Biotechnol. Prog. 1999, 15, 81−90 81

Modeling of Overflow in Batch and Fed-Batch Cultures of

Bo Xu, Mehmedalija Jahic, and Sven-Olof Enfors*

Department of Biotechnology, Royal Institute of Technology, S-100 44 Stockholm, Sweden

A dynamic model of overflow metabolism in batch and fed-batch cultivations of Escherichia coli W3110 under fully aerobic conditions is presented. Simulation based on the model describes cell growth, respiration, and formation as well as acetate reconsumption during batch cultures, the transition of batch to fed-batch culture, and fed-batch cultures. E. coli excreted acetate only when specific glucose uptake exceeded a critical rate corresponding to a maximum respiration rate. In batch cultures where the glucose uptake was unlimited, the overflow acetate made up to 9.0 ( 1.0% carbon/ carbon of the glucose consumed. The applicability of the model to dynamic situations was tested by challenging the model with glucose and acetate pulses added during the fed-batch part of the cultures. In the presence of a glucose feed, E. coli utilized acetate 3 times faster than in the absence of glucose. The cells showed no significant difference in maximum specific uptake rate of endogenous acetate produced by glucose overflow and exogenous acetate added to the culture, the value being 0.12-0.18 g g-1 h-1 during the entire fed-batch culture period. Acetate inhibited the specific growth rate according to a noncompetitive model, with the inhibition constant (ki) being 9 g of acetate/L. This was due to the reduced rate of glucose uptake rather than the reduced yield of biomass.

Introduction nol production (Sonnleitner and Ka¨ppeli, 1986), this process is now known as glucose overflow metabolism. Acetic acid formation by aerobically growing Escheri- High specific growth rate (Majewski and Domach, 1990; chia coli was already documented more than four decades Britten, 1954), high specific glucose uptake rate (Han et ago (Britten, 1954). Since then, there has been an array al., 1992), bottlenecks in the Krebs cycle (Hollywood and of literature reports bringing up the same topic (Farmer Doelle, 1976; Gray et al. 1966; Amarasingham and Davis, and Liao, 1997; Holms, 1996, 1986; Pan et al., 1987; 1965), limited respiratory capacity (Ingledew and Poole, Meyer et al., 1984). In particular, when E. coli was to be 1984), or a combination of any of the above has been considered as a host organism to mass produce important suggested to trigger the acetate overflow metabolism. For human pharmaceutical proteins or other foreign proteins, better understanding and quantitative prediction of the a detailed documentation of acetic acid formation became acetate overflow phenomenon, a number of mathematical important. An example of this is that 19 out of the 23 models (Ko et al., 1993, 1994; El-Mansi et al., 1994; studies on recombinant E. coli reviewed by Lee (1996) Varma and Palsson, 1994; Majewski and Domach, 1990; reported on acetate accumulation during the fed-batch Bajpai, 1987) were reported. Another type of model, using processes. This is also true when the continuous culture visual programming of aerobic acetate formation, was technique was applied (Curless et al., 1989; Brown et al., also proposed (Regan and Gregory, 1995). Most modeling 1985). Acetate produced in a culture has been shown to of E. coli deals with acetate formation only and with inhibit several physiological properties of the culture continuous culture, while the industrial use of E. coli is itself. There is evidence suggesting that acetate acts as mainly based on fed-batch culture, in which acetate is an uncoupler of the proton motive force of E. coli (Axe formed or consumed, depending on the conditions. and Bailey, 1995; Repaske and Adler, 1981). Its proto- nated state diffuses through the lipid membrane of a cell. This paper deals with dynamic modeling of acetate Thereafter it dissociates in the cytoplasm, causing a pH production and subsequent reconsumption during batch decrease (Axe and Bailey, 1995; Luli and Strohl, 1990). and fed-batch cultures of E. coli K-12 strain W3110. It Various genetic and biochemical engineering or combined was found necessary to include the inhibiting effect of strategies have been tried to avoid or reduce acetate acetate on consumption of oxygen and glucose in the formation (Farmer and Liao, 1997; Chou et al., 1994; model. The model is applied directly to results of batch Konstantinov et al., 1990; El-Mansi and Holms, 1989; and fed-batch cultivation experiments. Bajpai, 1987). Today, much knowledge has accumulated concerning Materials and Methods aerobic acetic acid formation in E. coli. Together with its Bacterial Strain. The wild-type E. coli K-12 strain counterpart phenomenon in , i.e., the aerobic etha- W3110 was obtained from the Genetic Stock Center, Yale University (New Haven, CT). The strain was stored at * Corresponding author. Telephone: +0046-8-790 9164. Fax: -80 °C in the below-described mineral medium supple- +0046-8-723 1890. E-mail: [email protected]. mented with 20% glycerol.

