Lovastatin biosynthesis depends on the carbon-nitrogen proportion: Model development and controller...

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James Gomes1

Juhi Pahwa2

Sanjay Kumar3

Bhaskar Sen Gupta4

1School of Biological Sciences,Indian Institute of TechnologyDelhi, Hauz Khas, New Delhi,India

2Department of BiochemicalEngineering & Biotechnology,Indian Institute of TechnologyDelhi, Hauz Khas, New Delhi,India

3College of Pharmacy, The OhioState University, Columbus, OH,USA

4School of Planning, Architectureand Civil Engineering, Queen’sUniversity, Belfast, UK

Research Article

Lovastatin biosynthesis depends on thecarbon–nitrogen proportion: Modeldevelopment and controller design

Lovastatin biosynthesis depends on the relative concentrations of dissolved oxygenand the carbon and nitrogen resources. An elucidation of the underlying relation-ship would facilitate the derivation of a controller for the improvement of lovastatinyield in bioprocesses. To achieve this goal, batch submerged cultivation experi-ments of lovastatin production by Aspergillus flavipus BICC 5174, using both lactoseand glucose as carbon sources, were performed in a 7-L bioreactor and the dataused to determine how the relative concentrations of lactose, glucose, glutamine,and oxygen affected lovastatin yield. A model was developed based on these resultsand its prediction was validated using an independent set of batch data obtainedfrom a 15-L bioreactor using five statistical measures, including the Willmott in-dex of agreement. A non-linear controller was designed considering that dissolvedoxygen and lactose concentrations could be measured online, and using the lactosefeed rate and airflow rate as process inputs. Simulation experiments were performedto demonstrate that a practical implementation of the non-linear controller wouldresult in satisfactory outcomes. This is the first model that correlates lovastatinbiosynthesis to carbon–nitrogen proportion and possesses a structure suitable forimplementing a strategy for controlling lovastatin production.

Keywords: Aspergillus flavipus / Glucose:glutamate ratio / Lovastatin model / Non-linearcontrol / Submerged fermentation

� Additional supporting information may be found in the online version of this article atthe publisher’s web-site

Received: January 28, 2013; revised: October 2, 2013; accepted: October 27, 2013

DOI: 10.1002/elsc.201300011

1 Introduction

Lovastatin is a drug used in the treatment of hypercholes-terolemia. It acts by inhibiting the enzyme hydroxymethylglu-taryl coenzyme A reductase [EC 1.1.1.34]. It catalyzes the reduc-tion of hydroxymethylglutaryl coenzyme A to mevalonate, whichis the committed step in cholesterol biosynthesis. Lovastatin be-longs to the class of secondary metabolites called statins andpossesses a polyketide structure. State-time profiles of variablesduring lovastatin production, as in the case of other secondarymetabolites, exhibit strong non-linear behavior. Since sensorsfor measuring lovastatin online are not available, standard con-trol modules cannot be used for process control and advanced

Correspondence: Prof. James Gomes ([email protected];[email protected]), School of Biological Sciences, In-dian Institute of Technology Delhi, Hauz Khas, New Delhi 110016,India

controllers are required for achieving productivity goals. Thesecontrollers are designed using models that accurately describeprocess dynamics. Therefore, it is important to understand andcapture the relationship between process variables for developinga satisfactory model.

Natural statins are produced by different species of fungi andprimarily by those belonging to the genus Aspergillus, Monascus,and Penicillium. Since the first report in the 1970s [1], the nat-ural statins have been produced by fungal cultivation. Althoughlarge-scale processes have been developed industrially, there ap-pear to be very few reports in the literature. Nevertheless, thereports that are available, provide a better understanding ofthe mechanisms of statin synthesis [2, 3]. Recent studies sug-gest that statins can inhibit vascular formation of oxygen-freeradicals. Thus, statins might be able to improve endothelial dys-function in heart failure by inhibiting free radical formation[4]. Hence, there is a continuing interest in the production oflovastatin.

C© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Eng. Life Sci. 2014, 14, 201–210 201

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Hajjaj et al. [2] had investigated the influence of carbon andnitrogen sources on lovastatin production in a chemically de-fined medium. They used glucose and lactose in separate experi-ments along with glutamate as the nitrogen source. Casas Lopezet al. [5] also studied the effect of carbon and nitrogen sources onlovastatin production. They used lactose, glycerol, and fructoseas carbon sources and yeast extract, corn steep liquor, and soy-bean meal as nitrogen sources. They observed that increasing thecarbon:nitrogen ratio from 23.4 to 41.3 lovastatin concentrationin the shaken flasks increased from 150 to 200 mg L−1. Theirdata showed that the slowly metabolizable sugar, lactose, gavethe highest yield of lovastatin. The influence of carbon:nitrogenratio on lovastatin production has been observed by other re-searchers [6, 7]. A surface response optimization to determinemedium constituents and composition for enhancing lovastatinproduction has also been reported [8]. When environmentalconditions were studied, it was observed by Lai et al. [9,10], thatdissolved oxygen concentration significantly influences growthof cells and production of lovastatin. While there is sufficientinformation on the cultivation of fungi for the production oflovastatin, there are no reports on how yields may be improvedor how modeling and process control methods may be appliedto achieve desired objectives.

In this work, we propose a model that accounts for theeffect of glucose: glutamate ratio and dissolved oxygen con-centration on lovastatin production. The parameters of themodel were determined by non-linear regression using data fromexperiments performed for this purpose. Furthermore, its struc-ture was checked by control theory methods for correctnessand found to be suitable for process control applications. Sim-ulations results for a non-linear controller designed using thismodel showed satisfactory performance.

2 Materials and methods

2.1 Microorganism and inoculum preparation

The fungus used in this study was a mutant strain ofAspergillus flavipes BICC 5174 obtained from Biocon India. Thestrain was maintained by sub-culturing every 2 wk on potatodextrose agar (Hi Media) slants and storing these at 4◦C. Theseed culture was prepared by adding 50 mL of spore suspen-sion having an initial concentration of 1 × 108 spores/mL [11]to 450 mL of potato dextrose broth medium in 2 L Erlenmeyerflasks. The flasks were incubated at 30◦C and a constant agitationspeed of 150 rpm for 16 h in an orbital shaker (Adolf-Kuhner,Germany).

2.2 Submerged cultivation

Submerged cultivation experiments were carried out in a 7-Lreactor (Applikon, Holland) and a 15-L reactor (Biostat-C, BBraun, Germany). The composition of the medium constituentswas as follows: lactose 26 g L−1, dextrose 22 g L−1, Na-glutamate14.48 g L−1, KH2PO4 5 g L−1, K2HPO4 5 g L−1, MgSO4·7 H2O0.1 g L−1, CaCl2 2H2O 20 mg L−1, H3BO3 11 mg L−1, CuCl2

2H2O 5 mg L−1, (NH4)6Mo7O24 4 H2O 5 mg L−1 and adjusted

to pH 6.5 [2]. The airflow rate, impeller speed, temperature, pH,dissolved oxygen concentration, and the off gas CO2 were mon-itored online. For batch experiments, the reactor was controlledat 30◦C, 150 rpm, 6.5 pH, and 0.5 vvm airflow rate. Samplescollected every 8 h were analyzed in duplicates.

2.3 Analysis of dry cell weight, lovastatin, sugar, andglutamic acid

Samples drawn from the reactor were filtered through pre-weighed filter paper (Whatman No. 1), the cell residues washedtwice with distilled water, and then dried overnight at 60◦C.These were then equilibrated at room temperature inside a des-iccator and their weights were measured for determining the drycell weight.

For lovastatin extraction, a sample taken in a flask was mixedwith an equal volume of methanol; the pH of this mixture wasadjusted to 7.7 and the flask incubated at 30◦C and 200 rpmfor 2 h in an orbital shaker. The mixture was subsequently fil-tered through 0.45 μm membrane [12]. The extract was usedto measure the acid form of lovastatin by HPLC using a NovaPakTM C18 column (Water, USA). The method given by CasasLopez et al. [5] was used to prepare the lovastatin standardand a modified Friedrich’s method [13] for lovastatin estima-tion [11]. Lovastatin measurements by HPLC were performed induplicates.

