Biotechnol. Prog. 1993, 9, 298-308
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Fractional Factorial Study of Hybridoma Behavior. 1. Kinetics of Growth and Antibody Production John G. Gaertner and Prasad Dhurjati* Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716
A comprehensive approach was taken toward the quantitative study of hybridomagrowth and antibody production. A fractional factorial experimental method was used to identify important variables and variable interactions affecting hybridoma behavior. The variables studied include temperature, pH, dissolved oxygen, glucose, glutamine, base medium, serum, lactate, and ammonium. The growth rate was strongly affected by the levels of dissolved oxygen, pH, temperature, and base medium. Interactions between temperature, pH, and dissolved oxygen were important. The optimal p H for growth depends upon the temperature and dissolved oxygen concentration. In general, growth was fastest at low dissolved oxygen levels. The growth rate was very sensitive to low concentrations of base medium, but was relatively insensitive to the serum concentration at levels above 2.5%. Antibody production was stimulated by high concentrations of base medium and serum and inhibited by ammonium and lactate. Antibody production increased linearly with serum concentration. In general, conditions that favored a high growth rate also favored a high specific rate of antibody production. The functional dependencies of antibody production on base medium and ammonium were similar to those for cell growth; however, antibody production and cell growth exhibited different dependencies on serum. Mathematical descriptions of cell growth and antibody production were developed. These experimental results have significant implications for the optimization of hybridoma growth in bioreactors.
Introduction One of the primary objectives of large-scale hybridoma cultivation is to maximize the rate of monoclonal antibody production. Optimization of product formation in a reactor requires a knowledge of the reaction system. The cellular reaction system of the hybridoma converts glucose, glutamine, oxygen, and other nutrients into cellular material, antibody, and waste products. Although hybridomas are of considerable commercial importance, cell growth and antibody production are not well understood; it is unclear what environmental factors affect these processes and over what range of levels these factors are important. An understanding of the hybridoma reaction system and a knowledge of the dependence of the cellular reaction rates on the local envirolimentalconditions should enable optimization of reactor operating conditions to achieve maximum antibody production. Hybridoma growth and antibody production have been addressed by some studies; these studies have, in general, focused on a few variables and have not investigated all of the variables in a comprehensive manner. Several studies (Velez et al., 1986;Tharakan and Chau, 1986;Low and Harbour, 1985) have focused on the effect of serum. In general, these studies have found that it is necessary to add at least a small amount of serum or growth factors to the culture medium. Dalili and Ollis (1989) have found that the specific growth rate ( p ) exhibits a Monod-type dependence on the serum concentration. Nutrient limitation in batch cultures has been addressed by several studies (Dalili et al., 1990;Joet al., 1990;Low and Harbour, 1985). Miller et al. (1989a,b) studied the transient
* Author to whom correspondence should be addressed; (302)8312879. 87567938/93/3009-0298$04.00/0
responses of hybridomas to pulses and step changes of glutamine and glucose in continuous culture. Reuveny et al. (1986) studied methods for prolonging cell viability and maximizing total antibody production in batch reactors by varying temperature, dissolved oxygen, and concentrations of nutrients and waste products. In studies of batch cultures, McQueen and Bailey (1990) found that pH had minor effects on growth and that ammonium concentrations of 10 mM strongly inhibited growth but had no effect on specific antibody productivity. Sureshkumar and Mutharasan (1991) found that temperature strongly affected cell growth and antibody production in batch cultures. Some environmentalfactors have been observed to have different effects on hybridoma behavior in different studies. For example, Birch et al. (1985) noted that dissolved oxygen levels between 8% and 100% of air saturation had no significant effects on cell growth; however, Miller et al. (1987) found that use of reduced oxygen concentrations resulted in improved cell growth and antibody production. Several studies have examined the relationship between the rates of cell growth and antibody production. In studies of continuoussuspension culture, Low et al. (1987) found that the specific antibody production rate achieved its maximum value at an intermediate specificgrowth rate, while Miller et al. (1988) found that the specific antibody production rate initially decreased and then approached a constant value as the growth rate was increased. One of the most comprehensive studies has been reported by Glacken et al. (1988). Glacken et al. quantified the effects of the concentrations of glucose, glutamine, base medium, serum, lactate, and ammonium on the rates of cell growth and antibody production for the hybridoma line HFN 7.1. Equations were developed that described
0 1993 American Chemical Society and American Institute of Chemical Engineers
Bbtechnol. Prog., 1993, Vol. 9, No. 3
the dependence of the specific growth rate on the concentrations of glutamine, serum, ammonium, lactate, and cells and the dependence of specific antibody productivity on the lactate concentration. Due to the complexity of hybridoma metabolism, there may be important interactions between the effects of environmental factors. In general, existing studies do not address this potential for complex interactions; in addition, mathematical descriptions of the dependencies of cell growth and antibody production are generallylacking. This study takes a comprehensive approach toward the quantitative study of hybridoma growth and antibody production. In this study, a fractional factorial experimental approach was used to identify important variables and interactions that affect cell growth and antibody production. The results of Glacken et al. (1988)were considered in the design of the fractional factorial experiment in the current study; however, the study of antibody production by Glacken et al. was of limited use since it focused on culture conditions resulting in moderate to high growth rates. In large-scale hybridoma cultivation, cells may be exposed to conditions that result in low cell growth rates (for example, due to poor mass transfer in parts of a reactor). In the current study antibody production was characterized over a wider range of conditions. The variables studied include temperature (TI,pH, dissolved oxygen (DO), glucose (C), glutamine (Gt), base medium (B),serum (S),lactate (L),andammonium(A). Important variables were studied in greater detail in order to develop mathematical descriptions of the dependencies of the rates of cell growth and antibody production. Other variables that may have potentially large effects on hybridoma behavior (e.g., cell concentration) can be studied using an approach similar to that described here.
