FEMS Microbiology Reviews 14 (1994) 39-44 (~ 1994 Federation of European Microbiological Societies 0168-6445/94/$26.00 Published by Elsevier

39

FEMSRE 00375

Modeling of high cell density fed batch cultivation

L e n a A n d e r s s o n *, La r s S t r a n d b e r g ~, L e n a H~iggst ram and S v e n - O l o f E n f o r s

Dq~artment Of Biochemisto' and Biotechnolo~,~.,, Royal Institute ~j~ Technolo~', S-IO0 44 Stockhohn, Sweden

Abstract: Escherichia coli was grown in carbon- and energy source-limited fed batch cultures to study the effect of osmotic stress and different feed rates on the growth kinetics. An unstructured model based on the linear equation for substrate consumption provided an adequate description of the bacterial growth during the first phase of biomass production (20 h), except for cultures exposed to osmotic stress by the addition of 0.5 M NaCI, The addition of salt to the culture media had a large effect on the energetics, that could not simply be described in terms of an increased maintenance requirement. In the later phase of growth, an extensive decline in viability for all cultures was observed. Coincidentally, the specific sugar uptake rate approached a lower limit. It is concluded that the total obtainable biomass in a fed batch culture is strongly affected by the magnitudes of the substrate feed rate and tile ionic strength of the culture medium.

Key words: Modeling; High cell density: Fed batch: Maintenance: Viability

Introduction

Bacterial growth systems that yield high biomass concentrations are of considerable inter- est for the industrial production of recombinant proteins. Fed batch culture is the most widely used technique in this field. The advantage with this technique is the possibility to control the specific substrate consumption rate (qS) and thereby avoiding phenomena such as overflow metabolism, catabolite repression a n d / o r oxygen limitation that would lower the growth yields [1].

A series of energy source-limited fed batch cultivations of Escherichia coli were run to inves- tigate the influence of substrate feed rates and increased salt concentration in the culture media

* Corresponding author. i Present address: Kabi Pharmacia AB, BioScience Center,

S-112 87 Stockholm, Sweden.

on growth kinetics and final obtainable amount of biomass. An unstructured model based on the linear equation for substratc consumption [2] was applied and compared with the experimental data on biomass production and oxygen consumption rate.

Materials and Methods

Bacterial strain and growth medium Strain E. coli KA197, a K-12 derivate, was

maintained at - 7 0 ° C in test tubes with 20% glycerol in nutrient broth. The strain was grown in mineral salt medium as described before [3] without antibiotics. The cultivations were started as batch cultures with an initial glucose concen- tration of 20 g 1-~ for experiment 1 and 10 g 1- for experiment 2 and 3. The feed was started when glucose was almost exhausted. In experi- ment 2, 0.25 M NaC1 was also added to the

SSDI 0 1 6 ~ - 6 4 4 5 ( 9 3 ) E 0 1 0 1 - O

4(I

culturc medium and feed solution in order to induce an increased maintenance requirement. pH was controlled at 7.0 with 2 M H2SO 4 and 25% NHs. Additional MgSO 4 was added to the bioreactor intermittently.

Cultit,ation conditions Inoculum was prepared from shake flask cul-

tures grown overnight at 37°C. The experiments were carried out in a 5-1 bioreactor with an initial working volume of 3.5 1. The temperature was kept at 37°C. The dissolved oxygen tension did not fall below 20% in any cultivation.

Analyses Optical density was measured at 58{I nm. Dry

weight was determined by centrifuging 3 × 5 ml of cell suspension in preweighed tubes, washing the samples with distilled water and drying overnight at 105°C beff)re weighing. Viable count was performed on tryptic soy broth agar plates, incubated at 37°C ff)r 24 h. The dissolved oxygen tension was continuously measured with a polaro- graphic oxygen electrode. The oxygen and carbon dioxide content in the effluent gas were analysed with a paramagnet ic analyser and an IR analyser, respectively.

