- Email: [email protected]
Selective detection of viable bacteria using dielectrophoretic impedance measurement method
Journal of Electrostatics 57 (2003) 157–168
Selective detection of viable bacteria using dielectrophoretic impedance measurement method Junya Suehiro*, Ryo Hamada, Daisuke Noutomi, Masanori Shutou, Masanori Hara Department of Electrical and Electronic Systems Engineering, Graduate School of Information Science and Electrical Engineering, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan Received 16 April 2002; received in revised form 22 July 2002; accepted 2 August 2002
Abstract This paper describes a selective detection technique of viable bacteria based on dielectrophoresis and electrical impedance measurements. The authors have previously proposed a detection technique of biological particles called dielectrophoretic impedance measurement (DEPIM) method using positive dielectrophoretic force to capture biological cells in suspension onto an interdigitated microelectrode array. By combining antigenantibody reaction with the DEPIM, selective detection of a particular species of bacteria was demonstrated. In this present work, the authors demonstrated another selective DEPIM method utilizing cell viability dependency of dielectrophoretic force without introducing the antigen-antibody reaction. It was found that dielectrophoresis of heat-treated Escherichia coli showed strong dependency on viability when applied field frequency was as high as 1 MHz. As a result, viable bacteria could be exclusively collected by positive dielectrophoresis and selectively detected by the DEPIM technique from a suspension also containing heat-treated nonviable cells. On the other hand, nonviable bacteria obtained by UV irradiation showed little dielectrophoresis dependency on viability. According to a theoretical analysis of the dielectrophoretic force, it is suggested that heat treatment alters the dielectric properties of treated cells. In particular, a decrease in cytoplasmic conductivity, which might be caused by heat-induced perforation of cell membrane, was expected to considerably affect dielectrophoresis characteristics. Proposed selective DEPIM method was also applied to evaluation of heat sterilization effect on a real time basis. It was experimentally proved that DEPIM could evaluate viable cell number variation with heat treatment time in a considerably shorter time
*Corresponding author. Tel.: +81-92-642-3912; fax: +81-92-642-3964. E-mail address: [email protected] (J. Suehiro). 0304-3886/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 8 8 6 ( 0 2 ) 0 0 1 2 4 - 9
158
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
than conventional microbiological method based on cell incubation. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Dielectrophoresis; Impedance measurement; Bacteria detection; Viability; ‘‘DEPIM’’
1. Introduction Detection of microorganisms such as bacteria is important in a variety of fields such as bioscience research, medical diagnosis and hazard analysis in food industry. Conventional microbiological detection methods, such as a colony counting technique, based on cell incubation are well established and reliable. However, they are rather time consuming, requiring a few days and therefore not capable of fast diagnosis in case of emergency. The authors have previously proposed a new detection technique of biological cells by using dielectrophoresis (DEP) [1]. The technique called dielectrophoretic impedance measurement (DEPIM) method utilizes the positive dielectrophoretic force to capture suspended biological particles onto an interdigitated microelectrode array in the form of pearl-chains. Higher cell concentration result in faster development of the pearl-chains, which are electrically connected in parallel to the electrode gap and hence increase the conductance and the capacitance between the electrodes. By monitoring the temporal variation of the electrode impedance, it is possible to quantitatively evaluate the cell population according to a theoretical model of cell collection process. DEPIM can realize fast and simple bacteria inspection by using only electrical phenomena and instruments. A similar impedance technique for measuring dielectrophoretic collection of biological cells has been demonstrated by Milner et al. [2]. In practical microorganism inspection and identification, however, there are many cases in which a specific bacterium is to be detected according to the species or its physiological state. The authors have previously proposed a selective DEPIM technique, which utilized antigen-antibody reaction to realize selective detection of bacteria of a certain cell strain [3]. The antigen-antibody reaction was utilized in DEPIM measurements in two different ways. In the first method, antibody was added to the cell suspension after dielectrophoretic enrichment of bacteria in order to cause agglutination of the antibody-specific bacteria. The DEP force exerted on agglutinated bacteria, whose apparent size increased, became more dominant than hydrodynamic drag force in a continuous liquid flow. In the second method, antibody molecules were immobilized onto the microelectrode surfaces before the application of dielectrophoresis so that only antibody-specific bacteria would be bound to the immobilized antibody. These two methods provided the means whereby that specific bacteria could be selectively left between the electrode gap when the electric field was reduced after the preliminary DEP cell collection procedure. Selective DEPIM inspection without introducing immunoassay may also be possible if dielectric properties of wanted cell are so different from those of others that the target cell population can be selectively enriched by making use of the
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
159
positive DEP effect. Selective DEP handling has been realized for biological cells with different viability [4–7] and species [8,9]. These studies suggest that differences in the dielectric properties of cells result in DEP force variations that can be utilized for selective cell manipulation. In this work, selective DEPIM inspection of viable Escherichia coli (E. coli) from a mix of viable and nonviable bacteria was examined. In order to examine effects of the sterilization method on dielectrophoretic cell manipulation and selective DEPIM detection, nonviable bacteria were prepared by two different sterilization methods of heat treatment and UV irradiation. It was found that heat-treated bacteria exhibited a considerable change in the dielectric parameters as well as dielectrophoresis while UV based sterilization hardly affected those properties and hence the observed electrokinetic phenomenon. For the heat sterilization, real time diagnosis of viable cell population during heat treatment was realized by using the proposed selective DEPIM technique.
