software sensors for the monitoring of perfusion cultures: evaluation of the hybridoma density and...

Cytotechnology 15: 291-299, 1994. 291 @ 1994 Kluwer Academic Publishers. Printed in the Netherlands.

Software sensors for the monitoring of perfusion cultures: Evaluation of the hybridoma density and the medium composition from glucose concentration measurements

Franqois Pelletier, Christian Fonteix, Aur61io Lourenqo da Silva, Annie Marc and Jean-Marc Engasser tnstitut National Potytechnique de Lorraine, Laboratoire des Sciences du Gdnie Chimique, CNRS, 2, avenue de la ForOt de Haye, BP 172, F-54500 Vandoeuvre-les-Nancy Cedex, France

Key words: Estimator, Extended Kalman Filter, hybridoma, kinetic model, perfusion culture.

Abstract

New software sensors based on the Extended Kalman Filter technique have been developed for the monitoring of animal cell perfusion cultures. They use a kinetic model describing the growth, death and metabolism of hybridoma cells as a function of the medium composition. The model was initially validated on a batch culture and found to correctly predict the continuous perfusion culture kinetics, except for the production of ammonia and lactate. Using the measurement of a single component in the culture medium, in this case glucose, the Extended Kalman Filter provides an excellent evaluation of the time variation of the concentrations of living and dead cells, of glutamine and antibodies, during the whole perfusion culture for a retained cell density rising from 1 to 11 x 106 cells.m1-1 inside the reactor.

Nomenclature

Kinetic model A, death rate constant (h- 1); D, dilution rate (h- 1 ); Glc, glucose concentration (raM); Gin, glutamine concentration (raM); kb, specific death rate (h-l); kt, specific lysis rate (h-l); Kcz,~, glutamine saturation constant (raM); KLan, lactate inhibition constant (raM); + KNH 4, ammonia inhibition constant (mM); Lac, lactate concentration (raM); Mab, monoclonal antibodies concentration (rag.l-I); NH +, ammonia concentration (mM); X, living cell density (cells.ml-1); Xb, dead (blue) cell density (cells.ml-1); Y, yield coefficients (mmol. 10 -9 cells or mg. 10 -9 cells).

Greek symbols a, retention coefficient of antibodies; ~ln, glutamine kinetic constant for death rate expression (raM); ~Lac, lactate kinetic constant for death rate expression (mM-a); t~Nn+, ammonia kinetic constant for death rate expression

(raM-l); u, specific consumption rates (mmol.h - t . 10 -9 cells); #, specific growth rate (h-l); #max, maximum specific growth rate (h-l); 7r, specific production rates (mmol.h -1. 10 -9 cells or mg.h -1. 10 -9 cells).

Extended Kalman Filter f, vector of system dynamics; h, measurement equation; K, Kalman gain matrix; t, time; v, measurement noise vector; w, system noise vector; x, state vector; y, measurement or output vector.

Superscripts and subscripts ~, estimation; ~, prediction; in, feeding.

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Introduction

The efficient operation of high cell density perfusion (Graf & Schtigerl, 1991; Rolf et al., 1992; de la Broise et al., 1992) or fed-batch (Omasa et al., 1992) cultures requires an optimal feeding of nutrients during the phases of cellular growth and protein production. This necessitates a monitoring of the concentration of viable cells, of their metabolic activities and of the medium composition.

Unfortunately reliable physical sensors for on-line monitoring of cytoreactors are still rare. A feasible alternative is the use of indirect or software sensors which have been the subject of attention for many years (Bastin & Dochain, 1990; Stephanopoulos & San, 1984; Van der Heijden et al., 1989) and are increasingly utilized in the fermentation industry. They consist of algorithms which, through the use of simulation models of the process, provide an estimation of the medium composition from a limited number of on-line or off-line analyses.

