Thermodynamics of microbial growth and its implications for process design

483

Thermodynamics of microbial growth and its implications for process design Sef J. Heijnen

Several different approaches have been used in an attempt to define and analyse the thermodynamics of microbial growth in bioreactor culture. While thermodynamic theory has been developed sufficiently to enable satisfactory prediction of biomass and catabolic-product yield, prediction of non-catabolicproduct yield and growth kinetics has proven less successful. Further research in this area is required to develop models that would be useful in process design and optimization. A wide variety of nutrients can support the growth of microorganisms under a wide range of conditions (pH, temperature). For process design, the key factors that need to be considered are the biomass yield (Ysx) and the maximal growth rate (/,m~x) on any particular electron donor. These factors vary greatly: Ysx ranges between 0.01-1.0 C-mol biomass per C-mol electron donor, while /,m= ranges between 0.005 and 2 h <. Generally applicable methods that can provide a preliminary estimate of Ysx and/ohmaxfor any defined culture system are therefore clearly of interest for optimizing process design. One approach to characterizing microbial growth in terms of measurable parameters is based on defining the thermodynamics of the system. This review focuses on th e tJae'rmodynamic approach and specifically addresses the following points: • The definition of the growth system and its thermodynamic analysis. • A critical evaluation of various approaches to predict Ysx. • The effects of heat production and energy dissipation on growth. • Thermodynamic analysis of growth kinetics and the effect of nonstandaM conditions. Where appropriate, the predicted consequences for fermentation strategies are outlined. For detailed coverage of the thermodynamics of growth, the reader is referred to R e ~ 1-4. j. j. Heijnen is at the Department of Biochemical Engineering, Delft University of Technology, Kluyver Laboratory for Biotechnology, Julianalaan 67, 2628 BC Delft, The Netherlands. © 1994, Elsevier Science Ltd

Definition of the growth system and its thermodynamic analysis Microbial growth can be interpreted as a 'black box' (Fig. la), via which biomass is produced from an electron donor, a carbon (C) source, a nitrogen (N) source and an electron acceptor. In addition, H 2 0 , CO2, H + and other products are produced. A convenient way of describing such 'black box' growth is in the form of a macrochemical equation2,s which, by definition, produces 1 C-mol ofbiomass (the amount ofbiomass containing 1 mol carbon, equivalent to - 2 5 g dry biomass). The stoichiometry of this equation, for any particular system, can be derived by defining the system input and the measured biomass yield using the C, H, O, N and charge balance 5. These equations express the fact that elements and charge can neither be lost nor generated during a chemical reaction. An example of such an equation is shown in Fig. lb, for the growth of Pseudomonas oxalaticus on oxalate as C source.

In order to analyse growth in terms of its thermodynamics, values for the enthalpy (AH °) and Gibbs energy of formation (AG °1) of the reactant under standard biochemical conditions (i.e. 1 bar, 1 mol 1-1, 98 K and pH7) are usually used*. The thermodynamic properties ofbiomass have been discussed extensively by Battley2,6-11 and Mavrovouniotis 12, and reliable estimates of the enthalpy and Gibbs energy for biomass * The energies of formation (AHf°and A Gf°a), which carry the subscript 'f' to denote formation, are properties of chemical compounds (and may be found in the 'Thermodynamic Tables'). These are distinct from the changes in energy associated with the reaction (AH° and A G ° I ) , which carry the subscript R, to denote reaction, and are calculated from the reaction stoichiometry and energies of formation of the compounds involved. TIBTECHDECEMBER1994 (VOL 12)

484

reviews Glossary - Degree of reduction of a chemical compound, y is a stoichiometric property of a chemical compound that describes its electron content (mol electrons C-mol compound<: for example, for CO2, 3, = O; for glucose, ~, = 4; for CH4, -y = 8). ~/'/e or z~Ge - Enthalpy or Gibbs energy of formation of a chemical compound expressed per mole of electrons present in the compound (kJ mol electrons-i). "Y~/'/e or ~,AGe - Enthalpy or Gibbs energy of formation of a chemical compound expressed in kJ per mole of carbon (kJ C-mol-1). ~Gex - Gibbs energy of formation per electron in biomass (kJ mol electrons in biomassq). ~GeD - Gibbs energy of formation per electron for the electron donor (kJ mol electrons in electron donor-Z). z~GeA - Gibbs energy of formation per electron for the electron acceptor (kJ mol electrons in electron acceptorq). Ysx - Yield of biomass on substrate or electron donor (C-mol biomass C-mol donor-Z). YDA- Yield of electron acceptor on electron donor (C-mol acceptor C-mol donor-i). Ds°l/r x - The dissipation of Gibbs energy needed to produce 1 C-mol of biomass from a given C source (kJ C-mol biomassq). ASR, ~/'/R - The entropy (J moll Kq) and enthalpy (kJ moll) of a reaction. They can be calculated from reaction stoichiometry and tabulated entropies and enthalpies of formation for the chemical compounds involved. Black-box thermodynamic efficiency - The ratio of the total Gibbs energy of formation associated with the chemical compounds produced to the total Gibbs energy of formation of the chemicals consumed. Energy-convertor efficiency - The ratio of the Gibbs energy of reaction of a defined output process to the Gibbs energy of reaction of a defined input process. Conservation efficiency- The ratio of the Gibbs energy of reaction of the macrochemical equation to the Gibbs energy of reaction of the catabolic reaction in which all the substrate from the macrochemical equation is combusted.

