Simulation of penicillin production in fed-batch cultivations using a morphologically structured model.pdf

Simulation of Penicillin Production inFed-Batch Cultivations Using aMorphologically Structured Model

Teresa C. Zangirolami,1 Claus L. Johansen,2 Jens Nielsen,3

Sten Bay Jørgensen1

1Chemical Engineering Department, Technical University of Denmark,DK-2800, Lyngby, Denmark2Unilever Research Laboratorium, NL-3133 AT,Vlaardingen, The Netherlands3Center for Process Biotechnology, Department of Biotechnology,Technical University of Denmark, DK-2800 Lyngby, Denmark

Received 1 August 1996; accepted 19 December 1996

Abstract: A mathematical model is formulated to de-scribe trends in biomass and penicillin formation as wellas substrate consumption for fed-batch cultivations. Thebiomass is structured into three morphological compart-ments, and glucose and corn steep liquor are consideredas substrates for growth. Penicillin formation is assumedto take place in the subapical compartment and in thegrowing region of the hyphal compartment. Further-more, it is inhibited by glucose. Model parameters areestimated using an evolutionary algorithm and fitting themodel to a standard fed-batch cultivation. The model isvalidated on experimental data from three different fed-batch cultivations, including two repeated fed-batch cul-tivations. The model predictions show good agreementwith the measurements of biomass and pencillin concen-trations for all fed-batch cultivations. © 1997 John Wiley &Sons, Inc. Biotechnol Bioeng 56: 593–604, 1997.Keywords: structured model; fed-batch cultivation; re-peated fed-batch cultivations; penicillin production; Peni-cillium chrysogenum

INTRODUCTION

Penicillin production is one of the most important industrialcultivation processes. Traditionally it is carried out in afed-batch mode, and the development of mathematical mod-els for the process as a whole is crucial for gaining under-standing of the mycelial physiology as well as for processoptimization and control. There have been many attempts atmodeling penicillin production in fed-batch cultivations.The unstructured model developed by Bajpai and Reuß(1980, 1981) has become the reference model for otherunstructured models with different levels of complexity(Heijnen et al., 1979; Nicolaï et al., 1991; Menezes et al.,1994; Tiller et al., 1994). In some of these improved ver-sions, the contribution of the complex nitrogen source for

the biomass formation is taken into account and the bioticphase has been divided into two different cell types: active(metabolizing) and inactive (nonmetabolizing) biomass(Menezes et al., 1994; Tiller et al., 1994).

Despite these enhancements, the extended models fail toprovide a good description of the process, presumably duethe neglect of inevitable cellular differentiation observed incultivations of filamentous fungi.

In fact, Paul and Thomas (1996) demonstrated that peni-cillin formation is related to cellular differentiation duringgrowth. Recent measurements of different cell forms duringfed-batch cultures showed that penicillin production is cor-related with the fraction of subapical cells in the mycelium.As early as 1970, Megee et al. (1970) proposed a morpho-logically structured model describing the growth and prod-uct formation ofAspergillus awamori.The main drawbackof the Megee model is the large number of parameters,which makes its identification and validation difficult. LaterNestaas and Wang (1983) used a simplified version of themodel of Megee et al. (1970) to implement a control strat-egy for penicillin production. The kinetic expressions pro-posed for differentiation did not include the influence of alimiting substrate which severely restricts its applicability.Furthermore, in order to fit experimental data, different pa-rameter values had to be applied for the different phases ofthe fed-batch cultivations.

Recently Paul and Thomas (1996) formulated a verycomprehensive mathematical morphological model describ-ing growth, differentiation, and penicillin production inPenicillium chrysogenum.The model is structured into fourcompartments and contains five metamorphosis reactions.Penicillin production is assumed to occur only at the non-growing region. The model was validated by comparing thesimulation results with experimental data from four differ-ent fed-batch cultivations. For all cases, the model fits thebiomass concentration and penicillin concentration quitewell. However, the model is rather complex and has a large

Correspondence to:Jens NielsenContract grant sponsor: CAPES, BrazilContract grant number: DBE6351/94, PROC 1488/94

© 1997 John Wiley & Sons, Inc. CCC 0006-3592/97/060593-12

number of parameters, several biomass compartments, andmodel states. Besides, the contribution of corn steep liquor(CSL) to the biomass formation is not explicitly accountedfor.

