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A Kin etic Analysis of Hybridoma Grow thand Metabo l ism in Batch and Cont inuousSuspension Cultu re: Effect of Nutr ientCon cen tration , Dilutio n Rate, and pH

W. M. Miller*, H W. Blanch, and C. R. WilkeDepartment of Chemical Engineering, University of California,Berkeley, California 94720Accepted for publ ication November 30, 1987

Hybridomas are finding increased use for the produc-tion of a wide variety of monoclonal antibodies. Under-standing the roles of physiological and environmentalfactors on the growth and metabolism of mammaliancells is a prerequisite for the development of rationalscale-up procedures. An SP2/0-derived mouse hy bri-doma has been employed in the present work as amodel system for hybridoma suspension culture. In pre-liminary shake flask studies to determine the effect ofglucose and glutamine, it was found that the specificgrowth rate, the glucose and glutamine metabolic quo-tients, and the cumulative specific antibody productionrate were independent of glucose concentration overthe range commonl y employed in cell cultures. Only thespecific rate of glutamine uptake was found to dependon glutamine concentration. The cells were grown incontinuous culture at constant pH and oxygen concen-tration at a variety of dilution rates. Specific substrateconsumption rates and product formation rates weredetermined from the steady state concentrations. Thespecific glucose uptake rate deviated from the mainte-nance energy model at low specific growth rates, proba-bly due to changes i n the metabolic pathways of thecells. Antibody production was not growth-associated;and higher specific antibody production rates were ob-tained at lower specific growth rates. The effect of pHon the metabolic quotients was also determined. Anopti mum in viable cell concentration was obtainedbetween pH 7.1 and 7.4. The viable cell number andviability decreased dramatically at pH 6.8. At pH 7.7 theviable cell concentration initial ly decreased, but then re-covered to values typical of pH 7.1-7.4. Higher specificnutrient consumption rates were found at the extremepH values; however, glucose consumpt ion was inhib-ited at low pH. The pH history also influenced the behav-ior at a given pH. Higher antibody metabolic quotientswere obtained at the extreme pH values. Together withthe effect of specific growth rate, this suggests higherantibody production under environmental or nutritionalstress.

* Present address: Department of Chemical Engineering, NorthwesternUniversity. Evanston, IL 60208.

Biotechnology and Bioengineering, Vol. 32, Pp. 947-965 (1988)0 988 John Wiley & Sons, Inc.

INTRODUCTIONMonoclonal antibodies (MAbs) produced by hybridomas

have an expanding market for use in diagnostic and chem i-cal assays, as well as for affinity separation of other valu-able fermentation products and for therapeutic uses.' Mi-crobial production of MAbs is desirable because mam-malian cells grow more slowly, are more sensitive to shear,and require more expensive media than bacteria or yeast.Functional antibod ies have been expressed in yeast andb a ~ t e r i a , ~ut the large number of different antibodies re-quired makes cloning less attractive than for less complexproducts such as insulin or human growth hormone. Micro-bial antibodies may not be identical to those made by hy-bridomas' and efforts to amplify product formation rates inmam malian cells are pro gressing .6 Thus it is likely thatMAbs will be produced in cell culture for the foreseeablefuture. Before promising applications can be efficientlycommercialized, however, basic information must be ob-tained on the environmental and physiological factors thataffect cell growth and metabolism.Several general reviews on mammalian cell culture tech-nology have appeared during the past few Thestatus of hybridoma production has been recently reviewedby Randerson. Many of the techniques proposed to in-crease antibody production employ various forms of cellimmobilization. This precludes obtaining representativecell samples and often results in metabolite concentrationgradients. The uniform cell and metabolite concentrationscharacteristic of suspension culture facilitate the modellingof cell growth and metabolism. The status of suspensionculture for mammalian cells has been reviewed by Katingerand Scheirer. Hybridomas have been studied in suspen-sion culture by a number of investigators. I Hybridomashave been investigated in continuous suspension culture byFazekas de St. Groth '? and at Celltech.''.'' Similar studies

CCC 0006-3592/88/080947- 19$04.00



have been also conducted using other mammalianMost of these studies covered a limited range of dilutionrates and/or provided limited data on nutrient and by-product c oncentrations.Batch and continuous suspension cultures have been em-ployed in the present work to determine the effects of themajor nutrients, dilution rate, and pH on the growth andmetabolism of an SP2iO-derived mouse hybridoma line.Steady-state viable cell, total cell, glucose, lactate, anti-body, glutamine, and ammonia concentrations were ob-tained over a wide range of dilution rates (0.31-1.32 day -)and culture pH (6.8-7.7) at constant dissolved oxygenconcentration; and were used to calculate the metabolicquotients. Th e cellular responses to changes in culture con-ditions were also obtained.

Glucose and glutamine are the major carbon and energysources in most cell culture media and both nutrients arerequired for cell growth. Glu tamin e metabolism can provide30-65% of the energy for m am m al ian cel l g r ~ w t h . ~ ~ , * ~hemetabolic fates of these major nutrients are illustrated inFigure 1. The proportion of each nutrient consumed by thedifferent pathways depends on the metabolic state of thecells. The metabolic byproduct ammonia has been shownto inhibit cell grow th in culture.3325 actate ca n also inhibitcell growth,26although Reuveny et. al.I3 found that addi-tion of as much as 2.5 g/L lactate can stimulate the growthof some hybridomas.

MATERIALS AND M ETHODSCell Line and Medi um

Cell l ine AB2-143.2 (provided by G . L e w i s a n dJ . Goodm an, University of C alifornia, San Francisco C A)is an SP2/0-derived mouse hybridoma that produces anIgG2a antibody to benzene-arsonate. Th e cells were grownin Dulbeccos Modified Eagles Medium (with bicarbonatebuffer) supplemented with 10% fetal bovine serum (Hy-clone ) and 1% each of lOOX M EM none ssential ami noacids and 11 g/L sodium pyruvate (all except serum fromGibco). Initial glucose and glutamine concentrations aregiven below for shake flask studies. For 1-L suspensioncultures the initial (and feed) concentrations were 22mMglucose and 4.8m M glutamine. No antibiotics were usedand periodic mycoplasma samples were negative.

Shake Flask Cultu resCells were inoculated into 25 mL of complete mediumto g i v e a n i n i t i a l c o n c e n t r a t i o n o f -3 X lo4 v i a b l ecells/mL. The 200-mL polystyrene bottles (Coming ) wereplaced on a shaker (-70 rpm) and equilibrated with 7%CO, in air in a 37C incubator. Samples (1. lmL) weretaken daily.

