automated fed-batch culture of kluyveromyces fragilis based on a novel

Biochemical Engineering Journal 9 (2001) 221231

Automated fed-batch culture of Kluyveromyces fragilis based on a novelmethod for on-line estimation of cell specific growth rate

Zairossani M. Nor, Melih I. Tamer, Jeno M. Scharer, Murray Moo-Young, Eric J. JervisDepartment of Chemical Engineering, University of Waterloo, Waterloo, Ont., Canada N2L 3G1

Received 11 December 2000; accepted after revision 16 August 2001

Abstract

A corrected feed-forward control strategy was developed for automated substrate feeding in aerobic fed-batch cultures. The controlstrategy incorporates a novel method for on-line estimation of specific growth rate as a performance indicator of the fed-batch culture. Theestimation is based on the measurement of the maximum substrate uptake rate (MSUR) using on-line dissolved oxygen (DO) concentrationdata and mass balances. It allows the controller to track changes in the specific growth rate to compensate for process disturbances. Thecontrol strategy was applied to fed-batch culture of Kluyveromyces fragilis to maximize the volumetric productivity of lactase. A maximumvolumetric lactase productivity of 2.98 U/ml h was achieved. The control was shown to be stable throughout the culture period even atthe highest cell density of 69 g/l. This technique is applicable to various aerobic systems, especially for microbial cultures showing highspecific oxygen uptake rates, since it only requires on-line measurement of DO concentration without the need for off-gas analysis. In acomparison carried out with three other fed-batch control strategies (DO-stat, exponential feeding and exponential feeding with manualfeedback control), the corrected feed-forward control strategy exhibited the best performance by achieving the highest volumetric lactaseand biomass productivity. Crown Copyright 2001 Published by Elsevier Science B.V. All rights reserved.

Keywords: Fermentation; Aerobic processes; Fed-batch culture; Kinetic parameters; Yeast; Lactase

1. Introduction

Fed-batch culture has been used successfully to improvethe productivity of both homologous and heterologous pro-teins in high cell density cultures. It is an effective techniquefor overcoming cellular regulatory mechanisms such as theCrabtree effect [1], catabolite repression [2] and productinhibition [3]. Moreover, several recent studies have demon-strated the ability of fed-batch culture to enhance plasmidstability in recombinant cell fermentations [4,5]. Fed-batchcultures are frequently operated in feed-forward modeswith feedback controls to provide a corrective scheme tocompensate for process disturbances and model inaccura-cies. The effectiveness of feedback controls depends on thechoice of control variables and their ability to reflect cultureperformance [6].

In a fed-batch culture with direct feedback control, theconcentration of carbon source is typically used as thedirect feedback variable. However, lack of robust sensorsor analytical equipment for the on-line measurement ofcarbon source concentrations limits the application of this

Corresponding author. Tel.: +1-519-888-4567; fax: +1-519-746-4979.E-mail address: [email protected] (E.J. Jervis).

control [7,8]. The variables commonly used in fed-batchcultures with indirect feedback control are dissolved oxy-gen (DO), respiratory quotient (RQ), pH, partial pressure ofCO2 (pCO2) and ethanol concentrations [9]. Except for DOand pH, determination of these variables requires special-ized sensors or analytical equipment in addition to sensorstypically installed in fermenters.

An obvious problem with the implementation of feed-forward control is the knowledge of the projected substratedemand, which is difficult to estimate and depends on cellconcentration, specific growth rate and cell specific yield.Several methods have been developed for on-line estimationof cell concentration, involving either direct measurementsusing on-line sensors such as laser turbidimeter [7] or in-direct estimations using mass balances based on off-gasanalyses from the fermenter [9,10]. Estimation of cell spe-cific growth rate is usually made after the value for cellconcentration is available, although the two variables canbe estimated independently. The specific growth rate canbe estimated by using either appropriate models based oncell growth kinetics [9] or optimal estimators based on theextended Kalman filter (EKF) [11].

This work describes the development of a correctedfeed-forward control strategy that incorporates a novel

1369-703X/01/$ see front matter Crown Copyright 2001 Published by Elsevier Science B.V. All rights reserved.PII: S1 3 6 9 -703X(01 )00147 -4

222 Z.M. Nor et al. / Biochemical Engineering Journal 9 (2001) 221231

Nomenclature

f accumulated lactose (g)F lactose feed rate (g/h) or (l/h)G lactose pulse feed during MSUR test (g)H excess lactose during MSUR test (g)MSUR maximum substrate uptake rate (g/h)S lactose concentration in medium