In the simplified morphologically structured model for-mulated by Nielsen (1993), the hypha is divided into threemorphological forms (apical, subapical, and hyphal com-partments). The model comprises three metamorphosis re-actions as well as growth reactions for apical and subapicalcompartments. The result is a flexible model containingonly eight parameters with well defined physical meaning.The model is capable of representing morphologicalchanges of four different filamentous microorganisms.

This article investigates the applicability of Nielsen’smorphologically structured model (1993) to describe peni-cillin production in fed-batch cultivations. It is assumed thatpenicillin production takes place in the subapical and part ofthe hyphal compartments and the specific penicillin produc-tion rate is represented by Haldane kinetics. In addition,corn steep liquor is also taken into account as a substrate forgrowth. Considering the complexity of the process, the finalresult is a relatively simple model containing eight statesand 14 parameters. The predictive power of the model isillustrated by comparison of simulation results to experi-mental data from four different fed-batch cultivations, in-cluding two repeated fed-batch fermentations. In the fol-lowing, a detailed description of the model is presented,accompanied by an outline of the methodology used forparameter estimation, model validation and sensitivityanalysis, as well as a discussion of simulated results.

MODEL DESCRIPTION

In the model described here, glucose is regarded as the onlylimiting substrate for growth and penicillin production. Theother key nutrients such as phenoxyacetic acid and oxygenare assumed to be in excess during the whole cultivation.Although the supply of sufficient amounts of oxygen maybecome a critical problem at high biomass concentrations,as long as the dissolved oxygen concentration is kept above45% of the saturation value, oxygen limitation on both bio-mass and product formation is unlikely to occur.

Morphologically Structured Model

The morphological structure of the model is described indetail in Nielsen (1993, 1995) and is therefore only sum-marized here. The hyphae are divided into three cell types:apical, subapical, and hyphal. Active growth (e.g., uptake ofsubstrates and formation of biomass) occurs mainly in theapical and subapical compartments. Theapical compart-ment(Za) is defined as the part of the hyphal element be-tween the tip and the first septum. The cells just behind theapical compartment have an intracellular composition verysimilar to the apical cells and this part of the hyphal element

is called thesubapical compartment(Zs) (Fiddy and Trinci,1976).

Cells further away from the tip contain large vacuoles.These cells do not participate directly in the tip extensionprocess, but they are believed to be of importance in creat-ing a sufficient intracellular pressure that ensures transportof protoplasm toward the tip section. This part of the hyphalelement is referred to as thehyphal compartment(Zh). Thetransition from active subapical cells to completely vacu-olated hyphal cells takes place gradually. Therefore, thehyphal cells located in the vicinity of the subapical com-partment belong to a transition state and, to some extent,they are assumed to still retain the same metabolic activityand growth ability exhibited in the subapical compartment.Figure 1 shows the position of the three compartments andthe transition zone in an enlarged picture of the main hypha.

Metamorphosis Reactions

Three metamorphosis reactions are considered in the model:branching, tip extension, and differentiation (Nielsen, 1992,1993, 1995). When a tip extends some apical cell massbecomes subapical cell mass and the net result of thetipextensionis the formation of subapical cells from apicalcells. Branching is the mechanism by which new apicalcompartments are formed and it is mainly observed in thesubapical compartment. When the cell age increases, thecell becomes more and more vacuolated. These vacuolatedcells have a completely different metabolism than the ac-tively growing apical and subapical cells and eventually donot contribute to the overall growth process.Differentiationrepresents the sum of processes by which vacuolated hyphalcells are formed from the subapical cells. The kinetic ex-pressions for branching (u1) [Eq. (1)] and tip extension (u2)[Eq. (2)] are considered to be first order in the morphologi-cal form that disappears. The kinetic expression for differ-entiation (u3) [eq. (3)] is also first order inZs, and it isfurthermore assumed to be inhibited by the total substrate athigh concentrations. The total substrate concentrationST is

Figure 1. Division of the hyphal element into three compartments: api-cal, subapical, and hyphal. Septa in the subapical compartment and thetransition zone are also shown.