I GLUCOSEentose Phosphate

CELL M A S S L A C T A T E & WATER

Glutamate 1T

CYCLE0A M M O N I A GLUTAMINE

Figure 1.sources for mammalian cell culture.Summary of the metabolic pathways for the major carbon and energy

948 BIOTECHNO LOGY AN D BIOENGINEERING, VOL. 32, OCTOBER 1988



Suspension CulturesA 1-L glass reactor (Pegasus) was used with 600 mLworking volume. Agitation was provided by a 5-cm axial

flow turbine operating at - 50 rpm. Oxygen transport wasvia surface aeration and the partial pressure was controlledat 80 ?5 mm Hg by varying the oxygen concentration inthe headspace. Temperature was maintained at 37 .0 0.2 Cwith a circulating water bath. The pH was controlled at7 .1 k0.1 by addition of 1M NaO H in batch experiments.Base 0 . 5 M NaHCO,) addition was also used for automaticpH control of the continuous suspension cultures, but theCO, concentration in the headspace was also adjusted tooptimize control and minimize base addition at each pH.Samples 5 mI, including purge) were taken twice daily.A multichannel peristaltic pump (Gilson) was used formedium addition and product removal in continuous cul-ture. Product was removed from the surface at a higherrate than the feed to maintain the liquid level at the heightof the outlet line. Silicone tubing was used for the feedline because inhibition had previously been observed whenmedical-grade PVC was used.2sSample Analyses

Th e cell samp le was diluted 1: 1 with 0.16% trypan bluein normal saline and counted on a hemacytometer; nonvi-able cells stained blue. An average of two (shake flask andbatch experiments) or four (continuous experiments) deter-minations was used to calculate the viable cell concentrationand percent viability. A minimum of four hemacytometerfields and 250 viable cells (or all nine fields for slides withless than 250 viable cells) were counted per determination.The remainder of each sample was centrifuged to removethe cells, preserved with sodium azide and frozen for lateranalysis. Glucose was measured using a clinical glucoseanalyzer; lactate was determined by an enzymatic assay;and ammonia was measured with an ion-selective elec-trode. Samples were reacted with o-phthaldialdehyde toform fluorescent amino acid derivatives. Glutamine wasseparated from the other amino acids via HPLC using anRP-18 column with gradient elution from 25% methanol(the balance was O.1M sodium acetate, pH 6.8) to 80methanol over 25 min.Antibody was determined using a sandwich ELlSA as-say in 96-well microtiter plates. The benzene-arsonateantigen was conjugated to bovine serum albumin and ad-sorbed to the wells. Six duplicate dilutions were used foreach standard or sample evaluated. Alkaline phosphataseconjugated to goat anti-mouse IgG was used to detect thebound antibody.The dissolved oxygen concentration was measured witha polarographic oxygen e lectrode (Ingold). Medium satu-rated with air was estimated to have an oxygen concentra-tion 194pM. 9 ,3 0 The volumetric mass transfer coefficientK L a was experimentally determined in sterile medium byfollowing the increase (or decrease) in oxygen concentra-tion when air (or nitrogen) was passed through the reactorheadspace.

Determinat ion of Specif ic Grow th Rate andMetabol ic Quot ientsThe experiments described below were carried out inbatch or constant-volume, continuous-flow (with sterilefeed) reactors. A material balance around the reactor yieldsthe following equations for cell growth:

1)(2)(3)

k , = p - D at steady state (4)

dn/dt = paPpn D n = pn - D ndn, /dt = pn - k,n, - D n ,

p = pap ,(n /nJ = n / n , ) don n)/dt + Dl

The distinction between p and papps based on the assump-tion that only viable cells can divide. The difference be-tween p and papps especially important when the viabilityis low. The specific metabolic quotients for substrate andoxygen consumption and product formation were obtainedfrom:

5 )(6)(7)

q, = [ D s , - s) - ds/dt]/n,qo* = [K,aG, COJ - d(Co,)/dfl/n,

q A b = [ D A b ) -I- d(Ab)/dtI/n,Note that these quantities are per viable cell.

RESULTS AND DISCUSSIONBatch Culture

Typical batch growth curves are shown in Figure 2(a).There is an initial period of exponential growth followedby a decline in viable cell concentration and a plateau intotal cell concentration. The peak in the viable cell countcorresponds to the time at which the glutamine has beenexhausted [Fig. 2(b)], which suggests that glutamine is thelimiting nutrient for this medium. Glucose consumptionand the complementary production of lactate ceased about24 h later. The apparent molar yield of lactate from glu-cose was about 1.5 (75% of the theoretical maximum).Antibody production also continued after the maximum inv iab le ce l l concen t r a t ion [F ig . 2 (c ) ] . T h e cum ula t ivespecific antibody production rate declined somewhat be-fore reaching a constant value of 22 X pg/cell/day.The maintenance energy model' for nutrient consump-tion may be written as:

(8)Data for the glucose metabolic quotient [Fig. 2(d)] ap-pear to fit this model with yglucose 2.0 X 10 cells/mmol

and mglucose 1.2 X mmol/cell/day. This value ofmgfucoses - 5 of the value for qglucov t pm ax 1 .3 day-'.There is more scatter in the glutamine metabolic quotientdata.A generally employed model for product formation is:

4 s = E.L/y:,, = P/Y , , , + me

q A b = ffp+ (9)MILLER, BLANCH, AND WILKE: KINETIC ANALYSIS OF HYBRIDOMA 949



CE

L LO LG s

IrnL

Spec i f i cgrowth ra te

2,

50

40IIE30Cq fI 20da

Y 10

0

35 T T 6

- - 8G l ucose

rnrnol -_ 7-- Y

-- 6= -- 5

-- 4-- 3-- 2-- 1

1 : r O

/Ant i body /,ng \ \--\

-- / /7

I G l u t ami nernrnolA

100

20

00 1 2 3 4 5 6 7

TIME days)(C)

E62o ceII/10 d

0

Figure 2 . Hybridoma batch growth in a I-L reactor with dissolved oxygen and pH control: (a) cell concentration and specific growth rate vs.culture time; (b) glucose, glutamine and lactate concentrations vs . culture time; (c) antibody concentration and average specific antibody pro-duction rate vs. culture time; (d) antibody (squares), glutamine (triangles) and glucose (circles) metabolic quotients vs. specific growth rate.

For totally growth-associated products /3 is zero, and fornon-growth-associated products a is zero. T he data for theantibody metabolic quotient in Figure 2(d) and the cumula-tive data in Figure 2(c) suggest that antibody production ispartially growth-associated. The scatter in the metabolicquotients is not unexpected for batch data, as culture con-dit ions are constantly changing, and precludes one fromobtaining reliable values for the constants in eq. 8) and 9).

Effect of Varying Glucose and GlutamineConcentrationA series of batch experiments was carried out in shakeflasks to determine the effect of different initial glucose

and glutamine concentrations on cell growth and metabo-lism. Shake flask growth and nutrient concentration curves(data not shown) were essentially the same as those ob-tained in a 1-L reactor; however, the shake flask glucoseconsumption ceased earlier.

