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Model of Dissolved Organic CarbonDistribution for Substrate-SufficientContinuous Culture

Yu Liu1,2

1School of Civil and Structural Engineering, Nanyang TechnologicalUniversity, Nanyang Avenue, Sinapore 639798; telephone: +65 790 6913;fax: +65 791 0676; e-mail: cyliu@ntu.edu.sg2Department of Chemical Engineering, Beijing Industry and BusinessUniversity, No. 11, Fu Cheng Road, Beijing 100037, P.R. China

Received 19 March 1999; accepted 5 June 1999

Abstract: The growth yields (Yobs) are greater under sub-strate-limited conditions than those under substrate-sufficient conditions in continuous cultures. This indi-cates that the excess substrate should cause uncouplingbetween anabolism and catabolism. It appears that theexcess substrate could determine metabolic pathways ofmicroorganisms, which further control dissolved organiccarbon (DOC) distribution under substrate-sufficient con-ditions. However, how to quantitatively describe the DOCdistribution remains unclear in substrate-sufficient con-tinuous culture. Based on a balanced DOC reaction, aDOC distribution model was developed in relation to re-sidual substrate concentration for substrate-sufficientcontinuous cultures. Results showed that a considerableportion of the DOC consumed was directly oxidized tocarbon dioxide through energy spilling under substrate-sufficient conditions. The proposed model for the firsttime quantified the DOC distribution between non-growth-associated and growth-associated metabolismsof cells. The proposed model was verified with literaturedata very well. © 1999 John Wiley & Sons, Inc. BiotechnolBioeng 65: 474–479, 1999.Keywords: DOC distribution; substrate-sufficient culture;energy uncoupling; CO2; growth; residual substrate con-centration

INTRODUCTION

Metabolism is the sum of biochemical transformation thatincludes interrelated catabolic and anabolic reactions. It hasbeen assumed that catabolism and anabolism are coupledtogether in a largely reversible reaction continuum (Burk-head and McKinney, 1969; Lehninger, 1975; Gray, 1989;Bitton, 1994). Lehninger (1975) postulated that “cells arecapable of regulating their metabolic reactions and the bio-synthesis of their enzymes to achieve maximum efficiencyand economy.” However, experimental evidence showedthat under substrate-sufficient conditions, the variation inrespiration was far greater than the amount that could beascribed to ATP production (Bauchop and Elsden, 1960;Hempfling and Mainzer, 1975; Westerhoff et al., 1982;

Brooke et al., 1990; Tsai and Lee, 1990). Substrate-sufficient cultures are known to have different metabolicbehaviors from substrate-limited cultures with regard to thesubstrate removal rate, growth yield, and maintenance re-quirements (Hueting and Tempest, 1979; Brooke et al.,1990; Liu, 1996; Liu and Chen, 1997).

Liu (1996) developed a growth yield model in relation toresidual substrate concentration (Cs), and a model describ-ing the degree of energy uncoupling between anabolism andcatabolism was further proposed by Liu and Chen (1997)for substrate-sufficient continuous cultures. These previousworks indicated that the residual substrate concentrationcould regulate and control metabolic pathways of microor-ganisms under substrate-sufficient conditions. Obviously,metabolic pathways would finally determine dissolved or-ganic carbon (DOC) distribution. In fact, the influent DOCcan be channeled into biomass, metabolic products, carbondioxide as well as residual original DOC in a substrate-sufficient continuous culture. Therefore, it appeared that theDOC distribution should be related to residual substrateconcentration under substrate-sufficient conditions. How-ever, few attempts were made to establish a quantitativeexpression of DOC distribution to the residual substrateconcentration for substrate-sufficient continuous cultures.Based on those previous studies on energy uncoupling un-der substrate-sufficient conditions (Liu, 1996; Liu andChen, 1997), the specific objective of this work was todevelop aCs-dependent DOC distribution model for sub-strate-sufficient continuous culture.

