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Dielectrophoretic dynamic lightscattering (DDLS) spectroscopy

Communicated by James L. Dye, Michigan State University, East Lansing, MI, June 18, 2003 (received for review December 10, 2002)
Abstract
Dielectrophoretic dynamic lightscattering (DDLS) spectroscopy is presented. DDLS identifies macromolecules based on their dielectric, or polarizability, properties. DDLS measurements are carried out in an oscillating, nonuniform electric field. The field induces macromolecules to undergo dielectrophoretic motion, which is detected by the modulation in the dynamic lightscattering autocorrelation function. The DDLS experimental setup, data analysis, and data on latex particles and yeast cells are presented.
Identification of macromolecules, particles, and biological cells‡ constitutes an essential part of their production, purification, and eventual utility. Identifying components in solution is important for the biotechnology and chemical industries. In chemical polymerization, for example, control and measurement of the distribution of polymer size are critical to successful manufacturing and product quality. The situation undoubtedly is more complicated in biological systems, with many details affecting biomolecules and cell populations. The present article introduces dielectrophoretic dynamic lightscattering (DDLS) spectroscopy, a tool in the identification of macromolecules based on their dielectric, or polarizability, properties.
When a uniform electric field is applied to polarizable molecules, electrical charge separation, or rearrangement, takes place. After polarization of a molecule and its subsequent reorientation to comply with applied field, equal and opposite forces are exerted on each end of the resulting dipole.§ For an electrically neutral molecule, no net translation occurs. If the electric field possesses a spatial gradient, unequal forces will be experienced by each end of the dipole, causing the molecule to undergo net translational (dielectrophoretic) motion. These effects have been described for many scientific applications and are richly described in a large number of publications (see, for example, refs. 14 and references therein).
The translational motion occurs for a polarizable molecule even when the molecule is, overall, electrically neutral. For the effects discussed above to be observable, the molecular dimensions must be large enough to allow a measurable difference between the forces on each end of the dipole. The term macromolecule is used to recognize this fact.
Additionally, under the influence of an oscillating electric field gradient, the dielectrophoretic motion is frequencydependent. The response to an oscillating electric field is a function of the time it takes for charges to rearrange (relaxation time). The response depends on the mode of polarization (14), and subsequently a particular mode of polarization can be made to prevail by the choice of frequency.
It is the thesis here that polarizable macromolecules present in emulsions, polymer solutions, and cell suspensions can be characterized by their response to the dielectrophoretic effect. It is also demonstrated that this effect can be studied from the modulations in the autocorrelation function in DLS (hence DDLS) measurements as outlined below.
The force exerted by dielectrophoresis depends on several factors including the oscillating electric field strength, its gradient and frequency, the dielectric constant, and conductivity of the particle and the suspending medium. Ignoring outofphase (loss) terms, this force, F, can be represented as 1 where r is the radius of the particle, ε is the dielectric constant of the medium, and E is the electric field strength. It can be seen that the force imposed by dielectrophoresis depends on both field strength and field gradient, because may also be written as . Eq. 1 also indicates that the force is proportional to the volume of the molecule. g is a function of the electrical permittivities of the particle and the medium, 2 where ε*_{p} and ε*_{m} are the complex permittivities of the particle, p, and the medium, m, respectively. From Eq. 2 it can be seen that the motion will be toward the maximum field intensity when the dielectric constant of the particle is larger than that of the medium or away from the maximum when the dielectric constant of the particle is smaller.
The magnitude of the force affecting macromolecules in an electric field gradient thus is influenced by intrinsic and external factors. The intrinsic factors are inherent to the molecular species and provide parameters that can be used to identify the macromolecules such as the macromolecule's volume and polarizability. External factors include the strength, gradient, and frequency of the electric field. Instrumental and experimental arrangements can vary the magnitude of the external factors to detect (changes to) intrinsic properties. As with other spectroscopic or analytical techniques, the interplay between the external and intrinsic properties characterizes the performance characteristics and utilization of the technique.