a C-source

Biomass

N-source

C02 H20

Electron donor Electron acceptor

b

Products

IL

IL

}t

Ysx=o.086 C-mol biomass C-mol oxalate -1

+10.63 HCOa-0.2 NH4+ -1.857 O2

l

I

}'

-5.415 H20

i -0.8 H+

Corresponding macrochemical equation -5.815 0 2 0 4 2 - -0.2 NH4+ -1.857 02 -0.8 H÷ -5.415 H20 +1.0 CH,.800.sNo.2 +10.63 HCO a- = 0

Figure 1 (a) Black-boxdescription of microbial growth. (b) Aerobic growth of Pseudomonas oxalaticus on oxalate described in terms of a macrochemical equation. The yield value, Ysx,means that (0.086)-I = 11.63 °C-mol oxalate, or 5.815 mol oxalate are used to produce 1 C-tool biomass. The other stoichiometric values (-0.2, -1.857, 10.63, -5.415 and -0.8) follow from the C, H, O, N electric-chargeconservation equations. (Redrawnfrom Ref. 5.)

are now available. It is therefore relatively straightforward to calculate the heat produced (AHR0) and the Gibbs energy dissipation (AGR°1) for the production of 1 C-mol biomass using the macrochemical equation, which incorporates an empirically determined value for Ysx (biomass yield). TIBTECH DECEMBER1994 (VOL 12)

For the example shown in Fig. lb, with a measured value of Ysx = 0.086 C-mol biomass C-mol oxalat~ 1, one can calculate, using tabulated values of Gibbs energy of formation, that AGR°I = -1048kJ and AHR° = -939 kJ. This means that the formation of 1 C-mol ofbiomass from oxalate requires dissipation of 1048 kJ of Gibbs energy and produces 939 kJ heat. In this article, the parameter (-A GRm) of the macrochemical equation is defined as Ds°l/rx, measured in kJ C-mol biomass-1. Although this calculation is straightforward, Heijnen et al. 13 showed that the macrochemical equation can be simplified still further by introducing a reference system that combines the assignment of values for the enthalpy and Gibbs energy of formation with a definition of the 'degree of reduction' of the chemical reactants (Box 1). (The concept of'degree of reduction' has already been used extensively to simplify stoichiometric calculations by R o d s 1, for example.) In the reference system, each chemical compound is characterized by its electron content [which is equal to the degree of reduction, and is defined as Ti (units: electrons C-mol-1)] and the standard enthalpy, or Gibbs energy of formation per mole of electrons (AHe° and AGe°i, respectively). The enthalpy or Gibbs energy of formation for a chemical compound in this reference system is then equal to (yiAHe°) and (yiAGe°l). In this reference system, Yi, AHe° and AGem of H +, H C O 3 (or C02) , the N source and H 2 0 have, by definition, values of zero, and this forms the basis for the simplified equations. It should be noted that this proposed reference system is a generalization of the 'aerobic-combustion reference' proposed by Roels 1. In the new reference system, the energedcs of growth become more obvious:

485

reviews pounds were recently refined and modifications have been proposed TM. • As the values for enthalpy and Gibbs energy of reaction in anabolism during growth on organic compounds are always close to zero, it is obvious that heat production and Gibbs energy dissipation will only be associated with catabolism2,7,15. • As the AG e ofbiomass and organic donor are nearly equal (AGex = AGED), a simple equation that couples Y~x to the Gibbs energy dissipation per C-mol produced biomass (Ds°l/r x in kJ C-mol biomass<) may be derived (Box 2) 13. This equation shows that Y~x decreases at higher dissipation values, is lower for electron donors with fewer electrons (TD is then smaller), and is a hyperbolic function of A GeD-A GeA, the Gibbs energy released in the catabolic reaction per electron present in the electron donor. AGeD-AGeA applies only to the catabolic reaction (electron donor-acceptor reaction). For aerobic growth on a variety of organic compounds, this value is nearly constant at ~110 kJ e-mol <. For anaerobic growth, however, this value is variable (2-25kJe-mol <) (Ref. 13). The derived equation for Y~x (Box 2) shows how Y~x depends directly on the value of AGeD-AGeA of the donor-acceptor couple. The greater the energy released in catabolism, the higher the value of Ysx. • The Y~xequation also gives us the thermodynamic theoretical maximal biomass yield, which is reached at equilibrium, where D ? l / r x = 0. Ysx is equal to

• The enthalpy of formation per electron (AHe°) is virtually constant for all organic (including biomass) materials13; AHe° = -28 kJ e-mol-L For O2, AHe° = -143kJe-mol -i. This means that the oxidation of organic matter releases -[(-143)-(-28)] = 115 kJ of heat per transferred electron. This is equivalent to 4.115 = 460kJ heat released per mol 02 consumed, which is a well-known constant (see Refs 1,4). • The Gibbs energy of formation per electron for organic matter (including biomass) is also nearly constand 3, AGe° = +32 kJ e-mol <. This means that there is hardly any difference in Gibbs energy between the organic electron donor and the biomass. AG R (and also AHR) of the anabolic process is therefore close to zero (an observation known as the 'Battley hypothesis', and stressed again recently by Battley2,6-il). Battley's observation, that the values of AG R, A H R, and ASR are close to zero for anabolic reactions, results from the fact that anabolism involves the conversion of low-molecular-weight compounds into biomass, without the transfer of electrons in catabolic reactions. The AG R value referred to by Battley relates to this anabolic reaction only, and is much smaller than the AG associated with the consumption of ATP that is also required for biomass production. If ATP is also taken into account, the resulting overall values when calculating AG, AS and AH for anabolic reactions are very large. The constants of enthalpy and Gibbs energy of formation per electron for organic com-

