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Developmentofnewunstructuredmodelforsimultaneoussaccharificationandfermentationofstarchtoethanolbyrecombinantstrain

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Biochemical Engineering Journal 28 (2006) 243–255

Development of new unstructured model for simultaneous saccharificationand fermentation of starch to ethanol by recombinant strain

Alexander Dimitrov Kroumov∗, Aparecido Nivaldo Modenes, Maicon C. de Araujo TaitWest Parana State University-Toledo, Department of Chemical Engineering, Faculty str., N 645, Garden “La Salle”, CEP 85903-000, Toledo-Parana, Brazil

Received 30 March 2005; received in revised form 3 October 2005; accepted 11 November 2005

Abstract

The development of simultaneous saccharification and fermentation of starch to ethanol (SSFSE) by genetically modified microbial strains hasbeen studied intensively [M.M. Altintas, B. Kirdar, Z.I. Onsan, K.O.Ulgen, Cybernetic modelling of growth and ethanol production in a recombinantSaccharomyces cerevisiae strain secreting a bifunctional fusion protein, Process Biochem. 37 (2002) 1439–1445; G. Birol, Z.I. Onsan, B. Kirdar,S.G. Oliver, Ethanol production and fermentation characteristics of recombinantSaccharomyces cerevisiae strains grown on starch, EnzymeMicrob. Technol. 22 (1998) 672–677; F. Kobayashi, Y. Nakamura, Effect of repressor gene on stability of bioprocess with continuous conversionof starch into ethanol using recombinant yeast, Biochem. Eng. J. 18 (2004) 133–141; F. Kobayashi, Y. Nakamura, Mathematical model of directeK onmentalf y ar sa .As SFSE step.I go hem.3 f starch toe ization andb bolization toe ecompositiona or differento ns.©

K

1

iltbc

rnedi-ologypro-

ratesiduesandpapermed

en-t of

1d

thanol production from starch in immobilized recombinant yeast culture, Biochem. Eng. J. 21 (2004) 93–101; M.M. Altintas, K.O. Ulgen, B.irdar, Z.I. Onsan, S.G. Oliver, Improvement of ethanol production from starch by recombinant yeast through manipulation of envir

actors, Enzyme Microb. Technol. 31 (2002) 640–647; K.O. Ulgen, B. Saygili, Z.I. Onsan, B. Kirdar, Bioconversion of starch into ethanol becombinantSaccharomyces cerevisiae strain YPG-AB, Process Biochem. 37 (2002) 1157–1168].Saccharomyces cerevisiae YPB-G strain secretebifunctional fusion protein containing enzymatic activity of theB. subtilis alpha-amylase and of theAspergillus awamori glucoamylase [M.Mltintas, B. Kirdar, Z.I. Onsan, K.O. Ulgen, Cybernetic modelling of growth and ethanol production in a recombinantSaccharomyces cerevisiaetrain secreting a bifunctional fusion protein, Process Biochem. 37 (2002) 1439–1445], and therefore is distinguished in relation to Sn this work we have used the experimental data, presented in the paper [M.M. Altintas, B. Kirdar, Z.I. Onsan, K.O. Ulgen, Cybernetic modellinf growth and ethanol production in a recombinantSaccharomyces cerevisiae strain secreting a bifunctional fusion protein, Process Bioc7 (2002) 1439–1445] to develop two-hierarchic-level unstructured mathematical model describing kinetics of direct bioconversion othanol. The first level has modeled enzymatic hydrolysis of starch to glucose by bifunctional protein and the second level includes utilioconversion of glucose to ethanol by yeasts. The second level has unified the enzymatic degradation of starch, and glucose metathanol by microorganisms. The response surface analysis was used to develop the rates models. A hybrid genetic algorithm and a dpproach were used in the nonlinear parameters identification procedure. The proposed model demonstrated excellent flexibility fperational conditions of SSFSE process, and can be used successfully to describe microbial physiology of genetically modified strai2005 Elsevier B.V. All rights reserved.

eywords: Recombinant yeast; Modeling; Kinetics; Ethanol; Simultaneous saccharification and fermentation

. Introduction

Ethanol has constantly been an object of interest because ofts multifaceted potential as fuel, beverage and precursor for aarge number of chemicals[7]. Ethanol has a capacity to matchhe features of petroleum and has the additional advantage ofeing produced from wide range of feedstock at relatively lowost. When blended with gasoline, ethanol improves fuels’ com-

∗ Corresponding author. Tel.: +55 45 3 379 7092; fax: +55 45 3 379 7002.E-mail address: adkrumov@unioeste.br (A.D. Kroumov).

bustion and reduces tailpipe emissions of CO and unbuhydrocarbons that form smog[8]. Recently, the world scence has focused on biomass-ethanol (“bioethanol”) techndevelopment, and on the commercialization of bioethanolduction. Special attention is given to the technology that libemonomeric sugars from biomass carbohydrates. The resfrom agricultural activities such as corn stover (corn cobsstalks), sugar cane waste, wheat or rice straw, forestry andmill discards, and dedicated energy crops, collectively ter“biomass”, can be converted to fuel ethanol[9]. The primarydifficulty for commercialization of ethanol produced by fermtation is its high cost of production relative to the local cos