10.1021/bp9801087 CCC: $18.00 © 1999 American Chemical Society and American Institute of Chemical Engineers Published on Web 01/05/1999 82 Biotechnol. Prog., 1999, Vol. 15, No. 1

Table 1. Carbon per Carbon Yield on Glucose for rate started to decline. To estimate the biomass, and Biomass (X), Acetate and Carbon Dioxide: Summary of thereby following the proceeding of cultivation, the optical Six Batch Cultures of E. Coli W3110 density of the culture was measured at 500 nm by using - initial carbon yield on carbon aUV vis spectrophotometer (Lot-Oriel, Darmstadt, Ger- expt glucose glucose (mol C/mol C) recoveryd many). a c run concn (g/L) X acetate CO2 (%) Shake flask experiments were performed in 1-L baffled 1 10.01 0.57 0.08 0.41 106 Erlenmeyer flasks containing a medium volume of 100 2 9.19 0.71 0.05 0.32 108 mL. The mineral medium was supplemented with 5 g/L 3 4.03 0.67 0.12 0.28 107 - 4 4.84 0.59 0.10 0.28 97 of glucose plus 0 8 g/L of sodium acetate at pH 7. 5 13.86 0.59 0.08 0.28 95 Cultivations were carried out at 35 °C at a rotating speed 6 7.47 0.72 0.12 0.29 113 of 200 rpm. mean ( SEb 0.64 ( 0.03 0.09 ( 0.01 0.31 ( 0.02 104 ( 2 For seed preparation, the glycerol frozen storage cells (OD ) 1) were slowly thawed, and 0.5 mL was a Experiment 5 is graphically shown in Figure 2, and experi- 500 nm ment 6 in Figure 3. b Standard error. c The elemental composition seeded into 100 mL of the medium. The initial glucose was estimated as CH1.72O0.47N0.24 (Andersson et al., 1996), hence concentration was 10 g/L. When the seed reached OD500 nm the biomass having 40 mmol of carbon per gram dry cell weight ) 4-5, the spent medium was removed by centrifugation, based on this formula. This was consistent with the study of and the cells were resuspended in a smaller volume of Andersen et al. (1980). d Total carbon recovered from biomass, fresh medium. This suspension was used as inoculum. acetate, and carbon dioxide as percentage of glucose carbon Analyses. Off-line enzymatic analyses of glucose, consumed. acetate, , formic acid, and lactate were performed using the kits provided by Boehringer Mannheim GMbH Medium and Culture Conditions. The defined (Mannheim, Germany) with the kit catalog numbers 716 mineral medium comprised the following (g/L): Na2SO4, 251, 148 261, 176 290, 979 732, and 1 112 821, respec- ‚ 2; (NH4)2SO4, 2.468; NH4Cl, 0.5; K2HPO4, 14.6; NaH2PO4 tively. The incubation during the enzymatic reactions and - H2O, 3.6; (NH4)2-H-citrate, 1; and thiamin, 0.01 0.1. the absorbance readings was performed on a semiauto- Three milliliters of MgSO4 (1 M) and trace element mated ELISA machine (Labsystem iEMS, Helsinki, solution were sterile-filtered (0.2 µm) into a 1-L auto- Finland), providing four repeated measurements for each claved medium. The trace element solution contained the sample. ‚ ‚ ‚ following (g/L): CaCl2 H2O, 0.5; ZnSO4 7H2O, 0.18; MnSO4 On-line gas composition was measured with a para- H2O, 0.1; Na2EDTA, 20.1; FeCl3‚6H2O, 16.7; CuSO4‚ ‚ magnetic oxygen analyzer (Sybron, Boston, MA) and an 5H2O, 0.16; and CoCl2 6H2O, 0.18. The initial batch infrared carbon dioxide analyzer (Leybold-Heraeus GmbH, glucose concentrations were varied from 4 to 14 g/L as Hanau, Germany). The exit gases were cooled and dried indicated in the figures and Table 1. The feeding solution through a silica column prior to analysis. Gas analysis had a glucose concentration of 500 g/L prior to analysis data were monitored with an eight-channel data acquisi- with double salt concentrations. All batch and fed-batch tion unit (PC-logger 2100, INTAB, Stenkullen, Sweden) cultivations