Materials and Methods Cell Line and Culturing Techniques. The hybridoma cell line HFN 7.1 (Schoen et d.,1982)was studied; it was obtained from the American Type Culture Collection (Rockville, MD, ATCC No. CRL 1606). This cell line is anchorage independent and produces an antibody specific for human fibronectin. Cells were cultured in Dulbecco’s Modified Eagle’s Medium (DMEM; Morton, 1970)containing 10.0% fetal calf serum (FCS) and supplemented with 100 units of penicillin, 0.1 mg of streptomycin, and 0.25 pg of amphotericin B per milliliter of medium. Cultures were grown at 37 OC in 75 cm2T-flasks (Becton Dickinson) in a 10.0% COZ atmosphere. A bicarbonate/COn buffering system was used to control media pH. Cell cultures were maintained by diluting approximately 2 mL of culture in approximately 30 mL of fresh medium (in a new T-flask) every 2-3 days as described by Freshney (1983). Periodic mycoplasma testing of cultures by fluorescent staining (Freshney, 1983) was negative. The cell culture was replaced monthly with stock culture frozen in liquid nitrogen. Experiments. Experiments were performed in 75 cm2 T-flasks using a triple gas, water-jacketed incubator (Napco Scientific). Concentrated solutions of each of the individual medium components in DMEM (lacking glutamine, glucose, sodium chloride, and sodium bicarbonate) were prepared. In experiments where different base medium concentrations were used, a set of concentrates was prepared for each base medium concentration. Media formulations were made by combining appropriate volumes of each of these concentrated solutions. The glucose,glutamine, lactate, and ammonium present in the
200
FCS were taken into account. Concentrated sodium chloride solution was added to each formulation to raise the overall osmolality to 325.0 mOsm/kg. Medium pH was adjusted by the addition of HCl qr NaOH solution. All cultures contained 3.7 g/L sodium bicarbonate, 0.015 g/L phenol red, 100 units/mL penicillin, 0.1 mg/mL streptomycin, and 0.25 pg/mL amphotericin B. The dissolved oxygen concentration was adjusted by controlling the gas-phase concentration of oxygen (the incubator was equipped with an oxygen sensor, controller, and circulating fan). The temperature dependence of oxygen solubility was taken into account. Analysis of oxygen transfer through the medium verified that the oxygen gradient was very small. Literature values of the cellular oxygen uptake rate (Wohlpart et al., 1990;Lavery and Nienow, 1987;Low et al., 1987;Miller et al., 1987)and the diffusion coefficient of oxygen (Ju et al., 1988;Glacken et al., 1983;McLimans et al., 1968) were used in this analysis. On the basis of an analysis of the reaction and diffusion of COZ(Jensen, 1976),the carbon dioxidegradient was insignificant. The transients in the concentrations of glucose, glutamine, lactate, and ammonium were mathematically described by partial differential equations accounting for cellular nutrient uptake and waste production and diffusional transport between the cells and bulk medium. Measured and literature values of the rates of glucose and glutamine uptake and lactate and ammonium production for the hybridoma HFN 7.1 (Gaertner and Dhurjati, 1993;Glacken et al., 1988)were used; the diffusion distance was conservatively assumed equal to the total medium height. On the basis of this analysis, no significant gradients of these nutrients and waste products developed during the experiments. Design of the Fractional Factorial Experiment. Nine independent variables were considered. There could be as many as 502 different interactions between these nine variables; this includes everything from two-variable to nine-variable interactions. A full factorial experimental design could be used to determine the importance of all of these variables and interactions. If two different levels of each variable (i.e., a two-level full factorial design) are used, then a minimum of 512 experiments is necessary. In general, most of the 502 interactions between variables will be small or insignificant. High-order interactions tend to be small; in general, main variables tend to be more important than two-variable interactions, which tend to be more important than three-variable interactions, etc. (McLean and Anderson, 1984;Box et al., 1978). Consequently, a full factorial design provides unnecessary information about interactions that are expected to be insignificant. In general, economy in experimentation can be achieved by using a fraction of the full factorial design without greatly sacrificing the usefulness of the results. In order to develop a fractional factorial experimental design, it was necessary to first identify potentially important variables and interactions. This was done using existing knowledge about hybridoma behavior and the following principles: (1)low-order interactions tend to be more important than high-order interactions, and (2) variables which have large main effects are more likely to interact with other variables in a significant manner than variables which have small main effects. A total of 52 potentially important variables and interactions was identified with respect to cell growth; these are grouped into three categories: (a) variables and interactions found to be important by Glacken et al. (19881,S, A, B, S-L, S-A, A-B; (b) newly introduced variables and interactions between these variables, DO, T, pH, DO-T, DO-pH, T-pH,
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300 Table I. Levels of the Variables Used in the Fractional Factorial Experiment
variable serum dissolved oxygen temperature PH glucose glutamine 1acta te ammonium base medium
low (-) 2.5% 0.07 mM 34.0 "C 7.05 1.7 mM
1.0 mM 5.0 mM 1.0 mM 0.2x
high (+) 9.0% 0.20 mM 37.0 "C 7.50 16.7 mM 5.0 mM
40.0 mM 6.7 mM
1.ox
DO-T-pH; and (c) interactions between the above two groups of variables (interactions between five or more variables were assumed to be negligible), DO-S, DO-A, DO-B, T-S, T-A, T-B, pH-S, pH-A, pH-B, DO-T-S, DOT-A, DO-T-B, DO-pH-S, DO-pH-A, DO-PH-B, T-pH-S, T-pH-A, T-pH-B, DO-T-pH-S, DO-T-pH-A, DO-T-pHB, DO-S-L, DO-S-A, DO-A-B, T-S-L, T-S-A, T-A-B, pHS-L, pH-S-A, pH-A-B, DO-T-S-L, DO-T-S-A, DO-T-A-B, DO-pH-S-L, DO-pH-S-A, DO-pH-A-B, T-pH-S-L, T-pHS-A, T-pH-A-B. Interactions between variables, for example, the interaction between dissolved oxygen and temperature, have been represented using the following notation: DO-T. These 52 variables and interactions may be expected to have the largest effects on cell growth; however, it is possible that some of the other 459 variables and interactions have significant effects. The variables and interactions expected to have the largest effect on antibody production were identified in a similar manner. Identification of the potentially important variables was aided by the observation that in previous work (Glacken et al., 1988) the specific antibody productivity generally increased with increasingcell growth rate (at low to moderate growth rates). Consequently, variables that strongly affect the growth rate may also strongly affect antibody production. The variables and interactions identified as being potentially important with respect to antibody production are grouped into three categories: (a) all main variables, A, B, C, DO, Gt, L, pH, S, T; (b) all two-variable interactions, A-B, A-C, A-DO, A-Gt, A-L, A-pH, A-S, A-T, B-C, B-DO, B-Gt, B-L, B-pH, B-S, B-T, C-DO, C-Gt, C-L, C-pH, C-S, C-T, DO-Gt, DOL, DO-pH, DO-S, DO-T, Gt-L, Gt-pH, Gt-S, Gt-T, L-pH, L-S, L-T, pH-S, pH-T, S-T; (c) variables and interactions found to have the largest effect on p (that do not already appear in the above two groups of variables), DO-T-pH, DO-T-A, DO-T-S. A one-sixteenth fraction of a full factorial design was used. This design was developed using the methods described by Deming and Morgan (1987),Diamond (1981), and Box et al. (1978). Since only 32 replicated experiments were run, it was not possible to separate the effect of each potentially important variable (or interaction) from the effect of all other potentially important variables and interactions (i.e., "confounding" of variables occurred). Two different levels were used for each of the nine variables; these are summarized in Table I. Levels resulting in low cell viability were not studied. Procedure for the Fractional Factorial Experiment. The 32 sets of culture conditions were run in two separate experiments. All high-temperature (37 "C) culture conditions were run in the first experiment, and all low-temperature (34 "C) culture conditions were run in the second experiment. In each experiment all cultures were grown simultaneously. Prior to the experiments, each media formulation was incubated for about 8 h in order to equilibrate with respect to temperature and dissolved gases. Each T-flask was then inoculated with cells. The