A new estimator for mammalian cell cultures, developed as a central part of an advanced control procedure, is presented. It entails a kinetic model initially established on a batch culture. The properties of the estimator are illustrated on a continuous perfusion culture yielding a high hybridoma cell density.

Materials and methods

Cell cultures

Cell line and culture medium The 6H2 murine cell line provided by Sorin Biomed- ica (Sallugia, Italy) results from the fusion of mouse BALB/c spleen cells and Sp2.0 myeloma cells. The monoclonal antibody produced is an IgG2a directed against a high molecular weight melanoma-associated antigen. Cells have been routinely cultivated in T-flasks for 6 days, before transferred inside the bioreactor at a concentration of 0.15 to 0.2 x 106 cells.m1-1.

Batch culture The batch culture was performed in a 2 liters reactor (Inceltech-SGI, France) with 1.2 liter working volume. The DMEM/HamF12 (3:1) basal medium was supple- mented with 15.6 mM glucose, 4 mM glutamine, 5% (v/v) Fetal calf serum, 2% (v/v) essential amino acids, 1% (v/v) non essential amino acids and antibiotics

K G In KLa c NH~

~t = gmax" G In+ K G In" Lac + KLa c " NI-t~ + K NH2

kb = A'(~c"'u+" NH~ + ~:Lac'Lac + \ "n4 G ln+~ZGln I ~ G In

VGlc = YGlc'g

VG In = YG In" ~t

7~NH~ = YNH~" l't

r~Lac = YLac. ~t

gMab = YMab'g

Fig. 1. Specific rate expressions used in the kinetic model for cell growth and death, glucose and glutamine consumption, ammonia, lactate and antibodies production.

Living ceils: dX = ( g _ kb _ kl). X dt

Dead cells: dXb = kb.X dt

dGlc Glucose:

dt = -VGlc.X + D.(Glcin - Glc)

dG In Glutamine:

dt = -VG In" X + D. (G lnin- G In)

dLac Lactate:

dt = rCLac.X + D.(Lacin - Lac)

Ammonia: drm; + D. ;in- .x (

dMab Antibodies: d-'--~ = ~Mab'X - D. (1 - ot).Mab

Fig. 2. Mass balance equations for viable and dead cells, glucose, glutamine, ammonia, lactate and antibodies for a continuous perfusion culture. In the case of a batch culture the dilution rate is set to z e r o .

(100 UI.m1-1 penicillin, 100 #g.ml - t streptomycin). The temperature and agitation levels were controlled at respectively 37 ~ and 50 rpm. The dissolved oxygen concentration was regulated around the set point of

293

measurement moments

I I - tk tk+ 1 Time

measurements measurements Y(tk) Y(tk+l)

Predictio~..I estimation prediction "1~ I estimation x(tv) [ algorithm ~(tk+l) [ algorithm ...

estimation ~ estimation

�9 .. ~(tk) , " ~,(tk+ 1)

Fig. 3. Schematic illustration of the Extended Kalman Filter procedure which uses a kinetic model to continuously predict the state variables and periodic measurements to correct the model calculations.

Table 1. Parameters used for the kinetic model.

Parameter Value Unit

#max 0.065 h - 1

Kgln 0.3 mM

KLac 55 mM

KNH4 + 5 mM

A 0.006 h -1

t~Gl n 0.1 mM

eCI~ac 0.0.14 m M - 1

~NH + 0.05 raM- 1

YO~c 4.9 mmol, 10 .9 cells

YLac 3.5 mmol. 10 - 9 cells

YOln 1.9 mmol. 10 - 9 cells

YNH + 1.9 mmol.10 -9 cells

YMab 18 mg. 10 - 9 ceils

kl 0.0095 h - I

40% by direct bottom sparging with pure oxygen and the pH was maintained at 7• by either COs injection into the headspace or delivery of 0.2 N NaOH solution in the culture medium.