Polarizability arises from the ability of electrical charges inside or on the macromolecules to move or align in the presence of an electric field to create dipoles. For a macromolecule or biological cell under nonionizing field strengths, there are various modes of polarizability, e.g., by migration or reorientation of charged ions and proteins and by the effect of the electrical double layer. The time dependence of the charge redistribution (relaxation time) gives rise to frequency dependence of dielectrophoresis on the applied field. Although ultimately important to the understanding of and correlating to macromolecular properties, mechanisms for the creation of dipoles will not be elaborated on here. An alternative explanation was given by considering the effect of surface conduction on the interfacial polarization (57).
There are numerous studies demonstrating that variations in cell or medium conditions lead to a discernible response to the dielectrophoretic force. These studies include, for example, cell and particle manipulation (8, 9) and separation of dead cells from viable cells (10), human leukocytes (11), and viruses (12). Correlation of the electrical properties (and their changes) to biological properties has been the subject of numerous studies (refs. 1215, for example). In the treatment of the effect of oscillating electric fields on biological systems, a great number of studies focused on the detection, by electrical means, of the changes in the electrical properties of the biomolecules.
In solution, the dielectrophoretic motion is superimposed on the Brownian (random) motion and the gravitational sedimentation (or buoyancy) of the molecules. By choice of electrode configuration and other experimental conditions, it is possible to achieve a reasonably distinguishable dielectrophoretic motion (3).
The detection scheme presented in this article is based on the use of the autocorrelation function derived from DLS measurements. Particular attention is paid to modulation of the autocorrelation function caused by macromolecular motion in an electric field gradient. As outlined below, this scheme offers the potential to deconvolute spectra that arise from complex biological systems.
In a typical DLS experiment, a laser light impinges on a solution of macromolecules, and the intensity of the scattered light is measured at an angle, θ. The frequency of the scattered light is Dopplershifted because of the Brownian motion of the scattering macromolecules in the scattering volume. The scattering volume is defined by the intersection geometry of the incident beam and the scattered light (as sensed by the detector). In the absence of other fields, the frequency shifts are proportional to the diffusion coefficients of the scattering species. Current DLS experiments measure the Fourier transform (FT) of these frequency shifts as the timeautocorrelation function of the intensity fluctuations. Timeautocorrelation functions are exponential, with time constants characteristic of the diffusion coefficients of the scattering species. From these coefficients, useful information can be obtained on the scattering molecules, primarily a measure of their sizes in solution. For a monodisperse system of particles, the heterodyne intensity timedomain autocorrelation function, C(τ), can be written as (16) 3 where is the average number of particles per unit volume, τ is the delay or shift time, and q is an experimental function: 4 Here, n is the refractive index of the solution and λ is the wavelength of light. In Eq. 3, D is the diffusion coefficient, which for a spherical particle is 5 where k is the Boltzmann constant, T is the absolute temperature, η is the viscosity, and r is the radius of the particle.
The corresponding frequency domain (power spectrum) is obtained by the FT of Eq. 3, 6
Analysis of the autocorrelation functions by using Eqs. 36 can lead to the extraction of the diffusion coefficients of the scattering species and, hence, a measure of their sizes.
In polydisperse systems, the measured autocorrelation function is a sum of exponentials (or, for continuous distribution, an integral) representing the different species present, 7 where Γ is the exponent in Eq. 3. Eq. 7 shows that, except for a single (monodisperse) solute systems, C(τ) data will be composed of a sum of exponentials. Analysis of multiple exponentials is difficult even though intricate computational methods have been developed for the deconvolution of overlapping exponentials (see ref. 17, for example). The origin of the difficulty is that the exponentials overlap quite strongly, with no discernible structure developed in the resulting functional form. The present method provides a guide for overcoming these difficulties by giving an estimate of the number of components present.
Under an electric field gradient, as discussed above, a directed (nonBrownian) motion is exhibited by the polarizable particles. Following an approach and approximations developed earlier (16, 18) the effect of the directed motion on the autocorrelation function can be estimated. This directed motion modulates the exponential decay of the Brownian motion measured in DLS experiments, in the form 8a 8b where C(τ) is the timeautocorrelation function for the Brownian motion (Eq. 3 or 7), i = √1, and v is the instantaneous velocity of the particles undergoing directed motion under the applied external field in the scattering volume. The prime indicates that a field is applied.