An HPLC with an RI detector was used to estimate lactose.Samples were injected into an Aminex HPX-87H column (Bio-Rad, USA) held at 50◦C through which 0.01N H2SO4 mobilephase was passed at a flow rate of 0.5 mL min−1 [2]. The totalreducing sugars were determined by the DNS method [14]. Aspectrophotometric method was used to measure glutamic acid[15].

2.4 Development of the model

The medium for lovastatin production contained two carbonsources, glucose and lactose. The nitrogen source used wassodium glutamate. It was observed that lovastatin productionwas primarily non-growth associated. The time profiles showedthat glucose was consumed at a faster rate than lactose; glucosewas utilized within 96 h while lactose remained in the mediumtill the end of the process. Oxygen was utilized during the growthas well as the production phase (Fig. 1). It was also observed thatwhen the glucose (g): glutamate (n) ratio dropped below unity,the rate of lovastatin production increased. A term κ defined asn/(g + n) correlated well with the state-time profile of lovas-tatin production and accounted for how the nitrogen sourceswere distributed between growth (κ) and production (1 − κ).Fed-batch lovastatin production was described using the lactosefeed rate FL and the air flow rate FA as inputs for controlling theprocess along a desired trajectory. The nine parameters of themodel and their description are given in Table 1. The kinetic partof model, the batch model obtained by excluding the transportterms, was used in the identification of the process parameters.

202 Eng. Life Sci. 2014, 14, 201–210 C© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim


Figure 1. Schematic diagram showing how the glucose, lactose,and glutamate contribute to cell growth and lovastatin production.The factor κ accounts for the allocation of nitrogen source. Lactoseis used preferably for the production of lovastatin while oxygen isneeded during both growth and production.

Table 1. Desription of the model parameters and their values.

Parameter Value Units Description

μM 0.021 h−1 Maximum specific growthrate

KG 1.700 g L−1 Monod constant forglucose

KL 3.000 g L−1 Monod constant forlactose

πM 1.22 × 10−4 h−1 Maximum specificlovastatin production rate

YXL 1.648 g g−1 Yield coefficient of cellmass based on lactose

YPL 0.021 g g−1 Yield coefficient oflovastatin based on lactose

YXN 2.212 g g−1 Yield coefficient of cellmass based onNa-glutamate

YXG 0.892 g g−1 Yield coefficient of cellmass based on glucose

qA 0.015 h−1 Rate coefficient foroxygen utilization

The set of equations constituting the model is:

dx

dt= (μ1 + μ2) x − F L

Vx

dp

dt= πx − F L

Vp

dl

dt= − 1

YX Lμ2x − 1

YPLπx + F L

V(lF − l)

dn

dt= − 1

YX N(μ1 + μ2) x − F L

Vn (1)

dg

dt= − 1

YX G(μ1 + μ2) x − F L

Vg

dcL

dt= kla

(c∗

L − cL

) − qA x − F L

VcL

dV

dt= F L

The kinetic terms appearing in the model are described asμ1 = μM ( g

K G +gcLc∗

L)κ, μ2 = μM ( l

K L +l) (1 − κ), π = πM ( l

K L +l)κ,

and κ = nn+g

. The model variables denoted by x, p, l, n, g, andcL are the cell mass, lovastatin, lactose, sodium glutamate, glu-cose, and dissolved oxygen concentrations. The growth rate hastwo components, μ1 dependent on glucose concentration andμ2 dependent on lactose concentration. Lovastatin productionis described by the term π which is dependent directly on lac-tose and indirectly on glucose and glutamate through the term(1 – κ). The lactose dynamic equation takes into account how theoxygen requirement varies during lovastatin production. Lactoseis added into the reactor at a rate FL and its concentration in thefeed stream is lF. The reactor volume is V. The oxygen masstransfer coefficient is denoted by kla and cL

∗ is the saturationconcentration of oxygen in the medium. The airflow rate was

calculated using the relation F A = 1.55364 × 103( kl aV0.2467

N1.14 )0.25.It was derived based on the work of Van’t Riet [16] and the gassedpower number empirical correlation, the detail of which is givenin [17].

