A Metabolic Model of Cellular Energetics
`and Carbon Flux During Aerobic
`Escherichia coli Fermentation
`
`Yun-Fei Ko,1·3 William E. Bentley,1.2 and William A. Weigand1·h
`1 Department of Chemical Engineering, 2 Center for Agricultural
`Biotechnology, and 3Center for Biotechnology Manufacturing,
`University of Maryland, College Park, Maryland 20742
`
`Received June 24, 1993/Accepted October 21, 1993
`
`An integrated metabolic model for the production of
`acetate by Escherichia coli growing on glucose under
`aerobic conditions was presented previously (Ko et al.,
`1993). The resulting model equations can be used to ex(cid:173)
`plain phenomena often observed with industrial fermen(cid:173)
`tations, i.e., increased acetate production which follows
`from high glucose uptake rate, a low dissolved oxygen
`concentration, a high specific growth rate, or a combina(cid:173)
`tion of these conditions. However, several questions still
`need to be addressed. First, cell composition is growth
`rate and media dependent. Second, the macromolecu(cid:173)
`lar composition varied between E. coli strains. And fi(cid:173)
`nally, a model that represents the carbon fluxes be(cid:173)
`tween the Embden-Meyerhof-Parnas (EMP) and the
`hexose monophosphate (HMP) pathways when cells are
`subject to internal and/or external stresses is still not
`well defined. In the present work, we have made an
`effort to account for these effects, and the resulting
`model equations show good agreement for wild-type
`and recombinant E. coli experimental data for the ac(cid:173)
`etate concentration, the onset of acetate secretion, and
`cell yield based on glucose. These results are useful
`for optimizing aerobic E. coli fermentation processes.
`More specifically, we have determined the EMP pathway
`carbon flux profiles required by the integrated metabolic
`model for an accurate fit of the acetic acid profile data
`from a wild-type E. coli strain ML308. These EMP car(cid:173)
`bon flux profiles were correlated with a dimensionless
`measurement of biomass and then used to predict the
`acetic acid profiles for E. coli strain F-122 expressing
`human immunodeficiency virus-(HIV528 ) ,a-galactosidase
`fusion protein. The effect of different macromolecular
`compositions and growth rates between these two E. coli
`strains required a constant scaling factor for improved
`quantitative predictions. © 1994 John Wiley & Sons, Inc.
`Key words: Escherichia coli • cellular energetics • acetate
`production • carbon yield
`
`INTRODUCTION
`
`The excretion and accumulation of acetate has been shown
`to be a major factor
`related
`to
`the
`reduction of
`process performance in aerobic Escherichia coli fermenta(cid:173)
`tions.4·10·11·13 Mathematical models have been developed to
`describe acetate formation which qualitatively agree with
`experimental data. 1•12 In an attempt to progress toward
`developing a more comprehensive rationale for acetate
`
`* To whom all correspondence should be addressed.
`
`secretion, we propose an approach9 that combines the
`entire set of 12 metabolic precursor metabolites [glucose-
`6-phosphate,
`fructose-6-phosphate,
`ribose-5-phosphate,
`erythrose-4-phosphate,
`triose phosphate, 3-P-glycerate,
`phosphoenol-pyruvate, pyruvate, acetyl coenzyme A (CoA),
`a-ketoglutarate, succinyl CoA, and oxaloacetate] for
`biosynthetic pathways, the intact fueling pathways [the
`Embden-Meyerhof-Parnas (EMP) pathway, the hexose
`monophosphate (HMP) pathway, the tricarboxylic acid
`(TCA) cycle, and the anapleurotic reactions], the Crabtree
`effect, the Pasteur effect, and details of the bacterial
`respiratory system.
`This hypothesis is stated as: (1) at a high glucose up(cid:173)
`take rate the TCA cycle may become saturated, hence
`substrate level phosphorylation produces more adenosine
`triphosphate (ATP) than usual with the result that acetate is
`overproduced. (2) If oxygen is limited, the rate of reduced
`nicotinamide-adenine dinucleotide [NAD(P)H] oxidation
`will become slower than that for the fully aerobic case.
