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Langmuir 2007, 23, 3840-3848
Using Nonuniform Electric Fields To Accelerate the Transport of Viruses to Surfaces from Media of Physiological Ionic Strength Aristides Docoslis,*,† Luis A. Tercero Espinoza,‡,⊥ Bingbing Zhang,† Li-Lin Cheng,§ Barbara A. Israel,§ Paschalis Alexandridis,*,| and Nicholas L. Abbott*,‡ Department of Chemical Engineering, Queen’s UniVersity at Kingston, Kingston, Ontario K7L 3N6, Canada, Department of Chemical and Biological Engineering and Veterinary School, UniVersity of WisconsinsMadison, Madison, Wisconsin 53706, and Department of Chemical and Biological Engineering, UniVersity at Buffalo, The State UniVersity of New York, Buffalo, New York 14260 ReceiVed May 25, 2006. In Final Form: NoVember 26, 2006 Nonuniform ac (alternating current) electric fields created by microelectrodes are investigated for their influence on the transport of the vesicular stomatitis virus (VSV) from aqueous suspensions of physiological ionic strength to surfaces on which the VSV is captured. Whereas passive diffusion did not lead to detectable levels of virus captured on a surface when using titers of VSV as high as 107 PFU/mL, nonuniform electric field-mediated transport led to the detection of 105 PFU/mL of virus in 2 min. An order-of-magnitude analysis of the time scales associated with virus transport to the microelectrodes inside media of physiological relevance indicates that electrothermal fluid flow (and the resulting viscous drag forces on the virus) rather than dielectrophoresis likely constitutes the major mechanism for virus transport far from the electrodes. The influence of dielectrophoresis was calculated to be confined to a region within a few micrometers of the electrodes and to lead to collection patterns of both virus and fluorescently labeled particles near the electrodes that were found to be in qualitative agreement with experiments. These observations and conclusions are discussed within a theoretical framework presented in the paper. The results presented in this work, when combined, suggest that ac electrokinetic phenomena can be used to expeditiously transport and capture viruses onto surfaces from solutions of high ionic strength, thus providing a potentially useful approach to addressing a bottleneck in the development of devices that allow for rapid sampling and detection of infectious biological agents.
I. Introduction
* To whom correspondence should be addressed. E-mail: docoslis@ chee.queensu.ca (A.D.);
[email protected] (P.A.); abbott@ engr.wisc.edu (N.L.A.). † Queen’s University at Kingston. ‡ Department of Chemical and Biological Engineering, University of WisconsinsMadison. § Veterinary School, University of WisconsinsMadison. | University at Buffalo. ⊥ Current address: Bereich Wasserchemie, Engler-Bunte-Institut, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany.
and sensitivity of surface-based detection methods are limited by the slow rates at which (sub-micrometer-sized) virus particles are transported to surfaces by diffusion. In this paper, we report on a study that sought to address this problem. Specifically, we demonstrate that planar microelectrodes can be employed for providing accelerated transport and capture of the virus to a surface by means of alternating current (ac) electrokinetic effects, namely, dielectrophoresis and electrothermal fluid flow. Alternating current electrokinetic manipulation of viruses by using microelectrodes has been reported previously.7-12 In these past reports, collection of the virus took place inside suspensions of low ionic strength (typical range: 1-100 mS m-1) and/or high particle concentrations (e.g., >1010 particles mL-1). The aforementioned experimental conditions allow for convenient demonstration of the capabilities of nonuniform electric fields, namely, manipulation and observation of virus collection patterns, trapping, differential separation of virus populations, as well as characterization of their dielectric and biophysical properties. From these past studies, however, it is not apparent if the use of nonuniform electric fields can result in (i) in situ collection
(1) Walpita, P.; Darougar, S. Double-Label Immunofluorescence Method for Simultaneous Detection of Adenovirus and Herpes Simplex Virus from the Eye. J. Clin. Microbiol. 1989, 27, 1623-1625. (2) Hayden, O.; Bindeus, R.; Haderspock, C.; Mann, K.-J.; Wirl, B.; Dickert, F. L. Mass-Sensitive Detection of Cells, Viruses and Enzymes with Artificial Receptors. Sens. Actuators, B 2003, 91, 316-319. (3) Huang, L.-F.; Yang, H.-H.; Su, C.-C.; Wu, T.-Z.; Chen, L.-K. Application of Simultaneous Immunosensor for Early Detection of Dengue Virus. Chem. Sens. 2001, 17 (Suppl. B), 478-480. (4) Tercero Espinoza, L. A.; Schumann, K. R.; Luk, Y.-Y.; Israel, B. A.; Abbott, N. L. Orientational Behavior of Thermotropic Liquid Crystals on Surfaces Presenting Electrostatically Bound Vesicular Stomatitis Virus. Langmuir 2004, 20, 2375-2385. (5) Brake, J. M.; Daschner, M. K.; Luk, Y.-Y.; Abbott, N. L. Biomolecular Interactions at Phospholipid-Decorated Surfaces of Thermotropic Liquid Crystals. Science 2003, 302, 2094-2097. (6) Pohl, H. A. Dielectrophoresis; Cambridge University Press: Cambridge, U.K., 1978.
