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Naturwissenschaften 83, 172-176 (1996) © Springer-Verlag 1996

Trapping of Viruses in High-Frequency Electric Field Cages T. Schnelle, T. MOiler, S. Fiedler, S.G. Shirley, K. Ludwig, A. Herrmann, G. Fuhr

Humboldt-Universit / i t zu Berlin, Insti tut for Biologic, D-10115 Berlin, Germany

B. Wagner

Fraunhofer-Inst i tut far Siliziumtechnologie (ISiT), D-14199 Berlin, Germany

U. Z immermann

Universit~t Wtirzburg, Lehrstuhl for Biotechnologie, D-97074 Wtirzburg, Germany

fCM-- gp- ~ with f f = a + i c o e . (2)

In nonrotat ing electric fields, the time- averaged force is propor t ional to the real part of the Clausius-Mosott i factor and to the gradient of the mean square value of the electric field strength (/~rms)" At high frequencies this yields:

iO= 2z~r3el e1-ep ~ ; ~ 2 • (3) 2 e t + ep rms

In aqueous solutions and at high frequencies, particles of lower effective permitt ivi ty are repelled from the electrodes (negative dielectrophoresis) and focused into regions of low field

High-frequency electric field cages can stably trap cells and microparticles in aqueous media [1, 2]. Such cages can be made by semiconductor fabricat ion techniques and are not to be confused with electromagnetic field devices used for t rapping atomic and elementary particles [3]. The behavior of various dielectric microparticles in uniform and nonuniform a.c. electric fields was investigated by Pohl in the 1970s and discussed in his monograph [4]. The mot ion of in- dividual cells in nonuniform a.c. fields, termed dielectrophoresis (DP), was studied in subsequent decades [5]. The force, F, acting on a spherical dielectric particle of radius, r, in a time- periodic electric field, f , can be ex- pressed as a dipole approximat ion by

F(t) = (rh (t)" ¢ ) f ( t ) , (1)

with the induced dipole moment de- fined as rn (t) = 4 ~zelr3fcMt~(t). The Clausius-Mosott i factor fcM depends on the specific conductivity (a) and permitt ivity (e, absolute value) of the liquid and particle (index l and p), as well as on the radian frequency (co) of the applied field. For a homo- geneous particle it is:

J a

Fig. 1. The principle of virus collection in high-frequency electric fields, a) Collection of viruses (1) in a field funnel (2) created by four planar electrodes (3). Shown is a surface of constant vertical force acting on virus particles modeled as dielectric spheres. The interplay of sedimentation, dielectrophoretie, and hydrodynamic forces stabilizes the levitated virus aggregate. Hydrodynamic forces are indicated by arrows, b) Modeling of viruses being trapped in an octopole cage. Liquid, streaming through a microchannel, carries viruses from left to right. As only the electrodes 1, 1 ', 2, and 2' are driven with high-frequency signals, a force barrier is developed, collecting the viruses. The polarization force increases with the volume of the aggregate, c) After aggregation, all electrodes (1-4,1 ' - 4 ') are energized. A cushion-shaped aggregate is formed and trapped. Simulations show that even a single particle of 10 nm diameter should typically, remain for minutes within the

172 Naturwissenschaften 83 (1996) © Springer-Verlag 1996

strength. This allows low-stress mani- pulation of biological objects, and ad- vantage over optical laser tweezers [6, 7]. Additionally, at high frequencies, the induced membrane potential is only a few mV [1], and electrolytic processes are suppressed.

A problem in applying large electric fields in conductive solutions is the removal of Ohmic heat to prevent severe temperature rises, which would damage biological materials. Tempera- ture rise can, however, be limited by re- ducing the size (i.e., the ratio of heated

