On-line monitoring of the aggregate size distribution of Carthamus tinctorius L. cells with multi-frequency capacitance measurements

Abstract

This study provided an effective methodology for the aggregate size distribution measurement of Carthamus tinctorius L. cells during suspension culture. The results demonstrated that the changes of the cell aggregate size could be reflected in the β-dispersion by the multi-frequency capacitance measurements. Furthermore, a non-linear optimization model was established and validated for predicting the cell aggregate size distribution. In addition, the on-line predicted data agreed well with off-line measurements using microscopic observation and laser-based image analysis.

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Introduction

Production of valuable medicinal metabolites through plant cell suspension cultivation has proven to be an effective method in many industrial processes.^1–3 Cell aggregate distribution is one of the most important, yet also the most difficult to obtain, physiological parameters that can provide valuable information for process development, optimization and control.^2–4 The plant cell aggregation diameter has a broad range from 10 to 2000 μm.⁵ The cell aggregation state not only has serious effects on the nutrient and oxygen transfer rate, but also improves the cell sensitivity to shear force.^6,7

Much research has been carried out on quantifying the effect of aggregates on plant cell growth and secondary metabolite biosynthesis.^4,8–13 Kolewe's study demonstrated that smaller aggregates could significantly enhanced higher paclitaxel production than that with larger aggregates in Taxus suspension cultures, similar results has also been found in Vaccinium pahalae and C. tinctorius L. cultures.^4,9 These researches revealed that high oxygen transfer rate and nutrient supply in the center of the aggregated cell with small size would promote the cell growth rate and the secondary metabolite biosynthesis. However, some researches showed that the growth rate of larger aggregates are more rapid than that of small one, because the larger aggregates are facilitate well for the signal transduction from cell-to-cell.^9,11,12

Microscopy and mechanical sieving were commonly applied in most studies to precisely analyse the plant cell aggregates size distribution.^14,15 However, direct on-line size distribution analysis in the bioreactor would be more advantageous to get real-time information and avoid any interference with external sample manipulations. In recent years, many in situ probes have been developed for the direct on-line determination of cells size distribution and concentration based on several principles: in situ microscopy image analysis, laser-based image analysis, flow particle image analysis and so on.^16–19 But, these equipment are big in volume, precision, also very expensive. E.g. FPIA (Flow Particle Image Analysis) method, also need additional recycle system to sample the cells to the devices. Furthermore, sterilizing process is another limitation, normally they are not easy to sterilize and apply in industrial process.

The capacitance measurements is becoming an established tool for the estimation of viable biomass in many different cells culture.^20–23 The measuring capacitance at different frequencies causes a spectrum called “β-dispersion” (Fig. 1), which is proven to be related with the cell size distribution.^24,25 The underlying theory on the dielectric properties of biological cells has been extensively described elsewhere.²⁴ Many researches had illustrated that the cell size distribution could be predicted through the β-dispersion parameters, like characteristic frequency (fC) (the frequency at which the rate of polarization is one-half complete) shown in Fig. 1c, and α-angle of β-dispersion curve in fC (Fig. 1d).²⁵ The sensitivity of dielectric spectroscopy towards cell size has been used to monitor the major transition points of the culture in CHO perfusion cluture process.²⁴ It was further utilized by Sven Ansorge to estimate the cell size changes of CHO cells,¹⁷ and by Hauttmann and Müller to estimate the radius of hybridoma, yeast, and bacterial cells.²⁶ On the other hand, in Henry and Sven Ansorge's work,²⁵ they used multi-frequency capacitance measurements method with partial least square (PLS) models to monitor cell size distribution of mammalian cell cultures. The results demonstrate the method is accurately enough. But until now, hardly any information could be found for this method applying in the field of plant cell suspension culture process.

Fig. 1 Principle of culture capacitance measurements at several frequencies. Δε_max is mostly a function of the biomass concentration. The characteristic (or critical) frequency fc is the frequency at which the rate of polarization is one-half complete. fc depends mainly on the cell diameter and the conductivity. α means the homogeneous degree of the aggregation (figure adapted from Cannizzaro et al.²⁴).

The objective of this study was to demonstrate that the utility of multi-frequency capacitance measurements spectrum for plant cell size monitoring. More specifically, correlated capacitance performed at multi-frequency with changes in the cell size distribution, a constrained non-linear optimization model was built and used to predict the aggregates size distribution during the suspension culture process.