`Hence the cells will produce more acetate in order to main(cid:173)
`tain sufficient ATP production. (3) At high specific growth
`rates, the cell energy (ATP) is overproduced. Thus, the
`cells will also produce more acetate in order to balance the
`rate between the catabolic, energy-generating and anabolic,
`energy-requiring reactions. We have utilized the network
`analysis technique suggested by Majewski and Domach12
`to formulate this hypothesis. An integrated metabolic model
`for the production of acetate by E. coli growing on glu(cid:173)
`cose under aerobic conditions was presented in a previous
`article. 9 This model is consistent with the phenomena
`observed during the aerobic E. coli fermentation process,
`that is, acetate production increases during high specific
`growth rate (p.), high glucose concentration (n), and low
`oxygen concentration ( 71 ). It also explains mechanistically
`why the common bioreactor control strategies are designed
`to manipulate both the glucose and oxygen concentrations
`10
`11
`simultaneously. 4
`•
`•
`The model equations were derived using flux relations
`for the strain of E. coli ML308 at fast growth conditions,
`p. = 0.94. 7 That is, the model is based on steady state
`precursor metabolite concentrations for E. coli ML308
`during balanced growth. In order to apply this model for
`different strains and growth conditions, three questions still
`
`Biotechnology and Bioengineering, Vol. 43, Pp. 847-855 (1994)
`© 1994 John Wiley & Sons, Inc.
`
`CCC 0006-3592/94/090847-09
`
`BEQ 1047
`Page 1
`
`

`
`need to be addressed. First, bacteria such as E. coli live
`as single cells in changing environments and the growth
`rate increases when the nutritional supply becomes richer.
`For instance, E. coli grows more rapidly with glucose as the
`sole source of carbon and energy than with acetate, and still
`more rapidly when the glucose minimal medium is supple(cid:173)
`mented with amino acids, vitamins, etc. Concomitant with
`changes in the growth rate, the composition of the cells is
`altered. For example, when growth is faster, the individual
`cells become larger and contain more replication forks on
`the chromosome. Second, the macromolecular compositions
`between various strains of E. coli are different. Finally,
`the fractions of carbon fluxes flowing through the EMP
`and HMP pathways vary, depending on the internal and/or
`external stresses upon the cells. For example, the lower the
`oxygen uptake rate the higher the fraction of carbon flux
`flowing through the EMP pathway .14
`In order to account for these effects, an extended model
`was derived and tested by sets of experimental data. The
`model calculates well the emergence of acetate and the
`effects on cell yield. This will be addressed in detail in
`the following sections.
`
`MODEL SUMMARY
`
`In an earlier article,9 we utilized the network analysis tech(cid:173)
`nique presented by Majewski and Domach 12 to formulate
`our model. The resulting equations and criteria for acetate
`production during aerobic fermentations are given by
`v = 0.672K1[1L - 3.571 ~~ J
`
`(1)
`
`T/ = 1.372 + 0.231 ln[DO]
`
`(0.174 + 0.094z)T/
`2.229 + 9.209z -
`1.749 + 2.749"1
`
`Kz =
`
`-1._1_14_+_0_.6_8_7_,_"1
`1.749 + 2.749"1
`
`(2)
`
`(3)
`
`(4)
`
`where z, fL, v, and T/ are the fraction of carbon flux
`which flows into the EMP pathway, the specific growth
`rate, the specific acetate production rate, and the normal(cid:173)
`ized efficiency coefficient, respectively. When the criterion,