(g lactose/g medium) or (g/l)Si lactose concentration in feeding

solution (g lactose/g feed) or (g/l)t culture time (h)T fed-batch feeding interval (h)V culture volume (l)X cell concentration (g/l)X0 initial cell concentration (g/l)YX/S cell yield on lactose (g cell/g lactose)Greek symbol cell specific growth rate (h1)

method to estimate the specific growth rate and to compen-sate for process disturbances. The control strategy employson-line estimation of the specific growth rate as a perfor-mance indicator of the fed-batch culture. The estimation isbased on mass balances and on-line measurement of themaximum substrate uptake rate (MSUR) as feedback pa-rameters. The MSUR measurement requires only on-linemonitoring of DO levels in the medium. Significantly, itenables the estimation of the specific growth rate withouton-line measurement of cell density, substrate concentra-tions or off-gas analyses. Thus, the strategy requires lowoperational cost and is applicable to fermenters equippedwith standard probes. It represents a simple alternativestrategy for the implementation of a feed-forward controlwith feedback in aerobic fed-batch cultures.

In this study, a wild-type Kluyveromyces fragilis was em-ployed for the production of intracellular -galactosidase,EC 3.2.1.23 (lactase). K. fragilis exhibits the Crabtree ef-fect, causing undesirable lactose fermentation to ethanoldue to high lactose concentrations in the culture mediumeven under highly aerobic conditions [12]. The volumetriclactase productivity in high cell density fed-batch culture ofK. fragilis was maximized using the corrected feed-forwardcontrol strategy to regulate lactose feeding. The perfor-mance of the feed-forward control strategy was comparedwith that of DO-stat, exponential feeding and exponen-tial feeding with manual feedback control for improvingvolumetric lactase productivity of K. fragilis.

2. Control strategy development

The general growth dynamics of microbial cells in vari-able volume fed-batch cultures has been described previ-ously [6,13]. Under balanced growth conditions, exponential

cell growth in a variable volume fed-batch culture is givenby

VX = V0X0 exp(t) (1)where V and V0 are the culture volume and the initial vol-ume, respectively, is the specific growth rate, X and X0are the cell concentration and the initial cell concentrations,respectively; and t is the culture time. The instantaneousfeed rate of a growth-limiting substrate, F at a constantspecific growth rate is given by

F = YX/S(Si S)V0X0 exp(t) (2)

where YX/S is the theoretical cell yield on substrate, and Siand S are substrate concentrations in the feeding solution andin the reactor, respectively. The unit of F can be expressedas mass of substrate per h or volume of substrate per h de-pending on the unit of S and Si . Eq. (2) gives the design forfed-batch cultures with exponential feeding schedule and itis the basis for the design of feed-forward control strategies.

In Crabtree-positive yeast cultures, cell metabolism mustutilize the oxidative pathway to prevent the Crabtree effectand thus ethanol formation. In a fully aerobic culture, theCrabtree effect has been widely accepted to be initiated byhigh substrate concentrations in culture medium althoughflux imbalances through glycolysis in cell metabolisms havebeen shown to initiate the Crabtree effect [14,15]. There-fore, in a substrate-limited culture, substrate concentrationsshould be maintained below the critical level for the on-set of the Crabtree effect. An indirect control of substrateconcentration is possible by monitoring the specific growthrate due to a direct relationship between the two variables.This is achieved by matching the substrate feed rate withthe exponential growth rate according to Eq. (2), resulting ina constant specific growth rate while maintaining substrateconcentrations below the critical level.

Feedback control is required to compensate for devia-tions in the cell specific growth rate and cell yield. Althoughcontrol of substrate feeding according to Eq. (2) shouldtheoretically fix , deviations in can occur due to processperturbations, changes in growth conditions or inaccuracyin the growth models employed. Often, on-line estimationof the cell yield is unnecessary since it can be assumedto be constant provided there is no abrupt change in cellmetabolism [16]. Therefore, a fast and accurate method foron-line determination of specific growth is important foreffective applications of Eq. (2).

The adaptive feed-forward control strategy developed inthis study includes a new method for estimating the specificgrowth rate based on on-line monitoring of MSUR. Theconcept of MSUR was first introduced by Konstantinov [17]to estimate the degree of glucose limitations and its physi-ological effects in mammalian cell culture. Unlike substrateconcentration, MSUR reflects the potential ability of cellsto utilize the substrate. On-line monitoring of MSUR hasbeen used for automated control of substrate feeding in

Z.M. Nor et al. / Biochemical Engineering Journal 9 (2001) 221231 223

aerobic fed-batch cultures of recombinant Escherichia coli[18] and recombinant Saccharomyces cerevisiae [5].

Conventional control strategies based on MSUR areessentially continuous feeding protocols with stepwise in-crease in feed rate according to on-line measurement ofMSUR. Initially, substrate is continuously fed at a constantrate for a fixed feeding period. Substrate feeding is theninterrupted and a MSUR test is carried out to estimate anew feed rate for the next feeding period. Substrate feedingresumes with the new feed rate and the entire estimationprocess is repeated. Due to the constant feed rate, the cellswill be subjected to substrate starvation towards the end ofeach feeding interval owing to increased cell density. Thus,this strategy only supports linear growth because the MSURdesign underestimates the actual culture demand at the endof a feeding interval.