594 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 56, NO. 6, DECEMBER 20, 1997

taken to be the extracellular glucose concentration plus theconcentration of nutrients in corn steep liquor convertedinto glucose equivalents according to Eq. (4).Branching:

Zs → Za u1 4 ku1Zs (1)

Tip extension:

Za → Zs u2 4 ku2Za (2)

Differentiation:

Zs → Zh u3 =ku3

Zs

ST Ku3+ 1

(3)

ST 4 SGLU + aCSL SCSL (4)

whereaCSL is a conversion factor for the nutrients in cornsteep liquor.

Growth Reactions

Simplified stoichiometric expressions for apical and subapi-cal compartments as well as for the active fraction of thehyphal compartment (fh) are formulated in Eqs. (5), (6), and(7). The stoichiometric coefficientsa1a, a1s, anda1h are in(C mol glucose)/(C mol biomass). The elemental composi-tion for biomass is CH1.7O0.55N0.16 (Christensen, 1992).Apical compartment:

a1a SGLU → X + (a1a − 1)CO2 (5)

Subapical compartment:

a1s SGLU → X + (a1s − 1)CO2 (6)

Active fraction of the hyphal compartment:

a1h SGLU → X + (a1h − 1)CO2 (7)

The growth of apical, subapical, and the active fractionfh ofhyphal cells is described by Monod kinetics [Eqs. (8), (9),and (10), respectively].

ma = kaST

ST + Ks

(8)

ms = ksST

ST + Ks

(9)

mh = khST

ST + Ks

(10)

The specific growth rate of the total biomass is given by

m 4 maZa + mSZS + fhmhZh (11)

Since the cells located at the transition zone (the apical andthe subapical cells) are fairly similar in composition andfunction, it is reasonable to assume the same growth kineticsfor them. Thus, in expressions (5), (6), and (7) the stoichi-ometric coefficientsa1a, a1s, and a1h will be taken to beequal (a1a 4 a1s 4 a1h 4 a1). For the same reason, therate constants in the expressions for the specific growth rate[Eqs. (8), (9), and (10)] are assumed to be the same (ka 4ks 4 kh 4 k).

Notice that fragmentation, cell lysis, degeneration, andmutation are not considered in this model. According toPaul et al. (1994), there is a link between vacuolation andfragmentation. Because vacuolation takes place mainly atthe hyphal compartment, it will be more susceptible tobreakage under the shear caused by mechanical forces.Thus, fragmentation will affect the total hyphal lengths andthe mean number of tips per mycelium, but the fractions ofapical, subapical, or hyphal cells in the total biomass willremain unchanged. Fragmentation will lead to some celllysis. However, since there is no experimental evidence tosupport cell lysis, it is not considered in the model.

Product Formation

The formation of penicillin from glucose and phenoxyaceticacid can be expressed by the simplified stoichiometric equa-tion represented below. The stoichiometric coefficients arein (C mol glucose)/(C mol penicillin) and (C mol phenoxy-acetic acid)/(C mol penicillin). The elemental compositionfor penicillin is CH1.1875O0.3125N1/8S1/16 (Nielsen, 1995).

0.5SGLU + 0.5SPHOX → P (12)

Penicillin production is assumed to occur at the subapicalcompartment and at the growing part of the hyphal com-partment as a consequence of differentiation. In addition,the presence of excess glucose can inhibit penicillin forma-tion. This effect is expressed by Haldane type kinetics.

rP = k2

SGLU

SGLU + K2 +S2GLU

KI

~Zs + fhZh! (13)

For all experiments considered in this work, the measure-ments of penicillin V and hydrolysis products were pooledinto one fraction called total penicillin V equivalents. Thus,the hydrolysis reaction does not need to be included, but themodel of Christensen et al. (1992) could easily be applied incombination with the present model to describe the profileof both penicillin V and penicilloic acid.

Consumption of Glucose and Corn Steep Liquor

Corn steep liquor is the major nitrogen source present inpenicillin cultivations. It contains a large number of nutri-ents such as free amino acids (around 40% in weight), pro-teins, and vitamins, as well as lactate in high concentrations(Johansen, 1993; Nielsen, 1995). Due to this complex com-position, it is difficult to specify each of the componentscontributing to growth. In this model, the fraction of cornsteep liquor utilized for growth is converted into glucoseequivalents by the conversion factoraCSL. Thus, the totalamount of substrate available for biomass formation can beexpressed by Eq. (4).