2.5 Development of non-linear control

2.5.1 Model structure analysisSubmerged cultivation of lovastatin is dependent on the relativeconcentrations of the glucose and glutamate in the medium, andon the availability of oxygen. The non-linear time characteristicsobserved in the state-time profiles and the interactions betweenthe states variables have been described by the model proposedhere. However, for this model to be useful in a process control ap-plication, it must also satisfy the controllability and observabilitycriteria. Controllability is an algebraic test that determines if theform in which the manipulated variables (process inputs) appearin the model would enable the system to reach a final state alongany desired trajectory. Likewise, observability is an algebraic testthat determines if the chosen measurements would enable us toreconstruct how the system evolved from any final state to itsinitial state [18]. Satisfying these algebraic tests ensures that themodel has the correct theoretical structure for process controlapplications. The model equation (1) can be rewritten in thegeneral form, as shown in the supplementary text

x = f(x) + g(x)uy = h(x)

(2)

Where x ∈ �N is the vector of N state variables, u ∈ �M is thevector of M manipulated inputs, and y∈�P is the vector of P mea-sured outputs. Here the outputs y are the measurements that canbe made from among all the state variables. The functions f and gare smooth vector fields, and represent the kinetics and transportterms. For this process, the state vector is x = [ x p l n g cL ]T

and the input vector is u = [ F L /V kla ]T . In actual imple-mentation, the inputs to the process are the substrate feedingrate FL and the airflow rate FA. If sensors are available for mea-suring two of the six state variables, the system is square, thatis, M = P = 2. A systems analysis is required to check thestructural correctness of the proposed model. A structurallycorrect model will permit the control variable to traverse thestate space and the measurements made to reconstruct the pathof process evolution. Hence, the model must satisfy controlla-bility and observability conditions with the given inputs and



Figure 2. A schematic diagram of non-linear controller designed using the principle of input-output linearization and in which the controlloops FL – l and FA – cL are decoupled. The variables l and cL are measured and the others x, p, n, and g are estimated from the model. Twoblocks responsible for linearization and decoupling, respectively, together constitute the non-linear controller. The process inputs FL andFA are calculated from u1 and u2.

outputs. This is an important first step in the analysis of non-linear systems and, is in some sense, a mathematical validationof the model.

2.5.1.1 Proposition 1The system (2) is controllable with any input ui if the non-linearcontrollability matrix defined by

C = [ad0

f gi ad1f gi · · · adN−1

f gi

]is of full rank

2.5.1.2 Proposition 2The system (2) is observable with any measurementyi = hi(x), if the observability matrix defined by O =∇ [

L 0f hi L 1

f hi · · · L N−1f hi

]Tis of full rank.

Where Lf h = ∇h · f and Lif h = (∇Li−1

f h) · f is the direc-tional derivative called the Lie derivative; ad1

f g = [f, g

] = ∇g ·f − ∇f · g and adi

f g = [f, adi−1

f g]

defines the successive Liebrackets.

Our analysis shows that the system is controllable with eachinput. Therefore, we have the freedom of using either or bothinputs in designing control strategies. Normally, for non-linearsystems, it would be possible to construct an input-output lin-earizing controller that may be implemented online. We have de-veloped a 2 × 2 decoupled input-output linearizing non-linearcontroller [17] and a similar formalism can be applied for thisprocess (Fig. 2). It was determined that the process is controllableusing lactose feeding for fed-batch operation of the reactor alongwith the manipulation of the airflow rate to obtain the desiredlevel of cL in the medium. Similarly, the states of the processdescribed by this model were observable with the measurementof cL or a combination of any two variables. This means that bymeasuring only cL, it would be possible to determine the otherstate variables by constructing a series of non-linear observers.Since the lack of online sensors is one of the problems of biopro-cess monitoring, observable models can be used to design softsensors.