The application of field gradient thus modulates the autocorrelation function. This bears implications on data analysis and interpretation: Modulation of a function in the time domain produces a shift in the FT in the frequency domain (19). The frequency of the scattered light is again Dopplershifted by the application of the electric field gradient. The frequency shift indicates and is proportional to the velocity of the macromolecules under the dielectrophoretic effect. The FT of the autocorrelation function obtained under electric field gradient would lead to determination of the frequency shifts due to the field gradient. The shifts then are used to calculate the velocity of the macromolecules in the presence of the field gradient. Note that performing FT of the unmodulated C(τ) would not be of much assistance in resolving multicomponent DLS spectra (multiple exponentials), because the FT of an exponential function is a Lorentzian function. Lorentzian functions, similar to exponentials, also lack discernible features that would aid in their resolution.
The power spectrum is obtained by the FT of Eq. 8a, 9
Lineshape analysis indicates a shift in the maximum by +q·v, whereas the halfwidth at halfmaximum, (q^{2}D)^{2}, remains unchanged. The dataanalysis scheme described below simplifies the extraction of the velocities by removing the component due to the Brownian motion from C(τ).
Analysis of data may be performed by the FT after removal of the component due to the Brownian motion from C′(τ). The FT would produce a spectrum representing the macromolecular dielectrophoretic velocity distribution. The spectrum is proposed to be characteristic of a given dispersion under a defined (experimental) set of field geometry and field frequency. Additionally, the peaks in the transform (v space) may be assigned to species present in the dispersion. Each (polarizable) population present, in principal, would contribute a peak in v space (spectrum). Under normalized conditions of field strength and gradient, a peak represents the dielectrophoretic mobility¶ of the species.
Electrophoretic light scattering has been demonstrated previously and was used to characterize monomer and dimeric BSA in solution (18). The method uses electrophoresis to induce uniform motion, which modulates the timeautocorrelation function and discriminates between molecules depending on their electrophoretic mobility.
A modification to electrophoretic light scattering was achieved by the application of a lowfrequency field [frequencies <100 Hz (20)]. The lowoscillation field, called a sinusoidal electric field (DLSSEF), was proposed to avoid some of the drawbacks in electrophoretic light scattering by reducing the Joules heating and the bubble formation as well as reducing the electrodic polarization encountered in dc electrophoresis. The method was used to estimate the electrophoretic mobility of biological molecules.
More recently, studies on cell rotation and its detection by light scattering (electrorotational light scattering) has been described (21). By using a homodyne DLS setup, electrorotational light scattering measures the frequency dependence of fieldinduced rotation of single particles. Also, dielectrophoretic phaseanalysis light scattering was presented. In dielectrophoretic phaseanalysis light scattering, the sample is illuminated by two laser beams with a small frequency difference [≈2 kHz, using Bragg cells (21, 22)] to create an interference region with a moving fringe pattern. By using the optical frequency difference of the two laser beams, phase demodulation of the Doppler signal yields the particle velocity. This method was used to characterize latexparticle velocities (23).
Experimental Setup
Fig. 1 shows a schematic of the DDLS setup. The sample cell was a cylindrical glass cell (Kimble Glass, Vineland, NJ) and was immersed in a bath of indexmatching fluid to minimize light scattering at the glassair interface. The bath was also made of glass and contained a holder for the sample cell. In the studies reported here, the electrodes (Pt wire) were shielded by heatshrink tubing. The tips were unshielded and typically <100 μm apart. The edge of one electrode was displaced (1 mm) from the edge of the other electrode to generate a field gradient. The electrodes were aligned such that the edge of the incident laser beam impinged an electrode to create a heterodyne mode. A sinusoidal radio frequency (RF) signal from a wave generator (Wavetek model 166, Fluke, Everett, WA) was amplified with a broadband amplifier and provided the electric power needed for the electric field and fieldgradient generation. The electrodes were supported on an acrylic disk with a Bayonet Neill Concelman connector that connected the electrode to the power supply and covered the cell.
The blue line (488 nm) of an argon ion laser (SpectraPhysics) was used for the present studies. The signal was attenuated so as not to saturate the autocorrelator. The optics consisted of mirrors and lenses that focused the incident beam to an ≈50μm cross section at the scattering volume. The scattered light at a 90° angle was picked by a fiberoptic bundle and connected to a photoncounting photomultiplier tube and other signalprocessing electronics of a 128channel digital correlator (Brookhaven Instruments, Holtsville, NY) to calculate the timeautocorrelation functions.
