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Determination of Cell Structures, Electrophysical Parameters, and Cell Population Heterogeneity
JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.
180, 122–126 (1996)
0281
Determination of Cell Structures, Electrophysical Parameters, and Cell Population Heterogeneity VICTOR D. BUNIN, 1
AND
ALEXANDER G. VOLOSHIN
National Research Institute of Applied Microbiology, Obolensk, Moscow, Russia, 142279 Received July 20, 1995; accepted December 5, 1995
MATERIALS AND METHODS The paper deals with the theory and practice of cell electrophysical parameter determination and its use for cell population heterogeneity evaluation. Electrooptical measurements and cell electrophysical models are background for cell electrophysical parameter calculations. Different methods of electrophysically homogeneous fraction determination are shown. The results of the above-mentioned algorithm testing are discribed. Change of cell heterogeneity during cell cultivation is demonstrated. q 1996 Academic Press, Inc. Key Words: cell polarizability; heterogeneity; electrophysical parameter; cultivation.
INTRODUCTION
Use of suspensions in scientific research and for resolution of applied problems is based on the analysis of a number of suspended-particle parameters. The determination of the fractional composition of a suspension is the first step in the detailed analysis of these parameters. The determination of particle partial concentration permits investigation of properties of each particle fraction separately and removal of defects in integrated valuation of parameters. The determination of heterogeneity is especially important in the analysis of cell suspension, as cell population heterogeneity is unavoidable in some cases. Unfortunately, the possibility of efficient assessment of cell culture heterogeneity according to the functional features by direct methods is severely limited and indirect methods are considered to be preferable. An electrooptical method for determination of the electrophysical parameters of suspended particles is one example. The method involves the measurement of the cell polarizability under an imposed harmonic electric field (1). Data processing enables determination of the suspension heterogeneity by polarizability integral characteristics as well as by a specified electrophysical parameters of the cell structures. The results obtained can be used as a basis for assessment of suspended cell heterogeneity in terms of certain physiological parameters. 1
To whom all correspondence should be addressed.
JCIS 4163
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6g0f$$$841
Electrooptical Measurements of Polarizability Parameters of Suspended Cells The frequency dispersion of tensor polarizability anisotropy of a particle (FDPA) is the initial parameter for determining the suspension heterogeneity in terms of electrophysical characteristics. Let us examine this parameter: The results of electrooptical measurements of cell suspension are used for determination of particle polarizability. Electrooptical analysis of suspended cells is directed toward determination of their characteristics as electrophysical objects. Such an object represents a set of structures with
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0021-9797/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
AID
The measurements used suspensions of the cells of Escherichia coli. Bacteria were grown by shaking at 377C meat peptone broth for 3 h. After completion of the cultivation, cells were harvested by filtration through Millipore acetate membrane filteres of 0.4 mm pore diameter. Cells on the filter were washed from the nutritive medium with distilled water and resuspended in distilled water. The resulting 10 ml suspension with specific electroconductivity 3 1 10 03 l/ ohm∗ m and optical density 0.4 ( l Å 660 nm, l Å 10 mm) was divided into two parts. The first part of the sample was placed in the measuring cell of the electrooptical analyzer (2). The second part of the sample was heated for 5 min on a water bath at 957C. This sample was also placed in the measuring cell of the electrooptical analyzer in experiments to determine the accuracy of the method. For the investigation of cell population heterogeneity during cultivation, the bacteria E. coli were grown under the same conditions for 10 h. The culture for the electrooptical measurements was sampled each hour. Sample preparation was performed as mentioned above. The processing of experimental results was conducted with the help of ‘‘ELBIC’’ software, which permits determination of the optical density of suspensions, common concentrations of cells, and concentrations of viable cells. Independent evaluation of viable cell concentration was determined by means of serial decimal dilutions cultivated in plates containing meat–peptone–agar.