2. Materials and method 2.1. Cell preparation E. coli strain K12 bacteria were incubated on agar plates. Before each measurement, cells were harvested from agar and suspended in 0.1 M mannitol solution. After several washing by centrifugation, they were finally resuspended in 0.1 M manitol solution at desired concentrations as determined by a Neubauer haemacytometer. Unless otherwise stated, the electrical conductivity of suspension ss was adjusted to 0.2 mS/m. 2.2. Sterilization procedure Heat sterilization was carried out at 801C for 15 min, while UV sterilization was achieved by a 10 s exposure to UV light (254 nm central wavelength and 2.5 mW/cm2 power density). In both methods, a cell suspension of 100 ml was treated on a batch basis. Following the above sterilization treatments, 100 ml of suspension liquid was spread and incubated on agar plates for 48 h in order to examine the viability of the sterilized cell sample. 2.3. Electrodes Interdigitated microelectrode arrays of chrome were patterned on a glass substrate by photolithography technique. Two different electrode configurations were used. A smooth interdigitated electrode system was employed in all DEPIM experiments because this type of electrode configuration is suitable for accurate impedance measurement [1]. Each microelctrode strip had 50 mm width, 12 mm length and 5 mm clearance. The four strips formed three parallel gaps in which cells were trapped and formed pearl-chains by positive DEP. On the other hand, a castle-wall electrode
160
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
configuration [10] was preferred for visual observation of cell collection process by positive DEP. The castle-wall electrode was surrounded by a silicon rubber spacer to form a chamber in which cell suspension liquid of 200 ml was stored. 2.4. DEPIM equipment Details of DEPIM principle and apparatus had been described elsewhere [1]. Sinusoidal ac voltage was generated by a function generator (FG 110, Yokogawa, Japan) and applied to the microelectrode. Electrode impedance measurements were carried out using a DSP lock-in amplifier (Model 7280, Perkin Elmer Instruments, USA). The highest field frequency for DEPIM was restricted to 1 MHz due to the bandwidth limitation of the lock-in amplifier. The impedance measurement apparatus was controlled by a personal computer, which also served as a data logger and analyzer. 2.5. Experimental procedures DEPIM experiments were conducted using a smooth interdigitated electrode system, which was directly immersed into cell suspension liquid stored in a beaker. A magnetic stirrer continuously generated a circular flow in the beaker to enhance positive DEP cell trapping at the electrodes. Microscope observation of DEP process was performed using castle-wall electrodes on which a small chamber was constructed. Cell suspension liquid was introduced into the electrode chamber by a peristaltic pump at a flow rate of 0.9 ml/min. Experiments using sterilized bacteria were conducted in a few minutes following the sterilization procedures.
3. Results 3.1. Bacteria trapping process under positive DEP Photographs of the DEP collection of viable and heat-treated nonviable E. coli are shown in Fig. 1. The DEP collection observations were made at two different electric field frequencies of 100 kHz and 1 MHz. At 100 kHz, both viable and nonviable bacteria were trapped around the electrode corner due to positive DEP (Figs. 1a and b). On the other hand, only viable bacteria were trapped and nonviable cells were not collected by positive DEP at 1 MHz (Figs. 1c and d). These observation results suggest that positive DEP force exerted on the nonviable heat-treated bacteria is negligibly small at 1 MHz. Similar observations were also made on UV sterilized E. coli. In contrast to the heat sterilization case, both viable and nonviable bacteria were collected in the high field region under positive DEP at both 100 kHz and 1 MHz. 3.2. Effects of viability and sterilization method on DEPIM DEPIM experiments were conducted under the same conditions as the DEP trapping observations. Fig. 2 depicts temporal variation of electrode conductance
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
161
Fig. 1. DEP collection process of viable and heat-treated nonviable E. coli. An ac signal of amplitude 8 V peak–peak was applied to a castle-wall electrode. (a) Viable cells at 100 kHz frequency. (b) Nonviable cells at 100 KHz. (c) Viable cells at 1 MHz. Under those conditions, bacteria were trapped by positive DEP around the electrode corner where electric field strength becomes higher. (d) Nonviable cells at 1 MHz. No DEP trapping was observed.
increment measured with viable and heat sterilized E. coli at 107 cells/ml concentration. As explained in the authors’ previous work [1], the conductance increase is due to presence of bacteria that are trapped and enriched between the electrode gap under positive DEP. It was found that the conductance increase rate at t ¼ 0 was directly proportional to the cell population that was to be quantitatively evaluated by the DEPIM method. At 100 kHz frequency, the conductance increased with time in the same manner for both viable and nonviable bacteria (Fig. 2a). At a higher frequency of 1 MHz, however, the conductance change over time became less marked with nonviable heat-treated cells (Fig. 2b). DEPIM experiments were also conducted also on UV sterilized E. coli as shown in Fig. 3. The conductance increased with elapsed time and no measurable difference was found between viable and nonviable bacteria over the measurement frequency range from 100 kHz to 1 MHz. 3.3. DEPIM inspection of mix suspension of viable and nonviable bacteria From Figs. 1 and 3, it can be concluded that heat sterilized E. coli cannot be detected by DEPIM at 1 MHz because no positive DEP force is exerted on the
162
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
Fig. 2. DEPIM results measured with viable and heat sterilized nonviable E. coli at 107 cells/ml concentration. An ac signal of amplitude 3 V peak–peak was applied to a smooth interdigitated electrode. (a) At 100 kHz frequency, the conductance increased with time in the same manner for viable and nonviable bacteria. The conductance increase implies that a certain area of the electrode gap has been bridged by bacteria that has been trapped and enriched under positive DEP. (b) At 1 MHz, the conductance change became less remarkable with nonviable heat-treated cells.
Fig. 3. DEPIM results measured with viable and UV sterilized nonviable E. coli at 105 cells/ml concentration. An ac signal of amplitude 3 V peak–peak was applied to a smooth interdigitated electrode. The conductance increased with elapsed time and no remarkable difference was found between viable and nonviable bacteria independent of field frequency: (a) at 100 kHz frequency; (b) at 1 MHz frequency.
nonviable bacteria following heat treatment. If the viable cells can be selectively trapped and enriched from mixture of viable and heat-treated nonviable cells, it may be possible to selectively detect viable bacteria from the mixture by DEPIM. Fig. 4 shows DEPIM results of pure viable or heat sterilized nonviable cell suspension as well as their mixture. It was found that DEPIM results obtained with the mix
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
163
Fig. 4. DEPIM results of pure viable or heat sterilized nonviable cell suspension at 106 cells/ml as well as their mixture. An ac signal of amplitude 3 V peak–peak was applied to a smooth interdigitated electrode. Results obtained with the mix suspension almost agreed with those of pure viable cells. When viable cell concentration was reduced by half, the conductance increment measured with the mixture varied accordingly.
suspension almost agreed with those of pure viable cells. When viable cell concentration was reduced by half, the conductance increment measured with the mixture varied accordingly. This implies that conductance variation measured with the mixture is mainly caused by viable cell trapped under positive DEP. However, conductance increment of the mixture is always larger by 10% than that of pure viable cells. This may be attributed to mutual interaction between viable and nonviable cells. Viable cells, which move toward a high field region under positive DEP, may have higher chances to interact with a part of nonviable cells near the electrode gap. These nonviable cells may have direct dipole–dipole interaction [11] with enriched viable cells in the neighborhood. The direct interaction may attract nonviable cells to viable ones. As a result, a part of nonviable bacteria may be combined with viable ones and trapped in the electrode gap. In the DEPIM inspection of the mix suspension, these nonviable cells may contribute to the electrode conductance increase together with viable ones.
