Fluctuations in continuous mammalian cell bioreactors with retention

Biotechnol. Prog. 1992, 8, 397-403 397

Fluctuations in Continuous Mammalian Cell Bioreactors with Retention Hugo Vits and Wei-Shou Hu* Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue, Southeast, Minneapolis, Minnesota 55455

Continuous flow bioreactors with cell retention have been increasingly used for the cultivation of mammalian cells. The potential advantages of such bioreactors are high cell concentrations and volumetric productivities. In many reported cases, these systems have shown fluctuations in cell concentrations of various frequency and magnitude. To analyze the dynamics of the fluctuations, a model-based approach is followed. Simulations showed that large fluctuations in biomass resulted in response to fluctuations in the retention ratio when the system is operated at high dilution rate and high cell retention. The dependence of cell concentration fluctuations on variations in dilution rate and retention ratio was established by a cross-correlation statistical analysis on available experimental data. The slower dynamics and the fluctuation propensity of retention systems suggest that continuous culture without retention is more convenient for kinetic studies. In all likelihood, continuous culture with retention can be stabilized by controlling both the retention ratio and the dilution rate.

Introduction Mammalian cells have been used extensively in the

manufacturing of viral vaccines, monoclonal antibodies, and other proteins for therapeutic or diagnosticuses (Ogez and Builder, 1990). Many of these products, especially the viral vaccines, have been produced using cells which require the attachment to surfaces for propagation. In the last decade, an increasing number of products, notably monoclonal antibodies and proteins derived by gene technology, have been produced by cells which grow in suspension (Hu and Peshwa, 1991). Simple configurations such as batch and simple continuous culture systems lead to low cell concentrations and low volumetric productiv- ities. Considerable efforts have been devoted to develop production systems with high cell concentrations and long production periods. Hollow fiber systems, microencap d a t i o n , and entrapment in macroporous beads are some of the technologies finding applications in enhancing mammalian cell concentrations (Hu and Piret, 1992; Looby and Griffiths, 1991). However, mixed vessels, especially stirred tanks, still remain the choice in most cases.

In some reported cases, the cell concentration and, in general, also the product concentration were increased by nutrient feeding either to provide the limiting sub- strate(s) or to maintain a balanced condition for cell growth and production (Jain et al., 1991). However, the accu- mulation of metabolites, such as lactate and ammonia, and substances released by dead cells can limit prolonged cultivation times in fed-batch mode operations. To sustain long production periods, continuous flow is necessary for culture fluid renewal. Simple continuous stirred tank bioreactors can sustain steady operations over extended time periods (Birch et al., 1987; Frame and Hu, 1991; Miller et al., 1988) and constitute a valuable tool for the investigation of kinetic behavior of mammalian cells in culture. For manufacturing purposes, one of their short- comings is the relatively low cell concentration attainable at steady states.

As demonstrated for many microbial-based processes and in waste treatment, cell concentration and volumetric

* To whom correspondence should be addressed.

productivity can be effectively increased by cell recycle or cell retention. Retention methods that have been em- ployed for mammalian cell suspensions include, among others, membrane filters (Seamans and Hu, 1990; de la Broise et al., 19911, settlers (Kitano et al., 1986; Takazawa and Tokashiki, 1989; Batt et al., 19901, and centrifugal devices (Tokashiki et al., 1990). Alternatively, some cell lines can be induced to form aggregates thus facilitating their retention by settling or filtration (Kyung et al., 1992). Coupling a cell retention device to a continuous bioreactor, in what is frequently called a perfusion bioreactor, can lead to 5-10-fold cell concentration increases.