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coidal
AP: Colloid
CELL POPULATION HETEROGENEITY EVALUATION
known electrophysical and morphometrical characteristics. The most convenient electrophysical model of a cell is that of an ellipsoid of revolution of a set confocal ellipsoids (envelopes). Each subsequent ellipsoid covers the previous one. The structure of four confocal ellipsoids adequately describes a cell, containing cytoplasm, cytoplasmic membrane, cell wall, and cell capsule. To a first approximation, it is possible to consider that the various thicknesses of confocal ellipsoids in longitudinal sections do not introduce essential errors. Then, the complete description of each cell structure uses two electrophysical parameters and the continuous thickness. The electrophysical parameter of cellular structure under study is a complex dielectric permeability, 1i , 1 Å 1i / s i / j v
[1]
where i Å ( 0 – 3 ) , 1i is the dielectric permeability of i structure, si is the electroconductivity of i structure, and v is the electric field frequency. In this electrophysical model the internal structure of the cell is the cytoplasm. Its morphometrical characteristics are the longitudinal ( a ) and transverse ( b ) size of cell, excluding the thickness of the external envelops. For the description of electrophysical properties of cells, a bulk Maxwell–Wagner polarizability of particles is used (3). Under the action of this polarizability, electric charges are formed along the boundaries of structures differing in dielectric permeability 1i or conductivity si . Their values are dependent on the relationship of the parameters, on the shape and size of the structures, and on the frequency and electric field strength. The polarizability tensor a ( v ) has a longitudinal component aÉ( v ) and two coincident transverse components a⊥ ( v ). The polarizability tensor a( v ) is an integral parameter for the charges distribution and registration. The difference between the longitudinal and transverse components is called ‘‘polarizability anisotropy,’’ da( v ) (FDPA), da( v ) Å aÉ( v ) 0 a⊥ ( v ).
[2]
Its value is dependent upon the electric field frequency ( v ) and independent of its strength. Interaction between the induced charges and electric field results in a rotational moment and orientation of cells along the vector of the electric field. The change of cell orientation results in the variations of the suspension optical properties, particularly light scattering. Changes in cellular light scattering leads to changes in optical density, but absorption of light by a suspension of cells is absent (4). The suspension turns opaque to some extent when cells orient along the light beam and becomes transparent for their transverse orientation. If the orientation is semi-random, the value of da( v ) is directly proportional to the change of optical density dD,
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da( v ) Å dD/(D ∗ t∗ Gc ∗ E 2 ),
123 [3]
where D is the optical density of cell sample, t is the optical transmission of cell sample, and Gc is the weight mean light scattering section of the cells. Progressive action of the electric field at some frequencies on the cell suspension enables plotting of the experimental function FDPA with the stationary value of optical density varying with frequency. Due to the electrophysical heterogeneity of the suspension, the experimental function FDPAe (dae ( v )) is defined as the sum of functions FDPAi (dai ( v )) which differ in shape from electrophysically homogeneous fractions with weight factors Ai from 0 to 1. The main problem arising in assessment of electrophysical heterogeneity of the suspension is to determine the FDPA functions corresponding to the fractions having identical electrophysical parameters. In the case of cell suspension heterogeneity analysis for viable and nonviable cells, it is possible to use the following method: For the determination of FDPAd of nonviable cells, the samples are subjected to damaging action (5). For the determination of FDPAv of viable cells another method is used, namely electrooptical measurements of a mix of fractions to determine FDPAe . The results of electrooptical measurement of FDPAd and FDPAe functions, and independent measurement of viable cell concentration, Nv and general cell concentration was used for the FDPAv calculation: FDPAv Å N ∗ (FDPAe 0 (1 0 Nv )/N) ∗ FDPAd )/Nv .
