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A modified probing feeding strategy: control aspects

Velut, Stéphane; de Maré, Lena; Hagander, Per

2004

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Citation for published version (APA):Velut, S., de Maré, L., & Hagander, P. (2004). A modified probing feeding strategy: control aspects.

Total number of authors:3

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A MODIFIED PROBING FEEDING STRATEGY: CONTROL

ASPECTS

Stéphane Velut Lena de Maré Per Hagander

Department of Automatic Control

Lund Institute of Technology

Box 118, SE-221 00 Lund, Sweden

{svelut,lena}@control.lth.se

Abstract The paper presents a fermentation technique, which combines the advantagesof the probing feeding strategy and the temperature limited fed-batch technique. Theearly phase of the cultivation is run under glucose limited conditions by using theoriginal probing technique. When the maximum oxygen transfer capacity of the reactoris reached, the temperature is decreased to lower the oxygen demand. A slight glucoseexcess, achieved by downwards probing pulses, guarantees that the temperature is theonly limiting factor. To achieve a good control of the dissolved oxygen a mid-rangingcontroller manipulating the stirrer speed and the temperature is used. A model describingthe temperature influence on the cell metabolism is derived to facilitate the controllerdesign. The feeding strategy is illustrated by an experiment.

1. INTRODUCTION

E. coli is a common host organism for production ofrecombinant proteins. It is a well-known bacteriumthat can be quickly grown to high cell density. Themain problem encountered when cultivating E. coli isthe accumulation of the by-product acetate. Formationof acetate occurs in two situations: under anaerobicconditions or under fully aerobic conditions by over-flow metabolism, that is when the carbon source in themedium is in excess. To limit the carbon source in thereactor it is usually fed continuously. When the car-bon source is the limiting factor, the technique is calledsubstrate limited fed-batch. One feeding strategy thatcan be used to dose the substrate feed and that avoidsacetate accumulation is the probing feeding strategydescribed in (Åkesson et al. (2001a)).

However a cultivation technique based only on themanipulation of the feed is not enough, it usuallyresults in the release of endotoxins into the media,as noticed in (Rozkov (2001)) and (Han (2002)).Endotoxins are unfavorable since it complicates thedownstream processing. To minimize the release onecan use the temperature limited fed-batch technique

described in (Silfversparre et al. (2002)). The methodconsists of decreasing the cultivation temperature tocontrol the oxygen consumption rate and thereby avoidoxygen limitation. Also, the substrate has to be fed inexcess in order to prevent substrate limitation.

The main obstacle with the temperature limited fed-batch technique is to achieve a non-growth limitingglucose concentration in the reactor without accumu-lating acetic acid, since an on-line glucose sensor isusually not available.

A new fermentation technique combining the advan-tages of the substrate limited fed-batch and the tem-perature limited fed-batch methods is described in thepaper. In section 2, a brief description of the probingfeeding strategy is given. The influence of the temper-ature is investigated in section 3 where a model of thebioreactor is derived. In section 4 a modified probingfeeding technique is presented where the temperatureis used to lower the oxygen demand of the bacteria.One experiment with the new technique is shown insection 5.

2. THE PROBING FEEDING STRATEGY

Usually glucose is used as the substrate and the prob-ing feeding strategy leads to a cultivation that is some-what glucose limited. The feeding strategy makes useof the following principle: under glucose limited con-ditions pulses added to the feed give rise to changesin the glucose uptake rate. These variations affect theoxygen uptake rate that can be seen in the dissolvedoxygen signal, which is usually measured. The infor-mation from the dissolved oxygen signal is used in afeedback algorithm that adjusts the feed rate after eachpulse.

• When the response in the dissolved oxygen islarge enough, the feed rate is increased propor-tionally to the size of the pulse response.

• When there is no visible response in the dis-solved oxygen, the feed rate is decreased witha fixed proportion.