MODEL DEVELOPMENT

A microbial culture can be classified to substrate-limitedand substrate-sufficient growth according to the relativeavailability of substrate and nutrients. This study was lim-ited in substrate-sufficient continuous culture using dis-solved organic carbon (DOC) as substrate for growth and

© 1999 John Wiley & Sons, Inc. CCC 0006-3592/99/040474-06

energy requirements. In a continuous culture, influent DOCconcentration (Co) can be channeled into biomass-carbon(Cg), carbon dioxide-carbon (CCO2

), soluble metabolite-carbon (Cm), and residual orginal DOC (Cs) in the effluentas schematically illustrated in Fig. 1, that is,

Co 4 Cg + Cco2+ Cm + Cs. (1)

It had been documented well that catabolism would seri-ously dissociate from anabolism under substrate-sufficientconditions, and such energy uncoupling led to energy spill-ing-associated substrate consumption (Tsai and Lee, 1990;Zeng and Deckwer, 1995; Liu and Chen, 1997; Liu, 1998).Thus, the observed carbon dioxide-C (CCO2

) consists ofCO2-C produced from growth-associated catabolism (CCO2

)g

and that generated due to energy spilling (CCO2)u:

CCO24 (CCO2

)g + (CCO2)u. (2)

On the other hand, the effluent DOC concentration (Ce) isthe sums of the residual original DOC (Cs) and metabo-lites–C (Cm), that is,

Ce 4 Cs + Cm. (3)

According to Gaudy and Gaudy (1980), the observedgrowth yield (Yobs) of a continuous culture can be calculatedas the increase in biomass concentration (DX), divided bythe corresponding decrease of DOC concentration (DC):

Yobs=DX

DC. (4)

Obviously,DC and be expressed as the difference betweenCo andCe:

DC = Co − Ce. (5)

Substituting Eqs. (1)–(3) and (5) into Eq. (4) gives

Yobs=DX

Cg + ~CCO2!g + ~CCO2

!u. (6)

It is reasonable to consider that the growth-associated DOC

consumption (DCg) is the sums of the DOC channeled intobiomass and CO2-C produced from growth-associated ca-tabolism. Thus,DCg is written as

DCg = Cg + ~CCO2!g. (7)

According to Liu (1996), the true growth yield (Yg) can bedefined as

Yg =DX

DCg. (8)

Substitutions of Eqs. (7) and (8) into Eq. (6) gives

Yobs=Yg

1 + ~CCO2!u/DCg

. (9)

Eq. (9) can be arranged to the following form:

~CCO2!u

DCg=

Yg

Yobs− 1. (10)

Liu (1996) developed the followingCs-dependentYobs

model for substrate-sufficient continuous culture as follows:

1

Yobs=

1

~Yobs!max+

1

~Yw!min

Cs

Cs + Ks*, (11)

where (Yobs)max and (Yw)min are the maximum observedgrowth yield under substrate-limited conditions, and theminimum energy spilling-related growth yield, respectively.Ks* is a substrate-related constant. (Yobs)max was defined as

~Yobs!max =mg

qg + ms, (12)

wheremg andqg are the true specific growth rate and spe-cific growth-associated substrate removal rate, respectively.ms is the specific maintenance coefficient. According to Pirt(1965), the true growth yield,Yg, can also be expressed as

Yg =mg

qg. (13)

Under substrate-sufficient conditions, it is a reasonable as-sumption that the maintenance coefficient would be negli-gible as compared with substrate consumption rate (Cookand Russell, 1994; Liu, 1998). Thus, Eqs. (12) and (13) mayreduce to

(Yobs)max 4 Yg. (14)

Obviously, model development would be simplified whilesacrificing little in terms of accuracy. By substituting Eqs.(11) and (14) into Eq. (10), the following equation is ob-tained:

~CCO2!u

DCg=

~Yobs!max

~Yw!min

Cs

Cs + Ks*. (15)

Eq. (15) for the first time reveals the DOC distributionbetween nongrowth-associated and growth-associated me-tabolisms at different residual substrate concentrations. Thisin turn implied that metabolic pathways of microorganismsFigure 1. Schematic presentation of DOC flux in a continuous culture.