Despite their potential in the manufacturing and development of mammalian cell products, little analysis exists on perfusion bioreactors (Hu and Peshwa, 1991). The criteria for selecting the time point at which con- tinuous flow is initiated, the flow rate magnitude, and the extent of retention are generally not available. Specifi- cation of dilution rates and retentions can determine the concentrations of residual substrates, metabolites, and potentially inhibitory substances. In principle, the choice of flow rate and retention allow for growth rate to be manipulated and could possibly lead to conditions asso- ciated with high specific productivity. Attempts to set a perfusion rate to maintain a constant growth rate based on on-line kinetic parameter estimation (Seamans and Hu, 1990) have not been effective so far. However, the development of optimal feeding policies is of relevance as the medium cost may represent a significant portion of total operating cost.

The behavior of mammalian cells in continuous biore- actors with cell retention can be reduced to three general patterns. In some cases, a relatively constant viable cell concentration can be sustained over a long time period (Hamamoto et al., 1989). In other cases, a slow downward drift in viability without apparent steady state was observed (Kitano et al., 1986; Lutkemeyer et al., 1991). Finally and frequently, appreciable fluctuations in the viable and total cell counts develop and continue through- out the cultivation period (Tokashiki et al., 1990; de la Broise, 1991; Shintani et al., 1991). In a majority of the reported cases, the sampling interval period is relatively

8756-7938/92/3008-0397$03.00/0 0 1992 American Chemical Society and American Institute of Chemical Englneers

398 Biotechnol. prog., 1992, VOI. a, NO. 5

(I-a)F,s. X , , , X , F. s. 7 ,> 1 I aF, s

I 1 I I effluent stream contains the same biomass concentration as the well-mixed bioreactor. The working volume of the bioreactor is considered to be time invariant. The process then satisfies the following equations:

viable biomass

I & - I - Figure 1. Schematic of a perfusion bioreactor with internal cell retention device.

long; nevertheless, the magnitude and frequency of fluc- tuations suffice to back up the contention that the system is unlikely to be in true steady state. Such fluctuations may pose potential problems in the regulatory validation of manufacturing-scale processes. The causes of fluctu- ation are unknown, and its frequency and magnitude are highly variable. As evidence accumulates that changing environmental factors may affect some posttranslational modifications (Goochee et al., 1991; Hayter et al., 1991), the fluctuations may also elicit concerns related to "product" quality. Thus, the elimination or reduction of cell concentration fluctuations is desirable, and recent efforts to improve on-line instrumentation and control of mammalian cell bioreactors may lead to solutions (Hu and Piret, 1992). For example, the use of on-line turbidity sensors for the estimation of biomass (Konstantinov et al., 1992) can eventually lead to feedback control of flow rates and retention to stabilize the cell concentration. However, the implementation of any control will require some understanding of the system dynamics and the effectiveness of the manipulated variables in correcting the system behavior.

With the increasing employment of cell retention continuous flow bioreactors, an analysis of the system behavior is long overdue. In this communication, we report our analysis of mammalian cell retention bioreactors. We approach the problem through the formulation of a simple model and then simulate the effect of fluctuations in operational variables.

Model Unstructured unsegregated models have been applied

to represent bacterial recycle and wastewater sludge systems (Herbert, 1961; Pirt and Kurowski, 1970; Ra- manathan and Gaudy, 1971; Sheintuch, 1986). In all cases, cell death was assumed negligible which is not the case for mammalian cells subjected to slow growth regimes. Frame and Hu (1991), in a continuous culture study with glucose as limiting substrate, have shown that the kinetic behavior of a murine hybridoma can be described by a modified Monod model. Other mammalian cell studies have confirmed the adequacy of Monod-type models for growth description (Miller et al., 1988). In our analysis, a Monod dependence on substrate is used, cell death kinetics is taken as first-order, and cell lysis is not accounted for (Sinclair and Topiwala, 1970). The cell retention device is assumed ideal and with very fast dynamics. Since "perfusion rate", an often referred to concept, is ill-defined, we have opted to describe flow and retention in terms of a dilution rate D and a retention ratio a. D is defined as the total flow rate through the system divided by the working volume of bioreactor. The retention ratio a corresponds to the fraction of the total effluent stream that is free of cells (Figure 1); a fraction 1 - a of the total