Materials and methods

Cell line and bioreactor setup

C. tinctorius L. were maintained in Murashige and Skoog (MS) medium supplemented with sucrose (30 g L⁻¹), 1-naphthylacetic acid (NAA) (10⁻² mM), and 6-benzylaminopurine (6-BA) (10⁻³ mM). The pH of the medium was adjusted to 6.2 prior to sterilization. Cell suspension culture was initially conducted in 1000 mL Erlenmeyer flasks and subculture every 7 days.

Then exponentially growing cells were inoculated into two parallel 5L stirred tank bioreactor with a working volume of 3L. It was equipped with two standard six blade Rushton turbines with a diameter of 72 m (0.45T). During the entire cultivation period, air flow rates (0.8 L min⁻¹), temperature (25 °c), stirring speeds (100, 250 rpm) were maintained at constant levels, corresponding to impeller Reynolds numbers Re_imp = ρ_lND²/μ, (where N is the rotation speed, D is the impeller diameter) from 0.86 × 10⁴ to 2.16 × 10⁴. Under the conditions described above, two bioreactor runs were conducted in batch mode, inoculated cell densities was covered a range from 1.6 to 1.7 g L⁻¹. Each experiments were operated until the end of logarithmic phase (about 7 days), samples were taken daily for analysis.

Cell number and cell size distribution determination

A laboratory scale focused beam reflectance FBRM (model G400) coupled with iC FBRM software from Mettler Toledo was implemented to detect the particle size distribution. The measurement range is from 0.5 to 1000 μm. The time interval of the measurement is 3 s, our data point is the average result of over 50 measurements on every sample.

In addition, Image-Pro Plus 6.0 software (Media Cybernetics, Bethesda, MA) was used to automatically determine the cell count and cell size based on microscopic observation. First of all, light microscope images of bacteria acquired by a CCD camera (cells are magnified 10 × 4 times) are handled with best-fit equalization and contrast enhancement. Then, the effects of edge enhancement, noise cancellation and smooth are realized by binarization processing. Finally, the counted dark areas are projected cell areas. In parallel, the objects that are not interested in must be hidden, and the adhesive objects must be split. In this investigation, three repetitions are conducted to accomplish 50 microscope images taken from a cell sample at every time point.

On-line capacitance measurements

β-Dispersion of capacitance were measured under an real-time bioreactor operations using a capacitance probe (Biomass Monitor 220, Hamilton Switzerland). The Hamilton software automatically analyzes the capacitance over a total of 17 frequencies from 0.3 to 10 MHz. Two data sampling type were used to monitor the normal viable biomass and cell size distribution. Low frequency data sampling type was acquired in intervals of 6 min, which was used for daily monitoring and high frequency data sampling type was acquired in interval of 6 s along 5 min measurement. All the data were saved in a comma-separated values (CSV) format file for subsequent analysis using Hamilton Software.

Standard capacitance β-dispersion measurement

In order to obtain the standard β-dispersion under different ranges of aggregate size, mechanical sieving was carried out to separate the aggregation to different range. A known volume sample was sieved through 6 cm diameter sieves of 1400, 880, 600, 425 and 96 μm (d₁, d₂…d₆ in Table 1) sieve apertures by rinsing with small volumes (40–50 mL) of 15 mM CaCl₂ solution. At least 300 n mL⁻¹ cell number was conducted in the smallest classification of 1400 μm aggregation size. Then, each classification was measured over the full range frequency.

Table 1 Aggregate size of the mechanical sieving

	d1	d2	d3	d4	d5	d6
Mesh number (n)	12	18	28	35	60	160
Aggregate diameter (μm)	1400	880	600	425	250	96

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Capacitance data analysed method

The matrix of the standard capacitance β-dispersion (A_eq[x]) means the β-dispersion produced by the specific cell aggregate in some certain size under different frequencies. So A_eq is a matrix composed of these standard β-dispersion under different ranges of aggregate size (d₁, d₂…d₆). Assume that an mixture cell aggregate sample was composed by these size classification (d₁, d₂…d₆). And if we have known the percentage of cell numbers in different size classifications (x = x₁, x₂…x₆). Then, the measured β-dispersion by this sample (b_eq) can be described by the standard β-dispersion (A_eq) using a mathematical equation (b_eq = A_eqx).