`(5.056z + 1.141)n 2: Cr, is satisfied, acetate formation
`during the aerobic fermentation can be described as follows:
`
`(5)
`
`= vx
`
`d[HACJrer
`dt
`where n is the total glucose flux, Cr is the total capacity
`of cytochrome chain to turnover reducing equivalents,
`and the subscript "ref' indicates the reference state upon
`which the model equations were derived, that is, based
`on flux relations for the strain of E. coli ML308 at fast
`growth conditions, IL = 0.94 h-1. 7 In order to determine
`the acetate time profile in a batch E. coli fermentation by
`using Equation (5), one needs experimental data, or model
`predictions, for the exponential specific growth rate, the cell
`
`and dissolved oxygen concentrations, and values of the car(cid:173)
`bon flux partitioning at the junction of the EMP and HMP
`pathways. Normally, the fraction of carbon flux flowing
`into the EMP pathway is 0.72 during exponential growth. 15
`
`COORDINATE BETWEEN THE EMP
`AND HMP PATHWAYS
`
`In a previous article,9 it was shown that by considering the
`branching of glucose into the EMP and HMP pathways,
`better model predictions were produced for the data of wild(cid:173)
`type E. coli from Yang and Wang. 19 These experiments
`were carried out with E. coli B, ATCC 11303, in 10-L
`working volume fermentors with pH controlled at 7 .0. The
`temperature was maintained at 3rC. The initial glucose
`concentration was 8 g/L and the initial biomass concentra(cid:173)
`tion was 0.01 OD600 . Measurements taken every hour in(cid:173)
`cluded the cell mass, dissolved oxygen, glucose, and acetic
`acid concentrations. The fraction of carbon flux which flows
`into the HMP pathway is 1 - z. Under certain growth con(cid:173)
`ditions, its value is 0.28. Due to the complex interrelation(cid:173)
`ships between the EMP and HMP pathways, the value of
`1 - z varies, depending on growth conditions. In general,
`the EMP pathway becomes more important as the fermen(cid:173)
`tation proceeds, because the energy and precursor require(cid:173)
`ments for biosynthesis increase. By using Equations (1) to
`(5), we can calculate the fraction of carbon flux, z, which
`flows through the EMP pathway. With this calculation we
`determined the values of z vs. t which give zero error
`between the measured acetate (HAC) time profiles and the
`model prediction. As shown in Figure 1, the calculated val(cid:173)
`ues of 1 - z through the fermentation process varies from
`14
`0.57 to 0.007, which is consistent with the literature.3
`•
`
`1.00
`
`,--.....
`N
`-...._.,.0.80
`X
`::J
`u...
`I 0.60
`u
`I
`Q_
`20.40
`w
`
`I
`
`0.20
`2.00 3.00 4.00 5.00 6.00 7.00 8.00
`Time (hr)
`
`the EMP pathway of
`into
`flux
`Figure 1. Fractions of carbon
`experiments I to VI via the model calculation. The order of magnitude of
`these calculated carbon fractions from the upper part to the low part of the
`figure is I, III, IV, V, VI, II. This sequence is in opposite order of the oxy·
`gen transfer rates.
`
`848
`
`BIOTECHNOLOGY AND BIOENGINEERING, VOL. 43, NO. 9, APRIL 15, 1994
`
`BEQ 1047
`Page 2
`
`

`
`Table I. Operating conditions of fermentations. 9•19
`
`Experimental conditions
`
`II
`
`III
`
`IV
`
`Headspace pressure, psia
`Saturated oxygen concentration, ppm
`Agitation speed, rpm
`Initial glucose concentration g/L
`Initial biomass concentration, OD6oo
`Aeration rate, vvm
`
`15.6
`7.1
`175
`7.55
`O.ot
`
`15.6
`7.1
`300
`7.52
`0.007
`
`20.0
`9.06
`175
`8.00
`0.004
`
`28.0
`12.7
`175
`8.05
`0.005
`
`v
`
`35.0
`15.8
`175
`7.96
`0.009
`
`VI
`
`RE-I
`
`RE-I!