The strategy is illustrated in figure 1, which shows apart of a cultivation. The feed rate is first increasedsince there are large responses in the dissolved oxygensignal and thus no acetate accumulation. The absenceof response to the third pulse indicates that acetateis produced and the feed rate is therefore decreased.The dissolved oxygen is controlled between the pulsesusing the stirrer speed. A gain-scheduled PID withrespect to the stirrer speed is used and a setpoint valueof 30 % is chosen. During a feed pulse the stirrer speedis frozen. Otherwise it would have been difficult toquantify the response in the dissolved oxygen signal.

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16 16.1 16.2 16.3500

600

700

800

16 16.1 16.2 16.30.03

0.04

0.05

DO [%]

F [l/h]N [rpm]

Time [h]

Fig. 1 A part of an experiment where the probing feeding strategyis used. From top: dissolved oxygen DO, feed F and stirrerspeed N (dashed).

When the maximum oxygen transfer capacity of thereactor is reached i.e. the maximum stirrer speed, theprobing feeding strategy decreases the feed rate tokeep the reactor working under aerobic conditions.The decrease is done at a constant rate:

dF

dt= −γF

The strategy has been successfully used for E. coli

cultivations on 3 l up to 12 m3 reactors, see (Ram-churan et al. (2002)), (Velut et al. (2002)). It has also

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0.04

0.06

12 13 14 15 16 17 18 19 20 21

400

600

800

1000

DO [%]

F [l/h]

N [rpm]

Time [h]

Fig. 2 A cultivation where the original probing feeding strategyis used. The fed-batch part of the cultivation is shown. Fromtop: dissolved oxygen DO, Feed F and the stirrer speed N. Att = 16.7 h and t = 17.5 h antifoam is added which has a largeimpact on the dissolved oxygen.

been tested on other microorganisms presenting sim-ilar overflow metabolism phenomenon, see (de Maréet al. (2003)).

Figure 2 shows an experiment performed in a 3 l

reactor where the probing feeding strategy is used.Here the maximum stirrer speed is reached 2 hoursafter the feed started. Then the feed is decreasedfor about 6 hours. The low feed rate may lead tostarvation and endotoxins formation, (Rozkov (2001))and (Han (2002)).

An alternative way to lower the oxygen demand ofthe bacteria would be to decrease the temperature, see(Bauer and White (1976)).

3. PROCESS MODEL

To investigate the influence of the temperature onthe process a model was derived. A model of afed-batch cultivation described in (Xu et al. (1999))and (Åkesson et al. (2001b)) is modified to incorpo-rate temperature dependence.

The mass balance equations for the media volume V ,the glucose concentration G, the acetic acid concentra-tion A, the cell mass X and the oxygen concentration

Co are:

dV

dt= F

d(VG)

dt= FGin −qg(G)VX

d(VA)

dt= qa(G,A)VX

d(VX)

dt= µ(G,A)VX

d(VCo)

dt= KLa(N)V(C∗

o −Co)−qo(G,A)VX

Into the model an equation describing the outletgas concentration O2 is added (Enfors and Häg-gström (1994)):

d(VgO2)

dt= Q(O2i −O2)−KLaV (C∗

o −Co)RT

PM

Q is the gas flow into the reactor, R the gas-constant, M

the molar mass, P the pressure and T the temperature.Vg is the gas volume in the reactor and it is calculatedas Vtot −V where Vtot is the total volume of the reactor.The saturated dissolved oxygen in the medium C∗

o iscalculated as follows

C∗

o =O2Ptot

O2iPcalH

Henry’s law gives the dissolved oxygen concentrationDO in %:

DO = HCo

The relation between KLa and the stirrer speed N isapproximated as

KLa(N) = α(N −N0)

The equations for the growth rate µ and the uptake-rates qa, qg, qo are given in the appendix.