[4]
In some cases, an accuracy improvement in FDPAv follows from a parity increase as the relative content of viable cells tend to 1. For separation of homogeneous electrophysical properties, various more complex approaches and preparative methods can be used, such as division in a gradient of density, electrophoretic division, etc. Specific representation of the experimental FDPAe function leads to the necessity of transition from the set of electrophysical parameters to the composition FDPAi functions. In the general case, the explicit frequency relationship of the imaginary part of the complex dielectric permeability results in appearance of the frequency relationship of the theoretical FDPA function. Accurate calculations of FDPA values at each frequency v in bulk polarizability of a layered cell approximation could be made by using the relationship ( 6 ) a É, ⊥ ( v ) mÅn
Å
∑ ( HÉ, ⊥ (HÉ, ⊥ ( 1m01 / 1m , Vm01 ), 1m / 1m/1 , Vm ), [5]
mÅ2
where É, ⊥ are the longitudinal and transverse component symbols, n is the number of layers when being counted from outside to inside, 11 is the complex dielectric permeability
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TABLE 1 Electrophysical and Morphometrical Parameters of Cell Structure Cell wall
Cell membrane
Cell cytoplasm
Size
ew
d 1 1003 1/ ohm∗m
zw∗mkm
em
dv 1 1004 1/ ohm∗m
zmrmkm
ec
dc 1 1002 1/ ohm∗m
a (mkm)
b (mkm)
65
5.5
0.1
30
5
0.08
38
1.2
3.0
0.7
Note. zw and zm and the thickness of the cell wall and cell membrane, respectively.
of the medium, 1m is the complex dielectric permeability of the layer m, Vm is the m envelope volume, and HÉ, ⊥ ( ) are the rated recurrent factors. Determination of factor Ai is performed by minimizing the end function R, which is the incoherence between the experimental FDPAe function and the rated function that is equal to the sum of known experimental and/or model FDPAi (dai ( vj )) functions and unknown weight factors Ai , ( ( Ai Å 1), iÅp jÅk
R Å ∑ ∑ ((dae ( vj ) 0 Ai ∗ dai( vj ) 2 ),
[6]
iÅ1 j Å1
where p is the number of fractions and k is the number of frequencies. Achievement of the minimum of the end function enables selection of the best evaluation procedure for factor Ai . By using the modified simplex method and normalizing to the range interface, the error in weight factor calculations with known shape of components of FDPAi function exceeds the dispersion of the noise component only slightly. RESULTS
Determination of Accuracy Electrophysical Parameters Calculation We wish to evaluate the accuracy of determination of the some of the cell electrophysical parameters using the cell electrophysical model. The electrophysical model parameters similar to E. coli cell parameters is shown in the Table 1. Table 2 shows the values of relative error d 1 / 1 in the recovery obtained with different ratios of FDPA signal to noise (S/N). S/N is equal to the relationship of maximum TABLE 2 Relative Error de/e as Function of Modeling Signal FDPA to Noise (S/N) S/N
2
5
10
50
100
d ec / ee
40
20
7
4
2
AID
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value of FDPA function to the normal noise dispersion of the experimental (model) data. When other electrophysical parameters are being recovered, the dependence of relative error on the relationship S/N is identical, but the absolute value can vary slightly. Determination of Viable and Nonviable Suspended Cells Concentration A test of the algorithms was carried out by using the experimental data obtained using the ELBIC electrooptical analyzer. In order to evaluate the accuracy of determination of heterogeneity of the suspension consisting of viable and nonviable cell fractions using E. coli cells as a model, the functions FDPA were obtained for each fraction and mixture. Mixing the suspensions in a different ratio gave samples with different viable cell content. The resultant FDPA function are presented in Fig. 1. The absolute value of cytoplasm electroconductivity calculated for viable and nonviable cell fraction are 12 and 1 1 10 02 l/ohm∗ m, respectively. Shape variations of the FDPA function for viable and nonviable cells, and the ease of obtaining the FDPA functions, make it possible to perform efficient analysis of the mixtures having similar physiological characteristics (i.e., viability). A graph of the regression value of the concentration of viable cells measured by the electrooptical method and the same value measured by means of the serial dilutions cultivated in plates containing meat–peptone–agar is presented in Fig. 2. It can be seen that concentrations of the viable cells measured by the two methods differed by no more than 10%. Figure 3 shows the measurements of the relative content of E. coli viable cells and their total concentration as a function of culture time. DISCUSSION
As previously reported, the FDPA function shape depends upon the electrophysical parameters of cell envelopes and cytoplasm. The low frequency region of dispersion is defined by dielectric permeability and conductivity of the outer envelopes including the double electric layer and hydrated complexes enclosing the cell. On exposure to a destructive factor, this region of the FDPA appears to be very labile and depen-
coidal
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CELL POPULATION HETEROGENEITY EVALUATION
125
FIG. 1. FDPA of the viable E. coli cell suspension ( 1 ) and nonviable E. coli cell suspension ( h ) as well as of their mixtures: ( / ) 30% of viable cells; ( n ) 50% of viable cells; ( L ) 70% of viable cells.
