Journal of Biotechnology 125 (2006) 252–268

Constant specific growth rate in fed-batch cultivationof Bordetella pertussis using adaptive control

Z.I.T.A. Soons a,b,∗, J.A. Voogt a, G. van Straten a, A.J.B. van Boxtel a

a Wageningen University, Agrotechnology and Food Sciences, Systems and Control Group, P.O. Box 17, 6700 AA Wageningen, The Netherlandsb

Netherlands Vaccine Institute, Antonie van Leeuwenhoeklaan 9-11, P.O. Box 457, 3720 AL Bilthoven, The Netherlands

Received 3 August 2005; received in revised form 8 February 2006; accepted 3 March 2006

Abstract

Monitoring and control of production processes for biopharmaceuticals have become standard requirements to support con-sistency and quality. In this paper, a constant specific growth rate in fed-batch cultivation of Bordetella pertussis is achieved bya newly designed specific growth rate controller.

The performance of standard control methods is limited because of the time-varying characteristics due to the exponentiallyincreasing biomass and volume. To cope with the changing dynamics, a stable model reference adaptive controller is designedwhich adapts the controller settings as volume and biomass increase. An important asset of the design is that dissolved oxygenis the only required online measurement.

An original design without considering the dissolved oxygen dynamics resulted experimentally in oscillatory behaviour.Hence, in contrast to common believes, it is essential to include dissolved oxygen dynamics. The robustness of this novel designwas tested in simulation.

The validity of the design was confirmed by laboratory experiments for small-scale production of B. pertussis. The controllerwas able to regulate the specific growth rate at the desired set point, even during a long fed-batch cultivation time with exponentiallyincreasing demands for substrates and oxygen.

© 2006 Elsevier B.V. All rights reserved.

Keywords: Model-reference adaptive control; Biopharmaceuticals; Fed-batch cultivation; Specific growth rate; Dissolved oxygen; Bordetellapertussis

∗ Corresponding author. Tel.: +31 30 274 2066;fax: +31 30 274 4426.

E-mail address: zita.soons@wur.nl (Z.I.T.A. Soons).

1

fmF

0168-1656/$ – see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.jbiotec.2006.03.005

. Introduction

Monitoring and control of production processesor biopharmaceuticals have become standard require-ents to support consistency and quality. Recently,DA encourages with its view on process analytical

Z.I.T.A. Soons et al. / Journal of Biotechnology 125 (2006) 252–268 253

Nomenclature

a, b, c, d constants for dual substrate model ofBordetella pertussis

C nominal value of controller (mmol l−1)CG glutamate concentration (mmol l−1)CG0 initial glutamate concentration

(mmol l−1)CL lactate concentration (mmol l−1)CL0 initial lactate concentration (mmol l−1)CX biomass concentration (OD)CX0 initial biomass concentration (OD)CX software sensor biomass concentration

(OD)Cin

G glutamate concentration in the feed(mmol l−1)

CinL lactate concentration in the feed

(mmol l−1)DO dissolved oxygen, oxygen concentration

in the medium (mmol l−1)DOset set point for oxygen concentration in the

medium (mmol l−1)DOsensor oxygen concentration measured by the

sensor (mmol l−1)E objective functionEDO relative variation of DOEµ relative variation of µ

fG Monod kinetics for glutamatefL Monod kinetics for lactateFO2 (enriched) airflow through the

headspace (l h−1)F1 “proportional” correction substrate feed

rate (l h−1)F2 feed rate by prior calculation (l h−1)F3 integral correction substrate feed rate

(l h−1)F in

G+LFtot total substrate feed rate (glutamate+ lactate) (l h−1)

ISE integral squared error (h−1)kLa oxygen transfer coefficient (h−1)KC gain for dissolved oxygen controlKG Monod constant on glutamate

(mmol l−1)KL Monod constant on lactate (mmol l−1)K1, K2 gains for specific growth rate controlKh

C gain for headspace controlLPS lipopolysaccharide

mG maintenance coefficient on glutamate(mmol OD−1 h−1)

mL maintenance coefficient on lactate(mmol OD−1 h−1)

mO maintenance coefficient on oxygen(mmol OD−1 h−1)

Oa2 auxiliary oxygen concentration

(mmol l−1)Oh

2 oygen concentration in the headspace(mmol l−1)

Oin2 oygen concentration in the incoming air

(mmol l−1)OD optical density at 590 nm (OD590 ml−1)OTR oxygen transfer rate (mmol l−1 h−1)OUR oxygen uptake rate (mmol l−1 h−1)OURnoise noise on the oxygen uptake rate

(mmol l−1 h−1)PRN Pertactinrpm rounds per minutet cultivation time (h)v, w constants for normalised Monod

equationsV liquid volume (l)V software sensor liquid volume (l)Vh volume of the headspace (l)YG1 yield on glutamate over pathway

1 (OD mmol−1)YG2 yield on glutamate over pathway

2 (OD mmol−1)YL yield on lactate (OD mmol−1)YO yield on oxygen (OD mmol−1)

Greek lettersβ ratio between normalised Monod equa-

tionsβ1, β2 convergence speed of reference modelγ1, γ2 tuning parameters for MRACµ specific growth rate (h−1)µ software sensor specific growth rate

(h−1)µenh enhanced specific growth rate (h−1)µmax maximum specific growth rate (h−1)µset set point specific growth rate (h−1)µ0 initial software sensor specific growth

rate (h−1)

254 Z.I.T.A. Soons et al. / Journal of Biotec

τI reset time for dissolved oxygen control(h)

τsensor response time for dissolved oxygensensor (h)

taim

inottdga

ciaraLtc

mttfbo

lapaatatg

tRttaftapbaotwpf

sa

((

((

dmmctfbsftsdobtbi

τhI reset time for headspace control (h)

echnology (PAT) the introduction of new technology,mongst others methods for monitoring and control, tomprove manufacturing and quality assurance in phar-

aceutical processes (FDA, 2004).Currently, most biopharmaceuticals are produced

n batch cultivation, where cells grow until the mainutrients are depleted. In such a cultivation system,nly dissolved oxygen (DO), stirrer speed, pH, andemperature are controlled. In a typical batch cultiva-ion, specific growth rate cannot be controlled. With theecreasing substrate concentration in time, the specificrowth rate (µ) correspondingly changes and eventu-lly becomes zero due to depletion.