(7) Green, N. G.; Morgan, H.; Milner, J. J. Manipulation and Trapping of Sub-micron Bioparticles Using Dielectrophoresis. J. Biochem. Biophys. Methods 1997, 35, 89-102. (8) Schnelle, T.; Mu¨ller, T.; Fiedler, S.; Shirley, S. G.; Ludwig, K.; Hermann, A.; Fuhr, G.; Wagner, G.; Zimmermann, U. Trapping of Viruses in High-Frequency Electric Field Cages. Naturwissenschaften 1996, 83, 172-176. (9) Mu¨ller, T.; Fiedler, S.; Schnelle, T.; Ludwig, K.; Jung, H.; Fuhr, G. High Frequency Electric Fields for Trapping Viruses. Biotechnol. Tech. 1996, 10, 221226. (10) Morgan, H.; Hughes, M. P.; Green, N. G. Separation of Submicron Bioparticles by Dielectrophoresis. Biophys. J. 1999, 77, 516-525. (11) Hughes, M. P.; Morgan, H.; Rixon, F. J. Dielectrophoretic Manipulation and Characterization of Herpes Simplex Virus-1 Capsids. Eur. Biophys. J. 2001, 30, 268-272. (12) Hughes, M. P.; Morgan, H.; Rixon, F. J. Measuring the Dielectric Properties of Herpes Simplex Virus Type 1 Virions with Dielectrophoresis. Biochim. Biophys. Acta 2002, 1571, 1-8.
The increasing frequency of virus-related disease outbreaks creates a growing need for methods that permit rapid detection of infectious biological agents, such as viruses, within small sample volumes and without amplification of the agent. One set of promising approaches involves the selective capture of viral particles from a sample onto a surface and subsequent detection via optical transduction. While optical transduction can be achieved by a number of methods, ranging from conventional fluorescent antibody labeling1 and mass-sensitive detection2,3 to emerging label-free methods such as liquid crystals,4,5 the speed
10.1021/la061486l CCC: $37.00 © 2007 American Chemical Society Published on Web 02/27/2007
Use of ac Electric Fields for Virus Transport
of the virus from suspensions of physiological ionic strength (e.g., g880 mS m-1) or (ii) the generation of detectable signals of surface-bound virus particles at low virus concentrations (e.g., 106 V m-1) and nonuniformity. To meet these conditions, while avoiding the application of large potential differences, microelectrodes separated by only a few micrometers have been used. A second ac electrokinetic phenomenon that we consider in this paper is electrothermally induced flow of the suspending medium, which occurs concurrently with dielectrophoresis and can exert significant viscous drag forces on the viral particles, thus affecting their transport patterns inside a nonuniform electric field. Electrothermal fluid flow is an electrohydrodynamic effect that is caused by the action of a body force produced by a nonuniform electric field acting on a medium with spatially inhomogeneous electrical properties (permittivity and conductivity).13 The latter can be produced by local ohmic heating and subsequent development of temperature gradients. Being a direct function of electrical conductivity, the phenomenon has been shown to be particularly intense inside aqueous media of high electrical conductivity.14 The important role that electrohydrodynamic effects can play toward enhancing the manipulation, collection, and trapping of bioparticles in microelectrode chips has been demonstrated by Hoettges et al.,15 Wu et al.,16 Zhou et al.,17 and Wong et al.18 An experimental/numerical investigation of the effects of operating voltage, frequency, and medium conductivity on ac electrohydrodynamic effects and their influence on polymeric spheres or yeast cells in dilute suspensions inside a microelectrode chamber was provided by Bhatt et al.19 Moreover, reports by Mu¨ller et al.20 and Green et al.21 show that the presence of electrohydrodynamic effects can radically alter the observed collection patterns of polymeric sub-micrometer spheres in microelectrode arrays. By successfully combining dielectrophoresis and electrohydro(13) Ramos, A.; Morgan, H.; Green, N. G.; Castellanos, A. AC Electrokinetics: A Review of Forces in Microelectrode Structures. J. Phys. D: Appl. Phys. 1998, 31, 2338-2353. (14) Morgan, H.; Green, N. G. AC Electrokinetics Colloids and Nanoparticles; Research Studies Press Ltd.: Baldock, U.K., 2003. (15) Hoettges, K. F.; Hughes, M. P.; Cotton, A.; Hopkins, N. A. E.; McDonnell, M. B. Optimizing Particle Collection for Enhanced Surface-Based Biosensors. IEEE Eng. Med. Biol. Mag. 2003, 22, 68-74. (16) Wu, J.; Ben, Y.; Battigelli, D.; Chang, H.