Measurement Techniques, Vol. 55, No. 11, February, 2013

MEDICAL AND BIOLOGICAL MEASUREMENTS PULSED CONDUCTOMETER FOR BIOLOGICAL CELLS AND LIQUID MEDIA

V. A. Shigimaga

UDC 543.555:57.086.8

A new, nonstandard measuring device for the conductometry of biological cells and liquid media in a pulsed electric field with increasing field strength is developed. Departmental metrological certification is carried out for a pulsed conductometer according to working, standard documents of the Commonwealth of Independent States (CIS) and Ukraine. Certain results with the use of a conductometer are shown. Keywords: pulsed conductometer, metrological certification, biological cell, liquid medium.

A pulsed conductometer is a device for measuring the electrical conductivity of biological cells, in particular, reproductive cells (oocytes), embryos, and liquid media in a pulsed electric field (PEF). It is intended for use in the biotechnology of animal reproduction (reconstruction of embryos by means of electrofusion), investigation of the dynamics of electroporation of a membrane in an increasing PEF, stimulation of the development of oocytes in vitro, study of the nature of the interaction of a membrane with cryoprotectors for the lifetime estimate of the hidden deviations in the development of oocytes, estimates of the quality of the liquid media, in particular, deionized water and biotechnological media based on it [1, 2]. The initial data for development of a pulsed conductometer were the results of preliminary research on the nature of the electrical conductivity of oocytes, mammalian embryos, and various aqueous solutions in PEFs with increasing field strength, obtained with the help of models of the measuring apparatus developed during research [3–5]. Later on, for that reason we used the well-known methods of the foundations of radio technology and calculations of the circuits for radioelectronic measurement apparatus [6]. For theoretical generalization of the process itself and the results of the measurement of the conductivity, we constructed several models for the interaction of a PEF with biological cells – electrodynamic, radiotechnical, and mathematical – which also enabled us to find the optimal parameters of the measurement apparatus. Construction of the Conductometer. Construction of a conductometer is represented by a system of electronic, optical, and mechanical apparatus, which enables us to measure the specific electrical conductivity of a single biological cell or a liquid medium when a PEF acts on it. The measuring apparatus contains a square-pulse generator (SPG) for a voltage with variable amplitude and wavelength; a RIGOL (DS5-060308) digital, two-channel oscillograph; microelectrodes made from gold wire, sealed in a glass capillary made of Pyrex [7], positioned for micromanipulation (P54.135.028 TO); and an inverted BIOLAM-P1 (Yu-33.23.719 TO) microscope, with automatic temperature regulation of the stage. In one of the eyepieces of the microscope, a scale is inserted for the measurement of the geometric parameters of the cell and the microelectrode cell. Connection of the radioelectronic devices of the measurement technology (DMT) is carried out by using an external connection board. The board is fixed to the microscope stage near the microelectrodes in order to reduce the electrical distance to the signal cable. The output of the SPG is connected to the board by an RK-50 cable. The microelectrodes are fixed to the positioner holders, have three degrees of freedom, and have measurements that are within the visual field of the microscope. A coaxial configuration is used since it is convenient for the conductometry of cells and liquid media, and it also

Institute for Animal Husbandry, National Academy of Agrarian Sciences of Ukraine, Kharkov, Ukraine; [email protected]. Translated from Izmeritel’naya Tekhnika, No. 11, pp. 45–49, November, 2012. Original article submitted September 11, 2012.

1294

0543-1972/13/5511-1294 ©2013 Springer Science+Business Media New York

MME SPG

Osc

Rcal

Fig. 1. Measuring circuit of pulsed conductometer: SPG – square-pulse generator; MME – measuring microelectrodes; OSC – two-channel oscillograph; Rcal – calibrated precision resistor, chosen for a scale that covers the range 0.01–100 kΩ (0.05%) by the use of decade switches.