In order to ensure a high level of batch-to-batchonsistency, it is preferable to control metabolic activ-ty. However, it is not possible to measure metabolicctivity directly. To cope with this limitation, indi-ect measurements can be used. Portner et al. (2004)pply the oxygen mass balance to monitor respiration.evisauskas et al. (1996) make use of the fact that

he biosynthesis of many intracellular components islosely related to the particular specific growth rate.

Control of the specific growth rate as a measure foretabolic activity, implies constant substrate concen-

rations and thus, partly, control of the environment ofhe cells. So, to realise specific growth rate control aeed of substrate is necessary and as a consequence theatch-wise operations must be shifted to a fed-batchperation mode.

Antigen level (Westdijk et al., 1997) andipopolysaccharide (LPS) content (Rodriguez etl., 1994) are important aspects for the quality of B.ertussis suspensions used for vaccine productiongainst infection with whooping cough. Westdijk etl. (1997) demonstrated that, during batch cultivation

he growth phase determines the antigen productionnd release. No conclusion, however, is given abouthe relation between antigen production and specificrowth rate or nutrient composition.

aa

s

hnology 125 (2006) 252–268

In literature, limited information is available onhe effect of specific growth rate on product quality.odriguez et al. (1994) and Licari et al. (1991) show

hat the production of pertussis toxin (which is one ofhe important antigens) is strongly growth-associatednd that a high specific growth rate is an effective wayor producing pertussis toxin. Although this favourshe traditional batch cultivation, the work of Rodriguezlso indicates that with increasing growth rate LPSroduction increases. This is regarded as a drawbackecause LPS is suspect of causing adverse reactionsnd should therefore be reduced in the vaccine. So, inrder to obtain a high quality-vaccine, it is importanto restrict lipopolysaccharide content of the vaccine,hile still providing efficient pertussis toxin. This isossible by controlling the cultivation at constant levelor the specific growth rate.

Portner et al. (2004) implemented several feedingtrategies for fed-batch cultures and discussed the char-cteristics:

1) fixed feed trajectory,2) a priori calculation of the feed trajectories based

on a kinetic model,3) predictive control with feedback in intervals,4) feedback control via OUR.

The first two methods are open-loop methods ando not correct for deviations, arising from model mis-atches. These options are not suitable to controletabolic activity. The third method is a predictive

ontrol method with a prediction update interval equalo the interval between manually taken samples. So,eedback takes only place at the sampling moments. Inioreactors, the time between samples may go up toeveral hours, thus jeopardizing the effectively of theeed-back. The fourth method, control via OUR, hashe capability of responding fast to deviations from theet point, regardless of the cause and duration of theisturbance. Metabolic activity is regulated regardlessf external disturbances and varying yields and kineticsy adjusting the feed rate every minute. Feedback con-rol using OUR measurements is applied in this workecause it is able to correct errors, does not requirentensive process development, and is applicable in all

reas, provided that OUR can be measured (Portner etl. (2004)).

Neeleman (2002) and Neeleman et al. (2004) used atandard “PI” controller to control the specific growth

f Biote

reibbt

ctmbktt(eaet

sattp

Gmsptmelsrwl

tbtivui

Z.I.T.A. Soons et al. / Journal o

ate during fed-batch cultivation of B. pertussis. How-ver, the performance of such standard control methodss limited due to time-varying characteristics of a fed-atch process. To incorporate exponentially changingiomass and volume, the controller needs to have adap-ive properties.

In the literature on adaptive control two approachesan be distinguished. The adaptation of controller set-ings in the first group is based on controller perfor-

ance, where the error between desired and actualehaviour (which can be caused by uncertainties in theinetic parameters or mismatch in the total model) ishe driver for adaptation. Babuska et al. (2003) applyhis method to control dissolved oxygen, Frahm et al.2002) to control substrate concentrations, and Akayt al. (2002) to control medium temperature in biore-ctors. To achieve enough adaptation in this approach,rrors must be introduced by applying systematic exci-ation signals to the system.

The other group of adaptive controllers is repre-ented by e.g. Bastin and Dochain (1990), van Impe

nd Bastin (1995), and Smets et al. (2002, 2004). Inhis approach, the adaptive expressions for the con-roller parameters are linked to measured or estimatedrocess states.

iw

l

Fig. 1. System con

chnology 125 (2006) 252–268 255

The work of Chang (2003) fits to the second group.ain scheduling for a PI2D controller is based on theeasured states. Levisauskas et al. (1996) apply the

ame methodology by using a controller that adapts itsarameters to the changing states. A drawback of thesewo controllers is the requirement for explicit measure-

ent of part of the states (e.g. substrates, biomass, orthanol). Alvarez and Simutis (2004) present a controlaw for regulation of the specific growth rate for a singleubstrate model, where estimation of specific growthate and biomass is performed by a Kalman filter. Thisork is based on simulations, and is not qualified by

aboratory experiments.Applying excitation signals is not desired in cul-

ivation systems for biopharmaceutical production,ecause it may affect critical variables. In this work,herefore, adaptation according to the second categorys used to cope with the time-varying biomass andolume. Robustness and accuracy are evaluated by sim-lations with time-varying or drifting kinetics, changesn set point, and external disturbances and by evaluat-

ng controller performance in laboratory experimentsith the dual substrate-using B. pertussis.In this work, bioreactor control is based on two

oops: the standard DO control loop (which was not

figuration.