To facilitate the description of the algorithm, the size distribution is included into a vector x = [x₁, x₂…x₆]. Based on linear algebra principles, determination of x needs at least 6 independent equations. While, the β-dispersion were measured over a range of 0.1–10 MHz at 17 different frequency channels. For this case, the non-linear optimization model will provide the best fitting to the measurements, which is expressed by f(x) in eqn (1), and constraint conditions in eqn (2). The algorithm is easily implemented in the MATLAB.

min_xf(x) = abs(A_eqx − b_eq) (1)

Where c(x), and c_eq(x) are non-linear functions. c(x) means the different capacitance between adjacent frequency. c_eq(x) ensure the sum of x is equal to one. lb and ub is the lower and upper bounds in x, which is [0, 0⋯0] and [1, 1⋯1] in this research.

If the calculation follows a non-linear model, the f(x) as described by eqn (1) may have multiple local minima, but only the true value of x corresponds to its global minimum, i.e., the smallest one among all local minima. The presence of local minima often represents a problem because the initial setting for x at start would determine where the solution converges. When the initial x setting is close enough to its true value, x will converge to the global minimum. For this reason, a general known of the cell size distribution needs to be identified first, based on which a series of initial values can be selected. Theoretically, more frequency channels' data or independent equations will help the solution but the measuring error at high frequency maybe make the results more accurate or worse.

For comparing this capacitance method to other experimental data, a residual error, γ, was calculated as follows:

where x and x̂ are the cell size distribution based on capacitance measurement and other experimental method, respectively. This residual allows for a direct comparison of results between different method, and values of γ were used to judge the quality of the optimization function.

Result and discussion

Calibration curves of β-dispersion under different aggregate size

In order to build the calibration capacitance β-dispersion matrix A_eq, mechanical sieving was used to separate the aggregates to different range (d₁, d₂…d₆ in Table 1). The original unit of the measurement was in pF cm⁻¹, which means capacitance value in a certain volume. Then the results was divided by the cell counting numbers in n ml⁻¹ to obtain the specific capacitance, the unit of which is pF n⁻¹. The specific capacitance means the capacitance produced by a single cell aggregate, and the specific β-dispersion curves have the character of each aggregate size. This curves are correlated with the total volume of the cells or the size of the cell aggregate. Fig. 2 presents the specific capacitance β-dispersion of different ranges of aggregate size obtained through mechanical sieving. The results showed that they are corresponding well with the theory mentioned above, capacitance value increase with larger aggregate size.

Fig. 2 Calibration curves of β-dispersion under different cell aggregate size.

In the double logarithm coordinate, the relation between the measurement frequencies and the specific capacitance is linear and the capacitance β-dispersion is almost parallel to each other. Signals corresponding to the lower frequencies have the higher amplitudes. Fortunately, with the homogeneous aggregate size distribution in the determination, the measuring error is less than 5% of the average data (relative error).

Initiation and frequency optimization

If the calculation follows a non-linear model, the f(x) as described by eqn (1) may have multiple local minima, but only the true value of x corresponds to its global minimum, i.e., the smallest one among all local minima. The presence of local minima often represents a problem because the initial setting for x at start would determine where the solution converges. When the initial x setting is close enough to its true value, x will converge to the global minimum. For this reason, a general known of the cell size distribution needs to be identified first, based on which a series of initial values can be selected. Based on the maximum change range of the aggregate size from previous experience, three initial value were chosen to investigate the effect of the initiation on the capacitance data analysed method. First one is a value close to the normal distribution; in addition, a zero x and a relatively opposite to the distribution value were chosen. A set of capacitance data from an unknown aggregate size are utilized to validate the detected method. These three initial values are used as initial setting points to solve the non-linear optimization model, respectively. The aggregate size distributions determined by microscopic observation and laser-based image analysis were used to judge the quality of the model predictions. The laser-based image analysis method used as the control result, considering of fewer manual steps.