2.5.2 Non-linear control synthesisLovastatin production described by the system Eq. (1) showsthe dependence of the rates on state variables. We assume thatlactose and oxygen are measured online while the other vari-ables are not. It is also possible to measure glucose and nitrogenconcentrations online using suitable sensors and these may beused to obtain better estimates of unmeasured states. For exam-ple, in a submerged fungal cultivation, it is difficult to make anaccurate measurement of the cell mass concentration and goodestimators often require a number of supporting measurements.During fed-batch production of lovastatin, the inputs to the reac-tor are lactose feed rate (FL) and airflow rate (FA). As conditionsin the reactor changes, new values for these inputs are calculatedand implemented by the controller to drive the process along adesired trajectory meant for achieving production targets. Be-low, we present the design of the non-linear controller usingthese inputs. From the system Eq. (1), the lactose and oxygendynamics can be rewritten in the functional form as[

lc L

]=

[σ2(g , l, n)x + π(g , l, n)x

−qA x

]

+[

(lF − l) 0−cL (c∗

L − cL )

] [u1

u2

](3)

where σ2 = − 1YX L

μ2, u1 = FL/V and u2 = kla, from which FA

can be obtained as given in Section 3. Hence, the desired controlinput to the process can be obtained by rearranging Eq. (3) intothe following form,

[u1

u2

]=

[(lF − l) 0−c∗

L (c∗L − cL )

]−1 {[l

c L

]

−[

σ2(g , l, n)x + π(g , l, n)x−qA x

]}(4)

The error dynamics (l – ld) and (cL – cLd ), where ld and cLd arethe desired values of lactose and dissolved oxygen concentrations,can be made exponentially stable by selecting suitable tuning



parameters ki,j {i, j = 1, 2} for the equation

l = ld + k11(ld − l) + k12

t∫0

(ld − l)dt

cL = c L d + k21(cL d − cL ) + k22

t∫0

(cL d − cL )dt(5)

Since we assumed that only lactose and oxygen are measuredonline, to complete the design of the controller, we performedthe zero dynamics analysis of the system. This analysis exam-ines the stability of internal dynamics of the unobserved states,namely, x, p, g, and n, when the control actions u1 and u2 (andhence FL and FA) calculated from Eq. (4) are imposed on theprocess. The process is operated in zero dynamics mode, by im-plementing the control actions u1 and u2 that was calculatedby setting the measured outputs l and cL, to zero. Choosing theoutput measurement function h(x) = [(l + ε �t) cL]T it can beshown (see Supporting information) that the zero dynamics isstable.

3 Results and discussion

The process analytical technology guidelines published by theUS Food and Drug Administration encourage building qualityinto the process [FDA 2004]. A successful implementation ofthe guidelines translates to the application of all necessary toolsincluding different methods of analysis, model building, devel-opment of soft sensors, data acquisition, and process control.The work carried out here is a step in that direction for lovas-tatin production. A systematic study, including theoretical andexperimental work was performed starting with the develop-ment of a model satisfying the conditions for control design, theestimation of its parameters, its validation by an independent setof experimental data, and concluding with a series of simulationsto demonstrate controller performance. We will first discuss themodel validation and then the performance of the controller.

3.1 Parameter estimation and validation of model

The parameters of the model were determined from the 7-Lbatch reactor data by non-linear regression using the Levenberg–Marquardt algorithm (Table 1). The total root mean square errorbetween model prediction and experimental data was 5.2 × 10−4

for the accepted parameters. From the dimension of the reac-tor, the airflow rate and the agitation speed used for performingthese experiments, kla equal to 35 h−1 was calculated. [16]. It wasobserved that the model described accurately the trends of thestate-time profiles (Fig. 3A). The incorporation of the parameterκ described well the observation that lactose utilization for theproduction of lovastatin increased when the glucose concentra-tion dropped below the glutamate concentration. The parameterκ shifts from low to high value as the fed-batch process progressesand is instrumental in capturing the change in metabolism fromcell growth to lovastatin production.

Using the parameters determined for the 7 L experimentaldata, the state-time profiles for the 15 L reactor was predicted.