The viable cell concentration curves and metabolite pro-files are shown in Figure 3 for different glucose and glu-tamine concentrations. There was a significant increase inmaximal cell concentration when the glucose concentrationwas increased from 5mM to 13mM [Fig. 3(a)]. A furtherincrease to 21mM glucose extended the duration of the sta-tionary phase, but did not significantly increase the maximalcell concentration. Increasing the glutamine concentrationfrom 3.0 to 7.6mM at 21mM glucose also resulted in an

30

25C0N 20C

rn15

M 105

950 BIOTECHNOLOG Y AN D BIOENGINEERING, VOL. 32, OCTOBER 1988



/\\

5 rnM

0

4.5 1- A4 0 I

1 2 3 4 5 6TIME (days)(a)

0 Glutamme-0 Glucose

25 21 mMc 20NC 1 5mM 10

5

00 1 2 3 4 5 6

TIME days)(c)

6.0CE

O LG sI 5.0mL

L L 5.5

4.5

0 1 2 3 4 5 6 7 8TIME days)

(b)

0N \

\

0 1 2 3 4 5 6 7 8 9TIME days)

( 4

9

876543210

Figure 3. Effect of glucose and glutamine concentrations on hybridoma growth and metabolism in shake flask culture: (a) viable cell concentra-tion vs. culture time as a function of initial glucose concentration in medium containing 5.0mM glutamine; (b) viable cell concentration v s. culturetime as a function of initial glutamine concentration in medium containing 21mM glucose; (c) glucose and glutamine concentration profiles as afunction of initial glucose concentration in medium containing 5.0mM glutamine ; (d) glucose and glutamine conc entration pro files ah a function ofinitial glutamine concentration in medium containing 21mM glucose.

extended stationary phase without a significant increase inmaximal cell concentration [Fig. 3(b)]. For both nutrientsthe growth curves for different concentrations initially fallon the same line. This suggests that the specific growthrate is not sensitive to differences in nutrient concentra-tion within the range ev aluated . Low a nd Harbour3' ob-ta ined s imi lar resu l ts fo r the ef fec t o f g lucose on themax imu m ce l l co n cen t r a t io n an d g r o wth r a t e f o r twohybridoma cell lines.By varying the glucose concentration [Fig . 3(c)] it is seenthat either glucose or glutamine may limit cell growth. At5mM glucose the cells are limited by glucose and -1mMglutamine remained at the end of the batch; for 13mM glu-cose the glucose and glutamine were exhausted at the same

time; and for 21mM glucose the glutamine was exhaustedwith -5mM residual gluco se. Th e overlapping glutamineconcentration profiles indicate that the specific glutamineconsumption rate does not depend on the glucose concen-tration within the range tested. Constant initial glutamineconsumpt ion ra tes have a lso been observed for humandiploid fibroblasts grown in 0.03 mM to 5. 5m M glucose.'*Similar results were obtained by varying the glutamineconcentration [Fig. 3(d)]. All of the experiments were lim-ited by glutamine, but more glucose was consumed athigher initial glutamine concentrations. The overlappingglucose concentration profiles indicate that the glucosemetabolic quotient is independent of glutamine concentra-tion in this range. The glucose metabolic quotient is also

MILLER, BLANCH, AND WILKE: KINETIC ANALYSIS OF HYBRIDOMA 951



independent of glucose concentration in the range tested(data not shown), which agrees with the results of Lowand Harbour.31 However, the glutamine metabolic quotientis higher at higher glutamine concentrations (Fig. 4). Thedifference is much more than can be accounted for by in-creased glutamine degradation (0.03mMlday at 37C foran initial concentration of 5 m M in complete medium).This indicates that glutamine is used less efficiently athigher concentrations, which agrees with data obtained byButler and Spie? for BHK cells.Antibody production is summarized in Table I. The anti-body concentration increased with increasing glucose orglutamine concentration, as expected. This increase wasdue to an increase in the available cell days for antibodysynthesis, rather than an increase in the specific antibodyproduction rate. The cumulative specific production ratefor all of these experiments is about the same as that ob-tained in 1-L batch cultures [Fig. 2(c)]. The decrease inglutamine utilization efficiency mentioned above can beobserved in the decreasing yield of antibody from glu-tamine, as the glutamine concentration is increased.

Fed-Batch Addi tion o f Glucose and GlutamineA similar extension of the stationary phase is shown inFigure 5(a) for an experiment with incremental nutrient ad-

di t ion ( fed-batch) . Glutamine and glucose were addeddaily to a shake flask in amounts based on the viable cellcount and the nutrient consumption rates observed in theexperiments described above. The actual and potential (theamount that would be present if none had been consumed)glutamine and glucose concentrations for the fed-batchflask are shown in Figures 5(b) and 5(c), respectively.Glucose consumption and lactate production [Fig. 5(d)]ceased near the maximum in the viable cell curve for boththe fed-batch and control flasks, even though the fed-batchviable cell count did not decline for several days. The final

6 Ti

IE9/d

i 3

c 2

1

0I 4.9 rnM ---+ \

I1 2 3 4 5 6

TIME days)Figure 4. Effect of initial glutamine concentration on the glutaminemetabolic quotient (mmol glu tamine /109 viable cells/day) in shake flaskhybridoma culture.

values of glucose consumed and lactate produced were es-sentially the same for the two flasks, even though the fed-batch glucose concentration eventually reached 41mM.However, the fed-batch glutamine consumption was abouttwice as high as that of the control; and significant glu-tamine consumption continued until the viable cell concen-tration declined to a low value. The decrease in cell countat high residual glucose and glutamine concentrations maybe due to depletion of other nutrients, toxin buildup, or theincrease (estimated at 50 mOsm) in osmolality due to theadded nutrients. Th e antibody data (Table I) are consis-tent with the results described above. More antibody wasproduced in the fed-batch flask, but the cumulative pro-duction rates in the two flasks were equal and were aboutthe same as those for the other exper iments shown inTable I . The yield of antibody from glutamine was alsolower in the fed-batch flask with its higher level of glu-

Table I. Effect of glucose and glutamine concentrations on antibody production in shake flasks.Initial concentration

(mM ) Z(ce1l A t ) X Antibody 9 ( X Y ,gln'5.0

13212121212Id21

5.05.05.03.04.91.65.410.0

1.64.45 . 53.65 .16. I4.61.3

32128377

100121100160

2016152120202222

---2620161916

a Cumulative cell-days available for antibody production, calculated as the area under the viablecell-vs.-time curve.

Average metabolic quotients, as the antibody concentration divided by Z(cel1 A t ) .Fed-batch study control flask.Fed-batch flask.Equivalent concentration of glutamine consumed.

'Apparent yield coefficient of antibody from glutamine.