Perfusion culture The perfused cell culture was performed in a 2 liters working volume Cytoflow| bioreactor (Inceltech- SGI, France) with two different dilution rates of 0.04 h -1 and 0.08 h -1 . The cells have been initially seeded in a DMEM/HamF 12 (3:1) basal medium supplement-

ed with 35 mM glucose, 4.5 mM glutamine, 5% (v/v) Fetal calf serum, 2% (v/v) essential amino acids, 1% (v/v) non essential amino acids and antibiotics (100 UI.m1-1 penicillin, 100 #g.m1-1 streptomycin). The composition of the feed medium was previously determined to yield high densities with the 6H2 hybridoma cell line (Pinton, 1991). It is the same as in the batch culture except for the glucose concentration which was fixed at 18 raM. The operating conditions, pH, pO2, temperature and agitation were controlled in the same way as for the batch culture.

Analyses In order to avoid some interpretation difficulties clue to insufficient experimental points (Phillips et al., 1991), samples were taken twice a day from the bioreactor for metabolic assays and cell numeration. The viable and dead cells densities were determined by trypan blue dye exclusion using a hemocytometer. The stained cells were treated as dead cells. The samples were cen- trifuged and the supernatants aliquoted and frozen for subsequent analyses. Glucose, lactate and glutamine concentrations were determined by enzymatic methods, while NH + ions concentrations were analyzed with a selective electrode (Orion). The monoclonal antibody concentration was measured by the ELISA technique as previously described (Pinton, 1991). All measurements have been realized threefold for each culture sample.

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Kinetic model

The kinetic model for the hybridoma cultures used in this study has been contructed according to a previously proposed methodology (Goergen et al., 1994). The selected rate expressions for cellular growth and death, nutrients consumption, metabolites and protein production which have been choosen are given in Fig- ure 1.

Cellular growth is characterised by a maximum specific growth rate, # , ~ . During cultures the specific growth rate, #, usually decreases because either depletion of essential nutrients or accumulation of inhibitory metabolites. In the present case, as glucose was nev- er limiting, the specific growth rate is described as a function of the concentration of glutamine, lactate and ammonia in the medium, Other amino acids were not found limiting in the investigated cultures (Pinton, 1991).

In batch culture, hybridoma lysis is usually negligible and the cellular death rate is given by the rate of appearance of cells counted as blue by the trypan blue technique. The kinetics expression for the specific rate of cellular death, kb, describes the possible increase of death rate with limitation in glutamine or accumulation in lactate and ammonia.

For many investigated cell lines, the specific rates of nutrient uptake, u, and metabolite or protein production, 7r, have been found growth associated and are thus described as proportional to the specific growth rate (Goergen et aL, 1992, Hiller et al., 1993).

The rate expressions of Figure 1 have been used for the modelling of both the batch and continuous perfusion cultures. In the case of long term continuous cultures, lysis has been shown to represent a significant additional process for cell death (Goergen etal., 1993). Thus, for the perfusion culture, a constant specific rate of cell lysis, kt, was added to the previously introduced death constant, kb, to express the global rate of cell death.

Mass balance equations

The set of differential equations describing the time variation of the concentrations of the different medium components for the perfusion culture is given in Fig. 2. The perfusion reactor, which consists of a stirred ves- sel with a microfiltration membrane on an external loop with a small recirculating volume (Pinton, 1991) can be considered as a well stirred homogeneous system. The derived equations also simulate the kinetics

295

of batch cultures when the dilution rate is set to zero. For the perfusion culture, cells are totally retained by the microfiltration membrane. As previously reported for the filtration of antibodies (Piret & Cooney, 1990; Schmid et af., 1992), a partial retention of the antibodies is integrated in the mass balance equations, with a retention coefficient, ~, proportional to the cellu- Iar density. The degradation of glutamine is neglected, considering the relatively low level inside the reactor. The release of ammonium from dead cells was also considered as negligible.