Box 1. Stoichiometric calculations with the concept of degree of reduction (1) Consider the example in Fig. l b and suppose that the stoichiometric coefficient 0 2 (coefficient O) is not known. The values of 1, (degree of reduction) of the chemicals are: Oxalate 02

1, = 1 C-tool -t = 2 moll 1, = - 4

Biomass

1, = 4.2

NH4+, H+, H20, HCO 3-

1, = 0

We can now write the balance of degree of reduction: Oxalate electrons + 02 electrons

+

biomass electrons = 0

(-5.815x2)

+

4.2

+

(-4xO)

=0

(Eqnl)

This means that 0 = -1.857 (2) Consider a 'short' macrochemical equation involving only donor, acceptor and biomass, because 3, for all other compounds is zero 1 1 - Ysx C-mol donor - ~ acceptor + 1 C- mol biomass = 0 (Eqn 2) The degree of reduction of the donor is 1,D,for the acceptor is 1,A and for biomass 1,x = 4.2. Using these values, we can now write the balance of degree of reduction:

~o

Solving for

1

-

+?A

+4.2=0

(Eqn 3)

leads to the relationship between YAx andYsx :

YAx

YAx

- 1,X -

(Eqn 4)

TIBTECH DECEMBER1994 (VOL 12)

486

reviews Box 2. Thermodynamic analysis of the macrochemical equation Macrochemical equation A short macrochemical equation (omitting H20, C02, N source and H +, for which the degree of reduction 7 and 1 AGe is zero) runs as (using the relationship derived in Box 1, which relates ~ to the stoichiometric coefficient of acceptor 1 ) . YAx" -1 d o n o r - [ T D - ~ , D ] [ 1 ] acceptor +1C-molbiomass =0 LY~x JL-~/Ad

Ysx

(Eqn 1)

Gibbs energy balance over the macrochemical equation using the Gibbs energy of formation for: Electron donor =

TDAGeD01;

electron acceptor =

TAAGeA01;

O= Gibbsenergy of donor + i

i

biomass =

TxAGex°1 = TxAGeD01

Gibbs energy of acceptor [

Biomass + Gibbsenergy + Dissipation 1

I

-

-

[

1

-

-

+ D°l/rx

=

S

(Eqn 2)

~IATD]

SolvingforYsxandYDA(=[YSX~AA )givestheequati°nsthatsh°wh°wYsxandYDAdepend°nDs°z/rx: rsx=,

01 01 ~'D(AGeD-AGeA )

----~---01

01

^

01

,

,b-moJ biomass C- mol electron donor (Eqn 3)

YDA =

ro/(-rA)(Ds°l/'x ) +

(,Ge°l-,Go °')

TD/Tx, which is the ratio of the degree of reduction of electron donor (TD) and biomass (Tx)- This relationship has been noted previously by tLoels 1, and a refined equation has recently been derived using the A G e frame of reference 13. • The ratio between heat production and Gibbsenergy dissipation during growth is equal to the ratio of heat production and Gibbs-energy dissipation of the catabolic process 13. Using the A G e frame of reference, it is obvious that heat production and Gibbsenergy dissipation are nearly equal during aerobic growth. However, this is not the case for anaerobic growth, where there are major differences between heat production and Gibbs-energy dissipation (see below). • It is easy to derive an equation to determine product yield for a particular electron donor under anaerobic conditions (Box 2) 13. This yield YDA (C-tool acceptor/C-tool donor <) increases with increasing energy dissipation (D~°1 rx) and decreasing values of (AGeD-AGeA). This is quite logical because it implies lower values of Y~x, and it is obvious that a lower biomass yield leads to a higher product yield. Recognition of this relationship enables selection of the IBTECHDECEMBER1994 (VOL12)

mol acceptor C- tool donor -1 (Eqn 4)

optimal electron donor and process conditions, and thus increases the yield of catabolic products. • The derived relationships in Box 2 are generally applicable to any donor-acceptor-N source combination. The equations in Box 2 show that the only parameter needed to predict the biomass yield Y~x or product yield YDA is D s ° l / r X, because for a given growth system Tx, ")/D, AGeD and AGeA are known. Correlations to estimate D s ° l / r x have recently been obtained 5,13 (see Box 3).

Thermodynamic approaches to predicting biomass yield A critical evaluation of the published methods of predicting Y~×has recently been performed s,1s,16. The criteria used for the evaluation were: (1) General applicability to all chemotrophic growth systems. (2) Conforming to the second law of thermodynamics. (3) The requirement for black-box information only (such as that depicted in Fig. 1), and no need for detailed knowledge of the reaction pathway. (4) The absence of intrinsic problems in the approach.