According to Johansen (1993), after 30 h of cultivationthe amino acids content in corn steep liquor is almost de-pleted. This time period coincides with the sharp initial

ZANGIROLAMI ET AL.: STRUCTURED MODELING OF PENICILLIN PRODUCTION 595

increase in the biomass concentration typically observed infed-batch penicillin cultivations. Tiller et al. (1994) in-cluded corn steep liquor in the model by adding anotherexpression for the specific growth rate as a function of cornsteep liquor concentration. However, the specific growthrate is found to be the same in a defined and in a complexmedium (Nielsen and Krabben, 1995). To account for thequick assimilation of the individual nutrients in corn steepliquor, the uptake rates of these nutrients are assumed to beproportional to the relative amount of nutrients, which issimilar to the approach used by Menezes et al. (1994). Withall the nutrients of corn steep liquor pooled together, thisgives only two substrates: glucose and the pool of nutrientsin corn steep liquor [Eqs. (14), (15)]. The uptake rate ofeach substrate is taken to be proportional to its relativeamount. The expression for the specific rate of glucose up-take also includes the consumption of glucose for mainte-nance and product formation [second and third terms in Eq.(14), respectively].

rGLU = a1

SGLU

SGLU + aCSL SCSLm + ms + a2rP (14)

rCSL = a1

SCSL

SGLU + aCSL SCSLm (15)

Differential Balances

All kinetic expressions related previously are combinedwith the differential balance equations for fed-batch biore-actors in Eqs. (16)–(23).

Morphological Compartments

The formation rate of each morphological form is deter-mined by the metamorphosis reactions and by the growth-associated reactions for each form. Because the concentra-tions of morphological forms are given as fractional con-centrations of total biomass, the last term in Eqs. (16), (17),and (18) represents the dilution effect due to biomassgrowth.

Apical cells:

dZa

dt= u1 − u2 + Zama − Zam (16)

Subapical cells:

dZs

dt= u2 − u1 − u3 + Zsms − Zsm (17)

Hyphal cells:

dZh

dt= u3 + fhZhmh − mZh (18)

Reactor Volume

In fed-batch cultures the total volume changes mainly due tothe following factors: feed of glucose and other nutrients to

the fermentor (F), withdrawal of manual samples (FPsp), con-

tinuous on-line sampling (Fols), evaporation and mediumcarryover by the air flow, and addition of base and acid forpH control. The latter two factors tend to compensate eachother and they were omitted from the volume balanceshown in Eq. (19). For repeated fed-batch cultivations, thedrain of cultivation medium (FP

drain) and the addition offresh medium (FP

rep) must also be taken into account.

dV

dt= F − FP

sp − Fols − FPdrain + FP

rep (19)

Total biomass

dX

dt= mX − SF + FP

rep

V D X + XFols

V(20)

The second term in Eq. (20) reflects the dilution of biomassconcentration due to the additions to the bioreactor. Duringon-line sampling, filtrated medium flows from the bioreac-tor and the last term represents the biomass retention causedby the on-line sampling.

Penicillin V production

dP

dt= rPX − SF + FP

rep

V D P (21)

Glucose consumption

dSGLU

dt= SSF

F

V+ Srep

FPrep

V D − SF + FPrep

V D SGLU − rGLUX

(22)

Consumption of the nutrients pool in corn steepliquor

dSCSL

dt=

FPrep

VSCSLrep

− SF + FPrep

V D SCSL − rCSLX (23)

The second right-hand side terms in Eqs. (21), (22), and (23)represent the dilution effect caused by the additions to thebioreactor. The first terms in Eqs. (22) and (23) reflect themass flow of substrate added to the bioreactor due to thefeed and the addition of fresh medium in repeated fed-batchcultivations.