4. Discussion 4.1. Effects of sterilization method on dielectric properties of bacteria It has been reported that the DEP force exerted on biological cells is strongly influenced by their viability [4–7]. In general, viable cells undergo stronger positive
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
164
DEP than nonviable ones at field frequency over 1 MHz. In those literatures, nonviable cells were prepared only by heat sterilization and effects of the other sterilization methods such as UV, radioactive rays and chemicals have not been clarified yet. In this study, effects of two different sterilization protocols, heat and UV treatments, on DEP and DEPIM were investigated. Results obtained with heat sterilized bacteria agree approximately with those in previous reports. That is, positive DEP force exerted on heat-treated nonviable bacteria becomes small when the field frequency is increased from 100 kHz to 1 MHz. However, cell viability does not affect the frequency dependency of the DEP force when nonviable bacteria are prepared by UV radiation. The DEP force acting on a spherical particle of radius r suspended in a medium of permittivity es is given by [12] F DEP ¼ 2pr3 es Re½KðoÞrE 2 ;
ð1Þ
where E is the magnitude (RMS) of the applied field and Re½KðoÞ is the real component of the Clausius–Mossotti factor given by KðoÞ ¼
ep es ; ep þ 2es
ð2Þ
where ep and es are the complex permittivity of the particle and surrounding medium, respectively. For a real dielectric, the complex permittivity is defined as s ð3Þ e ¼ e j ; o pffiffiffiffiffiffiffi where j ¼ 1; e is the permittivity and s is the conductivity of the dielectric and o is the angular frequency of the applied field. Effects of cell viability on DEP force have been attributed to modification of parameter Re½KðoÞ after heat treatment. Huang et al. [5] studied dielectrophoresis and electrorotation of viable and nonviable yeast cells. Comparing the experimental data with a theoretical modeling revealed that the conductivity of the cytoplasmic membrane and cytoplasm of nonviable cells considerably increased and decreased, respectively. Docoslis et al. [7] investigated the DEP spectrum of heat-treated nonviable myeloma cells by DEP levitation technique [13] and found the cytoplasmic conductivity decreased to approach that of the surrounding medium. Those results suggest that the membranes of heat-treated cells are perforated as a result of the structural modification. Ionic materials in the cytoplasm can pass through those pores and leak out to the surrounding medium. The ionic exchange between the cytoplasm and the external medium will affect dielectric properties of cells, parameter Re½KðoÞ and the DEP force. An example of a theoretical prediction of the cytoplasmic conductivity dependency of parameter Re½KðoÞ is shown in Fig. 5. One E. coli cell is modeled as a dielectric sphere covered by two shells. The inner and outer shells represent the cytoplasmic membrane and cell wall, respectively. The sphere covered by these shells represents the cytoplasm. The complex permittivity of the particle ep in Eq. (2) is replaced with an effective complex permittivity of E. coli cell eeff ; which can be
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
165
Fig. 5. Theoretical prediction of the cytoplasmic conductivity si dependency of Re½KðoÞ spectra. E. coli cells is modeled as a dielectric sphere covered by two shells. Parameters used in calculation are listed in Table 1. Table 1 Parameter values employed in the theoretical predictions of Re½KðoÞ shown in Fig. 5. These values of E.coli cell were determined by referring literatures [14,15]. Component
Parameter
Value
Cell
Radius
1 mm
Cell cytoplasm
Relative permittivity Conductivity (viable)
60 100 mS/m
Cell membrane
Relative permittivity Conductivity Thickness
10 50 nS/m 5 nm
Cell wall
Relative permittivity Conductivity Thickness
60 500 mS/m 20 nm
Suspension medium (deionized water)
Relative permittivity Conductivity
80 0.2 mS/m
calculated by using the ‘‘smeared-out sphere’’ model [5]. Parameter values of E. coli care determined referring literatures [14,15] and listed in Table 1. Fig. 5 indicates that Re½KðoÞ or the DEP force decreases with decreasing the cytoplasmic conductivity si at a higher field frequency. For example, when the cytoplasmic conductivity decreases from the initial value of 100 to 1 mS/m, the DEP forced decreases by approximately 30% at the field frequency 1 MHz. On the other hand, the DEP force is hardly altered at 100 kHz. In these calculations, it was assumed that heat treatment
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
166
Table 2 Effects of the field frequency and suspension conductivity on the selective DEPIM detection of viable bacteria Experimenta conductivity (mS)
Theoryb Re½KðoÞ
Frequency
Suspension conductivity ss (mS/m)
100 kHz
0.2 2.0
1.3 0.5
0.02 0.03
1 MHz
0.2 2.0
31.4 34.9
0.23 0.27
Note: Larger differences in the electrode conductance (DEPIM experiments) and the calculated parameter Re½KðoÞ are preferable for the selective DEPIM detection. At 1 MHz frequency, viable cells could be selectively detected by DEPIM in the conductivity range from 0.2 to 2.0 mS/m. Theoretical predictions of Re½KðoÞ agreed with these experimental results. a The conductance difference at t ¼ 100 s between viable and nonviable cell measured by DEPIM (see Fig. 2 for ss ¼ 0:2 mS/m). b Re½KðoÞ difference between viable (si ¼ 100 mS/m) and nonviable (si ¼ ss ) cells calculated by Eqs. (2) and (3) for 1 MHz (see Fig. 5 for ss ¼ 0:2 mS/m).
