Quantitative modeling of viable cell density,cell size,intracellular conductivity,and membrane capacitance in batch and fed‐batch CHO processes using dielectric spectroscopy

Dielectric spectroscopy was used to analyze typical batch and fed‐batch CHO cell culture processes. Three methods of analysis (linear modeling, Cole–Cole modeling, and partial least squares regression), were used to correlate the spectroscopic data with routine biomass measurements [viable packed cell volume, viable cell concentration (VCC), cell size, and oxygen uptake rate (OUR)]. All three models predicted offline biomass measurements accurately during the growth phase of the cultures. However, during the stationary and decline phases of the cultures, the models decreased in accuracy to varying degrees. Offline cell radius measurements were unsuccessfully used to correct for the deviations from the linear model, indicating that physiological changes affecting permittivity were occurring. The β‐dispersion was analyzed using the Cole–Cole distribution parameters Δε (magnitude of the permittivity drop), f_c (critical frequency), and α (Cole–Cole parameter). Furthermore, the dielectric parameters static internal conductivity (σ_i) and membrane capacitance per area (C_m) were calculated for the cultures. Finally, the relationship between permittivity, OUR, and VCC was examined, demonstrating how the definition of viability is critical when analyzing biomass online. The results indicate that the common assumptions of constant size and dielectric properties used in dielectric analysis are not always valid during later phases of cell culture processes. The findings also demonstrate that dielectric spectroscopy, while not a substitute for VCC, is a complementary measurement of viable biomass, providing useful auxiliary information about the physiological state of a culture. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Multifrequency permittivity measurements enable on‐line monitoring of changes in intracellular conductivity due to nutrient limitations during batch cultivations of CHO cells

Lab and pilot scale batch cultivations of a CHO K1/dhfr^? host cell line were conducted to evaluate on‐line multifrequency permittivity measurements as a process monitoring tool. The β‐dispersion parameters such as the characteristic frequency (f_C) and the permittivity increment (Δε_max) were calculated on‐line from the permittivity spectra. The dual‐frequency permittivity signal correlated well with the off‐line measured biovolume and the viable cell density. A significant drop in permittivity was monitored at the transition from exponential growth to a phase with reduced growth rate. Although not reflected in off‐line biovolume measurements, this decrease coincided with a drop in OUR and was probably caused by the depletion of glutamine and a metabolic shift occurring at the same time. Sudden changes in cell density, cell size, viability, capacitance per membrane area (C_M), and effects caused by medium conductivity (σ_m) could be excluded as reasons for the decrease in permittivity. After analysis of the process data, a drop in f_C as a result of a fall in intracellular conductivity (σ_i) was identified as responsible for the observed changes in the dual‐frequency permittivity signal. It is hypothesized that the β‐dispersion parameter f_C is indicative of changes in nutrient availability that have an impact on intracellular conductivity σ_i. On‐line permittivity measurements consequently not only reflect the biovolume but also the physiological state of mammalian cell cultures. These findings should pave the way for a better understanding of the intracellular state of cells and render permittivity measurements an important tool in process development and control. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Passive electrical properties of the membrane and cytoplasm of cultured rat basophil leukemia cells. II. Effects of osmotic perturbation