369-703X/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.bej.2005.11.008

244 A.D. Kroumov et al. / Biochemical Engineering Journal 28 (2006) 243–255

Nomenclature

Enz enzyme concentration (U/m3)Et ethanol concentration (kg/m3)Glu glucose concentration (kg/m3)k rate constant (kg/U/h)K inhibition and saturation constants (kg/m3)Km Michaelis’ constant (kg/m3)per percent of susceptible starchqp specific ethanol production rate (1/h)R starch utilization rate (kg/m3/h)Renz enzyme synthesis rate (U/m3/h)RGlformation glucose formation rate (kg/m3/h)RGlutilization glucose utilization rate (kg/m3/h)S starch concentration (kg/m3)t time (h)X biomass concentration (kg/m3)Yp/s yield coefficient of product (kg/kg)Yx/s yield coefficient of cell growth (kg/kg)

Greek symbolsβ enzyme degradation rate (1/h)µ specific growth rate (1/h)

Subscripts0 initialmax maximumres resistant starchsus susceptible starchtotal total

gasoline. The production of ethanol from sugar cane is a relatively simple process. Starch is one of the renewable resourcethat are used for ethanol production. Traditional method of starchsaccharification involves actions of amylolytic enzymes (alpha-amylase and glucoamylase) and the process is completed in festeps such as liquefaction and saccharification[10]. A challeng-ing perspective is to apply one-step process of SSFSE[11]. Theprocess is much more economical not only in terms of savingoverall fermentation time but also in term of reducing reactor.The other direct advantage of SSFSE is that the concentratioof enzymatic formed glucose is kept low which decreases inhi-bition effect of glucose on amylolytic enzymes[12].

A large number of studies have been published concerningthis matter. Different systems of SSFSE were applied involvingfree [11,13,14]and immobilized mixed culture[15–17]. Somestudies have shown that using the industrial wastes for SSF process could reduce production cost[18–20].

Nowadays, the most challenging perspective for SSFSEprocess is to use recombinant strains[21–24], mainly Saccha-romyces cerevisiae [1–6]. Microorganisms used in the SSFSEhave undergone continuous improvement, especially with theapplication of genetic engineering. Recently,S. cerevisiaehave been genetically engineered to convert directly starchto ethanol. A recombinant strainS. cerevisiae YPB-G, whichsecretes a bifunctional fusion protein that contains both the

Bacillus subtilis alpha-amylase and theAspergillus awamoriglucoamylase activities, was studied in a SSFSE process forethanol production[1,2].

In order to increase starch conversion efficiency several kinet-ics models have been developed[25–28]. The obtained expe-rience from application of cybernetic modeling approach inmultisubstrate environment[29–35]has been applied one moretime for description of SSFSE process by recombinant strainof S. cerevisiae YPB-G by authors[1]. In cybernetic modelingthe crucial parts are the key enzyme synthesis rates descriptionand the enzyme balance equation. They combine the knowl-edge of catabolic repression and induction processes from amolecular level with the phenomena of enzyme degradation anddilution, which take place on the population level of biomassgrowth [1,29–35]. Such accumulation of knowledge is espe-cially important and useful for the authors’ efforts to developa new unstructured model of SSFSE process by recombinantstrains.

In the present work, experimental data of SSFSE processusingS. cerevisiae YPB-G recombinant strain[1] were evaluatedin order to develop two-hierarchic-level unstructured model. Themodel development included an application of surface responseanalysis methodology for evaluation of the key parameters ofthe kinetic rates models and for the analysis of the amylolyticenzymes synthesis rate and balance equation. The proposedhere model describes the following physiological properties oft cs ofs olvedi tion,r duc-t andp

2

turalmY d ont

2

byg com-b etica thisk g oft odeld of theh is ther ctionsh tiono tionswa is byr sh

-s

w

n

-

he recombinant strain in starch-containing media: dynamitarch enzyme degradation and key enzyme synthesis inv

n the hydrolysis process, glucose accumulation and utilizaecombinant strain growth characteristics and ethanol proion in the SSFSE step. Dynamics of enzyme excretionlasmid stability are out of consideration.

. Model development

The objective of this study was to develop a non-strucodel describing a SSFSE by recombinant strain ofS. cerevisiae

PB-G [1]. The strategy of model development was basehe two hierarchic level of knowledge.

.1. First hierarchic level

The first level considers enzymatic hydrolysis of starchlucoamylase (this enzyme in our case is secreted by the reinant strain). We studied the thermodynamics and kinspects of the network of hydrolytic reactions and utilizednowledge in the modeling. On the other hand, modelinhe starch structure seems to be the key stage of the mevelopment process. The most significant phenomenonydrolysis process of starch is its slow second phase, whicheason to structure starch into susceptible and resistant fraaving different hydrolyzing rates. A mathematical descripf the hydrolysis process of starch as two substrate fracas developed and published in details by authors[27]. Wepplied and adapted this knowledge to the starch hydrolysecombinant strain ofS. cerevisiae YPB-G. The enzyme kineticydrolysis model can be written as follows:

A.D. Kroumov et al. / Biochemical Engineering Journal 28 (2006) 243–255 245

Enzymatic rate of susceptible starch fraction degradation:

Rsus= ksus× Enz(t) × Ssus(t)

Km

(1 + Glu(t)

Kglu

)+ Ssus(t)2

Kstarch+ Ssus(t) + Sres(t)

(1)

Enzymatic rate of resistible starch fraction degradation:

Rres = kres× Enz(t) × Sres(t)

Km

(1 + Glu(t)

Kglu

)+ Sres(t)2

Kstarch+ Ssus(t) + Sres(t)

(2)

Mass balances of starch susceptible and resistant fractions:

dSsus(t)

dt= −Rsus (3)

dSres(t)

dt= −Rres (4)

Balance of total starch degradation:

dStotal(t)

dt= dSsus(t)

dt+ dSres(t)

dt(5)

Balance of glucose produced during starch susceptible and resis-tant fraction degradation:

dGlu(t)

dt= 1.111(Rsus+ Rres) (6)

The model assumptions on this level are based on the concept toa onb

1 d iylaetio

eym

2 ion

3 ncethentr

4 oby

ctio

5 f th

2

opul hysi

roduf

with simple unstructured mathematical formulas taken fromour kinetic models catalogue date base[36–38]. We assumedthat specific growth rate of recombinant strain is influencedby glucose, and by initial and total starch concentrations. Sev-eral kinetics models were tested and sensitivity analysis showedthat our mathematical mode best fitted the experimental data.Specific ethanol production rate was described as a function ofglucose, initial starch and ethanol concentrations. On the otherhand, this rate can be interpreted as a nonlinear function of spe-cific growth rate.