b

volume to surface) of the system. Therefore, we use ultramicroelectrode structures allowing the application of some M V m -1 with temperature increases of the order of 1 K (see also [81). Planar, quadrupole, microelectrode assemblies combine polarization forces with sedimentation and hydrodynamic forces to entrap suspended patMes in "field funnels" (Fig. l a). (For pre- liminary results of virus trapping with such structures see [91.) Three-dimensional octopole arrangements of micro- electrodes (Fig. 1 b, c) allow the creation of electric field cages, which entrap particles by polarization forces only. Particles can also be confined by two ring-shaped electrodes. In the center of an octopole cage the electric field has a local minimum; between two rings a saddle point is created (Fig. 2a) allowing particle enrichment on the top and bot tom plates (Fig. 2 b, c). For suspended submicron particles (such as viruses), Brownian motion becomes significant. Polarization forces scale with the third power of the particle radius, whereas thermal motions vary inversely with it. According to earlier estimations [4], particles with radii of less than 500 nm could not be moved or trapped in field cages. How- ever, miniaturized cages allow the application of larger fields, due to an in- crease in the breakdown strength of aqueous solutions, and fields which are more inhomogeneous. Both effects in- crease polarization forces. In addition, the particle radius should include any surface layers; these become important for submicron particles. A sufficient criterion for trapping of single particles is that the potential barrier of the deter- ministic force exceeds the thermal ener- gy (kT) by at least tenfold (see, e.g., [6]). For low-permittivity particles, this gives a critical radius above which long- term trapping reliably occurs of:

C

Fig. 1 (continued) f cage. Based on: electrode spacing of 500 nm; 10-MHz four-phase rotating sinusoidal drive of 12.7V; virus permittivity 3, conductivity 0.8mSm-l; liquid permittivity 80, conductivity 3 mS m -~ . Theoretically, cages with 200-nm electrode spacing (which can be fabricated using e- beam lithography) should trap even smaller particles

3 2 refit ~ ~/10 kT/neH2 o OErm s . (4)

The value of the barrier (0E2ms) depends not only on the applied field strength but also on the electrode ge- ometry and arrangement. To estimate the smallest particle that can be stably trapped, OErZms i s assumed to be ten times smaller than the applied value. Then, at room temperature and at the

Naturwissenschaften 83 (1996) © Springer-Verlag 1996 173

maximum field strength that has so far been applied to ultramicroelectrodes (28 MVrm s m -1 [10]), the critical diameter would be about 27 nm. If confine- ment of particles is required only for a

limited experimental time, this value can be even smaller. For real three-dimensional electrode configurations, the mean escape time has to be determined numerically, e.g.,

by solving the corresponding Langevin equation. We have found that a 10-nm particle will typically remain for some minutes in a cage at an applied field strength of about 18 MVrm sm -~ (see


Fig. 1 c). I t is to be expec ted t h a t even

single v i ruses cou ld be s tab ly t r apped .

T h e m a i n p r o b l e m will n o t be the crea-

t i on o f h igh -ene rgy bar r ie rs , b u t the in-

t r o d u c t i o n o f a s ingle par t i c le in to the

cage. It m i g h t , therefore , be a d v a n t a -

geous to c o m b i n e laser tweezers w i th

d i e l ec t rophore t i c cages, especia l ly s ince

the cr i t ical r ad ius is o f the s ame o rde r

o f m a g n i t u d e for b o t h m e t h o d s , a n d

t r a n s p a r e n t e lec t rodes (e.g., i n d i u m t in

oxide) c an be used. T h e a d v a n t a g e o f

ou r cages is t h a t par t ic les are focused to

f ie ld m i n i m a (latex b e a d s o f less t h a n

100 n m in d i a m e t e r c an be t r a p p e d wi th

laser tweezers for some seconds only,

because o f l a se r - induced par t i c le

d a m a g e [6]).

Fig. 2. Trapping of particles in a two-electrode structure. Two ring electrodes produced by laser ablation of platinum on glass wafers were mounted face to face at a separation of the in- ner ring diameter and driven with a.c. electric fields. Applied field strength was 0.3 MVrm s m -~. a) Principle of particle collection between two ring electrodes. The contour plot of the mean square value of the electric field between two ring electrodes (determined using a finite-difference method) is combined with the dielectrophoretic force field (arrows). Due to the rotational symmetry, only the field in a plane through the centers of the two electrodes has to be considered. Near the electrodes (dark regions) both the electric field (heating) and the dielectrophoretic force is large. The arrow length is proportional to the magnitude of the force. For the sake of clarity, only arrows smaller than a limit were drawn. With no additional forces, particles showing negative dielectrophoresis move on trajectories perpendicular to the contour lines into lighter regions (lower field strength) and are either collected at the top and bottom plates or are repelled from the interelectrode region to the bulk solution (left and right), b,c) Trapping of latex beads (900 nm diameter) from 1 °70 suspension in PBS (conductivity 1.4 S m -z) at the cover electrode (b) and at the bottom (c). d) Influenza virus particles (3 x 101~ ml -~) in phosphate-buffered 300 mOsm sorbitol, fluorescently labeled with Clg rhodamine (Molecular Probes, Inc., USA), trapped in the top ring plane, e) Latex beads, 14rim in diameter (FluoSpheres, Molecular Probes, Inc., USA) concentrated from a 2% aqueous suspension. In (b) - (d) electrodes were driven at 5 MHz and in (e) at 50 MHz a.c. Videoframes were reprocessed using the Leica Confocal Microscopy image-processing software (Leitz, GOttingen, Germany). Frames (d) and (e) show confined particles only at the top electrode plane

