COMMUNICATION TO THE EDITOR

Model of Energy Uncoupling forSubstrate-Sufficient Culture

Yu Liu,1 Guang Hao Chen2

1Department of Chemical Engineering, Beijing Institute of Light Industry,Beijing 100037, P.R. China2Department of Civil and Structural Engineering, Hong Kong University ofScience and Technology, Clear Water Bay, Kowloon, Hong Kong; telephone:85223588752; fax: 85223581534; e-mail: ceghchen@usthk.ust.hk

Received 30 August 1996; accepted 3 January 1997

Abstract: The growth yields (Yobs) are greater under sub- growth yield, eobs is the observed specific growth rate,strate-limited conditions than those under substrate-suf- and ms is the maintenance metabolism rate.ficient conditions in continuous cultures. This indicates Substrate-sufficient cultures are known to have differ-that the excess substrate should cause uncoupling be-

ent metabolic behaviors from substrate-limited culturestween anabolism and catabolism, which leads to energywith regard to the substrate removal rate, maintenancespilling. Although the uncoupling between anabolism

and catabolism has already been recognized in the micro- requirements, and growth yield (Brooke et al., 1990;biology literature, how to quantitatively describe such Hueting and Tempest, 1979; Tsai and Lee, 1990; Zenguncoupling remains unclear. Based on a balance on sub- and Deckwer, 1995). In fact, much research shows thatstrate reaction, a growth yield model was developed in

under substrate-sufficient conditions, Yobs decreasesrelation to residual substrate concentration for substrate-with increasing residual substrate concentration for con-sufficient continuous cultures. On the basis of that yield

model, the concept of an uncoupling coefficient between tinuous and batch cultures (Chang et al., 1993; Chudobaanabolism and catabolism is defined in this work. A model et al., 1992; Liu, 1996; Rao and Gaudy 1966; Yamanedescribing the effect of the residual substrate concentra- et al., 1992). Lowered growth yields show dissociation oftion on the uncoupling coefficient of anabolism to catabo-

anabolism from catabolism. Under substrate-sufficientlism is proposed. This model agrees very well with litera-conditions, energy generation from catabolism-associ-ture data. 1997 John Wiley & Sons, Inc. Biotechnol Bioeng

55: 571–576, 1997. ated substrate consumption is in excess with respect toKeywords: substrate-sufficient culture; anabolism; catab- the anabolism requirement that excessive energy wouldolism; energy uncoupling; growth yield; residual sub- be spilled out (Brooke et al., 1990; Russell and Cook,strate concentration

1995; Tsai and Lee, 1990; Westerhoff et al., 1982; Zengand Deckwer, 1995). Thus, the interpretation of growth

INTRODUCTION yield by the Pirt theory is questionable under substrate-sufficient conditions. Tsai and Lee (1990) introducedSince Pirt (1965) postulated his well-known mainte-the concept of overutilization of the substrate to explainnance energy equation, nongrowth-associated energythe particular behaviors of microorganisms in substrate-requirements have usually been attributed to mainte-sufficient cultures. However, few attempts were madenance. Many studies have been carried out to determineto establish a quantitative expression of the uncouplingmaintenance coefficients and growth yield of microor-degree between anabolism and catabolism to the resid-ganisms (Brooke et al., 1990; Chang et al., 1993; Chu-ual substrate concentration for substrate-sufficient con-doba et al., 1992; Pirt, 1975; Rao and Gaudy, 1966;tinuous cultures. The specific objective of this work wasYamane et al., 1992). According to the Pirt theory, theto develop a concept of the uncoupling coefficient ofobserved growth rate has an effect on the observedanabolism to catabolism, from which a model of thegrowth yield, which can be described by Eq. (1) underenergy uncoupling coefficient is proposed for substrate-substrate-limited conditions.sufficient continuous culture.

1Yobs

51

Yg1

ms

eobs, (1)

CONCEPT DEVELOPMENTwhere Yobs is the observed growth yield, Yg is the true

A culture of microorganisms can be classified into sub-strate-limited and substrate-sufficient growth accordingCorrespondence to: G. H. Chen

1997 John Wiley & Sons, Inc. CCC 0006-3592/97/030571-06

Figure 1. Relationship between Yobs and the residual methanol concentration in nitrogen-limited continuous culture of a Bacillus strain (D5 0.2 h21); data from Brooke et al. (1990) (3) The model prediction is shown. (Yobs)max 5 20.0 g dry wt/mol, (Yw)min 5 4.18 g dry wt/mol,K*

s 5 23.6 mmol/L.