Software sensors

A software sensor is an algorithm for the on-line estimation of concentrations which are not measurable in real time, based on a simulation model of the process and on one or several accessible measurements. The Extended Kalman Filter (EKF) used in this study is an extension of the Linear Kalman Filter (Kalman, 1960; Kalman & Bucy, 1961) to non-linear systems. Its application to the monitoring of microbial fermentation processes has been extensively described (Albiol et al., 1993; Dubach & Mfirkl, 1992; Valero et al., 1990). In this study, the EKF is used in its version with a continuous model for the process simulation and a discrete model for measurements (Miller & Leskiw, 1987). The general methodology is briefly outlined in the following.

The dynamic of the system, i.e. the time variation of the medium components concentrations, is represented by the general equation:

dx d--t = f(x(t) , t ) + w(t) (1)

where x is the state vector (the concentrations of the medium components), f is a vector of non-linear functions ofx and time, which corresponds to the different rate expressions of formation or disappearance of the components, and w is the vector of the system random disturbances, which represents the degree of uncertain- ty of the kinetic model (process noise).

In this work, a single measurement, the concentration of glucose, was used for the Kalman filter. At a given time tk, this measurement, y, is reIated to the state vector by the following model:

Y(tk) = h(X(tk), tk) q- V(tk), k = 1,2, ... (2)

where h is a vector of nonlinear functions of x and t, and v is the random error vector accounting for the

296

uncertainties in the measurements. In our case, the vec- tors y, h and v are reduced to scalars (one-dimension vector) because only one variable is measured.

As schematically described in Fig. 3, the EKF pro- ceeds in two steps: a prediction step, which take place between measurements times, and a correction step which only occurs at the times of measurement. The predicted state vector, ~(tk), is given by integrating the system model between the previous and the new measurement times tk-1 and tk, according to

dR d t = f(z~(t),t) (3)

The predicted state vector is then corrected by a term proportional to the difference between the *measured and predicted glucose concentration:

z~(tk) = :~(tk) + Kk(y(tk) - h(z~(tk), tk)), k = 1,2,... (4)

where the matrix Kk is the Kalman gain which is opti- mized at each measurement time.

The algorithm was implemented on an Apollo 9000 Model 720 GRX Hewlett-Packard workstation using C programming language. Glucose concentration in the culture medium was measured off-line at 10 hours intervals and the results transferred to the computer.

R e s u l t s a n d d i s c u s s i o n

Kinetic model development in batch cultures

For the 6H2 hybridoma cells cultures in a batch reactor, the measured concentrations of glucose, glutamine, living and dead cells, lactate, ammonia and monoclonal antibodies are presented in Fig. 4. A maximal cell density of 1.5 x 106 cells.m1-1 was reached after 80 hours of culture, corresponding to a total depletion of glutamine. Ammonia and lactate, which reached 8 mM and 5 mM concentrations respectively, may also con- tribute to the inhibition of growth rate and stimulation of cellular death.

The rate expression and mass balance equations described in Figs. 1 and 2 were used to model the hybridoma kinetics in the batch culture. Some of the model parameters were estimated directly from the experimental data (Goergen et al., 1994). Others were evaluated with a genetic algorithm to obtain the best fit between the model and the experimental data (Bicking et al., 1994). With these values of parameters (Table 1),

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15- u ~3 10-

i

57 0-

0 50

D=0.04 h 4 D=0.08 h 4

1 i " 1 ' i I

100 150 200 250 3t30 350 Time (h)

Fig. 5. Time variation of the glucose concentration in a continuous perfusion culture of 6H2 hybridoma cells under controlled pH and dissolved oxygen: (o) represent the experimental measurements, the dotted curve (- - -) the concentrations predicted by the kinetic model and the continuous curve ( - - ) the concentrations estimated by the Extended Kalman Filter.

except for some discrepancies for the utilisation of glutamine, the model yielded a satisfactory simulation of the hybridoma growth, death and metabolism.

