prediction of dynamic metabolic behavior of pediococcus ...drops/ramkipapers/213_2012_adler... ·...

Prediction of Dynamic Metabolic Behavior of Pediococcus pentosaceus ProducingLactic Acid from Lignocellulosic Sugars

Philipp AdlerInstitute of Nutrition and Food Sciences, Division of Food Technology and Biotechnology, University of Bonn, D-53117 Bonn, Germany

Hyun-Seob SongSchool of Chemical Engineering, Purdue University, West Lafayette, IN 47907

Katharina KastnerInstitute of Nutrition and Food Sciences, Division of Food Technology and Biotechnology, University of Bonn, D-53117 Bonn, Germany

Doraiswami RamkrishnaSchool of Chemical Engineering, Purdue University, West Lafayette, IN 47907

Benno KunzInstitute of Nutrition and Food Sciences, Division of Food Technology and Biotechnology, University of Bonn, D-53117 Bonn, Germany

DOI 10.1002/btpr.1521Published online February 9, 2012 in Wiley Online Library (wileyonlinelibrary.com).

A dynamic metabolic model is presented for Pediococcus pentosaceus producing lacticacid from lignocellulose-derived mixed sugars including glucose, mannose, galactose, arabi-nose, and xylose. Depending on the pairs of mixed sugars, P. pentosaceus exhibits diverse(i.e., sequential, simultaneous or mixed) consumption patterns. This regulatory behavior ofP. pentosaceus is portrayed using the hybrid cybernetic model (HCM) framework whichviews elementary modes of the network as metabolic options dynamically modulated.Comprehensive data are collected for model identification and validation through fermenta-tion experiments involving single substrates and various combinations of mixed sugars. Mostsugars are metabolized rather sequentially while co-consumption of galactose and arabinoseis observed. It is demonstrated that the developed HCM successfully predicts mixed sugardata based on the parameters identified mostly from single substrate data only. Further, wediscuss the potential of HCMs as a tool for predicting intracellular flux distribution withcomparison with flux balance analysis. VVC 2012 American Institute of Chemical EngineersBiotechnol. Prog., 28: 623–635, 2012Keywords: lactic acid, hybrid cybernetic model, elementary mode, lignocellulose,Pediococcus pentosaceus

Introduction

Lactic acid has received considerable attention as a poten-tial raw material for various industrially valuable chemicals(i.e., ethyl lactate, propylene oxide, acetaldehyde, acrylicacid) and as a feedstock monomer for biodegradable lacticacid based plastics so-called poly(lactic acid) (PLA).1 Thegrowing field of PLA application in particular leads to a con-tinuously increasing demand for lactic acid.1,2 Recently, lac-tic acid has been classified by the US Department of Energyas one of the ‘‘Top 10’’ biobased chemicals.3

Lignocellulosic residues are an attractive resource for theproduction of lactic acid. This renewable resource is inex-pensive and available in large quantities and thus consideredan alternative to petrochemical resources.1,4 Worldwide,�3.5 billion tons of agricultural crop residues are produced

per year.4 The quantitatively most relevant sugars derivedfrom lignocellulose are glucose, mannose, galactose, arabi-nose, and xylose.5 The individual fractions of these com-pounds in lignocellulosic biomass vary considerably.6

Overall process efficiency depends on the rates and yields atwhich the individual sugars are metabolized. While the trans-ferability of results from empirical studies among differentlignocellulosic substrates is limited, models can help todecrease the time and effort required for substrate screeningand process optimization. Thus, for efficient evaluation ofany lignocellulosic substrates, it is necessary to use a com-prehensive metabolic model which incorporates metabolismof all quantitatively relevant sugars present in lignocellulosicbiomass.

Several models describing lactic acid production by lacticacid bacteria have been proposed. Many studies combinelogistic growth functions with the Luedeking-Piret model,e.g.,7 but these models are not effective for making reliablepredictions. Some researchers use unstructured kinetic modelsfor single substrates, e.g.,8 There are only a few modeling

Additional Supporting Information may be found in the onlineversion of this article.

Correspondence concerning this article should be addressed to P. Adlerat [email protected].

VVC 2012 American Institute of Chemical Engineers 623

efforts focusing on multiple substrates. Nielsen et al. intro-duced a fundamental compartment model9 which was subse-quently used to model growth on a mixture of glucose, lactoseand galactose10 and successfully verified with chemostatcultures.11 Despite the potential of this approach, model devel-opment is demanding as it requires extensive experimentalinvestigations including RNA content measurements. Bajpai-Dikshit et al. presented a model that represented growth ofLactobacillus rhamnosus on multiple substrates.12 In theirmodel, they applied linear programming (LP) to assign controlcoefficients for consumption of substrates.

Neither Nielsen’s nor Bajpai-Dikshit’s model include met-abolic reaction networks. Integration of metabolic pathwayanalysis into dynamic modeling framework, however,provides a more realistic and detailed image of cellularprocesses. Flux balance analysis (FBA) and dynamic FBA(dFBA) models have been applied to analyze metabolism oflactic acid bacteria such as Lactococcus lactis13,14 and Lacto-bacillus plantarum.15 To estimate metabolic states, theseconstraints-based approaches take a LP solution (amongpossibly many alternatives) maximizing a prescribed staticquantity (such as biomass yield). Their prediction of meta-bolic shifts along the transient change of environments maybe limited due to neglect of dynamic regulation.