The second level model equations are written as follows:Specific growth rate model:

µ =µmax × Glu(t) ×

(Stotal(t)

S0

)

Ks + Glu(t)(7)

Ethanol production rate model:

qp =qpmax × Glu(t) × Et(t) ×

(1 − Et(t)

Etmax

)

(Ks1 + Glu(t))(Kps1+ Et(t) + Et(t)2

Kpi

) (8)

Biomass balance:

dX(t)

dt= µX(t) (9)

Product balance:

ientua-ent

ierar-

:

-

1.111.e and

pply robust model[27] for description of starch saccharificatiy one additive enzyme activity:

. The model considers one additive enzyme activity involvethe saccharification process of starch (sum of glucoamand alpha-amylase activity during the process of secrby S. cerevisiae YPB-G). It is assumed that this two-enzymaction can be simplified and represented like additive enzactivity.1

. The starch structure can be considered as a composittwo fractions in relation to its degradation rate.

. The susceptible fraction hydrolysis rate depends on cotration of two starch fractions and is inhibited by both,action of glucose and susceptible starch fraction concetions.

. The resistant fraction hydrolysis rate is a functionconcentration of two starch fractions and is inhibitedboth, the action of glucose and resistant starch fraconcentrations.

. Mass transfer limitations and conformation changes oenzyme structure are out of consideration.

.2. Second hierarchic level

The second hierarchic level involves knowledge about pation microbial kinetics. We were trying to describe some pological phenomena of recombinant strainS. cerevisiae YPB-G

1 One unit of enzyme (U) represents an enzyme necessary quantity to prom starch 1 kg of glucose per hour.

nsen

e

of

n-

a-

f

n

e

--

ce

dEt(t)

dt= qpX(t) (10)

Glucose balance:

dGlu(t)

dt= RGlformation− RGlutilization (11)

where:

RGlformation = 1.111(Rsus+ Rres) (11a)

RGlutilization = 1

Yx/s

dX(t)

dt+ 1

Yp/s

dEt(t)

dt(11b)

Coefficient “1.111” included in Eqs.(6) and (11a) isdefined as the theoretical yield or stoichiometric coeffic(YGl/St = 1.111).2 It was obtained from the stoichiometric eqtion of hydrolysis of starch into glucose in the water environm[39].

Microbial kinetics model is flexible and Eq.(11) (glucosebalance) is a key equation, which unites first and second hchical levels of knowledge. This glucose balance Eq.(11) has

2 The equation of starch hydrolysis to glucose can be written as follows

(C6H10O5)n + (n − 1)H2O → n(C6H12O6)

The theoretical yield coefficient for starch conversion to glucoseYGl/St is therefore:

YGl/St = 180× n

(180× n − (n − 1) × 18)

as n becomes large, as in the starch molecule, this factor becomesTherefore, complete hydrolysis of 1 g of starch yields 1.111 g of glucoscorresponds to a theoretical yield.

246 A.D. Kroumov et al. / Biochemical Engineering Journal 28 (2006) 243–255

shown dynamics of glucose formation and glucose utilizationfor different cell purposes. In our case, glucose is used mainlyfor biomass and ethanol overproduction.

Enzyme balance:

dEnz(t)

dt= Renz− (µ + β) × Enz(t) (12)

Renz = (µmax + β) × Enzmax × Stotal(t)

Kenz+ Stotal(t)(13)

β is enzyme degradation rate;Renz is enzyme synthesisrate;µEnz represents “dilution” of the enzyme as a result ofthe growing cell mass.

In our caseRenzsynthesis rate includes only an enzyme induc-tion term multiplied by total starch concentration. The term,which may represent the catabolic repression by glucose formedduring hydrolysis process, is considered negligible because ofthe low glucose concentration in the medium. In batch culturethe total enzyme pool is constant, and the key enzyme synthesisrate for starch is assumed to be proportional to the fraction of thetotal population utilizing starch. It means that the key enzymesynthesis balance can be written as follows:

dEnz(t)

dt= Renz− µEnz(t) − βEnz(t) (14)

The model of SSFSE is completed and it describes enzymeh inans h,a tiona

w hodsR de”p r thi

reason Rosenbrock numerical method was used for the mostcomputer simulations.

3. Nonlinear parameter identification procedure

The values of kinetic and stoichiometric parameters wereestimated using experimental data[1]. Several sets of batch dataof recombinant strain cultivation on starch were examined. Themodel Eqs.(1)–(14)were used to search parameters values byfitting experimental data.