-C. Long-Range Electroosmotic Trapping and Detection of Bioparticles. Ind. Eng. Chem. Res. 2005, 44, 28152822. (17) Zhou, H.; White, L. R.; Tilton, R. D. Lateral Separation of Colloids or Cells by Dielectrophoresis Augmented by AC Electroosmosis. J. Colloid Interface Sci. 2005, 285, 179-191. (18) Wong, P. K.; Chen, C.-Y.; Wang, T.-H.; Ho, C.-M. Electrokinetic Bioprocessor for Concentrating Cells and Molecules. Anal. Chem. 2004, 76, 69086914. (19) Bhatt, K. H.; Grego, S.; Velev, O. D. An AC Electrokinetic Technique for Collection and Concentration of Particles and Cells on Patterned Electrodes. Langmuir 2005, 21, 6603-6612. (20) Mu¨ller, T.; Gerardino, A.; Schnelle, T.; Shirley, S. G.; Bordoni, F.; De Gasperis, G.; Leoni, R.; Fuhr, G. Trapping of Micrometer and Sub-micrometer Particles by High-Frequency Electric Fields and Hydrodynamic Forces. J. Phys. D: Appl. Phys. 1996, 29, 340-349. (21) Green, N. G.; Ramos, A.; Morgan, H. AC Electrokinetics: A Survey of Sub-micron Particle Dynamics. J. Phys. D: Appl. Phys. 2000, 33, 632-641.
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dynamic effects, Green and Morgan demonstrated differential separation of mixtures of sub-micrometer-sized spheres.22 Finally, a recent study by Sigurdson et al.23 showed that electrothermally driven fluid flow in microelectrode systems can cause intense mixing effects inside media of physiological ionic strength and lead to a significant enhancement of the binding kinetics in diffusion-limited, surface-based immunoassays. Their numerical and experimental results showed that relatively modest values of applied voltage (7 Vrms) can cause electrothermally driven fluid velocities on the order of 100 µm s-1 at an ac frequency of 200 kHz. The study reported in this paper investigates the roles of DEP and electrothermally induced fluid flow in the capture of viruses at surfaces. We perform experimental measurements of the capture of viruses at surfaces from media with high ionic strength and interpret these results within theoretical frameworks that consider the role of DEP and electrothermally induced fluid flow. We conclude that our experimental observations can be explained by the simultaneous action of dielectrophoresis and electrothermally induced fluid flow. II. Materials and Methods Microelectrodes. Nonuniform ac electric fields were generated by sets of planar gold microelectrodes fabricated on the surfaces of oxidized silicon substrates (SiO2 thickness: 500 nm). The overall dimensions of each microelectrode chip were 1.5 × 1.5 cm2. The chips were fabricated by using photolithography and metal evaporation (gold deposition). The adhesion of the gold electrodes (thickness: ∼100 nm) onto the substrate was enhanced by the deposition of a thin layer (20 nm) of titanium between the gold and silicon oxide. The gap between opposite electrodes was l ) 2 µm. Power to the microelectrodes was supplied by a 20 mW power amplifier (Mini-Circuits, model ZHL-32A), connected in series to a signal generator (BK Precision, model 2005A). The microelectrodes were connected to the source in an alternating fashion (180° phase difference between adjacent electrodes), and the (peak-to-peak) value of the applied voltage (Vptp ) 8 V) across the electrodes was monitored with an oscilloscope (Leader, model LBO-520). The ac frequency of 1 MHz was used so as to prevent electrochemical reactions due to capacitive