487

reviews Box 3. Correlations to calculate the dissipation of Gibbs energy for growth Total dissipation is the sum of growth-related and maintenance-related components: DsOl/rx = , , Total dissipation

(DsOl/rx)gr ,--~ Growth

+

mE~IX , , Maintenance

(Eqn 1)

The maintenance-related component of the Gibbs-energy dissipation is temperature dependent according to an Arrhenius relationship: [~-f1 - ~ 1 ) ] rr~ : 4.5 x e x p[-69000 [~

kJ C- mol <

h_ 1

(Eqn 2)

The growth-related component of the Gibbs-energy dissipation depends on the C source (C, 70 for heterotrophic growth/autotrophic growth [-reversed electron transport (RET)] and is a constant for autotrophic growth (+RET), Heterotrophic growth/autotrophic growth (-RET): (Dsm/rx)g r = 200 + 18(6-C) 1.8 + exp [((3.8 - 702)°.16 x (3.6 + 0.4C)] kJ C-mo1-1

(Eqn 3)

Autotrophic growth (+RET): (DsOl/rx)gr = 3500 kJ C-mo1-1 C "/s T R

= = = =

(Eqn 4)

Number of C-atoms of C source Degree of reduction of C source Absolute temperature (K) Gas constant (= 8.314 J mo1-1 K-1)

The most disturbing conclusion reached by this survey is that none o f the proposed methods satisfies all o f these simple criteria s,ls. To illustrate some o f the problems, let us consider attempts to correlate thermodynamic efficiency with biomass yield. This approach has been pursued by B a t t l e y 2, Roels 1, and Westerhoffand Van Dam 3, all of whom, however, proposed different definitions of efficiency. A problem with all definitions of efficiency is that one arbitrary assumption is always made in formulating the deftnition 16. For example, 1Loels's 'black box' definition o f efficiency would vary if a different frame of reference for Gibbs energy of formation were chosen. Recently, the feasibility of using a umque reference for all growth systems has been discussed16,17; however, it appears that it is impossible to define such a unique reference. Westerhoff and Van Dam's 'energy convertor' efficiency3 is based on a definition of anabolism that is biochemically unrealistic because 0 2 can be produced in heterotrophic growth 16. Their conclusion 18 that growth can be described as an optimized Gibbsenergy convertor for maximal growth rate at optimal Gibbs-energy efficiency is therefore invalid. Battley's definition o f 'conservation efficiency'2 is based on a definition of catabolism during growth that is also biochemically incorrect: he assumes flail catabolism of all substrate whereas, in reality, part of the substrate is converted into biomass and is not catabolized. Therefore, although these proposed definitions o f efficiency have all been used, with some success, to correlate thermodynamic efficiency with biomass

yield, they cannot be regarded as representing the true efficiency of the growth process. Another approach to defining efficiency has been proposed by McCarty 2°,32. This is based on known biochemical pathways o f anabolism, catabolism and N-source incorporation, and focuses on the energytransformation efficiencies of each of these processes. This method resembles the ATP-based approach o f Stouthamer21; however if, as in the 'black-box approach', detailed knowledge o f the stoichiometry of the biochemical reaction is not available, McCarty's method cannot be used reliably. If, however, the stoichiometry of the biochemical reaction is available, then the ATP-based approach is much more accurate 21. An alternative, measurable, thermodynamic parameter that complies with the four requirements listed above, that has none of the problems associated with other methods, and which leads to a more accurate prediction o f Ysx over a wide range of conditions, has been proposed 5,1s. This parameter is Dsm/rx, the Gibbs energy that must be dissipated to produce 1 C-mol of biomass. From the equations in Box 2, it is clear that Ysx and YDAcan be calculated if one knows D~°l/r x. It is known 1,22that, during growth, part o f the substrate is used for biomass synthesis, and part is catabolized to provide the energy required to maintain the integrity o f the organism. In accordance with this idea, energy dissipation can be attributed to growth-related and maintenance-related components (Box 3) 1'22 . The growth-related energy dissipation, (D~°l/rx)g r, depends only on the C source used 5,1s. The type of TIBTECHDECEMBER1994(VOL12)

488

reviews

I

o.1[

im

example, a constant maintenance Gibbs energy predicts that the endogenous decay coefficient is three times less for autotrophic than for heterotrophic growth 22. Using the correlations for calculating the dissipation of Gibbs energy (Box 3) in combination with the Ysx-equation (Box 2) enables Y~xto be predicted with an accuracy of 10-20% in the range Ys~ = 0.01-0.8 C-mol C-mol electron donor -1 for any C source, electron donors-acceptors, N-source, temperature or growth rate (Fig. 2) (Ref. 5). Box 4 shows an example of such a calculation. Application of this approach also indicates the conditions that should be selected to optimize productivity. For example, for anaerobic-product formation (YDa), this could be achieved by selecting:

F

0.01 ~ 0.01

0.1 Ysx measured

Figure2 Comparison between measured and estimated values of Ysx-using the DsOl/rx correlation. (Redrawnfrom Ref. 5.)

electron acceptor involved (02, N O 3 - , fermentation where an internal electron acceptor functions) exerts only a minor effect and may be ignored. It appears that, for organic C sources, (Ds°l/rx)gr increases for C sources with fewer C-atoms, or whose degree of reduction is different from that of biomass (Tx = 4.2 for NH4+ as N source). Furthermore, it has been found that, for autotrophic growth on electron donors (such as Fe2+ or NH4+), which requires reversed electron transport (RET), D~m/rx is very high. These findings are easy to understand if one considers that a C source with one C-atom needs much more metabolic 'tinkering' than a C source with six C-atoms for the synthesis of biomass. In addition, a C source that is either less, or more highly, reduced than biomass requires additional oxidation (TD > Tx) or reduction (TD < T~)- If required, R E T is an additional energyrequiring process that must be taken into account. The high values for D~m/rx simply reflect the larger number of chemical reactions and consequent energy dissipation required to produce biomass from a given C source. This result is also in broad agreement with Stouthamer's approach, which shows that more ATP is needed for 'poor' substrates 21. The maintenance-related energy dissipation (mE) depends primarily on the temperature, according to an Arrhenius relationship with an energy of activation of 6 9 k J m o P 1 (Box 3), and is independent of tile C source or electron acceptor 22. Analysis of maintenance-related dissipation is optimal if based on Gibbs energy of dissipation. The other approaches to quantifying maintenance are based on concepts such as biomass decay, substrate consumption or consumption of electrons, but give much more variable results; for IBTECHDECEMBER1994(VOL12)