952 BIOTECHNOLOG Y AN D BIOENGINEERING, VOL. 32,OCTOBER 1988



6.5 4 -.2o T.0

c lEL L 5.5

5.0rn

0 1 2 3 4 5 6 7 8 9 1 0TIME (days)a)

50

0 30S20 .c--E 4 1o

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Ac t ua l

0 1 I I ; : : I I :0 1 2 4 5 6 7 8 9 10TIME days)

(C)

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Actual

15

0 1 I ; I : I I I 10 1 2 4 5 6 7 8 9 10

TIME days)(b)

30

GLC0SE

10m 5M

00 1 2 3 4 5 6 7 8 9 10

TIME days)(d)

LATATE

2o c

10,mM

0

Figure 5. Fed-batch addition of glucose and glutamine in hybridoma shake flask culture: (a) viable cell concentration vs. culture time;(b) potential and actual glutamine concentration vs. culture time in the fed-batch flask; (c) potential and actual glucose concentration vs. culturetime in the fed-batch flask; (d) cumulative concentration of glucose consumed and lactate produced vs. culture time.

tamine consumption. Reuveny et.al. l3 also found that dailyaddition of glucose and glutamine extended the time athigh viable cell concentration and increased the final anti-body con centration.For the shake flask experiments described above (Figs. 3-5) glucose consumption decreased at the maximum viablecell concentration, while glutam ine consumption continuedduring the stationary and decline phases. This suggests thatglucose consumption is required for rapid growth and thatglutamine is preferentially used for cell maintenance andproduct formation. This is consistent with the results ofZielke et .a1.3J who found that hu man diploid fibroblastscould grow without glucose in medium containing glu-tamine and supplemented with purine and pyrimidine nu-c le osid es. W ic e a nd c o - ~ o r k e r s ~ ~btained similar results

for many different cell types. The glycolytic products lac-tate and pyruvate produced from glutamine metabolism, orserum-derived ketone bodies and fatty acids, could providethe acetyl CoA needed for glutamine oxidation in the TCAcycle.6 The glucose requirement durin g active growth maythen be attributed to production of the five-carbon sugarsrequired for nucleotide synthesis.24

Glucose consumption may also be limited by lactatebuildup and the resulting low pH. The primary effect ap-pears to be the lowe r pH (see below) because an increase inlactate concentration from 24mM to 43mM did not inhibitcell growth or glucose metabolism in continuous culture(unpublished results). This is consistent with the greaterglucose consumption and lactate production in a 1-L reac-tor with pH control (Fig. 2). The higher glucose consump-




t ion at higher glutamine concentrations [Fig. 3(d)] maythen be attributed to the increased ammonia production. at 0 = 0 .4 1 day-' occurred after the pH was decreased from7. 6 to 7.1. It can be seen from Figure 6(a) that the viablecell concentration is relatively insensitive to dilution rate atCont inuous Cu l tu reCell and Metabolite Concentrations

The 1-L reactor was inoculated with -670 mL of com-plete medium containing - 2 x 104cells/mL. The viablecell concentration and cell viability curves are sh own in Fig-ure 6(a). When the viable cell concentration reached 7.4 Xlo5 cells/mL after 3 days of batch growth, the feed wasstarted at a dilution rate of 0.30 day -' and the reactor vol-ume was maintained at 600 mL. The dilution rate was laterincreased to 0.41 day-' to increase cell viability. The risein cell concentration and spike in viability (time -9 days)

lower dilution rates, whereas the percent viability is verysensitive. The opposite is true at higher dilution rates. It isapparent that the cell count and viability often overshootthe new steady-state values following a change in dilutionrate. A similar oscillatory approach to steady state was ob-served for mou se L S cells by Griffiths and Pirt.37 Theovershoot can be more clearly observed in the glucose con-centration [Fig. 6 b)]. When the dilution rate was changedfrom 0.41 to 0.62 day-', several days were required forthe cells to adjust to the higher nutrient levels present inthe reactor. Subsequent increases in dilution rate resultedin shorter lags. This is probably due to a combination ofthe smaller relative changes in dilution rate and the fact

7.0

6.50

6.0C

5.5LL

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4.5

4.00 10 2 0 3 0 4 0 5 0

TIME days)(a)

100959 0

Ye8 5 V8 0 I

A7 5 BL7 0 E656055

0 10 2 0 30 4 0 5 0

(b)Figure 6. Continuous hybridoma culture with pH and dissolved oxygen control at differentdilution rates (day- ): (a) viable cell concentration (squares) and percent viability (circles) vs.culture time; (b) residual glucose concentration vs. culture time.

TIME days)

954 BIOTECHNOLOG Y AND BIOENGINEERING, VOL. 32, OCTOBER 1988



4 . 0c 3.50CE 2.5NT 2.0RA 1.5TI 1.00

N 3.0

0.50.0

1.61.41.2

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3530252 0

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0.4 0.6 0.8 .o 1.2 1.4DILUTION RATE (l/day)

(a)

/,/ I,/,

I 1 1 I 0.21.4

/,0.0

0.0 0.2 0.4 0 6 0 8 .o 1.2DILUTION RATE (llday)

(b)Figure 7. Effect of dilution rate in continu ous hybridoma culture: (a) steady-state cell l o6vi-able cells/mL, solid squares; lo6 total cells/mL, open squares) and metabolite (mM glucose,solid circles; mM lactate, open circles; mM glutamine, solid triangles; mM ammonia, open tri-angles) concentrations vs. dilution rate; (b) steady-state specific growth rate (squares) and frac-tion viable cells (circles) vs. dilution rate.

that the higher viability and growth rate allowed the cellsto adjust more quickly to the new conditions. An oscilla-tory response was also observed when the dilution rate wasreduced from 1.33 to 0.31 day-'. Part of the oscillation inglucose concentration may be due to the lower apparentyield of lactate from glucose (Y lac ,glc) t lower glucose con-centrations. A delayed increase in Y lac,glc would allow theglucose concentration to increase temporarily before de-creasing again to the steady- state value.The steady-state metabolite and cell concentrations areshown in Figure 7(a) as a function of dilution rate. The to-tal cell concentration decreases monotonically as the dilu-tion rate is increased, unlike the constant cell mass foundwith microbial systems. Part of this difference may be ex-plained by the observation** that s pecif ic cell mass in-

creases with increasing D . The viable cell curve has amaximum at D = 0.6 day- ' . The decrease in viable cellconcentration at lower dilution rates can be attributed tothe dramatic decrease in viability at these dilution rates dueto low nutrient and/o r high toxin conc entratio ns. The effectof dilution rate on viability is shown in Figure 7(b); viabil-ity decreases markedly below a dilution rate of -0.8 day-'.The low viability at low dilution rates means that the ac-tual specific growth rate is significantly higher than the di-lution rate, as can be seen from the equations presentedabove. Th e results shown in Figure 7(b) suggest that a min-imum growth rate is required to maintain cell viability, asproposed by Tovey and Brouty-Boyt.22 Boraston et.al. 9 ob-served a maximum in viable cell concentration for oxygen-limited continuous culture (with pH control) of mouse



http:///reader/full/a-kinetic-analysis-of-hybridoma-growth-and-metabolism-in-batch-an