Improvement of the original fed-batch control strategybased on MSUR requires a method to estimate specificgrowth rate to enable exponential feeding during each feed-ing interval. If this can be obtained from the MSUR test,overall exponential growth rates can be realized. Signifi-cantly, it allows the control strategy to track changes in thespecific growth rate to compensate for process deviations.This approach can prevent substrate overfeeding and min-imize the Crabtree effect to maintain balanced exponentialcell growth. Thus, the method will enable a feed-forwardcontrol strategy without requiring on-line measurement ofeither substrate or cell concentrations.

Fig. 1 shows time profiles of accumulated feed, lactosefeed rate, residual lactose and DO during the period ofMSUR test as adapted from Oh et al. [5]. The only processvariable being monitored during the test is the DO concen-tration. The MSUR test is essentially an on-line perturba-tion and response analysis procedure. The test is initiated bystopping substrate feeding and the DO is used to monitor thetime taken by the cells to utilize the remaining substrate. Arapid increase in DO level is detected when the substrate isdepleted since the cells stop consuming oxygen for oxida-tive metabolism. At this instant, a pulse feed with a known

Fig. 1. Time profiles of related process variables during on-line measurement of MSUR as adapted from Oh et al. [5].

amount of substrate is injected into the culture. The amountof pulse feed is designed to provide substrate supply for ashort period of time and the resulting substrate concentrationshould not exceed the critical level. DO is once again usedto detect the time for complete substrate utilization. Imme-diately after the second rapid increase in DO, the MSURcan be calculated according to Eq. (3) to estimate the newfeed rate for the next feeding period

MSUR = Gt3 t2 (3)

where G is the amount of substrate in the pulse addition, t2and t3 represent the time of start and end of MSUR test. Theprocedure described thus far represents the original designof the MSUR test [5].

It was found that significant additional information couldbe extracted from the MSUR test that readily allows estima-tion of specific growth rate. By measuring the time taken bythe cells to consume the excess lactose at the beginning ofthe test (t1 to t2), it is possible to relate the amount of excesssubstrate to cell density and thus specific growth rate. Theexcess substrate can be estimated from the known amountof substrate added during pulse feed using a linear correla-tion between time periods of t1 to t2 and t2 to t3. The linearcorrelation is justified by assuming that the cell density re-mains essentially constant for the short period from t1 to t3.As the initial cell density at the start of fed-batch culture isknown, Eq. (2) and a substrate mass balance can be used toestimate the actual specific growth rate and final cell densityof the first feeding interval that would give the same amountof excess substrate. This procedure is used to estimate thespecific growth rate for each subsequent feeding interval.

Fig. 2 shows hypothetical profiles of predicted and actualaccumulated substrate feed during a fed-batch culture withthe corrected feed-forward control strategy. It illustrates op-erations of the fed-batch culture that enables the updates ofspecific growth rate and cell density estimates. Known val-ues of initial cell density and set-point specific growth rateare used for the first feeding interval. The specific growth


Fig. 2. Schematic diagram of process parameter updates during fed-batch culture with the corrected feed-forward control strategy. T1, T2, and T3 representfed-batch feeding intervals.

rate estimate for the controller is set to be 5% higher than theset-point rate to ensure a small substrate excess at the end ofthe feeding interval. An accurate initial cell density must beprovided since it affects the accuracy of later specific growthrate estimates. The initial cell density is the only indepen-dent reference value for specific growth rate estimations insubsequent MSUR tests.

The mathematical derivation for estimating specificgrowth rate and cell density are carried out with referenceto Figs. 1 and 2. The main assumptions are the specificgrowth rate and the cell yield remain constant during eachfeeding interval and the culture is carbon source limited.Thus, the specific growth rate obtained represents an overallrate rather than an instantaneous rate. The first feeding in-terval, T1 in Fig. 2 is used as a model for the mathematicalderivation. If a balanced growth is achieved, energy for cellmaintenance is negligible, thus the maintenance coefficientis omitted in the mathematical derivation. In addition, if thespecific growth rate is constant during the feeding interval,S can be assumed to be constant with 1 as the set-pointspecific growth rate. The excess substrate, H1 is obtainedby assuming a linear relationship with the pulse feed, G asfollows:

H1 = t2 t1t3 t2G (4)

The accumulated feed, f1, during the interval T1 is obtainedby integrating Eq. (2). T1 is represented by the period fromti to tf

f1 =1V0X0

YX/S(Si S) tfti

exp(1t) dt (5)

A mass balance on substrate is carried out for the interval T1to obtain a relationship between the actual specific growth

rate (1) and the set-point rate (1)

f1 H1 = V0X0YX/S(Si S) [exp(1t)]

tfti

(6)