`
`RE-III
`
`40.6
`18.2
`175
`7.87
`0.006
`
`15.6
`7.1
`200
`7.21
`0.024
`0.25
`
`15.6
`7.1
`100
`8.11
`0.016
`0.21
`
`15.6
`7.1
`200
`7.84
`0.026
`0.5
`
`Experiments I to VI are obtained from Yang and Wang. 19
`
`in Figure 1
`The order of carbon fraction curves
`corresponds to experiments I, III, IV, V, VI, and II of
`Yang and Wang. 19 The conditions for these experiments
`are listed in Table I. This order is consistent with the
`fact that the system which has the lower oxygen transfer
`rate would have a higher carbon fraction into the EMP
`pathway. 14
`If we consider the cells to be optimal control systems
`which maximize a performance goal, biomass produc(cid:173)
`tion, then we can simplify the analysis of their complex
`regulatory processes. This is the cybernetic view of micro(cid:173)
`bial growth,6•16•17 which assumes the existence of certain
`characteristic features in the model microorganism. For
`instance, (1) If the metabolic energy generated by the cells
`is equal to or less than that required for maintenance,
`then there will be no growth; (2) If the generated energy
`exceeds that needed for maintenance, then the cells use
`the excess to maximize biomass production. In general,
`cells generate more metabolic energy than they need for
`biosynthetic reactions and then utilize ATPase, futile cycles,
`etc., to control the excess. That is, cells do not simply
`produce adequate metabolic energy but rather they maxi(cid:173)
`mize metabolic energy production. In the previous article,9
`we defined the performance goal of cells as maximizing
`the metabolic energy. Now we assume a second criterion
`being maximizing biomass production. It is noted that the
`RNA/mass ratio increases in parallel with the growth rate,
`primarily because more ribosomes are formed per unit mass
`in the fast-growing cells, whereas the DNA mass/ratio
`and the protein/mass ratio are fairly constant parameters. 15
`Also, we note that the carbon flux into the HMP pathway is
`directly related to the RNA synthesis. Since the RNA/mass
`ratio, the flux into the HMP pathway, 1 - z, and, therefore,
`the flux into the EMP pathway, z, are related, the biomass
`produced during the growth is related to z. Consequently,
`we consider a relation between the carbon fraction into
`the EMP pathway and a dimensionless measure of bio(cid:173)
`mass, DB.
`When the glucose flux to the EMP pathway is plotted
`against a dimensionless measure of biomass, we obtain a
`set of six nearly parallel straight lines, as shown in Figure 2.
`It also can be seen clearly from Figure 2 that the system
`with the lower oxygen transfer rate has the higher fraction
`of carbon flux into the EMP pathway and the order of the
`parallel lines corresponds to, as before, experiments I, III,
`IV, V, VI, and II, respectively, We define the dimensionless
`
`biomass, DB, or normalized biomass, as
`
`DB= BHAC- B;
`Bao+- B;
`
`(6)
`
`where B; is the initial biomass concentration, Bao+ is the
`biomass concentration for the data point immediately prior
`to the first zero glucose measurement, or it is the maximum
`biomass concentration if no zero glucose measurement is
`obtained, and BHAC is the biomass concentration at each
`acetate sampling time.
`The parallel lines on Figure 2 can be expressed as
`z; = A*(DB) 1 + /*
`(7)
`where z; is the fraction of carbon flux into the EMP
`pathway at timet calculated by Equations (1) to (5) required
`to match the measured acetic acid concentration profile;
`A* is the slope; /* is the intercept; and (DB)1 is the
`dimensionless biomass at time t as defined above. The
`intercept, I*, is the fraction of carbon flux into the EMP
`pathway at time t = 0. In general, the fraction of carbon
`flux into the EMP pathway will depend on, in addition
`to the RNA synthesis, the strain, temperature, pH, ionic
`
`,.-....,
`N0.80
`-..__....-
`
`X
`::J
`'+-
`I
`u
`I 0.40
`o_
`2
`w
`
`0. 00 -frrlTTTlTTTrrTTTTTTTT1'TTTTrTTTTTTTT1'TTTTTTTTlTTTT1'TTTTTTTTTTi
`0.00 0.20 0.40 0.60 0.80 1.00 1.20
`Dimensionless Biomass
`Figure 2. Fractions of carbon
`flux
`into
`the EMP pathway of
`experiments I to VI plotted with dimensionless biomass. The order of
`these parallel lines from the upper part of this plot to the lower part
`of this plot is I, III, IV, V, VI, II. This sequence is in opposite order of
`the oxygen transfer rates.
`
`KO, BENTLEY, AND WEIGAND: METABOLIC MODEL OF CELLULAR ENERGETICS
`
`849
`
`BEQ 1047
`Page 3
`
`

`
`strength, nutrients, and dissolved oxygen concentration.
`Also, for any given experiment the strain is fixed, whereas
`the temperature, pH, ionic strength, and nutrients are either
`constant or not rate-limiting, and, most often, glucose is
`the only carbon source and rate-limiting substrate. Under
`these conditions, we replace z• by z to indicate that it is
`only a function of the glucose and dissolved oxygen con(cid:173)
`centrations. We also assume that the fermentation system
`normally has an adequate supply of molecular oxygen, a
`terminal electron acceptor, at t = 0. As defined earlier,9 the
`normalized efficiency coefficient, TJ, explicitly accounts for
`the ATP from oxidative phosphorylation and the coupling
`effect between the biosynthetic and the fueling reactions.