simplifies the calculations of the conductivity. The microscope and positioners are placed on a massive damping plate in order to suppress mechanical vibrations of the microelectrodes and the cell during the measurement process. The following devices were used as additional equipment for the unit. For observation and video recording of the morphological dynamics of the cells in the media (with the action of an increasing PEF), we insert a VA-32C color microvideocamera (Korea) in the ocular of the microscope, and we output it to a Panasonic videocassette recorder (Japan) and a Daewoo monitor (Korea). A pulsed conductometer enables us to measure the specific conductivity of single living cells and liquid media in the range 0.1–105 µS/cm (with error no more than 4%) in a PEF having field intensity 0.02–10 kV/cm and several biophysical cell parameters, e. g., electrical strength of the membrane and capacitance [1, 4]. Measuring Circuit, Measurement Method, and Processing of Initial Data. The conductivity of an object is determined by the use of a calibrated resistor in series with the object, as the basis for a known conductometric circuit [8]. It is convenient that, because of the equality of the currents flowing through the object and the resistor, it is sufficient to measure the voltage drop across the resistor and the input voltage. Then we calculate the conductivity of the object, ignoring the measurement perturbations. In this case, we obtain the predicted, systematic component of the measurement error, depending on the ratios of the conductivities of the resistor and the object. Having chosen a resistor having conductivity considerably greater than that of the object, we can reduce the error component to 1% or less. The measuring circuit for a pulsed conductometer is shown in Fig. 1. The electrical circuit of the SPG is based on domestic radio components. The technical characteristics of the generator are square-pulse amplitude 0–98 V (instability 0.1%), pulse length 2–300 µsec (instability 0.5%), pulse-edge length 50–120 nsec (depending on amplitude). Measurement of the conductivity of single living cells is carried out using an original method in a nonelectrolyte (dielectric) medium, for which we use mannitol, saccharose, or glucose (SIGMA) in a solution of deionized, nonheat-producing water. The objects under investigation are positioned on slides on the stage of the microscope in drops of the medium between two coaxial microelectrodes and are subjected to the action of a pulsed voltage that increases in amplitude with a given pulse length and a definite sequence depending on the measurement goal. The conductivity of the object in the interelectrode space is calculated according to the equation G = UR /[R(Uout – UR)],

(1)

where G is the conductivity, S; UR is the voltage drop, V, across a precision resistor of resistance R, Ω; and Uout is the output voltage of the SPG, V. The output voltage of the SPG is measured on one channel of the oscillograph, and the voltage across the precision resistor is measured on the other channel. The specific conductivity of the object is calculated as Gsp = Gk, where k is a geometrical factor of the microelectrode cell [9], 1295

⎛ 4 L2 k = 12 ⎜ 1 + 1 + ⎜ d2 ⎝

⎞ ⎟ ⎟ ⎠

⎧ ⎡ 2 ⎪ ⎢ d ⎨ π ⎢3 ⎪ ⎢ L ⎩ ⎣

⎛ 2 ⎜1 + 1 + 4 L ⎜ d2 ⎝

⎤⎫ ⎞ ⎟ + 4 L ⎥ ⎪⎬ ; ⎥ ⎟ ⎠ ⎥⎦ ⎪⎭

(2)