The carbon, nitrogen, hydrogen and oxygcn contents of the dry cells were determined with an elemental-analyser. The ash content was calcu- lated as the remaining mass fraction of the sam- pies after subtracting the above-mentioned com- ponents. The ash-free biomass content was used for analysis of the results.

Model of a fed batch culture

A simple unstructured model for a constantly fed batch culture, where the growth-Limiting sub- strate also is the energy source, can be repre- sented by the following equations

C H e O + A N H ; + BO,

-o Y,,CH fO, N,, + C H 20 + D CO, (Eq. 1)

in which the carbon containing compounds are cxpresscd in C-mol. Biomass and carbon dioxide are assumed to be the only products that are synthcsised. The total mass of biomaterial and substrate are considered in the equations as fol- lows:

d X - ~ x (Eq. 2)

dt

dS dt - F s - Rs (Eq. 3)

# X R, - + m X (Eq. 4)

Y,,

The maintenance rate is assumed to be inde- pendent of the specific growth rate, i.e. Eq. 4 is a linear equation for substrate conversion. An equation for the rate of oxygen consumption is given directly from the stoichiometry of Eq. 1 [4].

R,, ~32 T ~ - y x ~ - 7 ( E q . 5 )

According to this model, the specific growth rate # will decrease with time. A maximum amount of biomass (X ...... ) is consequently reached when /,t - 0. Under this condition, when the substrate fed into the bioreactor is immedi- ately consumed, d S / d t is negligible compared to other rates in Eq. 3. The maximum amount of biomass (g) is then obtained from Eqs. 3 and 4

x ...... - ( E q . (,I I?1

This equation has been proposed to be used to experimentally determine the value of the main- tenance coefficient, m [5,6].

Eq. 6 states that the maximum achievable total mass, X, ..... is a function of the substrate feed rate (F~) and the maintenance coefficient. The influence of these parameters on X ...... is demon- strated by the simulations of high cell density ted batch cultures in Fig. 1. According to the simula- tions, the substrate feed rate should be as high as possible to reach high cell densities. Further- more, small variations in the maintenance coefli- cient have a profound effect on the growth curve.

R e s u l t s

A series of prolonged glucose-limited fed batch cultivations of E. coli with constant feed rates, after an initial exponential batch phase, were run to investigate the effect of different substrate feed rates and osmotic stress on the growth kinet- ics. The biomass data are shown in Fig. 2. Ap- proximately the same substrate feed rate (F~) was applied in experiments 1 and 2 (11 and 12 g h ], respectively), whereas in experiment 3, F, was decreased to half the level (5.5 g glucose h- ~). In experiment 2, 0.25 M NaCI was also added to the culture medium. The results confirm the predic- tion by Eq. 6 that increased substrate feed rate raises the maximum obtainable biomass concen- tration. Considering the influence of NaC[ (ex- periment 2) on the growth kinetics, the produc- tion rate of biomass and maximum obtainable biomass concentration in the substrate-limited

4 0 0

3 0 0

2 0 0 fi

100 i

0 [

3O0

2 (} {1

~2

. . . . - - i

A m

/ ~ 0 . 0 4

/

B

!

F -12 s

0 . . . . ~ ~

0 5 0 O0 Time (h)

Fig. 1. Simulated biomass formation in a fed batch culture, Y,x=0-50 g g i initial values 1 /=3 .5 1, X = 3 4 g . (A) Effect of the maintenance coefficient, m = 0.02, 0.04 and 0.06 g g i h i at constant F, (12 g glucose h - t ) . (B) Influence of substrate feed rate on the total obtainable amount of biomass,

F, = 6, O and 12 g glucose h i at m = 0.04 g g i h i

41

5 0

5' 3 0 .E

2 0

I0

• • • ~F

• O :i!

7! :

exp 2

:~ exp 3

k J t

2 0 4 0 6 0 g

Hour s

Fig. 2. DD' weight data (g 1 i) from three glucose-limited fed batch cultivations of E. coil with difflerent F, and salt concen trations in the media (experiment I. 2 and 3, respectively). For all experiments the feed was started when the initially added glucose was almost exhausted. Hour 0 refers to the lime at which the culture became limitcd by glucose. Thc symbols represent: (o) experiment 1 with b~= II g glucose h 1: ( ~ ) experiment 2 with F, = I2 g glucose h i and 0.25 M NaC1 added to the culture medium: ( .7 )exper imen t 3 with 1'~,-5.5

g glucose h I

phase were lower compared to the reference cul- ture (experiment 1).