For this simulation, only the initial values were provided to themodel and the state-time profiles were generated by numericalintegration (Fig. 3B). The calculated oxygen mass transfer coef-ficient kla was 60 h−1 based on the dimensions and the operatingconditions of the 15 L reactor. It was observed that the model un-derpredicts the cell mass, lactose and lovastatin concentrationsbut predicts the trend correctly. Hence, to evaluate the quality ofprediction, the experimental data were plotted against the pre-dicted data for each state variable (Fig. 4A–F). The quality ofprediction was analyzed statistically using the correlation coef-ficient (R2), the slope the linear regression line (m), the relativeerror (RE), and the Willmott index of agreement (d) (Table 2).Using d and RE in combination [19], the prediction of glutamateconcentration (n) was very good, the prediction of cell mass andglucose concentration was good and the prediction of lactoseconcentration was acceptable. The prediction of lovastatin anddissolved oxygen concentrations was just below the acceptablevalue for RE. The dissolved oxygen concentration measurementsthat were acquired online show variability that is difficult to as-cribe to a particular phenomenon. Similarly, the variability oflovastatin production rate is difficult to explain. If the corre-lation coefficient R2 and the slope of the linear regression linem are considered together, we observe that the prediction forlovastatin and dissolved oxygen does not meet the criterion ofR2 > 0.85 and 0.9 < m < 1.1. Lovastatin data gave a lower slopewhile the cL data gave a lower correlation coefficient. Overall,considering the statistics of prediction of all the variables, theperformance of the model was satisfactory.

As in this work, Dey and Pal [20] also used the Willmottindex to validate the prediction of their model. They developedan unstructured model of a hybrid reactor system for continu-ous production of l-lactic acid by Lactobacillus delbrueckii. Themodel consisted of 15 parameters that were evaluated against ex-perimental data. Parameter identification is a key step in processmodeling. Jimenez-Hornero et al. [21] examined the problemof parameter estimation for an acetic acid fermentation model.They determined the residuals for the optimal parameter set andobserved that these values were randomly distributed aroundzero. In addition, they observed that the SDs were similar to themeasurement errors in the state variables. Based on these criteria,it was concluded that the model would give accurate predictions.There are other reports on modeling of bioprocesses [22], all ofwhich recognize the importance of parameter estimation andvalidation. The determination of an acceptable set of parame-ters depends on both the quality and amount of experimentaldata.

3.2 Evaluation of controller performance

The non-linear controller for lovastatin production was de-signed using input-output linearization. The objective of thedesign was to use the lactose feed rate (FL) and the air-flow rate (FA), the inputs that can be most easily imple-mented as the manipulated variables for controlling the lo-vastatin process. The design required the decoupling of twointeracting feedback loops FL – l and FA – cL using input-output linearization. The theoretical analysis established that the



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ns (g

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stat

in (m

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xyge

n (%

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BFigure 3. Time profile data of process vari-ables used for the determination of themodel parameters and validation of pre-diction of the model. (A) Batch submergedcultivation experiments of a mutant strainof A. flavipes BICC 5174 were carried outin a 7-L bioreactor controlled at 30◦C,150 rpm, 6.5 pH, and 0.5 vvm airflow rate.The data obtained were used for identi-fication of the model parameters (♦ cellmass, � lactose, � glucose, ◦ lovastatin,× Na-glutamate, ∗ dissolved oxygen). Thebest fit curves are shown in full lines.(B) Batch submerged cultivation was per-formed under the same conditions but in a15-L bioreactor. The model was validatedby comparing the data obtained with theprediction of the model (♦ cell mass,� lactose, � glucose, ◦ lovastatin, × Na-glutamate, — - — dissolved oxygen). Thepredicted profiles are shown in full lines.

controller was stable. Therefore, to test the controller, a simplesimulation study was performed where the dissolved oxygencL, and the lactose concentration l was controlled along pre-determined trajectories. The initial conditions for the simula-tion were taken from the batch experiment carried in the 15 Lbioreactor. However, for the simulations of lovastatin produc-tion with the controller included in the feedback loop, the initialconditions for the inputs FL and FA were set to zero.

The simulation was carried out in two stages. First, the param-eters ki,j {i, j = 1, 2} were tuned to achieve the control objective.In the next stage, the process was simulated under the action ofthe non-linear controller. To mimic experimental conditions, thedissolved oxygen and lactose concentration values were mixedwith 10% random noise about their true values and presented tothe controller. Simulations were carried out in such a way that thecontroller was unaware of the presence of noise but the controlaction was calculated by the control algorithm based on mea-surements containing noise. The desired trajectory for lactosewas a square wave while that for oxygen was a linear trajectory;

