Dependence of dielectrophoretic force on the size of cylindrical particles by the example of a suspension of erythrocytes

For the modeling of erythrocyte rouleaux (linear cell aggregations), we propose an approximation procedure for the dipole moment in short cylinders, which contains the case of ellipsoidal bodies only as a first approximation. The method allows one to introduce corrections that are more representative for these particles. Depending on the number of erythrocytes forming an aggregation, i.e., on different but discrete measures of rouleaux lengths, the dielectrophoretic force is calculated and represented against the frequency of the applied a.c. field. As a result, frequency regions in the upper MHz range appear in which the strength and direction of DEP forces are different for different rouleaux sizes. This property is suitable for the detection and spatial separation of rouleaux populations of different length in blood samples by means of a microelectronic array.     

Dual-frequency dielectrophoretic levitation of Canola protoplasts

A novel dual-frequency excitation technique is introduced which permits investigation of the low-frequency dispersion of Canola plant protoplasts using feedback-controlled dielectrophoretic levitation. The upper and intermediate frequency spectra obtained using the new technique are generally consistent with previous work. However, below some cross-over frequency f_OL, the protoplasts exhibit an apparent positive dielectrophoretic response that is not predicted by conventional theory. This cross-over frequency is linearly related to suspension conductivity, virtually independent of the suspension pH, and inversely proportional to the square of the cell radius. Examination of the complex Clausius-Mossotti polarization coefficient reveals that the observed positive dielectrophoretic response can not be accounted for in terms of Maxwell-Wagner polarization associated with a conventional layered model for the protoplast. The failure of straightforward enhancements to the protoplast model in explaining the low frequency behavior may indicate the presence of an electrophoretic contribution to the net observable force on the particle. To account for such fluid mechanical effects, it will be necessary to modify the existing dielectrophoretic force formulation.     

A Nomograph for Calculating the Optimal Frequency for Dielectrophoresis and the Characteristic Frequency of the β-Dispersion of Cell Membrane Vesicles

The first stage of the two-stage cell electrofusion technique involves the dielectrophoretic apposition, in an AC field, of protoplasts suspended in a medium of relatively low specific conductivity. A frequency at which the maximum dielectrophoretic force is exerted is given by the characteristic frequency for the dielectric relaxation by a Maxwell-Wagner type of mechanism. We provide a nomograph for the rapid calculation of this frequency.     

Dielectric approach to investigation of erythrocyte aggregation. II. Kinetics of erythrocyte aggregation-disaggregation in quiescent and flowing blood

A method based on dielectric properties of dispersed systems was applied to investigate the kinetics of RBC aggregation and the break-up of the aggregates. Experimentally, this method consists of measuring the capacitance at a frequency in the beginning of the beta-dispersion. Two experimental protocols were used to investigate the aggregation process. In the first case, blood samples were fully dispersed and then the flow was decreased or stopped to promote RBC aggregation. It was found that the initial phases of RBC aggregation are not affected by the shear rate. This finding indicates that RBC aggregation is a slow coagulation process. In the second case, RBCs aggregated under flow conditions at different shear rates and after the capacitance reached plateau levels, the flow was ceased. The steady-state capacitance of the quiescent blood and the kinetics of RBC aggregation after stoppage of shearing depend on the prior shear rate. To clarify the reasons for this effect, the kinetics of the disaggregation process was studied. In these experiments, time courses of the capacitance were recorded under different flow conditions and then a higher shear stress was applied to break up RBC aggregates. It was found that the kinetics of the disaggregation process depend on both the prior and current shear stresses. Results obtained in this study and their analysis show that the kinetics of RBC aggregation in stasis consists of two consecutive phases: At the onset, red blood cells interact face-to-face to form linear aggregates and then, after an accumulation of an appropriate concentration of these aggregates, branched rouleaux are formed via reactions of ends of the linear rouleaux with sides of other rouleaux (face-to-side interactions). Branching points are broken by low shear stresses whereas dispersion of the linear rouleaux requires significantly higher energy.     