The cybernetic modeling concept of Ramkrishna andcoworkers,16 based on organisms acting as optimal strategiststhat attempt to utilize resources with maximum efficiency,considers the complex processes of metabolic regulationthrough cybernetic control laws. The hybrid cybernetic model-ing (HCM) approach introduced by Kim et al.17 integratescybernetic control laws with metabolic pathway analysis. InHCMs substrate uptake fluxes are distributed among differentelementary modes (EMs) which may be viewed roughly assubnetworks or pathways composed of a minimal number ofreactions operating in steady state.18 The individual uptakerates through EMs are regulated such that a certain objectivefunction (e.g., growth rate, carbon uptake rate) is maximized.

In this article, we use the HCM framework to model lacticacid production by Pediococcus pentosaceus from mixedsugars (glucose, mannose, galactose, arabinose, xylose) rep-resenting lignocellulosic hydrolyzates. P. pentosaceus is usedin this work due to its ability to ferment pentoses. Study onthe dynamic metabolism of P. pentosaceus has not beenactive. Thus, we reconstruct the metabolic network ofP. pentosaceus. The subsequent development of HCM ismade by following the guidelines established from Songet al.19 and Song and Ramkrishna.20 In this article, wefurther introduce the necessity of incorporating the energyrequirement for growth into the framework towards improv-ing model predictions. Model parameters are identified onlyfrom single-substrate data except the ones for the galactose-arabinose pair exhibiting simultaneous consumption. Finally,the HCMs potential of predicting intracellular flux distribu-tion is explored through comparison with FBA.

Material and Methods

Strain and medium composition

The strain P. pentosaceus DSM 20336, obtained from theGerman Collection of Microorganisms and Cell Cultures(Braunschweig, Germany), was used in all the experiments. Itwas stored in MRS broth containing 10% glycerol at �70�Cand reactivated on MRS agar by two transfers (20�C, 48 h).

For all cultivations a MRS medium was used containing(per liter): 10 g peptone, 10 g meat extract, 5 g yeast extract,2 g K2HPO4, 5 g sodium acetate, 2 g triammonium citrate,0.2 g MgSO4, 0.05 g MnSO4�H2O, 1 mL Tween 80 and 20 gcarbon source [(D(þ)-glucose (monohydrate), D(þ)-mannose,D(þ)-galactose, D(þ)-xylose, and/or L(þ)-arabinose]. Concen-trated sugar solutions were prepared separately from all otheringredients and added after autoclaving.

Inoculum preparation and culture conditions

Inocula were grown on glucose (30�C, 24 h). These werethen washed (8,000 rpm, 10 min) and resuspended with0.9% NaCl solution and used as 5% (v/v) inoculum.

Fermentation was conducted anaerobically in a 3.6-L stirredfermentor (Labfors 3, Infors HT, Bottmingen, Switzerland)with a working volume of 1.8 L. The growth temperaturewas controlled at 30�C, stirring speed was 400 rpm, andthe pH-value was maintained at 6.0 by automatic additionof 4 M NaOH and 2 M H3PO4. Samples for off-lineanalysis were aseptically withdrawn by syringe at regularintervals.

Various experiments on different carbon sources were per-formed. First, the individual sugars (glucose, mannose, gal-actose, arabinose, and xylose) were used as single carbonsources (20 g/L). Experiments on single substrates were per-formed in duplicates. For model validation, individualexperiments with substrates composed of equal proportions(6.6 g/L) of respectively (1) glucose, galactose, and arabi-nose, (2) glucose, mannose, and galactose, (3) glucose, man-nose, and arabinose, or (4) glucose, arabinose, and xylosewere performed. For a more realistic situation, a mixture ofglucose (11.5 g/L), galactose (2 g/L), arabinose (4 g/L),xylose (2.5 g/L), which is equivalent to their proportion inapple pomace according to Grohmann and Bothast,21 wasused in another fermentation experiment.

Analytical methods

Cell growth was monitored by measurement of the opticaldensity at 660 nm using a UV/Vis-spectrophotometer (Gen-esys 6, Thermo Electron, Erlangen, Germany). Samples werediluted with distilled water to maintain absorbance values oflower than 0.5. For calibration, cell dry weight was alsodetermined gravimetrically by centrifuging (8,000 rpm, 10min), washing with distilled water and subsequent drying(105�C, 24 h). The concentrations of acetic and lactic acidand monosaccharides were determined by HPLC analysis(717plus; Waters, Eschborn, Germany) equipped with aNucleogel Ion 300 OA column (Macherey-Nagel, Duren,Germany). The mobile phase was 2.5 mM H2SO4 with aflow rate of 0.3 mL/min at 60�C. For the separation of galac-tose and xylose, a Nucleogel Sugar Pb column (Macherey-Nagel) with water as a mobile phase and a flow rate of 0.3mL/min at 80�C was used. All substances were detectedusing a refractive index detector (2414, Waters).

Modeling

Modeling framework

The mass balance for extracellular metabolites (x) can beformulated as follows:

1

c

dx

dt¼ Sxr (1)

624 Biotechnol. Prog., 2012, Vol. 28, No. 3

where Sx is the (nx � nr) stochiometric matrix of nx extracel-lular metabolites, r is rate vector of nr regulated fluxes,and c represents the biomass dry weight concentration in theculture.

Under quasi-steady-state approximation the vector r canbe represented as the convex combination of a set ofuniquely defined EMs that span the admissible region of thesystem, that is,

r ¼ ZrM; rM � 0 (2)

Z is the (nr � nz) EM matrix, where nz is the number ofEMs and rM is the vector of weights that can be interpreted asfluxes through EMs. Substitution of r in Eq. 1 by 2 leads to

dx

dt¼ SxZrMC (3)

where SxZ is a (nx � nz) matrix, in which each column canbe normalized with respect to a reference substrate.19 SxZ

then projects the uptake rate vector rM through each EMonto the vector of total exchange rates (dx/dt) of extracellu-lar metabolites.