The temperature dependence of the growth rate isincorporated into the model using Arrhenius law. Adecrease in the medium temperature from 37oC to25oC has been reported to lower the growth rate byhalf, see (Pirt (1985)) and (Esener et al. (1983)). Sincethe growth rate is proportional to the glucose uptakerate qg, one can write qmax

g (T ) as

qmaxg (T ) = qmax

g,37e−50( 1T −

137 )

qmaxg (25) ≈ 0.5qmax

g,37

The uptake rates qa and qo are changed in a similarfashion and also the maintenance coefficient qmc (Es-ener et al. (1983)).

We strive for a model that is as simple as possible,so the influence of the temperature on KLa and thesolubility of oxygen is neglected. The resulting effect

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0 0.5 1 1.5 2 2.5 3 3.512

14

16

18

DO [%]

T [oC]

N [rpm]

X [g/l]

O2 [%]

F [l/h]

Time [h]

Fig. 3 Simulation of the model together with experimental data.From top: dissolved oxygen DO (simulation dashed), stirrerspeed (dashed) N and feed F, temperature T (dashed) and cellmass X (experimental data ’*’), oxygen concentration in theoutlet gas O2 (simulation dashed). Time [h] after feed-start.

on the oxygen transfer is small in the range 20 oC to40oC (Enfors and Häggström (1994)).

Simulation of a cultivation is shown in figure 3 to-gether with experimental data.

The values of the parameters in the model are listed intable 1 in appendix. In the experiment the temperatureis lowered from 37 to 24 oC stepwise. As seen theprocess model fits remarkably well to the experimentaldata. In the literature (Pirt (1985)) it is mentioned thatthe behavior of the growth-rate drastically changesbelow 25 oC. This explains the poorer fit the last 30min. The model is still good enough for the purpose ofdesigning a dissolved oxygen - temperature controller

4. COMBINATION OF THE PROBING FEEDINGSTRATEGY AND THE TEMPERATURE

LIMITED FED-BATCH TECHNIQUE

Our idea here is to use the original probing strategy,described in section 2, until the maximum oxygentransfer capacity of the reactor is reached. Then thetemperature instead of the feed is decreased to lowerthe oxygen demand. To achieve a slight glucose excessin the reactor the up-pulses superimposed to the feedare shifted to down-pulses when the maximum stirrerspeed is reached.

4.1 Feed control

The same feed controller as described in the originalprobing control strategy is used until the maximum

F

N

T

DO

Tre fC

Oxygen Transfer

Oxygen

Uptake

Fig. 4 A description of the process. Stirrer speed, N, Feed, F ,Temperature T , Temperature reference Tre f , dissolved oxygenDO and a temperature controller C. C is typically a pulse widthmodulation of the cold and hot water flows.

stirrer speed is reached. Then the up-pulses superim-posed to the feed are shifted to down pulses. When adown-pulse is made the dissolved oxygen signal willincrease instead of decrease if the cultivation is glu-cose limited. The feed rate is adjusted as before de-pending on the size of the response in the dissolvedoxygen. With down pulses a slight glucose excess inthe reactor can be achieved. At a given feed rate adown-pulse may indeed lead to a response in the dis-solved oxygen when an up-pulse would not. The glu-cose excess is important since the goal in this part ofthe cultivation is to let the temperature be the limitingfactor and not the glucose concentration.

4.2 Dissolved oxygen control

Aerobic conditions should be maintained during theentire cultivation. For that purpose three control vari-ables can be manipulated between the pulses: the stir-rer speed N, the feed rate F and the temperature T , seeFigure 4. The stirrer speed affects the oxygen transferin the reactor whereas the feed rate and the tempera-ture act on the oxygen uptake rate.

Control allocation From a control point of view, dis-solved oxygen control is a regulation problem wherethe oxygen supply should be in balance with the oxy-gen consumption by the cells. The probing strategydetermines the feed rate that maximizes the glucoseuptake with respect to the respiratory capacity of thecells. The oxygen transfer and consequently the agi-tation speed should follow the cell growth to keep aconstant oxygen concentration.