were conducted in a 15-L stirred tank reactor which was connected to a PC (EM2 486) with the (Biostat E, Braun, Melsungen, Germany) if not otherwise Software PCLOG. The sampling frequency of the data indicated. As described in detail elsewhere (George, was 1 min-1. The specific rate of oxygen consumption, 1997), the reactor is equipped with controls for agitation, qO (mmol g-1 h-1), was obtained from the oxygen pH, temperature, and dissolved oxygen tension (DOT). consumption rate (OCR, mmol L-1 h-1) divided by the For pH control, 25% NH4OH was used. The DOT was biomass concentration. measured with a polarographic oxygen electrode (Ingold, For dry cell weight assay, the centrifugal test tubes Urdorf, Switzerland), and the signal was monitored with were predried to their constant weight. Ten-milliliter cell a two-channel recorder (ABB GoerZ AG, Vienna, Aus- samples were centrifuged and washed with deionized tria). DOT was ensured to be above 30% air saturation water and then dried at 105 °C overnight. throughout all cultivations. Foam was disrupted by addition of poly(propylene glycol) 2000 on demand, and Model Description. It has been suggested that, at foaming was not a general problem of this strain under high glucose concentrations, there might be a lack of regulation in the maximum glucose uptake velocity by the present conditions. The inlet gas flow rate was glc continuously monitored using a mass flow meter (Belach, the phosphotransferase system in E. coli. The Enz II , Stockholm, Sweden). Feeding of the substrate solution which is a membrane-bound glucose-specific permease, was controlled by a computer that controlled a peristaltic was believed not to respond to the normal regulatory pump via a D/A converter. The feeding solution was signal such as membrane potential when saturated with placed on a balance (Mettler PM34-K, Greifensee, Swit- glucose (Robillard and Konings, 1981). Consequently, the zerland), and the weight was logged so that the exact flux of glucose into the central metabolic pathways feeding profile during fed-batch cultivations could be produces more acetyl-CoA than can be oxidatively used derived. The constant specific growth rate of fed-batch for biosynthesis and energy generation (Holms, 1996). -1 The extra flux of glucose carbon can, however, exploit culture was maintained at about 0.3 h by using an - - exponential glucose feeding rate, F(t), as the high capacity of the Embden Meyerhof Parnas (EMP) pathway, which is in turn enhanced due to the increased glucose in-flux (Doelle, 1981). One portion of ) µ - F(t) (XV/Sfeed) exp[µ(t t0)] the extra glucose flux through the elevated EMP pathway YX/S still integrates into cell materials as E. coli normally does when only EMP is operative. The remainder of the flux -1 where µ is the desired specific growth rate (h ), YX/S is that ends up as additional pyruvate is catalyzed by the cell yield on glucose (g/g), X is the cell concentration to yield acetyl-CoA. By two (g/L), V is the culture volume (L), Sfeed is the concentra- subsequent enzymatic actions, catalyzed by acetyl-CoA: tion of glucose in the feed (g/L), and t0 is the time at which orthophosphate acetyltransferase and acetate kinase, one the feed is started. When the exponential feed had acetate is converted from an acetyl-CoA. Concomitantly proceeded for a determined time (usually for 5 h), the with this conversion, one ATP is formed (Majewski and feeding rate was kept constant, and the specific growth Domach, 1990). So, from the viewpoint of maximal energy Biotechnol. Prog., 1999, Vol. 15, No. 1 83