In HCMs EM fluxes are regulated by adjusting enzymelevels and enzyme activities, that is,

rM ¼ diagðvÞdiagðerelÞrkinM (4)

The vector of cybernetic variables v represents the mecha-nisms (of catabolite inhibition and activation) controlling theactivity of existing enzymes required for metabolic path-ways22; e

rel denotes the relative enzyme level (eirel ¼ ei/

eimax) related to the EMs and rkinM is the uptake rate vector in

the unregulated state which is a function of substrate concen-trations given by kinetic expressions. The operator diag(�)converts a vector into a diagonal matrix.

The balance equation for enzymes is defined as

de

dt¼ aþ diagðuÞrkinME � diagðbÞe� le (5)

where a and b are constants that denote the specific rates ofconstitutive enzyme synthesis and enzyme degradation,repectively; rkinME is the unregulated part of inducible enzymesynthesis rate which is modelled kinetically; u is the vectorof cybernetic variables regulating the induction and repres-sion of enzyme synthesis; le represents dilution rate ofenzymes by growth.

In the generalized form of the matching and proportionallaws23 the cybernetic variables are defined as follows:

u ¼ p

jjpjj1(6)

v ¼ p

jjpjj1(7)

where ||�||1 and ||�||1 denote the L1 and L1 norms and p rep-resents the return-on-investment of critical resources whichis given by a metabolic objective function. The carbonuptake is chosen as the return-on-investment, i.e.,

p ¼ diagðfcÞdiagðerelÞrkinM (8)

In Eq. 9 fc is the vector of carbon moles per mole of sub-strate assimilated through the EMs.

Construction of metabolic network

A metabolic network (Figure 1) for P. pentosaceus com-prising 110 reactions was constructed using databases ofP. pentosaceus ATCC 2574524,25 and network-based modelsof other lactic acid bacteria.14,15 The network includes theprimary metabolic pathways for glucose, mannose, galactose,arabinose, and xylose. The biomass formation and lumpedbuilding block synthesis reactions (e.g., proteins, lipids,DNA) from precursors were derived from a genome-scalemetabolic model of L. plantarum by Teusink et al.,15 assum-ing similar biomass composition among Lactobacillaceae.However, in the peptidoglycan forming reaction 2,6-diamino-pimelic acid was substituted by lysine, since Pediococci’scell wall peptidoglycans are of the lysine-aspartate-type.26

As P. pentosaceus, like most lactic acid bacteria, is adaptedto nutrient-rich environments, complex media are requiredfor growth. The MRS medium used in this study containsyeast extract, meat extract and peptone, which provide essen-tial amino acids, nucleotides and vitamins.27 Hence, weassume that all amino acids and nucleotides are provided bythe medium, and are thus external metabolites that are con-sumed for biomass formation. Vitamins contribute only verylittle to total biomass (compare Supporting Information ofTeusink et al.15) and are not considered in the present study.The full list of metabolic reactions is provided in theSupporting Information A.

Network decomposition and EM reduction

The Network was decomposed into 1829 EMs usingMETATOOL v.5.128 (The METATOOL input file is givenin the Supporting Information B). The incorporation ofall EMs in model identification would lead to a very largenumber of parameters. Such a large number is computation-ally not manageable. Furthermore, parameter uncertaintyincreases with the number of parameters in the model andnot every parameter may be sensitive to data of batch cul-tures. Hence, to prevent over-parameterization, reduction ofthe number of EMs is required. To determine the minimalnumber of EMs which describe the metabolism of P. pento-saceus, metabolic yield analysis (MYA) developed by Songand Ramkrishna20 was applied. MYA identifies the minimalset of EMs describing metabolic behavior from yield space.Metabolic fluxes are projected to yield space by normalizingwith respect to a reference metabolite. The solution space isthen a bounded convex hull. The methodology of MYAinvolves (i) identification of the vertices spanning the convexsolution space iteratively such that a prescribed threshold cri-terion is satisfied applying convex hull algorithm (a priorireduction) and (ii) selection of active EMs that describeexperimental yield data using constrained linear least squareoptimization.

Before EM identification, the stoichiometric coefficient ofATP in the biomass synthesis reaction was tuned with MYA(yATP,ga ¼ 40.0 mmol/g-DW) to meet growth rate-dependentATP requirement (GAR). Details of accounting for GAR inthe HCM framework are discussed in Appendix A. ActiveEMs were selected based on experimental yield data foreach individual substrate. Yields were obtained by normaliz-ing exchange fluxes with respect to the uptake flux of therespective reference substrate. Because acetate was neitherproduced nor consumed during growth on hexoses, acetateyield was neglected in the EM identification procedure ofthe hexose-related subgroups. The whole set of EMs was

Biotechnol. Prog., 2012, Vol. 28, No. 3 625

split into subgroups according to the reference substrate. EMreduction was then applied to the individual subgroups.Since it was observed in the experiments that arabinose andgalactose are consumed simultaneously, mixed modes wereidentified using experimental yield data of growth on botharabinose and galactose.

Results and Discussion

HCM for P. pentosaceus

The results of MYA are shown in Table 1. Using MYA11 EMs were identified. EM1 represents consumption of glu-cose, EM2 mannose, EM3-EM4 galactose, EM5-EM6

Figure 1. Metabolic map of P. pentosaceus.