did not affect any parameters except the cytoplasmic conductivity. It is indeed possible that the membrane conductivity is also increased in addition to the cytoplasmic conductivity decrease [5]. However, the calculation revealed that the membrane conductivity had little effect on DEP force spectra at high frequencies (not shown in Fig. 5). The theoretical calculations agree well with the experimental results shown in Fig. 1 where DEP collection of heat-treated nonviable cells is observed only at 100 kHz but not at 1 MHz. As expected from Eqs. (1)–(3), the calculation results depend also on the suspending medium conductivity. Since a suspending medium of biological cells, such as a liquid culture, may have higher ionic concentration or electrical conductivity, it is interesting to investigate how the suspension conductivity influences the selective DEPIM. Similar experiments and theoretical calculations were conducted for higher suspension conductivity ss ¼ 2:0 mS/m and main results were summaraized in Table 2 together with those for 0.2 mS/m. There was no remarkable conductivity effects on these results and the selective DEPIM detection of viable cells was possible in the conductivity range from 0.2 mS/m to 2.0 mS/m at 1 MHz frequency. Nonviable bacteria exposed to UV light did not show any change in DEP behavior in the tested frequency range. This implies that UV radiation does not alter the membrane structure or the dielectric properties of the cell interior. It is known that UV radiation damages chromosome DNA in the cytoplasm without direct alteration to the membrane structure. This may be a reason why the UV treated bacteria do not exhibit DEP force modification caused by ionic leakage through a perforated cell membrane. 4.2. Real time evaluation of heat sterilization effect by DEPIM In Fig. 2, DEPIM inspection of heat-treated nonviable cells was conducted after heat treatment for 15 min so that treated bacteria are completely inactivated. If the
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
167
treatment time is shorter than 15 min, a certain number of bacteria may survive after the heat treatment. As already shown in Fig. 4, DEPIM can selectively detect viable cells mixed with nonviable cells. This suggests that DEPIM may be used to evaluate the sterilization progress on a real time basis. This possibility was examined by experiments as follows. E. coli suspension (106 cells/ml) was heat-treated at 801C varying the treatment time. After the treatment, 100 ml of pure or diluted suspension liquid was spread and incubated on agar plates to evaluate surviving cell number by colony counting method (incubation for 48 h). At the same time, the rest of bulk suspension liquid was inspected by DEPIM for 5 min using an ac signal of 1 MHz frequency and 3 V peak–peak amplitude in order to selectively and quantitatively detect viable bacteria. As shown in Fig. 6, number of viable cells exponentially decreased with increasing treatment time as determined by colony counting method. No colony was formed when treatment time became longer than 5 min. It should be noted that viable cell number evaluated by DEPIM varied with treatment time in the same manner as colony counting results. However, DEPIM could not exactly evaluate when sterilization was completed because viable cell number reached the lower limit of DEPIM (in this case, about 104 cells/ml) as the heat treatment became effective. Although the colony counting method based on cell incubation can precisely estimate viable cell number even at very low concentration, it generally takes a long time (typically a few days) for evaluation. On the other hand, selective detection of viable cells by DEPIM can be completed in much shorter time (less than 10 min) on a real time basis. This can be a great advantage in some areas such as food industry that needs a faster inspection of viable bacteria to confirm sterilization efficiency and food safety. However, the selective DEPIM detection of viable bacteria cannot be applied to UV sterilization, which does not directly alter the
Fig. 6. Effects of heat treatment time on viable cell number determined by colony counting method and selective DEPIM at 1 MHz frequency (initial cell density is 106 cells/ml). Selective DEPIM, which does not need an incubation process for high sensitivity, can evaluate heat sterilization efficiency considerably faster than traditional microbiological methods.
168
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
dielectric properties of bacteria. Applicability to other sterilization methods such as radioactive rays, ozone or other chemicals is not clear at this point and should be clarified by further investigation in future.
5. Conclusion In this paper, we have proposed a method for selective detection of viable bacteria by using DEPIM. The method utillizes DEP force dependency on bacteria viability. By applying an ac electric field of 1 MHz, viable bacteria mixed with heat sterilized nonviable ones can be selectively collected by positive DEP and detected by DEPIM. However, this method is not applicable to UV sterilized bacteria whose dielectric properties are not directly altered by this method of sterilization. The proposed method can be useful in real time evaluation of heat sterilization efficiency, which takes a few days by the conventional colony counting method based on incubation of viable cells.
Acknowledgements The authors would like to thank Mr. F. Kusaba for his experimental works and valuable discussion. This work was partly supported by Nakatani Electronic Measuring Technology Association of Japan.
References [1] J. Suehiro, R. Yatsunami, R. Hamada, M. Hara, J. Phys. D: Appl. Phys. 32 (1999) 2814–2820. [2] K.R. Milner, A.P. Brown, D.W.E. Allsopp, W.B. Betts, Electron. Lett. 34 (1998) 66–68. [3] J. Suehiro, D. Noutomi, R. Hamada, M. Hara, Proceedings of the IEEE/IAS Annual Meeting, Chicago, IL, 2001. [4] G.H. Markx, R. Pethig, Biotechnol. Bioeng. 45 (1995) 337–343. . [5] Y. Huang, R. Holzel, R. Pethig, X.-B. Wang, Phys. Med. Biol. 37 (1992) 1499–1517. [6] M.S. Talary, J.P.H. Burt, J.A. Tame, R. Pethig, J. Phys. D: Appl. Phys. 29 (1996) 2198–2203. [7] A. Docoslis, N. Kalogerakis, L.A. Behie, K.V.I.S. Kaler, Biotechnol. Bioeng. 54 (1997) 239–250. [8] G.H. Markx, P.A. Dyda, R. Pethig, J. Biotechnol. 51 (1996) 175–180. [9] G.H. Markx, Y. Huang, X.-F. Zhou, R. Pethig, Microbiology 140 (1994) 585–591. [10] X.-B. Wang, Y. Huang, J.P.H. Burt, G.H. Markx, R. Pethig, J. Phys. D: Appl. Phys. 26 (1993) 1278– 1285. [11] R. Pethig, Dielectric and Electronic Properties of Biological Materials, Wiley, Chichester, 1979. [12] T.B. Jones, Electromechanics of Particles, Cambridge University Press, Cambridge, 1995. [13] K.V.I.S. Kaler, T.B. Jones, Biophys. J. 57 (1990) 173–182. [14] K. Asami, T. Hanai, N. Koizumi, Biophys. J. 31 (1980) 215–228. [15] E.L. Carstensen, Biophys. J. 7 (1967) 493–503.