Data Analysis
For display purposes, the raw data from the correlator were used to construct a normalized function, C′_{norm}(τ) = [C′(τ)  C′(τ)_{τ=∞}]/[C′(τ)_{τ=0}  C′(τ)_{τ=∞}], where C(τ)_{τ=0} is the value in the first channel of the correlator, and C(τ)_{τ=∞} is the value in the delay channel.
To isolate the oscillations due to dielectrophoresis (Eq. 8b) it was advantageous to first estimate the component of the spectrum due to the Brownian motion. This was accomplished by curvefitting C′(τ) to an exponential function, which is the functional form of C(τ). Fitting was accomplished by using the nonleastsquareminimization procedure (24) or by also using Microsoft EXCEL's Solver addin. Other methods of removing the exponential contribution to C′(τ) can be applied as in the convolution of C′(τ) by a Gaussian or similar function with appropriate width to dampen the oscillations (25, 26) and obtain an estimate of C(τ).
Oscillations due to (q·vτ) were obtained by dividing C′(τ) by the exponential estimation of C(τ) to reduce the occurrence of lowfrequency peaks in the FT. For the FT analysis described here, the form [(C′(τ)/C(τ))  1] was used to render the oscillations symmetrical around zero. This was performed to minimize highfrequency ripples (or side lobes) due to the presence of sharp truncation functions.
Finally, FT is performed on the oscillations, and peaks in the transform (v space) are assigned to species present in the dispersion. In specified cases, “zero filling” was used in the FT. The velocities in the FT can be normalized (by using the applied field strength and gradient) to assign a specific velocity, the dielectrophoretic mobility, to each species.
There are certain electrode configurations that produce uniform gradient [isomotive design (2, 27)]. In general, the field gradient varies with the location in the scattering volume where the measurement takes place. In a small volume, one expects a considerable field inhomogeneity, which would reflect broadening in the line widths in the FT. The field gradient was estimated from the geometry used, with typical estimates from 10^{12} to 5 × 10^{15} V^{2}/m^{3}, by using the approximation of parallel wire electrodes (2).
Results and Discussion
DDLS of 4.1μm Latex Particles.Fig. 2 illustrates the DDLS of 4.1μmdiameter polystyrene latex particles and the dataanalysis scheme. The particles (Polysciences) were diluted to a 1 × 10^{6} g/ml concentration with distilled water. The particles were described as generally neutral but with a slight adsorbed negative charge. The DDLS setup and conditions are described in the Fig. 1 legend. Heterodyne autocorrelation function measurements were carried out under the application of a 30V signal (peaktopeak nominal reading from the RF amplifier) at 350 kHz and a τ of 60 μs. Also displayed is the exponential fit to C′_{norm}(τ), as outlined above. The oscillations due to DDLS were calculated as [(C′_{norm}(τ)/C(τ))  1] and are shown in Fig. 2Inset. The FT of the oscillations in Fig. 2 produced a single distribution with a velocity of 6.45 × 10^{7} m/s.
Field Effect on the Dielectrophoretic Velocity of 2.98μm Latex Particles. Polystyrene latex particles (2.98 μm in diameter, Polysciences) were diluted to a 1 × 10^{6} g/ml concentration with distilled water. The suspension was placed in the sample cell. Other conditions were as described in Experimental Setup. Autocorrelation function measurements were collected under the application of varying field strength. The sample cell geometry and electric field frequency (350 kHz) were maintained constant. The results are displayed in Fig. 3.
In Fig. 3, the top trace shows C′_{norm}(τ) with no field application, and the oscillating traces show the effect of the application of the electric field/gradient with increasing strength. The number of oscillations increased with increasing field strength, as predicted by Eqs. 8a and 8b. As in Fig. 2, exponential functions were fitted to the individual C′_{norm}(τ). The oscillations due to the dielectrophoretic effect were calculated by using the scheme described above.
