Dielectric cytometry with three-dimensional cellular modeling

We have developed what we believe is an efficient method to determine the electric parameters (the specific membrane capacitance C(m) and the cytoplasm conductivity kappa(i)) of cells from their dielectric dispersion. First, a limited number of dispersion curves are numerically calculated for a three-dimensional cell model by changing C(m) and kappa(i), and their amplitudes Deltaepsilon and relaxation times tau are determined by assuming a Cole-Cole function. Second, regression formulas are obtained from the values of Deltaepsilon and tau and then used for the determination of C(m) and kappa(i) from the experimental Deltaepsilon and tau. This method was applied to the dielectric dispersion measured for rabbit erythrocytes (discocytes and echinocytes) and human erythrocytes (normocytes), and provided reasonable C(m) and kappa(i) of the erythrocytes and excellent agreement between the theoretical and experimental dispersion curves.     

Electric polarization of polyelectrolyte and colloid media: dielectric versus electro-optic approach

The theories of dielectric dispersion and of electric birefringence as a representative of electro-optic methods are considered and it is shown that they both depend in a similar way simply on the real part of the complex electric polarizability of the macromolecules or the particles. The latter also contains the permanent dipole moment. Experimental data on dielectric dispersion, electric birefringence and electric light scattering of strongly elongated, rod-like poly(tetrafluoroethylene) particles are compared and an attempt is made to extend the dielectric dispersion curve to lower frequencies using electric birefringence and electric light scattering data. Further, the experimental data on dielectric dispersion, electric light scattering, electro-orientation and dipolophoresis for the more complicated Escherichia coli particles are compared. Again, the possibility to extend the 10 kHz-100 MHz dielectric dispersion curve down below 1 Hz by using electric light scattering data is examined. The good matching of the dielectric dispersion and electric light scattering frequency curves found in the overlapping frequency range (10 kHz-5 MHz) essentially enhances the chance that dielectric dispersion below 1 MHz is related to alpha dispersion and not to electrode polarization. Thus it is not only possible to obtain additional information on the mechanism of polarization at lower-frequency dielectric dispersion, but also to extend our knowledge about the effective dielectric properties of biological complex fluids to frequencies essentially below 1 MHz. This could be important for the understanding of the effect of low-frequency electromagnetic fields on living matter.     

Molecular shape and dipole moment of alamethicin-like synthetic peptides

The peptides Boc-(l-Ala-Aib-l-Ala-Aib-l-Ala)_n-OMe, with n=2 (P10) and n=4 (P20), have been synthesized as purely hydrophobic models of the antibiotic alamethicin, which is known to be a voltage-dependent pore former in membranes and is apparently -helical in lipophilic media. These peptides were investigated in 1-octanol, a solvent which resembles the membrane environment. From dielectric dispersion studies quantitative information on the molecular shape and dipole moments could be derived. Further independent data concerning conformation and extent of aggregation of the peptides were obtained by circular dichroism and ultracentrifuge measurements. The results suggest that the peptides assume the form of elongated particles having a significant amount of ordered secondary structure and carrying a dipole parallel to the long axis. Apparently the monomeric peptide molecules undergo, to some extent, a head-to-tail aggregation which is slightly enhanced at lower temperatures. Based on the high-frequency parts of the dielectric dispersion curves the lengths, diameters, and dipole moments of the monomer particles have been determined as 22.5 Å, 10 Å, 36 D (P10) and 28.5 Å, 12 Å, 64 D (P20).     

Microdosimetric Study for Nanosecond Pulsed Electric Fields on a Cell Circuit Model with Nucleus

Recently, scientific interest in electric pulses, always more intense and shorter and able to induce biological effects on both plasma and nuclear membranes, has greatly increased. Hence, microdosimetric models that include internal organelles like the nucleus have assumed increasing importance. In this work, a circuit model of the cell including the nucleus is proposed, which accounts for the dielectric dispersion of all cell compartments. The setup of the dielectric model of the nucleus is of fundamental importance in determining the transmembrane potential (TMP) induced on the nuclear membrane; here, this is demonstrated by comparing results for three different sets of nuclear dielectric properties present in the literature. The results have been compared, even including or disregarding the dielectric dispersion of the nucleus. The main differences have been found when using pulses shorter than 10 ns. This is due to the fact that the high spectral components of the shortest pulses are differently taken into account by the nuclear membrane transfer functions computed with and without nuclear dielectric dispersion. The shortest pulses are also the most effective in porating the intracellular structures, as confirmed by the time courses of the TMP calculated across the plasma and nuclear membranes. We show how dispersive nucleus models are unavoidable when dealing with pulses shorter than 10 ns because of the large spectral contents arriving above 100 MHz, i.e., over the typical relaxation frequencies of the dipolar mechanism of the molecules constituting the nuclear membrane and the subcellular cell compartments.     