`Finally, using the assumption of adequate initial oxygen,
`the intercept, I or Z at t = 0, can be simplified to be only
`a function of the glucose concentration in this integrated
`metabolic model structure.
`Up to the present time, it has not been possible to deter(cid:173)
`14
`mine the value of I experimentally because of difficulties.3
`•
`In addition, the model equations can only be tested when
`acetate is formed. To calculate the carbon fractions flowing
`into the EMP and HMP pathways by Equation (7), we
`need to know the value of I. In addition, not only is I not
`available, but it is also system specific and changes from
`one set of experimental conditions to another. However,
`using the straight line relationship shown in Figure 2, we
`can extrapolate from the first nonzero acetate measurement
`to calculate the carbon fractions at the point when the cells
`start to secrete acetate. As a reference condition, we call
`the time when the cells start to secrete acetate the critical
`physiological point. Regardless of the cause for acetate
`secretion, i.e., either high glucose concentration or low
`dissolved oxygen concentration, high specific growth rate,
`or some combination of these, mathematically the critical
`physiological point, DBc or tc, represents the time when
`[HAC] = o+ and is related to normalized biomass. If the
`relation between carbon fraction into the EMP pathway
`and biomass growth, shown in Figure 2 in terms of z and
`DB, was a general property of E. coli batch fermentations,
`then this correlation could be used in a predictive fashion
`in the acetate model. An examination of the experimental
`data indicates that the intercept in Figure 2 is correlated
`to the glucose concentration when acetate first appears in
`the broth.
`Since samples are taken at discrete times, the first point
`of acetate appearance will not be measured directly but
`can be approximated well by extrapolation. For the data in
`Figure 2, it was found that the intercept, I, was approxi(cid:173)
`mately equal to 6% of the glucose concentration measured
`at the first nonzero acetate sample. Then the following
`equation can represent these six parallel lines:
`Z 1 = 0.460(DB) 1 + 0.06[GlucoseJc+
`
`(8)
`
`where 0.460 is the arithmetic average of the slopes.
`Figures 3a and b are representative plots comparing
`experimental acetate data 18 and model predictions using
`Equations (1) to (5) and (8) for two of the six previous
`
`2.00
`
`1.50
`
`~
`OJ
`'-.../1.00
`u
`<(
`I
`
`0.50
`
`*
`
`*
`
`*
`
`* ,'
`
`0. 00 ....... 1!1-r~'f'rtti>TT!"T"i"in-.-rttT"TTTTTTTT.,.,..,.'TT1"'1""'T'T"i
`8.00
`0.00
`2.00
`4.00
`6.00
`Time(hr)
`(a)
`
`,-----...,1.00
`~
`OJ
`"-..._../ u
`<(
`I 0.50
`
`0, 0 0 ....... T"'M''I"'r'"1'"M'""f.,...,.,rilf.i'T-ilor-fi(,.T""TTTTTT"TTT'T"T"TT'1...,.,......j
`2.00
`4.00
`6.00
`0.00
`8.00
`Time(hr)
`(b)
`
`Figure 3. Experiments and model predictions. The dotted line (Z =
`0.72) and the solid line, where Z's are generated by using Equation (8),
`are model predictions by the present work. The dashed line is Majewski
`and Domach's model. 12 (a) Experiment I. (b) Experiment V.
`
`fermentations. In brief, what we do is, first, find the z-vs.-t
`profile which is required if Equations (1) to (5) were to
`accurately predict the acetic acid concentration profile.
`Then, we correlate these z(t) profiles with a variable which
`corresponds to the time course of events which evolve
`through a batch, i.e., our normalized biomass. We then try to
`use this correlated z(t) profile for other batches, recombinant
`cells, in a "predictive" manner. This last point is illustrated
`in the next section.
`Accurate predictions of both acetate concentration and
`onset time of acetate secretion, when compared to other
`models, makes the present work useful for control pur(cid:173)
`poses. This model can predict concentrations throughout
`
`850
`
`BIOTECHNOLOGY AND BIOENGINEERING, VOL. 43, NO. 9, APRIL 15, 1994
`
`BEQ 1047
`Page 4
`
`

`
`the acetate production phase within (less than) 10% error.