The effects of osmotic perturbation on the dielectric behavior of cultured rat basophilic leukemia (RBL-1) cells were examined. Cells exposed to osmolalities (pi) of 145-650 mosmolal showed dielectric dispersions of the following characteristics: Permittivity increment delta epsilon(= epsilon l - epsilon h where epsilon l and epsilon h refer to the low- and high-frequency limit values) for a fixed volume concentration increased with pi; gross permittivity behavior was apparently of a typical Cole-Cole type; however, frequency dependence of conductivity was undulant and could be simulated by a superposition of two separate Cole-Cole type dispersions; separation of these subdispersions along the frequency axis was an increasing function of pi, and so was conductivity increment in the high-frequency region. As examined by light microscopy, the cells were spherical in spite of imposed anisotonic stresses and behaved as osmometers at 200-410 mosmolal. When normalized by dividing by number (not volume) concentration, delta epsilon remained relatively constant irrespective of pi. Apparent membrane capacities (Cm), analyzed by applying a single-shell model, increased systematically from a hypotonic value of approx. 1 microF/cm2 up to 5 microF/cm2 at 650 mosmolal. This increase was interpreted as due to increased cellular 'surface/volume' ratios that were confirmed by scanning electron microscopy. Cole-Cole's beta parameter, which culminated around 0.9 for isotonic cells and declined to approx. 0.8 for anisotonic cells, did not parallel the broadening of cell volume distribution but appeared to reflect changes in the intracellular conductivity caused by the anisotonic challenge. The results indicate that the dispersion method can probe changes in surface morphology as well as subcellular organelles' constitution of living cells.     

Real-time monitoring of adherent Vero cell density and apoptosis in bioreactor processes

This study proposes an easy to use in situ device, based on multi-frequency permittivity measurements, to monitor the growth and death of attached Vero cells cultivated on microporous microcarriers, without any cell sampling. Vero cell densities were on-line quantified up to 10⁶ cell mL⁻¹. Some parameters which could potentially impact Vero cell morphological and physiological states were assessed through different culture operating conditions, such as media formulation or medium feed-harvest during cell growth phase. A new method of in situ cell death detection with dielectric spectroscopy was also successfully implemented. Thus, through permittivity frequency scanning, major rises of the apoptotic cell population in bioreactor cultures were detected by monitoring the characteristic frequency of the cell population, f_c, which is one of the culture dielectric parameters. Both cell density quantification and cell apoptosis detection are strategic information in cell-based production processes as they are involved in major events of the process, such as scale-up or choice of the viral infection conditions. This new application of dielectric spectroscopy to adherent cell culture processes makes it a very promising tool for risk-mitigation strategy in industrial processes. Therefore, our results contribute to the development of Process Analytical Technology in cell-based industrial processes.     

Real-time monitoring of yeast cell division by dielectric spectroscopy.

To assay cell cycle progression in synchronized culture of yeast we have applied dielectric spectroscopy to its real-time monitoring. The dielectric monitoring is based on the electromagnetic induction method, regarded as a nonelectrode method, which has resolved the problems encountered in measurements with metal electrodes, namely electrode polarization and bubble formation on electrodes. In the synchronized culture with temperature-sensitive cell division cycle mutants, the permittivity of the culture broth showed cyclic changes at frequencies below 300 kHz. The increase and decrease in the cyclic changes of the relative permittivity correspond to the increase in cell length and bud size and to the septum formation between mother and daughter cells, respectively.     

On-line monitoring of infected Sf-9 insect cell cultures by scanning permittivity measurements and comparison with off-line biovolume measurements

Two infected Sf-9 cell cultures were monitored on-line by multi-frequency permittivity measurements using the Fogale BIOMASS SYSTEM^® and by applying different off-line methods (CASY^®1, Vi-CELL?, packed cell volume) to measure the biovolume and the mean diameter of the cell population. During the growth phase and the early infection phase the measured permittivity at the working frequency correlated well with the different off-line methods for the biovolume. We found a value of 0.67 pF cm^?1 permittivity per unit of total biovolume (CASY) (μL mL^?1). After the maximum value in the permittivity was reached, i.e. when the viability of the cultures decreased significantly, we observed different time courses for the biovolume depending on the applied method. The differences were compared and could be explained by the underlying measurement principles. Furthermore, the characteristic frequency (f_C) was calculated from the on-line scanning permittivity measurements. The f_C may provide an indication of changes in cell diameter and membrane properties especially after infection and could also be an indicator for the onset of the virus production phase. The changes in f_C were qualitatively explained by the underlying equation that is correlating f_C and the properties of the cell population (cell diameter, intracellular conductivity and capacitance per membrane area).     