L is the distance between the microelectrodes, and d is the diameter of one of them. In the conductometer being developed, d = 55 µm, and the distance between the electrodes can be varied during the experiment and directly measured in divisions according to the scale of the eyepiece-micrometer of the microscope; therefore, it is convenient to tabulate beforehand the geometrical factor k. Intrinsic Conductivity of a Cell as a Function of the Field Intensity of the PEF. First, we measure the general conductivity of a cell and a liquid medium in a PEF with an intensity that increases linearly from zero (with increasing output voltage of the SPG). Then, for the same action, we measure the conductivity of only the medium, ignoring the microelectrodes in the direction of the cell. We calculate both the specific conductivity of the cell with the medium and the medium without the cell according to a single algorithm – according to (1) and (2). We plot the results of the calculation on the graph Gsp = ƒ(E), where E is the electric field intensity: E = (Uout – UR)/L. To obtain the conductivity of the cell alone, we calculate the corresponding ordinates on the graph or we calculate the conductivity directly analytically according to the formula introduced in the algorithm for calculation of the conductivity [10]. Calculations and construction of the graphs are carried out by using any of the programming packages, e.g., Microsoft Excel 2000. Metrological Certification (MC) of a Pulsed Conductometer. The development of the construction of a new, nonstandard device and measurement method provides for the certification of the metrological characteristics of the apparatus. In order to do this, we create a program based on the prevailing, standard documents: national and international standards: DSTU 1.5:2003, National Standardization. Rules for the Construction, Formulation, and Execution of Normative Acts and Requirements for Their Content; DSTU 3215-95, Metrology. Metrological Certification of Measuring Instruments. Organization and Procedures; DSTU 2681-94, Metrology. Terms and Definitions; GOST 8.326-89, GSI. Metrological Certification of Measurement Devices; GOST 8.010-99, MVI. Fundamental Positions; GOST 8.009:2008, Normalizable Metrological Characteristics of the Measurement Apparatus. We also used supplementary technical documents – Proceedings of R&D of the Institute for Animal Husbandry NAAN (2006–2010). According to the measurement scheme, we determine the metrological characteristics, which depend on the certification: the conductivity measurement range, based on the relative instrumental measurement error, and the linearity of the measurement circuit. Conductivity Measurement Range. For determination of the conductivity, it is advisable to use precision resistors for the magnitude of the inverse resistance, for establishment of the measurement range of a pulsed conductometer. After determining the resistance of each of the groups of these resistors, it is necessary to compare it with the nominal value and, after taking the inverse quantity, to establish the conductivity measurement range. To do this, we used precision resistors, intended for operation in pulsed-current circuits, type S2-29V (BADK.430410.002 TU), 0.5 W, with guaranteed tolerance (±0.05%) and nominal values, multiplied by 10 (besides 500 Ω) in the interval 500–1·108 8 Ω or in units of conductivity 0.01–2·103 µS. Resistors were connected to the measurement circuit instead of microelectrodes to their standard connection (see Fig. 1). The conductivity measurement range that is established was 0.00997–2.003·103 µS. Fundamental Relative Instrumental Error. In order to obtain this, we calculated the conductivity GN of the group of resistances RN of the same precision resistors (Table 1). Based on the measured values Gi in the groups for each nominal resistance of the resistor we found the mean value of the conductivity G=

1296

1 5

5

∑ Gi , i =1

TABLE 1. Experimental Data for the Measurement of Precision Resistors Group No.

RN, Ω (GN, µS) 3

Gi, µS

G, µS

σG, µS

±ΔG, µS

±δG, %

1

500 (2·10 )

1992; 2016; 2008; 2008; 1992

2003

10.7

29.7

1.5

2

103 (103)

995; 1001; 993; 998; 1004

998

4.4

12.2

1.2

100.1; 99.2; 99.6; 100.2; 99.4

99.7

0.4

1.11

1.1

3

4

2

10 (10 ) 5

4

10 (10)

10.01; 10.08; 10.01; 9.92; 10.02

10.01

0.057

0.16

1.6

5

106 (1)

0.999; 1.008; 1.004; 0.994; 1.001

1.001

0.0053

0.015

1.5

7

6

10 (0.1)

0.0993; 0.1001; 0.0999; 0.1001; 0.0999

0.0999

0.00033

0.00092

0.9

7

108 (0.01)

0.01001; 0.00993; 0.00992; 0.00996; 0.01002

0.00997

0.000046

0.00013

1.3

and the root-mean-square (RMS) deviation of the conductivity in each group:

σG

1 = 4

5

∑ (Gi − G )2 . i =1

Then we calculate and record in Table 1 the absolute (ΔG) and relative (δG) instrumental measurement error in the groups: ΔG = ±tασG;

δG = ± ΔG/G.