`The error of the onset time of acetate production is less
`than 12%. These results can be used for optimizing the
`aerobic E. coli fermentation process. Also, for systems
`where the model and Equation (8) are accurate, it may be
`possible to estimate the EMP pathway carbon flux from the
`extracellular acetate profile.
`
`Media
`
`The medium was M9 m1mmum, supplemented with L(cid:173)
`tryptophan, L-leucine, L-proline, and vitamin B1 at levels of
`144, 82, 328, and 0.332 JLg/mL, respectively, according to
`Rodriguez and Tait. 18 All chemicals (Sigma) were reagent
`grade.
`
`Extension to Other Strains and Growth Conditions
`
`Cultivation
`
`Other problems associated with the use of Equations (1) to
`(5) and (8) result from the following observations:
`
`1. As noted previously, the composition of the cells is
`altered in a characteristic way with changes in the
`growth rate.
`2. The macromolecular compositions of cells are strain
`dependent, although the metabolic basis of the model
`structure is largely strain independent.
`
`to use a
`these observations, we propose
`Based on
`scaling factor in order to account for the difference of
`macromolecular compositions caused by either different
`growth rates and/or different strains. This factor, called G,
`should be determined experimentally. Using this factor, we
`express the dynamic acetate equation as
`
`[HAC] = G[HACJret
`
`(9)
`
`where [HAC]ref is calculated by using Equation (5). Be(cid:173)
`cause the properties stated in (1) and (2) above are true
`in general for a variety of E. coli strains, their behavior
`will be qualitatively similar, except that they may differ
`in level (e.g., protein/mass ratio is generally constant) but
`may differ in magnitude for different strains even at the
`same growth conditions, and so their physiological events
`(behavior) are similar but differ in magnitude. Therefore,
`metabolic phenomena, such as acetate formation, can be
`related from one strain of E. coli to another with a scaling
`factor. In this way, an expression for acetate formation
`[Equation (5)] developed for E. coli ML308 at fast growth,
`i.e., JL = 0.94 h-1, can be adopted for other strains or
`growth conditions.
`
`MATERIALS AND METHODS
`
`Batch fermentation experiments for a recombinant E. coli
`were performed and a comparison was made between
`Majewski and Domach's12 model and the present approach.
`The conditions for these recombinant experiments (RE I,
`II, and III) are listed in Table I, along with the wild-type
`experiments of Yang and Wang.18
`
`Bacterial Strain
`
`Escherichia coli strain F-122 obtained from Univax Bio(cid:173)
`logics was used as a host strain for expressing human
`immunodeficiency virus (HIV582) f3-galactosidase fusion
`protein under the control of the trp promoter with ampicillin
`resistance.
`
`Inoculum for the fermentor was prepared in 250-mL Erlen(cid:173)
`meyer flasks at 3rC and 250 rpm in a reciprocating water
`bath shaker (New Brunswick Scientific). The first step was
`to add 1 mL of E. coli frozen stock to 100 mL medium
`with 40 JLg/mL of ampicillin. This was grown overnight
`until the optical density was approximately 0.9 units OD
`(600 nm). Then, 2 mL of the culture was used to inoculate
`the flask containing 100 mL of the same medium as that
`employed in the overnight culture. One hour before inocu(cid:173)
`lation, these flasks were put in the shaker bath to heat them
`to 3rc.
`
`Growth Rate Measurement
`
`Optical density was measured on a Milton Roy Spectronic
`21. All measurements were made at 600 nm in the linear
`range (0.05 to 0.25 OD units). Samples with higher concen(cid:173)
`trations of cells were diluted with sterile deionized water
`to obtain an OD in the linear range. All the readings of the
`culture OD were corrected with the OD of the respective
`sterile media.
`
`Fermentation
`
`All fermentations were performed in a 5-L fermentor (Bioflo
`III, New Brunswick Scientific) with automatic control of
`temperature and pH and aeration rate and agitation speed
`fixed. The overnight culture (40 mL) was added to the
`fermentor. Fermentations were carried out with 4 L work(cid:173)
`ing volume maintained at 3rC. Culture medium was the
`same as described above, but with different initial glucose
`concentrations. The pH of the medium was controlled at
`7.0 with 5 N NaOH and 2 N HCI.