MODEL IDENTIFICATION

Material and Methods

The experimental data used in this work were from fourfed-batch cultivations carried out by Johansen (1993). Themicroorganism used was a high yielding strain ofP.chrysogenumdonated by Novo Nordisk A/S, Denmark. Allcultivations were carried out in a standard 41-L Chemapbioreactor with a working volume of 25 L. The experimen-tal conditions are reported in detail elsewhere (Johansen,1993; Jørgensen et al., 1995a,b; Nielsen, 1995) and are sum-marized in Table I. Experiment FB023 was performed as astandard fed-batch cultivation and it was used for parameterestimation. Runs FB022 and FB027 were started as normalfed-batch cultivations. After 147 h for FB022 and 144 and


286 h for FB027, approximately 40% of the bioreactor con-tent was drained and an equal amount of fresh medium wasadded. Cultivation FB028 was performed as a standard fed-batch fermentation, but the amino acids directly involved inpenicillin biosynthesis (cysteine, valine anda-aminoadipicacid) were added to the bioreactor in a separate feed.

Simulation and Parameter Estimation

The simulation and parameter estimation were performed ina MATLAB/SIMULINK environment. This approach wasalready successfully employed for identification of complexbiochemical models by Pisarra et al. (1995). The evolution-ary parameter estimation method is outlined in detail bySchmidt et al. (1995).

The model represented in Eqs. (1)–(23) was implementedin C code. After compilation using a Watcom 32 bit Ccompiler, the model equations were integrated by Gear’smethod for stiff systems. The inputs to the model consistedof the flows contributing to the volume changes. The sub-strate feed flow rate was implemented as a step changewhereas the on-line sampling flow rate was included as aconstant continuous flow. The intermittent flows (manualsampling, drainage of cultivation medium, and addition offresh medium) were implemented as pulses of determinedduration and intensity. For parameter estimation, the experi-mental measurements of biomass, penicillin, and substrateconcentrations from the standard cultivation FB023 werecompared to the simulation data generated for each set ofparameters. Optimization of the parameter vector was ac-complished by random perturbations of the parameter val-

ues and subsequent selection of the parameter that improvedthe objective function (sum of the squared deviation be-tween model predictions and experimental results).

From the 14 parameters originally present in the model,only six were estimated by the procedure described above(see Table II). The values ofku1, ku2, anda1 were obtainedfrom Nielsen (1992). The values ofku3 andKu3 were modi-fied from the ones proposed by Nielsen (1992) in order to fitthe repeated fed-batch cultivations. For the same reason,fhwas taken to be 0.13. The value for the rate constantk waschosen as 0.14, which is within the range reported (Menezes

Table I. Initial corn steep liquor concentration (SCSL) in the medium, glucose concentrationin the feed (SF) and feed profiles for fed batch cultivations FB023, FB022, FB027 and FB028.(Data from Johansen9)

Feed Rate Profile

Cultivation Characteristics Period (h) Feed rate (l/h)

FB023 Standard fed-batch 0–6 0Initial SCSL in the medium: 200 g/l 6–54 0.061(80 g/l of nutrients) 54–240 0.076SF 4 450 g/l

FB022 Repeated fed-batch 0–6 0Initial SCSL in the medium: 200 g/l 6–50 0.059(80 g/l of nutrients) 50–147 0.076SF 4 450 g/l 148–173 0.059Srep 4 3 g/l 173–264 0.076

FB027 Repeated fed-batch 0–5 0Initial SCSL in the medium: 100 g/l 5–48 0.059(40 g/l of nutrients) 48–144 0.076SF 4 450 g/l 144–168 0.059Srep 4 3 g/l 168–286 0.076

286–310 0.059310–406 0.076

FB028 Fed-batch supplemented with a 0–5 0solution of amino acids 5–53 0.059Initial SCSL in the medium: 100 g/l 53–110 0.069(40 g/l of nutrients)SF 4 450 g/l

Table II. Model parameters and reported values.

