Tetsuya Hanai

A dielectric theory of “multi-stratified shell” model with its application to a lymphoma cell

Abstract A theory of complex dielectric constant ( e ∗ ) for the suspension of “multi-stratified” spherical particles is presented. Based on Maxwells theory of interfacial polarization, we derive a general expression which correlates e ∗ with the electrical and geometrical parameters of each stratum. It can be shown that such a “multi-stratified” system in general should give rise to multiple dielectric dispersions, the number of which corresponds to the number of interfaces lying between the successive shell phases. The conditions for a full number of different “unit” dispersions to occur are also discussed. As an example, a special case of the “double-shell” model consisting of a spherical core and three layers of concentric phases is solved numerically by using a set of parameter values pertinent to a lymphoma cell. In light of the characteristic behavior of e ∗ thus revealed, we propose a scheme of procedure that applies to the determination of electrical parameters associated with the specific “double-shell” model.

Dielectric Approach to Suspensions of Ellipsoidal Particles Covered with a Shell in Particular Reference to Biological Cells

A dielectric theory of interfacial polarization is presented for a heterogeneous system containing ellipsoidal particles covered with shells, in order to make an analysis of dielectric behavior of suspensions of ellipsoidal biological cells. For the case of spheroidal shapes, dielectric dispersion curves are calculated numerically by using the electrical and morphological parameters relevant to biological cells. The results indicate that the calculated dielectric dispersion curves are seriously affected by varying the axial ratio of the spheroids. For the purpose of analyzing dielectric data of biological cell suspensions on the basis of the presented theory, a procedure is proposed to evaluate electrical parameters characteristic of biological cells. This procedure is shown to be successfully applied to the observed dielectric data of erythrocyte suspensions.

Theory of the dielectric dispersion due to the interfacial polarization and its application to emulsions

SummaryThe interfacial polarization of spherical dispersions is dealt with theoretically, and is discussed for the actual cases of emulsions.First it is shown that theMaxwell theory is not valid qualitatively for the dielectric properties of emulsions. Next the general solution of theWagner theory is derived. This solution shows that a dielectric dispersion due to the interfacial polarization is characterized by a single relaxation time. It is found that theWagner theory is not valid quantitatively for the actual emulsions.Finally a new theory of the interfacial polarization is developed on the assumption that theWagner equation holds for an infinitesimally increasing process in concentration of the dispersion system. Several dielectric properties of emulsions are interpreted quantitatively by this new theory. Dielectric dispersions due to the interfacial polarization have so far been observed only in the W/O emulsions, and no example of the interfacial polarization has been found in usual emulsions of the O/W type yet. According to the new theory it is suggested that, if the dielectric constant of the oil phase is much larger, the dielectric dispersion due to the interfacial polarization may be observed even in emulsions of the O/W type.ZusammenfassungDie Grenzflächenpolarisation kugeliger Dispersionen wird theoretisch behandelt und an Fällen von Emulsionen diskutiert.Zuerst wird gezeigt, daß dieMaxwellsche Theorie für die dielektrischen Eigenschaften von Emulsionen nicht einmal qualitativ gilt. Als nächstes wird eine allgemeinere Lösung derWagner- Theorie abgeleitet. Diese zeigt, daß eine dielektrische Dispersion einer Grenzflächenpolarisation, durch eine einzelne Relaxationszeit charakterisiert, zuzuschreiben ist. Auch dieWagnersche Theorie gilt für wirkliche Emulsionen nicht quantitativ.Schließlich wird eine neue Theorie der Grenzflächenpolarisation auf der Basis entwickelt, daß dieWagner-sche Gleichung für ein infinitesimales Anwachsen der Konzentrationen von dispersen Systemen gilt. Zahlreiche dielektrische Eigenschaften von Emulsionen sind mit dieser neuen Theorie quantitativ interpretierbar.Dielektrische Dispersion durch Grenzflächenpolarisation wurde bisher nur in W/O-Emulsionen beobachtet, und kein Beispiel von Grenzflächenpolarisation ließ sich in gebräuchlichen Emulsionen des O/W-Typs bis heute auffinden. Nach der neuen Theorie wird vermutet, daß die dielektrische Dispersion auf Grund von Grenzflächenpolarisation auch in Emulsionen des O/W-Typs beobachtet werden könnte, falls die Dielektrizitätskonstante der Ölphase viel größer wäre.

