. These first quantitative measurements of the force/separation dependence for intermembrane interactions induced by low frequency electric fields indicate that attractive forces, membrane deformation and contact area of cells depend strongly on intermembrane separation and field strength. The quantitative relationship between them are important for measuring membrane surface and mechanical properties, intermembrane forces and understanding mechanisms of membrane adhesion, instability and fusion in electric fields and in general.     

Spinning response of yeast cells to rotating electric fields

The frequency-dependent rotation or spinning motion of yeast cells subjected to a fourpole rotating electric field was examined over a very wide frequency range (500 Hz to 500 MHz). In the lower frequency range (500 Hz – 700 KHz) the yeast cells were observed to spin in a direction counter to the applied field, with a small peak at about 600 Hz and a more pronounced one at 20 KHz. For frequencies above 700 KHz the spinning of the cells switched direction from counter-field to co-field, with a maximum in the rotation rate at about 70 MHz and a subpeak at 20 MHz. The rate was also observed to exhibit a square dependence on the magnitude of the applied rotating field.     

Effect of the cytoskeletal prestress on the mechanical impedance of cultured airway smooth muscle cells.

We investigated the effect of the cytoskeletal prestress (P) on the elastic and frictional properties of cultured human airway smooth muscle cells during oscillatory loading; P is preexisting tensile stress in the actin cytoskeleton generated by the cell contractile apparatus. We oscillated (0.1 Hz, 6 Pa peak to peak) small ferromagnetic beads bound to integrin receptors and computed the storage (elastic) modulus (G') and the loss (frictional) modulus (G") from the applied torque and the corresponding bead rotation. All measurements were done at baseline and after cells were treated with graded doses of either histamine (0.1, 1, 10 microM) or isoproterenol (0.01, 0.1, 1, 10 microM). Values for P for these concentrations were taken from a previous study (Wang et al., Am J Physiol Cell Physiol, in press). It was found that G' and G", as well as P, increased/decreased with increasing doses of histamine/isoproterenol. Both G' and G" exhibited linear dependences on P: G'(Pa) = 0.20P + 82 and G"(Pa) = 0.05P + 32. The dependence of G' on P is consistent with our previous findings and with the behavior of stress-supported structures. The dependence of G" on P is a novel finding. It could be attributed to a variety of mechanisms. Some of those mechanisms are discussed in detail. We concluded that, in addition to the central mechanisms by which stress-supported structures develop mechanical stresses, other mechanisms might need to be invoked to fully explain the observed dependence of the cell mechanical properties on the state of cell contractility.     

The velocity of conduction in nerve fiber and its electric characteristics

The theory developed in this paper shows that the propagation of spike potential along a nerve fiber and the conduction of an electric wave along an inert inorganic conductor follow a common quantitative relationship. This result gives further support to the belief that propagation of excitation is an electrical process. The basic idea of the theory is derived from the consideration that velocity has, by its mathematical definition, a local meaning; conduction in a nerve is completely determined by the local characteristics of the latter, as well as those of the wave. The final formula derived does not make use of any other field of science beyond the fundamental principles of electricity. It gives the conduction velocity in terms of the electric characteristics of the fiber and of the duration of the spike potential. The formula is in agreement with the known dependence of the conduction velocity on various parameters characterizing the axon. The computed velocity agrees with the measured ones on the squid giant axon, crab nerve axon, frog muscle fiber and Nitella cell. The membrane inductance appears as a velocity controling agent which prevents also a possible distortion of the spike potential during conduction. The structural meaning of the electric characteristics of the axon membrane is discussed from the viewpoint of the diffusion theory. A formula for the velocity of spread of the electrotonus is also derived.     

A unified resistor-capacitor model for impedance, dielectrophoresis, electrorotation, and induced transmembrane potential.

Dielectric properties of suspended cells are explored by analysis of the frequency-dependent response to electric fields. Impedance (IMP) registers the electric response, and kinetic phenomena like orientation, translation, deformation, or rotation can also be analyzed. All responses can generally be described by a unified theory. This is demonstrated by an RC model for the structural polarizations of biological cells, allowing intuitive comparison of the IMP, dielectrophoresis (DP), and electrorotation (ER) methods. For derivations, cells of prismatic geometry embedded in elementary cubes formed by the external solution were assumed. All geometrical constituents of the model were described by parallel circuits of a capacitor and a resistor. The IMP of the suspension is given by a meshwork of elementary cubes. Each elementary cube was modeled by two branches describing the current flow through and around the cell. To model DP and ER, the external branch was subdivided to obtain a reference potential. Real and imaginary parts of the potential difference of the cell surface and the reference reflect the frequency behavior of DP and ER. The scheme resembles an unbalanced Wheatstone bridge, in which IMP measures the current-voltage behavior of the feed signal and DP and ER are the measuring signal. Model predictions were consistent with IMP, DP, and ER experiments on human red cells, as well as with the frequency dependence of field-induced hemolysis. The influential radius concept is proposed, which allows easy derivation of simplified equations for the characteristic properties of a spherical single-shell model on the basis of the RC model.     

Time series modeling of neuromuscular system

The dynamic response of the human ankle joint to a bandlimited random torque perturbation superimposed on a constant bias torque is observed in normal human subjects. The applied torque input, the joint angular rotation output, and the electromyographic activity using surface electrodes from the extensor and the flexor muscles of the ankle joint were recorded. Transfer function models using time series techniques were developed for the torque — angular rotation input-output pair and for the angular rotation — electromyographic activity input-output pair. A parameter constraining technique was applied to develop more reliable models. It is shown that the asymptotic behavior of the system must be taken into account during parameter optimization to develop better predictive models.This work was supported in part by National Science Foundation grant ENG-7608754 and grants from the National Institutes of Health NS-12877 and NS-00196