dead biomass

substrate

(3)

with initial conditions x, = xd, x d = XdO, s = SO, and D = 0 for t < t, (time of perfusion start). The concentrations of substrate, viable, dead, and total biomasses in the bioreactor a t the nontrivial steady-state condition are given by

xw (1 - a)D The same equations can be expressed in terms of cell concentrations N . While it is known that Monod-type kinetics predict a much faster dynamic response than that observed experimentally, this should be of little or no effect in the following analysis, as we are interested in the qualitative comparison of dynamic behavior under dif- ferent conditions.

Results The kinetic parameter values previously determined for

a hybridoma cell line, AFP-27NP, were used in the analysis (Frame and Hu, 1991) (see Table I). A number of simplifications were made in adopting the parameter values, notably by neglecting the non-zero intercepts and by assuming a constant yield coefficient and a constant specific death rate. For our purpose, these simplifications bear no effect on the analysis. Shown in Figure 2 are three- dimensional plots for viable and total biomass steady- state concentrations computed from eqs 4, as a function of dilution rate D and retention ratio a. The effect of changes in flow variables on the bioreactor content was examined. Significant increases in cell concentration can only be obtained a t large retention ratios. A t constant a values, the total biomass is rather insensitive to changes in the dilution rate. Viable cell concentrations can be increased, a t sufficiently large a values, by increasing the dilution rate. The predicted large amounts of dead cells within the system suggest that the high-cell density condition will be coupled to significant amounts of waste metabolites and degradation products. Figure 2 also hints

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Figure 2. Dependence of steady-state biomass concentration values on dilution rate D and retention ratio a: (A) total biomass; (B) viable biomass. Biomass values are expressed in dry weight (DW) concentration units. Model parameters are from Table I.

Table I. Model Parameter Values Derived from a Continuous Culture of the AFP-27NP Hybridoma Cell Line (Frame and Hu, 1991)

parameter value parameter value Pm 0.0630 h-l kd 0.0042 h-l KS 0.00613 mg cm-3 SO 1.0 mg cm-3 Yxs 0.355 mg m g l

at the fact that, at high retention ratios and dilution rates, both the total and viable cell concentrations will be more sensitive to perturbations in a. This derives from the steeper slope of constant dilution rate curves in that region. The graphs also show that the sensitivity to fluctuations in the dilution rate is acute only for the washout and very slow growth regions.

Time-dependent simulations of eqs 1-3 were performed, a t different retention ratios and dilution rates, with an initial value problem solver (IMSL, 1989). As shown in Figure 3, the transient stage is longer at high retentions, for a constant dilution rate. Overshoots are predicted at low dilution rates. This corresponds to situations where the process dynamics is initially controlled by the growth kinetics and then controlled by death kinetics as in a batch

Y a P

3.0 . 2.0 '

1.0 .

0 100 200 300 Time (hr)

o.o-. " " " " " " "

Figure 3. Simulated evolution of viable biomass concentration in bioreactor as a function of dilution rate D and retention ratio a. Numbers on curves correspond to D (h-l). Model parameters are from Table I. Continuous regime and perfusion were initiated at t = 10 h and maintained at a constant rate.

culture. If the rate of reduction in viable biomass by dilution is always much larger than the death contribution, no overshoot is observed, as suggested by results a t higher dilution rates. In the following discussion, the time period after the rapid rise in cell concentration, and in which the cell biomass is relatively stable, will be referred to as stationary phase.

A numerical eigenvalue analysis (IMSL, 1989) was performed at the steady states and showed that if the reactor operates close to total retention, the smallest eigenvalue-corresponding to the largest time constant of the process-approaches 0. This is another indication of slow dynamic behavior at high retentions. All eigen- values were negative, suggesting asymptotically stable states and precluding autonomous oscillatory behavior.