FT analysis (Fig. 4A) shows primarily a single peak in the velocity domain (the dielectrophoretic spectrum) for each field applied. A single peak is predicted because the sample contains monosized particles. As predicted, the velocity increased with increasing field strength. Fig. 4B shows the dependence of the DDLSmeasured velocity as a function of applied . Because the experiments were conducted at constant field geometry, the variations reflect velocity dependence on the applied field strength. A straight line is predicted from Eq. 1. Regression analysis showed a slope of 2.6 × 10^{19} m^{3}·V^{2} per s (with R^{2} of 0.99). The slope value is a measurement of the dielectrophoretic mobility. It is the same order of magnitude as that predicted from calculations performed by Morgan et al. (12) on particles of different sizes.
Effect of Field Frequency on the Dielectrophoretic Velocity of 2.98μm Latex Particles. The dielectrophoretic velocity of 2.98μm latex particles was measured at several frequencies of the applied field while keeping the field intensity and geometry unchanged. The results are shown in Fig. 5. The velocities exhibit a maximum near 1 MHz. Similar observations were cited (23) for the dependency of the dielectrophoretic effects of macromolecules on the electric field frequency.
DDLS of a ThreeComponent LatexParticle Mixture. A mixture of 0.95, 2.98, and 4.1μm latex spheres (Polysciences) was prepared at concentrations of 1 × 10^{6}, 1 × 10^{6}, and 5 × 10^{7} g/ml, respectively. Measurements were carried out under 40 V (P/P) at 350kHz frequency and a τ of 60 ms. Other conditions were as outlined above. Fig. 6 shows the resulting FT with three distinct peaks in the velocity domain. The peaks were assigned, respectively, from low to high values to the velocity of the 0.95, 2.98, and 4.1μm particles.
DDLS of a Baker's Yeast Solution. A sample of Baker's yeast (0.5 g in 100 ml water) was suspended in water and centrifuged at 2,000 × g for 10 min. The supernatant was discarded and the pellet resuspended (by vortex) in 100 ml of water. The process was repeated once, and the suspension was used in the DLLS measurements. The measurements and data analysis were carried out as outlined above. Fig. 7 shows the resulting spectrum from the mixture collected at 30 V (P/P) by using 500 and 300kHz frequencies. The data show more complex spectra in the FT. The resolution enhancement in discovering these populations would not be possible without the application of the nonuniform field. The FT peaks are stipulated to represent the velocities of the different species of yeast cells under the field.
Remarks
DDLS presents a technique for studying biological macromolecules and cells: an additional tool to add to the macromolecular characterization toolbox. The method may prove important in exploring fundamental as well as practical cellular and macromolecular solution properties. The essential criterion is that the macromolecules under study be polarizable. DDLS provides a greater leverage in characterizing heterogeneous populations of a large class of macromolecules. DDLS may be used to resolve neutral particle distributions and biological cells at their isoelectric points.
DDLS utilizes DLS as the detection method. By itself, DLS provides fast and useful information but has limited resolving power of components in solution because of the strong overlap of the autocorrelation functions as discussed earlier. The incorporation of dielectrophoresis into DLS enhances the resolving power by adding “structure” to the composite autocorrelation functions. The structure is postulated to be a manifestation of physical properties of the species under study, namely their sizes and polarizabilities. As illustrated in Figs. 6 and 7, resolving these populations into individual components would have been difficult without the application of the nonuniform field. For the yeastcell solution, the peaks in the FT (vspace spectrum) are stipulated to represent the velocities of the different species of yeast cells under the field. DDLS possesses the potential to resolve populations with the similar sizes if the populations differ in polarizability.
For DDLS measurements to be meaningful, the magnitude of the dielectrophoretic force must be larger than other competing forces acting on the molecules. In solution, competing forces are gravitational (or buoyancy) and Brownian. For smaller molecules, Brownian motion is an effective randomizing force, with values on the order of 10^{15} N. The gravitational force, for a 1μmdiameter particle or cell with a density of 11.05 kg/m^{3}, is also on the order of 10^{15} N. Although the gravitational and dielectrophoretic forces vary with the volume of the molecule, the Brownian force changes as r^{1}, indicating that for larger particles, the dielectrophoretic and the gravitational forces are more dominant. In the studies presented here, the electrode configuration and the applied voltages indicate that . For a typical experimental setup presented here and a g value of 0.5 (Eq. 2), the dielectrophoretic force is estimated to be on the order of 10^{13} N.