to the relative availability of the energy substrate. This biosynthesis and total energy flux can be partitionedinto growth and maintenance function. If growth is lim-study is limited only to energy substrate-sufficient con-

tinuous cultures. The substrate is consumed by microor- ited by nutrients other than energy, however, bacteriacan spill ATP in reactions that cannot be readily catego-ganisms to form various intracellular metabolites and

energy, which are then used for biomass formation, rized as maintenance per se.’’ This work only deals withenergy uncoupling due to the presence of excess en-maintenance, and product formation. Under substrate-

sufficient conditions it has been shown that the metabo- ergy substrate.As discussed above, utilization of ATP by bacteria islites and energy may also be consumed in biomass turn-

over by energy spilling or through futile cycles (Russell not directly related to growth and maintenance func-tions. Based on a mass balance on the substrate, theand Cook, 1995; Stouthamer, 1979; Tempest and Neijs-

sel, 1984; Tsai and Lee, 1990). Under substrate-sufficient overall consumption of substrate (DS) is thus taken tobe the sums of the substrate consumed for growth (DSg),conditions, cells are not able to effectively regulate sub-

strate consumption to adapt the exogenous substrate the substrate used for maintenance (DSm), and substrateconsumption due to energy spilling (DSw), that is,level. The literature shows that substrate-sufficient cul-

tures have much higher substrate consumption rates (2)DS 5 DSg 1 DSm 1 DSw .and lower growth yields than substrate-limited cultures

It is important to realize that Eq. (2) features the(Fiechter and Seghezzi, 1992; Forrest, 1969; Stouthamer,energy spilling associated substrate consumption with1977, 1979; Tempest and Neijssel, 1984). This impliesrespect to the Pirt maintenance theory. If catabolismthat under substrate-sufficient conditions, a discrepancyis tightly regulated to match energy requirements ofexists between the rate of ATP production by catabo-microorganisms, DSw should be negligible. In fact, alism and the rate of ATP utilization by anabolism forsemiempirical model was proposed by Zeng and Deck-growth purposes. Generally, such a phenomenon is thewer (1995) for describing the excessive consumptionso-called energy uncoupling. The energy uncouplingof substrate in substrate-sufficient cultures. From Eq.may also occur under abnormal growth conditions, such(2) Liu (1996) further developed the following modelas the presence of inhibitors or at unfavorable tempera-for describing the dependence of the observed growthtures, etc. (Forrest, 1969; Rao and Gaudy, 1966; Russellyield on residual substrate concentration under sub-and Cook, 1995; Stouthamer, 1977, 1979; Tempest andstrate-sufficient conditions:Neijssel, 1984; Tsai and Lee, 1990). In a review on ener-

getics of bacterial growth, Russell and Cook (1995) con- 1Yobs

51

(Yobs)max1

1(YW)min

Cs 2 C*s

Cs 2 C*s 1 K*

s, (3)cluded that ‘‘when bacteria are limited for energy

sources, the free energy change of catabolic reactions isgenerally tightly coupled to the anabolic steps of cellular where (Yobs)max is the maximum observed growth yield

572 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 55, NO. 3, AUGUST 5, 1997

Figure 2. Relationship between Yobs and the residual methanol concentration in potassium-limited continuous culture of a Bacillus strain(D 5 0.2 h21); data from Brooke et al. (1990) (3) The Eq. (6) prediction is shown. (Yobs)max 5 20.0 g dry wt/mol, (Yw)min 5 2.5 g drywt/mol, K*

s 5 22.4 mmol/L.

for substrate-limited cultures, (Yw)min is the minimal g/L, excretion of partially oxidized metabolites wasdetected, which showed a glucose-sufficient condition,energy spilling related growth yield, Cs is the residual

substrate concenration, C*s is the critical substrate con- and the residual glucose concentrations increased

sharply. A similar phenomenon was also reported bycentration for substrate-limited growth, and K*S is the

half-saturation constant. (Yobs)max and (Yw)min are de- Brooke et al. (1990) in methanol-sufficient continuouscultures of Bacillus strains. From these previous resultsscribed by Eqs. (4) and (5), respectively.it appears that for substrate-sufficient continuous cul-tures, Cs would be much greater than C*

s . Thus, Eq.(Yobs)max 5mg

qg 1 ms, (4)

(3) can be reduced to

(YW)min 5mg

(Dqw)max, (5) 1

Yobs5

1(Yobs)max

11

(YW)min

Cs

Cs 1 K*s. (6)