For the sake of lucidity, the biosynthesic reactions for the formation of building blocks and biomass components from precursors are lumped into asingle reaction in this figure. End points towards precursors are underlined.

Table 1. Result of EM Reduction

Subgroup Active EMsYield Vectors y of Components

Considered in MYA (mmol/mmol) MSRE*

Glc† 1 Exp. data [0.0283, 1.83] 2.8 � 10�3

Model [0.0268, 1.73]Man† 2 Exp. data [0.0297, 1.89] 8.2 � 10�3

Model [0.0268, 1.73]Gal† 3, 4 Exp. data [0.0252, 1.84] 1.2 � 10�3

Model [0.0250, 1.75]Ara‡ 5, 6 Exp. data [0.0216, 0.930, 0.930] 8.4 � 10�3

Model [0.0209, 0.793, 0.976]Xyl‡ 7, 8, 9 Exp. data [0.0236, 0.830, 1.10] 6.3 � 10�3

Model [0.0230, 0.763, 0.982]Gal/Ara‡ 10, 11 Exp. data [0.0416, 2.89, 0.678] 1.6 � 10�2

Model [0.448, 2.29, 0.682]

*MSRE ¼ 1nexp

Pððyexp;j � ymod;jÞ=yesp;jÞ2.†y ¼ [yBIOM, yLac].

‡y ¼ [yBIOM, yLac, yAc].


arabinose, EM7-EM9 xylose, and EM10-EM11 both galactoseand arabinose. Yield data can be represented well by the setof EMs as indicated by the low relative errors of fitting. TheEMs for glucose, arabinose and xylose consumption are illus-trated in Figure 2. Additional EMs that were predominantlyactivated are presented in the Supporting Information C.

The vector of extracellular metabolites x, SxZ matrix, andcarbon number vector fc are presented in Table 2. Since the

model contains 44 extracellular metabolites, we only presentthe metabolites of interest here. The balance equations forextracellular metabolites and enzymes are given by Eqs. 3–5.The cybernetic variables are computed by Eqs. 6–8.

By assuming quasi-steady-state, the specific growth rate is

l ¼ 1

c

dxBIOMdt

(9)

Figure 2. Reactions with nonzero fluxes in the main EMs for consumption of (a) glucose (EM1), (c) arabinose (EM6), and (b) xylose (EM8).

Table 2. Vector of Extracellular Metabolites x, SxZ Matrix and Carbon Number Vector fc

x ¼

xGlcxMan

xGalxAraxXylxBIOMxMAINT

xLacxAc

26666666666664

37777777777775

SxZ ¼

�1 0 0 0 0 0 0 0 0 0 0

0 �1 0 0 0 0 0 0 0 0 0

0 0 �1 �1 0 0 0 0 0 �1 �1

0 0 0 0 �1 �1 0 0 0 0:0324 317

0 0 0 0 0 0 �1 �1 �1 0 0

0:0268 0:0268 0 0:0268 0:0243 0 0 0:0243 0:0326 �1 �1

0 0 2 0 0 0 2 0 0 0 0

1:73 1:73 2 1:73 1 0:758 1 0:758 0 1:75 242

�0:0314 �0:0314 0 �0:0314 1 0:971 1 0:971 1:64 0 308

26666666666664

37777777777775

fc ¼

6

6

6

6

5

5

5

5

5

6:161591

266666666666666664

377777777777777775


where xBIOM is the biomass component in the metabolic net-work (Table A1, Supporting Information A).

The kinetic rates for substrate uptake (in Eq. 4) and induc-ible enzyme synthesis (in Eq. 5) through the individualmodes i are modelled using Michaelis-Menten-type kinetics.The Levenspiel-equation is used to model product inhibitionby lactic acid as done by Boontawan et al.,29 i.e., for EMsassociated with single substrates,

rkinM;i ¼ kmaxi

xjxj þ Ki;j

1� xLacxLac;max

� �n

j ¼ fGlcg ði ¼ 1Þj ¼ fMang ði ¼ 2Þj ¼ fGalg ði ¼ 3� 4Þj ¼ fArag ði ¼ 5� 6Þj ¼ fXylg ði ¼ 7� 9Þ

8>>>><>>>>:

(10)

and mixed substrates (i.e., galactose and arabinose)

rkinM;i ¼ kmaxi

xGalxGal þ Ki;Gal

xAraxAra þ Ki;Ara

1� xLacxLac;max

� �n

ði ¼ 10� 11Þ(11)

Similarly,

rkinME;i ¼ kE;ixj

xj þ Ki;j1� xLac

xLac;max

� �n

j ¼ fGlcg ði ¼ 1Þj ¼ fMang ði ¼ 2Þj ¼ fGalg ði ¼ 3� 4Þj ¼ fArag ði ¼ 5� 6Þj ¼ fXylg ði ¼ 7� 9Þ

8>>>><>>>>:

(12)

rkinME;i ¼ kE;ixGal

xGal þ Ki;Gal

xAraxAra þ Ki;Ara

1� xLacxLac;max

� �n

ði ¼ 10� 11Þ(13)

respectively, (Preliminary experiments demonstrated thatproduct inhibition by acetic acid is not significant (a ¼ 5%)enough to be considered in the model). In Eqs. 10–13 ki

max’sdenote the maximum substrate uptake rates, kE,i’s are therate constants of inducible enzyme formation, and Ki,j’s arethe saturation constants.