`
`Analytical Methods
`
`Dry cell weight was measured after drying overnight at
`105•c. Glucose concentrations were determined with a
`glucose analyzer (YSI model 27). All measurements were
`made in the linear range (0.2 to 5 g/L). Samples with higher
`glucose concentrations were diluted with sterile deionized
`water to obtain a reading in the linear range. Acetic acid
`was analyzed by a gas chromatograph (Hewlett Packard
`5890). The temperature at the injector port and column was
`2oo•c, whereas at the detector it was 24o•c. Sample pH
`was pretreated with 2 N HCl to bring it below 2.5 to ensure
`accuracy. 2
`
`KO, BENTLEY, AND WEIGAND: METABOLIC MODEL OF CELLULAR ENERGETICS
`
`851
`
`BEQ 1047
`Page 5
`
`

`
`RESULTS AND DISCUSSION
`
`The acetic acid formation time profiles of these three batch
`experiments exhibit diverse responses. This result arises
`from the following characteristics of these experiments:
`(1) The Crabtree effect occurs because the initial glucose
`concentrations for these experiments range from 7.21 to
`8.11 g/L. These concentrations are much higher than the
`Monod constant. (2) The values of the agitation speeds
`and air sparge flow rates for these experiments are in the
`range where the Pasteur effect occurs. (3) The combined
`effect of the Pasteur and Crabtree effects causes diverse
`acetate onset times. The times for acetate secretion for
`these experiments range from 7.5 to 10.0 h for a fer(cid:173)
`mentation time of around 13.0 h. In addition, the specific
`growth rates of these experiments (0.52 to 0.57 h-1
`) are
`far lower than the reference condition, f.-Lref = 0.94 h-1.
`Majewski and Domach's model12 does not correspond to
`the low specific growth rates of these experiments. These
`specific growth rates are smaller than the critical specific
`growth rate (0.64 h-1) in their model. The present work
`produces much better results by explicitly accounting for
`the carbon flux partitioning at the junction of the EMP
`and HMP pathways and by correcting for the differences
`between strains and growth rates compared to the reference
`state (strain). Figures 4(a-c) show comparisons between
`the model predictions and recombinant experiments, RE-I,
`RE-II, and RE-III, respectively.
`The acetate production equation (5) and the fraction of
`carbon flux [Equation (8)] are based on information from
`wild-type E. coli. In particular, Equation (8) is developed
`from experiments I to VI. 9•19 In order to test these equa(cid:173)
`tions, model predictions were performed in the following
`three stages:
`
`• Stage 1: The model [Equation (5)] was applied with
`the assumption that 28% of the glucose flux goes
`through the pentose phosphate cycle. Because of the
`low specific growth rates in these experiments, the
`model predicts no acetate secretion in RE-I and RE(cid:173)
`III, but only predicts acetate for RE-II. In addition,
`the model predictions are incompatible with the data
`of RE-II, as is seen by the dotted line shown in
`Figure 4b.
`• Stage 2: By combining the acetate production equa(cid:173)
`tion (5) with the carbon flux to the EMP pathway
`[Equation (8)), acetate production is predicted for all
`three experiments and the prediction of the onset times
`of acetate secretion is significantly improved. This is
`shown by dashed lines in Figures 4a-c.
`• Stage 3: Equation (5) produces accurate predictions
`for both acetate concentration and the onset of acetate
`secretion when a scaling factor [Equation (9)) is used
`to account for differences in growth rate and strain.
`The value of the scaling factor was found to be a
`constant (1.25) in all of the recombinant experiments
`of this study. These results are shown as solid lines in
`Figures 4a-c.
`
`0.25
`
`0.20
`
`r---.
`~0.15
`()l
`......_....