qS ) max S qS + + (1) 1 A/Ki,S S KS

The glucose flux is split into two metabolic ones, i.e., the fully oxidative metabolic flux, qSox, and the overflow, qSof, the split being determined by a boundary condition of qOs < qOmax, as will be further explained. At low rates of sugar consumption, all sugar is channeled through the oxidative pathway (qSox ) qS). This flux is further divided into a flux used for (qSox,an) and the remaining used for oxidative energy metabolism (qSox,en). The par- titioning between these fluxes is obtained from two expressions. The first is for the mass balance of carbon to the anabolism [mol of C (g of cells)-1 h-1]: ) carbon flux to the anabolism qSox,anCS

where Cs is the carbon content in moles per gram of sugar. The other expression is for the mass balance of carbon to the biomass growth: carbon flux converted to biomass ) - (qSox qm)YX/S,oxCX Figure 1. Kinetic model of aerobic overflow metabolism in E. coli. The inhibitory effect of acetate on µmax, qSmax, and qOmax is where YX/S,ox is the aerobic yield coefficient exclusive of not included but is applied to simulations as explained in the maintenance (qm) and CX is the carbon content in moles text. The conventional mass balance equations for glucose, per gram of cell. Since these carbon fluxes are equal, the acetate, and biomass and the equation for volumetric oxygen consumption rate are given in Materials and Methods. sugar flux to oxidatively energized anabolism is obtained as conservation, aerobic acetate production yields 4 ATP C qS ) (qS - q )Y X (2) molecules per glucose consumed, compared with 2 ATP ox,an ox m X/S,oxC molecules per glucose for fermentative metabolism if the S anabolic use of glucose is not considered. The remaining sugar is used for the aerobic energy As it is distinct from other models, we consider a metabolism, dynamic modeling of acetate formation and reutilization ) - in batch and fed-batch cultures. It is known that glucose qSox,en qSox qSox,an (3) represses cellular use of exogenous acetate, which is consumed only after glucose has been exhausted in a and oxidized through respiration, which gives the oxygen batch culture (Holms, 1986). This growth on acetate used for glucose oxidation, qOs, from the stoichiometry requires induction of to furnish the cell of respiration: anabolism with precursors from the glycolytic pathway. qO ) qS Y (4) However, in the presence of a limited amount of glucose, S ox,en O/S as in a fed-batch culture, acetate is consumed much faster However, when the rate of glucose uptake progressively than in the total absence of glucose. This is in line with increases at increasing glucose concentrations, a maxi- the study of Varma and Palsson (1994) on the same mum respiration rate (qOmax) is observed. This is a strain W3110. The acetate uptake system, products of critical metabolic state where the overflow metabolism ack and pta genes, is present in glucose-grown cells; thus, starts. Also, qOmax was shown to be inhibited by acetate it is not catabolite repressed (Brown et al., 1977). Acetate (Kleman and Strohl, 1994; this paper); thus, the non- is converted back to acetyl-CoA, which then enters the competitive inhibition term with a constant Ki,o is in- aerobic energy metabolism without any need to induce cluded (not shown in Figure 1). Therefore, the algorithm gluconeogenesis if a low flux of furnishes the used for simulation includes a boundary condition, qOs cell with the anabolic precursors. This model is formu- e qOmax/(1 + A/Ki,o), and the values for the anabolism lated as specific rate equations below and is displayed (qSox,an) and oxidative energy metabolism (qSox,en) are in Figure 1. proportionally reduced to satisfy the boundary condition. Mathematical Formulation of the Dynamic Glu- The resulting glucose flux used for the oxidative metabo- cose Overflow Model. The model is based on specific lism as a whole then becomes -1 -1 metabolic fluxes [q, g (g of cells) h ] and is summarized qS ) qS + qS (5) in Figure 1. The equation numbers refer to the order in ox ox,an ox,en which the specific rate equations are solved before being The rate of glucose channeled to overflow metabolism is inserted into conventional mass balance equations for then obtained as the difference between the total glucose glucose, acetate, and biomass. The total glucose uptake uptake (qS) and the total oxidative flux (qSox): rate is assumed to follow the Monod model. The inhibition ) - by acetate on glucose uptake comes from experimental qSof qS qSox (6) observations (Kleman and Strohl, 1994; this paper), and this is formulated into a noncompetitive mode of inhibi- The contribution to growth from this overflow glucose flux tion: is obtained in analogy with eq 2, 84 Biotechnol. Prog., 1999, Vol. 15, No. 1

C Table 2. Mean Value of Maximal Specific Rates of Cell ) X qSof,an qSofYX/S,of (7) Growth (µmax), Glucose Uptake (qSmax), Oxygen Uptake CS (qOmax), Acetate Production (qAp,max), and Acetate Reutilization (qAc,max) in the Six Experiments Shown in and the remaining flux is used for the energy production Table 1 via acetate formation, µmax qSmax qOmax (mmol qAp,max qAc,max (h-1) (g g-1 h-1) g-1 h-1) (g g-1 h-1) (g g-1 h-1) ) - qSof,en qSof qSof,an (8) mean 0.55 1.35 13.13 0.15 0.05b/0.15c SEa 0.01 0.11 0.81 0.02 0.01b/0.02c From this flux, the acetate formation rate is obtained by a Standard error. b Refers to acetate consumption in batch means of the stoichiometry of glucose conversion to culture part after glucose exhaustion. c Refers to acetate consump- acetate: tion in fed-batch culture part in the presence of a glucose feed.