A nonlinear parameter identification procedure can be for-mulated and the system of ordinary differential equations canbe rewritten as follows:

�η = f ( �X, �θ, t) (15)

where: vector�η = {η1, η2, . . . , ηm} is a measured state vector (inour casem = 4); vector�X = {X1(t), X2(t), . . . , Xk(t)} is a mea-sured vector of dependent variables (in our casek = 7); vector�θ = {θ1, θ2, . . . , θl} is a measured vector of kinetic and stoichio-metric parameters, with the unknown exact values (in our casel = 14); t time.

It is assumed that a vector of observations�y has a normallaw of distribution with the mathematical expectation equaltof ( �X, �θ, t). A vector �ε = {ε1, ε2, . . . , εm} is a normal vectorof observations errors. It is necessary, to evaluate values of vec-t �y

T on ofm resr nds toe

TD A in

S

1

2 Gl =

3 St =

4 St =

5 t = w

6

W

ydrolysis of starch by glucoamylase secreted by recombtrainS. cerevisiae YPB-G. It also describes microbial growtmylolytic enzyme synthesis, glucose synthesis and utilizand ethanol overproduction.

The system of nonlinear ordinary differential Eqs.(1)–(14)as solved using Maple software and numerical metKF45, Rosenbrock and Adamsfull method from the “lsoackage. The system did not manifest strong stiffness, fo

able 1ecomposition procedure of the multi-objective function SSt used by hybrid G

tep Search procedure Criterion

Global direct search SSt =4∑

j=1

wj

Nj∑i=1

(yi,j−fj ( �X,�θ,t)

yi,j

)2

wSt = wGl = wEt = wX = const.

Local search of starch SSSt = wSt

N1∑i=1

(yi,St−fSt( �X,�θ,t)

yi,St

)2

w

Local search of glucose SSGl = wGl

N2∑i=1

(yi,Gl−fGl( �X,�θ,t)

yi,Gl

)2

w

Local search of ethanol SSEt = wEt

N3∑i=1

(yi,Et−fEt( �X,�θ,t)

yi,Et

)2

w

Local search of biomass SSX = wX

N4∑i=1

(yi,X−fX ( �X,�θ,t)

yi,X

)2

wS

Global modified search SSt =Nc∑j=1

wj

Nj∑i=1

(yi,j−fj ( �X,�θ,t)

yi,j

)2

wSt = wGl = wEt = wX = const.

herej = number of state variables;i = number of experimental points.

t

,

s

or θ on the base of experimental data{y1, y2, . . ., yk}.

� = f ( �X, �θ, t) + �ε (16)

o obtain the evaluated parameters values, a minimizatiulti-objective function (error function) with weights we

earched (seeTable 1, Step 1), wherej = 1–4→ index; 1 cor-esponds to starch; 2 corresponds to glucose; 3 correspothanol; 4 corresponds to biomass.

the search of a global optimum

Initial guess of parameters bounds

�θmin ≤ �θ ≤ �θmax Modified bounds after the localsearch�θmin ≤ �θ ≤ �θmax

wEt = wX = 0 θi,max= θi,Step2(1 +pi); θi,min = θi,Step2(1− pi); θi = 10–14

wEt = wX = 0 θi,max= θi,Step3(1 +pi); θi,min = θi,Step3(1− pi); θi = 3–4

wGl = wX = 0 θi,max= θi,Step4(1 +pi); θi,min = θi,Step4(1− pi); θi = 2,5,7–9

Gl = wEt = 0 θi,max= θi,Step5(1 +pi); θi,min = θi,Step5(1− pi); θi = 1–6

If the solution is not acceptable, go to Step 1 withreduction of the parameters range�θmin ≤ �θ ≤ �θmax

A.D. Kroumov et al. / Biochemical Engineering Journal 28 (2006) 243–255 247

Table 2Information matrix of the system equations

θ1, µmax θ2, qpmax θ3, Yx/s θ4, Yp/s θ5, Etmax θ6, Ks θ7, Ks1 θ8, Kps1 θ9, Kpi θ10, Kglu θ11, Kstarch θ12, per θ13, ksus θ14, kres

Eq.(5) 0 0 0 0 0 0 0 0 0 1 1 1 1 1Eq.(9) 1 0 0 0 0 1 0 0 0 0 0 0 0 0Eq.(10) 0 1 0 0 1 0 1 1 1 1 0 0 0 0Eq.(11) 1 1 1 1 1 1 1 1 1 1 1 1 1 1

The conditions of minimum of SSt can be written as fol-low ∂SSt/∂θi = 0, and the multi-objective function SSt can beminimized using a global optimizer such as hybrid genetic algo-rithm (GA). In the preliminary computational studies, the directsearch of optimal parameters vector�θ (seeTable 1, Step 1) didnot give promising results. The initial guess of�θ for the chosenhybrid GA was transformed into the guess of a range of param-eters vector as follows�θi,min ≤ �θi ≤ �θi,max. The range of everykinetic or stoichiometric parameter was determined on the baseof its microbiological meaning. In hybrid GA, which we used inthis work the selection method of parents is based on a tourna-ment method. We used the performance of hybrid GA with, thefollowing parameters value: crossover = 0.6 and mutations = 0.2.As a rule of thumb, the crossover probability is generally in therange of 0.5–0.85, which includes recommended values[40].The best solution from every generation is preserved into thenext one. This is in case the GA does not find a better solutionduring the search. A higher value of this elitism operator typi-cally leads to premature convergence identified by the GA[41].Reinitialization of the chromosomes corresponds to 20% of newgeneration. More details about the hybrid GA can be found inthe literature[42–45]. If, during the search GA reaches theithlower or upper parameter bound a penalty on objective functionis applied. A population size of 40 has been determined and theGA was run for 300 generations. The results of this direct searchof a “global optimum” of SSwere far away from satisfactorious( alcul entow elle s. Bc formo ncef thed andk ettec forS edo sing2 le.