Apparatus for the electrical characterisation of conductive fluids

Non-invasive and fully automated conductimetric measurements of electrolyte and bacterial samples were achieved in a closed volume test cell, comprising a magnetic field coil and detector. By monitoring field induced currents in sample electrolytes the magnitude of the sample current was shown to vary as the inverse of the sample impedance. The impedance characteristic was shown to be that of an LCR resonant circuit. This characteristic is primarily a function of the applied frequency and the solution/cell properties being dependent on the solution conductivity and dielectric permittivity at any given concentration. Small changes in sample dielectric permittivity in the presence of a large background conductivity are shown to be significant.The apparatus described can provide fixed or swept frequency conductivity measurements in the range 1 kHz to 2.25 MHz with a lower conductivity sensitivity of 0.9 × 10⁻³ Scm⁻¹. Bulk impedimetric characteristics of cell suspensions are derived by a two stage measurement.     

Passive electrical properties of the membrane and cytoplasm of cultured rat basophil leukemia cells. I. Dielectric behavior of cell suspensions in 0.01-500 MHz and its simulation with a single-shell model

Frequency dependence of relative permittivity (dielectric constant) and conductivity, or the 'dielectric dispersion', of cultured cells (RBL-1 line) in suspension was measured using a fast impedance analyzer system capable of scanning 92 frequency points over a 10 kHz-500 MHz range within 80 s. Examination of the resulting dispersion curves of an improved reliability revealed that the dispersions consisted of at least two separate components. The low-frequency component (dispersion 1) had a permittivity increment (delta epsilon) of 10(3)-10(4) and a characteristic frequency (fc) at several hundred kHz; for the high-frequency component (dispersion 2), delta epsilon was smaller by a factor of 10(2) and fc = 10-30 MHz. Increments delta epsilon for both components increased with the volume fraction of cell suspension, while fc did not change appreciably as long as the conductivity of suspending medium was fixed. By fitting a model for shelled spheres (the 'single-shell' model) to the data of dispersion 1, the dielectric capacity of the plasma membrane phase (Cm) was estimated to be approx. 1.4 microF/cm2 for the cells in an isotonic medium. However, simulation by this particular shell model failed to reproduce the entire dispersion profile leaving a sizable discrepancy between theory and experiment especially at frequencies above 1 MHz where dispersion 2 took place. This discrepancy could not be filled up even by taking into consideration either the effect of cell size distribution actually determined or that of possible heterogeneity in the intracellular conductivity. The present data strongly indicate the need for a more penetrating model that effectively accounts for the behavior of dispersion 2.     

Dielectric properties of alginate beads and bound water relaxation studied by electrorotation

The electrical and dielectric properties of Ba²⁺ and Ca²⁺ cross‐linked alginate hydrogel beads were studied by means of single‐particle electrorotation. The use of microstructured electrodes allowed the measurements to be performed over a wide range of medium conductivity from about 5 mS/m to 1 S/m. Within a conductivity range, the beads exhibited measurable electrorotation response at frequencies above 0.2 MHz with two well‐resolved co‐ and antifield peaks. With increasing medium conductivity, both peaks shifted toward higher frequency and their magnitudes decreased greatly. The results were analyzed using various dielectric models that consider the beads as homogeneous spheres with conductive loss and allow the complex rotational behavior of beads to be explained in terms of conductivity and permittivity of the hydrogel. The rotation spectra could be fitted very accurately by assuming (a) a linear relationship between the internal hydrogel conductivity and the medium conductivity, and (b) a broad internal dispersion of the hydrogel centered between 20 and 40 MHz. We attribute this dispersion to the relaxation of water bound to the polysaccharide matrix of the beads. The dielectric characterization of alginate hydrogels is of enormous interest for biotechnology and medicine, where alginate beads are widely used for immobilization of cells and enzymes, for drug delivery, and as microcarriers for cell cultivation. © 1999 John Wiley & Sons, Inc. Biopoly 50: 227–237, 1999     

Theory of dipolar relaxation in aqueous macromolecular solutions

Recent advances in dielectric theory are applied to two models representing an aqueous solution of dipolar macromolecules. In one model the water is treated as a dielectric continuum and the macromolecule as a finite-sized sphere; in the other both components are represented as point dipoles suspended in a background dielectric. The predicted frequency dependences of the complex permittivity in these two cases agree and the validity of the dielectric technique for estimating macromolecular size and shape is established. The model in which water is treated as a dielectric continuum predicts a larger dielectric dispersion in the radio frequency region, which is consistent with the experimental data available for myoglobin. The validity of the Debye formula for relaxation time and the effect of “dielectric friction” in macromolecular solutions are also discussed.     