or Faradaic charging on the microelectrodes. It was observed that, under the experimental conditions of 8 Vptp, medium conductivity of 880 mS m-1, and electrode separation of 2 µm, the application of any frequency lower than 900 kHz led to the formation of bubbles and to severe electrode damage (selection of a smaller applied potential value, e.g., 2 Vptp, permitted the use of lower frequencies but did not result in measurable virus capture). Virus and Suspending Media. Vesicular stomatitis virus-Indiana (VSV) was obtained from the American Type Culture Collection (ATCC, Chantilly, VA) and was prepared using procedures published previously.4 These procedures led to stock suspensions of VSV concentrations of 108 infectious particles per milliliter (denoted as PFU/mL, plaque-forming units per milliliter). Suspensions of VSV were diluted from freshly thawed aliquots of VSV stock in TSE (10 mM Tris-Cl, 0.1 M NaCl, and 1 mM EDTA) at pH ) 8.0. The conductivity of the stock suspension (σM ) 880 mS m-1) was measured at room temperature with a conductivity meter. Sample Handling and Imaging. All experiments were carried out at room temperature (21 °C) under biosafety level two conditions. All work involving the suspended virus was conducted in a Class II biosafety cabinet. The virus suspensions were used immediately after dilution. The experiments were performed on a custom-designed stage that supported the microelectrode chips and provided connections to the electrical source. Suspensions of VSV (8 µL) were dispensed directly onto microelectrodes using a micropipet. (22) Green, N. G.; Morgan, H. Separation of Submicrometer Particles Using a Combination of Dielectrophoretic and Electrohydrodynamic Forces. J. Phys. D: Appl. Phys. 1998, 31, L25-L30. (23) Sigurdson, M.; Wang, D.; Meinhart, C. D. Electrothermal Stirring of Heterogeneous Immunoassays. Lab Chip 2005, 5, 1366-1373.
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Figure 1. Fluorescence images showing dielectrophoretic sampling of the virus from suspensions at various concentrations in TSE buffer (σM ) 880 mS m-1). The virus capture patterns are consistent with negative dielectrophoresis. Concentrations (PFU/mL): (a) 107 control sample, (b) 107, (c) 106, and (d) 105. Experimental conditions: f ) 1 MHz, Vptp ) 8 V, tDEP ) 2 min. Prior to each experiment, the microelectrode surface was coated with a (positively charged) layer of poly-L-lysine to electrostatically retain the dielectrophoretically captured virus during sample postprocessing (immunofluorescence assay and imaging, see below). Briefly, a small drop of aqueous 0.1% poly-L-lysine (Ted Pella Inc., Redding, CA) was dispensed onto the microelectrodes, and adsorption was allowed to take place for 30 min at room temperature in a water-saturated atmosphere. Excess poly-L-lysine was removed from the electrodes by rinsing with a phosphate-buffered saline (PBS) solution and deionized (DI) water, and the microelectrodes were then left to dry under ambient conditions. Observations of the DEP-induced virus collection patterns on the microelectrodes were made under a fluorescent microscope coupled to a CCD camera. First, the samples were incubated with drops of rabbit anti-VSV IgG (150-200 nM, affinity purified, Sigma, St. Louis, MO) for 2 h. The samples were then rinsed with TSE buffer and incubated in solutions of bovine serum albumin (IgG-free, 1 mg/mL, Jackson ImmunoResearch Laboratories, West Grove, PA) for 1 h. This incubation step was necessary to prevent nonspecific adsorption of the fluorescently labeled antibody (next step), especially to areas of electrode damage. The samples were then rinsed with TSE buffer and incubated with drops of fluorescently labeled goat anti-rabbit IgG (Cy3-conjugated IgG, 30-40 nM; Sigma, St. Louis, MO) for 1 h. All incubation steps took place at room temperature in a water-saturated environment.