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were Cs-dependent in substrate-sufficient continuous cul-ture. In this study, the (CCO2

)u/DCg ratio is designated as theDOC distribution coefficient between nongrowth-associatedmetabolism and growth-associated metabolism, namelyl,while the (Yobs)max/(Yw)min ratio is defined as the maximumDOC distribution coefficient (lmax). Therefore, Eq. (15) iswritten as the following form:

l = lmax

Cs

Cs + Ks*. (16)

It should be pointed out that (Yobs)max, (Yw)min, andK*s aredetermined from Eq. (11) using the same graphical methodas proposed by Liu (1996), whilelmax can be calculatedfrom (Yobs)max and (Yw)min.

Liu and Chen (1997) considered that the difference be-tween the observed growth yields under substrate-limitedand substrate-sufficient conditions reflected the uncouplingdegree between catabolism and anabolism. They introduceda new parameter, the so-called energy-uncoupling coeffi-cient, to describe the observed uncoupling between catabo-lism and anabolism under substrate-sufficient conditions.The energy-uncoupling coefficient (Eu) was defined as

Eu =~Yobs!max − Yobs

~Yobs!max. (17)

This coefficient features dissociation degree of catabolismfrom anabolism under substrate-sufficient conditions. Ac-cording to Eq. (17), the fraction of DOC consumed due toenergy spilling isEu, while 1-Eu represents the fraction ofDOC utilized for growth purposes under substrate-sufficientconditions. Therefore, the ratio of carbon consumed throughenergy spilling to carbon utilized for growth can be ex-pressed as follows:

energy spilling− associated DOC consumption

growth− associated DOC utilization=

Eu

1 − Eu.

(18)

Substitution of Eqs. (11) and (17) into the right side of Eq.(18) gives

Eu

1 − Eu=

~Yobs!max

~Yw!min

Cs

Cs + Ks*. (19)

Comparison of Eqs. (15) and (16) with Eq. (19) shows that

l =~CCO2

!u

DCg=

Eu

1 − Eu. (20)

Eq. (20) displays an interrelationship between DOC distri-bution and energy uncoupling under substrate-sufficientconditions. With increasing the energy uncoupling degree,the DOC distribution between carbon dioxide and biosyn-thesis shows an increasing trend. After determination of theobserved growth yields by experiments,Eu and l can becalculated using Eqs. (17) and (20), respectively.

MODEL VERIFICATION

In order to test the proposed DOC distribution model, ex-perimental data published by Brooke et al. (1990) wereused. Those data were collected during the growth of ther-motolerant methylotrophicBacillus strains in methanol-sufficient continuous cultures. Figure 2 and 3 show com-parison between the observed growth yields with valuescomputed using Eq. (11) forBacillus strains grown onmethanol under nitrogen-limited and potassium-limitedconditions, respectively. TheYobs model agrees with thoseexperimental data very well. Using Eq. (11), values of(Yobs)max, (Yw)min, and K*s were obtained. In their study,Brooke et al. (1990) also determined the rates of methanolconsumption, CO2 production rates and carbon conversionefficiencies under nitrogen and potassium limitations. TheDOC distribution coefficient (l) was then obtained fromthose data for each corresponding residual methanol con-centration. As pointed out earlier,l can also be calculatedusing Eq. (20). The effect of residual methanol concentra-tion on the DOC distribution coefficient is shown in Figs. 4and 5 for nitrogen and potassium limitations, respectively.As can be seen in these two figures, Eq. (16) can provide asatisfactory description for experimental data. It is worthnoting in Fig. 4 that the DOC distribution coefficients de-termined by experiments are in good agreement with thosecalculated from Eq. (20). It should be pointed out that in thecase of potassium limitation (Fig. 5), the DOC distributioncoefficients were calculated using Eq. (20) only since thecarbon recovery was not satisfied. Although no more dataare shown here, other experiments also support Eq. (16)(Heuting and Tempest, 1979).