Effects of shear rate on rouleau formation in simple shear flow

A kinetic equation for rouleau formation in a simple shear flow is derived, based on several assumptions. These are (a) colliding rouleaux stick to one another with a certain probability to form a single rouleau; (b) simultaneous collisions between more than two rouleaux are negligible; (c) rouleaux are broken by a viscous force exerted by the suspending fluid on the surfaces of rouleaux; (d) when a rouleau is broken by viscous forces, only two fragments are formed. Based on a simple mathematical model, collision rate, sticking probability and degradation rate are obtained as functions of applied shear rate. From the solution of the kinetic equation, the average size of rouleaux is obtained as a function of time with shear rate as a parameter. It is shown that the average size of rouleaux increases monotonically with increasing time and tends to an equilibrium size. The average size of rouleaux in a dynamical equilibrium decreases monotonically with increasing shear rate and tends to one cell as shear rate approaches infinity. It is also found that the initial rate of rouleau formation increases with increasing shear rate at very low shear rate, but this trend is reversed at higher shear rates. The theoretical results are compared quantitatively with experimental data.     

Dielectrophoretic manipulation and characterization of herpes simplex virus-1 capsids

The dielectrophoretic behaviour of the capsids of herpes simplex virus type-1 has been measured over a range of conductivities of KCl solutions, with and without the addition of mannitol. The dielectrophoretic response of the capsids was recorded by measuring the frequency corresponding to zero dielectrophoretic force. The data were analysed using a multi-shelled model, and the permittivity and conductivity of the particles estimated. The capsid was modelled as a porous protein shell through which suspending medium passes, an inner chamber containing suspending medium in equilibrium with the outside, and a central core of protein (the scaffold). Capsids suspended in KCl without mannitol exhibited a different behaviour to those suspended in KCl with mannitol.     

Dielectrophoretic study of human erythrocytes

This paper is concerned with the dielectrophoretic study of human erythrocytes under cylindrical field geometry. The influence of physical variables such as the frequency and voltage of the applied electric field, conductivity of the medium in which the cells are suspended, cell concentration and exposure time of the cell to the non-uniform electric field on dielectrophoretic collection rate (DCR) is determined in a systematic manner. It is interesting to note from the DCR spectrum of human erythrocytes that the DCR is minimum at one frequency, maximum at another and there is practically no yield over a certain frequency range. This may be attributed to the variation of complex dielectric constant of the particle and medium over that frequency range. From the DCR spectrum of different groups, it is clear that DCR behaviour is different in the frequency range from 0.3–1.5 MHz, under similar conditions of temperature, conductivity and concentration of erythrocyte suspension and strength of applied AC field. The response of DCR with voltage of the applied field, concentration of cell suspension and square root of elapsed time of the cells confirms the theory of dielectrophoresis.     

Dielectrophoretic properties of yeast cells dividing by budding and by transversal fission

The dielectrophoretic behaviour of yeast cells dividing by budding or by transversal fission was analyzed. The results obtained show that the dielectrophoretic yield is a linear function of alternating voltage, cell concentration and the square root of the time of collection in all the species assayed. Dependence of the rate of collection on the frequency of the voltage applied (between 0.2 and 5 MHz) was also found. This behaviour is similar in the three microorganisms studied. The scale factor correlating the frequency spectrum for Saccharomyces cerevisiae and Saccharomycopsis lipolytica is proportional to cell size. However, these results can not be extended to Schizosaccharomyces pombe. A relationship between the dielectrophoretic yield and the age of the culture and the consumption of glucose has been established for the three yeast strains. Dielectrophoresis also permits the differentiation between viable and non-viable cells.     

Segregation into separate rouleaux of erythrocytes from different species. Evidence against the agglomerin hypothesis of rouleaux formation.

Erythrocytes from one species were labelled with fluorescein isothiocyanate and mixed with unlabelled erythrocytes from another species. Albumin polymers were added to generate rouleaux. The species of origin of erythrocytes in rouleaux was determined by fluorescence microscopy. Erythrocytes from different species segregated into independent rouleaux. However, fluorescent and non-fluorescent erythrocytes from one individual were mixed randomly in rouleaux. These results confirm, using a novel experimental approach, previous observations of Sewchand & Canham [(1976) Can. J. Physiol. Pharmacol. 54, 437-442]. Since rouleaugenic agents are not species-specific, under the 'agglomerin' hypothesis of rouleau formation they would be expected to form bridges between cells from different species. It follows that either the agglomerin hypothesis is incorrect, or additional species-specific surface components are involved in the aggregation of agglomerin-cross-bridged cells.     

