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A Thermodynam ically BasedCorrelation for M ainten ance GibbsEnergy Requirements in Aerobic andAnaerobic Chemotrophic GrowthL. Tijhuis, M.C.M. van Loosdrecht, and J.J. HeijnenDepartment of Biochemical Engineering, Delft U niversity of Technology,JulianaLaan 67, 262 8 BC Delft, The NetherlandsReceived November 11 , 1992/Accepted March 8, 1993

A t he r mody na mic f ra me w or k ha s be e n p r ov ided for t h edescr iption of ma in t e na nc e r e qu i r e me n t s of microor-ga n i sms . T he c e n t r a l pa r a me te r is the b i o m a s s s p e -cific G ibbs e ne r gy c onsumpt ion for maintenance , mE(kJ /C-mol biomass . h ) . A large set of da t a ha s be e nused inc luding ( i ) a la rge range of di f fe rent organisms(bacter ia , yeasts, plant cells), ( i i ) mixed cultures, ( i i i )hete rot rophic and autot rophic growth, ( iv) growth un-der ae robic a nd anaero bic condi t ions , and (v) a la rget e mpe r a tu r e r a nge (5-75C). t a ppe a r s t ha t on ly thetemp era ture has a major inf luence, wi th an energy ofactivation of 69 kJ/mol. Different electron d o n o r s ore lect ron acc eptors only sho w a very m inor inf luence onm E . On the bas is of the data se t , t empera ture cor re la -t i ons of mE ha ve be e n de r ive d f o r a e r ob ic a n d a na e r o -bic growth. The genera l ized concept for m a i n t e n a n c eG ibbs e ne r gy is used to establish a correlat ion whicha l lows the es t imat ion of the biomass yie ld on electrondonor a s a f unc ti on of C-source, electron donor , e lec-t ron acceptor , N sour c e , g r ow th r at e, a n d t e mpe r a tu r e .T he a dva n t a ge of using the t n E pa r a me te r ove r othermaintenance- re la ted parameter s (like p e rmoz,m D , Y D m o )is d i sc usse d . 0 993 John Wiley & Sons, Inc.K ey w or ds : G ibbs e ne r g y r e qu i r e me n t s c he mot r op h i cg r ow th ma in t e na nc e a na e r ob i c a nd a e rob i c

INTRODUCTIONRecently a new thermodynamically based method has beenprovided to estimate the maxim al biomass yield on electrondonor , Ygy, or arbitrary chemotrophic growth systemsunder aerobic, denitrifying or anaerobic, carbodenergy-limited condition^.^^^^^ However, it is well known thatgrowth yields are influenced by the specific growth ratep . This is conventionally described using the concept ofHerbert32 of endo geno us respiration o r of Marr et al.37and Pirt46 of substrate maintenance or of a combinationthereof as proposed by Rh amkrishna et al.48 and by Beeftinket al.4 These descriptions define a so called maintenancecoefficient, which is a measure of the required maintenanceenergy. These coefficients may be provided as substrate,C02 , 0 2 , or heat requirement or as an endogen ous decay co-efficient, all of which are stoichiometrically ir~terrelated.~,~~

* To wh o m all correspondence should be addressed.

Nowadays many maintenance coefficients have beenmeasured for many microbial growth systems, organicsubstrates, and under aerob icfana erob ic conditions fromstudies of the dependence of YDX on p in carbon-limitedchemostat studies. Although there are some indications thatthe maintenance coefficient is dependent on p , this is still amatter of debate.3*0,46,64ere maintenance is considered asa black box parameter whic h gives a very useful descriptionof the dependence of YDX n p . Such a relation is neededto describe industrial fed-batch fermentations or to quantifysludge production in wastewater treatment systems, andhence knowledge of the maintenance coefficient is of greatpracticalFurthermore, it is also clear that one should distin-guish the maintenance requirement for microorganismsunder optimal carbodenergy-limited growth from theincreased maintenance requirement under suboptimal~ o n d i t i o n s . ~ ~ , ~ ~ , ~ *or example, the maintenance require-ment increases due to osmo tic or solvent22 anddue to the presence of undissociated acidsb9 or ~ n c o u p l e r ~ ~which dissipates the transmembrane protonmotive force.Also it has been noted that calculated maintenance coef-ficients from YDXmeasurements can strongly be influencedby the occurrence of cellysis or a drop in cell viability,35under presumably suboptimal conditions. A method todistinguish cell lysis and maintenance has been provided35.