N B l hybridoma cells. The viability as a function of dilu-tion rate from their study corresponds to the results of thepresent work [Fig. 7(b)], but this may not be universal forall cell Ma xima are also present [Fig. 7(a)] forthe lactate and amm onia co ncentratio ns. Sinclair21 ob-served a near-linear decline in cell concentration with in-creasing D and a maximum in lactate concentration insemicontinuous culture (without pH and DO control) ofmouse LS cells . In contrast with the present work, themaximum lactate concentration occurred at the maximumtotal cell concentration. Con tinuo us culture of mouse leu-kemia L1210 cells (without pH and DO control) by Toveyand Brouty-Boye22 showed a near-linear decline in cellconcentration with increasing D.The glucose and glutamine curves [Fig. 7(a)] show anincrease in residual concentration with increasing dilutionrate. Low concentrations of lactate and amm onia are presentat high dilution rates because less glucose and glutaminehave been consumed. The maxima in the lactate and am-monia concentrations occur because the lower Ylac, lc andYamm,glnTable 11) at lower dilution rates more than com-pensate for the increased level of nutrient consumption.Ylac,glc can be greater than two because some glutamine ismetabolized to lactate, but the great majority of lactate isderived from glycolysis .23,32 inclair observed a moredramatic increase in Ylac,glc rom essentially zero at low Dto 1 .32 near D,,,.Nutr ien t and Oxygen Metabo l i c Quot ien ts

The specific glucose and glutamine consumption ratesare shown as a function of the specific growth rate in Fig-ure 8. The results for glutamine fit the maintenance energymodel (eq. 8) reasonably well with mgln= 0 and Yn,gln6.3 X 10 cel ls /mmol glutamine. The specif ic g lucoseconsumption rate is not linear in growth rate and the formis similar to that observed by Sinclair.21There are several

rnn

g lg E1 9c e0 1S Ie l

daY

u c

9.08.07.06.05.04.03.02.01 .o0.0

Table 11.cients in continuous hybridoma culture.

Effect of dilution rate on steady state byproduct yield coeffi-

Dilution rate yh , lc Y L m . ln(day-) (mol/mol) (rnol/mol)0.31 1.60 0.420.41 1.60 0.510.62 1.72 0.490.78 1.70 0.561.02 1.94 0.471.33 2.12 0.66

possible explanations for the deviation from linearity. Thefirst is that Yl,c,plc (and q,ac) s lower at lower dilution rates.Equation (8) can be rewritten to account for glucose metab-olism to lactate:

(10)The glucose metabolic quotient will be lower at lower dilu-tion rates because less lactate is producted. The lactate termcannot be simply subtracted to give a corrected qglucosebecause lactate production generates energy via glycolysis.

The lower Ylac, lc at lower glucose concentration reflectsa change in the metabolic pathway, resulting in an increasein the efficiency of glucose utilization. It has been ob-served24 hat cells grown at 40pM glucose use only 7% asmuch glucose as those grown on 5mM glucose and pro-duce very little lactate. Studies with Chinese hamster fi-b r o b l a s t ~ ~ *uggest that little glucose enters the TCA cycleeven at low glucose concentrations. As mentioned above,the limiting requirement for glucose is to provide nucleo-tide precursors via the pentose phosphate pathway. It hasalso been that glucose and glutamine inhibiteach others oxidation via the TCA cycle. Thus, the higherefficiency at low dilution rate (with lower glucose and glu-tamine concentrations) may also reflect a reduction inthese inhibitory effects. Glucose and glutamine are par-

q g l c = ~ / Y n , g l c+ mglc + 41ac/Y1ac,glc

3.0

2.5

2.0

1.5

1 o0.5

0.00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

P l/day)Figure 8.specific growth rate in continuous hybridoma culture.

Glucose (squares) and glutamine (circles) metabolic quotients as a function of

956 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 32, OCTOBER 1988



0.90.8

c 0.7AL 0.6

0.50.4

a

--- prnax = 1.5ldayKlac = 140 rnM- - Kglc = .15 mM

Kgln = .15 m M-- Karnm = 20 m M----

A Constitutive Expression for the Specific GrowthRateThe steady-state values for p and the nutrient concentra-

tions can be used to develop a model for p As a first ap-proximation, the Monod model can be expanded to accountfor two limiting nutrients and the inhibitory by-products:

A value of 1 .5 da y-' was obtained for pmaxsing batch andcontinuous culture data. Limits can be obtained for all ofthe K s by using the data at the highest dilution rate em-ployed in the present study, and assuming that the differ-ence between p m a xnd p (1.34 day-') at that dilution rateis due solely to each of the metabolites in turn. This givesupper limits of 2.0mM for K, and 0 .44mM for K,, ndlower limits of 103mM for KL nd 12mM for KA. ddi-tional upper limit estimates can be obtained for K, and KNSince p was essentially constant for batch cultures withinitial glucose concentrations of 5mM, 13mM, and 21mM,K , < 5mM glucose. Assuming that a 10% change in pcan be detected, we obtain an upper limit of 0.5mM forK,. In a similar manner we can obtain an upper limit of0.3mM for KN. hese values are in agreement with the Kvalues determined for glucose (ca. 0.4mM glucose) andglutamine metabolism (0.3-0.4m M glutamine) for humandiploid fibroblast^.^^A comparison of experimental and calculated values forp/pmaXs shown in Figure 9 , along with the values of theparamenters used. A reasonable fit was obtained for thesimple model, which suggests that the parameter estimatesare reasonable. One limitation to obtaining a better fit isthat the four metabolite concentrations do not change inde-pendent ly as the di lu t ion rate is changed; lactate is aproduct of glucose metabolism and ammonia is a productof glutamine metabolism. The deviation from the model is

/. /'/,//'

/2

0.00.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

EXPERIMENTALFigure 9.the experimental values obtained in continuous hybridoma culture.Comparison of p/pmar)alues calculated from a modified Monod model with




1 4 0 T

1 3A 1 2N;; 1 - -;d 1 0B cY aY 9

A 1 0 0 t ~N IT P1 9B /o mD LY

- -- -

- ---

1 51 4

CI 1 39

0 . 2 0 . 4 0.6 0.8 1.0 1 . 2 1 . 4D ( l / d a y )

(a)1 5 r

l 4

0.5 0.6 0.7 0.8 0.9 1 . 0 1 . 1 1 . 2 1 . 3 1.4F ( l / d a y )

0 . 2 0 . 4 0.6 0.8 1.0 1 . 2 1 . 4D ( l / d a y )