where tα = 2.78 is the Student coefficient (α = 0.95, n = 5). The maximum, fundamental, relative instrumental measurement error is calculated according to the equation [11] δ = ± δ 2G + δ 2N + δ 2os + δ 2t + δ 2R and equals δ = ±3.4% , where δG = ±1.6% is the maximum relative instrumental measurement error by group (see Table 1); δ N = ± 4 kT ( Rc + RN )Δf / U R = ±0.1% is the relative measurement error of the voltage owing to the Nyquist thermal noise across the calibrated (Rc) and precision (RN) resistors; Δƒ = (2.5τf)–1 is the bandwidth; τf = 100 nsec is the length of the pulse front; k is the Boltzmann constant; T = 300 K is the absolute temperature; δos = ±3% is the relative error of the digital oscillograph RIGOL DS5022M (according to its certificate); δt = ±0.015% is the relative error with respect to the temperature coefficient of the resistance of the precision resistors of type S2-29V (TU tolerance); δR = ±0.1% is the relative error of the resistance of the same resistor. Linearity of the Measuring Circuit. Verification of the linearity of the measuring circuit of a pulsed conductometer includes the simultaneous measurement of a two-channel oscillograph of voltage amplitude UR across the calibrated resistor Rc and output voltage Uout from the SPG, construction of the function UR(Uout), i.e., the spread function [12] and determination by linear approximation of the measured values of the maximum deviation of the experimental points of the straight-line approximation. Figure 2 shows the graph of the experimental dependence (the spread function). Measurements were carried out across a resistor of type S2-29V of resistance 1 kΩ (±0.05%), but instead of the measuring microelectrodes MME (see Fig. 1) in the series circuit we connect a precision resistor of type S2-29V of resistance 1 MΩ (±0.1%). From Fig. 2, it follows that the experimental points are well approximated by a linear dependence. The linear regression equation has the form 1297

UR, mV

Uout, V

Fig. 2. Graph of the experimental points of the spread function smoothed by a linear approximation.

G, μS/cm

E, kV/cm a

b

Fig. 3. Conductivity as a function of intensity of PEF: a) oocyte (1) and two-cell mouse embryo (2) in 0.3-M saccharose; b) glucose (1), saccharose (2), mannitol (3) (all 0.3 M), lime copper (4), and deionized water (5).

UR = 0.997Uout + 0.0287,

(3)

with coefficient of determination R2 = 0.9999. The maximum calculational deviation of the experimental points from the straight-line approximation (3) is no more than ±0.8%. This enables us to confirm that for all the nonlinearities exceeding the indicated deviation and arising during measurement of the conductivity of real biological objects and liquid media as a function of the intensity of the PEF, it is necessary to refer only to the calculation of the individual nonlinear properties of these objects. The investigated metrological characteristics of a pulsed conductometer in comparison with the instructions for its use are brought together in Table 2. Thus a pulsed conductometer based on fundamental technical characteristics is metrologically certified by the Departmental Commission of the Institute for Animal Husbandry of the National Academy of Agrarian Sciences of Ukraine as nonstandard devices for the measurement of the conductivity of single cells and liquid media with delivery of certification No. 1 from June 17, 2011.

1298

TABLE 2. Metrological Characteristics of Conductometer Value of characteristic Characteristic claimed

actual

Range of measurement of conductivity, µS

0.01–2·103

0.00998–2.003·103

Fundamental, relative instrumental error of measurement of conductivity, %

±3.5

±3.4

Nonlinearity of measuring circuit, not more than, %

±1

±0.8

In Fig. 3, as examples of a fundamental application of a pulsed conductometer we show the conductivity as a function of the field intensity E of the PEF for certain cells and liquid media. In Fig. 3a, the conductivity curve for an oocyte 1 has a sharp rise – an irreversible electrical breakdown of the membrane at E = 3.1 kV/cm; on the conductivity curve for a two-cell embryo 2 we see a reversible breakdown at the point of contact of the membrane of two blastomeres for a field intensity of about 1.1 kV/cm and an irreversible breakdown at 2.7 kV/cm. For both of these curves we see multiple, reversible oscillations of conductivity (electroporation) of the cell membrane. The conductivity of liquid dielectric media in Fig. 3b is almost independent of the field intensity. The oscillations in conductivity on certain curves show the presence in solution of a substance conducting impurities, which is not in the solvent (deionized water). The measuring unit developed can also be used for other operations with the application of pulsed, electrophysical actions, on which conductometry is based: the reconstruction of embryos (cloning, the obtaining of cell chimeras, etc.) [1, 4]; investigations of the parameters of electroporation of cell membranes in various media, including in solutions of cryoprotectors [13–15]; controlling the purity of liquid dielectrics, distilled water, water from natural sources, copper [16], various water-based, biotechnical media, etc. Thus, we have also developed and metrologically certified a pulsed conductometer in the structure of the unit of the apparatus for measurement of the electrical conductivity of biological cells and liquid media in a pulsed electric field with variable intensity.