Both Figures 2 and 3 also show that increasing the dilution rate by itself may not lead to increases in the volumetric reactor productivity. If the desired product is not growth associated, productivity is determined by the amount of viable biomass in the reactor. Even at retention ratios as high as 0.5 (Figure 3B), doubling the dilution rate from 0.05 h-' to 0.10 h-' has a very marginal effect on the biomass concentration. Moreover, the transient stage at 0.10 h-l is considerably longer and is associated with lower biomass concentrations. At large cell retentions like a = 0.9 (Figure 3C), increasing the dilution rate can lead to significant biomass increases before a plateau is attained.

The sensitivity of the system to fluctuations in the retention ratio is examined dynamically. In each simu- lation, a was allowed to fluctuate, randomly and uniformly, within a prespecified band, Aamax, centered a t (YO. Each a realization was applied to the system for a time interval of constant length T. The results (Figure 4) show that the time courses for cell biomass are jagged at higher retention ratios, especially when combined with high dilution rates. By varying T, the distance between large peaks and valleys, as well as the fluctuation amplitudes, could be modified. I t is also notable that the perturbations are only visible in the stationary phase. The standard deviation in viable

400

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1 -

X d

( A ) 0.95 . . . . , . . . . , , , . . , . . . . , . . , . J

1.0 ~:~E o.oo 0.5 200 400 600 800 1000

Time (h)

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200 400 600 800 1000 ~ L 1 " " l ~ " ' l " " l " "

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(D) 0 . 9 5 t . , , , I . . . . , . . . . , . . . . I . . . . J

Figure 4. Simulated profiles of viable (X,) and dead (Xd) biomass, under regimes of fluctuation in the retention ratio and constant dilution rate. In each case, CY was allowed to fluctuate, randomly and uniformly, within an interval ha, centered at ao, and then maintained constant over a time interval of length T . The upper panels reflect the resultant a regimes. Simulation conditions: (A) D = 0.05 h-l, a0 = 0.90, Aa- = 0.05, T 5 h; (B) D = 0.05 h-', a0 = 0.20, Aa- = 0.05, T = 5 h; (C) D = 0.05 h-l, a0 = 0.90, Aa, = 0.05, T = 30 h; (D) D = 0.30 h-l, a0 = 0.90, Aamax = 0.05, T = 5 h. In all cases, the continuous regime was initiated at t = 10 h.

biomass, a(X,), was computed by sampling the stationary phase regime over 1500 simulated hours (Figure 5) to obtain well-converged values. The quantification of the fluctu- ations shows not only an increase in a(X,) at large retention ratios but also that the 7 period of the fluctuations in a! strongly influences the biomass variance. Low frequency noise or drifts that are corrected only every so often lead to wider biomass distributions than high frequency variations of the same amplitude. No significant devia- tions in the mean of the viable biomass time series were detected.

Data series showing concurrently the variations in flow rates and cell concentrations in perfusion systems are scarce. Shintani et al. (1991) continuously perfused a human-human hybridoma line in a 2-L jar fermenter coupled to a gravitational settler and presented dilution rate and cell concentration data (Figure 6A,B). In an attempt to establish a causal relation between variations in the flows and fluctuations in the biomass, a cross- correlation analysis (Box and Jenkins, 1976) was employed. With this method, it is possible to estimate cross- correlation coefficients p for two stationary time series, at lag intervals that are a multiple of the observation interval. Statistically speaking, a time series (a realization of a stochastic process) is stationary if its characteristic prop- erties are unaffected by changes in the time origin. Absolute values for p that are close to 1 indicate good cross-correlation and that the fluctuations in one time series have corresponding fluctuations in the other. Negative p values correspond to opposite trends for the