DISCUSSION

Figures 2–5 show that the reduction ofYobs is associatedwith an increase in the DOC distribution coefficient. As theresidual methanol concentration becomes greater than 40

Figure 2. Relationship betweenYobs and the residual methanol concen-tration in nitrogen-limited continuous culture of aBacillusstrain (D 4 0.2h−1); (d) data from Brooke et al. (1990); (—) Eq. (11) prediction. (Yobs)max

4 20.0 g dry wt/mol, (Yw)min 4 4.18 g dry wt/mol,K*s 4 23.6 mmol/L.

476 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 65, NO. 4, NOVEMBER 20, 1999

mmol/L, the DOC distribution coefficient reaches 3.0 mmolCO2-C/mmol biomass-C under nitrogen-limited conditions,and the samel value was observed at residual methanolconcentrations higher than 15 mmol/L in potassium-limitedcultures. These imply that the DOC mineralized to carbondioxide is at least 3-fold higher than that utilized for growth.Decline inYobsdisplays a serious dissociation of catabolismfrom anabolism with the increase of the residual methanolconcentration, which leads to energy spilling (Liu and Chen,1997; Liu, 1998). It can be reasonaby considered that in theenergy uncoupling state of cells, an important part of thesubstrate consumed would be converted to carbon dioxidethrough the energy spilling pathway, without relationship tobiosynthesis. It appears from Figs. 2–5 that the residualmethanol concentration may play an important role in regu-lating the interrelationship between catabolism and anabo-lism.

The lmax value obtained under potassium limitation (8.0mmol/mmol) was nearly 2-fold higher than that in nitrogen-limited culture (4.8 mmol/mmol). The metabolic responseto the potassium limitation seems to be much more sensitivethan to the nitrogen limitation. In fact, Brooke et al. (1990)found that the carbon conversion efficiency in potassium-limited cultures dropped to 26.5% of that obtained withcarbon-limited cultures while the carbon conversion effi-ciency value in the nitrogen-limited culture was 62%. Theseindicate that under substrate-sufficient conditions, the DOCdistribution would also be related to the nature of thegrowth-limiting nutrient other than residual substrate con-centration.

Microbiologists believe when the energy and carbonsource is in excess, microorganisms would tend to dispensethe excess energy and carbon by the formation of storagecompounds or extracellular products (Pennock and Tem-pest, 1988; Brooke et al., 1990; Zeng et al., 1990). Howeversome of the metabolic products are toxic to microbialgrowth, and microbial growth ultimately may be inhibitedwith accumulation of those products. In fact, most of mi-croorganisms are able to produce a variety of metabolicproducts, which have different energetic efficiencies andtoxicities. Under excess carbon conditions, microorganismswould prefer metabolic pathways, which lead to less toxicproducts to maximize the growth. As a result, energeticefficiency of substrate conversion is lowered, and more sub-strate is thus required to obtain the same amount of energyproduction for growth. As is illustrated in Fig. 1, whenmicroorganisms are grown in continuous culture with agrowth-limitation other than the carbon source, not all of theDOC would be fluxed into biomass or completely oxidizedto carbon dioxide, but overflow metabolites could beformed and released into the culture filtrate. Brooke et al.(1990) found that overflow metabolites, which accumulatedin significant amount was acetate only, and an additionalsmall amount of 2-oxoglutarate with nitrogen-limited

Figure 4. Effect of residual methanol concentration on the DOC distri-bution coefficient in nitrogen-limited continuous culture of aBacillusstrain (D 4 0.2 h−1); (d) data from Brooke et al. (1990); (D) data calcu-lated using Eq. (20); Eq. (16) prediction.lmax 4 4.8 mmol C/mmol C,K*s4 23.6 mmol/L.

Figure 3. Relationship betweenYobs and the residual methanol concen-tration in potassium-limited continuous culture of aBacillus strain (D 4

0.2 h−1); (d) data from Brooke et al. (1990); (—) Eq. (11) prediction.(Yobs)max 4 20.0 g dry wt/mol, (Yw)min 4 2.5 g dry wt/mol,K*s 4 22.4mmol/L.

Figure 5. Effect of residual methanol concentration on the DOC distri-bution coefficient in potassium-limited continuous culture of aBacillusstrain (D 4 0.2 h−1); (d) data calculated using Eq. (20); (—) Eq. (16)prediction.lmax 4 8.0 mmol C/mmol C,K*s 4 22.4 mmol/L.