III. Experimental Results Virus Capture in Physiological Ionic Strength Media. The hypothesis that nonuniform electric fields can be used to rapidly capture virus particles from physiological solutions onto surfaces was tested in a series of experiments performed at virus concentrations ranging between 107 and 104 PFU/mL in physiological (TSE) buffer (σM ) 880 mS m-1). The experimental results reported in this paper were obtained after exposure of the virus samples for t ) 2 min to nonuniform electric fields created by planar quadrupolar microelectrodes with opposing electrode tips separated by a distance of l ) 2 µm. The applied potential difference and frequency used were V ) 8 V (peak-to-peak) and f ) 1 MHz, respectively. The results from these experiments are shown in Figure 1 as fluorescence images of the immunostained virus collected on the microelectrode surface. Figure 1a presents a control sample, i.e., without application of the external electric field. Inspection
Docoslis et al.
Figure 2. Fluorescence images showing collection of the virus from suspensions in TSE buffer diluted with DI water. The corresponding concentrations (PFU/mL) and dilution ratios are as follows: (a) 107 and 1:10, (b) 106 and 1:100, (c) 105 and 1:1000, and (d) 104 and 1:104. The virus is shown to be collected by positive dielectrophoresis at the edges of the electrodes. Higher concentration is observed at the electrode tips, where the field strength is at its maximum. At 104 PFU/mL (part d) it appears that only virus aggregates are collected at the electrodes. Experimental conditions: f ) 1 MHz, Vptp ) 8 V, tDEP ) 2 min.
of this image reveals that passive diffusion of the virus from solutions containing a virus concentration of 107 PFU/mL does not generate a measurable fluorescent signal within 2 min. Significant virus collection on the surfaces, however, is observed when the ac electric field is applied across the microelectrodes. The capture patterns obtained at virus concentrations between 107 and 105 PFU/mL are shown in Figure 1b-d, respectively. Inspection of these images reveals that the spatial distribution of the surface-captured virus is essentially independent of the suspension concentration. Specifically, it is observed that the viral particles are attracted to and captured in the center of the microelectrode array and, to a lesser degree, midway in the gap between adjacent electrodes. Inspection of Figure 1 also shows that the fluorescence intensity of the captured virus decreases dramatically with the virus titer in the sample. At a concentration of 105 PFU/mL (Figure 1d), only aggregates of virus appear to collect on the electrodes. The weak signal that is seen at the electrode edges in Figure 1d is attributed to nonspecific adsorption of the fluorescently labeled secondary antibody. At even lower concentrations (104 PFU/mL; results not shown), the virus is not measurably captured under the conditions of these experiments. Comparison with Virus Capture at Lower Ionic Strength. To examine the effect of medium ionic strength on the acquired collection patterns of the virus and relative signal intensity, the experiments described above were repeated using virus suspensions of the same concentration but of lower ionic strength. The latter was achieved by direct dilution of the original virus stock (880 mS m-1) with DI water. Specifically, experiments were performed with a number of virus suspensions ranging in conductivity (dilution) from 88.00 (1:10) to 0.088 (1:104) mS m-1. The results from these experiments are shown in Figure 2. The virus collection patterns observed in these experiments are in striking contrast to those seen in Figure 1 (corresponding to physiological ionic strength). In Figure 2, the virus is seen to collect at the tips (primary collection areas) and edges of the microelectrodes and is largely absent from the center of the microelectrode array. Similar to Figure 1, the intensity of the
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fluorescent signal can be observed in Figure 2 to be a function of virus concentration in the bulk; however, the amount of virus collected does not appear to decay in Figure 2 as quickly with the bulk concentration of virus as in Figure 1, thus allowing distinct patterns to be observed in Figure 2 at concentrations as low as 105 PFU/mL. It is interesting to note that the result in Figure 2c corresponds to the detection of only 800 PFU from the 8 µL droplet of virus used in the experiment.