Selective detection of viable bacteria using dielectrophoretic impedance measurement method Junya Suehiro*, Ryo Hamada, Daisuke Noutomi, Masanori Shutou, Masanori Hara Department of Electrical and Electronic Systems Engineering, Graduate School of Information Science and Electrical Engineering, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan Received 16 April 2002; received in revised form 22 July 2002; accepted 2 August 2002
Abstract This paper describes a selective detection technique of viable bacteria based on dielectrophoresis and electrical impedance measurements. The authors have previously proposed a detection technique of biological particles called dielectrophoretic impedance measurement (DEPIM) method using positive dielectrophoretic force to capture biological cells in suspension onto an interdigitated microelectrode array. By combining antigenantibody reaction with the DEPIM, selective detection of a particular species of bacteria was demonstrated. In this present work, the authors demonstrated another selective DEPIM method utilizing cell viability dependency of dielectrophoretic force without introducing the antigen-antibody reaction. It was found that dielectrophoresis of heat-treated Escherichia coli showed strong dependency on viability when applied field frequency was as high as 1 MHz. As a result, viable bacteria could be exclusively collected by positive dielectrophoresis and selectively detected by the DEPIM technique from a suspension also containing heat-treated nonviable cells. On the other hand, nonviable bacteria obtained by UV irradiation showed little dielectrophoresis dependency on viability. According to a theoretical analysis of the dielectrophoretic force, it is suggested that heat treatment alters the dielectric properties of treated cells. In particular, a decrease in cytoplasmic conductivity, which might be caused by heat-induced perforation of cell membrane, was expected to considerably affect dielectrophoresis characteristics. Proposed selective DEPIM method was also applied to evaluation of heat sterilization effect on a real time basis. It was experimentally proved that DEPIM could evaluate viable cell number variation with heat treatment time in a considerably shorter time
*Corresponding author. Tel.: +81-92-642-3912; fax: +81-92-642-3964. E-mail address: [email protected] (J. Suehiro). 0304-3886/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 8 8 6 ( 0 2 ) 0 0 1 2 4 - 9
158
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
than conventional microbiological method based on cell incubation. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Dielectrophoresis; Impedance measurement; Bacteria detection; Viability; ‘‘DEPIM’’
1. Introduction Detection of microorganisms such as bacteria is important in a variety of fields such as bioscience research, medical diagnosis and hazard analysis in food industry. Conventional microbiological detection methods, such as a colony counting technique, based on cell incubation are well established and reliable. However, they are rather time consuming, requiring a few days and therefore not capable of fast diagnosis in case of emergency. The authors have previously proposed a new detection technique of biological cells by using dielectrophoresis (DEP) [1]. The technique called dielectrophoretic impedance measurement (DEPIM) method utilizes the positive dielectrophoretic force to capture suspended biological particles onto an interdigitated microelectrode array in the form of pearl-chains. Higher cell concentration result in faster development of the pearl-chains, which are electrically connected in parallel to the electrode gap and hence increase the conductance and the capacitance between the electrodes. By monitoring the temporal variation of the electrode impedance, it is possible to quantitatively evaluate the cell population according to a theoretical model of cell collection process. DEPIM can realize fast and simple bacteria inspection by using only electrical phenomena and instruments. A similar impedance technique for measuring dielectrophoretic collection of biological cells has been demonstrated by Milner et al. [2]. In practical microorganism inspection and identification, however, there are many cases in which a specific bacterium is to be detected according to the species or its physiological state. The authors have previously proposed a selective DEPIM technique, which utilized antigen-antibody reaction to realize selective detection of bacteria of a certain cell strain [3]. The antigen-antibody reaction was utilized in DEPIM measurements in two different ways. In the first method, antibody was added to the cell suspension after dielectrophoretic enrichment of bacteria in order to cause agglutination of the antibody-specific bacteria. The DEP force exerted on agglutinated bacteria, whose apparent size increased, became more dominant than hydrodynamic drag force in a continuous liquid flow. In the second method, antibody molecules were immobilized onto the microelectrode surfaces before the application of dielectrophoresis so that only antibody-specific bacteria would be bound to the immobilized antibody. These two methods provided the means whereby that specific bacteria could be selectively left between the electrode gap when the electric field was reduced after the preliminary DEP cell collection procedure. Selective DEPIM inspection without introducing immunoassay may also be possible if dielectric properties of wanted cell are so different from those of others that the target cell population can be selectively enriched by making use of the
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
159
positive DEP effect. Selective DEP handling has been realized for biological cells with different viability [4–7] and species [8,9]. These studies suggest that differences in the dielectric properties of cells result in DEP force variations that can be utilized for selective cell manipulation. In this work, selective DEPIM inspection of viable Escherichia coli (E. coli) from a mix of viable and nonviable bacteria was examined. In order to examine effects of the sterilization method on dielectrophoretic cell manipulation and selective DEPIM detection, nonviable bacteria were prepared by two different sterilization methods of heat treatment and UV irradiation. It was found that heat-treated bacteria exhibited a considerable change in the dielectric parameters as well as dielectrophoresis while UV based sterilization hardly affected those properties and hence the observed electrokinetic phenomenon. For the heat sterilization, real time diagnosis of viable cell population during heat treatment was realized by using the proposed selective DEPIM technique.