The maximum enzyme concentration at steady state foreach EM is given by

emaxi ¼ ai þ kE;i

bi þ kmaxi ½SxZ�BIOM;i

(14)

Parameter identification

Model parameters were estimated using growth data onsingle substrates and a mixed set of galactose and arabinosecollected from batch cultivations of P. pentosaceus DSM20336. The maximum specific uptake rates ki

max through theEMs were approximated by nonlinear fitting of experimentaldata with the model simulations, minimizing the mean squaredrelative error between model and data. Maximum specificuptake rates through the individual EMs are listed in Table 3.

To circumvent over-parameterization, only maximum specific

uptake rates were fitted with all other parameters fixed.

Half saturation constants are usually small and were setequally among all modes (Ki,j ¼ 0.2 mmol/L). This value issimilar in its magnitude to saturation constants reportedfor lactic acid bacteria.30 Lactic acid inhibition parameters T

able

3.Maxim

um

SpecificUptakeRateskm

axi

DeterminedbyFitting

EM

group

Glc

Man

Gal

Ara

Xyl

Gal/Ara

EM

12

34

56

78

910

11

kmax

i(m

mol/g-D

W/h)

23.4

�0.0081

20.2

�0.0072

0.88�

0.29

12.4

�0.015

0.5

�1.4

19.8

�0.12

0.70�

0.89

2.82�

0.0014

0.0

�1.1

21.5

�0.013

7.8

�10�2�

1.0

�10�2

MSR

E*

3.3

�10�3

2.1

�10�3

2.4

�10�3

5.9

�10�3

6.3

�10�3

2.3

�10�3

*MSRE¼

1nexp�n x

P nx j¼1

P nexp

l¼1ððx

exp;j;l�x m

od;j;lÞ=� x e

xp;jÞ2.


(xLac,max¼ 889 mmol/L, n¼ 0.44) were taken from Boontawanet al. who investigated the effect of product inhibition ongrowth of P. pentosaceus.29 Parameters associated withenzyme synthesis and decay are not sensitive to experimentaldata and are usually set based on considerations by Kompalaet al.22 and Turner and Ramkrishna.31 Thus, they were takenfrom Song and Ramkrishna32 and were assumed to be sub-strate-independent [ai ¼ 0.01 1/h, bi ¼ 0.05 1/h, kE,i ¼ 1/h].The initial relative enzyme concentrations were fixed accordingto the preculture conditions. Since all precultivations wereperformed on glucose, the initial enzyme levels in the glucose-group were set to 0.8, all others except for those of the mannoseconsuming modes were set to 0.2. Mannose related initialenzyme levels were fixed at 0.6 due to the similarity in metabo-lism of glucose and mannose (compare Table A1, Supporting

Information A). Model fits to experimental data are shown inFigures 3a,b.

Consumption patterns of mixed substrates

Figures 4–7 show experimental data for mixed substratesand model predictions. When P. pentosaceus was cultivatedon the mixture of glucose, galactose, arabinose, and xylose, aresidual amount of 8.93 mmol/L xylose was observed after71 h of fermentation. Because the xylose concentration did notdecrease significantly during the time interval of 30–71 h, thetime scale in Figure 7 was limited to the first 30 h offermentation.

In all experiments glucose was consumed preferentially overmannose, galactose, arabinose, and/or xylose. It is well-known

Figure 3. (a) Experimental and fitted concentration profiles obtained during cultivation of P. pentosaceus DSM 20336 on singlesubstrates.

(I) glucose, (II) mannose, (III) galactose, (IV) arabinose, and (V) xylose. Experimental data are average values from duplicate experiments anderror bars indicate the range of experimental data for each measurement. (b) Experimental data and fitted simulations for P. pentosaceus DSM20336 cultivated on a mixture of 6.6 g/L glucose, 6.6 g/L galactose, and 6.6 g/L arabinose. Only maximum specific uptake rates through mixedEMs (k10

max, k11max) were fitted.


that in most organisms glucose acts as a catabolic repressor forthe metabolism of other sugars. In gram-positive bacteria thismechanism is mainly coupled to phosphoenolpyruvate-phos-photranferase systems (PEP-PTS) for carbohydrate uptake.33

Thus, it is obvious that glucose is a catabolite repressor for

other sugars in P. pentosaceus as indicated by the presence of aPEP-PTS for glucose-uptake.34 Like glucose, mannose is a

PTS sugar, but it does not entirely repress the consumption

of arabinose and galactose (compare Figures 4 and 5).

Co-consumption of PTS and non-PTS sugars was also observed

in S. thermophilus.35

As can be seen from Figures 3b and 7, galactose and arab-inose were cometabolized after depletion of glucose. Thisshows that galactose does not repress the assimilation ofarabinose and underlines the results of Dobrogosz andDeMos who investigated L-arabinose isomerase formation byP. pentosaceus on various sugars.36

It is not fully clear from our results whether xyloseconsumption is repressed by arabinose and/or galactose.When grown on a mixture of glucose, arabinose and xylose

(Figure 6), P. pentosaceus started metabolizing xylose afterexhaustion of arabinose (t ¼ 7–8 h). However, when the sub-strate was a mixture of glucose, galactose, arabinose, andxylose (Figure 7), slight consumption of xylose started whengalactose was exhausted and arabinose was still present in themedium (t 7 h, xAra ¼ 19.3 mmol/L). These observationsagree well with the lag-phase of �10 h, which was observedwhen P. pentosaceus was cultivated solely on xylose. For thisreason, it seems reasonable that the predominant factor thatdetermined xylose uptake in the multiple-substrate fermenta-tions was the time required for enzyme synthesis.