FIG. 2. The line of regression of the viable cell concentration measured by the electrooptical method and the same value measured by means of the serial dilutions cultivated in plates containing meat–peptone–agar.
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FIG. 3. Monitoring the general cell concentration and viable cell concentration of E. coli by the electrooptical method during batch cultivation. ( h ) general cell concentration; ( / ) viable cell concentration.
dent on the variation of surface polarizability, an aspect not covered in this paper. The FDPA high frequency region is defined by the dielectric permeability and electroconductivity of the bacterial cell membrane and cytoplasm. Exposure to factors which damage the protective functions of cell envelopes (mechanical factors, heat, some chemicals) results in an increase of membrane conductivity and a decrease in cytoplasm magnitude. If the measurements are being conducted in a conventional medium with high dielectric permeability and relatively low electroconductivity (in distilled water, for example), then exposure to the destructive factors results in a predictable decrease of the high frequency maximum of FDPA to the low frequency region (Fig. 1). This FDPA behavior is supported by the results from the simulation procedure. The independent measurements of parameters by the time and labor-consuming methods within the regions of monotonic variation in viable cell concentration showed a correlation between the parameters with errors of no more than {10%.
3. Solution of the direct task of determination of the FDPA function according to the electrophysical parameters of the cell and the reverse task of recovery of these parameters by use of experimental FDPA function is described. 4. The results from practical determination of the heterogeneity of E. Coli suspensions during the cultivation process are presented. The experimental results confirm that the calculation procedures influence the accuracy of determination of weight factors only slightly. 5. The relationships between the electrophysical parameters and physiological characteristics of cells are shown. ACKNOWLEDGMENT These investigations were supported by the Ministry of Science and Technical Policy, RF within the International Project ‘‘EOST’’.
REFERENCES
1. Theoretical and practical bases for the electrophysical analysis of suspensions are considered. 2. The theory for determination of the suspension heterogeneity involving fractions of cells which differ in polarizability or electrophysical parameters is presented.
1. Dukhin, S. S., ‘‘Electrooptic of Colloids.’’ Naukova Dumka, Kiev, 1973. 2. Andreew, S. N., Brezgunov, V. N., Bunin, V. D. et al., Biotechnology (Rus). 5(2), 214 (1989). 3. Bottcher, G. P. F., ‘‘Theory of Electrical Polarisability.’’ Academic Press, N.Y., 1982. 4. Shchyogolev, S. Y., Khlebtsov, N. G., and Bunin, V. D., Proc. SPIE 2081, 167 (1994). 5. Brezgunov, V. N., Bunin, V. D., and Shvetz, N. V., Microbiology (Rus) 54(4), 616 (1985). 6. Styopin, A. A., J. Exp. Theor. Phys. YIII, 1230 (1972).