Dielectric properties of mouse lymphocytes and erythrocytes

In order to study the effect of the nucleus on dielectric behavior of the whole cell, permittivity (dielectric constant) and conductivity of mouse lymphocytes and erythrocytes were measured over a frequency range from 0.1 to 250 MHz. Erythrocytes (spherocytes) showed a single dielectric dispersion, which was explained by a single-shell model that is a conducting sphere covered with a thin insulating shell. On the other hand, lymphocytes showed a broad dielectric dispersion curve which was composed of two subdispersions. The high-frequency subdispersion, which was not found for erythrocytes, was assigned to the Maxwell-Wagner dispersion of the nucleus occupying about 65% of the total cell volume. Analysis of the lymphocyte dispersion was carried out by a double-shell model, in which a shelled sphere, i.e., nucleus, is incorporated into the single-shell model. The following electrical parameters were consequently estimated; the capacitance of the plasma membrane, 0.86 microF.cm-2; the conductivity of the cytoplasm, 3.2 mS.cm-1; the capacitance and conductance of the nuclear envelope are, respectively, 0.62 microF.cm-2 and 15 S.cm-2, and the permittivity and conductivity of the nucleoplasm are 52 and 13.5 mS.cm-1.     

Cell-based screening for membranal and cytoplasmatic markers using dielectric spectroscopy

Dielectric spectroscopy (DS) of living biological cells is based on the analysis of the complex dielectric permittivity of cells suspended in a physiological medium. It provides knowledge on the polarization–relaxation response of cells to external electric field as function of the excitation frequency. This response is strongly affected by both structural and molecular properties of cells and therefore, can reveal rare insights on cell physiology and behaviour. This study demonstrates the mapping potential of DS after cytoplasmatic and membranal markers for cell-based screening analysis. The effect of membrane permittivity and cytoplasm conductivity was examined using tagged MBA and MDCK cell lines respectively. Comparing the permittivity spectra of tagged and native cell lines reveals clear differences between the analyzed suspensions. In addition, differences on the matching dielectric properties of cells were obtained. Those findings support the high distinction resolution and sensitivity of DS after fine molecular and cellular changes, and hence, highlight the high potential of DS as non invasive screening tool in cell biology research.     

Boundary-element calculations for dielectric behavior of doublet-shaped cells

In order to simulate dielectric relaxation spectra (DRS) of budding yeast cells (Saccharomyces cerevisiae) in suspension, the complex polarization factor (Clausius-Mossotti factor) beta for a single cell and the complex permittivity of a cell suspension epsilon(sus)* were calculated with a doublet-shaped model (model RD), in which two spheres were connected with a part of a ring torus, using the boundary element method. The beta values were represented by a diagonal tensor consisting of components beta(z) parallel to the rotation axis (z axis) and beta(h) in a plane (h plane) perpendicular to the axis. The epsilon(sus)* values were calculated from the complex permittivity of the suspending medium epsilon(a)* and the components of beta. The calculation was compared with that of a conventional prolate spheroid model (model CP). It was found that model CP could be used as a first approximation to model RD. However, differences existed in beta(z) between models RD and CP; beta(z) showed three relaxation terms in the case of model RD in contrast with two terms in model CP. Narrowing the junction between the two spheres in model RD markedly decreased the characteristic frequency of one of the relaxation terms in beta(z). This suggests that the structure of the junction can be estimated from DRS. Effects of the shape change from model RD to a two-sphere model (model RD without the junction) were also examined. The behavior of beta(z) in the two-sphere model, the relaxation intensity of which was much lower than model RD, was quite similar to that in a single-sphere model. These simulations were consistent with the experimental observations of the dielectric behavior of the yeast cells during cell cycle progression.     