No evidence for DNA in cyanobacterial carboxysomes

Abstract The dielectrophoretic yield of cell suspensions of Saccharomyces cerevisiae shows a maximum for a given frequency and this maximum shifts towards higher frequencies as the electrical conductivity of the medium increases. The addition of cations to cell suspensions of S. cerevisiae , maintaining the electric conductivity constant, leads to a decrease in the dielectrophoretic yield, depending of the valence of the cations added. Both results could be interpreted by a modified Maxwell-Wagner mechanism. Cetrimide is the most efficient detergent in permeabilizing yeast cells and the dielectrophoretic yield could be used as a method for quantifying cellular viability.     

Light-induced dielectrophoretic manipulation of DNA

Light-induced dielectrophoretic movement of polystyrene beads and lambda-DNA is studied using thin films of amorphous hydrogenated silicon as local photoaddressable electrodes with a diameter of 4 microm. Positive (high-field seeking) dielectrophoretic movement is observed for both types of objects. The absence of strong negative (low-field seeking) dielectrophoresis of DNA at high frequencies is in agreement with the similarity of the dielectric constants of DNA and water, the real part of the dielectric function. The corresponding imaginary part of the dielectric function governed by the conductivity of DNA can be determined from a comparison of the frequency dependence of the dielectrophoretic drift velocity with the Clausius-Mossotti relation.     

Conductometric study of shear-dependent processes in red cell suspensions. I. Effect of red blood cell aggregate morphology on blood conductance

The conductance and capacitance of flowing and quiescent red blood cell (RBC) suspensions were measured at a frequency of 0.2 MHz. The results demonstrate that the time-dependent changes in the conductance recorded during the aggregation process differ in nature for suspensions of short linear rouleaux, branched aggregates and RBC networks. It is shown that the conductance of RBC suspensions measured during the aggregation and disaggregation processes follows the morphological transformations of the RBC aggregates. Thus, this method enables characterization of the morphology of RBC aggregates formed in whole blood and in suspensions with physiological hematocrits both under flow conditions and in stasis. These results in combination with previous ones suggest that this technique can be used for studies of dynamic RBC aggregation and probably for diagnostic use.     

Introducing dielectrophoresis as a new force field for field-flow fractionation.

We present the principle of cell characterization and separation by dielectrophoretic field-flow fractionation and show preliminary experimental results. The operational device takes the form of a thin chamber in which the bottom wall supports an array of microelectrodes. By applying appropriate AC voltage signals to these electrodes, dielectrophoretic forces are generated to levitate cells suspended in the chamber and to affect their equilibrium heights. A laminar flow profile is established in the chamber so that fluid flows faster with increasing distance from the chamber walls. A cell carried in the flow stream will attain an equilibrium height, and a corresponding velocity, based on the balance of dielectrophoretic, gravitational, and hydrodynamic lift forces it experiences. We describe a theoretical model for this system and show that the cell velocity is a function of the mean fluid velocity, the voltage and frequency of the signals applied to the electrodes, and, most significantly, the cell dielectric properties. The validity of the model is demonstrated with human leukemia (HL-60) cells subjected to a parallel electrode array, and application of the device to separating HL-60 cells from peripheral blood mononuclear cells is shown.     

Dielectrophoretic behavior of yeast cells: effect of growth sources and cell wall and a comparison with fungal spores.

Saccharomyces cerevisiae showed different dielectrophoretic behavior depending on the source of carbon for growth. Growth on fermentable carbon sources produced a dielectrophoretic response that decreased according to the amount of sugar present in the culture medium. Growth on nonfermentable carbon sources produced a constant dielectrophoretic yield, independent of the amount and source of carbon present in the medium. The dielectrophoretic yield, however, was independent of the nitrogen source. The yield spectrum for S. cerevisiae protoplasts was similar to that for the cells, although a decrease in the absolute value was observed. This decrease could be explained by the reduction in cell size and by assuming that the cell wall contributes a negative net charge to the yield. Fungal spores responded to the nonuniform electric field in the same range of frequencies as assayed for yeast cells.     