IV. Discussion In the sections below, we compare the experimental results reported above to the predicted influences of DEP and electrothermally induced fluid motion in an attempt to identify the role of each phenomenon in the virus collection. We begin by describing the dependence of each mechanism on key experimental parameters, and then we compare the theoretical relationships between those parameters and the experimental observations. We also examine the relative influence of dielectrophoresis and electrothermal fluid motion by presenting order-of-magnitude calculations of the corresponding time scales required for virus transport as a function of medium ionic strength. Finally, we conclude our discussion by providing some evidence of a synergistic role for the two mechanisms through real-time observations of the motion of tracer particles (fluorescent beads) inside a physiological buffer. Presentation of the Mechanisms Involved in Virus Capture. While dielectrophoresis exerts a direct force on the virus, electrothermal fluid flow influences virus transport by means of viscous drag forces. Both these effects depend not only on the electric field characteristics (intensity and nonuniformity) but also on the electrical properties (conductivity and permittivity) of the medium.13 In the presentation of the two mechanisms below, we first consider dielectrophoresis and then electrothermal fluid motion. (a) Dielectrophoresis. Dielectrophoresis (DEP) of particles is an electrokinetic phenomenon that is brought about by induced polarization effects inside spatially nonuniform electric fields. Particle polarization inside a nonuniform electric field gives rise to a dipole moment and, hence, to a nonzero net force (termed “dielectrophoretic force”, FDEP). The magnitude of FDEP acting on a polarizable spherical particle (e.g., a virus) inside an ac electric field can be calculated from the following equation:24
〈FDEP〉 )
2πr3pM
Re[K/e ]∇|E Brms|2
(1)
where 〈F BDEP〉 is the time-averaged force, rp is the radius of the polarizable particle, M is the real part of the dielectric permittivity of the suspending medium, B Erms is the root-mean-square value of the electric field intensity, and Re[K/e ] is the real part of the effective polarizability (also known as the Clausius-Mossotti factor):
K/e )
/p - /M /p + 2/M
(2)
where /p () p + σp/jω) and /M () M + σM/jω) are the complex permittivities and σp and σM are the conductivities of the particle and the suspension media, respectively, ω is the angular frequency () 2πf) of the alternating electric field, and j ) (-1)1/2. The numerical sign of FDEP depends on the value of the effective polarizability (-0.5 e Re[K/e ] e 1.0), which is a function of the (24) Jones, T. B. Electromechanics of Particles; Cambridge University Press: New York, 1995.
dielectric properties of the particles and suspension medium, as well as the applied ac frequency. Positive values of effective polarizability give rise to “positive” dielectrophoresis, which causes transportation of the particles to regions of electric field intensity maxima (typically the edges of the microelectrodes). The opposite phenomenon (Re[K/e ] < 0) is termed “negative” dielectrophoresis and directs particles to regions corresponding to local electric field intensity minima (e.g., the center of the microelectrode array or away from the electrode edges). (b) Electrothermal Fluid Flow. The application of an electrical potential difference of Vptp ) 8 V across electrodes with a separation of l ) 2 µm inside an electrolytic solution of σM ) 880 mS m-1 causes significant local ohmic heating of the medium. For the present case, the volumetric heat generation [W ) σM(Vrms/l )2] is of the order of 1012 W m-3. Dimensional analysis of the heat balance equation can provide an estimate of the resulting temperature rise (∆T) under the aforementioned conditions. Assuming that heat dissipation in the electrolyte takes place mainly through heat conduction, a maximum value for the expected temperature rise around the microelectrodes can be calculated from13
σMV2rms ∆T = κ
(3)
where κ is the thermal conductivity of the medium. For water, κ ) 0.58 J m-1 s-1 K-1; therefore, a local temperature rise of about ∆T ) 12 °C is expected to occur. These local temperature gradients are responsible for spatial variations in the (temperature-dependent) electrical conductivity and permittivity of the medium, which, under the influence of an electric field, bring about an electrothermally induced body force on the medium (fluid streaming). In the present case (σM ) 880 mS m-1), the charge relaxation frequency of the liquid13
( )
1 ∂σM σM ∂T σM 2 fC ≈ 2πM 1 ∂M M ∂T
|
|
0.5
≈ 600 MHz
(4)
is much higher than the operating ac frequency (f ) 1 MHz); therefore, the electrothermal effects are generated by conductivity gradients, i.e., by Coulomb forces on the medium.13 Here, the quantities (1/σM)(∂σM/∂T) and (1/M)(∂M/∂T) are approximately constant and taken to be equal to 2 × 10-2 K-1 and -4 × 10-3 K-1, respectively.25,26 Virus Capture inside Media of Physiological Ionic Strength. As mentioned above, the mode of dielectrophoresis (positive vs negative) that a viral particle will exhibit while suspended in a medium can be predicted though evaluation of the parameter Re[K/e ]. In the present case, Re[K/e ] is calculated by approximating the virus with a single-shelled spherical particle of radius rp,eff composed of a dielectrically uniform interior (conductivity σint, relative permittivity int) and a thin, electrically insulating shell with thickness d and surface conductance Ks.27 The precise dimensions of VSV are reported elsewhere.28,29 The (25) Lide, D. R. CRC Handbook of Chemistry and Physics, 81st ed.; CRC Press: London, U.K., 2001. (26) Kaatze, U. Complex permittivity of water as a function of frequency and temperature. J. Chem. Eng. Data 1989, 34, 371-374. (27) Turcu, I.; Lucaciu, C. M. Dielectrophoresis: A Spherical Shell Model. J. Phys. A: Math. Gen. 1989, 22, 985-993. (28) Nakai, T.; Howatson, A. F. The Fine Structure of Vesicular Stomatitis Virus. Virology 1968, 35, 268-281.