Modification of the erythrocyte membrane dielectric constant by alcohols

Summary Aliphatic alcohols are found to stimulate the transmembrane fluxes of a hydrophobic cation (tetraphenylarsonium, TPA) and anion (AN-12) 5–20 times in red blood cells. The results are analyzed using the Born-Parsegian equation (Parsegian, A., 1969,Nature (London) 221:844–846), together with the Clausius-Mossotti equation to calculate membrane dielectric energy barriers. Using established literature values of membrane thickness, native membrane dielectric constant, TPA ionic radius, and alcohol properties (partition coefficient, molar volume, dielectric constant), the TPA permeability data is predicted remarkably well by theory. If the radius of AN-12 is taken as 1.9 Å, its permeability in the presence of butanol is also described by our analysis. Further, the theory quantitatively accounts for the data of Gutknecht and Tosteson (Gutknecht, J., Tosteson, D.C., 1970,J. Gen. Physiol. 55:359–374) covering alcohol-induced conductivity changes of 3 orders of magnitude in artificial bilayers. Other explanations including perturbations of membrane fluidity, surface charge, membrane thickness, and dipole potential are discussed. However, the large magnitude of the stimulation, the more pronounced effect on smaller ions, and the acceleration of both anions and cations suggest membrane dielectric constant change as the primary basis of alcohol effects.     

The dielectric method of investigating bound water in biological material: An appraisal of the technique

Three independent dielectric methods for the measurement of water of hydration (bound water) in a biological material are described and discussed comparatively. For well-defined aqueous solutions of biological molecules, hydration can be obtained from direct observations made on the δ dispersion or from measurement of the dielectric values of the β dispersion. For whole tissue, however, neither of these two methods is applicable, and to deduce the hydration, it is necessary to use the third technique in which the volume of the hydrated biological particle is obtained by measuring the effect of it on the known dielectric properties of pure water. The hydration can then be calculated by deducting the volume of the anhydrous particle from the experimentally determined volume of the hydrated particle. Owing to possible systemmatic errors the uncertainty in the absolute hydration value associated with this technique is rather larger than that obtained with the other two dielectric methods. For studying the differences between hydration in similar tissues, however, this objection disappears.     

The dipolar origin of protein relaxation

1. A set of parameters is proposed to check the interpretation of the dielectric behaviour of protein solutions as a rigid-dipole relaxation of prolate ellipsoids of revolution in the frequency range between 20 kHz and 10 MHz. Besides the delta(b)-function of Scheraga, another analogous function (delta(a)) is presented to establish size and shape of globular proteins. A study of the influence of solvent viscosity on the dielectric dispersion also gives strong evidence in favour of rigid-dipole relaxation. 2. Measurements of the dielectric dispersion of monomer solutions of bovine serum albumin and transferrin are reported. Monomers of bovine serum albumin were obtained by fractionation on Sephadex G-150. Low-conductivity solutions of both proteins are obtained by passage through an ion-exchange resin. 3. Computer analysis of the experimental dispersion curves by use of a two-term Debye dispersion gives valuable information about transferrin and leads to an axial ratio 4.5 for a prolate ellipsoid of revolution. The dielectric increment of bovine serum albumin is very low and no conclusive results have yet been obtained.     