2. Materials and method 2.1. Cell preparation E. coli strain K12 bacteria were incubated on agar plates. Before each measurement, cells were harvested from agar and suspended in 0.1 M mannitol solution. After several washing by centrifugation, they were finally resuspended in 0.1 M manitol solution at desired concentrations as determined by a Neubauer haemacytometer. Unless otherwise stated, the electrical conductivity of suspension ss was adjusted to 0.2 mS/m. 2.2. Sterilization procedure Heat sterilization was carried out at 801C for 15 min, while UV sterilization was achieved by a 10 s exposure to UV light (254 nm central wavelength and 2.5 mW/cm2 power density). In both methods, a cell suspension of 100 ml was treated on a batch basis. Following the above sterilization treatments, 100 ml of suspension liquid was spread and incubated on agar plates for 48 h in order to examine the viability of the sterilized cell sample. 2.3. Electrodes Interdigitated microelectrode arrays of chrome were patterned on a glass substrate by photolithography technique. Two different electrode configurations were used. A smooth interdigitated electrode system was employed in all DEPIM experiments because this type of electrode configuration is suitable for accurate impedance measurement [1]. Each microelctrode strip had 50 mm width, 12 mm length and 5 mm clearance. The four strips formed three parallel gaps in which cells were trapped and formed pearl-chains by positive DEP. On the other hand, a castle-wall electrode
160
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
configuration [10] was preferred for visual observation of cell collection process by positive DEP. The castle-wall electrode was surrounded by a silicon rubber spacer to form a chamber in which cell suspension liquid of 200 ml was stored. 2.4. DEPIM equipment Details of DEPIM principle and apparatus had been described elsewhere [1]. Sinusoidal ac voltage was generated by a function generator (FG 110, Yokogawa, Japan) and applied to the microelectrode. Electrode impedance measurements were carried out using a DSP lock-in amplifier (Model 7280, Perkin Elmer Instruments, USA). The highest field frequency for DEPIM was restricted to 1 MHz due to the bandwidth limitation of the lock-in amplifier. The impedance measurement apparatus was controlled by a personal computer, which also served as a data logger and analyzer. 2.5. Experimental procedures DEPIM experiments were conducted using a smooth interdigitated electrode system, which was directly immersed into cell suspension liquid stored in a beaker. A magnetic stirrer continuously generated a circular flow in the beaker to enhance positive DEP cell trapping at the electrodes. Microscope observation of DEP process was performed using castle-wall electrodes on which a small chamber was constructed. Cell suspension liquid was introduced into the electrode chamber by a peristaltic pump at a flow rate of 0.9 ml/min. Experiments using sterilized bacteria were conducted in a few minutes following the sterilization procedures.
3. Results 3.1. Bacteria trapping process under positive DEP Photographs of the DEP collection of viable and heat-treated nonviable E. coli are shown in Fig. 1. The DEP collection observations were made at two different electric field frequencies of 100 kHz and 1 MHz. At 100 kHz, both viable and nonviable bacteria were trapped around the electrode corner due to positive DEP (Figs. 1a and b). On the other hand, only viable bacteria were trapped and nonviable cells were not collected by positive DEP at 1 MHz (Figs. 1c and d). These observation results suggest that positive DEP force exerted on the nonviable heat-treated bacteria is negligibly small at 1 MHz. Similar observations were also made on UV sterilized E. coli. In contrast to the heat sterilization case, both viable and nonviable bacteria were collected in the high field region under positive DEP at both 100 kHz and 1 MHz. 3.2. Effects of viability and sterilization method on DEPIM DEPIM experiments were conducted under the same conditions as the DEP trapping observations. Fig. 2 depicts temporal variation of electrode conductance
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
161
Fig. 1. DEP collection process of viable and heat-treated nonviable E. coli. An ac signal of amplitude 8 V peak–peak was applied to a castle-wall electrode. (a) Viable cells at 100 kHz frequency. (b) Nonviable cells at 100 KHz. (c) Viable cells at 1 MHz. Under those conditions, bacteria were trapped by positive DEP around the electrode corner where electric field strength becomes higher. (d) Nonviable cells at 1 MHz. No DEP trapping was observed.
increment measured with viable and heat sterilized E. coli at 107 cells/ml concentration. As explained in the authors’ previous work [1], the conductance increase is due to presence of bacteria that are trapped and enriched between the electrode gap under positive DEP. It was found that the conductance increase rate at t ¼ 0 was directly proportional to the cell population that was to be quantitatively evaluated by the DEPIM method. At 100 kHz frequency, the conductance increased with time in the same manner for both viable and nonviable bacteria (Fig. 2a). At a higher frequency of 1 MHz, however, the conductance change over time became less marked with nonviable heat-treated cells (Fig. 2b). DEPIM experiments were also conducted also on UV sterilized E. coli as shown in Fig. 3. The conductance increased with elapsed time and no measurable difference was found between viable and nonviable bacteria over the measurement frequency range from 100 kHz to 1 MHz. 3.3. DEPIM inspection of mix suspension of viable and nonviable bacteria From Figs. 1 and 3, it can be concluded that heat sterilized E. coli cannot be detected by DEPIM at 1 MHz because no positive DEP force is exerted on the
162
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
Fig. 2. DEPIM results measured with viable and heat sterilized nonviable E. coli at 107 cells/ml concentration. An ac signal of amplitude 3 V peak–peak was applied to a smooth interdigitated electrode. (a) At 100 kHz frequency, the conductance increased with time in the same manner for viable and nonviable bacteria. The conductance increase implies that a certain area of the electrode gap has been bridged by bacteria that has been trapped and enriched under positive DEP. (b) At 1 MHz, the conductance change became less remarkable with nonviable heat-treated cells.
Fig. 3. DEPIM results measured with viable and UV sterilized nonviable E. coli at 105 cells/ml concentration. An ac signal of amplitude 3 V peak–peak was applied to a smooth interdigitated electrode. The conductance increased with elapsed time and no remarkable difference was found between viable and nonviable bacteria independent of field frequency: (a) at 100 kHz frequency; (b) at 1 MHz frequency.
nonviable bacteria following heat treatment. If the viable cells can be selectively trapped and enriched from mixture of viable and heat-treated nonviable cells, it may be possible to selectively detect viable bacteria from the mixture by DEPIM. Fig. 4 shows DEPIM results of pure viable or heat sterilized nonviable cell suspension as well as their mixture. It was found that DEPIM results obtained with the mix
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
163
Fig. 4. DEPIM results of pure viable or heat sterilized nonviable cell suspension at 106 cells/ml as well as their mixture. An ac signal of amplitude 3 V peak–peak was applied to a smooth interdigitated electrode. Results obtained with the mix suspension almost agreed with those of pure viable cells. When viable cell concentration was reduced by half, the conductance increment measured with the mixture varied accordingly.
suspension almost agreed with those of pure viable cells. When viable cell concentration was reduced by half, the conductance increment measured with the mixture varied accordingly. This implies that conductance variation measured with the mixture is mainly caused by viable cell trapped under positive DEP. However, conductance increment of the mixture is always larger by 10% than that of pure viable cells. This may be attributed to mutual interaction between viable and nonviable cells. Viable cells, which move toward a high field region under positive DEP, may have higher chances to interact with a part of nonviable cells near the electrode gap. These nonviable cells may have direct dipole–dipole interaction [11] with enriched viable cells in the neighborhood. The direct interaction may attract nonviable cells to viable ones. As a result, a part of nonviable bacteria may be combined with viable ones and trapped in the electrode gap. In the DEPIM inspection of the mix suspension, these nonviable cells may contribute to the electrode conductance increase together with viable ones.