Parameter

FB023FB022FB027 FB028 Source

ku1 (h−1) 2.3000 2.3000 Nielsen (1992)ku2 (h−1) 0.7000 0.7000 Nielsen (1992)ku3 (h−1) 0.1900 0.1900 AttributedKu3 (l/g glucose) 20.0000 20.0000 Attributedfh (g active Zh/g Zh) 0.1300 0.1300 Attributeda1 (g glucose/g DW) 2.2000 2.2000 Nielsen (1992)a2 (g glucose/g

penicillin) 0.6858 0.6858 Calculated[eq. (12)]

aCSL (g glucose/g CSL) 0.42 ± 0.01 0.4200 Estimatedk (h−1) 0.1400 0.1400 AttributedKs (g glucose/l) 0.0015 ± 0.0004 0.0015 Estimatedms (h−1) 0.0281 ± 0.0008 0.0281 Estimatedk2 (h−1) 1.35 ± 0.02 1.77 ± 0.03 EstimatedK2 (g glucose/l) 0.0132 ± 0.0002 0.0132 EstimatedK1 (g glucose/l) 0.0101 ± 0.0002 0.0101 Estimated


et al., 1994). Exactly the same set of parameters estimatedfor FB023 was used in the simulation of FB022 and FB027.For cultivation FB028 the rate constant for the penicillinproduction reaction was estimated again in order to copewith the changes in the penicillin kinetics caused by theaddition of the three precursor amino acids.

It is not possible to directly compare the estimated valuesfor the parameters with the reported ones because most ofthe parameters depend on the strain ofP. chrysogenumaswell as on the model structure. However, some of the dif-ferences are worthy of mention.

The value calculated fora2 is lower than the reportedrange (0.83–1.2) (Bajpai and Reuß, 1981; Menezes et al.,1994; Paul and Thomas, 1996; Tiller et al., 1994) due toinclusion of phenoxyacetic acid in the stoichiometric equa-tion for penicillin prodution [Eq. (12)].

The value estimated fork2 (FB023) is significantly higherthan the reported range (0.003–0.015) (Menezes et al.,1994). However, it is important to note that the fraction ofthe subapical compartment plus the active part of the hyphalcompartment is a multiplicative factor in the expression forpenicillin production rate. If the value ofk2 is multiplied by(Zs + fhZh) after 100 h of cultivation, it is reduced to about0.18 h−1.

RESULTS AND DISCUSSION

Figure 2 shows experimental data and simulation results forthe standard cultivation FB023 used for parameter estima-tion. The model predictions fit the data for biomass andpenicillin concentration very well. In Figure 2a the threedistinct growth phases characteristically observed when fed-batch cultivations are carried out on a complex medium areclearly delineated by the model. A rapid growth phase tookplace during the first 30 h. The initial sharp increase in thebiomass concentration coincided with the simulated de-crease of the nutrients concentration in corn steep liquor(Fig. 2b), indicating that they were the main support for thegrowth during the early stage. When these nutrients weredepleted, a linear growth phase was initiated. This phaselasted until approximately 150 h of cultivation, and at thatpoint the biomass concentration reached about 45 g/L. Athigh biomass concentrations, the feed of substrate only al-lowed very slow growth.

The model was not successful in predicting the changesin glucose concentration as can be observed in Figure 2b.The simulated dynamics of glucose accumulation and con-sumption when the feed is started was faster than experi-mentally observed. In the production phase, the estimatedglucose concentration was approximately 5 × 10−4 g/L,which is 10 times lower than the expected value. By de-creasing the value ofk to 0.13, a better agreement for glu-cose concentration in the production phase would beachieved; however, an amplified initial overshoot would beobtained. Similar problems were detected in the simulationof glucose concentration for FB022, FB027, and FB028(Figs. 4b, 5b, 6b, respectively).

This deviation is likely to be a consequence of a too

simple description of the glucose uptake and catabolism inthe model, especially the description of the transients takingplace in the presence of free amino acids until the depletionof this source. To improve the fit for glucose, a more de-tailed modeling of glucose uptake as well as modificationsin the morphological structure, which would require experi-mental determination of the morphological compartments infed-batch cultivations, could be attempted. Furthemore, themisfit of the glucose data may be explained by two othereffects: the role of oxygen as substrate was ignored; andinitially there were some pellets in the culture (Nielsen etal., 1995) and it may have resulted in a nonhomogeneouspopulation of cells.