Model validation

The predictive capabilities of the developed model formultiple-substrates are demonstrated in this section. For thispurpose, we have taken additional batch-fermentation data ofP. pentosaceus DSM 204336 with various mixtures of sub-strates which were not used for model identification.

The HCM captures the patterns of substrate consumptionwell and predicts the shifts from homolactic to heterolactic

Figure 5. Experimental data and model predictions for P. pentosaceus DSM 20336 cultivated on a mixture of 6.6 g/L glucose, 6.6 g/Larabinose, and 6.6 g/L mannose.

Figure 4. Experimental data and model predictions for P. pentosaceus DSM 20336 cultivated on a mixture of 6.6 g/L glucose, 6.6 g/Lgalactose, and 6.6 g/L mannose.


fermentation when pentoses are metabolized (Figures 3b and5–7). Co-consumption of arabinose and galactose isdescribed accurately by the model (Figures 3a and 7). With-out EMs co-consuming both substrates (i.e., EM10-EM11),the model would predict preference of arabinose over galac-tose due to the higher maximum specific uptake ratesthrough arabinose consuming EMs. In fact the averageuptake rate of galactose (6.3 mmol/g-DW/h) is higher thanconsumption rate of arabinose (5.8 mmol/g-DW/h). Physio-logically this may be reasonable because during growth on

glucose the major part of enzymes required for galactosemetabolism (glycolytic enzymes) is produced, whereas arabi-nose specific enzymes are repressed. Furthermore, it can beobserved that arabinose consumption is down-regulated inthe presence of galactose, because arabinose uptake rate islower than when cells only metabolize arabinose (7.4 mmol/g-DW/h, compare Figure 6). Nevertheless, co-consumption isfavorable because higher overall substrate uptake rates canbe achieved. The HCM framework accounts for these effectsby introducing EMs co-consuming both substrates. Since

Figure 6. Experimental data and model predictions for P. pentosaceus DSM 20336 cultivated on a mixture of 6.6 g/L glucose, 6.6 g/Larabinose, and 6.6 g/L xylose.

Figure 7. Experimental data and model predictions for P. pentosaceus DSM 20336 cultivated on a mixture of 11.5 g/L glucose, 2 g/Lgalactose, 4 g/L arabinose, and 2.5 g/L xylose (in the period between 10 and 20 h of cultivation no samples were taken).


co-consumption of arabinose and galactose is preferred here,gal/ara-modes (mixed modes) are primarily activated, andcarbon flux through these modes is high (Figure 8a).

In Figures 5 and 6 lactic acid yield on arabinose is margin-

ally underpredicted by the model. In the HCM the yields are

given by the structure of the network, thus the maximum theo-

retical lactic acid yield on arabinose is 1 mol/mol (EM5-EM6,

compare Table 3). In the biomass forming mode (EM6) of the

arabinose-group, which is predominantly activated during

arabinose consuming phases (compare Figure 8b), lactic acid

yield is 0.758 mol/mol. Experimentally, however, lactic acid

yields of 0.93 mol/mol were observed when P. pentosaceuswas grown only on arabinose.

Further minor deviations are observed with respect toxylose metabolism. In the experiments with the mixtures ‘‘glu-cose/arabinose/xylose’’ and ‘‘glucose/galactose/arabinose/xylose’’ as substrates, xylose was not completely exhausted.This may be due to product inhibition by dissociated lacticacid (lactic acid inhibition is mainly attributed to the nondis-sociated state and based on pKa ¼ 3.85 at pH 6 only 0.7% ofthe total lactic acid is nondissociated).7 Such a strong inhibi-tory effect was not observed during growth on the other sug-ars. Furthermore, at maximum lactic acid concentrationsobserved in this study (�220 mmol/L) the inhibition modelaccounts for only 10% reduction of specific substrate uptakerate. While in other studies product inhibition was assumed tobe independent of the kind of substrate, e.g.,19 our resultsmay lead to the conclusion that lactate inhibits, in particular,the metabolism of xylose. In pH-controlled media organicacids primarily act on mass transfer by lowering the protongradient across the cell membrane, which has to be main-tained under dissipation of ATP. Hence, an increased inhibi-tory effect on xylose consumption is reasonable, as xyloseuptake rate is itself small resulting in a low ATP productionthrough catabolism of xylose.37 When P. pentosaceus was culti-vated on xylose alone (Figure 3a), only small amounts of lacticacid were produced; hence, product inhibition appears to be in-significant in this experiment so that xylose was exhaustedentirely. Although at the final stage of fermentation, slowingdown of growth was observed, this effect cannot be attributedwith certainty to lactic acid inhibition based on these batch dataalone. This is because other effects such as limitation ofnutrients and/or higher substrate saturation constants than usedin this study could also be implicated. Observations similar tothis study have also been made by Taniguchi et al.38 who inves-tigated lactic acid production by cocultivation of lactic acid bac-teria. Although E. casseliflavus was able to metabolize xylosewhen it was the only substrate, it did not ferment xylose effi-ciently when cultivated on a mixture of 100 g/L glucose and 50g/L xylose. This phenomenon was also explained by product in-hibition which acts on expression of genes for xylose-specificenzymes. In this regard, it may be interesting to inoculate cellspregrown on xylose into a medium that already contains highlevels of lactate. Another explanation for the observed lack ofxylose consumption in mixed-substrate cultures may be due tolimited availability of nutrients. However, it is not clear fromour results why this may play an important role only in mixedsubstrates. Some future work should study the factors that deter-mine xylose consumption, for instance, by continuous cultiva-tion at alleviated levels of lactate. In summary, although somelimitations with respect to xylose metabolism were suggested inour study, the overall resulting error in prediction of lactic acidproduction is low and does not significantly affect the quality ofthe model.