qA ) qS Y (9) Table 3. Parameters, Initial Variables, and Other p of,en A/S Coefficients Used in the Simulations Figure Figures 3 Figure When the rate of glucose uptake is so low that the 2b and 6b 4 origin and source respiration is not saturated [qOs < qOmax/(1 + A/Ki,o)], acetate, if present in the medium, is reconsumed, and in Apulse1 (g/L) na na 0.765 experimental procedure A 2 (g/L) na na 1.388 experimental procedure the fed-batch process this does not demand induction of pulse Apulse3 (g/L) na na 1.651 experimental procedure gluconeogenesis, since glucose is continuously supplied. CA (mol C/g) 1/30 1/30 1/30 chemical formula Assuming that acetate uptake also follows the Monod CS (mol C/g) 1/30 1/30 1/30 chemical formula model, the specific rate of acetate consumption would be CX (mol C/g) 0.04 0.04 0.04 experimental data (Table 1) F0 (L/h) na 0.04 0.04 experimental procedure F (L/h) na 0.188 0.180 experimental procedure A const qA ) qA (10) G 1.10 1.10/1.30 1.20 model fitting c c,max + K (g/L) 0.05 0.05 0.05 Paalme at al., 1997 A KA A Ki,O (g/L) 4 4 3 fitting to experimental data Ki,S (g/L) 5 5 4 fitting to experimental data A hypothetical flux to anabolism may be obtained from KS (g/L) 0.05 0.05 0.05 Postman and Roseman, 1976 -1 mass balances on the in the cell in qAc,max (g g 0.06 0.20 0.14 experimental data (Table 2) - analogy with eq 2. h 1) -1 -1 qm (g g h ) 0.04 0.04 0.04 Andersson et al. 1994; Paalme et al., 1997 CX qOmax (mmol 15.6 13.4 17.2 experimental data (Table 2) ) -1 -1 qAc,an qAcYX/A (11) g h ) C -1 A qSmax (g g 1.30 1.25 1.40 experimental data (Table 2) h-1) When acetate is being consumed, it is converted to acetyl- S0 (g/L) 13.86 7.47 10 experimental procedure Sfeed (g/L) na 520 520 experimental procedure CoA, which can be further oxidized via TCA cycle and SFR (/h) na 0.3 0.28 experimental procedure . In this way, some glucose that Spulse (g/L) na 3.70 2.0 experimental procedure would be used for energy metabolism is saved for bio- YA/S (g/g) 0.667 0.667 0.667 stoichiometric constant synthetic use. Therefore, we call qAc,an a “biomass equiva- YO/A (g/g) 1.067 1.067 1.067 stoichiometric constant lent” flux. For details about the cometabolism of glucose YO/S (g/g) 1.067 1.067 1.067 stoichiometric constant YX/A (g/g) 0.4 0.4 0.4 experimental data (Figure 5) and acetate, readers are referred to Varma and Palsson a YX/S,of (g/g) 0.15 0.15 0.15 Varma and Palsson, 1994; (1994) and to Nystro¨m and Neidhardt (1993). Chen et al., 1997 Subtraction of the anabolic flux from the total acetate YX/S,ox (g/g) 0.51 0.51 0.49 experimental data (Table 1) uptake gives the flux of acetate for respiratory combus- a Assumed to be the same as the anaerobic biomass yield on tion, and a constraint for this is that the remaining glucose. b na, not applicable. respiration capacity is liberated from the declining glucose metabolism (due to increasing glucose limitation): dS ) (F(t)/V)(S - S) - qSX (15) dt feed qA ) qA - qA e (qO - qO )/Y (12) c,en c c,an max S O/A dA ) (qA - qA )X - (F(t)/V)A (16) dt p c If qAc,en has to be reduced due to this constraint, corre- sponding reductions in qAc,an and qAc are calculated. dX ) (-F(t)/V + µ)X (17) The total oxygen consumption rate is then obtained as dt a sum of the parts used for oxidation of glucose and dV acetate, respectively. ) F(t) - F (18) dt sample qO ) qO + qA Y (13) S c,en O/A OCR ) (qO/32)X × 1000 (19)

The specific growth rate is obtained as a sum of the three where Fsample is the mean rate of culture medium with- substrate fluxes by means of the related yield coefficients: drawn for various sample analyses.

) - + + Results and Discussion µ (qSox qm)YX/S,ox qSofYX/S,of qAcYX/A (14) Batch Cultures. Aerobic batch cultivations of E. coli The parameters used in the model are listed in Table 3. were performed with DOT being maintained above 30% The conventional mass balance equations for glucose, during the entire batch culture. Figure 2 shows cell acetate, biomass, and culture volume as well as the growth, sugar and oxygen consumption, and acetate equation for volumetric oxygen consumption rate for a accumulation. Cell growth was exponential at µmax ) 0.56 fed-batch process are h-1 before it slowed when glucose approached exhaustion Biotechnol. Prog., 1999, Vol. 15, No. 1 85