`u
`<( 0.10
`I
`
`0.05
`
`*
`
`I
`
`I
`
`0. 0 0 --h-n-rrTTT1r'forrrr't>t-rrrf-mTTrrTTTTTT1rTTTTTTTTTTI"TTT"T"l
`8.00
`9.00
`10.00
`11.00 12.00 1.3.00
`(hr)
`Time
`(a)
`
`0.40
`
`0 . .30
`
`0.10
`
`0.00
`2.00
`
`4.00
`
`v __ _
`
`6.00
`Time
`
`8.00
`(hr)
`
`10.00 12.00
`
`(b)
`
`Figure 4. Recombinant experiments and model predictions. The solid
`line and the dashed line are model predictions by present work with and
`without the generalization factor, G = 1.25, respectively. Majewski and
`Domach's model 12 does not apply, given the growth rates of these ex(cid:173)
`periments. (a) Recombinant experiment I. (b) Recombinant experiment II;
`note that the dotted line is the model prediction of the present work with
`Equation (5) and constant carbon flux, z = 0.72.
`
`It is apparent from Figure 4b that improved model pre(cid:173)
`dictions are produced when the branching of glucose flux
`into HMP and EMP pathways is considered to vary during
`the batch as correlated by Equation (8). The predictions
`are further improved by applying the scaling factor to
`account for the difference of macromolecular compositions
`between different growth rates and strains. One important
`feature of this modeling approach is that the onset of
`the acetate secretion is predicted very well, even without
`the scaling factor. This is seen from Figures 4a-c. Also,
`
`852
`
`BIOTECHNOLOGY AND BIOENGINEERING, VOL. 43, NO. 9, APRIL 15, 1994
`
`BEQ 1047
`Page 6
`
`

`
`0.40 - . - - - - - - - - - - - - - - - - - ,
`
`of phenomena covered by these experiments represents a
`reasonable test for the model.
`
`0.30
`
`~
`CJ"l
`'---"' 0.20
`u
`<t
`::r::
`
`0.10
`
`/
`
`I
`
`I
`
`'/
`
`0.00
`8.00
`
`9.00
`
`11.00 12.00
`(hr)
`
`13.00
`
`10.00
`Time
`(c)
`
`Figure 4.
`
`(continued)
`
`(c) Recombinant experiment III.
`
`it appears that the fraction of carbon flux to the EMP
`pathway given by Equation (8), which was developed from
`the wild-type E. coli, can be used with the recombinant
`E. coli system examined. A point to be considered here
`is that the better correspondence between the model and
`the data produced when a fitted value of Z(t) is used may
`well be the result of the fitting procedure rather than the
`mechanistic nature of the model. Although this possibility
`exists, the useful mechanistic nature and validity of the
`model is favored for three reasons: (1) All of the carbon
`fraction flowing into the EMP pathway is consistent with
`literature data. 3•14 (2) The Z(t) function generated from
`wild-type E. coli enables the acetate profiles to be predicted
`for a recombinant E. coli strain. Without the Z(t) profile,
`the predicted acetate profiles for the recombinant organism
`would not even be qualitatively correct. (3) Although some
`fitting procedures are employed, the basic structure of the
`model is based on pathways and mechanisms known to be
`important.
`Although the experiments listed in Table I have essen(cid:173)
`tially the same initial glucose concentration, the difference
`in oxygen transfer conditions should be noted. The six
`wild-type batch fermentations are designed to examine the
`influence of oxygen transfer on E. coli cultures, whereas
`the glucose concentration is well above the Monod con(cid:173)
`stant. With this in mind, the saturation dissolved oxygen
`concentrations are different in these experiments. The three
`recombinant-cell batch fermentations also have different
`oxygen transfer rates caused by changes in the aeration
`rate and agitation speed. It is also clear that the range
`of acetate concentrations produced in these experiments is
`significant, 0.4 to 1.6 g HAC/L from 7 to 8 g/L glucose.
`Also, the onset of acetate secretion occurs between 7 and
`13 h for a total fermentation time of 16 h, and the biomass
`concentration varies between 1 and 3 g/L. Thus, the range
`
`Factors Affecting Cellular Yield
`
`The form of the proposed integrated metabolic model
`allows us the flexibility to explicitly account for the cou(cid:173)
`pling effects of the biosynthetic and fueling pathways and
`to use the cellular energetics to analyze factors which
`affect the carbon yield. The central fueling pathways of
`E. coli, the EMP pathway, the HMP pathway, and the TCA
`cycle, can function cyclically to degrade glucose to carbon
`dioxide and water, thereby generating energy and reducing
`power. They can also function unidirectionally to produce
`the 12 precursor metabolites for biosynthetic reactions.
`The TCA cycle fulfills two pr