For each feeding interval, ti = 0 as time count is restarted atthe beginning of each interval. The right hand side of Eq. (6)represents the actual accumulated feed during interval T1and it can be solved to obtain a final equation for estimating1

1 = 1tf

ln[

exp(1tf )H1YX/S(Si S)

V0X0

](7)

The final cell density of the feeding interval can be estimatedfrom Eq. (1) as follows:

X1 = 1VV0X0 exp[1(tf ti )] (8)

Eq. (8) can be solved if values of V, V0 and X0 are available.These values are obtained by writing a control program tokeep track of the changes in culture volume from substratefeeding and increase in cell density according to Eq. (1).The value of 1 and X1 obtained for the previous feedinginterval will be set as the set-point specific growth rate andinitial cell density, respectively, for the subsequent interval.

The accuracy of the MSUR test for estimation of specificgrowth rate is dependent on its ability to detect when sub-strate is completely exhausted (Fig. 1). A general method todetect substrate exhaustion based on the DO response profilehas to be developed to determine the moment of completesubstrate consumption. Pattern recognition is not straight-forward as cell density, type of cell metabolism, presenceof other carbon sources and various culture conditions in-fluence the DO response. Information on this aspect is stilllacking and is not explicitly dealt with in the work carried


out by Oh et al. [5] and Takagi et al. [18]. In this study, asimple pattern recognition method has been used for detec-tion of substrate exhaustion.

During the MSUR test, the cells are forced to undergo twoperiods of substrate starvation. Although the starvation pe-riods are brief, they cause fluctuations in DO and may leadto adverse effects on the cell metabolism and physiology[17]. Paca [19] showed that aerobic starvation of Bakerssyeast caused immediate changes in catabolic potentials andthe ability of the cells to assimilate glucose was graduallylost. The frequency of MSUR tests should be minimized toreduce the effect of aerobic starvation on the overall cultureperformance. The requirement for reducing the frequencyof MSUR test during a fed-batch culture can be achievedby implementing an adaptive control strategy. The durationof each feeding interval in Fig. 2 can be varied dependingon the performance of the culture feeding model in main-taining the set-point specific growth rate. Thus, the periodof feeding interval between tests can be prolonged or short-ened depending on the error of the predicted . This willminimize the effect of MSUR test on cell growth withoutcompromising controller accuracy and sensitivity.

3. Materials and methods

3.1. Microorganism and culture medium

The yeast strain used was a wild-type mutant of K.fragilis, obtained from Professor Yukio Kakuda of theUniversity of Guelph, Ontario, Canada. A defined mediumwas employed based on the improvement of the mediumreported by OConnor et al. [9] for high cell density Bakersyeast cultures (Table 1). The vitamin solution was improvedfor K. fragilis culture by an on-line medium improvementmethod adapted from the method introduced by Matelesand Battat [20]. Vitamin solutions were filter-sterilized(0.45m pore diameter, Gelman Sciences, Ann Arbor, MI)and stored at 4C for less than 1 month.

A continuous trace salt feeding method was adaptedfrom a strategy applied to high cell density yeast fed-batchculture by Suzuki et al. [21]. The feeding method wasdesigned to maintain constant concentrations of trace saltsin the culture medium by predicting trace salt consumption.This feeding method resulted in the formulation of tracesalt solution given in Table 1. In this study, a continuoustrace salts feeding method was applied and coupled withthe lactose feeding solution. By assuming a constant min-eral composition of K. fragilis, the composition of tracesalt feeding solution was formulated. Trace salt solutionwas prepared in 0.1 M H2SO4 and sterilized in an auto-clave. A food-grade -lactose monohydrate with 97% pu-rity was used (Les Fromages Saputo Ltee., St. Hyacinthe,Quebec).

Seed cultures were used as inoculum in all experimentsto ensure cultures were inoculated with cells possessing

Table 1Composition of the defined medium for K. fragilis cultureComponent Concentration

Lactose (g/l) 35.0Mineral salts medium (g/l)

NH4H2PO4 10.0KH2PO4 10.0CaCl22H2O 0.5NaCl 0.5MgSO47H2O 3.0

Vitamin solution 10.0aTrace salt solution 2.0aAntifoam (silicone, Sigma Antifoam 289) 0.2a

Trace salt solution (g/l)FeSO47H2O 5.40H3BO3 0.20CuSO45H2O 0.85KI 0.20MnSO4H2O 0.16Na2MoO42H2O 0.80ZnSO47H2O 4.40CoCl26H2O 0.80

Vitamin solution (mg/l)Biotin 30.0Ca-pantothenate 400.0Folic acid 40.0Inositol 1800.0P-aminobenzoic acid 80.0Niacin 200.0Pyridoxine 160.0Riboflavin 80.0Thiamine 360.0

a These values are in ml/l.

similar physiological characteristics. The seed cultures wereprepared from a shake flask culture in defined mediumby inoculating a loopful of the master plate culture intoa 250 ml flask containing 50 ml of defined medium. Theculture was allowed to reach mid-exponential growth phasebefore harvesting and preserved in the original broth withsterile glycerol solution added to 16% v/v. The culture wasaliquotted in 1.5 ml microcentrifuge vials, each containing1.0 ml of culture and stored at 55C.