• A 'poor' C source, which requires a large energy dissipation to produce biomass. • An electron donor that is much more reduced than the product (3'D > -TA) (for example, the anaerobic production of acetate from methanol 29 and the production of acetate from glycerol, Box 4). • A low growth rate, because this raises D?l/r x (Eqn 1, Box 3; Box 4). • A poor electron donor-acceptor combination, which leads to a low value of (A GeD-AGeA). Anaerobic-product formation linked to catabolism (Box 4) is related to biomass yields in a straightforward manner. However, the thermodynamics of product formation not directly linked to growth is a relatively neglected area of research, and an obvious area for further investigation. Although this approach yields satisfactory results, it should be stressed that the value of Ysxobtained is only a preliminary estimate based on the average behaviour of many growth systems. Even for the same C source or electron donor, there is often more than one catabolic route: for example, for gltlc0~se (glycolysis, Entner-Doudoroff) or for methanol (serine, ribulose, autotrophic route). Clearly, this influences Y~x- Conversely, if the predicted value of Y~x deviates strongly from the measured value, then one might have found an organism with an unusual biochemical route that merits special attention.

Heat production during growth The study of heat produced in biological systems (calorimetry) in relation to metabolism has a long history (see P,.e~ 2 and 4 for overviews). The production of heat is used as a characteristic energetic parameter of growth, and can be used to calculate growth using the enthalpy balance 4,23,33,34. In aerobic systems, heat and O2-consumption are intimately linked (460kJ mol O2-1). In anaerobic systems, heat production is still a useful parameter to measure in relation to metabolism. It is widely4, but incorrectly5, believed that growing systems always produce heat: the second law of thermodynamics only requires that the Gibbs energy is dissipated; heat can therefore either be produced or

489

reviews Box 4. Example of the estimation of Ysx and anaerobic product yield YoA Consider the anaerobic growth of a microorganism on glycerol, which only produces acetate at 4542. According to Table III in Ref. 13, AGeD01-AGeA01 = 37.8 - 26.86 = 10.94 kJ e-molq. If one assumes that NH3 is the N source, then the degree of reduction of biomass b/) = 4.2. The degree of reduction of glycerol is 4.66. Glycerol contains three carbon atoms; hence C = 3. The temperature is 4542, therefore T = 318 K. Box 3 (after substitution of C = 3, 7s = 4.66, and T = 318 into Eqns 1-3) leads to the estimated total Gibbs-energy dissipation per C-mol of biomass as a function of growth rate: Ds°i / rx I

= I

Total dissipation

428 I

Growth-related dissipation

+ I

2__6_6 L

tJ,

kJ C- mol biomass -1 J

Maintenance-related dissipation

(Eqn 1)

At/~ = 1.0 h-1, one can calculate Ds01/f x = 454 kJ C-mo1-1, while at ~ = 0.05 h-1, one can calculate Dsm/rx = 948 kJ C-mol q . The biomass yield Ysx follows from Box 2, Eqn 3, using [AGeD01-AGeAol = 10.94, 7D = 4.66, 7x = 4.2]: For/, = 1.0 h-1, one obtains Ysx = 0.10 C-mol C-mo1-1 For/, = 0.05 hq, one obtains Ys× = 0.05 C-mol C-mo1-1 Using the value of (-~'k) = 4 (for the product, acetate), one obtains, from the YDA equation (Eqn 4) in Box 2, the following yields of acetate on glycerol: For t* = 1 h-1, one obtains YDA ---- 1.058 C-mol acetate C-mol glycerol q For/, = 0.05 h-1, one obtains YDA= 1.111 C-mol acetate C-mol glycerol -1 Clearly, the product yield on carbon is >100%, which is due to the fixation of CO 2 because glycerol is more reduced than acetate. In addition, one observes that the product yield increases at low growth rate as a result of maintenance requirements.

taken up during growth. Table I indicates the measured biomass yield, the calculated Gibbs-energy dissipation, the calculated heat production/consumption and the calculated entropy-related dissipation, all per C-mol produced biomass for three substrates (glucose, H 2 and acetate) under aerobic and anaerobic conditions. It can be seen that, for a given electron donor, the Gibbsenergy dissipation is nearly the same under both aerobic and anaerobic conditionss. The relative contributions of heat and entropy are, however, markedly different. For aerobic growth on glucose, Gibbs-energy dissipation and heat production are nearly equal, with very little contribution from the entropy term. Under anaerobic conditions, however, two-thirds of the energy dissipated is due to an increase in entropy (Table 1). As the overall dissipation does not change significantly, the heat production per C-mol biomass is only one-third of that associated with aerobic growth. For aerobic growth on H2, there is a significant decrease in entropy, because small gaseous molecules (H2, 02, CO2) are converted into large molecules (biomass), and into liquid (water). This leads to 'extra' heat production, because dissipation of Gibbs energy is constant. This effect is even more pronounced under anaerobic conditions, where 4 H 2 + C O 2 are converted into C H 4 and H20, resulting in a huge decrease in entropy and significant production of heat. For H2, the heat production per C-mol biomass is greater under anaerobic conditions than under aerobic conditions. For aerobic growth on acetate, nearly