In Figure 3 the simulated time profiles for the morpho-logical compartmentsZa, Zs, andZh are represented. Whenthe glucose concentration decreased and stabilized at a lowvalue, the differentiation processes were no longer inhib-ited, leading to an increase inZh and a simultaneous de-crease inZa andZs. Similar trends for the time profiles ofthe morphological forms were observed in FB022, FB027,and FB028 (data not shown). Unfortunately it was not pos-sible to experimentally quantify the fractions of cell com-partments during any of the fed-batch cultivations. Image

Figure 2. Experimental data and simulation results for standard cultiva-tion FB023.


analysis measurements of cells cultivated on solid mediashowed that at poor growth conditions the biomass wascharacterized by long hyphae with few branch points, whichcorresponds to a high fraction of the hyphal compartment(Nielsen, 1995). However, the hyphae characteristics in fed-batch cultivations were quite different. Due to fragmenta-tion the total hyphal length and the mean number of tipsremained approximately constant in FB027 and FB028 (Jo-hansen, 1993).

The measurements of biomass and penicillin concentra-tions in FB022 are shown in Figure 4a together with modelsimulations. The simulated biomass and penicillin concen-trations showed good agreement with the experimental val-ues almost throughout the whole cultivation. The overpro-Figure 3. Simulated time profiles for the morphological forms.

Figure 4. Experimental data and simulation results for repeated fed-batch cultivation FB022. Penicillin was monitored on-line using an FIA-system witha biosensor (Carlsen et al., 1993).


duction of penicillin after 230 h of cultivation was not fol-lowed by the model and might have been caused byexperimental errors in the determination of the penicillinconcentration.

The model also describes the experimental data for bio-mass and penicillin concentration in the cultivation FB027remarkably well (Fig. 5a). Here the model shows its pre-dictive capacity by following the dynamics of the threeconsecutive fed-batch cultivations, where the feed rate waschanged 7 times. Notice also the qualitatively correct de-scription of the glucose concentration at the beginning ofeach addition of fresh medium. At the end of the thirdrepeat, the model predictions for penicillin concentrationare higher than the experimental data. This loss of produc-tivity was also verified in glucose limited continuous cultureafter 200 h, and it is attributed to degeneration of the strain(Christensen, 1992; Nielsen, 1995).

The results for fermentation FB028 presented in Figure 6

demonstrate the predictive power of the proposed model. InFB028 the influence of the precursor amino acids of peni-cillin biosynthesis was investigated. Despite the alterationsin the cultivation conditions, only one parameter had to bereestimated for FB028. When the new value of the rateconstant for the penicillin formation reaction was used to-gether with the same parameters estimated for FB023, avery good fit between simulation results and experimentaldata for biomass and penicillin concentrations was obtainedfor FB028. Indeed, the value ofk2 estimated from FB028was higher than the original value estimated from FB023(see Table II). It corresponds well with the experimentalverification that the specific rate of penicillin productionincreased due to the addition of the amino acids solution(Johansen, 1993; Nielsen, 1995).

The influence of the nutrients pool in corn steep liquor onthe initial growth is clear when the changes in the biomassconcentration for FB028 (Fig. 6a) are compared to the cor-

Figure 5. Experimental data and simulation results for repeated fed-batch cultivation FB027.


responding changes in FB023 (Fig. 2a). The initial concen-tration of corn steep liquor in FB023 was 200 g/L, and at theend of the rapid growth phase the biomass concentrationwas over 20 g/L. In FB028 the initial concentration of cornsteep liquor was only 100 g/L, and the biomass concentra-tion at the end of the rapid growth phase reached approxi-mately 15 g/L.

The sensitivity of the model states to changes in the dif-ferent parameters was investigated according to the methodproposed by Holmberg (1982). The original model was ex-tended to include the parameter sensitivity functions andintegrated again. The time profiles for the relative sensitivi-ties are plotted in Figure 7a–d. The relative values are ob-tained by multiplying the sensitivity functions (Yp) by thecorresponding parameter (p). In this way it is possible tocompare the influence of the different parameters on a vari-able. The results obtained for different variables show com-mon features. In the batch phase, the concentration of bio-mass, glucose, and nutrients in corn steep liquor (Fig.