I M E 0.4 1 I a' ..j j

n 0.5 0.6 0.7 0.8 0.9 1

a

Figure 5. Standard deviation in viable biomass as a function of retention ratio for different dilution rates and fluctuation characteristics: (A) D = 0.30 h-l, T = 30 h; (0) D = 0.20 h-l, T = 30 h; (m) D = 0.10 h-l, T = 30 h; (A) D = 0.05 h-l, T = 30 h; ( 0 ) D = 0.30 h-l, T = 5 h. Aa- = 0.05 in all simulations. o(X,) was evaluated with 300 points sampled at 5-h time intervals from the stationary portions of the simulated biomass time series (pa- rameters are as in Table I).

time series; that is, increases in one series correspond to decreases in the other.

In this case, a total of 35 data points, corresponding to 38 days of culture (note that the requirement of constant sampling was somewhat relaxed as there are 3 missing points), were assumed to comply with statistical station- arity. The results obtained with a packaged routine (IMSL, 1989) show cross-correlation between the time series for (1 - a!)D and the total cell concentration Nt and for cQ and total cell concentration (Figure 6C). The fit was slightly better and with a smaller standard error for the ((1 - a)D, Nt) pair, with the cell number series lagging

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10 20 30 40 5 0 60 Time (day)

0 ~ ~ ~ " " " " ' " ' ' ' ~ ~ ' ~ ' ~ ~

~

10 20 30 40 50 60 Time (day)

h

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-0.5

- 6 - 4 - 2 0 2 4 6 Time Lag (day)

1

0.5

0 w Q

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-6 - 4 - 2 0 2 4 6 Time Lag (day)

Figure 6. Cross-correlation statistical analysis of the relationship between flow rates and cell concentration in a perfusion bioreactor equipped with a gravitational settler. Data are from Shintani et al. (1991). (A) Fluctuations in total cell number, Nt (A), and viable cell number, N , (A), in the stationary phase. (B) Fluctuations in the bleed dilution rate (1 - a)D (O) , and cell-free dilution rate, OrD (m). (C) Cross-correlation coefficient p as a function of lag, for the time series pairs (CUD, Nt; 0) and ((1 - a)D, Nt; +). The error bars indicate the standard error for p. (D) Cross-correlation analysis for the viable and total cell number concentrations (Nv, Nt) .

the flow time series by one time interval (one day). p was negative, indicating that an increase in (1 - a)D led to a decrese in Nt. No correlation was found between D and Nt. Similar trends were detected when correlating (1 - a)D, aD to the viable cell concentration, Nt. This was not surprising as the viable and total cell concentration series cross-correlated well with no time lag (Figure 6D).

The cross-correlation analysis of simulated time series permits us to evaluate the sensitivity to various parameters. Time-series pairs (a, Xt) were tested at different 7, D and Aamax values (Table 11). When the frequency of the fluctuations was increased, the cross-correlation deteri- orated. A similar trend was observed when the dilution rate was decreased. A smaller Aamax reduced cross- correlation, but to a lesser extent than a shorter 7. In all cases, reductions in retention ratios correlate with de- creasing cell concentrations with a lag of 17. These trends indicate that the system dynamics are more dependent on the flow characteristics at the high dilution rates.

Discussion Our simple, model-based analysis suggests that fluc-

tuations in the retention ratio may translate into significant fluctuations in biomass concentration. The limited avail- able experimental data give credence to the numerical results; however, full confirmation should be based on longer time series.

A few observations can be made. The increasing correlation between flow variables and cell concentrations a t the higher dilution rates clearly suggests that the system dynamics is dominated, under those circumstances, by the flow characteristics rather than by growth. It is therefore important to design these systems with special consideration to their flow and retention properties. For example, flow-dependent and load-dependent retention

devices will be prone to fluctuations of the nature indicated here. In this category, we can group filters and settlers. Centrifugal systems are probably less sensitive. The inclusion of a separate bleed stream can dampen the perturbations or provide a degree of freedom for control, in load-dependent systems.