cell inoculum consisted of exponentially growing cells with a viability of at least 98%. The culture volume in each T-flask was approximately 23 mL; duplicate cultures were run for each culture condition. A low initial cell concentration (5500 viable cells/mL) was used in order to minimize changes in the concentrations of nutrients and waste products during the experiment. Over the course of the experiment, the concentrations of glucose and lactate changed by about 0.050.10 mM and the concentrations of glutamine and ammonium changed by about 0.23 mM. No changes in medium pH occurred during the experiment. Four samples were taken of each culture during the experiment. The first sample was taken 15 h after the start of the experiment, and the final sample was taken after 45-48 h. During culture sampling the T-flask caps were removed only briefly to minimize the escape of T-flask gases. A portion of each sample was used for cell concentration measurements, and the remaining volume was centrifuged. The resulting supernatant was mixed with a small volume of sterile preservative solution (containing aprotinin, BSA, and EDTA in PBS-Tween) and stored at -77 "C. These samples were used for monoclonal antibody (MAb) measurements completed later. Viability measurements were done periodically during the experiment. From an analysis of mass transfer across the medium, it was determined that the dissolved oxygen gradient was always less than 5.5%. Dissolved COz gradients (and resulting pH gradients) were also determined to be insignificant. Procedure for Other Experiments. The important variables identified in the fractional factorial experiment were studied in further experiments. These experiments were performed using the same general procedure used in the fractional factorial experiment. The base levels used were as follows: 7.0 or 9.0% serum, 15.0 mM glucose, 7.0 mM glutamine, 1.OX base medium, 37.0 "C, pH 7.45, and 0.20 mM dissolved oxygen (unless noted otherwise). No lactate or ammonium was added (except for that present in theserum). Samples (4-6) were taken during the course of each experimental run. Analytical Techniques. Osmolality was determined either by osmometer measurement (Osmette A osmometer, Precision Systems) or by calculation of the concentrations of all chemical species (multiplied by the number of dissociable parts). Medium pH was measured using a pH electrode. The glutamine concentration of the serum was measured using Mecke's method (Bergmeyer, 1985), which is an enzymatic method based on the conversion of glutamine to y-glutamylhydroxamate by glutamine synthetase. Lactate and ammonium were measured using a Yellow Springs Instruments Industrial Analyzer and an enzymatic method (Bergmeyer, 19851, respectively. Cell concentration was measured using a Coulter cell counter (Model ZM) equipped with a 100 pm aperture tube. Culture samples were diluted to 1200-11000 cells/ mL with Isoton, and each sample was measured eight times. Cell viability was measured using the trypan blue exclusion method (Kruse and Patterson, 1973); after the culture sample was centrifuged, the supernatant was removed, and the cells were resuspended in a small volume of salt solution. Trypan blue stain was added to the sample, and the sample was then observed under the microscope. Monoclonal antibody (MAb) concentration was measured using the indirect method of the enzyme-linked immunosorbent assay (ELISA). The following procedure
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Table 11. Levels of the Variables Used for Each Experimental Run of the Fractional Factorial Design and the Resulting Average Specific Growth Rate and Specific Antibody Productivity*
exptl run
DO
T
PH
S
C
1
Gt
L
A
B
+
+
+
LL
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
For each variable the - and
0-l)
0.019 0.011 0.013 0.026 0.011 0.020 0.021 0.014 0.025 0.015 0.018 0.017 0.019 0.014 0.016 0.031 0.029 0.011 0.013 0.015 0.013 0.022 0.018 0.016 0.015 0.016 0.016 0.016 0.022 0.009 0.017 0.020
QP
Wce1l.h) 3.56 0.49 0.73 3.04 0.34 2.24 5.83 0.39 2.13 5.15 3.81 2.74 2.87 2.05 4.43 6.60 3.55 0.13 0.66 1.03 0.46 3.14 1.14 1.23 1.02 2.52 4.32 3.88 6.00 0.84 3.49 3.47
+ signs correspond to the low and high levels, respectively, listed in Table I.
was developed and used in this study. Human fibronectin (160 pL; 10 pg/mL) in carbonate/bicarbonate buffer was added to each well of a 96-well plate (Immulon I flat bottom, Dynatech Labs) and incubated for 2.5 h at 37 "C. The wells were then rinsed with Dulbecco's phosphatebuffered saline/Tween 20 (DPBS-Tween). DPBS-Tween (200 pL) containing 1.0% bovine serum albumin (BSA) was added and incubated for 2 h a t 37 "C. The wells were then rinsed. Culture samples were diluted with DPBSTween containing 0.75% BSA. A volume of 180 pL of the samples and MAb standards was added to the plate (each sample was run in triplicate), which was incubated for 3 h a t 25 "C. After the wells were rinsed, 170 pL of alkaline phosphatase/antibody conjugate (1:3OOO in DPBS-Tween) was added and the plate was incubated for 80 min at 37 "C. After the wells were rinsed, 200 pL of 1 mg/mL p-nitrophenyl phosphate in 10.0 % diethanolamine buffer was added to each well. After the plate was incubated at 37 "C for 3 h, the absorbances were measured at 405 nm (450-nm reference) using a Molecular Devices Emax precision microplate reader. The MAb concentrations of the samples were calculated from a calibration curve (generated from the absorbances of the standards). Antibody standard had been produced using the following procedure: grow cell culture and centrifuge, filter and concentrate supernatant, purify using a Protein A column, dialyze, and quantify using the Modified Lowry Protein assay (Hurrell, 1982). Analysis of Experimental Results. Cell growth was described using the following equation: dX/dt p X (1) where p is the specific growth rate, X is the viable cell concentration, and t is the time. p was calculated from a linear regression of the log of the cell concentration versus time using all of the sample data.
Antibody production was described using the following equation: dP/dt = q p X (2) where P is the antibody concentration and q p is the specific antibody productivity. Integration of eq 2 results in the following:
P = [Po-,]QPXO
+[:I.
(3)
where POand X Oare the initial concentrations of antibody and cells, respectively. The quantity q p / p , which was calculated from a linear regression of the antibody concentration versus the cell concentration using all of the sample data, was multiplied by p to obtain the value of q p . The viable cell concentration was used in the calculation of q p .