3.2. Analytical methods

Cell concentration was measured by gravimetric andturbidimetric methods. For the gravimetric measurement,cell dry weight was obtained by drying the washed cellsat 80C overnight. The turbidimetric method was carriedout by measuring the absorbance of washed cells at 650 nmwith a spectrophotometer (Pye Unicam SP6-550 UVVIS,Philips Scientific and Analytical Equipment).

Lactose concentration in the cell free samples was deter-mined by a colorimetric method using the phenol-sulfuricacid reaction as described by Dubois et al. [22]. Ethanolconcentration was measured using a Hewlett-Packard 5890series II gas chromatograph, equipped with HP-624 column


and a flame-ionization detector (FID). Cell disruption wascarried out prior to the assay of intracellular lactase. Thecells were separated from 2 ml of sample by centrifugationand resuspended in 6 ml of phosphate buffer at pH 7.3. Lac-tase was released by disrupting the cells with 7.0 g glassbeads using a vortex mixer for 5 min. Cell homogenate wasseparated from the aliquot containing the lactase by cen-trifuging the samples at 5000 rpm at 4C for 10 min. Lactaseactivity was measured according to the Sigma enzymaticassay method (Sigma Chemical Co., St. Luis, MO) usingo-nitrophenyl -d-galactopyranoside (ONPG) as a substrate.One unit of enzymatic activity (U) is defined as the amountof lactase that hydrolyzes 1.0mol of ONPG per minute atpH 7.3 at 37C.

3.3. Fed-batch cultures

Fed-batch cultures required inoculum preparation involv-ing two stages of preculture. In the first stage, 1 ml of seedculture was inoculated into a 250 ml flask containing 50 mlmedium and incubated at 30C in a rotary shaker at 160 rpmfor 19 h. This was used to inoculate the second preculturein a 2 l flask containing 450 ml medium and incubated un-der the same conditions for 16 h. All batch and subsequentfed-batch cultures were carried out in a 15 l stirred tankfermenter, equipped with two five-blade marine impellers(MCS 10, MBR Bioreactor AG, Wetzikon, Switzerland).The fermenter was equipped with controllers for pH, tem-perature, agitation rate and DO concentration. Culture con-ditions were set at 33C and pH 4.5. The pH was controlledby the addition of 20% w/v ammonia solution. Initial agita-tion speed and air flow rate were set at 500 rpm and 2 vvm,respectively. The agitation speed was varied at a fixed airflow rate during the culture to maintain the DO concen-tration above 20% of air saturation. At cell concentrationsabove 40 g/l, pure oxygen was mixed with air to meet thehigh oxygen demand during fed-batch operation.

A 10% v/v inoculum size was used for the initial 4 l batchcultures. Batch cultures were operated for 13.5 h, whichwas the estimated period for complete utilization of initiallactose in the medium. Fed-batch cultures were started byinitiating substrate feeding using a computer-controlledperistaltic pump. The composition of the feed solution wasthe same as that described in Table 1 except the lactose con-centration was 360 g/l and the concentrations of mineralssalts and vitamin solutions were increased 10-fold.

3.4. The corrected feed-forward control

Control of the fed-batch cultures was implemented us-ing the LabView graphical programming software pack-age (National Instruments, Austin, TX), installed on aPentium-based personal computer (PC). LabView wasused for on-line monitoring of all process variables, estima-tion of kinetic parameters and control of substrate feed rate.

Fig. 3. Flow diagram of the corrected feed-forward control strategy withinduced starvation period.

The pH, temperature, DO and agitation of the culture werecontrolled separately by the process control unit of the MBRfermenter. A peristaltic pump and an electronic balance (formonitoring the amount of feed solution) were controlled bythe LabView control program through direct interfaceswith the PC. The initial settings of the fed-batch culture were = 0.20 h1, YX/S = 0.50 g cell/g lactose and S = 0.5 g/l.From our preliminary studies, the critical specific growthrate before the onset of the Crabtree effect for K. fragilis wasestimated to be 0.20 h1 corresponding to lactose concen-tration of 4.4 g/l. The corrected feed-forward algorithm wasimplemented according to the flow diagram shown in Fig. 3.