256 Z.I.T.A. Soons et al. / Journal of Biotec

Fig. 2. Oscillations in measured and software sensor results of thefed-batch phase due to interaction of control loops. (A) Oxygenus

arsmttbtac

f

•

•

••

•

t

sc

2

2

dt

2

tqcc

•••

3tagritFs

bstssts(

ptake rate (OUR). (B) Software sensor specific growth rate andet point. (C) Total substrate feed rate.

llowed to change) and the adaptive specific growthate control loop (Fig. 1). Oxygen and substrate con-umption are strongly coupled and in the same order ofagnitude. If dissolved oxygen dynamics are ignored,

uning of the specific growth rate controller may leado oscillations (Fig. 2). So, in contrast to commonelieves, incorporation of DO dynamics is essential forhe design of specific growth rate control in order tovoid interactions between dissolved oxygen and spe-ific growth rate control.

For the design of the specific growth rate control theollowing performance specifications were set:

It has to cope with changing process dynamics dur-ing fed-batch cultivation.Set point tracking and disturbance rejection must berealised during a long cultivation time.The only required measurement is dissolved oxygen.Oscillations due to interaction with other controllersmust be absent.Batch-to-batch consistency and quality has to be

improved.

In the next sections, first the model is given; thenhe adaptive control law is derived and evaluated by

sta

hnology 125 (2006) 252–268

imulation. Finally, performance of the controller isonfirmed in laboratory experiments.

. Materials and methods

.1. Strain and culture media

B. pertussis strain 509 is grown in chemicallyefined medium containing glutamate and l-lactate ashe main carbon sources (Thalen et al., 1999).

.2. Bioreactor conditions

In the PAT framework, process control is one ofhe four tools with the goal of ensuring final productuality (FDA, 2004). To obtain a constant process, theultivation must meet three requirements to ensure aonstant environment:

Medium must be of constant quality.Gases must be of constant quality.Cultivation must be controlled within tight boundsfor among others dissolved oxygen, temperature,and specific growth rate.

The cells were grown in 5-l bioreactor containingl medium. A six-bladed impeller was used to agi-

ate the medium. Temperature was controlled at 34 ◦C,gitation speed at 300–750 rpm depending on the oxy-en demand, and dissolved oxygen at 20% air satu-ation by headspace aeration only (by changing thencoming oxygen fraction in an oxygen/nitrogen mix-ure). The total gas flow was kept constant at 1 l/min.ig. 1 shows the configuration of the experimentalet up.

Cultivation was performed in two phases. First,atch cultivation was performed until the limiting sub-trates are depleted. Second, controlled fed-batch cul-ivation was performed to ensure batch-to-batch con-istency and quality by adding a feed with limitingubstrates. The fed-batch automatically started whenhe specific growth rate dropped to the set point. Theet point for specific growth rate was chosen at 0.05 h−1

Neeleman, 2002).

In the fed-batch phase, two 500 ml concentrated

tock solutions of glutamate and lactate were used forhe two separate feeds and placed on analytical bal-nces. The feeds were added to the bioreactor with a

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µ

Z.I.T.A. Soons et al. / Journal o

xed ration by two pumps (101 U/R 32 rpm, Watsonarlow Ltd., Cornwall UK) connected to the bioreac-

or control system.

.3. Analysis

A polarographic electrode (Applikon, The Nether-ands) was used to measure dissolved oxygen in the

edium. A pH electrode (Mettler Toledo, Udorf,witzerland) was used to measure pH, and tempera-

ure was measured with a Pt100 temperature sensor.lutamate and L-lactate were measured offline withYSI 2750 select analyser (Yellow Springs Instru-ents, Yellow Springs, USA). Biomass was measured

ffline by measuring optical density (OD) at 590 nm ofml suspension using a Vitalab 10 (Vital Scientific,he Netherlands). Quantification of cell-associatedrotein pertactin (PRN) in whole-cell suspensionsas done using ELISA developed by Westdijk et al.

1997).

.4. Hard and software set-up

All sensors were connected to the bioreactor controlystem ADI1040 (Applikon, Schiedam, The Nether-ands), which in turn was connected to a UNIX machineith BCSV (Compex, Belgium (Wieten et al., 1995)).CSV-software performed the basic control-loops (dis-

olved oxygen, temperature, and agitation speed) andogged these control-data on the UNIX machine. UsingTP, a Windows XP machine downloaded new datavery minute. A routine written in Matlab (Mathworks,A, USA) processed data to estimate specific growth

ate and biomass, and to calculate feed rate and new setoints for the substrate pumps. BCSV then uploadedhe new set points for the pumps to the UNIX machineand to the pumps).

Matlab 6.5 was used for the development and appli-ation of the software sensor (Extended Kalman Fil-er) and the adaptive control law. Fig. 1 shows anverview of the cultivation process. The software sen-or is based on an extended Kalman filter and estimatesvery minute the specific growth rate and biomasssing the oxygen uptake rate as an input. A simple

odel is used with only two parameters: the yield andaintenance coefficient on oxygen. The parameteri-

ation of the software sensor is based on simulation.ystem and output noise were chosen in such a way

f

chnology 125 (2006) 252–268 257

hat the deviation between estimation and simulationata is minimal. Afterwards the software sensor wasvaluated on experimental data. The software sensorhowed fast convergence and fitted well to the data.herefore, in the design of the controller estimationsf the software sensor are considered as ideal measure-ents.Because dissolved oxygen is controlled, accumu-

ation of dissolved oxygen is small, and the oxygenptake rate (OUR) can be set equal to the oxygen trans-er rate (OTR). OUR, therefore, was assumed to bequal to OTR. OTR was calculated every minute usinghe average of the last four incoming oxygen concen-rations (Oin

2 ) and dissolved oxygen values, and fromLa, measured in advance of the cultivation at a rangef agitation speeds assumed to be time invariant. Thealculated OTR will be named “OUR measured” fromow on.