Dielectric behavior of the frog lens in the 100 Hz to 500 MHz range. Simulation with an allocated ellipsoidal-shells model.

In an attempt to correlate the passive electrical properties of the lens tissue with its structure, we measured ac admittances for isolated frog lenses, lens nuclei, and homogenate of cortical fiber cells, over the frequency range 10(2)-5.10(8) Hz. The whole lenses molded into discoid shape show a characteristic "two-step" dielectric dispersion with a huge permittivity increment of the order of 10(5) at 1 kHz. Of the two subdispersions disclosed, dispersion 1 has a permittivity increment (delta epsilon) of 2.10(5) with a characteristic frequency (fc) of 2 kHz, and dispersion 2 has a delta epsilon of 400 with an fc of 2 MHz. In terms of loss tangent, these dispersions are more clearly located as two separate peaks. Data are analyzed using an allocated ellipsoidal-shells model which has been developed by taking into account fiber orientation inside the lens tissue. Dispersion 1 is assigned to the equatorial cortex, where fiber cells run parallel to the applied electric field, and dispersion 2 to the nucleus with a complex fiber arrangement and also to the polar cortex, in which the fiber alignment is predominantly perpendicular. In addition, the model analysis reveals that, in the frog lens, the nucleus occupies approximately 30% in volume and that relative permittivity and conductivity for the cell interior are, respectively, 45 and 3 mS/cm for the cortical cells, and 28 and 0.3 mS/cm for the nuclear cells.     

Theoretical examination of aggregation effect on the dielectric characteristics of spherical cellular suspension

Dielectric dispersion analysis of cellular suspension is generally based on the analogy to equivalent periodic material made up of identical inclusions. However, under true physiological conditions, when coupling and aggregation events usually occur, this analogy can introduce severe errors when attempting to probe the dielectric characteristics of the suspended fraction. In the framework of this study, a theoretical examination of the effect of aggregation on the dielectric characteristics of spherical cellular suspension is presented. Here, small clusters of coupled and fused (gap connected) shelled spheres were used to imitate the presence of aggregates when suspended in a homogenous suspension of spherical cells. The permittivity spectra of the aggregate-cell mixtures were numerically calculated by applying computational solution of complex potential problem using 3D Boundary Element Method. The dispersion characteristics of the mixtures have been determined as function of both aggregates shape and concentration. Those reveal significant deviations in comparison to the characteristics of homogenous cellular suspension. Quantitative analyses of the induced fields and transmembrane potential gradients of the interacted cells suggest that those deviations are mainly induced due to changes occur on the polarization state of the membranes.     

Characterizing cellular systems by means of dielectric spectroscopy

The dielectric behavior of a suspension of synchronized, spherical cells has been investigated in relation to the electrical parameters of certain cell structures. In the quasistatic approximation, Poisson's equations are solved for the respective diffusive media, and the local charge distributions are derived by taking into account the continuity equations. The results describe both α and β dispersion and reduce, in the corresponding limiting cases, to previous reports. The dependence of suspension permittivity in α-and β-dispersion ranges on the diffusive effects, the conductivity, and the permittivity of cytoplasm, of membrane, and of culture medium as well as on membrane thickness is pointed out. The possibility is pointed out of characterizing cellular behavior by means of the evolution of certain electrical and morphological parameters during cell cycle progression as well the effects of different stimuli on cellular systems derived by fast dielectric spectroscopy. © 1996 Wiley-Liss, Inc.     