The line shapes in the FT of the vspace spectra reflect the contribution from two major factors. The first is the distribution of particles, as reflected in their sizes, residual charges, and other factors influencing dielectrophoresis. The second is the effect of local fieldgradient inhomogeneity. Note that the dataanalysis scheme adopted here essentially removes the contribution from the Brownian motion.
It is reasonable to postulate that the state of a biological cell will correspond to a certain configuration of charges inside and on the cell surface. Without comprehensive knowledge of the details of the mechanics of DDLS effects, a practical benefit is anticipated from furnishing a “signature” to characterize “normal” populations of polymers or biological cells. Although additional studies are required for a more thorough understanding, this may furnish a scheme for the quick identification of “abnormalities” in, for example, cell populations.
The dependence of dielectrophoresis on the field frequency (resonancelike) has theoretical as well as practical implications. Biological cells show a complicated response to the field frequency. It has been shown (7, 8) that some cells respond specifically to certain frequencies of the field. DDLS may prove to be the method of choice for providing a practical technique to probe these effects.
The DDLS setup produces lowJoule heating and no or insignificant electrolysis, or electrodic polarization. DDLS can be applied to heterogeneous mixtures and would be insensitive to light scattering from small and nonpolarizable molecules. The contribution of these molecules can be factored out, because it occurs on a different time scale.
There are several limitations to DDLS. In solutions of colored molecules, light absorption may contribute to heating of the solution. In many cases, this could be mitigated by the choice of a wavelength at which the molecules do not absorb. Another potential limitation is what is called “pearl chain formation,” a chaining of cells that occurs when the field strength is larger than a certain threshold value (7). Pearl chains can potentially complicate the interpretation of DDLS results, because they may form their own peaks in the FT. The formation of pearl chains may be avoided by applying a field lower than the threshold value that is required for their formation and/or completing the measurement in a short time. Another limitation in biological cell suspensions may arise because of the high conductivity of the solution, which may cause heat generation and reduce the resolution of DDLS. In the case of plant cells, yeast, and some bacteria, this effect can be minimized because the cells can easily survive the duration of the experiments when suspended in lowconductivity solutions. Due to the speed of the measurements, this effect can probably be overcome. This effect, however, needs to be studied and quantified and may be remedied by the use of the choice of isotonic media, electrode insulation, and geometry. Also, as mentioned earlier, for DDLS to be observed, a minimum particle size of ≈100 Å, and for practical purposes ≈500 Å, may be required. DDLS will be insensitive to most proteins and polysaccharides.
This, however, leaves a vast number of cells, large DNA dispersions, and polymers that are sensitive to DDLS. The insensitivity to small molecules may be a blessing, because smaller molecules and proteins usually used in cell culture media may otherwise complicate the interpretation of the measurements.
Acknowledgments
I thank Dr. James L. Dye (Chemistry Department, Michigan State University, East Lansing), Dr. Robert Gray (Abbott Laboratories, Abbott Park, IL), and Dr. Don Stimpson (Biostrand, Aurora, CO) for critical reviews and helpful discussion. This work was supported by National Institutes of Health Small Business Innovation Research Grant 1 R43 GM 48936. Support from Dr. Lon Wilkins and the Biology Department of the University of Missouri, St. Louis, is greatly appreciated.
Footnotes

↵† Present address: Abbott Laboratories, D09N9, AP20, Abbott Park, IL 60064. Email: folim.halaka{at}abbott.com.

Abbreviations: DLS, dynamic light scattering; DDLS, dielectrophoretic DLS; FT, Fourier transform; RF, radio frequency.

↵‡ The terms “particles,” “cells,” “macromolecules,” “particulates,” and “polymers” are used here interchangeably unless otherwise noted.

↵§ Charges in larger molecules with complicated charge distribution may not neatly rearrange to form a single classical “dipole.” The resultant from the vector addition of all the possible dipoles would represent the dipole meant here.

↵¶ Dielectrophoretic mobility is the dielectrophoretic velocity normalized to units of field strength and field gradient in analogy to electrophoretic mobility.
 Received December 10, 2002.
 Copyright © 2003, The National Academy of Sciences
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