Since the oxygen transfer capacity of the reactor islimited, it is necessary to manipulate the oxygen con-sumption rate to keep the oxygen balance. The tem-perature or the feed rate should consequently be de-creased. It is preferable to use the temperature sincea larger decrease in the feed rate may lead to starva-tion. At high cell densities the heat production is highand both the temperature and the flow of the coolingwater introduce limitations. When the maximal cool-ing capacity of the reactor is reached, the feed ratecan be used to control the dissolved oxygen. Thus thefeed rate should be used only when both the the stirrer

R1

R2

N

N

Nre f Tre f

DOsp

DO

sat

Process

Fig. 5 A block-diagram over the mid-ranging controller. Sat standsfor saturation. R1 is used even when ’only’ N is controlling thedissolved oxygen, a gain scheduled PID. R2 is a PID controller.

speed and the temperature are saturated.

Mid-ranging The model derived in the previous sec-tion reveals that the dissolved oxygen-temperature dy-namics is comparable to the dissolved oxygen-stirrerone. However, cooling of the reactor introduces ad-ditional dynamics. The resulting dynamics from Tre f

to DO is much slower than the DO-stirrer one. Fastdisturbances in the dissolved oxygen such as feed ad-justments and antifoam addition cannot be quicklyhandled by the temperature. Dissolved oxygen con-trol based on the sole manipulation of the tempera-ture would result in a poor performance. One wayto handle this problem is shown in figure 5. Here aso-called mid-ranging controller structure, see (Alli-son and Isaksson (1998)), is chosen to control the dis-solved oxygen. The first controller R1 manipulates thestirrer speed N and it is tuned to handle the fast dis-turbances. The second controller R2 manipulates thetemperature to keep the stirrer speed at Nre f , belowNmax. The second controller R2 is much slower than R1and takes typically care of slow disturbances like cellgrowth. The second loop involving the temperature isactivated once the stirrer speed has reached Nre f . Themodel derived in Section 3 can be used to determine agood value for Nre f . A typical short term perturbationin DO should not saturate the stirrer speed.

5. EXPERIMENT

The feeding strategy was evaluated by simulations us-ing the model from section 3. Then it was implementedand tested on a 3 l bioreactor. Figure 6 shows an ex-periment run with the new technique. At t ≈ 13.5 h theinitial glucose amount from the batch phase is totallyconsumed and the glucose starts to be fed into the reac-tor. After 1.5 h of feeding the stirrer speed reaches Nre f

and the temperature starts to decrease. The pulses inthe feed are performed downwards to achieve a slightglucose excess. The initial decrease in the tempera-ture does not affect the dissolved oxygen concentra-tion. This can be explained by the model which pre-dicts a lack of authority when the oxygen uptake rateis not saturating. Induction occurs at t = 15 h. Whenthe dissolved oxygen is stabilized at 30 %, no pulseresponses are visible. The feed rate is therefore de-creased by the algorithm. At t = 16 h pulse responses

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600

800

1000

12 13 14 15 16 17 18 19 20 21

25

30

35

N [rpm]

T [oC]

F [l/h]

DO [%]

Time [h]

Fig. 6 Experiment using the modified probing strategy togetherwith the temperature limited fed-batch technique. The fed-batch part of the cultivation is shown. From top: DO dissolvedoxygen, F feed, N stirrer speed, T temperature. Nre f is dashed.At t = 18.2 h antifoam is added which has a large impact on thedissolved oxygen signal.

are seen in the oxygen signal, which indicates thatglucose becomes limiting again. Unlike the substrate-limiting technique, over-feeding can easily occur afterthe maximum stirrer speed is reached. Indications ofglucose excess from the probing pulses led to a de-crease in the feed at four occasions. This shows theimportance of the glucose feeding in temperature lim-ited fed-batch cultivations. It is interesting to comparethe feed profiles from figures 2 and 6. In the first ex-periment, a 50% decrease in the feed was necessary tokeep the reactor working in aerobic conditions. In thesecond experiment, the temperature was instead low-ered and it was never necessary to decrease the feedto control the dissolved oxygen. This should be a lessstressful way to limit the oxygen demand of the bacte-ria, as indicated by less foaming.