AID
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SUMMARY
JCIS 4163
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04-23-96 20:58:17
AP: Colloid
180, 122–126 (1996)
0281
Determination of Cell Structures, Electrophysical Parameters, and Cell Population Heterogeneity VICTOR D. BUNIN, 1
AND
ALEXANDER G. VOLOSHIN
National Research Institute of Applied Microbiology, Obolensk, Moscow, Russia, 142279 Received July 20, 1995; accepted December 5, 1995
MATERIALS AND METHODS The paper deals with the theory and practice of cell electrophysical parameter determination and its use for cell population heterogeneity evaluation. Electrooptical measurements and cell electrophysical models are background for cell electrophysical parameter calculations. Different methods of electrophysically homogeneous fraction determination are shown. The results of the above-mentioned algorithm testing are discribed. Change of cell heterogeneity during cell cultivation is demonstrated. q 1996 Academic Press, Inc. Key Words: cell polarizability; heterogeneity; electrophysical parameter; cultivation.
INTRODUCTION
Use of suspensions in scientific research and for resolution of applied problems is based on the analysis of a number of suspended-particle parameters. The determination of the fractional composition of a suspension is the first step in the detailed analysis of these parameters. The determination of particle partial concentration permits investigation of properties of each particle fraction separately and removal of defects in integrated valuation of parameters. The determination of heterogeneity is especially important in the analysis of cell suspension, as cell population heterogeneity is unavoidable in some cases. Unfortunately, the possibility of efficient assessment of cell culture heterogeneity according to the functional features by direct methods is severely limited and indirect methods are considered to be preferable. An electrooptical method for determination of the electrophysical parameters of suspended particles is one example. The method involves the measurement of the cell polarizability under an imposed harmonic electric field (1). Data processing enables determination of the suspension heterogeneity by polarizability integral characteristics as well as by a specified electrophysical parameters of the cell structures. The results obtained can be used as a basis for assessment of suspended cell heterogeneity in terms of certain physiological parameters. 1
To whom all correspondence should be addressed.
JCIS 4163
/
6g0f$$$841
Electrooptical Measurements of Polarizability Parameters of Suspended Cells The frequency dispersion of tensor polarizability anisotropy of a particle (FDPA) is the initial parameter for determining the suspension heterogeneity in terms of electrophysical characteristics. Let us examine this parameter: The results of electrooptical measurements of cell suspension are used for determination of particle polarizability. Electrooptical analysis of suspended cells is directed toward determination of their characteristics as electrophysical objects. Such an object represents a set of structures with
122
0021-9797/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
AID
The measurements used suspensions of the cells of Escherichia coli. Bacteria were grown by shaking at 377C meat peptone broth for 3 h. After completion of the cultivation, cells were harvested by filtration through Millipore acetate membrane filteres of 0.4 mm pore diameter. Cells on the filter were washed from the nutritive medium with distilled water and resuspended in distilled water. The resulting 10 ml suspension with specific electroconductivity 3 1 10 03 l/ ohm∗ m and optical density 0.4 ( l Å 660 nm, l Å 10 mm) was divided into two parts. The first part of the sample was placed in the measuring cell of the electrooptical analyzer (2). The second part of the sample was heated for 5 min on a water bath at 957C. This sample was also placed in the measuring cell of the electrooptical analyzer in experiments to determine the accuracy of the method. For the investigation of cell population heterogeneity during cultivation, the bacteria E. coli were grown under the same conditions for 10 h. The culture for the electrooptical measurements was sampled each hour. Sample preparation was performed as mentioned above. The processing of experimental results was conducted with the help of ‘‘ELBIC’’ software, which permits determination of the optical density of suspensions, common concentrations of cells, and concentrations of viable cells. Independent evaluation of viable cell concentration was determined by means of serial decimal dilutions cultivated in plates containing meat–peptone–agar.