all energy dissipated is due to heat production, with very little contribution from changes in entropy. However, for anaerobic growth (where acetate is converted into C H 4 and CO2), there is such a large increase in entropy that heat is taken up during growth. Clearly, this shows that Gibbs-energy dissipation (which must be positive) is the key thermodynamic parameter that must be considered, whereas heat can be produced or taken up during growth. As shown above, Gibbs-energy dissipation and heat production are nearly equal for aerobic systems. The correlations in Box 3 therefore provide us with a direct estimate of the expected heat production and the O2-consumption (460 kJ mol O2-1), for aerobic growth as a function of C source and growth rate. For example, growth on glucose at/z = 0.5 h -1 produces heat at a rate of 229 kJ C-tool biomass-1 at 25oc, and 1543 kJ C-mol biomass-1 at 90°C. This is equivalent to a biomass yield of 2 C-mol mol 02 -1 and of 0.30 C-molmol 02 -1 at 25°C and 90°C, respectively. The difference results from maintenance-related energy requirements. Increased heat production resulting from maintenance requirements is obviously an important factor, leading to greater heat production per C-mol biomass at low/z, and lower heat production at high /z. Because of the limited cooling capacity of a fermenter, processes designed to produce biomass [such as single cell protein (SCP) processes] are usually carried out at high growth rate 19. It should also be realized that the efficiency of aerobic growth at high temperatures suffers from extremely high maintenance TtBTECHDECEMBER1994 (VOL 12)

490

reviews Table 1. Gibbs energy dissipation and heat production for aerobic and anaerobic growth a Dissipation resulting from:

Microbial system

Conditions

Saccharomyces cerevisiae

Glucose/02; aerobic Glucose; anaerobic H2 + C02/02; aerobic H2 + C02/CH4; anaerobic Acetate/02; aerobic Acetate/CH4; anaerobic

S. cerevisiae H2 bacterium

Methanobacterium arborophilus Pseudomonas oxalaticus Methanobacterium soehngenii

YDx (C-mol C-mol donor-Z)

Total dissipation Heat (kJ C-mol {kJ C-tool biomass-Z) biomass-Z)

Chemical entropy (kJ C-mol biomass-Z)

0.57

332

+339

-7

0.14

270

+95

+175

0.13

1265

+1686

-421

0.015

1035

+3923

-2888

0.406

562

+593

-31

0.024

597

-90

+687

aDatafrom Ref. 5.

requirements: this leads to very high Oi-consumption per C-mol biomass. Only very low biomass concentrations can therefore be achieved in aerobic processes at high temperatures, where a severe bottleneck in 0 2transfer in the reactor from the gas to liquid phase is always a problem 19.

Thermodynamic approaches to understanding growth kinetics As described above, the Gibbs-energy dissipation has been used to predict Y~x.The calculations of Gibbs energy are generally based on standard conditions (298 K, 1 mol 1-1, 1 bar, pH7). However, the concentration ofsubstrate in many culture systems is frequently much lower (10-3-10 -6 mol 1-1). In addition, the culture of organisms under extreme conditions (temperatures up to 100°C and pH values ranging 1-14) is attracting increasing interest. In such situations, conditions deviate considerably from the standard. The Y~x equation in Box 3 shows that these deviations can be accounted for in the calculation of (AGeD-AGeA). This value is directly related to the Gibbs energy of reaction (AGp.) of the catabolic process, and consideration of the effects of concentration and temperature on the value of AGp. for the catabolic process is sufficient to quantify their influence on Y~x, as has been demonstrated in a number of cases. %

Concentration effects in aerobic-growth kinetics It has already been noted that, in the aerobic catabolism of organic electron donors, (AGeD--AGeA) is very large, and differences in concentration or temperature therefore exert only a very small effect on (AGer)-AG~A). However, during aerobic growth on inorganic electron donors (for example, Fei+), the value of AG~D-AGeA is large at pH = 1,.whereas, at pH = 7, this difference is close to zero, leading to Y,x = 0: this explains why microbial growth that is dependent on Fe2+ oxidation only occurs at low pH. IBTECHDECEMBER1994(VOL12)

Concentration and temperature effects in anaerobic-growth kinetics For fermentative growth, or growth with 8042- as the electron acceptor, the value ofA GeD-A GeA is quite small (2-25 kJ e-mo1-1) and concentration effects then become very important. In some natural microbial communities, Hi-producing and Hi-consuming species frequently grow in close association, and the effect of Hi-partial pressure on the process of interspecies Hi-transfer is very well known 24-26. The influence o f H i (stimulation/inhibition) and acetate (inhibition) on the growth kinetics of Hi-producing and Hi-consuming organisms is easily understood, considering its effect on AGp, of the catabolic process. It may be calculated that the optimal thermodynamic H i concentration, in this food chain, of a Hi-producer and a Hi-consumer is such that the AGe. of the catabolic reactions of both the Hi-producer and the Hi-consumer are equal: this has been observed for some systems27,28. The optimal Hi-concentration is very low (10 -4 bar), and therefore interspecies H i transport is promoted, as observed26, by direct physical contact. Differences in H 2 partial pressure can also influence product formation. For instance, the formation of reduced products at increased Hi-pressures is thought to be due to catabolic processes that operate close to equilibrium (for example, the formate/H 2 system) 29. It has been f o u n d 23,25 that, for such anaerobic growth processes, there appears to be a minimal value of AGg of the catabolic process required to sustain growth, and this lies in the range o f - 5 to -15 kJmol Hi -1 (Table 2). The physiological basis of such a minimum value probably lies in the quantization of the cellular energy carriers: i.e. the Gibbs energy for H+-pumping (proton-motive force) is thought to be -10 to 15 kJ per mol H +. This minimal Gibbs energy leads to threshold values of electron donor concentration (for example, H2) to sustain growth.