Results Cell Growth. In the fractional factorial experiment the cells grew exponentially after the initial lag phase. The 32 sets of culture conditions used in the fractional factorial design and the resulting average specific growth rates are listed in Table 11. The specific growth rates ranged from 0.009 to 0.031 h-l. Most of the cultures maintained relatively high viabilities. Nearly one-half of the cultures had a final viability greater than 97%, and only one culture had a final viability less than 70%. The effects of the variables and interactions were calculated from the specific growth rates by constructing a table of contrast coefficients (Mead, 1988;Das and Giri, 1986;Box et al., 1978). The variables and their effects are listed in Table 111. The "effect" represents the average difference between the specific growth rate at the high and low levels of each variable/interaction. The sign associated
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Table 111. Tabulation of the Effects of the Variables and Interactions on the Specific Growth Ratee
effect
(lo4 h-l) 58 37 -38 -25 21 -19 -19 17 17 -15 -15 -13 13 12 -11 10 10 9 9
variable/interaction B, DO-T-PH-S DO-T
A DO-T-DH T-pH A-B, pH-S-L DO-T-A DO-pH DH-B.DO-T-S DO-pH-A pH-S-A, DO-T-A-B T-A-B, T-pH-S-L, DO-pH-S-A DO-T-pH-A DO-B, T-pH-S T-pH-A T T-S, DO-PH-B pH-S, DO-T-B S,DO-T-pH-B DO-S-L. T-S-A.. DO-DH-A-B 7 . .--------------------------------------------------6 T-B, DO-pH-S -6 DO-A-B,DO-pH-S-L, T-pH-S-A -6 S-A, DO-T-S-L -6 DO-S, T-pH-B -6 DO 5 PH 4 pH-A 4 T-S-L, DO-S-A, T-pH-A-B -3 DO-A 1 5-L, pH-A-B, DO-T-S-A -1 T-A The standard error of an effect is indicated by the dashed line. Table IV. Dependence of the Specific Growth Rate on the Base Medium Concentration base medium base medium fi (h-') concentration M 0-l) concentration 0.15X 0.30X
0.019 0.036
0.55X 1.oox
0.037 0.040
with each effect (positive or negative) indicates whether the variable had a beneficial or adverse effect on the cell growth rate. The variables and interactions are arranged in decreasing order of the magnitude of their calculated effect. Only the variables and interactions that had been previously identified appear in Table 111. Since only 32 experiments were run, it was not possible to isolate the effects of all of the potentially important variables and interactions. The effects of variables and interactions appearing in the same row of Table I11 are confounded; for example, the main effect of the base medium could not be isolated from the effect of the interaction of DO, T, pH, and S. The boldfaced variables in Table I11are those variables found to be important in a previous study (Glacken et al., 1988). In the present study, B, A, and A-B were also found to have large effects on cell growth as indicated by their high position in Table 111. Serum and its interactions with ammonium and lactate appear lower in Table 111, indicating a lesser importance. The reduced effects of serum and its interactions with ammonium and lactate observed in the present study are probably due to the fact that a narrower range of serum concentrations was used in the present study than in the previous study. Serum levels of 2.5% and 9.0% were used in the present study; levels of 1.0 % and 9.0 % were used in the previous study. Low viability was observed in the previous study when serum concentrations of 1.0% were used. These results suggest that the cell growth rate may exhibit a strong
dependence on the serum concentration over the concentration range of 1.0-2.5%. In addition, it appears that there may be strong interaction between serum and ammonium and also between serum and lactate at serum concentrations between 1.0% and 2.5%, but not at serum concentrations above 2.5%. Differences in the properties of the serum used in the two different studies could also have contributed to the observed differences in the effects of serum, serum-ammonium, and serum-lactate. Since duplicate cultures were run for each condition, the standard deviations of the specific growth rates could be calculated. The average standard deviation for the 32 pairs of runs was calculated to be 0.002 h-' using the method described by Box et al. (1978). The standard error of an effect was estimated to be 6 X lo4 h-' using the method described by Box et al. (1978); this standard error corresponds to the 95% confidence level and is indicated by the dashed line in Table 111. Variables and interactions with calculated effects greater than this are considered to be statistically significant. A large number of variables and interactions were observed to have a significant effect on the cell growth rate over the ranges of the variables studied. Temperature, pH, and dissolved oxygen do not appear to have large main effects as indicated by their relatively low positions in Table 111. However, interactions among these variables have very large effects on the cell growth rate. This is unusual in that main effects are usually more important than the effects of interactions. The relatively large interactions between temperature, pH, and dissolved oxygen and the relatively small main effects of these variables may be due to the mechanisms by which these variables affect cell growth. For example, temperature and pH both affect the activities of the cellular enzymes. It is possible that the calculated main effect for one or more of these three variables is misleading. This could occur as a result of any of the following: (1) strong curvature of the response surface; (2) since the calculated effect is an average, a large positive effect of a variable under one set of conditions will be negated by a large negative effect of the variable under a different set of conditions; and (3) the effect of the variable may be confounded with the effects of other variables which strongly affect cell growth. Dependence of Cell Growth on Base Medium. Although the effect of base medium was confounded with the effect of the DO-T-pH-S interaction in the fractional factorial experiment, this large effect is probably due to the base medium and not due to DO-T-pH-S because base medium was found to be important in the earlier study of Glacken et al. (1988) and because main variables tend to be more important than four-variable interactions. Furthermore, it was found that serum and its interactions with other variables generally had small effects in the experiment (so it is unlikely that the interaction between serum and DO-T-pH had a large effect). The effect of base medium on F was studied by growing cultures at four different levels of base medium: 0.15X, 0.30X, 0.55X, and LOOX. The results are summarized in Table IV. The average standard deviation of the specific growth rate was 0.0010 h-l. A t concentrations below about 0.3X, the specific growth rate increased rapidly as the concentration of base medium was increased. Over the range 0.3-1.0X, the concentration had a relatively small effect on growth rate. These results agree with the results of the fractional factorial experiment in which base medium concentrations of 0.2X and 1.OX were used; the specific growth rates were, on average, much greater at a
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pH 6.95 0.05
3
0.01
0.02
8
8-0.00-
0.01
0.00 0.05 0.10 0.15 0.20
0.0 0.2 0.4 0.6 0.8 1.0
Concentration of Base Medium Figure 1. Experimental data ( 0 )and equation (-) describing the effect of base medium concentration on the specific growth rate.
concentration of LOX than at 0.2X. In a bioreactor the adverse effects resulting from low base medium concentrations can be largely avoided by operating at a minimum concentration of 0.3X. Equation 4, which was derived from a nonlinear regression of the data in Table IV, describes the dependence of p on the base medium concentration, [Bl. This equation and the experimental data are shown in Figure 1.