4. Discussion 4.1. Effects of sterilization method on dielectric properties of bacteria It has been reported that the DEP force exerted on biological cells is strongly influenced by their viability [4–7]. In general, viable cells undergo stronger positive
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
164
DEP than nonviable ones at field frequency over 1 MHz. In those literatures, nonviable cells were prepared only by heat sterilization and effects of the other sterilization methods such as UV, radioactive rays and chemicals have not been clarified yet. In this study, effects of two different sterilization protocols, heat and UV treatments, on DEP and DEPIM were investigated. Results obtained with heat sterilized bacteria agree approximately with those in previous reports. That is, positive DEP force exerted on heat-treated nonviable bacteria becomes small when the field frequency is increased from 100 kHz to 1 MHz. However, cell viability does not affect the frequency dependency of the DEP force when nonviable bacteria are prepared by UV radiation. The DEP force acting on a spherical particle of radius r suspended in a medium of permittivity es is given by [12] F DEP ¼ 2pr3 es Re½KðoÞrE 2 ;
ð1Þ
where E is the magnitude (RMS) of the applied field and Re½KðoÞ is the real component of the Clausius–Mossotti factor given by KðoÞ ¼
ep es ; ep þ 2es
ð2Þ
where ep and es are the complex permittivity of the particle and surrounding medium, respectively. For a real dielectric, the complex permittivity is defined as s ð3Þ e ¼ e j ; o pffiffiffiffiffiffiffi where j ¼ 1; e is the permittivity and s is the conductivity of the dielectric and o is the angular frequency of the applied field. Effects of cell viability on DEP force have been attributed to modification of parameter Re½KðoÞ after heat treatment. Huang et al. [5] studied dielectrophoresis and electrorotation of viable and nonviable yeast cells. Comparing the experimental data with a theoretical modeling revealed that the conductivity of the cytoplasmic membrane and cytoplasm of nonviable cells considerably increased and decreased, respectively. Docoslis et al. [7] investigated the DEP spectrum of heat-treated nonviable myeloma cells by DEP levitation technique [13] and found the cytoplasmic conductivity decreased to approach that of the surrounding medium. Those results suggest that the membranes of heat-treated cells are perforated as a result of the structural modification. Ionic materials in the cytoplasm can pass through those pores and leak out to the surrounding medium. The ionic exchange between the cytoplasm and the external medium will affect dielectric properties of cells, parameter Re½KðoÞ and the DEP force. An example of a theoretical prediction of the cytoplasmic conductivity dependency of parameter Re½KðoÞ is shown in Fig. 5. One E. coli cell is modeled as a dielectric sphere covered by two shells. The inner and outer shells represent the cytoplasmic membrane and cell wall, respectively. The sphere covered by these shells represents the cytoplasm. The complex permittivity of the particle ep in Eq. (2) is replaced with an effective complex permittivity of E. coli cell eeff ; which can be
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
165
Fig. 5. Theoretical prediction of the cytoplasmic conductivity si dependency of Re½KðoÞ spectra. E. coli cells is modeled as a dielectric sphere covered by two shells. Parameters used in calculation are listed in Table 1. Table 1 Parameter values employed in the theoretical predictions of Re½KðoÞ shown in Fig. 5. These values of E.coli cell were determined by referring literatures [14,15]. Component
Parameter
Value
Cell
Radius
1 mm
Cell cytoplasm
Relative permittivity Conductivity (viable)
60 100 mS/m
Cell membrane
Relative permittivity Conductivity Thickness
10 50 nS/m 5 nm
Cell wall
Relative permittivity Conductivity Thickness
60 500 mS/m 20 nm
Suspension medium (deionized water)
Relative permittivity Conductivity
80 0.2 mS/m
calculated by using the ‘‘smeared-out sphere’’ model [5]. Parameter values of E. coli care determined referring literatures [14,15] and listed in Table 1. Fig. 5 indicates that Re½KðoÞ or the DEP force decreases with decreasing the cytoplasmic conductivity si at a higher field frequency. For example, when the cytoplasmic conductivity decreases from the initial value of 100 to 1 mS/m, the DEP forced decreases by approximately 30% at the field frequency 1 MHz. On the other hand, the DEP force is hardly altered at 100 kHz. In these calculations, it was assumed that heat treatment
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
166
Table 2 Effects of the field frequency and suspension conductivity on the selective DEPIM detection of viable bacteria Experimenta conductivity (mS)
Theoryb Re½KðoÞ
Frequency
Suspension conductivity ss (mS/m)
100 kHz
0.2 2.0
1.3 0.5
0.02 0.03
1 MHz
0.2 2.0
31.4 34.9
0.23 0.27
Note: Larger differences in the electrode conductance (DEPIM experiments) and the calculated parameter Re½KðoÞ are preferable for the selective DEPIM detection. At 1 MHz frequency, viable cells could be selectively detected by DEPIM in the conductivity range from 0.2 to 2.0 mS/m. Theoretical predictions of Re½KðoÞ agreed with these experimental results. a The conductance difference at t ¼ 100 s between viable and nonviable cell measured by DEPIM (see Fig. 2 for ss ¼ 0:2 mS/m). b Re½KðoÞ difference between viable (si ¼ 100 mS/m) and nonviable (si ¼ ss ) cells calculated by Eqs. (2) and (3) for 1 MHz (see Fig. 5 for ss ¼ 0:2 mS/m).