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Table 1. Values of the Simulation Parameters Used for the Calculation of Re[K/e ] virus type VSV
rp,eff (nm)
d (nm)
σint (S m-1)
int/0
ζ-potential (mV)
65
7
0.1
70
-100
membrane conductivity, σm, is calculated from30
σm )
2Ks rp,eff
(5)
where Ks ) Kis + Kds , with Kis and Kds being the conductances of the stern and diffuse layers, respectively.31 The inclusion of surface conductance effects in the calculations is justified by the fact that the applied ac frequency used in the experiments (1 MHz) is significantly lower than the high-frequency dielectric dispersion limit, i.e., the frequency beyond which double layer effects can no longer influence the particle dielectrophoretic response. As suggested by O’Brien,32 for particles with rpκ . 1 (where rp corresponds to the particle radius and 1/κ corresponds to the Debye length of the double layer surrounding the particle), the high-frequency limit of colloidal dielectric dispersion is of the order of κ2D (where D is the diffusivity of ions in the double layer, taken as ∼10-9 m2 s-1),31 which, in the present case (σM ) 880 mS m-1, 1/κ ≈ 3 nm), corresponds to a frequency >100 MHz. The values of the dielectric parameters for VSV (see Table 1) are assumed to be approximately equal to those reported elsewhere for a similar, i.e., mammalian and enveloped, virus.33 The calculation of membrane conductance was performed according to the method described by Hughes.31 The values of the ionic mobilities were taken as equal to those corresponding to a symmetric electrolyte (KCl), and a ζ-potential value equal to 100 mV was assumed for the virus.31 The variation of the polarizability factor with respect to frequency is shown in Figure 3 for media conductivities in the range of interest. The predicted dielectrophoretic responses (Re[ K/e ] vs f) are found to be in qualitative agreement with other observations reported in the literature.27,31,33 As can be seen in Figure 3, the principal effect of ionic strength lies in the allowable mode(s) of virus dielectrophoresis. Specifically, the use of a suspending medium of high ionic strength, such as TSE, permits only negative virus dielectrophoresis to occur over the entire range of ac frequencies, a limitation that is primarily attributed to the fact that the buffer conductivity (ionic strength) is higher than the effective conductivity of the virus (σM > σint + σm ) σp,eff; cf. Table 1). In the present case, the use of planar quadrupolar electrodes allows the generation of a local electric field intensity minimum situated in the center of the array, thereby creating a distinct location for the collection of viral particles under conditions of negative dielectrophoresis. This local electric field minimum is also confirmed by numerical simulations of the electric field gradient (∇|E Brms|2) generated by microelectrodes with characteristics that closely match those used in our experiments. The simulations were performed with COMSOL (29) Bradish, C. J.; Kirkham, J. B. Morphology of Vesicular Stomatitis Virus (Indiana C) Derived from Chick Embryos or Cultures of BHK21/13 Cells. J. Gen. Microbiol. 1966, 44, 359-371. (30) Arnold, W. M.; Zimmermann, U. Electro-rotation: Development of a Technique for Dielectric Measurements on Individual Cells and Particles. J. Electrost. 1988, 21, 151-191. (31) Hughes, M. P. Nanoelectromechanics in Engineering and Biology; CRC Press: Boca Raton, FL, 2003. (32) O’Brien, R. W. The High-frequency Dielectric Dispersion of a Colloid. J. Colloid Interface Sci. 1986, 113, 81-93. (33) Hughes, M. P.; Morgan, H.; Rixon, F. J.; Burt, J. P. H.; Pethig, R. Manipulation of Herpes Simplex Virus Type 1 by Dielectrophoresis. Biochim. Biophys. Acta 1998, 1425, 119-126.