Production of lactase by K. fragilis in the presence oflactose is growth-associated and the maximum induction oflactase synthesis is achieved at low lactose concentrations.Therefore, to maximize lactase productivity, the fed-batchculture was designed to achieve the highest specific growthrate possible without initiating the Crabtree effect whilemaintaining very low lactose concentrations in the medium.During each feeding interval, the substrate feed rate wasupdated every 30 s according to Eq. (2). The period of the


first feeding interval was set for 1 h. The MSUR test wasconducted immediately at the end of each feeding interval.Depending on the accuracy of the estimated specific growthrate in comparison with the desired rate, the feeding periodwas varied from 0.5 to 1.5 h. This adaptive feature permitsminimization of process disturbances when the predictionis performing satisfactorily. Due to increasing cell density,the amount of the pulse feed was adjusted to maintain rela-tively constant MSUR test periods throughout the fed-batchculture.

3.5. Comparison of fed-batch control strategies

Three fed-batch control strategies were used for com-parison with the corrected feed-forward control strategy:DO-stat, exponential feeding and exponential feeding withmanual feedback control. DO-stat is an intermittent feed-ing strategy in which a constant level of DO in the culturemedium is maintained by controlling substrate feed rate. Inthis study, the DO-stat was set to maintain DO levels in arange from 25 to 35% air saturation. Exponential feedingstrategy is based on a continuos feeding with a fixed expo-nential profile. Theoretically, this strategy will allow expo-nential cell growth by feeding substrate according to growthdemand given by Eq. (2).

Exponential feeding strategy with manual feedback con-trol is exponential feeding strategy which includes a man-ual feedback control to compensate for fluctuations in due to process perturbations. This approach was based onthe assumption that the cell growth is slow enough to al-low for manual adjustment of feed rates; was updated on1 h intervals and off-line determination of was obtainedby measuring cell density of two consecutive samples us-ing the spectrometric method. Eq. (1) was used to calculatethe overall to account for the increase in culture volumewith substrate addition. The estimated time for determining after each sampling is 15 min. The update was enteredin the LabView control program to correct for the feedingrate. Except for DO-stat, all control strategies were operatedusing the same initial settings as described in Section 3.4and implemented using LabView control program

4. Results and discussion

4.1. Fed-batch culture

Profiles of cell density, ethanol and lactose concentrationduring fed-batch culture are shown in Fig. 4a. The adaptive,corrected feed-forward control strategy maintained an expo-nential growth throughout the culture although a brief lagperiod was observed initially from 1 to 2 h. A cell densityof 69.1 g/l was reached in 14.25 h, corresponding to a volu-metric biomass productivity of 4.21 g/l h. This productivityrepresents a 12-fold improvement over that of batch cultures

Fig. 4. Preliminary fed-batch culture with the adaptive, correctedfeed-forward control strategy. Fed-batch control settings: = 0.20 h1,YX/S = 0.50 g cell/g lactose and S = 0.5 g/l, T1 = 1.0 h. (a) Profilesof cell density (), lactose concentration () and ethanol concentration(H17009). (b) Profiles of lactase volumetric activity () and specific lactaseactivity ().

[23]. The maximum cell density of 69.1 g/l obtained is higherthan observations for other fed-batch cultures of K. fragilisreported previously [24]. After 6 h, the increasing trend ofethanol and lactose concentrations indicated that the culturewas being overfed. However, the overfeeding had minimalimpact on cell growth since the strategy was able to controlthe concentration of ethanol at low levels. During the cul-ture, the substrate feed rate varied from 54.0 to 620.6 g/hwhile the specific growth rate was controlled between 0.15and 0.20 h1.

Fig. 4b shows profiles of lactase production duringthe fed-batch culture. Volumetric lactase activity exhib-ited an exponential profile with a maximum final activ-ity of 45.26 U/ml. A lactase volumetric productivity of2.98 U/ml h was achieved. A linear profile of biomassspecific lactase activity was obtained for the first 4 h andthe activity remained relatively constant at 2.0 U/mg cellfor the remaining culture period. The specific activity wasexpected to maintain a constant value during a fully aerobic


Fig. 5. Cellular yield of K. fragilis on lactose in fed-batch culture with thecorrected feed-forward control strategy. The overall yield is 0.490.008 gcell/g lactose (at 95% confidence level and R2 = 0.998).

exponential growth (oxidative metabolism) where thepredominant cellular activity is cell-budding [25].

4.2. Performance of fed-batch control and error analysis

The main assumption of the feed-forward control model(Eq. (5)) is constant YX/S during the fed-batch culture. Theoverall effectiveness of the control strategy and the accuracyof the estimation by the MSUR test is strongly influencedby the value of YX/S. In principle, YX/S will remain constantat a value close to the maximum theoretical value if cellmetabolism is directed towards fully oxidative pathways andbalanced growth is provided. Fig. 5 shows the plot of celldensity versus the cumulative lactose concentration duringthe fed-batch culture. The overall yield is represented by theslope of the graph, estimated by linear regression as 0.490.008 g cell/g lactose (at 95% confidence level and R2 =0.998) with the instantaneous cell yields ranged from 0.41to 0.58 h1. The invariant cell yield obtained demonstratesthe validity of the constant YX/S assumption.