Figure 2. Experiment and simulation of a batch culture of E. coli W3110. Time profiles of concentration for (a) glucose (0), biomass (O), and (b) acetate. Time profiles of specific rate for (c) growth, (d) acetate production and reconsumption, (e) oxygen uptake, and (f) the volumetric oxygen consumption rate. Measured data are presented by symbols or dotted lines and simulation results by thick continuous lines. (Figure 2a,c). At the time of glucose depletion, acetate Table 2 summarizes five specific rates obtained from reached a peak value of 1.2 g/L, after which it was the above cultivations: the maximal specific rates of cell readsorbed from the medium (Figure 2b) with little growth (µmax), glucose uptake (qSmax), oxygen uptake additional increase in biomass. The specific oxygen (qOmax), acetate production (qAp,max), and acetate recon- uptake rate (qO) was initially rather constant but sumption (qAc,max). The dynamic model requires that declined gradually as acetate accumulated (Figure 2e). qSmax, qOmax, and qAc,max be specified for metabolic When the glucose was depleted and while acetate was simulations of batch and fed-batch cultures in order to being reused, qO dropped to a value of about 1.5 mmol restrict the respective metabolic capacity of the cell to a -1 -1 g h . After the depletion of both carbon sources, qO finite upper limit. The qSmax was determined by calculat- declined further to about 0.5 mmol g-1 h-1, which may ing the sugar depletion rate (-dS/dt) in batch experi- represent an endogenous respiration. The slight increase ments from the best polynomial-fitted glucose curve in biomass concentration during acetate reconsumption versus time and dividing by the biomass concentration. -1 -1 was 0.5 g/L (Figure 2a), which was equivalent to a This method gave the qSmax value 1.35 ( 0.11 g g h . biomass yield on acetate of 0.4 g/g. In another study (Varma and Palsson, 1994), the deter- Table 1 gives the summary of six batch cultivations mination of qSmax was calculated as the ratio of the cell performed. Acetate was formed in all aerobic batch growth rate to the biomass yield. This procedure gave -1 -1 cultures, and it constituted 0.09 ( 0.01 C/C of glucose qSmax ) 1.89 g g h in W3110. However, when the same consumed. Biomass yield on glucose was 0.64 ( 0.03 C/C procedure was applied in our case, qSmax became 1.06 g -1 -1 (equal to 0.52 ( 0.02 g/g). The balance between the g h . For qOmax, we obtained the value 13.1 ( 0.8 mmol carbon recovered from biomass, acetate, and carbon g-1 h-1 from the measurement of volumetric oxygen dioxide and the carbon of the glucose consumed was 104 consumption rate (OCR) divided by biomass concentra- ( 2%. The mixed-acid products formate, tion. We also used the plotting procedure of Andersen lactate, and ethanol were not found. The initial glucose and von Meyenburg (1980), which results in 12.6 mmol concentration had a good linear correlation with the sum g-1 h-1. These values are comparable to 15 mmol g-1 h-1 of carbon dioxide evolved and acetate produced at the end in W3110 by Varma and Palsson (1994) and to 14-18 of batch cultures. mmol g-1 h-1 by Paalme et al. (1997). 86 Biotechnol. Prog., 1999, Vol. 15, No. 1

Figure 3. Experiment and simulation of a fed-batch culture of E. coli W3110. Time profiles of concentration for (a) glucose (0), biomass (O), and (b) acetate. Time profiles of specific rate for (c) cell growth, (d) acetate production and reconsumption, (e) oxygen uptake, and (f) the volumetric oxygen consumption rate. Measured data are presented by symbols or dotted lines and simulation results by thick continuous lines. The time at which a glucose pulse was given is indicated by an arrow in (a) and the feed profile is given by the thin line in (b).

Fed-Batch Cultures. Time profiles of cell growth, made, neither acetate nor other mixed-acid fermentation sugar consumption, acetate accumulation, and recon- products were found. sumption are presented in Figure 3a,b. The initial batch To challenge the model, pulses of glucose or acetate growth, as seen before, was exponential, with a µmax of were made in the fed-batch cultures. The glucose pulse 0.54 h-1, and during the exponential glucose feeding experiment was carried out in the middle of the expo- phase, the µ of the culture was sustained at 0.3 h-1. When nential feeding phase when the cell density was about constant feeding started, µ gradually declined as biomass 10 g/L. Glucose was added to 3.7 g/L (Figure 3a), and concentration increased (Figure 3c). The batch-produced the culture responded instantly with a transient acetate acetate reached its peak value of 0.9 g/L (Figure 3b). accumulation (Figure 3b). Concurrently, qO rose rapidly Unlike pure batch culture, the acetate reassimilation in when the cells responded to the glucose pulse (Figure 3e). fed-batch culture was rapid when glucose feed had qAp increased rapidly, followed by an increase in qAc started. The calculated qAc,max in fed-batch culture was (Figure 3d), and the time profile of OCR had an abrupt -1 -1 0.16 g g h (Figure 3d), while qAc,max obtained in batch peak (Figure 3f). Pulses of acetate were made three times, culture after glucose exhaustion was only 0.05 g g-1 h-1 once in the middle of the exponential feeding part, when (Figure 2d). Thus, the cells consumed acetate about 3 the cell density was also about 10 g/L, and two times times faster in the presence than in the absence of during the constant feed stage. As shown in Figure 4, glucose. As seen earlier in Figure 2e, the batch qO was the cellular use of endogenous acetate (0.79 g/L produced rather constant (12.5 mmol g-1 h-1) but then declined from the overflow metabolism of the earlier batch part, (Figure 3e). The qO of exponential feed phase basically indicated by arrow a1) and exogenous acetate (0.77 g/L -1 -1 remained at about 6.5 mmol g h but gradually arrow a2) caused qO to increase, but it did not reach as declined when constant feed started. The volumetric high a level as the cells earlier displayed in batch phase oxygen consumption rate (OCR) is shown in Figure 3f. (Figure 4b). This was redemonstrated by two repeated In normal fed-batch cultures when no glucose pulse was pulses of acetate during the constant feeding (1.39 and Biotechnol. Prog., 1999, Vol. 15, No. 1 87

