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High-Tc SQUID-based impedance spectroscopy of living cell suspensions
PHYSlCA® ELSEVIER
Physica C 341-348 (2000) 2693-2694 www.elsevier.nl/locate/physc
High-Tc SQUID-Based Impedance Spectroscopy o f Living Cell Suspensions C. Prodan,a j. R. Claycomb," E. Prodanb and J. H. Miller, Jr) ~partment of Physics and Texas Center for Supet~nductivity, University of Houston, Calhoun Street, Houston, Tx-77204, U.S.A bDepartment of Physics-MS 61, Rice University, Houston, TX 77005-1892 U.S.A. We provide a method of measuring dielectric properties of living cell suspensions based on high sensitivity of High-Tc SQUID. The dispersion curves of conductivity and dielectric permittivity are measured in the range of low range of frequencies and small applied electric fields.
1.
INTRODUCTION
We have proved in a recent paper [1] that the membrane potential of living cells has a large effect on dielectric behavior of living cell suspensions. This implies that one can calculate the membrane electric potential from dispersion curves of dielectric permitlivity (Q and com:h~clivi~(o). Our theoretical a~lysis showed that only the low fa~queney range (less than 10s Hz) is important for this problem. It is extremely difficult to measure the dispersion curves in this range of frequencies. There are successful measurements (electro-rotation) [2] but they use high electric field to excite the suspension. It was proven in [3] that in these cases, the applied electric field has a large effect on the membrane potential. For this reason, the experiment_al data obtained by electro-rotation cannot be used in the calculation of membrane potential. Measurements are therefore required with low applied electric fields. We find that the extraordinaff sensitivity of High-Tc SQUIDs at luw frequencies[4] provides a solution to this problem. 2.EXPERIMENTAL SETUP
The cell suspension is placed inside a cylindrical containment vessel located inside of a parallel plate capacitor. Gold is deposited on the capacitor plates to prevent the formation of oxide layers that would
cause spurious signals. An ac voltage across the capacitor induces transport and displacement currents inside the cell suspension i.e., Y = oE + e dE/dt=(~+jcoe)E Here E = V/d, V is the potential difference across the capacitor and d is the plate separation. In the low field regime, V is chosen so that E < 1V/era [5]. A sitmzl generator (Wavetek model 80) sweeps the excitation frequency between 100 and 10kHz. A torroidal pickup coil coupled to a transformer circuit detects the magnetic field generated by currents in the cell suspension. Magnetic flux is coupled into the SQUID (YBCO grain-boundary directly coupled magnetometer [6]) with the secondary tran~ormer coil wound around the tail of a fibergla~ G-10 liquid nitrogen dewar. The SQUID, dewar and tra_n~ormer coil assembly is housed inside of a mumetal magnetic shield to eliminate environmental electromagnetic interference. The SQUID output voltage (proportional to the magnetic flux threading the coil) is fed into a lock-in amplifier (EG&G model 5210) referenced to the sitmal generator. The lock-in amplifier outputs both the magnitude and phase of the input voltage to a digital oscilloscope (LeCroy .9400 A) synchronized to the frequency sweeping time. Data is acquired from the oscilloscope via GPIB interface to a PC using the Labview software package.
0921-4534/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII S0921-4534(00)01481-7
2694
C Prodan et al./Physica C 341-348 (2000) 2693-2694
.
.
.
.
.
.
.
.
)
.
.
.
.
.
.
.
.
i
1.~=1o'
>~
°:
1.2x10 7
"~ 2 ~"
o
r
j
p (cells)
.
0
5
9.oxl(f
, ,2.0
1.5 1.0
6.oKl(f
lls)
0
0.5 3.(~¢10 a
0.o 100
1000
10000
10oo
Frequency(Hz)
0.0 10000
frequency (Hz)
Figure 1. Magnitude and phase of SQUID output measured with lock-in amplifier. Frequency dependent response is recorded for cell and acetone reference measurements.