did not affect any parameters except the cytoplasmic conductivity. It is indeed possible that the membrane conductivity is also increased in addition to the cytoplasmic conductivity decrease [5]. However, the calculation revealed that the membrane conductivity had little effect on DEP force spectra at high frequencies (not shown in Fig. 5). The theoretical calculations agree well with the experimental results shown in Fig. 1 where DEP collection of heat-treated nonviable cells is observed only at 100 kHz but not at 1 MHz. As expected from Eqs. (1)–(3), the calculation results depend also on the suspending medium conductivity. Since a suspending medium of biological cells, such as a liquid culture, may have higher ionic concentration or electrical conductivity, it is interesting to investigate how the suspension conductivity influences the selective DEPIM. Similar experiments and theoretical calculations were conducted for higher suspension conductivity ss ¼ 2:0 mS/m and main results were summaraized in Table 2 together with those for 0.2 mS/m. There was no remarkable conductivity effects on these results and the selective DEPIM detection of viable cells was possible in the conductivity range from 0.2 mS/m to 2.0 mS/m at 1 MHz frequency. Nonviable bacteria exposed to UV light did not show any change in DEP behavior in the tested frequency range. This implies that UV radiation does not alter the membrane structure or the dielectric properties of the cell interior. It is known that UV radiation damages chromosome DNA in the cytoplasm without direct alteration to the membrane structure. This may be a reason why the UV treated bacteria do not exhibit DEP force modification caused by ionic leakage through a perforated cell membrane. 4.2. Real time evaluation of heat sterilization effect by DEPIM In Fig. 2, DEPIM inspection of heat-treated nonviable cells was conducted after heat treatment for 15 min so that treated bacteria are completely inactivated. If the
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
167
treatment time is shorter than 15 min, a certain number of bacteria may survive after the heat treatment. As already shown in Fig. 4, DEPIM can selectively detect viable cells mixed with nonviable cells. This suggests that DEPIM may be used to evaluate the sterilization progress on a real time basis. This possibility was examined by experiments as follows. E. coli suspension (106 cells/ml) was heat-treated at 801C varying the treatment time. After the treatment, 100 ml of pure or diluted suspension liquid was spread and incubated on agar plates to evaluate surviving cell number by colony counting method (incubation for 48 h). At the same time, the rest of bulk suspension liquid was inspected by DEPIM for 5 min using an ac signal of 1 MHz frequency and 3 V peak–peak amplitude in order to selectively and quantitatively detect viable bacteria. As shown in Fig. 6, number of viable cells exponentially decreased with increasing treatment time as determined by colony counting method. No colony was formed when treatment time became longer than 5 min. It should be noted that viable cell number evaluated by DEPIM varied with treatment time in the same manner as colony counting results. However, DEPIM could not exactly evaluate when sterilization was completed because viable cell number reached the lower limit of DEPIM (in this case, about 104 cells/ml) as the heat treatment became effective. Although the colony counting method based on cell incubation can precisely estimate viable cell number even at very low concentration, it generally takes a long time (typically a few days) for evaluation. On the other hand, selective detection of viable cells by DEPIM can be completed in much shorter time (less than 10 min) on a real time basis. This can be a great advantage in some areas such as food industry that needs a faster inspection of viable bacteria to confirm sterilization efficiency and food safety. However, the selective DEPIM detection of viable bacteria cannot be applied to UV sterilization, which does not directly alter the
Fig. 6. Effects of heat treatment time on viable cell number determined by colony counting method and selective DEPIM at 1 MHz frequency (initial cell density is 106 cells/ml). Selective DEPIM, which does not need an incubation process for high sensitivity, can evaluate heat sterilization efficiency considerably faster than traditional microbiological methods.
168
J. Suehiro et al. / Journal of Electrostatics 57 (2003) 157–168
dielectric properties of bacteria. Applicability to other sterilization methods such as radioactive rays, ozone or other chemicals is not clear at this point and should be clarified by further investigation in future.
5. Conclusion In this paper, we have proposed a method for selective detection of viable bacteria by using DEPIM. The method utillizes DEP force dependency on bacteria viability. By applying an ac electric field of 1 MHz, viable bacteria mixed with heat sterilized nonviable ones can be selectively collected by positive DEP and detected by DEPIM. However, this method is not applicable to UV sterilized bacteria whose dielectric properties are not directly altered by this method of sterilization. The proposed method can be useful in real time evaluation of heat sterilization efficiency, which takes a few days by the conventional colony counting method based on incubation of viable cells.
Acknowledgements The authors would like to thank Mr. F. Kusaba for his experimental works and valuable discussion. This work was partly supported by Nakatani Electronic Measuring Technology Association of Japan.
References [1] J. Suehiro, R. Yatsunami, R. Hamada, M. Hara, J. Phys. D: Appl. Phys. 32 (1999) 2814–2820. [2] K.R. Milner, A.P. Brown, D.W.E. Allsopp, W.B. Betts, Electron. Lett. 34 (1998) 66–68. [3] J. Suehiro, D. Noutomi, R. Hamada, M. Hara, Proceedings of the IEEE/IAS Annual Meeting, Chicago, IL, 2001. [4] G.H. Markx, R. Pethig, Biotechnol. Bioeng. 45 (1995) 337–343. . [5] Y. Huang, R. Holzel, R. Pethig, X.-B. Wang, Phys. Med. Biol. 37 (1992) 1499–1517. [6] M.S. Talary, J.P.H. Burt, J.A. Tame, R. Pethig, J. Phys. D: Appl. Phys. 29 (1996) 2198–2203. [7] A. Docoslis, N. Kalogerakis, L.A. Behie, K.V.I.S. Kaler, Biotechnol. Bioeng. 54 (1997) 239–250. [8] G.H. Markx, P.A. Dyda, R. Pethig, J. Biotechnol. 51 (1996) 175–180. [9] G.H. Markx, Y. Huang, X.-F. Zhou, R. Pethig, Microbiology 140 (1994) 585–591. [10] X.-B. Wang, Y. Huang, J.P.H. Burt, G.H. Markx, R. Pethig, J. Phys. D: Appl. Phys. 26 (1993) 1278– 1285. [11] R. Pethig, Dielectric and Electronic Properties of Biological Materials, Wiley, Chichester, 1979. [12] T.B. Jones, Electromechanics of Particles, Cambridge University Press, Cambridge, 1995. [13] K.V.I.S. Kaler, T.B. Jones, Biophys. J. 57 (1990) 173–182. [14] K. Asami, T. Hanai, N. Koizumi, Biophys. J. 31 (1980) 215–228. [15] E.L. Carstensen, Biophys. J. 7 (1967) 493–503.