The accuracy of the applied model was tested by simulating the fed batch experiments. The growth patterns for experiments 1 and 3 were in agreement with the applied model in the first part of substrate-limited growth (Fig. 3). After about 20 h of limited growth, the biomass curve (dX /d t ) and oxygen consumption rate (OCR) gradually diverged from the simulated result. d X / d t abruptly decreased, the biomass quantity approached a maximum and the measured OCR became approximately constant. The model was further tested by simulating experiment 2, using initially the same parameters (m = 0.037 and Y,x = 0.50) as for the two other fed batch cultiva- tions, an increase of m with unvaried Y,x ( m = 0.047 and Y~ = 0.50) and finally a lowering Y~, (07 = 0.037 and y,~= 0.40) as shown in Fig. 4. The model showed progressively increasing devia- tions from the experimental data on biomass and OCR that could not simply be explained by change(s) in m a n d / o r y,~.

4 2

4 0 0 ~ - , ~ , , , ~ . . . . - ~ ~--~ T ~

-~2= 300 i . - - - _ - -

200 / "

]

: ]

300 - ~- ~ - - T . . . . . . . . . . . " B i . -

2 0 0 - ~ : / i I I I

f / • • ~ I I

~E 1 oo - "

i c j

F

r

r i

b I m _ i i m

f~(m I l

0 20 40 60 80 0 20 40 60 80 i00 H o u r s Hours

Fig. 3. Comparison of experimental data and simulations ot two fed hatch experiments (1 and 3). Parameters used are m = 0.037; Y,~ 0.50. Initial volume=3.5 I. (A) Observed (3} and predicted ( - - - - ) oxygen consumption rate, OCR (mmol h i) from experiment I with /7,~11 g ghicose h i. initial amount of biomass=34 g. (B) Obscwed ( • ) and predicted ( - - - - - ) biomass lkn'mation (g) from the same culture. {C) Observed { ~ ) and predicted ( - - - - - ) OCR from experiment 3. /~ 5.5 g glucose h l

initial amount o f biomass = 15 g. (I}) (_)bservcd ( • ) alld predicted ( - - - ) biomass production from experiment 3.

A n ex t ens ive loss of c o l o n y - f o r m i n g abil i ty was

o b s e r v e d in t he f inal s t age o f fed ba tch g rowth for

all cu l tu res , as can be s e e n in Fig. 5. Th i s loss o f

viabi l i ty was e n c o u n t e r e d w h e n the spec i f ic glu-

cose c o n s u m p t i o n ra te , qS a p p r o a c h e d 0.04 g g i

h ~ (Fig. 6).

Discussion

T h e subs t r a t e f e e d r a t e is a very i m p o r t a n t

p a r a m e t e r in the p r o d u c t i o n o f cel ls to a high

densi ty . H o w e v e r , a d e c l i n i n g par t of the sub-

s t r a t e is u t i l i sed for g r o w t h - a s s o c i a t e d p rocesses .

T h i s m e a n s tha t the oxygen c o n s u m p t i o n ra te will

p rog res s ive ly inc rease . T h e m a x i m u m oxygen

t r ans f e r capac i ty o f t he sys tem c o n s e q u e n t l y sets

a l imit to the level of t he subs t r a t e f e e d ra te and the f inal a m o u n t o f b iomass .

T h e a d d i t i o n o f N a C I to the cu l t u r e m e d i u m

was f o u n d to have an i m m e n s e e f fec t on the

g rowth pa t t e rn . Th is cou ld not be d e s c r i b e d by

the a p p l i e d m o d e l in t e r m s of an i n c r e a s e d ma in -

t e n a n c c or a l o w e r e d m a x i m u m yie ld coef f ic ien t .