04-23-96 20:58:17
coidal
AP: Colloid
CELL POPULATION HETEROGENEITY EVALUATION
known electrophysical and morphometrical characteristics. The most convenient electrophysical model of a cell is that of an ellipsoid of revolution of a set confocal ellipsoids (envelopes). Each subsequent ellipsoid covers the previous one. The structure of four confocal ellipsoids adequately describes a cell, containing cytoplasm, cytoplasmic membrane, cell wall, and cell capsule. To a first approximation, it is possible to consider that the various thicknesses of confocal ellipsoids in longitudinal sections do not introduce essential errors. Then, the complete description of each cell structure uses two electrophysical parameters and the continuous thickness. The electrophysical parameter of cellular structure under study is a complex dielectric permeability, 1i , 1 Å 1i / s i / j v
[1]
where i Å ( 0 – 3 ) , 1i is the dielectric permeability of i structure, si is the electroconductivity of i structure, and v is the electric field frequency. In this electrophysical model the internal structure of the cell is the cytoplasm. Its morphometrical characteristics are the longitudinal ( a ) and transverse ( b ) size of cell, excluding the thickness of the external envelops. For the description of electrophysical properties of cells, a bulk Maxwell–Wagner polarizability of particles is used (3). Under the action of this polarizability, electric charges are formed along the boundaries of structures differing in dielectric permeability 1i or conductivity si . Their values are dependent on the relationship of the parameters, on the shape and size of the structures, and on the frequency and electric field strength. The polarizability tensor a ( v ) has a longitudinal component aÉ( v ) and two coincident transverse components a⊥ ( v ). The polarizability tensor a( v ) is an integral parameter for the charges distribution and registration. The difference between the longitudinal and transverse components is called ‘‘polarizability anisotropy,’’ da( v ) (FDPA), da( v ) Å aÉ( v ) 0 a⊥ ( v ).
[2]
Its value is dependent upon the electric field frequency ( v ) and independent of its strength. Interaction between the induced charges and electric field results in a rotational moment and orientation of cells along the vector of the electric field. The change of cell orientation results in the variations of the suspension optical properties, particularly light scattering. Changes in cellular light scattering leads to changes in optical density, but absorption of light by a suspension of cells is absent (4). The suspension turns opaque to some extent when cells orient along the light beam and becomes transparent for their transverse orientation. If the orientation is semi-random, the value of da( v ) is directly proportional to the change of optical density dD,
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da( v ) Å dD/(D ∗ t∗ Gc ∗ E 2 ),
123 [3]
where D is the optical density of cell sample, t is the optical transmission of cell sample, and Gc is the weight mean light scattering section of the cells. Progressive action of the electric field at some frequencies on the cell suspension enables plotting of the experimental function FDPA with the stationary value of optical density varying with frequency. Due to the electrophysical heterogeneity of the suspension, the experimental function FDPAe (dae ( v )) is defined as the sum of functions FDPAi (dai ( v )) which differ in shape from electrophysically homogeneous fractions with weight factors Ai from 0 to 1. The main problem arising in assessment of electrophysical heterogeneity of the suspension is to determine the FDPA functions corresponding to the fractions having identical electrophysical parameters. In the case of cell suspension heterogeneity analysis for viable and nonviable cells, it is possible to use the following method: For the determination of FDPAd of nonviable cells, the samples are subjected to damaging action (5). For the determination of FDPAv of viable cells another method is used, namely electrooptical measurements of a mix of fractions to determine FDPAe . The results of electrooptical measurement of FDPAd and FDPAe functions, and independent measurement of viable cell concentration, Nv and general cell concentration was used for the FDPAv calculation: FDPAv Å N ∗ (FDPAe 0 (1 0 Nv )/N) ∗ FDPAd )/Nv .