The results are presented in Fig. 3, and the residual errors γ were calculated based on the laser-based image analysis results. The capacitance based method provide accurate prediction of the distribution in all three initial value. The smallest γ = 0.06 contributed from the initial value close to the distribution (Fig. 3a). When the initial value is far from the distribution and the zero, γ = 0.08 will be slightly higher (Fig. 3b and c), and the major error is from the large aggregate prediction. However, for laser-based image method itself is accurate to the small particles (<1 mm), but because of the principle of this electrode, they are insensitive to the particle above 1 mm. On the other hand, the microscopic observation results also showed large different from the laser-based image analysis results (γ = 0.24). Accurately, in the microscopic observation determine process, there are some cell aggregates overlapped each other, some of which are two or three aggregates merged together in the image. So the results shown there are more large aggregates. However, these results indicate that initial value have limited influence on the analysed method over a broad range.

Fig. 3 Effect of size distribution dependence on initial value, using microscopic observation and laser-based image analysis experiments result to judge the quality of the model predictions. Three initial value were chosen: (a) close to the distribution x = [0.2, 0.4, 0.2, 0.1, 0.05, 0.05], (b) zero x = [0, 0, 0, 0, 0, 0] and (c) a relatively opposite to the distribution value x = [0.05, 0.05, 0.1, 0.2, 0.4, 0.2].

Furthermore, theoretically, more frequency channels' data or independent equations will help the solution. But, capacitance in high frequencies always have the great amplitudes due to the inhomogeneous of the cell distribution. These measuring errors maybe cause the overdetermined error to the solution. To estimate the influenced of selected frequency channels on the detected results, three different frequency range are used to solve the nonlinear optimization model, respectively. The spectra are measured over the range from 0.3 to 10 MHz with 17 different frequency channels, so the frequency ranges are set to from 0.3 to 1.1 (7 channels), 0.3 to 4.2 (13 channels) and 0.3 to 10 MHz (17 channels). These different frequency range are used to solve the nonlinear optimization model, respectively. The results are shown in Fig. 4, the residual error are also calculated based on the laser-based image analysis results. Three different frequency range calculation results were significant different, and the smallest γ = 0.06 contributed from the 13 channels' data, and this results were used for further calculation. In addition, it is evident in Fig. 4a and c that less frequency channels' data would decrease the accurate of the non-linear optimization model, and full frequency channels' data slightly overdetermined error to the solution.

Fig. 4 Effect of size distribution dependence on frequency selected, using microscopic observation and laser-based image analysis experiments result to judge the quality of the model predictions. Three frequency band were chosen: (a) 300–897 kHz, (b) 300–3342 kHz and (c) 300–10000 kHz.

Evaluation of method sensitivity to the measurements data

The distribution of the β-dispersion cell aggregate has a broad range, so the mixed gradient changing of the plant cell aggregate distribution caused by the flow field always result in the fluctuation on the capacitance measurement. 50 times of capacitance β-dispersion data with a sample are shown in Fig. 5A. These measurements data present a remarkable difference in a single scan, especially during the high frequency data (double logarithm coordinate). To evaluate the sensitivity of the method to the fluctuant measurements data, some manual interventions to the measurements were performed to simulate the fluctuation in the real measurement process. Although the average of many sample points will reduce this effect, the influence taken from the measurement fluctuation is still necessary for evolution the validity of this method. Three different fluctuations were applied to mimic the measurement fluctuation in the real process. The first fluctuation is the whole frequency data increase and decrease 7 percentage of the average data, the second fluctuation is 7 percentage improvement and decrement of the data at a random low frequency. And the third fluctuations are the 20 percentage improvement and decrement of the data at a random high frequency.

Fig. 5 (A) 50 times of capacitance β-dispersion data with a sample, black line means the average result. (B) Model sensitivity of the size distribution to the measurements data, some manual intervention to the measurements were performed. (a) is the whole frequency data increase and decrease 7 percentage of the average data, (b) is 7 percentage improvement (red dash line) and decrement (blue dash line) of the data at a random low frequency. (c) is the 20 percentage improvement and decrement of the data at a random high frequency.