491

reviews A low Gibbs energy of catabolism has several kinetic consequences, which originate in the effects of concentration, temperature and the possible involvement of precipitates (Box 5). The effect of concentration has been dealt with above; examples of the role of precipitates can be found in sulphide-forming processes, where sulphide precipitates occur. The temperature effect is less well known 24,25,3° and is described in Box 6, using the Van't Hoff relation. It is clear that temperature has very significant effects on AGP` of catabolism, particularly in anaerobic systems. Depending on ASp., the catabolic process can generate either much more, or much less, Gibbs energy at elevated temperatures. An interesting case is the production of H e from the complete conversion of glucose. At 25°C, this provides hardly any energy, but at 95°C, the value of AGp. is high. This suggests the possibility of completely converting carbohydrate t o H 2 at high temperature anaerobically (provided that there are no unforeseen biochemical bottlenecks). This effect of temperature on AG R also helps to explain the rise in H2-threshold concentrations with temperature in the interspecies H2-transfer process24. Effects of highly irreversible reaction kinetics on growth kinetics The kinetic effects mentioned so far arise from the significant influence of concentration/temperature on A Gp`, if A G~° is close to zero, which means that the reactions are reversible. Such an approach does not hold for aerobic systems, where catabolism is essentially irreversible. In the past, attempts have therefore been made to formulate thermokinetic models for irreversible processes (see R.ef. 3 for an extensive review) as an alternative to conventional kinetic modelling. This approach is based on the realization that many metabolic reactions are coupled so that energy transfer is involved. Examples are chemiosmotic proton extrusion, the H+/ATPase in mitochondria, various transmembrane transport processes driven by the proton-motive force. Each of these coupled processes may be described as a linear Gibbs-energy transducer: the process kinetics are simple, and thermodynamic efficiencies agree with optimality criteria (i.e. maximal rate of energy production) 3. This approach has also been applied to growth by incorporating growth considerations into a coupled process of anabolism and catabolism3. However, a number of key difficulties with this approach were recently outlineds,ls (see above). Gnaiger 31 has also stressed the point that growth metabolism is composed of the coupled processes, linked either in series or in parallel. Accordingly, the overall growth efficiency is a complex function of the combined efficiencies of each coupled process. It is then not clear which optimality criterion should be applied. McCarty 32 has, however, proposed an approach for predicting values o f / x m~x. He suggested that microorganisms have a limited capacity for processing electrons through the catabolic pathway. From his limited

Table 2. Minimal required Gibbs energy of catabolic processes {AGR) to sustain growth Microbial process

AGR{kJ per mol H2)

Ref.

H2-consuming acetogens H2-consuming methanogens H2-producing acetogens (propionate/ethanol)

-5 to -6 -9 to -12 -5 to-10

24 24 26

Box 5. Kinetic consequences of catabolic processes with low Gibbs energy of reaction (AGR) • Strong effects of concentrations (particularly pH) on AGR, and hence on Ysxand product yields. • Strong temperature effect on AGR(see Box 6), and hence on Ysxand product yields. • Strong effect of precipitates on AGR (in sulphide-producing processes, for example). • Threshold concentration for H2 in H2-consuming processes. • Inhibition by, for example, H2 and acetate for H2-producing processes using propionate or ethanol. • Changes in product formation resulting from mass-action effects (bicarbonate+H2/formate system).

Box 6. Temperature effects on the Gibbs energy of reaction (AGR) of catabolic processes Van't Hoff relationship: AGR = AHR- T(ASR)

Reaction

Temp (°C)

AGR° (kJ)

Ref.

Glutamate- + 4 H20 --~ propionate + 2 HCO3+ H+ + H2

25 55

-7 -17

30

Glucose + 6 H20 ---, 6 CO 2 -I- 12 H2

25 95

-26 -151

25

4 H2 + 2 CO 2 --* acetate- + H÷ + 2 H20

25 90

-95 -8

24

Conclusions: • AGR becomes more negative with increasing temperature if ASR is positive (gas-producing reactions). • AGR becomes less negative with increasing temperature if ASR is negative (gas-consuming reactions).

data set (heterotrophic/autotrophic growth under aerobic/anaerobic conditions) at 25°C, a maximal electron transport rate of 1-2 e-mol C-mol biomass h -1 was found with an Arrhenius temperature dependence according to Eact ~ 60 kJ mo1-1. Another interesting result has been the thermodynamic description of maintenance, as pioneered by P-oels 1 and refined recently by Tijhuis et al. 22 (see also the discussion above on maintenance). In general, however, it must be concluded that the thermodynamic basis of kinetic behaviour of growth is, as yet, far less advanced than the thermodynamic TIBTECHDECEMBER1994(VOL12)

492

reviews basis of the stoichiometry of growth like the biomass yield. Furthermore, it is still unclear whether there is any specific advantage in applying a thermodynamically based kinetic description 3, compared with the more usual mass-action approach to understanding the kinetics of microbial systems1.