Accuracy of estimation by the MSUR test during thefed-batch culture is shown in Fig. 6. The plot illustrates thecumulative sum of errors (CuSum) in , calculated fromthe difference between the actual and the estimatedfrom the MSUR test. The actual was calculated using celldensity data based on Eq. (7) which incorporates dilutioneffects caused by the feed solution. The CuSum shows thatthe control strategy consistently overestimated except at 7,12 and 13.5 h. As implied by the design of the control strat-egy in Fig. 3, this bias is expected since the assigned bythe control program represents the maximum theoretical for the culture. Consequently, the actual would never ex-ceed the set for each feeding interval. To allow for highergrowth potentials in subsequent intervals, the controller wasdesigned to increase the if negligible excess lactose wasdetected during the MSUR test. This approach ensures that

Fig. 6. Cumulative sum of errors (CuSum) in the specific growth rateestimations by the on-line MSUR test.

the maximum is not limited to the set-point set at thestart of the fed-batch culture. It is suspected that the maxi-mum growth rate was exceeded at 7, 12 and 13.5 h due to cellgrowth on accumulated metabolites as alternative carbonsources.

The major source of process deviations which could sig-nificantly influence controller performance is errors in themodel parameters (YX/S, X0 and 1) assigned in Eq. (5).As illustrated by the CuSum (Fig. 6), a major proportionof these error occurred in the first 5 h. During this periodthe cumulative error increased at an overall rate of 0.03 h1.Beyond this period, the cumulative error stabilized and in-creased at a lower overall rate of 0.007 h1. These resultssuggest the influence of cell density on the accuracy of estimation by the MSUR test. The fraction of time spent forall MSUR tests is 7% of the 14 h fed-batch culture period.This fraction of culture time was shown to have negligibleeffects on cell growth and the overall culture performance.Robustness of the corrected feed-forward control strategy isindicated by its stability at high cell density and the CuSumshown in Fig. 6. The linear trend obtained particularly after5 h implies that the control strategy has low sensitivity toprocess deviations.

4.3. DO response profile analysis

Observations of typical DO profiles during prelimi-nary fed-batch culture studies of K. fragilis suggested therequirement for establishing a general DO response patternrecognition criteria for the detection of substrate exhaustion.The profiles indicated that the pattern could be identified byseveral characteristics, the simplest ones being the magni-tude of DO change from the point of lactose exhaustion andthe rate of increase in DO during the exhaustion period. Theuse of the rate of DO increase is less reliable if DO estimatesare influenced by noisy measurements. A data smoothingtechnique was developed to minimize the effects of mea-surement noise. Therefore, both the magnitude of increase


Fig. 7. Profiles of DO during MSUR test (a) initial stage (1 h) of fed-batchculture; (b) at the middle stage (6 h) of fed-batch culture.

and the rate of change of DO were included in the design ofthe controller for detection of complete substrate exhaustion.

Fig. 7a and b show DO profiles during MSUR tests at 1and 6 h of the fed-batch culture, respectively. The figures,plotted on the same time scale represent variations of DOpatterns and test periods as the culture progressed from theinitial cell density of 11.2 g/l to the final density of 69.1 g/l.The periods of MSUR tests varied from 480 to 128 s dur-ing the fed-batch culture. Both figures illustrate another timepoint (t4) introduced in the MSUR test design in additionto those described in Fig. 3. The period from t3 to t4 is abrief delay designed to allow the culture to consume accu-mulated ethanol that could lead to growth inhibitions. Theperiod, detected by the magnitude of DO change from t3 tot4, is expected to prevent the accumulation of ethanol forthe subsequent MSUR tests.

The effect of multiple carbon sources on DO responsepattern recognition during MSUR test is shown in Fig. 7a.The presence of low levels of ethanol (remaining after thebatch phase of the culture) masked the normally sharp risein DO following lactose exhaustion. Ethanol consumptionis represented by a period of steady DO level prior to the

lactose pulse feed. As a result, the period of excess lactoseconsumption was artificially extended, causing overestima-tion of excess lactose and thus underestimation of . Appar-ently, alternate carbon sources in the culture medium imposea significant effect on estimation of especially at low celldensities. The DO response pattern recognition criteria musttherefore be adjusted to account for other potential carbonsources to minimize the overestimation of excess substrate.In principle, a set of DO response pattern recognition crite-ria should be generated and applied for various MSUR testconditions. Fig. 7b shows the DO profile during lactose de-pletion at high volumetric oxygen uptake rates obtained atcell density of 26.2 g/l. The profile represents the desired testconditions that resulted in rapid detection of the instance oflactose depletion and thus accurate estimation of .