Figure 5. Measured µmax (O) in batch cultures of W3110 versus the concentrations of sodium acetate added prior to the cultiva- tion. The final biomass concentrations (0) produced from 5 g/L glucose and the acetate added are also shown. The thick solid line represents fitting to noncompetitive inhibition pattern of acetate as µmax ) µmax|A)0/(1 + A/Ki), with Ki ) 9 g/L. The dashed line shows the linear regression of biomass against acetate concentrations, while the dotted line represents the basic biomass yield on glucose.

respiration of the organism with an inhibition constant ki ) 9 g/L (Pham et al., 1998). Therefore, the inhibiting effect of acetate on sugar and oxygen uptake was included in the simulations. Figure 4. Experiment and simulation of a fed-batch culture of E. coli W3110. (a) Time profiles of concentration for glucose Simulations. Simulations were carried out by solving (b, S), biomass (O, X), and acetate (3, A). Symbols represent of the specific rate equations in the flux model (Figure measured data. The solid line is simulation of acetate, the 1) and numerically solving of the mass balance equations dashed line glucose, and the dotted line biomass. (b) Time for biomass, glucose, and acetate. The upper limits of the profiles of specific oxygen uptake rate. Experimental result is shown by the dotted line and simulation by the thick continuous cell to consume oxygen (qOmax) and glucose (qSmax) were line. The feed rate is shown by the thin continuous line, and calculated, taking into the account the noncompetitive the acetate pulses are indicated by arrows a2-a4. The glucose inhibition by acetate. The parameters used in the simu- pulse is indicated by arrow g, and the arrow a1 indicates the lations are listed in Table 3. The experimental and transition from batch culture to fed-batch culture. simulated data were directly compared. Lines in Figures 2, 3, 4, and 6, if not otherwise indicated, represent 1.65 g/L, as indicated by arrows a3 and a4, respectively). simulations based on the model shown in Figure 1 and During the fed-batch culture, the maximal specific rates the constants shown in Table 3. Symbols represent of acetate consumption of added acetate (a2-4) were 0.14, measured values. 0.14, and 0.19 g g-1 h-1, respectively. These values are -1 -1 It is demonstrated in Figure 2a and b that the model well comparable to the value of 0.13 g g h for the could well describe the batch concentration profile of endogenous acetate (a1) and to those qAc,max values biomass, glucose, and acetate and specific rates such as obtained in other fed-batch cultures (Table 2). When 2 µ, qAp and qAc, and qO (Figure 2c-e). In the model, qOmax g/L glucose was added (indicated by arrow g) near the controls the channeling of glucose via different pathways end of the fed-batch experiment, the respiration (qO) and hence represents the so-called “bottleneck” for aero- jumped to a high value, corresponding to that of the end bic glucose overflow metabolism in E. coli. For instance, of the batch culture (Figures 3e and 4). a value of 0.5 g g-1 h-1 (corresponding to 15.6 mmol g-1 Inhibitory Effect of Acetate. Addition of acetate to h-1) was observed in the batch culture (Figure 2). the initial medium of batch cultures decreased the µmax of E. coli. The inhibition followed a typical noncompetitive A physiological property that was not accounted for in this model is that E. coli contains alternative electron pattern, with an inhibition constant Ki of 9 g/L (Figure 5). However, acetate did not affect the final biomass transport chain limbs. Use of the cytochrome o limb instead of the cytochrome d system, for example, trans- concentration. At the end of the experiments, all glucose + and acetate was used, and a linear regression was found locates 4 H per mole of NADH2 oxidized, which gives a between the final biomass concentration and 0-8 g/L doubling in the efficiency of oxidative phosphorylation sodium acetate added to a medium with 5 g/L of glucose (Doelle et al., 1982). We found it necessary to apply this (Figure 5). This resulted in a yield of biomass per glucose factor to the model when simulating qO. This was done ) of 0.52 g/g and per acetate of about 0.4 g/g. Since the yield by introducing a scaling factor G; where G 1.10, the of biomass on glucose, represented by the dotted line in respiration qO/G represents a 10% increase in respiratory Figure 5, was not reduced by acetate, the growth rate efficiency, which may be caused by utilization of the inhibiting effect is probably by inhibition of the glucose cytochrome o system on top of the normal cytochrome d system that is used under batch conditions. As a result, uptake rate (qSmax). Inhibitions by acetate of both glucose and oxygen uptake were reported elsewhere (Kleman and the oxygen uptake demand by the cell would be decreased Strohl, 1994). The results presented earlier (Figures 2b,e, by the reciprocal of G. By considering this in the model, 3b,e, and 4) also gave the indication that a