3m

toh ec-tt n in

Table 2. Some kinetic parameters were fixed (β, Kenz, Enzmax,Km) during the identification procedure. Their values were takenfrom the literature[1] and are shown inTable 3. In order to min-imize the SSt we applied a step-by-step procedure of a search ofoptimal values of 14 parameters (Table 1), which includes thefollowing steps:

Step 1. The initial direct search of a “global optimum” ofSSt using GA starts with initial guess of parameters bounds,which are determined from microbiological point of view (seeTable 3). When a search is completed, a graphical represen-tation of the results is analyzed. It was observed that dur-ing the direct search of global optimum solution only starchconcentration profile from the model was fitted satisfactorywell to the experimental data. It means, that the global task(SSt → min) can be divided to the local tasks changing thevalues of weight coefficients (wi = 0). Hence, the first localtask can be solved by using SSSt criterion (seeTable 1, Step 2wherewSt = const.). In a step-by-step procedure of search-

Table 3Kinetic and stoichiometric parameters values and initial conditions of the model(Eqs.(1)–(14))

S30 SG30 SG50 Units

Initial conditions

F

E/h/h

Ks1 2.721 1.688 1.924 kg/m3

Kps1 0.094 2.531 0.783 kg/m3

Kpi1 88.7 238 210 kg/m3

tsimulation data are not shown). We have repeated all the cations for five times, but did not get any further improvemf the global task solution (ST→ min). The value of vector�θas far away from the optimum and the model did not fit wxperimental data of glucose and ethanol concentrationhanging GA parameters, weight values and mathematicalf SSt we did not find any improvement of the GA performa

or the given 14 model parameters. Using the analogy withecomposition principle from the system analysis theorynowledge about the GA performance, we tried to obtain boncentrations profiles and global or near global optimumSt multi-objective function. All computations were performn a Pentium IV processor at 2.0 GHz under Windows XP u56 MB of RAM. The software programs were written in Map

.1. Decomposition approach applied for theulti-objective function of SSt

A decomposition algorithm for SSt has been developedelp GA in the search of “global optimum” solution. The v

ors of chosen parameters for minimization of SSt criterion andheir distribution in balance equation of the model are show

-

y

r

Glu0 0.01 3.5 3.5 kg/m3

S0 24 30 42.5 kg/m3

X0 0.18 0.2 0.1 kg/m3

Et0 0.1 0.5 0.5 kg/m3

Enz0 0.001 0.001 0.001 U/m3

ixed parametersβ 0.05 0.05 0.05 1/hKenz 1 1 1 kg/m3

Enzmax 6.0 6.0 6.0 U/m3

Km 0.406 0.406 0.406 kg/m3

valuated parametersksus 0.0368 0.0820 0.0537 kg//Ukres 0.0106 0.0033 0.0030 kg//UKstarch 69.4 65.6 66.7 kg/m3

Kglu 1.176 1.226 2.132 kg/m3

Per 0.786 0.750 0.786µmax 0.101 0.0615 0.098 1/hYx/s 0.485 0.175 0.512 kg/kgKs 2.184 0.106 0.292 kg/m3

Etmax 11.16 10.6 20.8 kg/m3

qp,max 0.196 0.645 0.415 1/hYp/s 0.462 0.640 0.301 kg/kg

248 A.D. Kroumov et al. / Biochemical Engineering Journal 28 (2006) 243–255

ing local optima by GA, the following order of the localtask was obtained: SSSt→ SSGl → SSEt → SSX → min. In ourcase, biomass concentration can be considered as a key compo-nent of the system. For this reason, the local task (SSX → min)will be solved in the last step (see Step 5).Step 2. The search of local optimum solution (SSSt→ min)means to minimize the differences between starch concentra-tion of the model (seeTable 1, Step 2) with experimental starchprofile. Analyzing the solution of the search of the local task(SSSt→ min) we have observed “quasi” perfect match betweenmodel prediction and experimental data. To preserve this localoptimum solution we reduced the ranges of parameters, whichare included in the corresponding starch balance (θ10–14). Thisis the key moment of the decomposition procedure. The chosenvariance was between pi = 1–50% from the obtained estimatedparameters values (θ10–14) giving optimal solution of the localtask (SSSt→ min). It is important to notice that these modifiedparameters ranges are entering the next local task (Step 3) andother ranges of parameters continue to be equal to those fromthe Step 1.

Step 3. This step is a crucial one, because all parameters ofthe system (seeTable 2) are involved in the glucose bal-ance (Eq.(11)). A lot of runs of the GA were set to obtainlocal optimal solution not only for SSGl, but also for SSX andSSEt, as well. The search in this step includes “quasi” fixedparameters from the previous local task (θ10–14). After thesearch with GA it was observed that SSGl reaches a local opti-mum. Analysis of the graphical representation of the resultsshowed several local optima for the other local tasks. Topreserve this local optima, ranges of parameters (θ3–4) werereduced.Steps 4 and 5. In this way, solving the local tasks step-by-step,we were able to select “quasi” optimal solutions for the leftlocal tasks and to preserve them into the reduced parametersranges (seeTable 1, Steps 4 and 5).Step 6. Finally, when we have executed Step 6 we were ableto achieved “quasi global optimal” solution for the multi-objective function (SSt → min) and to stop the search or toreduce ranges of all parameters and to go back to the Step 1and continue (seeTable 1).