These fluctuation capacitance data are used to solve the non-linear optimization model, respectively. Results are shown in Fig. 5B, the fluctuation improve significantly the residual error γ. In the first case, the whole frequency data change showed a remarkable increase in prediction errors, which ranged from γ = 0.13 to 0.19 compared with the average result γ = 0.06 by the positive or negative fluctuation. In the point data change case, the average prediction errors are γ = 0.40 and γ = 0.09, respectively in low and high frequency change. Low frequency data change improve more error compared with the high frequency data. With the frequency selected rule mentioned above, it was evidenced that capacitance data in high frequencies contribute less influence to the result. Therefore, though the capacitance in high frequency fluctuate a lot in the measurement, the capacitance based method can also provide accurate prediction.

Fermentation validation

To examine the performance of the capacitance measurements based method of monitoring of aggregate size distribution in the real fermentation process, we hence performed two batches cultures at different shear environment, expecting that aggregate size distribution would different. Fig. 6 shows the comparisons of profiles under low and high shear conditions for: biomass growth curve, residual sugar concentration, the average aggregate diameter, and the number of aggregate. The results revealed that the cell growth and the lag phase could be serious inhibited and postponed with the increased shear force. Meanwhile, the aggregation diameter encountered great difference under various shear environments during the former culture phase. At the start point of 4 h, the cell aggregation diameter was 225 μm under the lowest shear stress, which is much close to the mean diameter in shaken flask cultures.

Fig. 6 The fermentation validation is conducted under two shear conditions: black line-low shear conditions and blue line-high shear conditions. (a) Biomass growth curve (b) residual sugar concentration, (c) the comparison between the FBRM results (solid line) and the multi-frequency capacitance measurements results (dash line) of the mean aggregate size, (d) number of aggregates.

While with shear stress up, the particle diameter in 4 h decreased to 165 μm, which was 36% lower than that in low shear conditions. In the whole process, the average aggregation diameter increases with the time until reaching the highest diameter level of 300 μm.

Fig. 7 shows the comparisons of laser-based image analysis, microscopic observation and capacitance measurements based results for the aggregate distributions at 4, 72, 144 h in the real fermentation process. Compare with laser-based method the capacitance analysis method provided accurate predictions, particularly during the beginning of the culture, indicating that the model worked well under normal processing conditions. However, in the latter stages of the growth curve in the high shear condition, the capacitance based method failed to provide a reliable prediction of the distribution. This is because capacitance measurements method can only measure alive cells, so in the later sate of the culture, cell programmed death and shear related death make the measurement influences a lots. A similar phenomenon was happened in Holland's study when using this probe to monitor plant cell biomass.²² They stated that dead cells do not contribute to the capacitance value, but may contribute to the overall signal obtained by conventional measurements of PCV, FW and DW. So it is in an aggregate, some dead cells do not contribute to the capacitance measurement, but the particle is still in its size. This make capacitance measurement result did not agreed well with the other off-line measurements in the later stage of the culture. But the conventional off-line results did not influence a lot. In a similar work, Ansorge and Olivier Henry first using a partial least square (PLS) model to predict the cell concentration, cell viability, cell diameter and size distribution. They demonstrated that the model were validated to provide real-time quantitative information about the mean cell diameter and also cell size distribution. For the small range of the animal cell distribution (10 to 20 μm), the model can only described three volume clusters.

Fig. 7 Comparison of laser-based image analysis experimental data, microscopic observation and capacitance predictions for the aggregate distributions at 4, 72, and 144 h.

Conclusions

Aggregate size distributions of plant cell culture was commonly considered as one of the important physiological parameter, which has key relationship with the cell growth, metabolism and productivity. Therefore, determination and control of the aggregate cell size distribution play a significant role on C. tinctorius L. cells suspension cultivation. The present work demonstrated that the capacitance measurement sensor not only was an established tool for the online estimation of viable cell concentration, but also could be applied to determine the aggregate size distribution. A feasible and effective model was established for analysing the aggregate size distributions based on the capacitances measurements obtained under the multiple frequencies. The real time viable cell concentration and aggregate size distributions determination and control could be effective applied on the process optimization control and scale up achievement in suspension culture of C. tinctorius L.

Acknowledgements

This work was financially supported by a Grant from the National Natural Science Foundation of China (Grant No. 31200024), the National High Technology Research and Development Program (2015AA021005), and 973 Program No. 2013CB733600. The Royal DSM and partially supported by NOW-MoST Joint Program (2013DFG32630). We also thank pharmacy corporation Practical Bio Co., Ltd. (DALIAN, China) for donating the industrial strain.

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