Dissolved Oxygen Concentration (mM)
(b) pH 7.54 Q
i UY
0.04
0.01 0.00 0.05 0.10 0.15 0.20
Dissolved Oxygen Concentration (mM)
(4)
(c) pH 7.72 Effect of Dissolved Oxygen, Temperature,and pH on p. On the basis of the tabulation of effects, interactions between dissolved oxygen, temperature, and pH strongly affected the cell growth rate. Interactions between these variables were experimentally studied by testing the effects of various combinations of the levels of these variables on p. The levels used are summarized: dissolved oxygen, 0.04,0.12,0.20 mM; temperature, 32.5,34.8,37.0 "C; pH, 6.43,6.57,6.79,6.95,7.15,7.35,7.54,7.72. A wider range of levels was studied for each variable in this set of experiments than in the fractional factorial experiment. For the cultures exposed to a low dissolved oxygen concentration (0.04 mM) it was not possible to maintain a uniform concentration of dissolved oxygen throughout the culture medium. On the basis of an analysis of mass transfer for these cultures, the dissolved oxygen concentration at the bottom of the culture medium was between 0.03 and 0.04 mM. The viability of the cell cultures was measured during the experiment; in all cases the viability at the end of the experiment was greater than 93% (and usually greater than 98% ), The average standard deviation of the specific growth rates for this set of experiments was 0.0010 h-l. The results are summarized in Figure 2 in which p is plotted as a function of the dissolved oxygen concentration at different levels of temperature (each graph corresponds to a different pH). At p H s below 6.95 there was relatively little interaction between dissolved oxygen, temperature, and pH. The shapes of the three curves in Figure 2a (pH 6.95) are similar to those observed for lower p H s (Le., 6.43,6.57, and 6.79). In general, over the pH range of 6.43-6.95 the specific growth rate increased as a result of any of the following: (1) an increase in temperature; (2) an increase in pH; or (3) a reduction in dissolved oxygen concentration. At p H s above 6.95 there was significant interaction between DO, T, and pH, as evidenced by the different shapes of the curves in Figure 2. However, there is no clear pattern as to how temperature, pH, and dissolved oxygen interact to affect p; this may be due to the complexity of the processes occurring within the hybridoma cell.
5 cr:
0.05 0.04
9
0.03
B
00.10.00 0.05 0.10 0.15 0.20
Dissolved Oxygen Concentration (mM) Figure 2. Specific growth rates a t different pH's: (a) 6.95; (b) 7.54; (c) 7.72. Temperatures: ( 0 )37.0; (0)34.8; (A) 32.5 OC.
Comparison of the growth rate curves for pH's of 6.95 and 7.72 reveals the interaction between temperature and pH. At a pH of 6.95 temperature had a large effect on p, as evidenced by the large gaps between the three temperature curves in Figure 2a. At a pH of 7.72 there were relatively small differences between the specific growth rates at 32.5,34.8, and 37.0 "C. At pH's of 7.15,7.35, and 7.54 temperature had an intermediate effect on p. In general, increases in temperature resulted in large increases in 1.1; however, the magnitude of the increase in p was strongly affected by the levels of DO and pH. The effect of temperature was especially pronounced at low levels of DO over the temperature range 34.8-37.0 "C. Changes in the dissolved oxygen concentration had different effects on p, depending upon the levels of temperature and pH. For some combinations of temperature and pH, an increase in the dissolved oxygen concentration resulted in an increase in p; however, for other combinations an increase in dissolved oxygen caused a reduction in p. This explains why the magnitude of the main effect for DO in Table I11 is so low. The effects tabulated in Table I11 represent the averages of the responses caused by changes in the variables; consequently, an increase in p resulting from a change in DO at one set of conditions of temperature and pH can be offset by a decrease in p resulting from a similar change in DO at a different set of conditions of temperature and pH. Although the two-level fractional factorial experimental
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304
(a) 0.04 mM
Table V. Tabulation of the Effects of the Variables and Interactions on the SDecific Antibody ProductivityB effect pgice1l.h) variablelinteraction 208 B, C-Gt 171 S -91 s-L -89 A, T-Gt -7 1 pH-A T, A-Gt 64 63 T-S -62 T-B, A-C -59 C, B-Gt -51 L, DO-Gt, DO-T-A 47 A-C-L, T-L-B, DO-A-B -45 A-B, T-C 43 T-pH -40 Gt, DO-L, C-B, T-A 40 S-Gt 37 pH-L 36 PH -34 DO, L-Gt -3 1 DO-T-pH, S-B ................................................... -24 DO-pH 23 DO-S -21 L-B, DO-C 19 S-A 18 pH-B, DO-T-S 16 pH-S -15 C-L, DO-B 8 DO-T, L-A 7 pH-Gt ~
0.04 O
0.01
'
0
5
I
m
L
0.12 mM
0'05m 0.04
0.01 6.3
1.5
7.1
6.1
1.9
7
PH
-3
pH-C T-L, DO-A a The standard error of an effect is indicated by the dashed line. 2
0.20 mM U.VJ I
I
0.03
0.014 6.3
s-c
'
'
6.1
'
'
'
'
1.5
'
'
7.9
Figure 3. Effect of pH on p a t dissolved oxygen concentrations of (a) 0.04, (b) 0.12, and (c) 0.20 mM a t temperatures of ( 0 )37.0, (0) 34.8, and (A)32.5 "c.
approach is unable to definitively identify important main variables such as DO which can have both beneficial and adverse effects on p, this approach is capable of detecting complex interactions that occur between important main variables, such as DO and the other variables. The use of a three- or four-level fractional factorial approach may enable the detection of main variables that can have both beneficial and adverse effects. The strong effect of pH onp is readily observed in Figure 3 in which p is plotted as a function of pH; each curve corresponds to a different temperature. Figure 3a-c represents the three different dissolved oxygen levels. The optimum pH depends upon the levels of temperature and DO. For seven of the nine curves the optimum pH appears to lie between 7.14 and 7.36. For the other two curves the optimum pH is between 6.79 and 6.84. The behavior of the cells under these two sets of conditions contrasts strongly with the behavior of the cells under the other seven sets of conditions and is evidence of the DO-T-pH interaction.
The shape of most of the curves in Figure 3 over the pH range 7.05-7.50 points out a limitation of the two-level fractional factorial approach. In this pH range many of the curves exhibit a maximum. In the fractional factorial experiment, pH levels of 7.05 and 7.50 were used; since these two levels were on opposite sides of the pH that resulted in the maximum, it was not possible to obtain an accurate measurement of the true effect of pH on p. This caused the calculated effect of pH to be lower than its true value. This limitation can be avoided by using three or more levels for each variable. A second factor which contributed to the relatively low calculated effect for pH is the mixed effect that pH has on p over the pH range 7.05-7.50. In some cases an increase in pH from 7.05 to 7.50 caused an increase inp, while in other cases an increase in pH caused a reduction in p. This example points out the importance of the selection of the levels for each variable. Antibody Production. The average specific antibody productivities for each of the 32 different culture conditions in the fractional factorial experiment are listed in Table 11. The specific antibody productivities ranged from 0.13 to 6.60 pg/cell.h; this wide distribution confirms that q p is strongly affected by the culture conditions. When the values of q p are plotted against p , the data points are widely scattered; however,there is an obvious trend that increases in q p are associated with increases in p. Thus, the decision to include the variables and interactions having the largest effects on p in the list of potentially important variables affecting antibody production seems justified. The effects of the variables and interactions on q p are listed in Table V. The concentrations of base medium, serum, lactate, and ammonium appear to have the largest effects on antibody production.