(C)Figure 10. Antibody production in continuo us hybridoma cu lture: (a) measured (solid circles, pH 7.1; solid squares, 1 month later at pH 7.2and 7.4) and corrected (open circles, see text) steady-state antibody concentration vs. dilution rate; (b) specific antibody production rate (perviable cell) vs. specific growth rate; (c) apparent specific antibody production rate (per total cell) vs. dilution rate.

not random. The curvature in the data is s imilar to thatshown for the glucose metabolic quotient in Figure 8. Thissuggests that cell growth which involves changes in themetabolic pathways can not be adequately modelled interms of a single limiting step.

periment. A smoo th curve was drawn through the points forD = 1.0 2, 1.3 3 and 0.31 day-' where the cells' antibodyproduction had reached a stable level. Corrected antibodyconcentrations for D = 0.41, 0.62, and 0.78 day- ' weretaken from this curve, as shown by the dotted lines inFigure 10(a) . Th e ant ibody concentrat ions measured a

An t i b o d y Pro duct ion month later at a D value of - 0 . 5 2 day- ' [ squares inFig. lO(a)] also fall on the corrected antibody curve.As shown in Figure 10(a), the antibody concentrationdecreases with increasing dilution rate. Antibody produc-tion by cell line AB2-143.2 decreases dramatically duringthe first month (after thawing) of shake flask propagation,followed by a gradual decline after that time (results notshown). It was therefore necessary to correct the antibodyconcentrations obtained early in the continuous culture ex-

The relationship between the antibody metabolic quotientand the specific growt h rate p ) how n in Figure 10(b) doesnot fit the general model for product formation [eq. (9)].The specific antibody production rate initially decreasesrapidly as p increases and then approaches a constant valueat higher p This is consistent w ith the higher specific anti-body production rates observed in perfusion culture (with958 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 32, OCTOBER 1988



low p , as compared to those observed in continuous orsemicontinuous culture. 4 l6 Birch et.al.Ix also found thatantibody production was not growth-associated in continu-ous culture. They found qAb o increase or decrease slightlywith increasing p , depending on whether glutamine, glu-cose, or oxygen was the limiting nutrient. One contribut-ing factor for q A bdecreasing with increasing p is that cellscease to produce many proteins during mitosis (cells withsmaller p spend proportionally less time in mitosis than docells with higher p .This is supported by the recent findingthat clones derived from non-producing cells are able toproduce antibodie~.~ second factor is that cells increaseproduction of some proteins when subjected to stress (e.g.,heat shock4); hybridomas may increase antibody produc-tion under adverse conditions present at low dilution rates.An alternate explanation is glucose (catabolite) repressionof product formation (as seen in penicillin prod~ction~~),but this is not supported by the results of the pH study de-scribed below. The antibody metabolic quotient shown inFigure 10(b) is the rate per viable cell. For microbial sys-tems the rate per unit of total cell mass is generally plottedas a function of the apparent specific growth rate (i.e., thedilution rate). Such a plot of the apparent antibody metab-olic quotient vs dilution rate [Fig. lO(c)] is more typical ofsecondary metabolites, but qk,, still decreases with increas-ing dilution rate. There is no evidence of any inhibition ofantibody production due to higher antibody concentration.This is in agreement with the results of Fazekas de St.Groth; the antibody metabolic quotient was essentiallyconstant at cell concentrations between lo5 and lo6 cells/m Lover a narrow range of dilution rates (0.96-0.8 9-). How-ever, there is some evidence of feedback inhibition for hy-br idomas that produce less than 1 pg/mL ant ibody i nb a t c h ~ u l t u r e . ~ Effect of pH in Cont inuous Cul tureCell and Metabolite Concentrations

The effect of pH was evaluated at a dilution rate of0 .52 20.3 day-. The viable cell concentration and viabil-ity are shown in Figure ll(a); and the steady-state valuesare shown in Figure ll(b) as a function of pH. The viabil-ity and viable count at pH 7.2 are essentially the same asthe interpolated values from Figure 7(a) for pH 7.1 at acorresponding dilution rate. The values at pH 7.4 are alsosimilar to those at pH 7.2. The viable count and viabilitydecreased when the pH was increased to 7.7 [Fig. ll(a)],but later recovered to values similar to those seen for pH 7.2and 7.4 [Fig. (ll)]. The cell count and viability also de-creased at pH 6.8 [Fig. ll(a)], but there was no indicationof recovery. The values for viable count and viability forpH 6 .8 in Figure ll (b ) are the lowest values obtained andare not steady-state values. The broad optimum plateau forcell concentration shown in Figure ll (b ) is typical of cellsin culture. although the optimum pH range varies with thespecies and cell line tested.%

The response of the specific growth rate to a change inpH can be obtained from a plot of the log total cell concen-tration versus time. This is illustrated in Figure 12(a) forthe pH change from 7.6 to 7.1. The linear sections of thecurve indicate a constant value for paPpsee eq. (2)l. Forthe pH change shown in Figure 12(a), pdPpapidly in-creased from a steady-state value of 0.41 day- to a con-stant value of 0.58 day- and then returned to 0.41 day-[Fig. 12(b)]. This suggests that the cells rapidly attain ahigher growth rate in response to a favorable change in pHand then maintain that higher growth rate until they haveadapted to the new conditions, at which time they return tothe original growth rate. However, since the viability ischanging during the increase in total cell count, the truespecific growth rate is not constant during this time [seeeq. (3)]. As shown in Figure 12(b), p rapidly increased af-ter the pH change and then gradually decreased in responseto changing metabolite levels during the increase in totalcell concentration. There was more variation in p than inpappuring the approach to the final steady state. Constantvalues of paPpere also obtained for the decline and recov-ery at pH 7.7 (0.40 and 0.74 da y-, respectively), the de-cline at pH 6.8 (0.24 day-) and the recovery due to thechange from pH 6 .8 to 7. 2 (0.98 day-). A significant over-shoot in total cell count was observed for the latter case.The s teady-s tate metabol i te prof i les shown in Fig-ure 13(a) paralle l those for the cell count and viability[Fig. 1 (b)]. Metabolite concentrations reported for thetwo steady states at pH 7.2 were different, depending onthe previous steady-state pH value. The glucose concentra-tion began to increase as soon as the pH dropped below7.0 [Fig. 13(b)], indicating a lower specific glucose con-sumption rate at the lower pH. The high residual glucoseand glutamine concentrations at pH 6.8 (Fig. 13) are re-sponsible for the overshoo t of viable cell concentration andviability after the increase to pH 7.2 [Fig. Il(a)].Glucose, Glutamine and Oxygen MetabolicQuotients