[4]
In some cases, an accuracy improvement in FDPAv follows from a parity increase as the relative content of viable cells tend to 1. For separation of homogeneous electrophysical properties, various more complex approaches and preparative methods can be used, such as division in a gradient of density, electrophoretic division, etc. Specific representation of the experimental FDPAe function leads to the necessity of transition from the set of electrophysical parameters to the composition FDPAi functions. In the general case, the explicit frequency relationship of the imaginary part of the complex dielectric permeability results in appearance of the frequency relationship of the theoretical FDPA function. Accurate calculations of FDPA values at each frequency v in bulk polarizability of a layered cell approximation could be made by using the relationship ( 6 ) a É, ⊥ ( v ) mÅn
Å
∑ ( HÉ, ⊥ (HÉ, ⊥ ( 1m01 / 1m , Vm01 ), 1m / 1m/1 , Vm ), [5]
mÅ2
where É, ⊥ are the longitudinal and transverse component symbols, n is the number of layers when being counted from outside to inside, 11 is the complex dielectric permeability
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TABLE 1 Electrophysical and Morphometrical Parameters of Cell Structure Cell wall
Cell membrane
Cell cytoplasm
Size
ew
d 1 1003 1/ ohm∗m
zw∗mkm
em
dv 1 1004 1/ ohm∗m
zmrmkm
ec
dc 1 1002 1/ ohm∗m
a (mkm)
b (mkm)
65
5.5
0.1
30
5
0.08
38
1.2
3.0
0.7
Note. zw and zm and the thickness of the cell wall and cell membrane, respectively.
of the medium, 1m is the complex dielectric permeability of the layer m, Vm is the m envelope volume, and HÉ, ⊥ ( ) are the rated recurrent factors. Determination of factor Ai is performed by minimizing the end function R, which is the incoherence between the experimental FDPAe function and the rated function that is equal to the sum of known experimental and/or model FDPAi (dai ( vj )) functions and unknown weight factors Ai , ( ( Ai Å 1), iÅp jÅk
R Å ∑ ∑ ((dae ( vj ) 0 Ai ∗ dai( vj ) 2 ),
[6]
iÅ1 j Å1
where p is the number of fractions and k is the number of frequencies. Achievement of the minimum of the end function enables selection of the best evaluation procedure for factor Ai . By using the modified simplex method and normalizing to the range interface, the error in weight factor calculations with known shape of components of FDPAi function exceeds the dispersion of the noise component only slightly. RESULTS
Determination of Accuracy Electrophysical Parameters Calculation We wish to evaluate the accuracy of determination of the some of the cell electrophysical parameters using the cell electrophysical model. The electrophysical model parameters similar to E. coli cell parameters is shown in the Table 1. Table 2 shows the values of relative error d 1 / 1 in the recovery obtained with different ratios of FDPA signal to noise (S/N). S/N is equal to the relationship of maximum TABLE 2 Relative Error de/e as Function of Modeling Signal FDPA to Noise (S/N) S/N
2
5
10
50
100
d ec / ee
40
20
7
4
2
AID
JCIS 4163
/
6g0f$$$842
04-23-96 20:58:17
value of FDPA function to the normal noise dispersion of the experimental (model) data. When other electrophysical parameters are being recovered, the dependence of relative error on the relationship S/N is identical, but the absolute value can vary slightly. Determination of Viable and Nonviable Suspended Cells Concentration A test of the algorithms was carried out by using the experimental data obtained using the ELBIC electrooptical analyzer. In order to evaluate the accuracy of determination of heterogeneity of the suspension consisting of viable and nonviable cell fractions using E. coli cells as a model, the functions FDPA were obtained for each fraction and mixture. Mixing the suspensions in a different ratio gave samples with different viable cell content. The resultant FDPA function are presented in Fig. 1. The absolute value of cytoplasm electroconductivity calculated for viable and nonviable cell fraction are 12 and 1 1 10 02 l/ohm∗ m, respectively. Shape variations of the FDPA function for viable and nonviable cells, and the ease of obtaining the FDPA functions, make it possible to perform efficient analysis of the mixtures having similar physiological characteristics (i.e., viability). A graph of the regression value of the concentration of viable cells measured by the electrooptical method and the same value measured by means of the serial dilutions cultivated in plates containing meat–peptone–agar is presented in Fig. 2. It can be seen that concentrations of the viable cells measured by the two methods differed by no more than 10%. Figure 3 shows the measurements of the relative content of E. coli viable cells and their total concentration as a function of culture time. DISCUSSION
As previously reported, the FDPA function shape depends upon the electrophysical parameters of cell envelopes and cytoplasm. The low frequency region of dispersion is defined by dielectric permeability and conductivity of the outer envelopes including the double electric layer and hydrated complexes enclosing the cell. On exposure to a destructive factor, this region of the FDPA appears to be very labile and depen-
coidal
AP: Colloid
CELL POPULATION HETEROGENEITY EVALUATION
125
FIG. 1. FDPA of the viable E. coli cell suspension ( 1 ) and nonviable E. coli cell suspension ( h ) as well as of their mixtures: ( / ) 30% of viable cells; ( n ) 50% of viable cells; ( L ) 70% of viable cells.