Probing protein electrostatic interactions through temperature/reduction potential profiles

 The change in the equilibrium reduction potentials of the iron-sulfur proteins, Pyrococcus furiosus rubredoxin and P. furiosus ferredoxin, and heme protein, horse cytochrome c, has been calculated as a function of temperature using a numerical solution to the Poisson-Boltzman equation. Working curves for different internal dielectric constants were generated to best reproduce experimental observation. Based on a comparison of the experimental and simulated change in reduction potential with temperature, it is concluded that the dielectric constant of proteins is temperature-dependent and varies from protein to protein. For example, the temperature-dependent reduction potential of cytochrome c can only be simulated using a different temperature-dependent dielectric constant for each oxidation state, but this was not the case for rubredoxin or ferredoxin. The role of changes in ionization states of cytochrome c at alkaline pHs, where the reduction potential is known to be pH-dependent at room temperature, is also discussed in terms of electrostatic interaction energies as a function of temperature. It appears that temperature/reduction potential profiles may provide a direct method for measuring relative changes in internal protein dielectric constants. Received: 29 April 1996 / Accepted: 1 August 1996     

A pulsing device for packed-bed bioreactors: I. Hydrodynamic behaviour

This paper describes a new pulsing device which permits the insertion in pulsing form of a liquid phase fed into an equipment where a microbial or enzymatic transformation occurs. It also analyzes the modifications of the flow model caused by the pulsation generated by means of three kinds of pulsators: A hydropneumatic pulsator, a selfpropelled pulsator and a newly designed elastic membrane pulsator.The hydrodynamic behaviour of a packed-bed column, to which each of these pulsators has been connected is compared with the correspondent system without pulsation. The flow model is determined by the study of the curves of residence times distribution, obtained by using a stimulus-response technique. A computer programme has been used to determine the axial dispersion coefficients from the response curves. In all cases we worked within a wide range of Re _p(10–215).     

Passive electrical properties of the membrane and cytoplasm of cultured rat basophil leukemia cells. I. Dielectric behavior of cell suspensions in 0.01-500 MHz and its simulation with a single-shell model

Frequency dependence of relative permittivity (dielectric constant) and conductivity, or the 'dielectric dispersion', of cultured cells (RBL-1 line) in suspension was measured using a fast impedance analyzer system capable of scanning 92 frequency points over a 10 kHz-500 MHz range within 80 s. Examination of the resulting dispersion curves of an improved reliability revealed that the dispersions consisted of at least two separate components. The low-frequency component (dispersion 1) had a permittivity increment (delta epsilon) of 10(3)-10(4) and a characteristic frequency (fc) at several hundred kHz; for the high-frequency component (dispersion 2), delta epsilon was smaller by a factor of 10(2) and fc = 10-30 MHz. Increments delta epsilon for both components increased with the volume fraction of cell suspension, while fc did not change appreciably as long as the conductivity of suspending medium was fixed. By fitting a model for shelled spheres (the 'single-shell' model) to the data of dispersion 1, the dielectric capacity of the plasma membrane phase (Cm) was estimated to be approx. 1.4 microF/cm2 for the cells in an isotonic medium. However, simulation by this particular shell model failed to reproduce the entire dispersion profile leaving a sizable discrepancy between theory and experiment especially at frequencies above 1 MHz where dispersion 2 took place. This discrepancy could not be filled up even by taking into consideration either the effect of cell size distribution actually determined or that of possible heterogeneity in the intracellular conductivity. The present data strongly indicate the need for a more penetrating model that effectively accounts for the behavior of dispersion 2.     

Dielectric analysis of Escherichia coli suspensions in the light of the theory of interfacial polarization.

Dielectric measurements of Escherichia coli suspensions were carried out over a frequency range from 10 kHz to 100 MHz, and marked dielectric dispersions having characteristic frequency of approximately 1 MHz were observed. On the basis of the cell model that a spheroid is covered with two confocal shells, a dielectric theory was developed to determine accurately four electrical parameters for E. coli cells such as the conductivity of the cell wall, the dielectric constant of the cell membrane, and the dielectric constant and the conductivity of the protoplasm. The observed data were analyzed by means of the procedure based on the dielectric theory to yield a set of plausible electrical parameters for the cells. By taking account of the size distribution of the cells and a dielectric relaxation of the protoplasm, the observed dispersion curves were successfully reconstituted by the present theory.     