In this article the above defined minimal maintenancerequirements of microorganisms will be studied undercarbon/energy-limited aerobic and anaerobic chemotrophicgrowth under optimal conditions where such phenomenamay be neglected. More specifically, a thermodynamicdescription will be presented based on the Gibbs energyrequirements for maintenance. As such, this provides anextension of an earlier attempt to obtain a description foronly the s ubstrate maintenance requirement du ring aerobiche te rot rophic gro~th.~ ,~he proposed thermodynamicdescription is based on an extensive data set taken froma literature which covers (1) a large range of differentmicroorganisms (bacteria, yeast, plant cells), (2) mixedcultures, ( 3 )growth on organic carbon sources and on C02,(4) growth under anaerobic and aerob ic conditions, and ( 5 )growth in a temperature range of 5-75C.

Biotechnology and Bioengineering, Vol. 42, Pp. 509-519 (1993)0 993 John Wiley & Sons, Inc. CCC 0006-3592/93/040509-11

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A GIBBS ENERGY-BASED DESCRIPTIONOFMAINTENA NCE ENERGY REQUIREMENTSIn recent paper^^^,^' it has been shown that the formationof biomass form its carbon and nitrogen source is neces-sarily accompanied by a specific amount of Gibbs energydissipation (in kJ/C-mol biomass), called (D:l/rAx)gr. neC-mo le of biomass is the amount of biomass which contains1 2 g C, which is about 26 g dry weight.The dissipation of Gibbs energy per C-mole producedbiomass (under high growth rate conditions) wa s foundto lie in the range of 200 -350 0 kJ/C-mol biom ass andappeared to depend primarily on the nature of the carbonsource and the occurrence or absence of the need forreversed electron transport (RET). The carbon so urce can becharacterized by its carbon chain length, C , and its degreeof reduction ys . Here ys is the number of electrons perC-mol of substrate upon complete oxidation. Its value is 8for CH4 and 0 for C02.The following correlations have been obtained for or-ganic substrate^^^, which do not require RET:- R E T ( D : l / r A x ) g r= 200 + 18(6 - C)"*

2 0.16+ exp ((3.8 - YS)* (3.6 + 0.4C) ( l a )

For sub strates which d o require reversed electron transport(Fe2', N0 2- , NH 4+, etc.)

[ 1+ R E T ( D : ' / ~ A ~ ) ~ ~3500 (1b)

This dissipation of Gibbs energy per C-mole of biomass,( D : l / r A x ) g r ,elates directly to the maximal biomass yieldaccording to Eq. (2), which has been der ived r e~ en tly .~ '

In this equation, ( D : ' / F - A ~ ) ~ ~s the Gibbs energy requiredto produce 1 C-mol biomass at high growth rates. Valuesare provided by Eqs. ( la ) and ( lb ) . The terms y x an d Y Dare the degrees of reduction of biomass and electron donor(which is often identical to the C source); YE? is themaximal biomass yield on electron donor at high growthrate p; an d AG;: (in kJ/e-mol) is the available Gibbsenergy of reaction for the redox reaction between electrondonor and acceptor, but calculated per electron. Becausethere are Y D electrons per (C)-mol electron donor, it isclear that Y D AG:; is the Gib bs energy of the redox reactionbetween donor/acceptor per C-mole of electron donor. Forany sp ecific redox reaction, AG:; follows directly fromthermody namic tables6'. For aerobic growth on organicsubstrates AG;; is more or less constant for all organic sub-stances, being 111 -C 5 kJ/e-m01.~ " For anaerobic growthAG:: is much lower and is in the range of 2 to 30 kJ/e-mo13". An example of the calculation of AG;; is presentedin Appen dix 1.Mo re details are provided by Heijnen et al.30

The re has also been derived3' a relation for Y T F :(3)

where YFF is the maximal yield of biomass on electronacceptor in C-mole of biomass per mole of acceptor andY A is the degree of reduction of electron acceptor. It isnoted that, by definition, Y A is negative. For example, 0 2ha s Y A = -430. ere ( - 7 ~ )G:; is the Gibbs energyproduction of the redox reaction, but calculated per moleof electron acceptor. Now the following relations [eq. (4)an d (S)] are well known5" for the calculation of the actualyield of biomass on electron donor or acceptor (YDX andY A X ) rom the maximal yield values (YE?, YF","") nd themaintenance coefficients (mD , mA):