Model development is simplified while sacrificing little inwhere mg and qg are the respective true specific growthrate and the growth-related specific substrate consump- terms of accuracy. In this work, (Yobs)max and (YW)min are

considered to be independent of the residual substratetion rate and (Dqw)max is the maximum excessive con-sumption rate of the substrate under substrate-suffi- concentration. The parameters in Eq. (6) can be graphi-

cally evaluated by the method proposed by Liu (1996).cient conditions.For substrate-limited culture, the Pirt theory shows Within the scope of our review, there is still a lack of a

realistic assessment of the energy uncoupling because thethat mobs 5 mg , and the excessive consumption of sub-strate (DSw) can be neglected; then Eq. (3) reduces to P-O ratio and ATP production yield cannot be directly

and simultaneously measured (Rao and Gaudy, 1966;the Pirt equation.In experimental studies of substrate-sufficient contin- Stouthamer, 1979). Under substrate-limited conditions,

anabolism for growth tightly matches with catabolism foruous cultures, the input substrate concentration usedis usually very high, e.g., 50–150 mmol/L methanol energy generation; that is, the energy uncoupling is negli-

gible. As Eq. (6) shows, under substrate-sufficient condi-by Brooke et al. (1990) and 40 g glucose/L by O’Brienet al. (1980). Hueting and Tempest (1979) reported tions, more substrate is required to obtain the same

amount of energy production for microbial growth withthat for an ammonia-limited continuous culture ofKlebsiella aerogenes at a growth rate of 0.4 h21, if respect to substrate-limited cultures. This implies that

ATP formed by catabolism is not used entirely in the for-input glucose concentrations were less than 7.5 g/L,the residual glucose concentrations were low. However, mation of biomass. Westerhoff et al. (1982) applied the

principles of nonequilibrium thermodynamics to theas the input glucose concentration increased from 7.5

COMMUNICATION TO THE EDITOR 573

study of bacterial growth. They found that microbialEu,max 5

(Yobs)max

(Yobs)max 1 (Yw)min, (9)growth yields were 50% less than the theoretical values

and anabolism was incompletely coupled to catabolism.Thus, it is reasonable to consider that the difference be-

K*y 5

(Yw)min

(Yobs)max 1 (Yw)minK*

s. (10)tween the observed growth yields under substrate-lim-ited and substrate-sufficient conditions reflects the un-

Eu,max is regarded as the maximum energy uncouplingcoupling degree of anabolism to catabolism. In this work,coefficient and K*

y is the yield-related saturation con-the concept of energy uncoupling coefficient is intro-stant. These two parameters can be determined fromduced to describe the observed uncoupling betweenEqs. (9) and (10), respectively. Equation (8) shows thatanabolismandcatabolismundersubstrate-sufficientcon-the energy uncoupling is a function of the residual sub-ditions. This coefficient is defined asstrate concentration under substrate-sufficient condi-tions and goes to its maximum because the residualsubstrate concentration is much greater than the K*

yEu 5(Yobs)max 2 Yobs

(Yobs)max, (7)

value. Brooke et al. (1990) studied the growth of thethermotolerant methylotrophic Bacillus strain in metha-where Eu is the energy uncoupling coefficient. This pa-nol-limited and methanol-sufficient continuous cultures.rameter features reduction in the efficiency of con-Their experimental data clearly showed that the metha-verting energy into cellular biosynthesis under sub-nol was oxidized solely to biomass and CO2 under meth-strate-sufficient conditions. For substrate-limitedanol-limited conditions; however, under methanol-suf-cultures, Yobs would be close to (Yobs)max; the energyficient conditions, anabolism was dissociated fromuncoupling is minor. After determination of (Yobs)max catabolism. Similar phenomena were also reported else-from Eq. (6) using a series of Yobs and Cs data, thewhere (Neijssel and Tempest, 1975; Russell andenergy uncoupling coefficient can be calculated by Eq.Cook, 1995).(7) for each corresponding residual substrate concentra-

Yield data published by Brooke et al. (1990) weretion. Substituting Eq. (6) into Eq. (7) produces the fol-used to test Eq. (8). Those data were collected duringlowing substrate-dependent expression for the energythe growth of thermotolerant methylotrophic Bacillusuncoupling coefficient:strains in methanol-sufficient continuous cultures. Fig-ures 1 and 2 show a comparison between the observed

Eu 5 Eu,maxCs

Cs 1 K*y, (8) growth yields with values computed using Eq. (6) for

Bacillus strains grown on methanol under nitrogen-lim-ited and potassium-limited conditions, respectively. Thewhere

Figure 3. Effect of residual methanol concentration on the energy uncoupling coefficient in a nitrogen-limited continuous culture of aBacillus strain (D 5 0.2 h21). (3) The Eq. (8) prediction is shown. Eu,max 5 0.83, K*

y 5 4.08 mmol/L.