305
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Table VI. Dependence of Specific Antibody Productivity, on the Base Medium Concentration specific specific base antibody antibody base medium productivity productivity medium (pg/cell.h) concentration (pg/cell-h) concentration 0.15X 0.30X
3.83 6.03
0.55X
1.oox
6.38 6.83
Base medium, ammonium, and temperature all have large effects on p; it is apparent from Table V that these three variables also have large effects on q p . For each of these three variables, the sign associated with the calculated effect on cell growth is the same as the sign associated with the calculated effect on antibody production (e.g., the sign associated with both of the effects of ammonium on cell growth and antibody production is negative). This may explain why, in general, the antibody production rate increased when the cell growth rate increased. However, there are many variables and interactions which strongly affect the growth rate but have relatively little effect on the antibody production rate and vice versa. For example, interactions between dissolved oxygen, temperature, and pH had relatively little effect on q p . This may be the cause of the large amount of scatter of data points which occurs in a plot of q p versus p. The standard deviation of the specific antibody productivities was calculated for each of the 32 culture conditions; these standard deviations were calculated from the known standard deviations of p and q p I p using the method described by Bevington (1969). The standard error of an effect was calculated from these standard deviations to be 0.28 pg1cell.h (this is indicated by the dashed line in Table V). As shown in Table V, a large number of variables and interactions have a significant effect on the antibody production process over the ranges of the variables studied. The variables and interactions having the largest effects were studied further. Dependence of Antibody Production on Base Medium. Either base medium or the glucose-glutamine interaction had the largest effect on q p (the effects of these two confounded with one another). The effect of base medium was isolated from the effect of the C-Gt interaction by studying the antibody production of cells exposed to different levels of base medium at constant levels of glucose and glutamine. Four different levels of base medium were tested: 0.15X, 0.30X, 0.55X, and 1.OOX. High cell viabilities were observed for all cultures during the experiment. The experimental results are shown in Table VI. The average standard deviation of the specific antibody productivity was 0.29 pg/cell.h. Comparison of the results in Table VI with the results for the effect of base medium on cell growth rate reveals a similarity in the effect of base medium. Over the range 0.15-0.30X the base medium concentration has a very large effect on antibody production, but over the range 0.30-1.OOX the concentration has only a small effect. In order to maximize antibody production in a bioreactor, a minimum base medium concentration of 0.3X should be used. On the basis of the similarity between the effects of base medium on 1.1and q p , an equation similar to eq 3 can be used to describe antibody production: qP=7’3(
[B] - 0.07 [B]
)
where q p has units of pg/cell.h. The experimental data and this equation are shown in Figure 4. These results
0
.
8
2.0 0.00.0
0.2
0.4
0.6
0.8 1.0
Concentration of Base Medium Figure 4. Experimental data ( 0 )and equation (-1 describing the effect of base medium concentration on the specific antibody productivity.
suggest that the large effect associated with base medium and the C-Gt interaction in Table V is probably due to base medium and not to the C-Gt interaction. Effect of Serum and Its Interaction with Lactate on qp. The effects of serum and lactate were studied in experiments in which cells were grown in medium containing different concentrations of these components. Five different levels of fetal calf serum (2.0, 3.5, 5.3, 8.0, and 11.0%)and three different levels of lactate (3.0,20.4, and 45.4 mM) were used; a lactate concentration of 3.0 mM was the lowest achievable level due to the presence of lactate in the serum. For all cultures the final viability was at least 97 7%. The results are tabulated in Table VI1 and plotted in Figure 5. Raising the concentration of serum resulted in higher rates of antibody production (as was indicated by the results of the fractional factorial experiment). Specific antibody productivity exhibited an approximately linear dependence on serum. In general, q p decreased as lactate was increased; this effect was especially prominent at high serum concentrations. The interaction between serum and lactate was evident at high lactate concentrations. For serum and lactate concentrations in the ranges 2.05.3% and 20.4-45.4 mM, respectively, the lactate concentration had relatively little effect on q p ; this behavior contributed to the large calculated effect for the serumlactate interaction in the fractional factorial experiment (the concentrations of serum and lactate used in the fractional factorial experiment were 2.5 and 9.0% and 5.0 and 40.0 mM, respectively). An equation describing the dependence of q p on serum and lactate was developed on the basis of the observations that antibody production exhibited a nearly linear dependence on serum concentration and that the magnitude of this dependence was influenced by the lactate concentration (i.e., the slopes of the curves in Figure 5 are a function of lactate concentration). The followingequation was derived from a nonlinear regression of the data in Table VII: 9.6[s] qp=
+ 5.2[L] + 296 [Ll + 57
where the units of q p , [SI, and [Ll are pg/cell.h, volume percent, and mM, respectively. Antibody production exhibited a linear dependence on the serum concentration, while cell growth exhibited a Monod-type dependence over the range of serum concentrations studied. This contrasts with the effect of base medium (in which it was found that p and q p exhibited similar dependencies on base medium concentration). Effect of Ammonium on Antibody Production. In the fractional factorial experiment the effects of ammo-
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306
Table VII. Effect of Lactate and Serum Concentrations on Antibody Production lactate serum 4P concn (mM) concn ( % ) (udce1l.h) 3.0 2.0 5.53 3.0 3.5 5.81 3.0 5.3 6.27 3.0 8.0 6.46 11.0 3.0 6.87 2.0 5.37 20.4 5.59 20.4 3.5 20.4 5.3 5.74 20.4 6.29 8.0 20.4 11.0 6.59 45.4 5.33 2.0 45.4 5.62 3.5 45.4 5.75 5.3 45.4 5.89 8.0 45.4 11.0 6.25
2
7.01
1
4 /
5.04. 1.5 3.5 3
I 11.5
.
5.5
7.5
9.5
Serum (Volume %) Figure 5. Experimental data (symbols) and equations (lines) describing the effect of serum on the specific antibody productivity a t different lactate concentrations: (A)3.0; (0)20.4;( 0 ) 45.4 mM.
Table VIII. Dependence of Specific Antibody Productivity on the Ammonium Concentration specific specific antibody antibody ammonium productivity ammonium productivity concn (mM) (pg/cell-h) concn (mM) (pgice1l.h) 0.70 6.83 5.86 4.31 2.36 6.17 7.56 2.80 4.06 5.31
nium and the temperature-glutamine interaction were confounded. In order to determine whether ammonium significantly affected the specific antibody productivity, an experiment was performed in which the temperature and glutamine concentration were held constant while the ammonium concentration was varied over a wide range. Five different ammonium concentrations were tested 0.70, 2.36, 4.06, 5.86, and 7.56 mM. These concentrations represent the average concentrations that were present in each of the five cultures. The lowest achievable level was 0.70 mM due to ammonium production from the spontaneous decomposition of free glutamine and the presence of ammonium in the serum. High cell viabilities were observed for all cultures during the experiment. The results of the experiment are summarized in Table VIII. Ammonium had a large effect on antibody production over the entire range of concentrations studied. This effect is especially strong a t high ammonium levels. These results reflect the large adverse effect of high ammonium concentrations indicated by the results of the fractional factorial experiment. The dependence of q p on ammonium can be described by eq 7 , which was derived from a nonlinear regression of the data in Table VIII:
- 7.0 qp - 1 + [A12/48
(7)
where the ammonium concentration, [A], has units of mM. The experimental data and this equation are shown in Figure 6. The form of eq 7 is the same as that used by Glacken et al. (1988), who developed it to describe the dependence of p on ammonium based upon the possible existence of noncompetitive-like inhibition between serum and ammonium. Although the results of the fractional factorial analysis for q p do not indicate a sighificant S-A interaction, qp and p exhibit a similar dependence on ammonium. The inhibition constant for cell growth (45 mM2) is nearly the same as that for antibody production (48 mM2). As is evident in Table V, the effects of base medium, serum-lactate, and ammonium are much greater than the
0.0
2.0
4.0
6.0
8.0
Ammonium Concentration (mM) Figure 6. Experimental data ( 0 )and equation (-) describing the effect of ammonium concentration on the specific antibody productivity.