Fv

ig. 1. Case S30: (a) total starch, susceptible starch, resistant starch and enzs. time; (c) ethanol and biomass concentration profiles vs. time.

yme concentration profiles vs. time; (b) total starch and glucose concentration profiles

A.D. Kroumov et al. / Biochemical Engineering Journal 28 (2006) 243–255 249

The search could be stopped if the results from Step 6 aresatisfactory good in terms of SSt, and�θ values. Otherwise, theidentification procedure has to continue from Step 1, where theinitial guesses of the parameters bounds will be chosen on thebases of information, which has been accumulated from Steps 1to 6 and preserved in the last search of SSt → min (see Step 6).

The global optimum solutions of GA for all cases S30, SG30,SG50 are classified as follows: the estimated values of kineticand stoichiometric parameters are shown inTable 3and the cor-responding with them model concentration profiles which havefitted the experimental data are presented in theFigs. 1–3.

4. Results and discussion

4.1. Modeling specific rates

Several models of starch hydrolysis[25–28]have been sub-ject of evaluation. There are lots of studies in enzyme kineticsabout substrate-inhibition effect when a nonproductive bindingof substrate to enzyme is considered and additional parametersuch asKi is required for description of the kinetics. A lin-

earization of the model is convenient to determinedKs, Ki andmaximum rate constants[46].

More complex models which include influence of more thanone state variable (two or three substrates and product) neednonlinear parameter identification. A response surface analysis(RSA) [16,47,48]of such models is a powerful tool for com-plex evaluation of the models behavior as a function of statevariables. Using RSA we have examined all the rate modelsincluded in the SSFSE process (see Eqs.(1)–(14)). The con-stants values used in RSA simulation are taken (seeTable 3)after the completion of data fitting procedure, and the ranges ofstate variables are chosen to cover the experimental operationalconditions. In theRsus andRres models (see Eqs.(1) and(2))the values of constantsKglu andKstarch have a crucial role onRsusandRres responses. If their values are low and close to theworking concentration values of glucose and starch, then thestrong inhibition effects on the hydrolyzing enzyme activity canbe observed. Otherwise, when their values are highRsusandRresare transformed into the simple models describing Glu and Stsubstrate limitations.Rsusdependence from three state variables(Ssus, Sres, and Glu) can be observed inFig. 4. In (Fig. 4a) Rsus

Fv

ig. 2. Case SG30: (a) total starch, susceptible starch, resistant starch and ens. time; (c) ethanol and biomass concentration profiles vs. time.

zyme concentration profiles vs. time; (b) total starch and glucose concentration profiles

250 A.D. Kroumov et al. / Biochemical Engineering Journal 28 (2006) 243–255

Fig. 3. Case SG50: (a) total starch, susceptible starch, resistant starch and enzyme concentration profiles vs. time; (b) total starch and glucose concentration profilesvs. time; (c) ethanol and biomass concentration profiles vs. time.

response depends exclusively on susceptible starch concentra-tion. The glucose inhibition effect onRsus hydrolysis rate, forthe given concentration range, can be neglected. The similarSsusconcentration effect can be observed because of the highKstarchvalue (Kstarch= 67). A combined effect of Glu andSres concen-tration results in minimum value ofRsusenzyme hydrolysis ratein the pointSres= 12.5, Glu = 3.5 (Fig. 4b), and the influenceof these state variables can be approximated as a linear. Theeffect of two-starch fraction on theRsusrate is shown inFig. 4c,where the hydrolyzing rate depends mainly on the susceptiblestarch fraction concentration. We evaluatedRressurface responsesimulation results and found close similarities with theRsusresults.

It is a well-known fact that the ethanol production rate isinhibited by product concentration[36–38]. The most impor-tant steps of unstructured kinetic model development of ethanolproduction are considered to be the modeling of specific growthrate and specific ethanol production rate. In order to developrobust and flexible models of specific growth (µ) and specificproduction rates (qp) we used glucose (Glu) and starch (St) con-centration as state variables in the RSA.

In order to select the best ethanol production rate descrip-tion we examined three kinetic hypothesis ofqp (seeFig. 5).The chosen by us complexqp model (seeFig. 5a) was subjectof detailed studies for different combination of constants andstate variables values and the model response was compared tothe different experimental values.Fig. 5a shows thatqp passesthrough the maximum (approximately in 1 kg/m3 of ethanol) andafter that the surface area is formed by the sets of second orderscurves whereqp decreases with the increasing of ethanol con-centration. The decreasing ofqp rate is determined byKpi (themeaning ofKpi was explained earlier in the paper) and Etmaxconstants values. Etmax is a crucial kinetic parameter in thismodel, because its value determines the minimum (zero) valueof ethanol production rate. The Etmax values can be found inthe literature and these values depend mainly on the operationalconditions and used microbial strain[36]. The Etmax weightis very significant when compared models responses from theFig. 5. As one can observeqp decreases linearly as a func-tion of ethanol concentration and reaches zero when Et = Etmax(Fig. 5b). Hence, for different recombinant strains and exper-imental conditions this parameter can serve as an indicator of

A.D. Kroumov et al. / Biochemical Engineering Journal 28 (2006) 243–255 251

Fig. 4. Response surface analysis of resistant starch utilization rate as a function of state variables: (a) glucose and susceptible starch concentrationksus= 0.05 kg/U h,Enz = 10 U/m3, Kglu = 2.32 kg/m3, Kstarch= 67 kg/m3, Km = 0.406 kg/m3, Sres= 13 kg/m3; (b) glucose and resistant starch concentrationksus= 0.05 kg/U h,Enz = 10 U/m3, Kglu = 2.32 kg/m3, Kstarch= 67 kg/m3, Km = 0.406 kg/m3, Ssus= 30 kg/m3; (c) resistant and susceptible starch concentrationksus= 0.05 kg/U h,Enz = 10 U/m3, Kglu = 2.32 kg/m3, Kstarch= 67 kg/m3, Km = 0.406 kg/m3, Glu = 3.5 kg/m3.