. Simulation of the process

.1. Model for cultivation of B. pertussis

Growth of B. pertussis is limited by two substrates.he metabolism of B. pertussis is described in detail byhalen et al. (1999) and can be generalised to the for-ation of biomass from glutamate and lactate by twoajor pathways: glutamate alone (pathway 1) or gluta-ate and lactate (pathway 2). The organism can grow

n glutamate only, but growth on lactate alone is notossible. In the current medium, glutamate is an essen-ial, and lactate is an enhancing substrate. Growth viahese two pathways is assumed to be parallel, and thushe individual growth rates can be added. Neeleman etl. (2001, 2004) described the cultivation by the follow-ng dual substrate model assuming Monod kinetics andxygen excess. Glutamate is essential for both path-ays

(CG, CL) = µmaxfG(CG) + µenhfG(CG)fL(CL)

(1)

CG CL

G(CG) =

KG + CGand fL(CL) =

KL + CL(2)

dV

dt= F in

G+L (3)

2 f Biotechnology 125 (2006) 252–268

Gs

wcocsMrdsbT

u

O

wiTpt(

O

Table 1Constants and initial values for simulation of the dual substrate modelfor Bordetella pertussis

V0 = 3 lCX0 = 0.03 ODCG0 = 9.61 mmol l−1

CinG =500 mmol l−1

CL0 = 16.24 mmol l−1

CinL =835 mmol l−1

YL = 0.018 OD mmol−1

mL = 0 mmol OD−1 h−1

µmax = 0.12 h−1

µenh = 0.055 h−1

KG = 0.5 mmol l−1

KL = 0.5 mmol l−1

YG1 = 0.055 OD mmol−1

YG2 = 0.061 OD mmol−1

mG = 0 mmol OD−1 h−1

Y −1

mµ

wa(

Dtsdr

O

O

3

(ddtd

58 Z.I.T.A. Soons et al. / Journal o

dCX

dt=(

µ − F inG+L

V

)CX =

(µmaxfG(CG)

+ µenhfG(CG)fL(CL) − F inG+L

V

)CX (4)

dCG

dt= F in

G+L

V(Cin

G − CG) −(

µmaxfG(CG)

YG1

− µenhfG(CG)fL(CL)

YG2+ mG

)CX (5)

dCL

dt= F in

G+L

V(Cin

L − CL)

−(

µenhfG(CG)fL(CL)

YL2+ mL

)CX (6)

lutamate consumption is subject to the following con-traint:

µenhfG(CG)fL(CL)

YG2<

µmaxfG(CG)

YG1(7)

here CG and CL are the glutamate, respectively lactateoncentration, YG1, YG2, and YL2 the biomass yieldsver the different pathways. µmax is the maximum spe-ific growth rate over pathway 1, µenh the “enhancing”pecific growth rate over pathway 2. KG and KL are

onod constants. The biomass growth rate is directlyelated to biomass (CX), specific growth rate (µ), andilution rate (which is described by the incoming sub-trate feed rate (F in

G+L) divided by the volume of theroth (V)). Values used for simulation are given inable 1.

The oxygen uptake rate (OUR) is the sum of oxygensed for growth and oxygen used for maintenance

UR =(

µ

YO+ mO

)CX (8)

here YO is the yield for biomass on oxygen, and mOs the maintenance coefficient for biomass on oxygen.he oxygen transfer rate between gas phase and liquid

hase is proportional to the concentration gradient inhe interfacial area and the mass transfer coefficientkLa)

UR = OTR = kLa(Oh2 − DO) (9)

Cct

O = 0.041 OD mmol

O = 0.41 mmol OD−1 h−1

ˆ O = 0.16 h−1

here Oh2 is the oxygen concentration in the headspace

t the gas–liquid interface following Henry’s lawNeeleman, 2002).

The output of the process (OUR) is calculated fromO, Oin

2 , and kLa. In practice, DO measurements con-ain a high level of noise increasing with OUR. Inimulations used for design and tuning, noise is intro-uced in the model by adding uniformly distributedandom noise as function of OUR

UR = OUR + OURnoise,

URnoise(OUR) = 0.05 OUR rand(1) (10)

.2. Model for dissolved oxygen control

The model for the cultivation of B. pertussisNeeleman et al., 2001, 2004) is extended with theissolved oxygen control loop. The development ofissolved oxygen in time is described by the oxygenransfer rate minus the oxygen uptake rate minus theilution due to the substrate feed rate

dDO = OTR − OUR − F inG+L DO (11)

dt V

ontrol of dissolved oxygen is based on a master-slaveontrol system. The inner or slave loop uses values ofhe oxygen concentration in the headspace (Oh

2) cal-

Z.I.T.A. Soons et al. / Journal of Biotechnology 125 (2006) 252–268 259

ontrol f

cvttp(

cio

Ts

O

wooit

O

F2

4

cb

cvaMI(Fmeagfgtmo

4

gdraβ

r

µ

I

Fig. 3. Master-slave c

ulated from the oxygen mass balance. The controlariable is the oxygen concentration in the gas flowo the headspace (Oin

2 ). The outer or master loop useshe dissolved oxygen measurement and controls the setoint of the slave controller via an ‘auxiliary’ variableOa

2). The situation is given in Fig. 3.The oxygen concentration in the headspace (Oh