E. colt e x p o s e d to h igh o s m o t i c p r e s s u r e has

p rev ious ly b e e n r e p o r t e d to a c c u m u l a t e o s m o r e g -

u la tory so lu tes such as K ' , t r e h a l o s e and glu-

t amic ac id w h e n g rowing in m i n i m a l m e d i a and in

excess of g lucose [7]. Ana lyse s of the b iomass did

not show any a p p e a r a n c e of t r e h a l o s e (da ta not

shown) . Thus , it a p p e a r s tha t E. colt g r o w i n g in

c a r b o n - and e n e r g y - l i m i t e d sys tems does not ex-

hibi t the s a m c p r o t e c t i v e p a t t e r n in r e s p o n s e to

o smo t i c s t ress as cu l tu re s in excess of nu t r i en t s . It

is e v i d e n t tha t the r e s p o n s e o f E. colt to o smo t i c

s t ress d u r i n g s u b s t r a t c - l i m i t e d g rowth has a se-

v e r c e f fec t on thc g rowth k ine t ics tha t n e e d s to be f u r t h e r inves t iga ted .

W h e n the f e e d o f t he g r o w t h - l i m i t i n g c a r b o n

sou rce is cons t an t , the c h a r a c t e r i s t i c f e a t u r e o f

such cu l t u r e s arc p rog re s s ive e n e r g y l imi t a t ion

and a g r adua l ly dec l in ing spec i f ic g rowth rate .

3 0 0 '.xZ

2 0 0

i O0

300 • . . . . . . . . ' ~ ~ w ' ~ ~ ' ~ ~ l b

, A

7 j < _ 1 , 2 0 0 ~ r -

E

,oo! / , ," !

B J

•

7 J

1 0 0

L i

2O 4 0 6 0 8 0 H o u r s

Fig. 4. (A) O b s e r v e d ( • ) biomass production (g). Comparison of experimental data and simulations of a fed batch culture with increased salt concentration in the m e d i u m (0.25 M

NaCI) . (B) O b s e r v e d (zx) oxygen consumption rate, O C R

(retool h i ) and simulated profiles with different values of the maintenance coefficient, m (g g ~ h - ~ ) a n d m a x i m u m growth yield, Y,× (g g i). The following values for the parameters were used ( . . . . . . ): m = 0 . 0 3 7 , y ~ × = 0 . 4 0 : ( ) m =

0.037, k~, = 0.50: ( - - - - ) : m = 0.047. Y,, 0.50.

E

I 0 0

5

1 0 >

<~\ ,I

/ :) "C) • !

exp 2

exp 3

0 2 0 4 0 6 0

Hours

'~, \ \, \, \\

O

8 0

Z J

I 0 0

Fig. 5. Viable count expressed as colony forming units (cfu)4

10 ') m l - ]) f r om e x p e r i m e n t I, 2 a n d 3. The symbols repre- sent (o) experiment 1 with F, = 11 g glucose h I; ( ~ ) experi- ment 2with F , = 1 2 g g lucose h i a n d 0.25 M N a C l a d d e d to the culture m e d i u m ; (©) experiment 3 with F~ = 5.5 g glu-

cose h 1

43

%

d

g

E

E

exp 2

exp 3

I 7

0 . 4

\

0 . 3 \ \

O. 2 ' \ ' \ EL,

\ "",4_1.

0 2 0 4 0 6 0 8 0 1 0 0 Hours

Fig. 6. The calculated specific substrate consumption rate, qS

(g g i h i) f r om e x p e r i m e n t s 1, 2 a n d 3. The symbols represent: (o) experiment 1 with F , - I 1 g glucose h x; ( N )

experiment 2 with F, = 12 g g lucose h ' a n d 0.25 M NaCI

added to the culture m e d i u m ; ( o ) experiment 3 with /~ - 5.5 g g lucose h -1

These features are common to fed batch and recycling fermenters. Van Versevelt et al. [8] con- cluded from their studies with E. col\, growing aerobically in a recycling fermenter, that the ex- perimental data yielded two growth phases, where the first could be explained with the linear equa- tion for substrate consumption. The altered growth behaviour in the second phase was sug- gested to be induced by the stringent response. When E. col\ was grown anaerobically in a recy- cling fermenter, the growth pattern was outlined by three growth phases [91. The initial growth phase, or domain, was characterised as saturcd growth; the second and third domains could be described as linear growth where the mainte- nance requirement was dependent on the growth rate in a non-linear way. The change in growth yield between the two last domains was explained to be caused by the stringent response.