(4)( 5 )

Equations (2) and (4) and (3 ) and (S ) , respectively,may now be combined by elimination of YE? an d YAF,respectively. This leads to Eq. (6 ) and (7) for the calculationof the actual yields from the dissipation:

Now it is well known that there always holds the stoichio-metric relation (8) between YDX an d YAX.30 This relationfollows directly from the balance of degree of reduction ofthe growth system:

This relation also holds for the maximal yield values YF?and YE?, as can be readily seen from Eqs. (2), (3), and(8). For aerobic growth ( y ~ -4) a well-known relationis obtained between yield of biomass on substrate andoxygen.*' If one now com bine s Eqs. (6), (7), an d (8), oneobtains the equality5'

~ D Y D G:~ = mA(-yA) ~ ~ , 9 f (9)Based on the definitions of mD, mA, yo , Y A , and AG;; itcan readily be seen that both sides of this equality representthe rate of Gibbs energy which is dissipated per C-mole ofbiomass for maintenance purposes. If this maintenance rateof Gibbs energy is denoted a s mE (kJ/C-mol biomass * h),one can write

mE = m D y D AG:; = mA(-yA)AG:; (10)Clearly one can calculate mE from measured values formD or mA and the known values of yo , Y A , and AG:;

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(which follow from the known electron donor and acceptor,Appendix 1).It is now also possible to define the total Gibbs energydissipation, D : ' / rAx , needed for growth and maintenance,which is then related to the actual yields YD X an d Y A X .Combination of the bracket terms in the denominator ofEqs. (6) and (7) together with Eq. (10) gives

Equations (6) and (7) can then be rewritten as

It can be seen that Eqs. (2) and (3), which give themaximal yields, are homologous to Eqs. (12) and (13),which give the actual measured yields. The only differencelies in the dissipation which must be used. The calculationof maximal yields must be based only on the growth-associated dissipation D !' / rAx , while the calculation of theactual yields [Eqs. (12) and (13)] requires the total dissi-pation ( D : ' / r A x ) g r , hich includes the growth-associatedand maintenance-associated dissipation [Eq. (11)]. In aprevious article2' a simple correlation has been providedfo r ( D : ' / r A x ) g r .n this article a correlation for mE will bepursued.A C ORRELATION FOR mE IN ANAEROBICAND AEROBIC CHEMO TROPHIC GROWTHThe minimal maintenance Gibbs energy requirementm E , as defined in the introduction, is generally relatedto unavoidable leak and denaturation processes whichoccur in biomass. One can think here of proteindenatu ration/h ydroly sis, other polymer hydrolysis, leak ofprotons, or other ions across membranes along theirelectrochemical gradient. All these processes must becompensated in order to maintain the desired steadystate membrane gradients and intracellular concentrations.Hence repolymerization and transport processes must occur.Each of these processes requires a certain Gibbs energydissipation, which add up to mE. Because microbialmembranes and biomass of different organisms underoptimal carbon and energy-limited conditions may besupposed to have com parable molecular comp osition, onemight speculate that for many different microorganismsthese rates are similar. The main parameter which wouldinfluence mE would then be the temperature, because thisinfluences the rates of the said processes. Different electrondonors or electron acceptors have in general a limitedinfluence on biomass composition, and therefore, one couldspeculate that mE is independent of the electron donor oracceptor. Summarizing, the simple view of the minimalmaintenance-related processes lea ds to speculation that mEmainly is dependent on temp erature and that m E s not muchinfluenced by the nature of the electron donor or acceptor.

Tables I and I1 contain a large number of maintenance co-efficient values (mD an d mA) taken from literature sourceswhere growth was studied under carbodenergy limitationsin a chemostat. T he grow th systems cover aerobic (Table I)and anaerobic (Table 11) system s, including organic andinorganic carbon sources. The mE may be calculated fromthe obtained mD and mA values using Eq. (lo ). Bothcalculations should give theoretically the same mE value.For combined mA, mD data, only data sets were takenwhere both calculated mE values did not differ more thana factor 2. Although this might seem a large span, it iswell kn ow n that in general large uncertainties are associatedwith the reported values of mD or mA . Confidence intervalsof 5 5 0 % are quite common." The reason lies in the factthat the maintenance contribution is generally small in thenormally studied range of growth rates of 0.05-0.50 h-' .Only recently the much lower growth rate regime of