574 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 55, NO. 3, AUGUST 5, 1997

Figure 4. Effect of residual methanol concentration on the energy uncoupling coefficient in a potassium-limited continuous culture of aBacillus strain (D 5 0.2 h21). (3) The Eq. (8) prediction is shown. Eu,max 5 0.89, K*

y 5 2.49 mmol/L.

Yobs model agrees with those experimental data very trations, and the observed growth yield is lowered. Theproposed model is capable of giving a theoretical basiswell. By Eq. (6) the values of (Yobs)max , (Yw)min , and

K*s were obtained. With these values, Eu , Eu,max , and for quantitatively interpreting the observed energy un-

coupling in relation to the residual substrate concentra-K*y are calculated from Eqs. (7), (9), and (10), respec-

tively. The effect of residual methanol concentration on tion for substrate-sufficient continuous cultures.the energy uncoupling coefficient is shown in Figs. 3 and4 for nitrogen and potassium limitation, respectively. ReferencesAs can be seen in these figures, Eq. (8) can provide a

Brooke, A. G., Attwood, M. M., Tempest, D. W. 1990. Metabolicsatisfactory description for experimental data. As thefluxes during the growth of thermotolerant methylotrophic Bacillusresidual methanol concentration becomes greater thanstrains in methanol sufficient continuous cultures. Arch. Microbiol.10 mmol/L, the energy uncoupling coefficient reaches 153: 591–595.

0.7, meaning that about 70% of substrate consumption Chang, J., Chudoba, P., Capdeville, B. 1993. Determination of thedissociates from anabolism for growth. For substrate- maintenance requirements of activated sludge. Water Sci. Technol.

28: 139–142.sufficient batch cultures, Chang et al. (1993) also re-Chudoba, P., Capdeville, B., Chudoba, J. 1992. Explanation of biologi-ported that more than 64% of the oxygen consumption

cal meanings of the So/Xo ratio in batch cultivation. Water Sci.did not contribute to microbial growth. This clearly Technol. 26: 743–751.shows that energy-excess cultures have mechanisms of Fiechter, A., Seghezzi, W. 1992. Regulation of glucose metabolism inspilling energy. Consequently, we can therefore say that growing yeast cells. J. Biotechnol. 27: 27–45.

Forrest, W. W. 1969. Energetic aspects of microbial growth, pp. 65–86.the proposed model is able to provide a quantitativeIn: B. A. Haddock and W. A. Hamilton (eds.), Microbial energetics.description for energy uncoupling under substrate-suf-Cambridge University Press, London.ficient conditions. Hueting, S., Tempest, D. W. 1979. Influence of the glucose inputconcentration on growth kinetics of metabolite production by Kleb-siella aerogenes NCTC 418: Growing in continuous culture in pot-

SUMMARY assium- or ammonia-limited environments. Arch. Microbiol. 123:189–194.

By analyzing the variation pattern of growth yield, the Liu, Y. 1996. A growth yield model for substrate-sufficient continuousconcept of an energy uncoupling coefficient was devel- culture of microorganisms. Environ. Technol. 17: 649–653.

Neijssel, O. M., Tempest, D. W. 1975. The regulation of carbohydrateoped for describing the dissociation of anabolism frommetabolism in Klebsiella aerogenes NCTC 418 oganisms, growingcatabolism under substrate-sufficient conditions. A sub-in continuous culture. Arch. Microbiol. 106: 251–258.strate-dependent model of the energy uncoupling was

O’Brien, R. W., Neijssel, O. M., Tempest, D. W. 1980. Glucose phos-then proposed for substrate-sufficient continuous cul- phoenolpyruvate phosphotransferase activity and glucose uptaketures. It is clearly shown that anabolism seriously disso- rate of Klebsiella aerogenes growing in continuous culture. J. Gen.

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COMMUNICATION TO THE EDITOR 575

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Pirt, S. J. 1975. Principles of microbe and cell cultivation. Blackwell Microbiol. 38: 459–486.Tsai, S. P., Lee, Y. H. 1990. A model for energy-sufficient culture.Scientific Publications, London.

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Pollut. Control Fed. 38: 794–812. Thermodynamics of growth: Non-equilibrium thermodynamics ofbacterial growth: The phenomenological and the mosaic approach.Russell, J., Cook, G. M. 1995. Energetics of bacterial growth: Balance

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