Also, once a few par t ic les have b e e n ac-

c u m u l a t e d , m u t u a l d ie lec t rophores i s

[11, 12] s h o u l d e n h a n c e a t t r a c t i o n o f

f u r t h e r par t ic les f r o m the s u r r o u n d i n g

m e d i u m , resu l t ing in aggregates . Ac-

co rd ing to [111, in h o m o g e n e o u s h igh-

f r equency electr ic fields, t he cr i t ical

r ad ius for a g g r e g a t i o n (pear l cha ins ) o f

l ow-pe rmi t t i v i t y par t ic les is f o u n d in

d ipole a p p r o x i m a t i o n to be: 3

Qggr -= 2.3 ]/kr/eH2oE~m s . (5)

• •

a b c d n

Ip

0 o Fig. 3. Time course of virus trapping, a - d) Sendai virus enrichment in two quadrupole traps (bar 25 ~tm). a) t = 0, b) t = 8 s, c) t = 12 s, d) t = 18 s. e) Magnified view of an octopole field cage (bar 10 ~tm). Two chips are mounted with a face-to-face spacing of 40 ~tm. The eight electrodes of each cage are at the corners of a cube. The electrodes of the lower plane are insulated by a l-gin polyimide layer except at their tips. f) Fluorescence image of a high-frequency cage 10 s after switching on the field (bar 20 ~tm). Viruses have collected and become trapped between the electrodes. Liquid streaming brings further viruses into the cage (light tails at top and bottom). After switching off the field, the clouds disappear within a few seconds. In (a ) - (d) and (f) the electrodes were driven with rectangular pulses from an HP 8116A generator at 1 MHz and J 1 Vpt p. The evolution of the fluorescence signal was recorded with a microscope-video system (Leica Metallux 3, LD 50 gm objective with a CCD Micro Camera CS 3130 in shutter mode, Tokyo Electronic Industry Co. Ltd.). The video processing was done with the software of the CLSM (Leica) and a video printer. Viruses (1 mg protein ml 1 [14]) were fluorescently labeled with 10 ~tM octadecylrhodamine B chloride (R 18, Molecular Probes) at room temperature for 30 min in the dark, centrifuged, washed, and resuspended in ice-cold phosphate-buffered 150 mM NaC1, then transferred to phosphate-buffered 300 mOsm sorbitol using a Sephadex G75 column. The final conductivity was about 74 mS m -1 and the final concentration was i mg protein ml 1 (2.5 x 10/2 viruses ml -z)