Dielectric Behavior of Yeast Cells Treated with HgCl2 and Cetyl Trimethyl Ammonium Bromide

The change in dielectric properties caused by the destruction of the transport barrier of yeast cells has been investigated. Dielectric measurements were made over the frequency range of 1 kc to 2 Mc by using “leaky” yeast cells prepared by treatments with HgCl₂ or CTAB (cetyl trimethyl ammonium bromide). The Hg-treated cells were observed to give smaller dielectric constants and lower critical frequencies as compared with that of the intact cells, while the CTAB-treated cells gave no clear-cut dielectric dispersion. These observations are interpreted on the basis of Maxwell-Wagner's theory as indicating the changes in the intracellular conductivity, the membrane capacitance and the membrane conductance.     

The dielectric increments of aqueous polyelectrolyte solutions: a scaling approach

This paper deals with dielectric dispersion curves (covering a frequency range from a few Hz to 100 MHz) of Na-poly(styrene-sulfonate) of 65,000 < or = Mw < or = 1,060,000 g mol(-1) in aqueous solutions. The values of the low frequency (dielectric increment1) and high frequency (dielectric increment2) dielectric increments, obtained from the experimental curves matched to a superposition of two Cole-Cole equations, have been analyzed in terms of their concentration and molar mass dependence. The concentrations C (g l(-1)) of the various solutions were mostly situated in the transition regime defined by Odijk [T. Odijk, Macromolecules 12 (1979) 688] between the dilute regime (C < Cg*) and the semi-dilute one (C > C**), and wherein the characteristic concentration C* marks the onset of flexibility effects on the polyion behavior. It has been shown that in the concentration range Cg* < C < C** the increments in both frequency domains satisfy a scaling relation dielectric increment(j) = Bj M(nu j) (C/C*)(mu j) with molar mass independent exponents nu j and mu j changing around C*. Their values are different for dielectric increment1 and dielectric increment2, except for mu above C* where both increments appear to become concentration-independent. Below Cg*, in the dilute regime, the two dispersion domains seem to merge. The increment dielectric increment = relative permittivity (0) - high frequency limit of relative permittivity is molar mass independent if scaled to (C/Cg*). The molar mass dependence of the increments as a function of the macromolecular concentration rhoP, dielectric increment or dielectric increment(j) approximately Mgamma (rhoP)mu, also reveals differences between the different concentration regimes. Extrapolation from above Cg* to zero concentration is thus unjustified.     

Breakthrough performance of linear-DNA on ion-exchange membrane columns

Breakthrough performance of linear-DNA adsorption on ion-exchange membrane columns was theoretically and experimentally investigated using batch and fixed-bed systems. System dispersion curves showed the absence of flow non-idealities in the experimental arrangement. Breakthrough curves were not significantly affected by flow-rate or inlet solution concentration. In the theoretical analysis a model was integrated by the serial coupling of the membrane transport model and the system dispersion model. A transport model that considers finite kinetic rate and column dispersed flow was used in the study. A simplex optimization routine coupled to the solution of the partial differential model equations was employed to estimate the maximum adsorption capacity constant, the equilibrium desorption constant and the forward interaction rate-constant, which are the parameters of the membrane transport model. Through this approach a good prediction of the adsorption phenomena is obtained for inlet concentrations and flow rates greater than 0.2 mg/ml and 0.16 ml/min.     

Dielectric analysis of mitochondria isolated from rat liver II. Intact mitochondria as simulated by a double-shell model

The dielectric dispersion of isolated intact mitochondria in suspension has been measured between 10 kHz and 500 MHz. In isotonic KCI media at 4°C, the mitochondria maintained their characteristic ‘double membrane’ structure as examined by electron microscopy, and the observed dispersion curves were successfully simulated in terms of a superposition of two sub-dispersions having different characteristic frequencies and different permittivity magnitudes. Taking these observations into account we analyzed the dispersion data on the basis of a ‘double-shell’ model in which two concentric shells are meant to represent the mitochondrial outer and inner membranes. The analyses by a computerized curve-fitting method revealed that: (i) electric capacities for the outer and the inner membrane are 1.7 and 0.5 μF/cm², respectively, (ii) relative permittivity for the inner compartment (or the equivalent homogeneous matrical space) = 50–60, (iii) outer compartment-to-external conductivity ratio = 0.4–0.6, and (iv) inner compartment-to-external conductivity ratio = 0.14. The implications of these parameter values are discussed with due attention paid to the limitations inherent in our ‘double-shell’ model approach.     