both objectives were imposed simultaneously to test rigorouslythe performance of the controller. The square wave trajectoryfor lactose was defined based on its value at 72 h – a positivestep change of 10% at 72 h, followed by a 20% negative stepchange at 96 h and ending in a 10% positive change at 140 h. Theoxygen trajectory started at 50% and increased linearly to thefinal concentration of 70%. The tracking of the output oxygenand lactose concentration profiles along the predetermined tra-jectories is presented in Fig. 5A and B. The controller efficientlyneutralized interaction between the two loops FL – l and FA – cL,which was evident from the smooth convergence of the dissolvedoxygen to the desired linear trajectory. However, the presence ofinteraction between the variables was observed in the time pro-files of other state variables, x, p, n, and g. It was observed thatat the instances when step changes in the desired lactose con-centrations occurred and control action was taken, there was anoticeable change in all state variables simultaneously (Fig. 5C).We also observed that the control action FA was better than thatof FL. This happened because the sampling interval for oxygen



y = 0.8993xR2 = 0.9526

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Experimental Cell Concentration (g/L)

Pred

icte

d C

ell

Con

cent

ratio

n (g

/L)

y = 1.022xR2 = 0.981

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Experimental Glucose Concentration (g/L)

Pred

icte

d G

luco

se

Con

cent

ratio

n (g

/L)

y = 0.7961xR2 = 0.9437

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0 50 100 150 200 250 300

Experimental Lovastatin Concentration (g/L)

Pred

icte

d Lo

vast

atin

C

once

ntra

tion

(g/L

)

y = 0.8957xR2 = 0.9218

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Experimental Lactose Concentration (g/L)

Pred

icte

d La

ctos

e C

once

ntra

tion

(g/L

)

y = 1.0331xR2 = 0.9258

5

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9

11

13

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Experimental Na-Glutamate Concentration (g/L)

Pred

icte

d N

a-G

luta

mat

eCo

ncen

trat

ion

(g/L

)

y = 0.8216xR2 = 0.8135

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Experimental DO (%)

Pred

icte

d DO

(%)

A B

C D

E F

Figure 4. Comparison of model prediction with the experimental data. The data obtained from submerged cultivation experiments performedin the 15-L bioreactor were plotted against prediction of the model. The correlation coefficient R2 and the slope of the linear regressionm line are shown in the figures. (A) Cell mass, (B) glucose, (C) lovastatin, (D) lactose, (E) Na-glutamate, and (F) dissolved oxygen. Fivedifferent statistical measures were used for model validation (see text).



Table 2. Statistical parameters used to validate model.

X p l n g a

R2 0.97 0.97 0.93 0.94 0.99 0.81M 0.90 0.83 0.91 1.02 0.99 0.91Willmott Index 0.96 0.97 0.97 0.98 1.00 0.95RE 0.12 0.28 0.18 0.10 0.13 0.27

was 0.5 min and that for lactose was 3 min, in accordance withthe measurement time required for the corresponding sensor.The longer duration required for lactose measurement and itsslower uptake introduced variations in the feed rate FL calculatedby the controller.

The simulation results showed that lovastatin productionmodel possessed a structure that permitted the synthesis of acontroller in a systems sense. In terms of the biological require-ment, the controller should enable the process to stay in a de-sired metabolic domain that maximizes the yield of the product.Since fed-batch processes have been the preferred operationalmode in biopharmaceutical industry, there is a host of literatureon control design and application on this subject. Roman andSelisteanu [23] studied the process of enzymatic synthesis ofampicillin. They carried out the modeling, kinetic estimation,and designed an adaptive controller for this process. The pseudo-Bond graph method was used for modeling and a high gainobserver was constructed for determining the unknown ki-netics. The adaptive controller, which consisted of an exact

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Figure 5. Simulation results showing the performance of the controller when the objective was to (A) control dissolved oxygen along alinear trajectory {— l; — FL} and (B) control lactose along a square wave trajectory {— cL; — FA}. The non-linear controller was designedto remove interaction from {l-FL} and the {cL-FA} loops; the profiles in (A) and (B) show that this was achieved. In (C), the presence ofinteraction in the other controlled variables x, p, n, and g is shown, at the instances when control action was taken to satisfy the step-up andstep-down changes in the square wave lactose trajectory. The desired linear trajectory cLd and the square wave trajectory ld are shown (—)in (A) and (B).