Comparison of Fig. 7a and b confirms the influence ofcell density on the DO profile resulting from lactose deple-tion. Since the specific oxygen consumption rate remainsconstant during a fully oxidative growth, the volumetricoxygen uptake rate is directly proportional to cell den-sity. The high volumetric oxygen uptake rates at high celldensities cause a rapid response during the MSUR tests,contributing to better detection of instances of lactose ex-haustion. The specific oxygen consumption rates estimatedfrom DO profiles during the MSUR tests vary from 7.0 to10.2 mmol O2/g cell h. The variation may be attributed tofluctuations of cell oxidative capacity due to rapidly chang-ing culture conditions during the tests. The rates are lowerthan the maximum rate of 15.2 mmol O2/g cell h obtainedby Inchaurrondo et al. [26] using the sulfide method in abatch culture study of K. fragilis.

4.4. Comparison of fed-batch control strategies

Fig. 8a shows the cell density profiles obtained with thefour control strategies. For the DO-stat, the cells followeda nearly linear growth trajectory for the entire fed-batchperiod. A linear growth trajectory was expected with theDO-stat as it was unable to supply lactose according to thecells metabolic demand. Poor cell growth is apparent withthe exponential feeding strategy. Instead of an exponentialgrowth profile, cells exhibited a linear growth for the first5 h before growth ceased. Poor cell growth can be attributedto the absence of a feedback control mechanism to compen-sate for process disturbances and model inaccuracies lead-ing overfeeding of lactose. Consequently, the Crabtree effectwas induced from the start of culture and was coupled withdilution effects caused by lactose overfeeding after 5 h.

The exponential feeding strategy with manual feed-back control resulted in a linear growth for the first 8 hof fed-batch culture. Although yielding linear growth, theperformance was better than that of the DO-stat. A maxi-mum cell density of 43.3 g/l was obtained and the estimated varied from 0.10 to 0.20 h1 during the fed-batch cul-ture. The linear growth observed suggests that the culturewas underfed. It further implies that was underestimated


Fig. 8. Comparison of fed-batch control strategy performance. (a) Profilesof cell density; (b) profiles of volumetric lactase activity. () DO-stat;() exponential feeding with manual feedback control; (H17009) correctedfeed-forward; () exponential feeding.

throughout this period. Apparently, this condition was theresult of inaccurate estimation of caused by several pos-sible sources. The main sources of error could be attributedto sampling and inaccuracies in cell density measurements.The corrected feed-forward control strategy was able tomaintain exponential growth throughout the culture pe-riod after a brief lag period. The prolonged exponentialgrowth phase demonstrate the effectiveness of the strategyin predicting substrate demand. Errors caused by processdeviations were minimized even at high cell density.

The profiles of volumetric lactase activity for all con-trol strategies are shown in Fig. 8b. As lactase is agrowth-associated product, its production is closely relatedto the cell growth. The highest production rate was obtainedwith the corrected feed-forward control strategy. Both theDO-stat and the exponential feeding strategy with manualcontrol showed linear production profiles, with the latterachieving a better performance. Although the maximumvolumetric lactase productivity was comparable in bothcases, the productivity achieved by the exponential feedingstrategy with manual control was 1.89 U/ml h as compared

to 1.49 U/ml h achieved by the DO-stat. The adverse im-pacts of the Crabtree effect caused by lactose overfeedingin the exponential feeding strategy is obvious consideringthe low volumetric lactase activity (below 7 U/ml).

5. Conclusions

A feed-forward control strategy for automated fed-batchaerobic cultures was developed to maximize the volumetricproductivity of lactase by K. fragilis. Balanced oxidativegrowth was achieved while the Crabtree effect and ethanolformation were minimized. The control has been shown tobe stable even at high cell density and was able to achievethe highest volumetric lactase productivity in comparisonto that obtained by DO-stat, exponential feeding and ex-ponential feeding with manual feedback control. As thecontrol only requires on-line monitoring of DO levels forestimating the specific growth rate, it can be used in culturevessels equipped with standards probes. The control strategyshould be applicable to any aerobic culture provided thatDO response profiles of the organism are first determinedfor identification of substrate exhaustion. In the presentapplication, the substrate requirement for cell maintenancecould be neglected. However, the control strategy could bereadily adapted for aerobic culture systems with significantmaintenance requirements. Although the controller adapt-ability minimizes the effects of identification of substrateexhaustion during MSUR tests, the control strategy maynot be effective for aerobic culture systems showing highsensitivity to substrate starvation.

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Automated fed-batch culture of Kluyveromyces fragilis based on a novel method for on-line estimation of cell specific growth rateIntroductionControl strategy developmentMaterials and methodsMicroorganism and culture mediumAnalytical methodsFed-batch culturesThe corrected feed-forward controlComparison of fed-batch control strategies

Results and discussionFed-batch culturePerformance of fed-batch control and error analysisDO response profile analysisComparison of fed-batch control strategies

ConclusionsReferences

automated fed-batch culture of kluyveromyces fragilis based on a novel

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