FIG. 2. The line of regression of the viable cell concentration measured by the electrooptical method and the same value measured by means of the serial dilutions cultivated in plates containing meat–peptone–agar.
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AP: Colloid
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BUNIN AND VOLOSHIN
FIG. 3. Monitoring the general cell concentration and viable cell concentration of E. coli by the electrooptical method during batch cultivation. ( h ) general cell concentration; ( / ) viable cell concentration.
dent on the variation of surface polarizability, an aspect not covered in this paper. The FDPA high frequency region is defined by the dielectric permeability and electroconductivity of the bacterial cell membrane and cytoplasm. Exposure to factors which damage the protective functions of cell envelopes (mechanical factors, heat, some chemicals) results in an increase of membrane conductivity and a decrease in cytoplasm magnitude. If the measurements are being conducted in a conventional medium with high dielectric permeability and relatively low electroconductivity (in distilled water, for example), then exposure to the destructive factors results in a predictable decrease of the high frequency maximum of FDPA to the low frequency region (Fig. 1). This FDPA behavior is supported by the results from the simulation procedure. The independent measurements of parameters by the time and labor-consuming methods within the regions of monotonic variation in viable cell concentration showed a correlation between the parameters with errors of no more than {10%.
3. Solution of the direct task of determination of the FDPA function according to the electrophysical parameters of the cell and the reverse task of recovery of these parameters by use of experimental FDPA function is described. 4. The results from practical determination of the heterogeneity of E. Coli suspensions during the cultivation process are presented. The experimental results confirm that the calculation procedures influence the accuracy of determination of weight factors only slightly. 5. The relationships between the electrophysical parameters and physiological characteristics of cells are shown. ACKNOWLEDGMENT These investigations were supported by the Ministry of Science and Technical Policy, RF within the International Project ‘‘EOST’’.
REFERENCES
1. Theoretical and practical bases for the electrophysical analysis of suspensions are considered. 2. The theory for determination of the suspension heterogeneity involving fractions of cells which differ in polarizability or electrophysical parameters is presented.
1. Dukhin, S. S., ‘‘Electrooptic of Colloids.’’ Naukova Dumka, Kiev, 1973. 2. Andreew, S. N., Brezgunov, V. N., Bunin, V. D. et al., Biotechnology (Rus). 5(2), 214 (1989). 3. Bottcher, G. P. F., ‘‘Theory of Electrical Polarisability.’’ Academic Press, N.Y., 1982. 4. Shchyogolev, S. Y., Khlebtsov, N. G., and Bunin, V. D., Proc. SPIE 2081, 167 (1994). 5. Brezgunov, V. N., Bunin, V. D., and Shvetz, N. V., Microbiology (Rus) 54(4), 616 (1985). 6. Styopin, A. A., J. Exp. Theor. Phys. YIII, 1230 (1972).
AID
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SUMMARY
JCIS 4163
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6g0f$$$842
04-23-96 20:58:17
AP: Colloid