The steady-state glucose and glutamine specific con-sumption rates are shown as a function of pH in Fig-ure 14(a). Changes in the specific glucose consumptionrate generally occurred more rapidly than those in cell con-centration (results not shown). The responses at pH 7.7were similar for glucose and glutamine. The specific con-sumption rates were 50-100% higher than those at pH 7.2during the initial period of low cell count at pH 7 .7; butthen decreased to 10-25% abov e those at pH 7 .2 followingrecovery. The specif ic g lutamine consumption rate atpH 6.8 was much higher than at pH 7.2. In contrast, thespecific glucose consumption rate was only -85 of thevalue at pH 7.2, even though the glucose concentrationwas much higher at pH 6.8 (Fig. 13). Lactate is the majorproduct from glucose metabolism and the lower glucoseconsumption rate at pH 6.8 is probably related to intracel-lular pH control. This is consistent with the trend in Yl,,,glc




7.06.8

0G 6.66.4E

LL 6.2S1 6.0rn

5.8

5.6 -

3.0 T

- - 1 0 0I II II , * -- 9 0I * 0 .--

6. I0 * ~ , f :.. . ~ ** -- 8 0 %d I * I ** 0.1 I- -

-- 7 0*a* 1 8 8188 0 Fr8 8 8 1 ~ 8 I 8 8 I8 I * 8 8

8 60 AI8 8 8 8I 8 8 88 I

I

8 8r 8* I 88 L88r 88 81- -

:.m8m818d m8 8 .I. B

L< l E

-I -- 508 I

8 8 1 III I I

~ 8II 1 m -- 30I

1 I , I I 2 0

. -- 40--8-

pH 7.4 7.7 ~ 7.2 ~ 6.8 7.2

Fraction viable T O FR

E 2 56T

E 0L NLs 1.5I /

Viable cells 0.6 I

1 --\ 0.4 I

A0.2 0LE

0.0PH

mL 1.0

0.56.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7 6 7.7

(b)Figure 11. Effect of pH on c ell concentration and viability in continuous hybridoma culture atD = 0.52 day-: (a) viable cell concentration (s quares) and percent viability (circles) vs. cul-ture time; (b) steady-state viable cell concentration and fraction viable vs. pH. Values for pH7.1 were interpolated from Figure 7 at D = 0.52 day-. Dashed arrows show the changes afteradaptation at pH 7 .7 .

shown in Figure 14(b). At low pH lactate production isminimized by lowering the fraction of glucose metabolizedto lactate and by reducing the amount of glucose that isconsumed. Barton4 obse rved a sim ilar trend of decreasingspecific glucose consumption rate and Ylac,gc with decreas-ing pH for HeLa cells in batch culture. Birch and Ed-w a r d ~ ~ ~lso found that Y,,,g,c was lower at low pH forbatch suspension culture of a lymphoblastoid cell line. Therecovery in cell concentration at pH 7.7 [Fig. l l(a )] corre-sponded to an increase in Y,ac,glc rom 1.52 to 1.78, whichmay have resulted in lower intracellular pH.Ammonia is a mjor by-product of glutamine metabo-lism. The effect of pH on Yamm,g,n s complementary to thaton Y,,c,g,c[Fig. 14(b)]. The higher specific glutamine con-

sumption rate at pH 6 . 8 is probably due to a number offactors. Energy from glutamine may be required to com-pensate for the lower level of glucose consumption. Thegreater g lutamine consumption is a lso cons is tent withhigher maintenance energy requirements for the cells underadverse conditions. However, the higher Yamm, and partof the increase in qg,utam,neay be due to additional enzy-matic hydrolysis of glutamine (to glutamate and ammonia)to increase the intracellular pH, or to a higher rate of un-catalyzed glutamine hydrolysis at the lower pH.

The deviations in the byproduct yield coefficients be-tween the two steady states at pH 7.2 [Fig. 14(b)], alongwith the pH trends, suggest that the yield coefficients (andpossibly the consumption rates) at a given pH depend on

960 BIOTECHNOLO GY AND BIOENGINEERING, VOL. 32, OCTOBER 1988



6.5 T0

6.4 tR

,/L I pH 7.6

6.3G L

L I

pH 7.1I;* /

6 8 10 1 2 1 4 1 6 1 8TIME days)(a)

O 9 T

H I pH 7.6 pH 7.10.3 I I 1

6 8 1 0 12 1 4 1 6 1 8TIME days)(b)

Figure 12. Effect of a pH decrease from 7.6 to 7.1 on cell growth in continuous hybri-doma culture at D = 0.41 day-: (a) total cell concentration vs. culture time; b) specificgrowth rate and apparent specific growth rate vs. culture time.

the pH history. A chronological summary of the yield co-efficients and specific consumption rates for each steadystate pH is given in Table 111. An increase in pH from 6.8to 7.2 results in a higher Yl,~glc and a higher specific glu-cose consumption rate than are obtained for a decrease inpH from 7.7 to 7.2. Similarly, Yamm,g,n t pH 7.2 is lowerafter an increase in pH than it is after a decrease in pH.Thus, an increase in pH gives a response similar to that ata higher pH and a dec rease in pH gives a response similar tothat at a lower pH. The different metabolic quotients andyield coefficients at the two pH 7.2 steady states account

well over the critical value of 2mM described by Frame andH u . ~ ~decrease in qo2 and a corresponding increase inqglucoceave been observed, however, when the glucose con-centration is increased at pH 7.2. The increase in qglucoaeat pH 7.2 is in contrast to the lower value observed at pH 6.8[Fig. 14(a)]. This suggests that a decrease in qo2 is linkedto an increase in qglucose.t pH 6.8 the production of lactateis inhibited, and the cells are not able to shift metabolicpathways to increase glucose consumption in response tothe higher glucose concentration.

for the different metabolite concentrations [Fig. 13(a)]. n ibody ProductionThe effect of pH on the oxygen consumption rate de-pends on the cell type.4y The oxygen metabolic quotientdetermined in the present work was essentially constantwith p H, a s shown in Figure 15. There was no decrease inqo2at pH 6.8, even though the glucose concentration rose

As shown in Figure 16, the antibody concentration didnot vary signifcantly with pH. The specific antibody pro-duction rate, however, was about three times as high atpH 6.8 as at pH 7.1-7.4. A large part of this increase may

MILLER, BLANCH, AND W ILKE: KINETIC ANALYSIS OF HYBRID OMA 96



40C0NC 30ENT

TI0N 1 0mM

0

2 0

1 5LUCO 10SEmM 5

0

6 06 8 6 9 7 0 7 1 7 2 7.3 7.4 7.5 7 6 7.7PH

(a)

50 5 5 6 0 6 5 70 75 8 0 85 9 0TIME days)

(b)Figure 13. Effect of pH on metabolite concentration in continuous hybridoma culture:(a) steady-state glucose (solid squares), lactate (open squares) , glutamine (solid circles) andammonia (open circles) concentrations vs. pH. Values for pH 7.1 were interpolated fromFigure 7(a) at D = 0.52 ay-'. Dashed arrows show the changes after adaptation at pH 7.7;(b) residual glucose concentration vs. culture time.

be attributed to the lower specific growth rate at pH 6.8(0.45 d a y - ] v s . - 0 .65 day - ' ) . The h ighe r an t i bodymetabolic quotient at pH 6.8 supports the suggestion m adeabove that antibody production is higher during periods ofstress. The behavior at pH 7.7 also supports this: the specificantibody productivity was high during the initial period atpH 7.7, and then dropped dow n to a value similar to thoseat pH 7.1-7.4 when the cells adapted to the higher pH.