Medium composition estimation during a perfused culture

The hybridoma were cultured in a continuous perfusion bioreactor in which the medium is recirculated through an external microfiltration membrane to recycle the cells. The measured concentrations of nutrients, living and dead cells, metabolites and proteins inside the reactor during the 350 hours of culture are shown in Figure 6, After an initial batch phase, the perfusion culture was first operated for 130 hours at a dilution rate of 0.04 h -1. During this period, the cell density increased to 5 x 106 cells.m1-1 and the antibody concentration to 70 mg.1-1. In a latter phase when the dilution rate was set at 0.08 h -1 , the cell and antibody concentrations further increased to 11 x 106 cells.ml - l and 120 mg.1-1. This viable cell density is in the range of previously reported perfusion cultures (Al-Rubeai et al., 1992; Biantemeyer et al., 1992; Goebel et al., 1990; Shintani et al., 1991; Takazawa & Tokashiki, 1989).

The hybridoma perfusion culture was then used to test the capacity of the Kalman filter estimator to predict the medium composition with the model previously validated on the batch culture. In this case, a single component was measured, namely glucose.

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Fig. 6. Time variation of the concentrations of living ceils, dead cells, lactate, glutamine, ammonia and antibodies inside the blot�9 during a continuous perfusion culture under controlled pH and dissolved oxygen: (e) represent the experimental measurements, the dotted curve (- - -) the concentrations predicted by the kinetic model and the continuous curve ( - - ) the concentrations estimated by the Extended Kalman Filter.

298

Figure 5 shows, in addition to the experimental points, the glucose concentration predicted by the model as well as the continuous estimation of the glucose concentration by the EKF. As seen, the measured glucose is correctly described by the model, except during the transition phase which follows the increase in dilution rate. For the measured component, the filter predictions closely follow the experimental values.

Based on these results, the filter was used to predict the concentrations of the other components inside the bioreactor. Figure 6 also shows the time variation of the concentrations as calculated by the model alone and as estimated by the Kalman filter. Since in this case the difference between the measured and calculated glucose concentration remains relatively small during the whole culture, only a limited correction term is observed, for the other components, between the values given by the model and the filter.

The different curves shown in Figure 6 demon- strate an excellent ability for the filter to estimate the actually measured concentrations of living and dead cells, of glutamine and antibodies at the two dilution rates of perfusion. A less satisfactory agreement is observed for the two metabolites lactate and ammonia. The large differences between the model and the experimental points, especially after the onset of perfusion and the change in dilution rate, probably reflect some major modification in cellular metabolism in continuous perfusion as compared to the ammonia and lactate metabolism observed during the batch culture.

Conclusions

A Kalman filter type estimator was found to yield an acceptable estimation of the medium composition during a hybridoma perfusion culture when using the measurement of a single medium component in outlet stream, the glucose, The estimation is particularly good for the viable cell density in a wide range of densities between ! and 11 x 10 6 cells.m 1 -l and for the antibody concentration inside the bioreactor. This result has been achieved with a relatively simple model of hybridoma kinetics initially validated on a batch culture and found applicable for the continuous perfusion culture in a wide range of cell densities.

Significant discrepancies, however, remain between the predicted and measured concentrations of lactate and ammonia. This is probably indicative of important changes in cellular metabolism when cells are cultured in a continuous mode for extended periods.

Thus, a better quantitative description of the production of lactate and ammonia by hybridoma in continuous perfusion cultures has to be achieved for a further improvement of the estimator performance.

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Address for offprints: F. Pelletier, Institut National Polytechnique de Lorraine, Laboratoire des Sciences du Gtnie Chimique, CNRS, 2, avenue de la Fordt de Haye, BP 172, F-54500 Vandoeuvre-l~s- Nancy Cedex, France.

software sensors for the monitoring of perfusion cultures: evaluation of the hybridoma density and...

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