Manual control of a perfusion system is probably associated with high amplitude oscillations and large variances in cell concentration. As a consequence, it is sensible to implement appropriate control mechanisms to avoid drifts in flow rates and changes in retention. On- line biomass measurements (Konstantinov et al., 1992) could be employed to adjust the ratio of effluent streams, as a function of the variations in total biomass concen- tration. The total cell number correlated well with the viable cell number from the cross-correlation analysis of experimental data (Figure 6). If this proves to be generally valid for retention systems, it could be used in a scheme to estimate indirectly the concentration of viable biomass concentrations in the bioreactor. Such an approach could certainly improve the performance of settling devices while their low-cost attractiveness is maintained.

From an experimental standpoint, the simple continuous culture system without retention is a better choice, whenever such a choice is possible, to determine steady- state kinetic data. Given that the variances in the biomass values can be large in a retention system, short runs, with infrequent sampling, may lead to significant errors in kinetic parameter estimation. Simple continuous culture is more resilient to the flow fluctuations and is charac- terized by shorter transient periods. Time series for continuous culture (Frame and Hu, 1991; Hiller et al., 1991) look smoother than those for retention systems.

Fluctuations in biomass concentrations are not restricted to animal cell culture. Ramanathan and Gaudy (1969)

402

Table 11. Cross-Correlation Analysis of Model Simulations between the Retention Ratio u and Total Cell Biomass Time Series (60 Observations at Intervals of Length T )

D, h-l 7, h a0 Aamax p(a ,Xt ) d P ) lag (T multiples)

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0.30 0.30 0.30 0.30 0.20 0.10 0.05 0.30

30 20 10 5 30 30 30 30

0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9

0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.01

attributed the observed fluctuations in an experimental wastewater treatment system to the coexistence of com- peting microbial species in the sludge. Such a n argument is justifiable only if spatial inhomogeneities or temporal fluctuations favor the growth of different species at different times or locations to override the principle of competitive exclusion. In a one-species culture such as animal cells, populations of different physiological states could possibly be established if a fraction of the cells undergoes significant metabolic changes. For example, inhibitory levels of waste metabolites could induce changes in the average physiological state of t he cells. If present, these effects are likely t o be more significant in retention continuous culture systems than in simple continuous culture, given the higher cell densities and, specifically, the higher concentrations of dead cells, as predicted by the model (Figure 2). As a result, i t is not implausible to conceive the occurrence of temporal changes in bioreactor cell concentrations. However, in a necessary first step to establish the existence of these mechanisms, the contri- bution of t he retention and dilution rate fluctuations will have to be minimized. In any case, flow and retention perturbations appeared to correlate well with the variations in cell concentrations in the bioreactor (Figure 6 and Table 11). The elucidation of the dynamics and ita causes will certainly benefit from more complete seta of measure- ments. I n particular, measurements of the biomass concentrations in the retention device, in the outflow, and in the recycle streams can be viewed as a necessary complement to bioreactor concentration measurements.

Notation Symbols D dilution rate k d specific death rate N cell concentration S substrate concentration so t time X biomass concentration YXS a retention ratio a0 P specific growth rate P cross-correlation coefficient

U standard deviation AcY,,

Subscripts d dead 9s steady state t total V viable

inlet and initial substrate concentration

yield coefficient of biomass on substrate

center point of Aa,, interval

7 holding time for a constant a in fluctuating regimes

interval for fluctuations in retention ratio

0.916 0.844 0.687 0.561 0.853 0.760 0.657 0.870

0.016 0.024 0.037 0.048 0.012 0.015 0.048 0.032

+1 +1 +1 +1 +1 +1 +1 +1

Acknowledgment

This work was partially supported by a grant from the National Science Foundation (BCS-8552670). The sup- port from ICBiotech, Osaka University, Osaka, Japan, where a substantial part of this work was developed while we were visiting, is gratefully acknowledged.

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