CONCLUSIONSBatch experiments are useful for providing preliminaryinformation on metabolic rates and nutrient requirements;

but, because conditions are constantly changing, they canp rov ide mi s l ead ing i n fo rma t ion o n t he e f fec t o f t he

Table 111. Chronological summary of steady-state metabolic quotientsand apparent yield coefficients as a function of pH in continuous hybri-doma culture.

Y L , g l c qzlc Y:mm,gl 491pH (mol/mol) (mm01/109 cell/day) (mol/mol) (mmol/109 ell/day)7.4 1.50 4.50 0.46 0.977.Tb 1.52 8.34 0.46 1.567.7 1.78 5.16 0.45 1.096.8d 1.28 3.02 0.60 1.867.2 1.66 4.47 0.34 1.037.2 1.42 4.18 0.45 .oo

a The pH changed in sequence from the top of the table to the bottom.Minimum in cell concentration and viability at pH 7.7.After adaptation by the cells to pH 7.7.Steady state was not obtained at pH 6.8; the values shown were ob-tained at the lowest cell concentration and viability.

962 BIOTECHNOLO GY A ND BIOENGINEERING, VOL. 32,OCTOBER 1988



I I I3 0.06.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7

PH(a)

2.0 T T l.of actate from glucoseI1.5: I

-_ r - t 0 5- ~- -~Ammonia f rom glutamine

0.5 I I I I I 1 0.3PH

6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7

(b)Figure 14 Effect of pH on hybridoma metabolism in continuou s culture; dashed arrowsshow the changes after adaptation at pH 7.7: (a)steady-state glucose and glutamine m etab-olic quotients (mmol/109 viable cells/day) vs. pH; (b)steady -state apparent yield coeffi-cients for lactate from glucose and ammonia from glutamine as a function of pH.

specif ic growth rate on metabolic quotients. Continuousculture at different dilution rates provides steady state datatha t can be used to p rov ide accura te es t imates o f themetabolic quotients.

Some of the specific conclusions drawn from the experi-ments described above are:1. Glucose and glutamine are both required for cellgrowth.2. The specific growth rate, the glucose metabolic quo-

tient and the cumulative specific antibody production rateare independent of glucose and glutamine concentrationover the range normally employed in cell culture media.The glutamine metabolic quotient is independent of glu-cose concentration, but is higher for higher glutamineconcentration.

3 . The maximum viable cell concentration occurs at anintermediate dilution rate because the viability drops offdramatically at low dilution rates. Maxima were also ob-tained for the lactate and ammonia concentrations.

4 . Antibody formation is not growth-associated. Theantibody metabolic quotient is higher during periods ofstress, such as at low specific growth rate and at low orhigh pH. This suggests that a cell recycle or suspension-perfusion system, which would support a large concentra-tion of cells under adverse conditions, may be optimal formonoclonal antibody production.

5 . There is an optimal plateau for cell growth and vi-ability between pH 7.1 and 7.4. At pH 6.8, the cell countand viability declined dramatically and the residual nutri-ent concentrations increased. At pH 7.7, the cells initiallydeclined, but were able to adapt and subsequently showed

MILLER, BLANCH, A ND W ILKE: KINETIC ANALYSIS OF HYBRIDOMA 963



m 0.50I 0.4

0.30 9

i IpH7.4 1 7.7 I 7.2 I 6.8 7.25 0 55 6 0 6 5 7 0 75 8 0 85 90

0.0 1

TIME days)Figure 15.ture. Oxygen metabolic quotient (mmol oxygen/1 09 viable cells/h) vs. culture time.Effect of pH on the specific oxygen uptake rate in continuous hybridoma cul-

A I

Y

l o----

2 0 e

\ daY

0 , 1 56.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7

PHFigure 16. Steady state antibody concentration (squares) and specific antibody production rate(circles, pg antibody/106 viable cells/day ) as a function of pH in continuous hybridoma cul-ture. Antibody concentration at pH 7.1 was interpolated from F igure 10(a) at D = 0.52 day-'.Dashed arrows show the change after adaptation at pH 7.7.

behavior similar to that at pH 7.1-7.4. The pH history ofthe cells also affects the values of the metabolic parametersat a given pH.6 . The specific oxygen uptake rate depends on manyfactors, including the specific growth rate and pH.

7. The effect of p on the glucose metabolic quotient isnot adequately described by the maintenance energy modelbecause the amount of glucose going into each of themetabolic pathways depends on the glucose concentrationand other factors, such as the pH and glutamine concentra-tion. Deviations in specific growth rate from a modifiedMonod model may also be due to the path changes. Newmodels for p and that account for these path changes arerequired.

8 . The metabolite concentrations can not be varied in-dependently by changing dilution rate. Kinetic analysis ofmetabolite pulse and step changes are required to providefurther insight into models for ,u and q .NOMENCLATURE

Ab antibody concentration pg/mL)C concentration m M )C * liquid concentration in equilibrium with the gas in the reac-tor headspace (mM)D dilution rate = (volumetric feed rate)/(reactor volume) (day -')K apparent Michaelis or inhibition constant (mM)k d specific death rate (day-')KLa volumetric mass transfer coefficient (h-')

964 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 32,OCTOBER 1988



maintenance energy requirement (mmol/cell/day)maintenance oxygen requirement (mmol/cell/h)total cell count (cells/mL)viable cell count (cells/mL)product concentration (mM)antibody metabolic quotient (pg/cell/day)apparent antibody metabolic quotient (wg/total c ell/day)oxygen metabolic quotient (mmol/cell/h)product metabolic quotient (mmol/cell/day)substrate metabolic quotient (mm ol/cell/day)substrate concentration m M )time (days)yield of cells from substrate (cell/mmol)oxygen consumed by substrate oxidation (mol/mol)yield of product from substrate (mol/mol)apparent yield of product from substrate = % / 9 mol/mol)factor for growth-associated antibody production (&cell)growth-independent portion of antibody metabolic quotienttrue specific growth rate (day-)apparent specific growth rate (day-)maximum true specific growth rate (day-)

(Ccg/cell/day)

SubscriptsA , amm ammoniaC, glc glucoseF feed streamN , gln glutamineL , ac lactate0 2 oxygen

This research was spon sored by the Center for Biotechnology Re-search (San Francisco). The authors thank the following individu-als for their help in ob taining the experimen tal data described inthis article: Patricia Boehm e, C harles McElroy, Anita M iller, TanNguyen, Edna Sugihara, Ed Sunoo, and Bennet Wang.

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