process duration. Appearance ofqp maximum in the complexmodel 6a profile is determined by the non-competitive productinhibition term. As it was mentioned previously the value ofqpmaximum and nonlinearity of theqp = f(Et) curves depend onKpi values. An evaluation of the influence of glucose concen-tration onqp (qp = f(Glu)) for the three chosen models (Fig. 5)showed that the well-known limiting effect of substrate dependsonKs1 value, that is usually very low for glucose substrate. Theeffect is very clearly manifested (seeFig. 5c) upon analysis ofthe surface response of the system (qp = f(Glu)) for the ethanolconcentration equal to 15 kg/m3.

Analyzing the possibility to representqp as a linear functionof (µ) by Leuderking–Pirt low (qp =αµ +βX), we found thatwe have to considered two substrate effects which take place inthe (µ) description. The total starch determines the linear depen-dence ofµ from its concentration, and the glucose concentrationhas a limiting effect on specific growth rate. Surface responseanalysis of this model showed that for our case this represen-tation does not have a good fundament. On the other hand, theterm in Leuderking–Pirt model describing the stationary phaseproduction of ethanol (βX) is operational even after the com-plete consumption of glucose by the cells. This phenomenontakes place in secondary metabolite overproduction but in case of

ethanol production this description should be a major drawbackand will give a mismatch between predicted and experimentaldata at the end of the process (seeFigs. 1c, 2c and 3c).

Finally, the surface response analysis of the ethanol produc-tion rate modelqp showed that the first mathematical form (seeFig. 5a) is very complex, flexible and robust and can be appliedfor the description of ethanol overproduction by recombinantmicrobial strain. The Etmax parameter can be interpreted like anindicator of strain sensitivity to elevated product concentrations,and when its value is very high the model can be reduced to amore simple form.

We reduced the level of sophistication in the kinetic hypothe-sis ofµ description (seeFig. 6). In the specific growth model GluandStotal were chosen as state variables. Observing the resultsof RSA (seeFig. 6) it can be found thatµ does not dependon Glu concentration above 1.5 kg/m3 and linearly depends ontotal starch concentration. In the initial time of SSFSE processwhen glucose is presented in the medium the recombinant strainreaches maximum specific growth rate in terms of the relationµ = f(Stotal).

Finally, we should notice that RSA was used repeatedly notonly for rates models evaluation but also in the procedure ofmodel development of SSFSE process.

252 A.D. Kroumov et al. / Biochemical Engineering Journal 28 (2006) 243–255

Fig. 5. Response surface analysis of specific ethanol production rate as a function of state variables glucose and ethanol concentration for the model: (a) qp =qp maxGlu(t)Et(t)(1−(Et(t)/Etmax))

(Ks1+Glu(t))(Kps1+Et(t)+(Et(t)2/Kpi)); (b) qp = qp maxGlu(t)(1−(Et(t)/Etmax))

(Ks1+Glu(t)) ; (c) qp = qp maxGlu(t)Et(t)

(Ks1+Glu(t))(Kps1+Et(t)+(Et(t)2/Kpi)).

4.2. Model behavior fitting experimental data

The results from developed decomposition algorithm for SStcan be seen in (Table 3andFigs. 1–3) The evaluated stoichiomet-ric and kinetic constants values are in agreement with the onespublished in the literature for the SSFSE process. The applica-tion of hybrid GA together with system decomposition showed

Fig. 6. Response surface analysis of specific growth rate (see Eq.(7)) as afunction of state variables: total starch and glucose concentration.

fast localization of “global optimum” solution. The dimensionof 14 parameters identification task was high and the directminimization of SSt was impossible to reach even after 300generation performing by GA. InTable 2is shown informa-tive matrix of the system equation and constants distribution inthe balance equations. It is obvious that Eq.(11) can be con-sidered as the key one in the search of global solution of SStcriterion. The preservation of local solution of SSSt, SSEt, SSXwere coordinated with the local solution of the SSGl. The modelof SSFSE process behaved very well and there were no drasticmismatch between experimental and simulation data (Figs. 1–3).We believe that some deviations between predicted and experi-mental profiles of biomass and ethanol at the end of the process(seeFig. 1c, 2c and 3c) are not a result from unstructured mod-eling simplification. Most probably, the reason is very complexand includes as well errors from the experimental design andperformance.

In Fig. 1a (case S30) the simulation profiles of total starchconcentrationStotal, two starch fractionSsus, Sres and Enz con-centrations are shown, where the starch is the only carbon andenergy source for the recombinant strain. It is clear that in SSFSEprocess low glucose concentration maintenance is required inorder to build up high ethanol productivity. The model simula-tions have shown the dynamics of starch degradation by overall

A.D. Kroumov et al. / Biochemical Engineering Journal 28 (2006) 243–255 253

enzymatic action of alpha-amylase and glucoamylase. By ana-lyzing SsusandSres andStotal concentration profiles, we recog-nized two periods of starch degradation. The first one ended at110th h, and theStotal starch concentration profile followed theSsusprofile. The second period was from 110th to 140th h and theStotal curve was alike with theSrescurve. This phenomenon wasthe base of model development of the starch enzymatic degrada-tion and was manifested very clearly in all presented cases (seealsoFigs. 2a and 3a). The enzyme activity increased rapidly fromthe 1st to 10th h and after that reached plateau between 20th and50th h. This fact could easily be explained with the glucose con-centration profile (seeFig. 1b). Glu concentration values duringthese hours are sufficient to inhibit the enzyme synthesis rate.After 50th h, the Glu concentration drastically decreased andenzyme concentration has reached the second maximum. Com-paring the simulation results with the experimental ones forStotal(seeFig. 1b) we found quasi-perfect match between them. InFigs. 2a and 3athe enzyme profiles are smooth and the glucoseinhibition can be neglected (seeFigs. 2b and 3b) because of itsfast utilization.