Figure 2. Relative values of ~ and o extracted from the data in Fig. 1. (ar.l=c,~.d~,D 3 ACKNOWLEDGEMENTS
The in-phase and out-of-phase SQUID output will be proportional to the respective conductivity and permittivity of the cell suspension in the absence of phase shifts. Such phase shifts are primarily due to the frequency dependent impedance of the transformer circuit. Other sources of phase shift include; (1) p~'l'a~diccapacitallce's in the measurement system and SQUID electronics, (2) imprecise alignment of the SQUID pickup coil with respect to tranfformer input coil, (3) mutual inductance between the tranfformer input coil and the SQUID pickup loop and (4) mutual inductance between the magnetic shield and the input coil. A reference measurement is therefore made with a fluid of known conductivity and permittivity to subtract parr/cidic phase shifts and to cancel unknown geometrical scale factors. Ill figure 1 we show the output of the lockin amplifier, representing the amplitude and phase of the signal for the living cell suspension (saccharomyces pombe (yeast) with a concentration of about l0 s ceHs/ml) and the reference (a solution of acetone 99.5% in our case). In figure 2, s and c are plotted as a function of frequency from 600 Hz to 10kHz. The bandwidth of the SQUID system is from dc to 20kHz in flux locked loop mode. Our prelimitmry experimental results are encouraging in that they qualitatively reproduce the theoretical curves from [I ]. Also, measurements with living tissues show the same qualitative behavior [7].
This research was supported by the state of Texas through the Texas Center for Superconductivity, the Rober A. Welch Foundation and by the Texas Higher Education Coordinating Board Advanced Research Program and Advanced Technology Program. REFERENCES 1. C. Prodsn, E. Predan, J. Phys. D 32, 338 (1999) 2. J. Gim,~a, R. Glaser and G. Full, Thoory and application of the rotation of biological cells in rotating electric fields (electro-rotation),
Physical Characterization of Biological Cells, 3. 4.
5. 6. 7.
Berlin: Gesundheit (1991) C. Grosse and H. P. Schwan, Biophys. J. 63, 1632 (1992) J. Clarke, SQUID Fundamentals, in SQUID Sensors: Fundamentals, Fabrication and Applications, H. Weinstock ed. Kluwer Academic Publishers, Netherlands, 1996, pp, 162 H.P. Schwan, IEEE Transactions of Medicine and Biology 6, 70a (1994) iMag system, Conductus (now Tristan Technologies, Ine) H. P. Schwan, Advances in Biological and Medical Physics Vol. V, Academic Press: New York (1957)
Physica C 341-348 (2000) 2693-2694 www.elsevier.nl/locate/physc
High-Tc SQUID-Based Impedance Spectroscopy o f Living Cell Suspensions C. Prodan,a j. R. Claycomb," E. Prodanb and J. H. Miller, Jr) ~partment of Physics and Texas Center for Supet~nductivity, University of Houston, Calhoun Street, Houston, Tx-77204, U.S.A bDepartment of Physics-MS 61, Rice University, Houston, TX 77005-1892 U.S.A. We provide a method of measuring dielectric properties of living cell suspensions based on high sensitivity of High-Tc SQUID. The dispersion curves of conductivity and dielectric permittivity are measured in the range of low range of frequencies and small applied electric fields.
1.
INTRODUCTION
We have proved in a recent paper [1] that the membrane potential of living cells has a large effect on dielectric behavior of living cell suspensions. This implies that one can calculate the membrane electric potential from dispersion curves of dielectric permitlivity (Q and com:h~clivi~(o). Our theoretical a~lysis showed that only the low fa~queney range (less than 10s Hz) is important for this problem. It is extremely difficult to measure the dispersion curves in this range of frequencies. There are successful measurements (electro-rotation) [2] but they use high electric field to excite the suspension. It was proven in [3] that in these cases, the applied electric field has a large effect on the membrane potential. For this reason, the experiment_al data obtained by electro-rotation cannot be used in the calculation of membrane potential. Measurements are therefore required with low applied electric fields. We find that the extraordinaff sensitivity of High-Tc SQUIDs at luw frequencies[4] provides a solution to this problem. 2.EXPERIMENTAL SETUP
The cell suspension is placed inside a cylindrical containment vessel located inside of a parallel plate capacitor. Gold is deposited on the capacitor plates to prevent the formation of oxide layers that would
cause spurious signals. An ac voltage across the capacitor induces transport and displacement currents inside the cell suspension i.e., Y = oE + e dE/dt=(~+jcoe)E Here E = V/d, V is the potential difference across the capacitor and d is the plate separation. In the low field regime, V is chosen so that E < 1V/era [5]. A sitmzl generator (Wavetek model 80) sweeps the excitation frequency between 100 and 10kHz. A torroidal pickup coil coupled to a transformer circuit detects the magnetic field generated by currents in the cell suspension. Magnetic flux is coupled into the SQUID (YBCO grain-boundary directly coupled magnetometer [6]) with the secondary tran~ormer coil wound around the tail of a fibergla~ G-10 liquid nitrogen dewar. The SQUID, dewar and tra_n~ormer coil assembly is housed inside of a mumetal magnetic shield to eliminate environmental electromagnetic interference. The SQUID output voltage (proportional to the magnetic flux threading the coil) is fed into a lock-in amplifier (EG&G model 5210) referenced to the sitmal generator. The lock-in amplifier outputs both the magnitude and phase of the input voltage to a digital oscilloscope (LeCroy .9400 A) synchronized to the frequency sweeping time. Data is acquired from the oscilloscope via GPIB interface to a PC using the Labview software package.