6. CONCLUSION

A cultivation strategy combining the probing feedingstrategy and the temperature limited fed-batch tech-nique was presented. The strategy was implementedand compared to a cultivation using the original prob-ing feeding strategy. The temperature instead of glu-cose was the limiting factor in the late phase of thecultivation. This should be less stressful for the bacte-ria.

A model of the process was derived and compared toexperimental data in order to design the controllers. Toachieve a good control of the dissolved oxygen a mid-ranging controller manipulating the stirrer speed andthe temperature was used.

7. ACKNOWLEDGMENT

The funding is gratefully acknowledged from Vin-nova (P10432-2) and NACO (contract no. HPRN-CT-1999-00046). For valuable work during the labora-tory experiments the authors would like to thank Kata-rina Bredberg, Eva Nordberg Karlsson and Olle Holstat the biotechnology department at Lund Institute ofTechnology and Tory Li at ABB.

8. REFERENCES

Åkesson, M., P. Hagander, and J. P. Axelsson (2001a):“Avoiding acetate accumulation in Escherichia

coli cultures using feedback control of glucosefeeding.” Biotechnology and Bioengineering, 73,pp. 223–230.

Åkesson, M., P. Hagander, and J. P. Axelsson (2001b):“Probing control of fed-batch cultures: Analy-sis and tuning.” Control Engineering Practice, 9,pp. 709–723.

Allison, B. J. and A. J. Isaksson (1998): “Design andperformance of mid-ranging controllers.” Journalof Process Control, 8:5, pp. 469–474.

Bauer, S. and M. D. White (1976): “Pilot scale ex-ponential growth of Escherichia coli W to highcell concentration with temperature variation.”Biotechnology and Bioengineering, 18, pp. 839–846.

de Maré, L., L. Andersson, and P. Hagander (2003):“Probing control of glucose feeding in Vibrio

cholerae cultivations.” Bioprocess and BiosystemsEngineering, 25, January, pp. 221–228.

Enfors, S.-O. and L. Häggström (1994): Biopro-cess technology: Fundamentals and Applications.Department of Biotechnology, Royal Institute ofTechnology, Stockholm, Sweden.

Esener, A. A., J. A. Roels, and N. W. F. Kossen(1983): “Theory and applications of unstructuredgrowth models: kinetics and energetic aspects.”Biotechnology and Bioengineering, 25, pp. 2803–2841.

Han, L. (2002): Physiology of Escherichia coli inBatch and fed-batch cultures with special empha-sis on amino acids and glucose metabolism. PhDthesis, Department of Biotechnology, Royal Insti-tute of Technology, Stockholm, Sweden. ISBN 91-7283-276-2.

Pirt, S. J. (1985): Principles of microbe and cellcultivation. Blackwell Scientific Publications.

Ramchuran, S. O., E. Nordberg Karlsson, S. Velut,L. de Maré, P. Hagander, and O. Holst (2002):“Production of heterologous thermostable glyco-side hydrolases and the presence of host-cell pro-teases in substrate limited fed-batch cultures ofEscherichia coli BL21(DE3).” Applied Microbiol-ogy and Biotechnology, 60:4, pp. 408–416.

Rozkov, A. (2001): Control of proteolysis of recom-binant proteins in Escherichia coli. PhD thesis,Department of Biotechnology, Royal Institute ofTechnology, Stockholm, Sweden. ISBN 91-7283-160-X.

Silfversparre, G., S.-O. Enfors, L. Han, L. Häggstöm,and H. Skogman (2002): “Method for growthof bacteria, minimising the release of endotox-ins from the bacteria into the surrounding me-dia.” Patent: International publication number WO02/36746.