Linear dichroism of bimolecular chlorophyll-lipid membranes. The role of anisotropy and dispersion

Polarised absorption and reflection spectra of chlorophyll-containing bimolecular lipid membranes were obtained in the spectral range of 590–710 nm. The spectra were analysed using the formalism of the complex dielectric tensor which characterizes the optical anisotropy of the membrane and the light absorption therein.The maxima of the absorption spectra recorded at a 45° angle of incidence are located at 665 and 670 nm for light in which the electric vector is oriented parallel and perpendicular, respectively, to the plane of incidence. The analysis of these spectra shows that the spectral shift is wholly due to the dispersion of the real part of the dielectric tensor.The angle between the dipole transition moment in the red and the normal to the membrane was estimated to be 42.3–45.3°.On the basis of these results, a model absorption spectrum, simulating the dichroic properties of oriented chloroplasts, was calculated for a system of parallel membranes.Some of the possible artifacts introduced into the dichroic spectra of chloroplasts due to anisotropy and dispersion are discussed.     

Structural flexibility and fast proton transfer reflected by the dielectric properties of poly-L-proline in aqueous solution

Dielectric dispersion curves for the helix-11 form of poly-L-proline in aqueous solution have been determined for various pH in the acid range of zwitterion formation. The results could be excellently described by means of a Cole-Cole dispersion function involving the three parameters Δ?⁰ (total dielectric increment), τ_r (effective rotational relaxation time) and h (characterizing the width of the dispersion region). The quantities τ_r, and h were found to be clearly independent of pH and added inert electrolyte. An analysis of the data permits an evaluation of the dipole moments and leads to the conclusion that the molecule cannot be considered to be a completely stretched rigid rod but must be more or less bent. Addition of formic acid slightly below pH 4 caused a distinct broadening of the experimental curves which could be quantitatively interpreted by a second dielectric relaxation process due to orientation of zwitterions by means of fast proton transfer.     

Modeling Plasmalemma Ion Transport of the Aquatic Plant Egeria densa

Fresh-water plants generate extraordinarily high electric potential differences at the plasma membrane. For a deeper understanding of the underlying transport processes a mathematical model of the electrogenic plasmalemma ion transport was developed based on experimental data mainly obtained from Egeria densa. The model uses a general nonlinear network approach and assumes coupling of the transporters via membrane potential. A proton pump, an outward-rectifying K⁺ channel, an inward-rectifying K⁺ channel, a Cl⁻ channel and a (2H-Cl)⁺ symporter are considered to be elements of the system. The model takes into consideration the effects of light, external pH and ionic content of the bath medium on ion transport. As a result it does not only satisfactorily describe the membrane potential as a function of these external physiological factors but also succeeds in simulating the effects of specific inhibitors as well as I-V-curves obtained with the patch-clamp technique in the whole cell mode. The quality of the model was checked by stability and sensitivity analyses. Received: 18 March 1996/Revised: 17 July 1996     

Amperometric glucose sensor based on catalytic reduction of dissolved oxygen at soluble carbon nanofiber

This work shows excellent catalytic activity of soluble carbon nanofiber (CNF), which was obtained with a simple nitric acid treatment, toward the electroreduction of dissolved oxygen at a low operating potential. Thus the CNF was applied in the construction of amperometric biosensors for oxidase substrates using glucose oxidase as a model. The good dispersion of CNF led to convenient preparation and acceptable repeatability of the proposed sensors. UV-vis spectra, Fourier transform infrared spectra, X-ray photoelectron spectra and titration curves demonstrated that the good dispersion resulted from the large numbers of surface oxygen-rich groups produced in the treatment process. The membrane of CNF showed good stability and provided fast response to dissolved oxygen with a linear range from 0.1 to 78 microM and detection limit of 0.07 microM. The proposed glucose biosensor could monitor glucose ranging from 10 to 350 microM with detection limit of 2.5 microM and sensitivity of 36.3 nA cm(-2) microM(-1). The coefficients of variation for intra-assay were 4.7 and 3.2% at glucose concentrations of 20 and 210 microM, respectively. The use of a low operating potential (-0.3 V) and Nafion membrane produced good selectivity toward the glucose detection. CNF-based biosensors would provide wide range of bioelectrochemical applications in different fields.