2)alculated from the mass balance. Oh

2 is the incom-ng minus the outgoing amount of oxygen minus thexygen transfer rate

dOh2

dt= FO2

Vh(Oin

2 − Oh2) − OTR (12)

he ‘auxiliary’ variable becomes (master PI control,ee Fig. 3)

a2 = KC(DOset − DOsensor)

+∫ t

0

KC

τI(DOset − DOsensor)dt + C (13)

here DOsensor is the output of the sensor for dissolvedxygen and C is the nominal value. The incomingxygen fraction is calculated from a calculated “auxil-ary” variable (Oa

2). The incoming oxygen concentra-ion (Oin

2 ) becomes (slave PI control, see Fig. 3)

in2 = Kh

C(Oa2 − Oh

2)+∫ t

0

KhC

τhI

(Oa2−Oh

2)dt + C (14)

inally, the response time of the sensor, which is around0 s, is modelled by a first order system

dDOsensor

dt= − 1

τsensorDOsensor + 1

τsensorDO (15)

. Specific growth rate control

In order to obtain batch-to-batch consistency andonstant quality, the cultivation of B. pertussis muste controlled. The controller has to maintain the spe-

Fg

µ

or dissolved oxygen.

ific growth rate close to set point in the presence ofarious uncertainties including external disturbancesnd time-varying or not exactly known parameters.odel-reference adaptive control (Berber et al. (1998),

oannou and Sun (1996), and Astrom and Wittenmark1995)) is applied to control the specific growth rate.ig. 4 shows the control diagram. The adjustmentechanism updates the controller gains (K1 and K2)

very minute from the estimated states (µ, CX, and V )nd the set point. Because the set point of specificrowth rate is constant, controller settings are updatedrom the estimated states and the set point specificrowth rate. For derivation of the adaptive control law,he software sensor is considered as an ideal measure-

ent; for simulation of the closed loop and for tuningf the controller, the software sensor is included.

.1. Model-reference adaptive control

Performance specifications of the controller areiven in the terms of a reference model. This modelefines how the specific growth rate ideally shouldespond. A second-order response is preferable to beble to cope with disturbances and offsets. β1 and2 determine the convergence speed of the model-eference controller

+ β1dµ

dt+ β2

d2µ

d2t= µset (16a)

d2µ

d2t= µset − µ

β2− β1

β2

dµ

dt(16b)

ntegration of Eq. (16b) gives

dµ

dt=∫ t

0

µset − µ

β2dt − β1

β2

∫ t

0

dµ

dtdt (17a)

ed-batch cultivation is started as soon as the specificrowth rate drops to the set point (t = 0). With

t=0 = µset (17b)

260 Z.I.T.A. Soons et al. / Journal of Biotechnology 125 (2006) 252–268

del-refe

tb

w

w

pieiBfiwg

wtK

K

IoTKaedA

ttnK

4

l

Fig. 4. Diagram for mo

he reference model for the specific growth rateecomes

dµ

dt=∫ t

0

µset − µ

β2dt + β1

β2(µset − µ) (17c)

ith γ2 = β2 and γ1 = β1

β2(17d)

dµ

dt= µset − µ

γ1+∫ t

0

µset − µ

γ2dt (17e)

here γ1 and γ2 are tuning parameters of the controller.Although closed loop stability of the cultivation

rocess is not an issue because of the exponentiallyncreasing biomass and volume, stability of the refer-nce model can be guaranteed. The reference models stable if γ1 and γ2 are strictly positive numbers.ecause the dynamics of the process plus controller are

orced to follow the dynamics of the reference model,n that case convergence of the error is guaranteed asell. The control law is derived in Appendix A andives

(18a)

vwtb

rence adaptive control.

here K1 and K2 are the controller gains directly relatedo the tuning parameters γ1 and γ2 in Eq. (18b). K1 and

2 are adapted to the changing process circumstances

1= V

γ1(aCinG + bCin

L )and K2= V

γ2(aCinG + bCin

L )

(18b)

n this application (vaccine production) only dissolvedxygen and volume measurements were available.herefore, a software sensor based on an extendedalman filter (EKF) estimates specific growth rate

nd biomass every minute. The controller uses thestimated values. The constants a, b, c, and depend on the model parameters as explained inppendix A.Note that the laws of model-reference adaptive con-

rol plus process differential equations lead to an adap-ive “PI” controller (Appendix A). In this PI control, theominal value (“feed rate calculation”) and the gains1 and K2 are functions of the states.

.2. Controller tuning

According to Bastin and Dochain (1990) closedoop stability cannot be guaranteed a priori. The state

ariables follow an exponentially growing trajectory,hich is characteristic of an unstable behaviour. Hence

he goal of a fed-batch cultivation process is not to sta-ilise it, but to optimise it while keeping an inherently

f Biotechnology 125 (2006) 252–268 261

ut

vbibbi(g

E

rtrgolcbiCmDao(

E

Ogotγ

csafao

4

ehdFsebp

goaiotcOspc

cc

Z.I.T.A. Soons et al. / Journal o

nstable type of behaviour under control. Thereforeuning is performed by minimisation of the error.