Dielectric increment and dielectric dispersion of solutions containing simple charged linear macromolecules. II. Experimental results with synthetic polyelectrolytes

The electric permittivity of aqueous solutions of different synthetic polyelectrolytes have been measured as a function of frequency in the range 5 kHz up to 100 MHz in the absence of added salt. Solutions of polymethacrylic acid and polyacrylic acid of different degrees of polymerization, both partially neutralized with NaOH, were investigated as well as solutions of Na-polystyrenesulphonate at different concentrations.For all systems a dispersion profile with two separated dispersion regions was obtained with a molecular weight dependent value of the static electric permittivity. The low frequency dispersion region was found to be characterized by a molecular weight dependent mean relaxation time while for the high frequency dispersion region both the mean relaxation time and the dielectric increment are molecular weight independent. It is shown that the reciprocal values of the specific increments and of the relaxation times depend linearly on the macromolecular concentration. Extrapolation of the corresponding quantities to infinite dilution was found to be possible. A comparison of these extrapolated values with calculated ones according to the previously derived theory also applicable to flexible macromolecules establishes that this theory describes satisfactorily the dielectric behaviour of the systems investigated.The conclusion is reached that the high frequency dispersion and relaxation can be attributed to fluctuations in the distribution of bound counterions along limited parts of the macromolecule. The relaxation time of the low frequency dispersion region seems to be essentially determined by the rotation of the complete molecule and the static electric permittivity can he explained in terms of fluctuations in the counterion density extending over the whole macromolecule.     

Detecting hydrogen peroxide in leaves in vivo – a comparison of methods

Four hydrogen peroxide detecting probes, 3,3′‐diaminobenzidine (DAB), Amplex Red (AR), Amplex Ultra Red (AUR) and a europium–tetracycline complex (Eu₃Tc) were infiltrated into tobacco leaves and tested for sensitivity to light, toxicity, subcellular localization and capacity to detect H₂O₂ in vivo. In the absence of leaves, in water solutions, AUR was very much sensitive to strong light, AR showed slight light sensitivity, while DAB and Eu₃Tc were insensitive to irradiation. When infiltrated into the leaves, the probes decreased the photochemical yield (Φ_PSII) in the following order of effect AR > DAB > AUR > Eu₃Tc. With the exception of Eu₃Tc, all probes stimulated the build‐up of non‐photochemical quenching either temporally (DAB, AUR) or permanently (AR), showing that their presence may already limit the photosynthetic capacity of leaves, even in the absence of additional stress. This should be taken into account when using these probes in plant stress experiments. Confocal laser scanning microscopy studies with the three fluorescent H₂O₂ probes showed that the localizations of Eu₃Tc and AUR were mainly intercellular. AR partly penetrated into leaf chloroplasts but probably not into the thylakoid membranes. Photosynthesis‐related stress applications of AR seem to be limited by the low availability of internal leaf peroxidases. Applications of AR for kinetic H₂O₂ measurements would require a co‐infiltration of external peroxidase, imposing another artificial modifying factor and thus taking experiments further from ideal, in vivo conditions. Our results suggest that the studied H₂O₂ probes should be used in leaf studies with caution, carefully balancing benefits and artifacts.     

Microwave dielectric measurements of erythrocyte suspensions.

Complex dielectric constants of human erythrocyte suspensions over a frequency range from 45 MHz to 26.5 GHz and a temperature range from 5 to 40 degrees C have been determined with the open-ended coaxial probe technique using an automated vector network analyzer (HP 8510). The spectra show two separate major dispersions (beta and gamma) and a much smaller dispersion between them. The two major dispersions are analyzed with a dispersion equation containing two Cole-Cole functions by means of a complex nonlinear least squares technique. The parameters of the equation at different temperatures have been determined. The low frequency behavior of the spectra suggests that the dielectric constant of the cell membrane increases when the temperature is above 35 degrees C. The real part of the dielectric constant at approximately 3.4 GHz remains almost constant when the temperature changes. The dispersion shifts with temperature in the manner of a thermally activated process, and the thermal activation enthalpies for the beta- and gamma-dispersions are 9.87 +/- 0.42 kcal/mol and 4.80 +/- 0.06 kcal/mol, respectively.