REFERENCES 1. 2. 3. 4. 5. 6.

7. 8. 9.

V. A. Shigimaga, “Method and apparatus of pulsed conductometry of single animal cells and of liquid media,” Urgent Questions of Biophysics and Chemistry: 7th Int. Sci.-Tech. Conf., Sevastopol (2011), pp. 25–26. V. O. Shigimaga and V. I. Lisin, Ukrainian Patent 22334, “A pulsed conductometer for liquids,” publ. April 25, 2007, Byull., No. 5. V. A. Shigimaga, “Determination of the conductivity of embryonic animal cells,” in: Problems of Bionics [in Russian], Kharkov (2003), Iss. 59, pp. 60–64. V. A. Shigimaga, “Experience in the development of the apparatus and technology of electromanipulation with living cells,” Elektrif. Avtomatiz. Silsk. Gospod., No. 1(20), 53–63, Kiev (2007). V. O. Shigimaga, Ukrainian Patent 20187, “A method for determining the conductivity of liquid media,” publ. Jan. 15, 2007, Byull., No. 1. V. A. Shigimaga and Yu. E. Megel, “Use of the method of pulsed conductometry for investigation of the electrical characteristics of biological cells,” in: Proc. Institute of Electrodynamics, NAN Ukraine, Kiev (2012), Iss. 31, pp. 147–155. V. I. Lisin, “Method for preparation of metallic microelectrodes,” Visn. Poltav. DSGI, No. 2–3, 41–42 (2001). V. S. Andreev, Conductometric Methods in Biology and Medicine [in Russian], Meditsina, Moscow (1973). V. A. Shigimaga, “Form-factor of a conductometric cell with variable geometry,” Vost.-Evrop. Zh. Pered. Tekhnol., No. 6/5 (48), 45–48, Kharkov (2010).

1299

10. 11. 12. 13. 14.

15. 16.

1300

V. A. Shigimaga, “Conductometry of living cells in media with arbitrary conductivity,” Vestn. NTU KhPI. Nov. Resh. Sovr. Tekhnol., No. 57, 100–104, Kharkov (2010). P. V. Novitskii and I. A. Zograf, Estimation of the Errors of Measurement Results [in Russian], Energoatomizdat, Leningrad (1991). A. V. Soloviev and L. A. Luizova, “Instructional modeling and elimination of apparatus distortions,” Fund. Issled., No. 3, 84–86 (2004). O. A. Strikha et al., “The effect of ovary hormone stimulation on mouse oocyte and early embryo electric conductivity. 8th EBSA Europ. Biophys. Congr., Budapest, Hungary,” Europ. Biophys. J., 40, p. 240 (2011). E. I. Smolianinova, V. A. Shigimaga, and E. A. Gordienko, “Effect of cryoprotectors on the electrical conductivity of mouse oocytes,” in: Biophysics of Living Cells: Proc. Conf. on Cryoconservation as a Method for Conserving Biological Diversity, Pushchino (2008), Vol. 9, p. 124. V. O. Shigimaga, Ukrainian Patent 30272, “A method for determining the parameters of electrical breakdown of cell membranes by the curvature of conductivity,” publ. Feb. 25, 2008, Byull., No. 4. V. A. Shigimaga and L. M. Kolbina, “Measurement of specific electroconductivity of natural copper,” Nauch.-Tekh. Byull. IZh NAAN, No. 100, 509–514, Kharkov (2009).