decline in qO the simulated qO and OCR agreed well with the mea- occurred while acetate accumulated above 0.3 g/L. More- sured values (Figure 2e,f). over, we had earlier observed that ethanol from the Also when the model was applied to fed-batch cultures, overflow metabolism of Saccharomyces cerevisiae inhibits it described accurately the time courses of cell concentra- 88 Biotechnol. Prog., 1999, Vol. 15, No. 1 tion, sugar concentration, acetate formation, and recon- sumption (Figure 3a,b). The parameters qAp and qAc given by the model could match the experiments too, not only before but also after the transition of batch to fed- batch culture (Figure 3d). The simulation of the glucose pulse showed that the uptake of added sugar (Figure 3a) and the produced acetate predicted by the model (Figure 3b) agreed with the experimental observations. Model and experiment agreed also for qAp and qAc (Figure 3d) during the pulse. The simulated µ (Figure 3c), however, showed some deviation from the experimental data, while simulation and experiment agreed better in the batch culture part and in the later fed-batch part. A scaling factor G ) 1.10 was applied to the batch simulation (Figure 3e,f), while an increase in G to 1.30 was used in fed-batch part simulation (Figure 3e,f) in order to account for the increased respiration efficiency. When the fed- batch culture received a glucose pulse, the qO jumped rapidly to a high value, comparable to that of the end part of the batch culture, but it did not reach the earlier maximum value (Figure 3e). This was partly ascribed to the fact that inhibiting acetate was produced from the glucose pulse as in batch culture. To investigate this, acetate and more glucose pulse experiments were performed. The thick lines in Figure 4 are simulations. The consumption of added acetate and the resulting respiration were well predicted by the model (Figure 4). When a glucose pulse was added at the end of the fed-batch culture, qO jumped rapidly to a high value, comparable to that of the end part of the batch culture but not to its original maximum value, indicating a change in the cell physiology during the fed-batch cultivation. The sensitivity of the simulation results to different model parameters was investigated, and it was found that qOmax and qSmax were important for the outcome of the simulations. qOmax does not represent the capacity of the respiration system per se, but rather all reactions involved in the hydrogen and electron flow from pyruvate to and including the respiration. As demonstrated in Figure 6, which uses Figure 3 as the reference, a small change in either qOmax or qSmax has a profound effect on acetate formation. As a comparison, the effect on other parameters such as biomass and glucose concentration -1 is low. An increase of qOmax from 13.4 to 16.5 mmol g h1, a range experimentally seen, caused a decreased Figure 6. Sensitivity of the model to capacity of specific oxygen accumulation of acetate. This occurred in both the batch (a and b) and glucose uptake (c and d). All other parameters culture part and the fed-batch part when a glucose pulse were the same as those of Figure 3, which are listed in Table 3. was given. When qSmax was decreased from 1.3 to 1.0 g -1 -1 -1 g h while keeping qOmax constant at 13.4 mmol g Acetate formed from the glucose overflow metabolism has h1, a similar effect was obtained. Exceedingly high qS inhibitory effects on the cells. At higher concentration forces cells to select acetate overflow as the pathway to (e.g., 1-8 g/L), it decreased the maximum specific growth dispose of surplus carbon in-flux. This occurs until qSis rate without reducing the biomass yield on glucose. The below a critical value, e.g., 1.0 g g-1 h1 as shown in Figure maximum glucose uptake rate and the maximum flux 6 and as reported elsewhere (Tocaj, 1997; Han et al., from pyruvate to the respiration, expressed as qOmax, are 1992). the most sensitive parameters that control the extent of acetate formation. Conclusion A kinetic model of aerobic growth and glucose overflow Acknowledgment metabolism in Escherichia coli in batch and fed-batch This study was financed within the EC Project BIO4- cultures was presented. The simulations could well CT95-0028: Bioprocess Scale-up Strategy Based on describe growth, respiration, and the transient acetate Integration of Microbial Physiology and Fluid Dynamics. accumulation, as a consequence of unlimited glucose utilization during aerobic batch and early fed-batch Notation cultures. The velocity of acetate consumption was much faster in the presence than that in the absence of glucose, A acetate concentration (g/L) and the cells showed no discrimination between using C carbon concentration in moles per gram of sub- endogenous acetate produced from glucose overflow stance (mol C/g) metabolism and exogenous acetate added to the medium. F glucose feed rate (L/h) Biotechnol. Prog., 1999, Vol. 15, No. 1 89

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