Prediction of intracellular flux distribution

The HCM approach may describe the dynamic behaviorof intracellular fluxes as a response to changing environ-ments by correlating dynamics of exchange fluxes with intra-cellular reactions via EMs. For instance, dynamic changes ofEM activities during growth on a mixture of glucose, arabi-nose and xylose can be seen in Figure 8b. The correspondingreactions with nonzero fluxes are highlighted in Figure 1. Byconvex combination of these EMs through cybernetic princi-ples the dynamic changes in intracellular fluxes can bedisplayed. The potential of predicting intracellular fluxes isdiscussed in the following.

In HCM, the flux vector is represented as weighted non-negative combinations of EMs as follows:

r ¼ ZrM (15)

It is noted that the HCM predicts the change of flux distri-butions with time as the weights to EMs (i.e., rM) dynami-cally vary depending on environmental conditions.

Prediction of flux distribution by the HCM is compared tothat by classical (i.e., steady state) FBA. As the former is adynamic framework while the latter a static one, this com-parison is made only at a specific steady state conditionwhere FBA is applicable. In both cases fluxes were scaledby the substrate uptake rate. Correlation between HCM andFBA for a set of cases is shown in Figure 9. Full flux

Figure 8. Carbon fluxes rM,ifc,i through individual EMs in theHCM at different substrate compositions: (a) mix-ture of glucose, galactose, arabinose, (experimentalresults: see Figure 3b) (b) mixture of glucose, arabi-nose, xylose (experimental results: see Figure 6).


vectors for glucose consuming P. pentosaceus, which pro-vide detailed information about flux distribution, are pre-sented in the Supporting Information D.

FBA potentially predicts flux distribution under constraintson energy requirement for growth and maintenance, and uptakeflux (from measurements). As multiple optima can exist inFBA, a range of feasible flux distributions that satisfy the con-straints are obtained using flux variability analysis (FVA). FBAwas performed such that biomass yield was maximized. Whenonly substrate uptake rate and energy requirement (i.e., GAR)are constrained, neither biomass formation nor lactic acid oracetic acid production is predicted well by FBA. Furthermore,some intracellular fluxes such as flux through pyruvate dehy-drogenase reaction (PDH) are physiologically unreasonable (formore detailed information see Supporting Information FigureD1). FVA did not reveal alternate optima (Figure 9a, also referto Figure D2), only GalT, TRF, and GlcT form an internal cycleand exhibit infinite boundaries. For this reason FBA cannot pre-dict predominant lactic acid production, so-called homolacticfermentation (Figure D2), which is observed experimentally.The inability of FBA in predicting homolactic fermentation,which is suboptimal with respect to biomass production, hasbeen reported earlier by Teusink et al.15

It is shown that FBA prediction is affected by the level ofimposed constraints. For more reliable results additional con-straints have to be imposed, i.e., by constraining internal orexternal fluxes. Thus, for predicting intracellular fluxes by FBAunder different conditions experimental data are required, orenzyme reactions have to be constrained by physiological con-siderations. To examine how FBA handles additional experi-mental data of exchange fluxes we first used experimental yielddata of lactic acid to constrain lactic acid excretion. Further-more, while it is not known explicitly for P. pentosaceus insome lactic acid bacteria pyruvate dehydrogenase (PDH) is notactivated under anaerobic conditions,39 which is critical for

predicting homolactic fermentation. Thus in a second step, weconstrained the PDH reaction as done by Oliveira et al.14 tomodel homolactic fermentation for L. lactis under anaerobicconditions. In both cases predicted internal fluxes were close tofluxes predicted by the HCM. High correlation of predictionsof flux distribution between the HCM and FBA is found(Figures 9b,c and Supporting Information Figs. D3 and D5).

Conclusion

The cybernetic model presented in this study is able topredict lactic acid production from various mixtures of ligno-cellulosic sugars. It performs well in describing preferentialconsumption of glucose, co-consumption of galactose and arab-inose and sequential consumption of other sugars. Dynamicbehavior of sequential consumption was predicted exclusivelyfrom model identification on single substrates. Although exper-imental data of co-consumption of galactose and arabinosewere used in model fitting, the strength of the model can beseen in its ability to describe the behavior under diverse condi-tions, i.e., whether only one of the two substrates or both areavailable. HCM is shown to predict intracellular flux distribu-tions with which FBA predictions agree only when it is fortifiedwith several other constraints in addition to the usual uptakerate and energy requirement. For experimental confirmation,however, fluxomic data from 13C-MFA are required.

Acknowledgments

The authors thank the Max Buchner Research Foundation(MBFSt 2824) andGermanAcademic Exchange Service (DAAD)

Notation

Acronyms

ATP ¼ adenosine triphosphatedFBA ¼ dynamic flux balance analysis

Figure 9. Correlation between flux distributions predicted by the HCM and FBA.

(a) Only glucose uptake flux and GAR were constrained in FBA, (b) glucose uptake flux, GAR and lactic acid excretion were constrained, (c) glu-cose uptake flux, GAR and PDH reaction were constrained. Error bars indicate flux variability in FBA.