The tuning parameters γ1 and γ2 determine the con-ergence speed of the controller. The controller is stabley definition of Eq. (17e), if γ1 and γ2 are strictly pos-tive numbers. The optimal trade-off between trackingehaviour, disturbance rejection, and stability shoulde pursued. Initially, tuning was performed withoutncorporation of dissolved oxygen dynamics (Eqs.12)–(15)). At implementation, tuning on the specificrowth rate only

µ = 1

µset

√∑Nk=1[µ(k) − µset(k)]2

(N − 1)(19)

esults in oscillatory bioreactor control due to interac-ions between dissolved oxygen and specific growthate control (Fig. 2), because time constants of oxy-en and substrate consumption are in the same orderf magnitude. Neglecting dissolved oxygen dynamicseads to improper tuning of the specific growth rateontroller and to oscillations. In contrast to commonelieves, simulation of the process, therefore, shouldncorporate dissolved oxygen control (Eqs. (12)–(15)).ontroller parameters γ1 and γ2 should be tuned byinimising a combination of the errors for µ as well asO in time. The ability to keep the specific growth rate

t the desired set point (Eµ) and the ability to reducescillations (EDO) are balanced in an objective functionE)

= Eµ + EDO = 1

µset

√∑Nk=1[µ(k) − µset(k)]2

(N − 1)

+ 1

DOset

√∑Nk=1[DO(k) − DOset(k)]2

(N − 1)(20)

ptimisation of this objective function (Eq. (20))ives the optimal tuning parameters. Calculation of thebjective function for a range of γ1 and γ2 results inhe profile shown in Fig. 5. It is important to choose1 and γ2 not too small, but the tuning parametersan be chosen larger than the optimal value without

ignificant loss of controller performance. This is ingreement with the practical findings: too small valuesor the controller tuning parameters lead to severe inter-ction and oscillations, whereas values larger than theptimal value have no effect on controller performance.

(pCmt

Fig. 5. Objective function (E) as a function of γ1 and γ2.

.3. Simulation results

Robustness and accuracy tests were performed toxamine controller performance. Several difficultiesave been introduced in the model: time-varying orrifting kinetics, changes in set point, and disturbances.or the purpose of the test, we assumed a drift plus ainus with different frequencies on the model param-ters (Fig. 6). External disturbances are introducedy observation noise (Eq. (10)). In the controller, thearameters were set constant.

Fig. 7A–E shows a characteristic simulation withood performance of the controller. As a result of thebjective function the interference of the controllerss observed in Fig. 2 for the case without consider-ng DO dynamics disappeared. The control was freef oscillations. Furthermore, the controller perfectlyracked the specific growth rate without offsets. Theontroller coped well with changes in set point, noise onUR, and time-varying biomass, volume, kinetics, and

ubstrate yields. Concluding, the adaptive controllerassed the robustness and accuracy tests with flyingolours.

Fig. 7 shows also a comparison of the adaptiveontroller with a standard PI controller, in which theontroller gains are constant during the cultivationFig. 7F). Performance of both controllers is com-

ared by calculating the integral squared error (ISE).ompared to the standard PI-controller the perfor-ance in terms of ISE improves 2.5 times by using

he model-reference adaptive controller. The improve-

262 Z.I.T.A. Soons et al. / Journal of Biotechnology 125 (2006) 252–268

F n for roo way 2f onstant

ma

5

f(ts

wfr

artiwTi

rdf

rfomipilaamwee

ig. 6. Injected time-variation of model parameters during simulation glutamate over pathway 1 (YG1). (C) Yield on glutamate over patheed (Cin

G ). (F) Lactate concentration in the feed (CinL ). (G) Monod c

ent is most pronounced during changes of set pointnd with respect to offset compensation.

. Experimental results and discussion

In the PAT framework, process control is one of theour tools with the goal of ensuring final product qualityFDA, 2004). The controller design in the previous sec-ion is put to a test in a laboratory cultivation. Figs. 8–10how the results.

In compliance with the PAT rules, the cultivationas controlled within tight bounds (Figs. 8 and 9)

or dissolved oxygen, temperature, and specific growthate (and therefore substrates).

The performance of the designed model-referencedaptive controller was satisfactory. The controlleresponds fast to deviations (Fig. 9). It properly trackedhe set point in the presence of various uncertainties

ncluding disturbances on dissolved oxygen, improperorking substrate pumps, and uncertain parameters.he controller properly coped with exponentially

ncreasing biomass. The estimated specific growth

ppir

bustness tests. (A) Maximum specific growth rate (µmax). (B) Yield(YG2). (D) Yield on lactate (YL). (E) Glutamate concentration in theon glutamate (KG). (H) Monod constant on lactate (KL).

ate was controlled close to the set point. The standardeviation was between 0.004 and 0.012 during theed-batch phase.

Time delays change process dynamics and tuningesults and may introduce oscillations. To stay awayrom oscillations, the tuning parameters were doubledr quadruplicated without loss of controller perfor-ance in comparison to their optimal values calculated

n simulation. The experiments showed good controllererformance (see Fig. 9 for doubled controller tun-ng parameters). As forecasted by simulations oscil-ations due to interference of the specific growth ratend the dissolved oxygen controller as in Fig. 2 werebsent with the chosen controller parameters. Further-ore, the controller tracked the specific growth rateithout offsets. Although the specific growth rate was

stimated from a noisy OUR signal, it was properlystimated and controlled.

At the start of the fed-batch (t = 23 h), it hap-

ened that only small amounts of substrates wereumped into the bioreactor due to improper work-ng pumps. As can be seen in Fig. 9, the controllereacted fast by immediately increasing the feed rate,

Z.I.T.A. Soons et al. / Journal of Biotechnology 125 (2006) 252–268 263

Fig. 7. Simulation results with time-varying parameters (Fig. 6)and changes of set point. (A) Oxygen uptake rate (OUR). (B)Specific growth rate (µ) using model-reference adaptive control,ISE = 1.2 × 10−4. (C) Biomass concentration (CX). (D) Substratefeed rate. F1: proportional action of the controller, F2: action of theft“t

ap

wtoT

FDc

bp5i

cmtTt

bavot

eet rate calculator, F3: integral action of the controller, and Ftot:otal feed rate. (E) Controller gain. K1: “proportional”-action, K2:integral”-action. (F) Specific growth rate (µ) using standard PI con-rol, ISE = 3.0 × 10−4.

nd bringing the specific growth rate back to the setoint.