7a,b,d) are predominantly sensitive tok, a, andaCSL. In thesame way, the morphological statesZa, Zs, and Zh aremainly sensitive to the rate constants of metamorphosis re-actions (ku1, ku2, andku3) and growth reaction (k) (data notshown). On the other hand, in the production phase therelative sensitivities do not follow a common pattern andeach variable is specifically more sensitive to different pa-rameter sets. Since experimental data for biomass, penicillinand glucose concentration were used for parameter estima-tion, it is interesting to analyse which parameters are sepa-rately identifiable under these experimental conditions.From the relative sensitivities with respect toX (Fig. 7a) itcan be concluded thataCSL andms are both distinguishable,the former just after the batch phase is started and the latterat the end of the cultivation. From Figure 7b, where therelative sensitivities forSGLU are represented, one can ob-serve that onlyKs is identifiable at the end of the cultivation.The analysis of the relative sensitivities with respect toP(Fig. 7c) is more complicated. The sensitivity functions of

Figure 6. Experimental data and simulation results for fed-batch cultivation FB028.


Figure 7. Time relative parameter sensitivities for (a)X, (b) SGLU, (c) P, and (d)SCSL for a fed-batch cultivation (parameter values shown in Table II).


k2, K2, ms, and Ks are almost linearly related and the pa-rameters are not completely distinguishable. Notice that theremaining parameter in the penicillin formation kinetics(KI) does not have a significant influence onP. This meansthat it is not easy to identify the kinetic parameters of peni-cillin production and different combinations of these param-eters could yield the same fit.

CONCLUSION

The model gives a good quantitative description of penicil-lin production in fed-batch cultivations. The inclusion ofcorn steep liquor in the model contributed to an improve-ment in the biomass prediction. All growth phases wereclearly identified and the rapid growth during the initialphase could be related to the consumption of the nutrients incorn steep liquor. The model also provided very good pre-dictions for penicillin concentration. The limited number ofstates and parameters as well as the demonstrated predictivestrength enable the model to be used for control strategies,design of estimators, etc.

We are grateful to Pedro Pissara and Karsten Schimdt whohelped in setting up the method for simulation and parameterestimation. The first author also gratefully acknowledges thefinancial support of CAPES, Brazil (Grant DBE6351/94, PROC1488/94).

NOMENCLATURE

FPsp pulse of manual sample (L/h)

Fols volumetric feed flow rate for on-line sampling (L/h)FP

drain pulse of medium drained from the bioreactor (L/h)FP

rep pulse of fresh medium added to the bioreactor (L/h)F volumetric feed flow rate (L/h)fh active part of the hyphal compartmentk rate constant for growth reactions (h−1)k2 rate constant for penicillin production reaction (h−1)K2 saturation constant for penicillin production reaction (g glu-

cose/L)KI inhibition constant for penicillin production reaction (g glu-

cose/L)Ks saturation constant for growth reactions (g glucose/L)ku1 rate constant for branching reaction (h−1)ku2 rate constant for tip extension reaction (h−1)ku3 rate constant for differentiation reaction (h−1)Ku3 saturation constant for differentiation reaction (L/g glucose)ms maintenance coefficient (h−1)pi value of parameterirCSL specific rate of uptake of nutrients in corn steep liquor (g/g

DW h)rGLU specific rate of glucose uptake (g/g DW h)rp specific rate of penicillin production (g/g DW h)SCSL concentration of nutrients in corn steep liquor (g/L)SF concentration of glucose in the feed to the bioreactor (g/L)SGLU concentration of glucose (g/L)SPhOX concentration of phenoxyacetic acidSrep concentration of glucose added to the bioreactor in repeated

fed-batch cultivations (g/L)ST total substrate concentration (g/L)u1 branching reaction (h−1)u2 tip extension reaction (h−1

u3 differentiation reaction (h−1)

V volume (L)Ypi sensitivity function for parameteriZa apical compartment or fraction of apical compartment (g/g

DW)Zh hyphal compartment or fraction of hyphal compartment

(g/g DW)Zs subapical compartment or fraction of subapical compart-

ment (g/g DW)a1 stoichiometric coefficient for glucose (biomass formation)

(g glucose/g DW)a2 stoichiometric coefficient for glucose (penicillin formation)

(g glucose/g penicillin)aCSL conversion factor (g glucose/g CSL)m total specific growth rate (g/g DW h)ma, ms, mh specific growth rate for apical, subapical, and hyphal cells,

respectively (g/g DW h)

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