linearizing law combined with the kinetic estimator, showedgood results in simulation experiments. Since the adoption ofprocess analytical technology guidelines, spectroscopic methodsare being used to obtain fast and reliable online measurementsand have become successful in certain cases to offset the problemof insufficient online data for control implementations. Schenket al. [24] have showed how mid-infrared FTIR spectroscopymay be implemented to monitor and control a methylotrophicPichia pastoris fed-batch fermentation process. In an indepen-dent work, Nui et al. [25] performed the dynamic modeling ofmethylotrophic Pichia pastoris with exhaust gas analysis. Themodel consisted of a biomass compartment and used metabolicstoichiometry so that a controller designed with the model couldmaintain the cells in a desired metabolic state. As in our work,there are reports on non-linear methods being applied to otherbioprocess control problems. For example, De Battista et al.[26], developed a non-linear proportional-integral (PI) con-troller to control the specific growth rate using on the mea-surements online. It was assumed that only the volume andcell mass concentration could be measured online; the sub-strate feed rate was used as the control input for the process.They also carried out simulation experiments in the presence ofmeasurement noise and offset, to test controller performance.The designed non-linear-PI controller exhibited robustness tomodel uncertainties and disturbances. Current publications inthis area show an encouraging trend in the development ofmodels, parameter identification, and control of bioprocesses,and a growing interest in developing mathematical frameworksto include more metabolic information for achieving cell-statecontrol.

4 Concluding remarks

The model for lovastatin production described the state-timeprofiles observed in experiments and the effect of glucose, lac-tose, and glutamate concentrations on lovastatin production.The model was validated with data obtained from a differ-ent reactor. A detailed statistical analysis showed a strong cor-relation between predicted and experimental data. The non-linear controllability and observability analysis demonstratedthat the model possessed the required structure for the onlineprocess control implementation. A non-linear controller wasdesigned using global linearization and decoupling of interac-tions between lactose and dissolved oxygen. The process wassimulated and the results obtained demonstrated satisfactoryperformance.

This research work was funded by the Department of Biotech-nology, Ministry of Science and Technology, Government of India(BT/PR6164/PID/06/276/2005).

The authors have declared no conflict of interest.

Nomenclature

A [m2] Cross-sectional areac∗

L [g L−1] Saturation value of dissolved oxygenconcentration

cL [g L−1] Dissolved oxygen concentrationcLd [g L−1] Desired value of dissolved oxygen

concentrationFA [L/m] Air flow rateFs [g L−1h−1] Glucose feed rateg [g L−1] Glucose concentrationKe [g L−1] Exponential equivalent of the Monod constantKG [g L−1] Monod constant for glucoseKi [g L−1] Glucose inhibition constantKL [g L−1] Monod constant for lactosekla [h−1] Oxygen mass transfer coefficientl [g L−1] Lactose concentrationld [g L−1] Desired value of lactose concentrationlF [g L−1] Lactose feed concentrationn [g L−1] Sodium glutamate concentrationN [rpm] Agitation speedp [g L−1] Lovastatin concentrationqA [h−1] Rate of oxygen utilizationV [m3] Volume of reactorV [L] Volume of reactorx [g L−1] Cell mass concentrationYPL [g g−1] Yield coefficient of lovastatin based on lactoseYXG [g g−1] Yield coefficient of biomass based on glucoseYXL [g g−1] Yield coefficient of biomass based on lactoseYXN [g g−1] Yield coefficient of biomass based on

Na-glutamateκ [g g−1] Parameter defined as n/(n+g)μ1 [h−1] Specific growth rate dependent on glucoseμ2 [h−1] Specific growth rate dependent on lactoseπ [h−1] Specific product formation rateμM [h−1] Maximum specific growth rateπM [h−1] Maximum specific lovastatin production rateadf

i g Successive Lie brackets of order iC Controllability matrixF(x) Vector of kinetic functionsG(x) Vector of transport functionsH(x) Vector of observation functionsLfh Lie derivative of h in the direction of fLgh Lie derivative of h in the direction of gN Dimension of the state vectorM Dimension of the input vectorO Observability matrixP Dimension of the output vectoru Vector of inputsv Vector of linearized inputsx Vector of state variablesy Output variables

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