Keeping the level of glucose concentration low was crucial forthe rapid starch degradation process (seeksusvalues inTable 3),as well. On the other hand, very low level of glucose in themedium decreases specific growth rate (seeµ values inTable 3).The model fits very well and representation of starch degradation(first hierarchic level of knowledge) is an excellent approxima-t g thevvTS nes

rw ofK theE 50i th (int eren andc sy toe lu-c entlt te os ringh press howb fors nflu-e tarch on-c cings l ane

rvet theva tedb (se

Figs. 1c, 2c and 3c). For all cases the biomass concentrationat the and of the SSFSE process reached the same level andethanol concentration gradually increased, but significant partof the substrate was used for growth maintenance.

Because of these facts, the most difficult part of parameteridentification procedure was to fit X and Et experimental pro-files. The biomass experimental data deviation was the highest,which has influenced the correct interpretation of the SSFSEprocess.

5. Conclusions

Two hierarchic levels of knowledge were combined todevelop an unstructured model of simultaneous saccharifica-tion and fermentation of starch to ethanol (SSFSE) by genet-ically modified strainS. cerevisiae YPB-G. The model wastested using the experimental data, presented in the paper[1].The first hierarchic level included a mechanism of enzymatichydrolysis of starch to glucose where combined actions oftwo enzymes (alpha-amylase and glucoamylase) secreted byrecombinant yeast were modeled as additive enzyme activity.The model simulations at this level proved the correctness ofthe model assumptions about representation of starch structurein two fractions and enzyme activity as an additive enzymeaction. For all three different cases (seeFigs. 1b, 2b and 3b)t eri-m rche archaa tionalc

gra-d on ofg bialp deds ores opedt

q statev entalo

bridG -t tionw h ofS The1 eval-u ose,b edurec ms.

flex-i ss,a logyo sf

ion to the hydrolyzing process. This can be proved analyzinalues ofKstarch, Kglu inhibition constants for all cases (Kstarchalue is above 65.6 kg/m3, Kglu value is above 1.226 kg/m3, seeable 3). Hence, for all cases (seeFigs. 1b, 2b and 3b), predictedtotal and Glu profiles matched perfectly the experimental o

For the given set of experimental data, theqp model behavioas controlled by Etmax value (seeTable 3) because the valuepi was very high (238 kg/m3 for case SG30). It means, thatt inhibition effect determined byKpi for case SG30 and SG

s not significant. Biomass and ethanol profiles were smooerms of diauxic growth interpretation for all cases) and we wot able to recognize diauxic growth of recombinant strainorresponding changes in ethanol profile. This fact is eaxplain with continuous fast liberation and utilization of gose and its low level during the SSFSE process. Consequhe yeast growth is based mainly on the glucose substraimultaneous utilization of various substrates liberated duydrolysis process of starch. In other words, catabolic reion control mechanism does not take place, which was sy the authors[1] interpreting biomass and ethanol profilesame experimental data. It is important to notice that the ince of intermediate products (oligosaccharides) from sydrolysis can be very significant when the initial starch centration is high. This effect can be evaluated if a total reduugar concentration is taken into account in both the modexperimental design.

Changing the initial starch concentrations one can obsehat Yx/s values in cases S30 and SG50 are similar andalues of stoichiometric coefficientYp/s are similar for S30nd SG30 (seeTable 3). The phenomenon can be interprey analyzing the biomass and ethanol profiles together

.

y,r

-n

h

d

d

e

he starch model profile has followed excellently the expental profile of starch degradation. The flexibility of stanzyme hydrolysis model was tested with various initial stnd glucose concentrations (see initial conditions inTable 3)nd showed excellent results for these experimental operaonditions.

The second level of knowledge unified the enzymatic deation of starch to glucose and simultaneous metabolizatilucose to ethanol by microorganisms. At this level, microhysiology was modeled and the specific growth rate incluubstrate limitation and product inhibition effects. A mophisticated model for ethanol production rate was develo reach the final goal of SSFSE step.

During the procedure of rates models development (Rsus,Rres,p, µ) the RSA methodology was used. The ranges ofariables involving in the rate models were covered experimperational conditions.

Nonlinear identification procedure was based on the hyA and a decomposition algorithm for SSt multi objective func

ion was developed. In this case, the “global optimum” soluas achieved by GA for 100 generation. The direct searcSt minimum by GA has failed even after 300 generation.4 kinetics and stoichiometric constants were successfullyated to predict the experimental profiles of starch, gluciomass and ethanol. The step-by-step identification procan be very useful for a modeling of biotechnological syste

Finally, the proposed SSFSE model showed excellentbility for different operational conditions of SSFSE procend can be used successfully to describe microbial physiof genetically modified yeastS. cerevisiae secreting enzyme

or starch degradation.

254 A.D. Kroumov et al. / Biochemical Engineering Journal 28 (2006) 243–255

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