Velut, S., L. de Maré, J. P. Axelsson, and P. Hagan-der (2002): “Evaluation of a probing feeding strat-egy in large scale cultivations.” Technical ReportISRN LUTFD2/TFRT--7601--SE. Department ofAutomatic Control, Lund Institute of Technology,Sweden.

Xu, B., M. Jahic, and S.-O. Enfors (1999): “Mod-eling of overflow metabolism in batch and fed-batch cultures of Escherichia coli.” BiotechnologyProgress, 15:1, pp. 81–90.

9. APPENDIX

The temperature dependency is introduced in the max-imal specific uptake rates. The maximal uptake ratesq

c,maxa (T ), qmax

g (T ), qmaxo (T ) and the maintenance co-

efficient qmc(T ) are given by:

qc,maxa (T ) = q

c,maxa,37 e−50( 1

T −1

37 ) = qc,maxa,37 f (T )

qmaxg (T ) = qmax

g,37 f (T ), qmc(T ) = qmc,37 f (T ),

qmaxo (T ) = qmax

o,37 f (T )

The uptake rates for acetic acid and glucose are mod-eled by Monod kinetics:

qc,pota (A,T ) = qc,max

a (T )A

ka +A

qg(G,T ) = qmaxg (T )

G

ks +G

Part of the glucose is used for maintenance:

qm(T ) = min(qg(G,T ),qmc(T ))

Symbol Value Description

Gin 500 g/l glucose conc. in feed

H 14000 Henrys const.

ks 0.01 g/l sat. const. for gluc. uptake

ka 0.05 g/l sat. const. for acet. uptake

α 3 (hRPM)−1 oxygen transf. const.

N0 289 RPM oxygen transf. const.

qc,maxa,37 0.2 g/gh max. spec. acet. uptake

qmaxg,37 1.5 g/gh max. spec. glucose uptake

qcritg,37 1.25 g/gh crit. glucose uptake

qmc,37 0.06 g/gh maintenance coefficient

qmaxo,37 0.66 g/gh max. spec. oxygen uptake

Yag 0.55 g/g acetate/glucose yield

Yoa 0.55 g/g oxyg./acet. yield

Yog 0.50 g/g oxyg./gluc. yield for growth

Yom 1.07 g/g oxyg./gluc. yield for maint.

Yxa 0.4 g/g biomass/acet. yield

Y oxxg 0.51 g/g oxidative biomass/gluc.

Yf e

xg 0.15 g/g fermentative biomass/gluc.

O2i 21 % oxyg. conc. in the inlet gas

Pcal 1 atm pressure when calib.

Ptot 1 atm pressure during cult.

Vtot 3 l total reactor volume

Q 2.4 l/min gasflow

M 32 g/mol Molar mass

Table 1 Parameters in the model

For clarity purposes the argument T is omitted in thefollowing equations. The acetic acid formation qa andthe growth uptake qgg are described by:

qa = qpa −qc

a, qgg = qg −qm

where qpa is the production of acetic acid and qc

a

stands for the acetic acid consumption. Splitting intoan oxidative flow and a fermentative flow gives:

qoxgg = min((qmax

o −qmYom)/Yog,qgg)

q f egg = qgg −qox

gg

The specific acetate production, acetate consumption,growth rate and oxygen uptake rate are given by thefollowing equations:

qpa = q f e

ggYag

qca = min(qc,pot

a ,(qmaxo −qox

ggYog −qmYom)/Yoa)

µ = qoxggY ox

xg +q f eggY f e

xg +qacYxa

qo = qoxggYog +qmYom +qacYoa

A consequence of the model assumptions is that µ andall q’s can be written on the form q(T ) = q37 f (T ). Thesaturation in the oxygen uptake rate therefore occursfor the same values of G and A independently of T .