Naturwissenschaften 83 (1996) © Springer-Verlag 1996 175

Strictly, this applies only to homo- geneous fields; for real structures nu- merical treatments are necessary. The criterion for particle aggregation is more easily fulfilled than that for stable particle trapping [Eq. (3)], at least near the electrodes. This is due to the strong gradients in our structures. Particle aggregation probably has an enormous impact on trapping in our experiments. To collect Sendai (strain Z) and influenza (strain A / P R 8/34) viruses, we used electrode assemblies with dimensions typically between 1 and 20 gm, both field funnels (Fig. 3 a - d ) and field cages (Fig. 2d, 3 f). The activity of fluorescently labeled influenza viruses was shown by fusion with target membranes using a fluorescence dequenching assay [13]. According to quasielastic light scattering (Coulter particle sizer, model N4MD) of the particle suspension, the size distribution of the influenza viruses was bimodal. Approximately 95% of the fluorescently labeled viruses were 100-150 nm in diameter (single viruses and aggregates of less than four), the remaining were virus aggregates sized between 0.5 and 1 gm. There was no apparent difference in size distribution using phosphate-buffered 150 m M NaC1 or phosphate-buffered 300 mOsm sorbitol. This was con- firmed by electron microscopy. Large particle aggregates can easily be detect- ed optically. The pictures of virus trapping were obtained without the initial presence of large aggregates in the cage. Since even smaller particles can be enriched (14-nm latex beads, see Fig. 2e), it is likely that viruses can also be trapped from a mono-disperse solution. The formation of aggregates en- hances the trapping rate. Most of the viruses in the suspension could be trapped in the central part of the electrode structure within a few seconds, and large aggregates were formed, whose typical size was one third of the electrode gap. Because of dielectric dif- ferences, the best enrichment for dif- ferent viruses was found at slightly dif- ferent frequencies.

I f no additional forces are applied, only particles originally within the cage volume can be concentrated by an electric field. However due to local Ohmic heating, the liquid becomes inhomo~ geneous and can stream through the cage, enhancing particle collection. In- dividual particles can enter the cage by streaming but remain trapped following aggregation. Experimentally, small clouds develop as viruses are brought into the funnel or cage by streaming, and most of the particles in the suspension can be collected. Additionally, the dielectrophoretic force can be made asymmetric and/or anisotropic by special electrode geometries to enhance particle collection. Planar arrays of traveling-wave-driven, interdigitated electrodes should be capable of virus trapping by the utilization of electrohy- drodynamically induced vortices [8]. Enrichment of viruses should be a valuable tool in electron-microscopy- based studies of solutions with low virus concentration. The dielectric dif- ferences between viruses should enable their separation. A cascade-like structure of differently sized and/or driven cages could act as a fractionating mi- crodevice that could find application in diagnosis and other fields. Since single latex beads (diameter 1 - 3 gm) can be stably held in cages despite streaming velocities up to about 200 ~tm s -1, collection of specific viruses or macro- molecules from liquids could be done with the help of specific ligand- or an- tibody-coated latex spheres trapped in a cascade structure.

This work was supported by the Ger- man BMFT (Grant no. 03120260 A and 13MV03032 to G .E and 13MV0305 to U.Z.) and the DFG (He 1928 /1 -3 and SFB 312,D9,YE3 to A.H.). We are grateful to Prof. M . E G . Schmidt for the kind gift of Sendai viruses.

Received August 29 and December 13, 1995

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2. Schnelle, Th., Hagedorn, R., Fuhr, G., Fiedler, S., Miiller, T.: Biochim. Biophys. Acta 1157, 127 (t993); Fuhr, G., Arnold, W.M., Hagedorn, R., MiNer, T., Benecke, W., Wagner, B., Zimmermann, U.: ibid. 1108, 215 (1992)

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4. Pohl, H.A.: Dielectrophoresis. Cambridge Univ. Press 1978

5. Pauly, H., Schwan, H.P.: Biophys. J. 6, 621 (1966); Masuda, S., Washizu, M., Kawabata, I.: I. IEEE Trans. Ind. Appl. 24, 217 (1988); Kaler, K.V.I.S., Jones, T.B.: Biophys. J. 57, 173 (1990); Pethig, R., Huang, Y., Wang, X.-B., Burr, J.P.H.: J. Phys. D 24, 881 (1991); Asami, K., Yamaguchi, T.: Biophys. J. 63, 1493 (1992); Wang, X.-B., Huang, Y., Burt, LEA., Markx, G.H., Pethig, R.: J. Phys. D 26, 1278 (1993)

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9. Fuhr, G.: Proc. St. Andrews Meeting, Animal and Cell Abstracts C2.18, p. 77, St. Andrews 1995; Green, N., Morgan, H., Wilkinson, C.D.: ibid. Abstracts C2.20, p. 77; Wilkinson, C.D.: Pers. commun, to G. Fuhr, tabac mosaic viruses with a diameter of 300 nm can be enriched in a four- electrode chamber within 20 min

10. Mttller, T., Gerardino, A., Schnelle, Th., Shirley, S.G., Bordoni, E, Gasperis, G. De, Leoni, R., Fuhr, G.: J. Phys. D (in press)

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