Measurements of the dielectric properties of peripheral blood mononuclear cells and trophoblast cells using AC electrokinetic techniques

The separation of trophoblast cells from the maternal circulation could provide a valuable diagnostic tool for prenatal diagnosis of genetic abnormalities. This has been attempted using antibody methods, but due to non-specificity of the antibodies, maternal cell contamination remains a problem. We have investigated the potential of dielectrophoretic separation methods as a means of isolating trophoblast cells from mixed peripheral blood mononuclear cells. To determine the potential of this method the dielectric properties of trophoblast cells and mixed peripheral blood mononuclear cells were measured using dielectrophoretic crossover and single cell electrorotation methods. Both dielectrophoretic crossover data and electrorotation data gave an average specific membrane capacitance of the peripheral blood mononuclear cells of 11.5 mF m(-2). Trophoblast cells prepared using three different methods had a higher average specific membrane capacitance in the range 13-18 mF m(-2). The differences in capacitance between the cell types could be exploited as the basis of an AC electrokinetic-based system for the separation of trophoblast cells from peripheral blood mononuclear cells.     

Electrorotation and levitation of cells and colloidal particles

We review dielectrophoretic forces on cells and colloidal particles, emphasizing their use for manipulating and characterizing the electrical properties of suspended particles. Compared with dielectric spectroscopy, these methods offer a measure of independence from electrode artifacts and mixture theory. On the assumption that the particles can be modeled as uniform dielectric objects with effective dielectric properties, a simple theory can be developed for the frequency variation in the field-induced forces. For particles exhibiting counterion polarization, dielectrophoretic forces differ considerably from predictions of this theory at low frequencies, apparently because of double layer phenomena.     

Kinetics of rouleau formation. II. Reversible reactions.

Red blood cells aggregate face-to-face to form long, cylindrical, straight chains and sometimes branched structures called rouleaux. Here we extend a kinetic model developed by R. W. Samsel and A. S. Perelson (1982, Biophys. J. 37:493-514) to include both the formation and dissociation of rouleaux. We examine thermodynamic constraints on the rate constants of the model imposed by the principle of detailed balance. Incorporation of reverse reactions allows us to compute mean sizes of rouleaux and straight chain segments within rouleaux, as functions of time and at equilibrium. Using the Flory - Stockmayer method from polymer chemistry, we obtain a closed-form solution for the size distribution of straight chain segments within rouleaux at any point in the evolution of the reaction. The predictions of our theory compare favorably with data collected by D. Kernick , A.W.L. Jay , S. Rowlands , and L. Skibo (1973, Can. J. Physiol. Pharmacol. 51:690-699) on the kinetics of rouleau formation. When rouleaux grow large, they may contain rings or loops and take on the appearance of a network. We demonstrate the importance of including the kinetics of ring closure in the development of realistic models of rouleaux formation.     

Applications of a new optical technique for measuring the dielectrophoretic behaviour of micro-organisms

It is shown that the dielectrophoretic behaviour (motion in non-uniform a.c. electric fields) of micro-organisms can conveniently and reproducibly be measured by monitoring the decrease in optical absorbance of a cell suspension as the cells are collected at a micro-electrode array. The dielectrophoretic behaviour, as a function of the frequency of the applied electric field and conductivity of the supporting solution, can be determined more quantitatively and rapidly than by methods so far described in the literature. Results are presented for Micrococcus lysodeikticus, Bacillus subtilis and Escherichia coli for the frequency range 20 Hz to 4 MHz and theoretical considerations are presented for the effect of solution conductivity. A value of 0.2 S/m has been derived for the effective conductivity of M. lysodeikticus.     

AC electrokinetic characterisation and separation of cells with high and low embryogenic potential in suspension cultures of carrot (Daucus carota)

Suspension cultures of Daucus carota L. were established, and cells with embryogenic potential were separated from those without by density gradient centrifugation in Ficoll at different stages in the growth curve. In order to obtain information about the electrical properties of individual cells, electrorotation spectra of single plant cells from different fractions were measured before and after induction of embryogenesis. The data were analysed using models based on Maxwell–Wagner's theories of interfacial polarisation. It was found that the denser cells had a higher embryogenic potential, a darker appearance and a higher internal conductivity (>1 S m^–1) than the less dense cells, which had less or no embryogenic potential and a lower internal conductivity (<1 S m^–1). Modelling the dielectrophoretic (DEP) response on the basis of the electrorotation data suggested that separation of cells with high embryogenic potential may be achievable in the frequency range 1–10 MHz. Actual dielectrophoretic separation of cells with high embryogenic potential from suspensions in which embryogenesis had not yet been induced was achieved using steric as well as hyperlayer dielectrophoretic Field-Flow Fractionation (DEP-FFF).