0921-4534/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII S0921-4534(00)01481-7
2694
C Prodan et al./Physica C 341-348 (2000) 2693-2694
.
.
.
.
.
.
.
.
)
.
.
.
.
.
.
.
.
i
1.~=1o'
>~
°:
1.2x10 7
"~ 2 ~"
o
r
j
p (cells)
.
0
5
9.oxl(f
, ,2.0
1.5 1.0
6.oKl(f
lls)
0
0.5 3.(~¢10 a
0.o 100
1000
10000
10oo
Frequency(Hz)
0.0 10000
frequency (Hz)
Figure 1. Magnitude and phase of SQUID output measured with lock-in amplifier. Frequency dependent response is recorded for cell and acetone reference measurements.
Figure 2. Relative values of ~ and o extracted from the data in Fig. 1. (ar.l=c,~.d~,D 3 ACKNOWLEDGEMENTS
The in-phase and out-of-phase SQUID output will be proportional to the respective conductivity and permittivity of the cell suspension in the absence of phase shifts. Such phase shifts are primarily due to the frequency dependent impedance of the transformer circuit. Other sources of phase shift include; (1) p~'l'a~diccapacitallce's in the measurement system and SQUID electronics, (2) imprecise alignment of the SQUID pickup coil with respect to tranfformer input coil, (3) mutual inductance between the tranfformer input coil and the SQUID pickup loop and (4) mutual inductance between the magnetic shield and the input coil. A reference measurement is therefore made with a fluid of known conductivity and permittivity to subtract parr/cidic phase shifts and to cancel unknown geometrical scale factors. Ill figure 1 we show the output of the lockin amplifier, representing the amplitude and phase of the signal for the living cell suspension (saccharomyces pombe (yeast) with a concentration of about l0 s ceHs/ml) and the reference (a solution of acetone 99.5% in our case). In figure 2, s and c are plotted as a function of frequency from 600 Hz to 10kHz. The bandwidth of the SQUID system is from dc to 20kHz in flux locked loop mode. Our prelimitmry experimental results are encouraging in that they qualitatively reproduce the theoretical curves from [I ]. Also, measurements with living tissues show the same qualitative behavior [7].
This research was supported by the state of Texas through the Texas Center for Superconductivity, the Rober A. Welch Foundation and by the Texas Higher Education Coordinating Board Advanced Research Program and Advanced Technology Program. REFERENCES 1. C. Prodsn, E. Predan, J. Phys. D 32, 338 (1999) 2. J. Gim,~a, R. Glaser and G. Full, Thoory and application of the rotation of biological cells in rotating electric fields (electro-rotation),
Physical Characterization of Biological Cells, 3. 4.
5. 6. 7.
Berlin: Gesundheit (1991) C. Grosse and H. P. Schwan, Biophys. J. 63, 1632 (1992) J. Clarke, SQUID Fundamentals, in SQUID Sensors: Fundamentals, Fabrication and Applications, H. Weinstock ed. Kluwer Academic Publishers, Netherlands, 1996, pp, 162 H.P. Schwan, IEEE Transactions of Medicine and Biology 6, 70a (1994) iMag system, Conductus (now Tristan Technologies, Ine) H. P. Schwan, Advances in Biological and Medical Physics Vol. V, Academic Press: New York (1957)