effects of the interactions between them. Due to the fact that there is only a small degree of interaction, the effect of base medium on the specific antibody productivity will be nearly the same at any level of serum, lactate, or ammonium (over the ranges of the variables studied). Similarly, the effects of serum-lactate and ammonium will be nearly independent of the levels of the other variables. Since the effects of noninteracting variables are additive (Box et al., 19781,eqs 5-7 can be superimposed. The combined effects of B, S,L, and A can be approximated by the following relationship: qP
([Bl - 0.07)(9.6[S] + 5.2[Ll + 296) a
[BI(l + [A12/48)([Ll + 57)
(8)
Discussion and Conclusions Fractional factorial statistical design of the experiments was, in general, an effective approach to the study of the complex metabolism of hybridoma cells, as it enabled the identification of important variables and interactions affecting cell growth and antibody production using a minimum number of experiments. For biological systems the variables appear to exhibit a large degree of interaction due to the complexity of these systems. On the basis of the results of this study, response surfaces for biological systems may be best studied using fractional factorial experiments with three (or more) levels per variable. The cell growth rate was strongly affected by the levels of base medium, dissolved oxygen, pH, and temperature. The adverse effects resulting from low concentrations of base medium can be largely avoided by maintaining a minimum concentration of 0.W. The rapid increase in CL at low base medium concentrations could be due to a requirement for base medium for cell maintenance; the
Blotechnol. hog., 1993, Vol. 9, No. 3
analysis suggests a maintenance requirement of about 0.07X. This requirement would be in addition to the base medium needed for cell growth. From the results of this study, it is not possible to determine which component of the base medium limits cell growth a t low base medium concentrations. If this limiting component were identified, then it should be ppssible to maintain high cell growth rates at base medium concentrations below 0.3X by supplementing the medium with an additional quantity of this limiting component. Interactions between dissolved oxygen, pH, and temperature were of considerable importance. The finding that the rate of cell growth is generally higher at low dissolved oxygen concentrations is of great benefit since maintenance of high levels of dissolved oxygen is frequently a difficult problem in bioreactor operation. Cellular metabolism did not appear to be limited by insufficient oxygen at the lowest oxygen concentration tested in this study (0.04 mM). In order to maintain high rates of cell growth and antibody production, the reactor temperature should be maintained near 37 OC. The hybridoma cells grew relatively quickly over a wide range of pHs. On the basis of the results of the study of c d l growth, the pH should be maintained between 6.70 m d 7.55. However, since the optimal pH at 37 "C is about 7.35, it is more desirable to maintain the pH between 7.3 and 7.4. Analysis of the experimental results revealed no clear pattern as to how temperature, pH, and dissolved oxygen interact to affect the growth rate; this may be due to the complexity of the processes occurring within the hybridoma cell. This interaction may be due to the effect of each of these three variables on the rates of free radical formation and cell damage caused by free radicals. High levels of dissolved oxygen can result in high rates of free radical formation, and both temperature and pH can affect the activity of enzymes involved in free radical formation and repair of cell damage in mammalian cells (Halliwell and Gutteridge, 1989). Interpretation of the results is limited by an incomplete understanding of free radical formation and the action of free radicals on cellular components and structures. The specific antibody productivity was strongly affected by the concentrations of base medium, serum, ammonium, and lactate. Due to the large effects of base medium and serum, future studies on the individual species composing base medium and serum are warranted. Identification of the important components of base medium and serum may enable the use of reduced base medium and serum concentrations by supplementing the medium with the important components. The linear dependence of q p on serum might be due to a growth factor that has a catalytic effect on antibody production being present at a limiting concentration, as suggested by Dalili and Ollis (1989).Due to the high cost of serum, it is advantageous to maintain a serum concentration of only about 2.5 5%. The fact that even low concentrations of ammonium and lactate caused reductions in the antibody production rate emphasizes the importance of minimizing the exposure of cells to these waste products. The ammonium concentration can be minimized by maintaining low concentrations of glutamine (in order to minimize the spontaneous decomposition of free glutamine). Ammonium and lactate concentrations can be reduced by minimizing cellular production of these waste products and by using low serum coqcentrations since serum typically contains ammonium and lactate. The reduction of cellular ammonium and lactate production through the maintenance of appropriate culture conditions are described in a related article.
307
Cell growth and antibody production exhibited similar dependencies on the base medium concentration. Likewise, cell growth and antibody production exhibited similar dependencies on the ammonium concentration. In contrast, cell growth and antibody production exhibited very different dependencies on the serum concentration. Antibody production was very sensitive to the serum concentration over the range 2.5-9.0%, while cell growth was much less sensitive to the serum concentration over this range. In general, conditions that favored high cell growth rates also favored high specific rates of antibody production. This may be partially due to the fact that the specific growth rate and the specific antibody productivity were similarly affected by several of the variables. This observation may have great significance with respect to bioreactor operation. It may be desirable to maintain the cells in a state of high growth rate. Although the behavior of the cells in the stationary growth state was not studied, the results of this study suggest the possibility that the rate of antibody production under conditions of zero net growth might be low. In this case, it might be undesirable to allowthe cellsto make the transition from an exponential growth state to a stationary growth state. In this study, some of the variables were found to have a relatively large effect on antibody production but relatively little effect on cell growth; consequently, it may be possible to achieve appreciable rates of antibody production at low growth rates by optimizing these variables.