Figure 3. Plot of the polarizability factor, Re[Ke] vs ac frequency (f) for various medium conductivities used in the experiments. The original medium conductivity (“TSE buffer”) was 880 mS m-1. The other curves correspond to suspending media prepared by the dilution of TSE buffer with DI water (see Table 1 for other simulation parameters).
Figure 4. Computer-simulated profile of the gradient of the electric field squared (3E2) at x0 ) 100 nm, created by a set of quadrupolar electrodes. Only the tips of the four electrodes are shown (electrode separation, l ) 2 µm across; Vpp ) 8 V). The scale bar indicates local 3E2-values (in V2 m-3).
Multiphysics (Cambridge, MA). As shown in Figure 4, the calculated electric field gradient (and intensity) is higher at the edges of the electrodes, which form the areas of attraction for particles subject to positive dielectrophoresis (cf. Figure 2). Away from the electrodes, the field becomes progressively weaker, forming a local minimum at the center of the electrode array. The latter represents the expected collection area (also referred to as “dielectrophoretic trap”) of particles driven by negative dielectrophoresis, which has been shown experimentally to occur in the case of the virus suspended in media of physiological ionic strength (cf. Figure 1). The accumulation of the virus in this area (see below for details) is more likely a synergistic effect, caused by the simultaneous action of dielectrophoresis (virus trapping) and electrothermally induced medium flow (virus transport from the bulk). It should be noted that the electric field profile shown in Figure 4 is independent of the applied ac frequency. These
Use of ac Electric Fields for Virus Transport
theoretical results offer a likely explanation for the experimentally observed virus collection patterns in TSE and also show that the same dielectrophoretic response should be expected at other ac frequencies. Effect of Lowering Ionic Strength on Virus Capture. When TSE is diluted with DI water, the aforementioned condition (σM > σp,eff) can be inverted, thus allowing the numerical sign of the polarizability factor to become a function of the selected frequency. The theoretical results depicted in Figure 3 indicate that a minimum dilution ratio of TSE with DI water around 1:10 is required to lower the conductivity of the suspending medium to below that of the virus interior and, thus, make positive dielectrophoresis possible. At much higher dilutions (e.g., 1:100), positive dielectrophoresis occurs at any frequency up to ∼100 MHz. These findings are also in agreement with the experimental results shown in Figure 2, demonstrating virus collection under positive DEP in all cases where TSE was diluted 10-fold or more with water. We also note that the similar fluorescence intensities seen in each part of Figure 2b-d indicate that the numbers of viral particles captured by dielectrophoresis are not greatly influenced by the concentration of the virus in the suspension. A possible explanation of this phenomenon can be found in Figure 3, where the value of Re[K/e ] (or, equivalently, FDEP) is seen to increase as the ionic strength of the suspending medium decreases through sample dilution with DI water. In other words, the effect of diminishing virus concentration in the bulk due to dilutions with water is moderated by a concomitant increase in FDEP (cf. responses 1:10 through 1:103). The observed responses, however, can be better explained if one considers the effect of electrothermal fluid flow, as discussed below. It is worth mentioning here that the simulations were also performed using a model that did not account for surface conductance effects. For all ionic strengths considered, the effective polarizability of the virus was found to vary with frequency in a manner similar to that shown in Figure 3, although an increase (less than 2-fold) in the predicted crossover frequencies (Re[K/e ] ) 0) was observed. A marked difference in the predictions given by the two models, however, appeared in the case of the virus suspended inside a medium with a conductivity of 88 mS m-1 (1:10 dilution with DI water). As seen in Figure 3, the predicted dielectrophoretic response of the virus suspended within a medium with a 1:10 dilution lies in the borderline between positive and negative dielectrophoresis. When the surface conductance was omitted in the simulations, the results suggested negative dielectrophoresis on the virus (Re[K/e ] ≈ -0.05) for the lower frequency window (