Depending on the oxygen demand, agitation speed

as adjusted in steps from 550 to 750 rpm during

he fed-batch phase (Fig. 8). When oxygen limitationccurred, agitation speed was increased with 100 rpm.wo peaks were observed during the cultivation caused

Pcnp

ig. 8. Experimental results for the environment of the cells. (A)issolved oxygen, (B) temperature, (C) agitation speed, (D) substrate

oncentrations: lactate and glutamate.

y increasing agitation speed (Figs. 8 and 9). The firsteak coincides with increasing agitation speed from50 to 650 rpm; the second peak coincides with increas-ng agitation speed from 650 to 750 rpm.

Fig. 10 shows details of two experimental fed-batchultivations for B. pertussis to compare the perfor-ance of the adaptive controller with a fixed PI con-

roller used in previous work (Neeleman et al., 2004).he ISE of the adaptive controller improved up to 10

imes compared to the standard PI-controller.PRN-activity was measured at the end of the fed-

atch. High cell surface densities of protective proteinsre likely to augment the potency of pertussis whole cellaccine. Therefore, it is important to examine densityf outer membrane components per cell besides pro-ein activity per volume (Westdijk et al., 1997). The

RN-activity and density for fed-batch cultivation wasompared with the activity and density of this compo-ent for traditional batch cultivation in Table 2 (batcherformed by Westdijk et al., 1997). First, variation in

264 Z.I.T.A. Soons et al. / Journal of Biotechnology 125 (2006) 252–268

Fig. 9. Experimental results for model-reference adaptive controlwith doubled controller tuning parameters. (A) Measured oxygenuptake rate (OUR). (B) Specific growth rate estimated by the softwaresensor and set point. (C) Estimated biomass concentration (CX). (D)Substrate feed rate. F1: proportional action of the controller, F2:aaa

Pcabfccia

rm

Fig. 10. Detail of two fed-batch experiments with specificgrowth rate control. (A) Using model-reference adaptive control,I(

tcisasltgotttAowonot a problem. Taking into account these requirements,the specific growth rate controller is well applicable onlarge scale using identical tuning parameters γ1 and γ2.

Table 2PRN activity and density after batch and fed-batch cultivation

−1 −1

ction of the feet rate calculator, F3: integral action of the controller,nd Ftot: total feed rate. (E) Controller gain. K1: “proportional”-ction, K2: “integral”-action.

RN-activity and density was smaller after fed-batchultivation despite the high amounts reached. Second,lthough PRN-density was equal or lower after fed-atch than after batch cultivation, PRN-activity aftered-batch was fourfold of the PRN-activity of the batchultivation. Concluding, applying controlled fed-batchultivation instead of traditional fed-batch cultivationncreased batch-to-batch consistency, vaccine potency,

nd quality.

The design of the specific growth rate controlleresults in a controller of PI type. The main achieve-ent is the broad applicability, because the settings in

FT

SE = 2.0 × 10−5. (B) Using PI control with fixed tuning parametersNeeleman et al., 2004), ISE = 2.2 × 10−4.

he adaptive PI controller are the result of the processharacteristics. In contrast to standard PI control, retun-ng is easy when the controller is applied in a differentituation by inserting the corresponding process char-cteristics. Simulations showed that performance of thepecific growth rate controller was good for a 10-foldarger scale bioreactor (figures are not shown). Impor-ant requirements for good performance of the specificrowth rate controller are accurate measurement of thexygen uptake rate and proper dissolved oxygen con-rol. The oxygen uptake rate can be calculated usinghe overall mass balance, in which the composition ofhe gas flows in and out the bioreactor are measured.ttention should be paid where to place the dissolvedxygen sensor in a large bioreactor in order to dealith non-homogeneity on large scale. Also, the designf the bioreactor must be such that supply of oxygen is

PRN activity (mg l ) PRN density (ng OD )

ed-batch 58 ± 4 16.5 ± 1.5raditionalbatch

14.5 ± 5.5 26 ± 10

f Biotechnology 125 (2006) 252–268 265

6

cdfct

•

•

•

•

•

•

•

A

V

Biotechnology BV (Schiedam, The Netherlands) andSiemens NV (The Hague, The Netherlands) in order toimprove the production process by release of biophar-maceuticals on the basis of new online techniques. Theproject is named “PaRel” or Parametric Release. Senter(a subsidiary of the Ministry of Economical Affairs),The Netherlands, supports the project under projectname TSGE3067. Experiments are performed at NVI.

Appendix A. Derivation of the control law

The adaptive controller is derived from combina-tion of two principles: from the dual substrate modelfor growth of B. pertussis on glutamate and lactate andfrom the reference model for ideal response of the spe-cific growth rate controller. The purpose is to comparethe dynamics of the dual substrate model (Eq. (A.3))to the dynamics according to the reference model (Eq.(A.15)) and to derive an adaptive control law for thefeed rate F in

G+L from these equations.

A.1. Dual substrate model for B. pertussis

The dual substrate model for growth of B. pertussis(Neeleman et al., 2001, 2004)

µ(CG, CL) = µmaxfG(CG) + µenhfG(CG)fL(CL)

(A.1)

with Monod kinetics

fG(CG) = CG

KG + CGand fL(CL) = CL

KL + CL(A.2)

Differentiation of Eq. (A.1) with respect to time givesthe behaviour of µ in response to changes in the sub-strate concentrations CG and CL

dµ

dt= µmaxKG

(CG + KG)2

dCG

dt+ fL

µenhKG

(CG + KG)2

dCG

dt

+ fGµenhKL

2

dCL = (µmax + fLµenh)

Z.I.T.A. Soons et al. / Journal o

. Conclusions

To control the metabolic activity during biopharma-eutical production, a specific growth rate controller isesigned and evaluated by simulation and experimentsor the production of the vaccine against whoopingough (B. pertussis). The qualifications of the con-roller are summarized below:

Using the laws of model-reference control in com-bination with mass balances, a stable adaptive “PI”controller was derived. The controller settings areadapted to the changing process dynamics (volume,biomass, and set point for specific growth rate).The method does not require online model identifi-cation, thus avoiding the need for process perturba-tion and complex implementation. Furthermore, itdoes not require online measurement of (part of) thestates. The designed controller only requires onlinemeasurement of the oxygen uptake rate.Tuning based on a combination of deviations inspecific growth rate and dissolved oxygen leads tobioreactor control without interactions between spe-cific growth rate and dissolved oxygen controller.The model-reference adaptive controller has an out-standing performance, both in simulation as wellas in experimental conditions. Although the oxygenconsumption rate contains a high level of noise, thespecific growth rate is controlled accurately.Simulations show that the controller is highly robustfor a large range of disturbances. Experimentsshowed the controller was good for its ability tocope with time-varying kinetics and states, noise,and external disturbances.Control of the specific growth rate at low level resultsin constant and high antigen activity of the vaccine.Application of the controller, therefore, contributesto batch-to-batch consistency and quality. It can bebroadly applied for the production of biopharmaceu-ticals during fed-batch cultivation.The designed control system is a step forward tomeet the PAT objectives as defined by the FDA.

cknowledgments

Wageningen University (WU) and The Netherlandsaccine Institute (NVI) work in a project with Applikon

(CL + KL) dt

× KG

(CG + KG)2

dCG

dt+ fGµenh

KL

(CL+KL)2

dCL

dt

(A.3)

266 Z.I.T.A. Soons et al. / Journal of Biotechnology 125 (2006) 252–268

F set poi

w

BnccsSa

C

R

C

RM

µ

µ

S(

ig. A.1. Diagram for Monod kinetics (fG and fL) as function of the

here glutamate and lactate concentrations in time are

dCG

dt= F in

G+L

V(Cin

G − CG)

−(

µmaxfG

YG1−µenhfGfL

YG2+ mG

)CX (A.4)

dCL

dt= F in

G+L

V(Cin

L − CL) −(

µenhfGfL

YL2+ mL

)CX

(A.5)

ecause the glutamate and lactate concentrations can-ot be measured online, Eqs. (A.4) and (A.5) will beombined with Eq. (A.3) in steps (A.6) to (A.13). Feedoncentrations (Cin

G and CinL ) are much higher than the

ubstrate concentrations in the bioreactor (CG and CL).o the latter can therefore be neglected in Eqs. (A.4)nd (A.5)

inG � CG and Cin

L � CL (A.6)

ewriting Eq. (A.2) gives

G = fGKG

1 − fGand CL = fLKL

1 − fL(A.7) I

a

nt (µ) at various �. (A) fG for glutamate and (B) fL for lactate.

ewriting Eq. (A.1) gives the normalised equations ofonod

maxfG = µ + µenhfGfL and

enhfGfL = µ + µmaxfG (A.8)

ubstitution of Eqs. (A.4), (A.5), (A.7) and (A.8) inA.3) give

dµ

dt= (µmax + fLµenh)(1 − fG)2 1

KG

×(

F inG+L

VCin

G −(

µ + µenhfGfL

YG1

− µ + µmaxfG

YG2+ mG

)CX

)

+ fGµenh(1 − fL)2 1

KL

(F in

G+L

VCin

L

( ) )

− µ + µmaxfG

YL2+ mL CX (A.9)

n these equations the unknowns are the kinetics fGnd fL. In principle, an unlimited number of combina-

f Biote

tNnm

β

Fµ

rc

m

FrM

f

wiµ

w

a

b

c

d

A

Am

toa

wt

K

K

Emt

R

A

A

A

B

B

Z.I.T.A. Soons et al. / Journal o

ions is possible (see Eq. (A.8)). Neeleman (2002) andeeleman et al. (2004) fixed the ratio (β) between theormalised equations of Monod (fG and fL) to obtainetabolic stability

= fL

fG(A.10)

ig. A.1 shows the values of fG and fL at various β and. The white parts of the figure show the admissible

egions of the normalised kinetics with the followingonstraint

ax

(0,

µ − µmax

µenh

)< β <

µmax + µenh

µ(A.11)

or the simulations and experiments in this study aatio of 1 was used. At µset = 0.05 h−1, the normalised

onod equations are linear approximated by

G = vµ and fL = wµ (A.12)

here v and w are constants. Substitution of Eq. (A.12)n (A.9) gives the behaviour of the specific growth rate

in response to the feed rate F inG+L

dµ

dt= a

(F in

G+L

VCin

G − cCX

)+b

(F in

G+L

VCin

L − dCX

)

(A.13a)

here

= (µmax + wµenhµset)(1 − vµset)2 1

KG,

= vµenhµset(1 − wµset)2 1

KL,

= µset − vwµenhµ2set

YG1− µset − vµmaxµset

YG2+ mG,

= µset − vµmaxµset

YL2+ mL (A.13b)

.2. Reference model

Recall the reference model (see Section 4.1)

dµ

dt= µset − µ

γ1+∫ t

0

µset − µ

γ2dt (A.14)

B

C

chnology 125 (2006) 252–268 267

.3. Combination of dual substrate and referenceodel

Combining the reference model (Eq. (A.14)) andhe dual substrate model (Eq. (A.13a)) by eliminationf dµ/dt and subsequent rewriting gives the followingdaptive control law:

(A.15a)

here the controller gains K1 and K2 are directly relatedo the tuning parameters γ1 and γ2 via

1 = V

γ1(aCinG + bCin

L )and

2 = V

γ2(aCinG + bCin

L )(A.15b)

q. (A.15b) shows that the controller gains are auto-atically adapted to the changing process condi-

ions.

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