Conclusions There now exists a well-established thermodynamic approach, based on dissipated Gibbs energy, to understanding and predicting values of biomass yield for microbial growth processes. It also appears that a thermodynamic approach can be used to evaluate maintenance-related requirements. Thermodynamic considerations with respect to process design relate primarily to being able to predict stoichiometric coeffluents (particularly for heat, oxygen and anaerobic products). In addition, it would be useful to be able to estimate any possible effects of temperature or concentration ofsubstrate/media components on growth processes with a low catabolic AGI,. value (i.e. anaerobic processes). The principal difficulties with analysing growth- and metabolic-network efficiencies have been addressed extensively over the past few years. By contrast, development of thermodynamic methods to predict kinetic behaviour (for example, values of/* m=') is far less advanced. Similarly, thermodynamic analysis of product formation that is not linked to catabolism has not been considered. Elucidating the thermodynamics of product formation, and the development of a thermodynamic framework for the kinetic description of growth and product formarion is an essential area of research for attention in the near future.

Acknowledgements The author would like to thank E. H. Batdey, H. V. Westerhoff, U. yon Stockar andJ. A. Roels for many interesting discussions on the thermodynamics of microbial growth in the past years.

References 1 Roels, J. A. (1983) Energetics and Kinetics in Biotechnology, Elsevier 2 Battley, E. H. (1987) Energetics of Microbial Growth, Wiley

TIBTECHDECEMBER1994 (VOL12)

3 Westerhoff, H. V. and van Dam, K. (1987) Mosaic Non-Equilibrium Thermodynamics and the Control of Biological Free Energy Transduction, Elsevier 4 von Stockar, U. and Marison, I. (1989) Adv. Biochem. Eng. Biotechnol. 40, 93-136 5 Heijnen, J. J. and van Dijken, J. P. (1992) Biotechnol. Bioeng. 39, 833-858 6 Battley, E. H. (1993) Biotechnol. Bioeng. 41,422-428 7 Batdey, E. H. (1991) Biotechnol. Bioeng. 37, 334-343 8 Battley, E. H. (1992) Biotechnol. Bioeng. 39, 589-595 9 Battley, E. H. (1992) Biotechnol. Bioeng. 40, 280-288 10 Battley, E. H. (1992) Biotechnol. Bioeng. 39, 5-12 11 Battley, E. H. (1991) Biotechnol. Bioeng. 38, 480-492 12 Mavrovouniotis, M. L. (1990) Biotechnol. Bioeng. 36, 1070-1082 13 Heijnen, J. J., van Loosdrecht, M. C. M. and Tijhnis, L. (1992) BiotechnoL Bioeng. 40, 1139-1154 14 Sandler, S. I. and Orbey, H. (1991) Biotechnol. Bioeng. 38, 697-718 15 Heijnen, J. J. (1991) Antonie van Leeuwenhoek 60, 235-256 16 Heijnen, J. J. and van Dijken, J. P. (1993) Biotechnol. Bioeng. 42, 1127-1130 17 R.oels, J. A. (1993) Biotechnol. Bioeng. 42, 1124-1126 18 Westerhoff, H. V., Hellingweff, K.J. and van Dam, K. (1983) Proc. Natl Acad. Sci. USA 80, 305-309 19 Heijnen, J. J., Terwisscha van Scheltinga, A. H. and Straathof, A. J. (1992) J. Biotechnol. 22, 3-20 20 McCarty, P. (1965) Int..]. Air Water PoUut. 9, 621-639 21 Stouthamer, A. H. (1979) in InternationalReview of Biochemistry, Microbial Biochemistry (Quayle,J. R., ed.), pp. 21-45, University Park Press 22 Tijhuis, L., van Loosdrecht, M. C. M. and Heijnen, J. J. (1993) Biotechnol. Bioeng. 42, 509-519 23 van Kleeff, B. H. A., Kuenen, J. G. and Heijnen, J.J. (1993) Biotechnol. Bioeng. 41,541-549 24 Conrad, R. and Wetter, B. (1990) Arch MicrobioL 155, 94-98 25 Sch~ifer, T. and Sch6nheit, P. (1992) Arch. Microbiol. 158, 188-202 26 Smith, D. P. and McCarty, P. L. (1989) Biotechnol. Bioeng. 34, 39-54 27 Seitz, H-J., Schink, B., Pfennig, N. and Conrad, tL. (1990) Arch. Microbiol. 155, 89-93 28 Seitz, H-J., Schink, B., Pfennig, N. and Conrad, R.. (1990) Arch. Microbiol. 155, 82-88 29 Wu, W-M., Hickey, tL. F., Jain, M. K. and Zeikus,J. G. (1993) Arch. Microbiol. 159, 57-65 30 Guangsheng, C., Plugge, C. M., Roeloi~e, W. R., Houwen, F. P. and Stares, A.J.M. (1992) Arch. Microbiol. 157, 169-175 31 Gnaiger, E. (1993) in Biothermokinetics (Westerhoff, H. V., ed.), pp. 23-30, Intercept 32 McCarty, P. L. (1971) in Organic Compounds in Aquatic Environments (Faust, S. D. and Hunter, J. V., eds), pp. 495-531, Marcel Dekker 33 Birou, B. and von Stockar, U. (1989) Enzyme Microb. Technol. 11, 12-16 34 von Stockar, U. and Marison, I. W. (1991) ThermochimicaActa 193, 215-242