Dielectric properties of yeast cells

SummaryDielectric measurements were made on suspensions of intact yeast cells over a frequency range of 10 kHz to 100 MHz. The suspensions showed typical dielectric dispersions, which are considered to be caused by the presence of cytoplasmic membranes with sufficiently low conductivity. Since the conductivity of the cell wall was found to be of nearly the same value as that of the suspending medium, composed of KCl solutions in a range from 10 to 80mm, the cell wall may be ignored in establishing an electrical model of the cells suspended in such media. An analysis of the dielectric data was carried out by use of Pauly and Schwans theory. The membrane capacitance was estimated to be 1.1±0.1 μF/cm2, which is compared with values reported so far for most biological membranes. The conductivity of the cell interior was almost unchanged with varying KCl concentrations and showed low values owing to the presence of less conducting particles, presumably intracellular organelles. The relatively low dielectric constant of about 50 obtained for the cell interior, in comparison with values of aqueous solutions, may be attributed also to the presence of intracellular organelles and proteins.

Passive electrical properties of cultured murine lymphoblast (L5178Y) with reference to its cytoplasmic membrane, nuclear envelope, and intracellular phases

SummaryDielectric dispersion measurements over a frequency range 0.01–100 MHz were made with the suspensions of a cultured cell line, mouse lymphoma L5178Y, and an attempt to explain the observed dielectric behavior by taking explicitly into consideration the possible involvement of cell nucleus has been presented.The use of a conventional “single-shell” model in which the cell is represented by a homogeneous sphere coated with a thin limiting shell phase did not duplicate the observed dispersion curves, whereas a “double-shell” model in which one additional concentric shell is incorporated into the “single-shell” model gave a much better fit between the observed and the predicted dispersion curves. Based on the latter model, we analyzed the raw data of dielectric measurements to yield a set of plausible electrical parameters for the lymphoma cell:CM≅1.0μF/cm2,CN≅0.4μF/cm2, εk≅300, κc/κa≅0.9, and κk/κc≅0.7. Here,CM andCN are the specific capacities of plasma and nuclear membranes; ε and κ are the dielectric constant and conductivity with subscripta, c andk referring respectively to the extracellular, the cytoplasmic and the karyoplasmic phases.

The number of interfaces and the associated dielectric relaxations in heterogeneous systems

Abstract In heterogeneous systems composed of some phases, mobile electric charges accumulate on the boundary surfaces between the constituent phase under the electric field applied. This charge accumulation, the so-called interfacial polarization, gives rise to dielectric relaxations. By the use of several examples, it is shown theoretically as well as experimentally that the dielectric relaxations are equal to the interfaces in the number. Typical examples of diphase systems are (i) a series combination of a polyethylene film and an aqueous solution, and (ii) water-in-oil emulsions. These systems contain one kind of interfaces, showing one dielectric relaxation. Practical examples of triphase systems are (i) a composite system of a Teflon film sandwiched between two aqueous solutions, and (ii) polystyrene microcapsules. These systems contain two kinds of interfaces, showing two dielectric relaxations. A pentaphase system composed of shell-spheres are discussed theoretically, showing four dielectric rela...