Notation A B C DO Gt L P Po 9P
S t
T X
xo P
ammonium base medium glucose dissolved oxygen glutamine 1actate antibody concentration initial antibody concentration specific antibody productivity (pg/cell-h) serum time (h) temperature viable cell concentration initial viable cell concentration specific growth rate (h-1)
Acknowledgment This work was supported, in part, by grants from E. I. du Pont de Nemours and Company, the Delaware Research Partnership Program, and the National Science Foundation Presidential Young Investigator Program. Literature Cited Bergmeyer, H. U. Methods of Enzymatic Analysis, 3rd ed.; Verlag Chemie: Deerfield Beach, FL, 1985; Vol. VIII. Bevington, R. R. Data Reduction and Error Analysis for the Physical Sciences; McGraw-Hill Book Co.: New York, 1969. Birch, J. R.; Boraston, R.; Wood, L. Bulk Production of
Monoclonal Antibodies in Fermenters. Trends. Biotechnol. 3, 162-166. Box, G. E.; Hunter, W. G.; Hunter, J. S. Statistics for Experimenters-An Introduction to Design, Data Analysis, and Model Building; John Wiley & Sons: New York, 1978. Dalili, M.; Ollis, D. F. Transient Kinetics of Hybridoma Growth and Monoclonal Antibody Production in Serum-Limited Cultures. Biotechnol. Bioeng. 1989, 33, 984-990.
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Dalili, M.; Sayles, G. D.; Ollis, D. F. Glutamine-Limited Batch Hybridoma Growth and Antibody Production: Experiment and Model. Biotechnol. Bioeng. 1990,36,74-82. Das, M. N.; Giri, N. C. Design and Analysis of Experiments, 2nd ed.; John Wiley & Sons: New York, 1986. Deming, S. N.; Morgan, S. L. Experimental Design: A Chemometric Approach; Elsevier: New York, 1987. Diamond, W. J. Practical Experiment Designs f o r Engineers and Scientists; Lifetime Learning Publications: Belmont, CA, 1981. Freshney, R. I. Culture of Animal Cells-A Manual of Basic Technique; Alan R. Liss, Inc.: New York, 1983. Gaertner, J. G.; Dhurjati, P. Fractional Factorial Study of Hybridoma Behavior. 2. Kinetics of Nutrient Uptake and Waste Production. Biotechnol. Prog., followingarticle in this issue. Glacken, M. W.; Fleischaker, R. J.; Sinskey, A. J. Large-scale Production of Mammalian Cells and Their Products: Engineering Principles and Barriers to Scale-up. Ann. N. Y. Acad. Sci. 1983,413,355-372. Glacken, M. W.; Adema, E.; Sinskey, A. J. Mathematical Descriptions of Hybridoma Culture Kinetics: I. Initial Metabolic Rates. Biotechnol. Bioeng. 1988,32,491-506. Halliwell, B.; Gutteridge, J. Free Radicals in Biology and Medicine, 2nd ed.; Oxford University Press: New York, 1989. Hurrell, J. G. Monoclonal Hybridoma Antibodies: Techniques and Applications; CRC Press, Inc.: Boca Raton, FL, 1982. Jensen, M. D. Diffusion in Tissue Cultures on Gas-permeable and Impermeable Supports. J. Theor. Biol. 1976,56, 443458. Jo, E. C.; Park, H. J.; Park, J. M.; Kim, K. H. Balanced Nutrient Fortification Enables High-Density Hybridoma Cell Culture in Batch Culture. Biotechnol. Bioeng. 1990,36, 717-722. Ju, L. K.; Ho, C. S.;Baddour, R. F. Simultaneous Measurements of Oxygen Diffusion Coefficients and Solubilities in Fermentation Media with Polarographic Oxygen Electrodes. Biotechnol. Bioeng. 1988,31,995-1005. Kruse, P. F.; Patterson, M. K. Tissue Culture-Methods and Applications; Academic Press, Inc.: New York, 1973. Lavery, M.; Nienow, A. W. Oxygen Transfer in Animal Cell Culture Medium. Biotechnol. Bioeng. 1987,30,368-373. Low, K.; Harbour, C. Growth Kinetics of Hybridoma Cells: (2) The Effects of Varying Energy Source Concentrations. Deu. Biol. Stand. 1985,60, 73-79. Low, K. S.; Harbour, C.; Barford, J. P. A Study of Hybridoma Cell Growth and Antibody Production Kinetics in Continuous Culture. Biotechnol. Tech. 1987,1, 239-244.
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McLean, R. A.; Anderson, V. L. Applied Factorial and Fractional Designs; Marcel Dekker, Inc.: New York, 1984. McLimans, W. F.; Blumenson, L. E.; Tunnah, K. V. Kinetics of Gas Diffusion in Mammalian Cell Culture Systems. 11. Theory. Biotechnol. Bioeng. 1968,10,741-763. McQueen, A.; Bailey, J. Effect of Ammonium Ion and Extracellular pH on Hybridoma Cell Metabolism and Antibody Production. Biotechnol. Bioeng. 1990,35, 1067-1077. Mead, R. The Design of Experiments-Statistical Principles forPractical Applications; Cambridge University Press: New York, 1988. Miller, W. M.; Wilke, C. R.; Blanch, H. W. Effects of Dissolved Oxygen Concentration on Hybridoma Growth and Metabolism in Continuous Culture. J. Cell. Physiol. 1987,132,524-530. Miller, W. M.; Blanch, H. W.; Wilke, C. R. A Kinetic Analysis of Hybridoma Growth and Metabolism in Batch and Continuous Suspension Culture: Effect of Nutrient Concentration, Dilution Rate, and pH. Biotechnol. Bioeng. 1988,32,947965. Miller, W. M.; Wilke, C. R.; Blanch, H. W. Transient Responses of Hybridoma Cells to Nutrient Additions in Continuous Culture: I. Glucose Pulse and Step Changes. Biotechnol. Bioeng. 1989a,33,477-486. Miller, W. M.; Wilke, C. R.; Blanch, H. W. The Transient Responses of Hybridoma Cells to Nutrient Additions in Continuous Culture: 11. Glutamine Pulse and Step Changes. Biotechnol. Bioeng. 1989b,33,487-499. Morton, H. J. A Survey of Commercially Available Tissue Culture Media. In Vitro 1970,6,89-108. Reuveny, S.;Velez, D.; Macmillan, J. D.; Miller, L. Factors Affecting Cell Growth and Monoclonal Antibody Production in Stirred Reactors. J. Immunol. Methods 1986,86,53-59. Schoen, R.C.; Bentley, K. L.; Klebe, R. J. Monoclonal Antibody Against Human Fibronectin Which Inhibits Cell Attachment. Hybridoma 1982,1,99-108. Sureshkumar, G. K.; Mutharasan, R. The Influence of Temperature on a Mouse-Mouse Hybridoma Growth and Monoclonal Antibody Production. Biotechnol. Bioeng. 1991,37,292-295. Tharakan, J. P.; Chau, P. C. Serum Free Fed Batch Production of IgM. Biotechnol. Lett. 1986,8,457-462. Velez, D.; Reuveny, S.; Miller, L.; Macmillan, J. D. Kinetics of Monoclonal Antibody Production in Low Serum Growth Medium. J. Immunol. Methods 1986,86,45-52. Wohlpart, D.; Kirwan, D.; Gainer, J. Effects of Cell Density and Glucose and Glutamine Levels on the Respiration Rates of Hybridoma Cells. Biotechnol. Bioeng. 1990,36,630-635. Accepted January 21,1993.