EM ¼ elementary modeFBA ¼ flux balance analysisHCM ¼ hybrid cybernetic model/hybrid cybernetic

modelingL-HCM ¼ lumped hybrid cybernetic modelMYA ¼ metabolic yield analysis

Variables

c ¼ biomass dry weight concentration (g-DW/L)e ¼ vector of enzyme levels (mmol/g-DW/L)fc ¼ vector of carbon numbers in the substrates

associated with EMskE,i ¼ specific rate associated with induced enzyme

synthesis in the EM i (1/h)kimax ¼ maximum specific uptake rate associated

with ith EM (mmol/L)Ki,j ¼ saturation constant of substrate j in the ith

EM (mmol/L)m ¼ vector of internal metabolites (mmol/g-DW)n ¼ exponentnr ¼ number of fluxesnx ¼ number of extracellular metabolitesnz ¼ number of EMsp ¼ vector of return-on-investmentr ¼ vector of uptake rates (mmol/g-DW/h)

rM ¼ vector of uptake rates through EMs(mmol/g-DW/h)

rkinM ¼ vector of unregulated uptake rates throughEMs (mmol/g-DW/h)

rkinME ¼ vector of unregulated enzyme syntheses inEMs (mmol/g-DW/h)

MSRE ¼ relative squared errorS ¼ stochiometric matrixt ¼ time (h)u ¼ vector of cybernetic variables for enzyme

synthesisv ¼ vector of cybernetic variables for enzyme

activityx ¼ vector of external metabolites (mmol/L)

xLac,max ¼ lactic acid concentration at which growthis fully inhibited (mmol/L)

y ¼ vector of yields normalized to referencesubstrate (mmol/mmol)

YATP/x ¼ fitted ATP requirement (mmol/g-DW)yATP,biochem ¼ ATP requirement for synthesis of biomass

componentsyATP,ga ¼ ATP requirement for growth-associated

maintenance/stoichiometric coefficient ofATP in the biomass synthesis reaction

Z ¼ EM matrix

Greek letters

a ¼ vector of specific rates associated with con-stitutive enzyme synthesis (1/h)

b ¼ vector of specific rates associated withenzyme decay (1/h)

l ¼ specific growth rate (1/h)

Subscripts and Superscripts

Ara ¼ arabinoseAc ¼ acetic acid

BIOM ¼ biomassE ¼ enzyme

exp ¼ experimentGal ¼ galactoseGlc ¼ glucose

i ¼ index associated with ith EMj ¼ substrate jl ¼ measuring point l

Lac ¼ lactic acidm ¼ internal

Man ¼ mannosemax ¼ maximummod ¼ model

rel ¼ relativex ¼ external

Xyl ¼ xylose

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Appendix: Incorporation of Energy Requirement intothe HCM Framework

One of the main tasks of the central metabolism is to provideenergy for the cell. The energy source supplies the organismwith ATP via catabolic processes, which is then used for thebiomass formation and maintenance. While some of theseprocesses with net ATP consumption are uncoupled fromgrowth (non-growth-associated maintenance), the major partis coupled to growth of biomass.15,27 If growth-associatedATP requirement (GAR) is not satisfied by the network, thiswould lead to unreasonable results when computing EMs. Tofit biomass and product yields in MYA additional ATP dissi-pation is provided by the maintenance reaction (ATPdrain).However, this process is not coupled to growth. Since theseEMs are allowed to move freely in HCMs only constrained bycybernetic principles, the model would not reflect the dynamicbehavior of the cell properly. Thus, in HCMs it is importantthat the network meets GAR of the cell. GAR can be subdi-vided into ATP requirement for synthesis of biomass compo-nents (yATP,biochem) and ATP required for growth associatedmaintenance (yATP,ga).

15,27 While the amount of ATP requiredfor synthesis of biomass components is given explicitly throughthe network, ATP consumption for growth-associated mainte-nance of the cell has to be accounted for in the biomass synthesisreaction (biomass components þ yATP,ga ! biomass þ yATP,ga).In the biomass synthesis reaction of Teusink et al.,15 which wasalso used in this study, 27.4 mmol ATP/g-DW were considered.However, this amount of ATP used for assembling biomass andfor growth-associated maintenance is not a universal constant,but may depend on the microorganism and conditions of cultiva-tion. Furthermore, if complex media are applied, like in thisstudy, the exact composition of the medium is not known andnutrients may be available in various states. Thus energy may berequired for interconversion of precursors through processes thatare not considered in the metabolic network.To estimate ATP requirement for growth-associated main-

tenance, we set yATP,ga ¼ 0, computed EMs and appliedMYA analysis with additionally incorporating GAR as a pa-rameter. The ATP requirement of lactic acid bacteria is inthe range of 41-73 mmol/g-DW.27 In this study, we set GARat 65 mmol/g-DW.15 This is in close proximity to ATPrequirement determined experimentally from growth onglucose by the traditional methodology.27 In lactic acid bac-teria, non-growth-associated ATP requirement for mainte-nance was found to be in the range 0-1.4 mmol/g-DW27

which is neglected in this study. To account for total (net)ATP consumption through the network, the complete set ofEMs was subdivided into biomass producing and nonbio-mass producing groups. First we computed the amount ofATP consumed in each EM for biomass synthesis only. Forthis, anabolic reactions of the network were identified,that is, reactions that only exist in biomass producingEMs. Next, excess ATP production through the maintenancereaction (ATPdrain) in nonbiomass and biomass producingEMs is computed. ATP requirement for growth-associatedmaintenance can be obtained from rATPdrain/rBIOMSynth

(yATP,ga ¼ 40.0 mmol/g-DW).

Manuscript received Oct. 3, 2011, and revision received Dec. 13, 2011.


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