On-line monitoring of cell concentrations by dielectric measurements

Dielectric measurements were made on solutions with cells to establish the feasibility of measuring on-line cell concentrations in bioreactors. Excellent linear relationships, in which correlation coefficients were more than 0.99, were obtained between values of electric capacitance (frequency range: 100 kHz to 10 MHz) and concentrations of yeast cells (immobilized in calcium alginate beads), Escherichia coli, Aspergillus niger, human leukemia (K562) cells, Madin-Darby bovine kidney (MDBK) cells on microcarriers and plant suspension cells of Sesamum indicum L. It was also found that the linearities were maintained practically under cultivating conditions in which temperature, pH, and salt and substrate concentrations were changing during cultivation. It is concluded that the dielectric measurement method is a promising method for estimating on-line cell concentrations in bioreactors.

Dielectric properties of emulsions

SummaryDielectric constants of O/W emulsions were measured over a wide range of concentration and at frequencies ranging from 20 cps. to 3 mc.No dielectric dispersion due to the interfacial polarization was observed in the experimental range of frequency, while the electrode polarization was observed below 100 kc.Experimental results were compared with theoretical values for spherical dispersions. It was concluded that the dielectric constants of O/W emulsions were expressed best byBruggemans equation over the whole range of concentration.ZusammenfassungDie DK von öl/Wasser-Emulsionen wurden über einen weiten Konzentrationsbereich und für Frequenzen zwischen 20 Hz und 3 MHz gemessen. Es war keine dielektrische Dispersion verursacht durch OberflÄchenpolarisation innerhalb des experimentellen Frequenzbereiches zu beobachten. Dagegen wurde unterhalb 100 kHz Elektrodenpolarisation bemerkbar.Die experimentellen Ergebnisse wurden mit den theoretischen Darstellungen der Misch-DK für Dispersionen mit kugligen Teilchen verglichen. Der Verlauf der DK der öl/Wasser-Emulsion wird am besten und über den ganzen Konzentrationsbereich durch die Gleichung vonBruggeman dargestellt.

Analysis of dielectric relaxations of w/o emulsions in the light of theories of interfacial polarization

An attempt is made to apply dielectric theories of interfacial polarization to observations of dielectric relaxations for W/O emulsions. Approximate formulas for disperse systems in a W/O type were derived from the two theories: one proposed by Maxwell and Wagner for dilute disperse systems of spherical particles, and the other developed by Hanai for concentrated disperse systems. Dielectric measurements were carried out on concentrated W/O emulsions prepared from kerosene and distilled water or KCl aqueous solutions by minimal use of emulsifiers. Marked dielectric relaxations were observed with the emulsions, the dielectric parameters having been determined to characterize the relaxation data. Phase parameters such as relative permittivity, electric conductivity and volume fraction of the disperse phase were evaluated from the dielectric parameters by use of the approximate formulas of the respective theories. The phase parameters evaluated and the frequency dependence of complex permittivity of the W/O emulsions deduced from the theory for concentrated disperse systems are in excellent agreement with the observed data in comparison to that for dilute disperse systems. It is concluded that the dielectric relaxations due to the interfacial polarization of disperse systems of spheres are explained satisfactorily by the theory for concentrated disperse systems.

A method for determining the dielectric constant and the conductivity of membrane-bounded particles of biological relevance

Numerical assessment is made regarding Pauly and Schwans theory which describes the dielectric behaviour of a suspension of “shell spheres” as a model of biological membrane-bounded particles. The results indicate that approximate expressions of the theory may give rise to serious errors when applied to particles smaller than about 1 Μm in diameter. With a view to performing analysis according to a general expression of the theory, some of the characteristic responses of dielectric parameters upon changes in phase parameters are examined with particular reference to some numerical ranges of biological interest. On this basis a simplified and systematic procedure is proposed for estimating the phase parameters of particles whose shell phase can be regarded as non-conductive. As the application of the procedure proposed, a set of dielectric data of a synaptosome suspension is analyzed, so that the following three phase parameters are successfully determined: membrane capacitance (or shell phase dielectric constant), internal phase conductivity and internal phase dielectric constant. Some limitations of the procedure are discussed for the cases of conducting shells and small particles.