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growth. Liu and Chen (1997) demonstrated that as the re-sidual methanol concentration exceeded 10 mmol/L, the en-ergy-uncoupling coefficients reached 0.7 under nitrogenand potassium limitations, meaning that about 70% ofmethanol consumption dissociated from anabolism forgrowth. However, the data of Brooke et al. (1990) showedthat the metabolic products (acetate and 2-oxoglutarate)only accounted for less than 15% of the energy source uti-lization in the nitrogen-limited and potassium-limited cul-tures, which could not match with the reduction inYobs asobserved in Figs. 2 and 3. Tempest and Neijssel (1978,1992) also reported that the metabolic products detected inKlebsiella aerogenescultures could not account for the ab-normally high rates of glucose consumption when energysource was in excess. Obviously, overflow metabolism ofcells cannot provide a plausible explanation for theYobsandDOC distribution patterns observed in Figs. 2–5. As pointedout earlier, the DOC consumed was finally converted tocellular materials, carbon dioxide, and metabolic products.Eq. (16) further displayed that under substrate-sufficientconditions, the majority of the DOC consumed should fluxinto carbon dioxide rather than metabolic products. There-fore, it appears that microorganisms should have othermechanisms dissipating nongrowth energy other than over-production of metabolites under carbon-sufficient condi-tions.

The experiments withEscherichia colishow that underspecific nutrient limitations, such as ammonia and potas-sium, bacteria can dissipate energy through futile cycles ofions through the cell membrane (Neijssel and Tempest,1975; Kleiner, 1985; Mulder et al., 1986). On the otherhand, Cook and Russell (1994) demonstrated that a futilecycle of protons through the cell membrane should be re-sponsible for most of the energy spilling in their study onenergy spilling. As compared to ion futile cycles, the protonfutile cycles can occur whenever there is an imbalance be-tween catabolic and anabolic rates. In fact, energy spillingcould have a very significant effect on the overall efficiencyof biosynthesis as shown in Figs. 2 and 3. There is evidencethat energy spilling also has the potential to protect bacteriafrom toxic products (Cooper, 1984; Ferguson et al., 1993).There might be an inverse relationship between energyspilling and production of toxic substances (Russell andCook, 1995). Just as Eq. (16) shows, microorganisms, in-deed, prefer to respire the substrate and not just secrete orstore carbon. Most of the energy generated from oxidationof DOC to carbon dioxide then could be used to drive futilecycles rather than for biosynthesis. It is obvious that thosefutile cycles of energy reduce efficiency of energy conver-sion, but in turn they would minimize production of toxicmetabolites in substrate-sufficient continuous culture. TheYobsandl variation patterns as shown in Figs. 2–5 indicatethat efficiency of energy production can be stimulated bysubstrate excess under substrate-sufficient conditions, how-ever efficiency of energy utilization for growth is reduceddue to energy spilling. In fact, Eq. (16) provides a quanti-tative description for the imbalance between energy produc-

tion and energy utilization for growth under substrate-sufficient conditions. As noted by Harold, “there is some-thing misleading about the fundamental assumption that thefree energy of catabolism is fully conserved as ATP andexpended necessarily either for biosynthesis or for usefulwork. Any departure from perfect coupling, either in thegeneration of ATP or in its utilization, will show up as ashortfall of the yield and exaggerate the apparent cost ofcellular upkeep.”

CONCLUSION

Based on a balance of dissolved organic carbon (DOC), amodel of DOC distribution was developed for substrate-sufficient continuous culture. It was demonstrated that finalDOC distribution was theoretically interrelated to energyuncoupling degree under substrate-sufficient conditions.The proposed model for the first time showed the DOCdistribution between nongrowth-associated and growth-associated metabolisms. Under substrate-sufficient condi-tions, most of DOC consumed was directly oxidized to car-bon dioxide rather than metabolic products, and energy gen-erated was sacrificed to make futile cycles run, but norelationship to biosynthesis.

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