The discrepancy between the applied model and our experimental data might be explained by the extensive decline in viability observed in all cultures. This decline could be caused by cell death, clumping of cells or increase of cell size. Microscopic observations did not reveal any mot-

44

phology changes that could explain the 90c,,f de- crease of viable count number during 50 h, sug- gesting that the cause is ceil death. 'Fhc observed loss in viability was encountered when the spe- cific substrate uptake rate approached a lower limit (0.04 g g ~ h J). This might reflect that the decline in viability is initiated by severe starva- tion, e.g. the stringent response. Clearly, further studies are needed to investigate the reguhitory mechanisms of cnergy-limitcd growth systems with respect to microbial death and lysis. The restllts imply that more refined and preferably segre- gated models arc necessary for dcscriplion of high cell density growth systems.

Nomenclature

Fs (g h I) DI (g g I h i)

/x ( g g i h I)

Y,~ ( g g ~)

OCR (retool h l) R i ( g h I)

Yi

X (g) M (g C - e e l ~) S (g)

substrate feed ratc maintenance coefficient based on substrate rc- quJrcmcnt specific growth ratc yield coefficient for bio- mass per substrate uti- lized excl. maintenance oxygen consumption rate convcrsion rate of con> pound i generalized degrec of re- duction of compound i biomass quantity C-molar mass glucose quantity

Subscript s glucose o oxygen x biomass max maximum value

References

1 gamand , T. and Shimizu, S. (1984) FedIbatch techniques in microbial processes. Adv, Biochcnl, Eng. Biotcchnol. 3(), 147-194.

2 Pirl, SJ. (1965) The maintenance cnergy of bacteria m growingcullurcs. Prec. R. Soc. lxmdon B 163, 224 231.

3 Slrandberg, L. and Enfors S.-O. (1991) Batch and fed balch cuhivalhms for tile tcmpcrltture induced production ol il recombinant protein in l:'schcrichia coil Biotechnol. l.etl. 13, f~(F)-614.

4 Reels. J.A, (It~83) Energclics and Kinetics in Biotcchnol- ogy. Elsevier Biomedical Press, Amsterdam, New York, ()xford.

5 Escner, A,A., Reels, J.A. and Kosscn, W.F. (It,181) Fed- batch culture: modeling and applications ill lhc study of microbial cnergetics. Biotcchnol, Bioeng. 23, 1851 1871.

6 Pirt, S.J. (1974)The theory of fed batch culture with refer- ence to the penicillin fermentation. ,1. Appl. Chem. Biotech- nol. 24,415 424.

7 l,arsen, P.l., Sydncs, L.K., Landfald, B. anti Strom, A,R. (lU)87) ()smoregulation in Echerichia colt by accumulation of organic osmolytes: bctaincs, ghitamic acid, and trehlilosc. Arch. Microbiol. 147, 1-7.

S Van Verseveld, ]l.W., tie Hollander, J.A., Fnuakena. ,1., Braster, M., l.ecuwerik, F.J, and Stouthamcr, A, t | . (1986) Modeling of microbial stlbstrat¢ conversion, growth and producl formation in a recycling fcrmenler, l\nl~mic ~. I.ceu\'<enhoek 52, 325 342.

t) Cllcsbro, W., Arbige, M. and t2iferl, R. (Ic)90} When nutri- ent limitation placcs bacteria in the domains of slow growth: mctabc~lic, morphologic and ccll cycle bchavior. FEMS Mi- crohiol. Ir~col. 74, 103 120,