Opinion

Energy-based models forenvironmental biotechnologyJorge Rodrıguez1,2, Juan M. Lema2 and Robbert Kleerebezem3

1 Sustainable Environment Research Centre, University of Glamorgan, 2 Forest Grove, Pontypridd CF37 1UB, UK2 Department of Chemical Engineering, Universidade de Santiago de Compostela, Rua Lope Gomez de Marzoa s/n,

Santiago de Compostela 15782, Spain3 Department of Biotechnology, Delft University of Technology, Julianalaan 67, Delft 2628 BC, The Netherlands

Environmental biotechnology is evolving. Currentprocess objectives include the production of chemicalsand/or energy carriers (biofuels) in addition to thetraditional objective of removing pollutants from waste.To maximise product yields and minimise biomassproduction, future processes will rely on anaerobicmicrobial communities. Anaerobic processes are charac-terised by small Gibbs energy changes in the reactionscatalysed, and this provides clear thermodynamicprocess boundaries. Here, a Gibbs-energy-based meth-odology is proposed for mathematical modelling ofenergy-limited anaerobic ecosystems. This method-ology provides a basis for the description of microbialactivities as a function of environmental factors, whichwill allow enhanced catalysis of specific reactions ofinterest for process development.

Environmental biotechnology is evolvingThe increase in prices of fossil fuels and the commitment totackle global warming are adding to the value of energycarriers and other products obtained from renewableresources. This has led to a recent shift in the prioritiesof environmental biotechnology from its traditional objec-tive of eliminating pollutants from waste streams to therecovery of resources. Significant research efforts are beingfocused on the development of new bioprocesses for therecovery of chemicals and energy carriers from waste [1].Although this approach changes the status of what usedto be merely waste to that of an important raw materialor substrate, one important characteristic remainsunchanged: open mixed microbial communities are stillresponsible for the catalysis of the redox reactions in thesystem.

Despite important research efforts, the use of puremicrobial cultures for treatment of waste streams remainstroublesome. The wide diversity and variability of com-pounds present in waste, as well as the need for sterilisa-tion of large substrate flows to prevent contamination byundesired microorganisms, make the use of pure microbialcultures economically unfeasible on a large scale [2]. Con-sequently, we believe that competitive large-scale pro-cesses must be based on (open) mixed microbial cultures.

Traditional operational experience in the field of bio-logical wastewater treatment has established a thorough

E-mail addresses: Rodrıguez, J. (jrodrigu@glam.ac.uk, jorger@usc.es)

366 0167-7799/$ – see front matter � 2008 Elsevie

basic knowledge of microbial ecosystem functioning [3],thereby opening up numerous possibilities for establishingnovel mixed-culture-based processes. In addition, novelmolecular-biology-based tools will further enhance the un-derstanding of microbial ecosystems [4].

An objective of novel mixed-culture processes is to con-serve the energetic value of the organic substrate in theproduct. Other objectives are the production of compoundsthat can be separated from the (diluted) stream and theproduction of a narrow range of useful products. In mostcases, this rules out the application of processes involvingstrong electron acceptors (O2, NO3

�) that are associatedwith organic substrate mineralisation. These processes arealso associated with significant energy dissipation forgeneration of the dominant end product – the biomass –and therefore do not conserve the energy in the form ofenergy-carrier products. Furthermore, biomass can beregarded as a highly complex mixture of products thathas only very limited potential for reuse.

In the absence of an external electron acceptor, micro-organisms depend on fermentation reactions implicatingthe use of the organic substrate both as electron donor andacceptor. Biogas (methane) production is the most import-ant energy-carrier-producing mixed-culture-based process[5]. Anaerobic fermentation processes have also been pro-posed for obtaining other biofuels, such as hydrogen andalcohol, as well as for the production of other valuablechemicals, such as solvents or bioplastics [2]. Microbial fuelcells are an example of a novel process of obtaining elec-trical energy directly from bioelectroactive microorgan-isms [6,7], and these systems also rely on the activity ofanaerobic microbial communities. Figure 1 presents anoverview of valuable products that can be produced (typi-cally in mixtures) by anaerobic mixed microbial commu-nities from carbohydrate-rich substrates.

For many of these processes, the potential for reliablelarge-scale development is currently limited by an insuffi-cient insight into the substrate and product fluxes withinthe system and the role of the different microorganismsinvolved. Metabolic variability and difficulties in obtainingthe same products under similar operational conditions areoften observed, particularly in non-methanogenic fermen-tative systems [8]. The mechanisms by which environmen-tal factors, such as pH, temperature and concentration,affect the fluxes are not yet fully understood in systems inwhich no clear selective pressure is imposed. In addition,

r Ltd. All rights reserved. doi:10.1016/j.tibtech.2008.04.003 Available online 29 May 2008

Figure 1. Overview of the range of valuable products that can be obtained from

carbohydrate-rich substrates thorugh catalysis by anaerobic mixed microbial

communities. A better understanding of the mechanisms involved will most

certainly benefit the development of large-scale processes for commercial

production.

Opinion Trends in Biotechnology Vol.26 No.7

the impact of the source and composition of the microbialinoculum on the final process remains largely unclear.

To achieve competitive bioprocesses for the productionof valuable products, it has been acknowledged thatenvironmental biotechnology and microbial ecology needto develop approaches for the effective management ofmicrobial ecosystems [9]. To this end, the available knowl-edge on microbial ecosystems needs to be integrated intoenvironmental biotechnology processes utilising bothmicrobiological and engineering tools [10,11].

Mathematical models are the ideal tools for integratinglarge numbers of microbial, chemical and physicalphenomena taking place within themicrobial communitiesof interest. The key role of models in environmental bio-technology has become clear over the previous decades,and well-established mathematical models are now indis-pensable at every stage of process development, from theearliest research phase to large-scale industrial imple-mentation [12]. Mathematical models allow the investi-gation and analysis of the numerous phenomena that occursimultaneously in a complexmicrobial ecosystem, and theycan also be used to test scientific hypotheses, to designexperiments or to control an existing process. Modelsusually have different levels of complexity and, dependingon the objective, can be made more mechanistic, therebyaccounting for actual mechanisms occurring in the system,or more empirical, thereby attempting to fit the observedbehaviour using mathematical correlations.

Most existing models have only a limited applicationpotential for many of the new environmental bioprocesses,

in particular for those in which mixed microbial commu-nities catalyse reactions in close proximity to thermodyn-amic equilibrium.Whereas most of the existing models arebased on kinetics alone, in this paper a new modellingapproach based on the integration of bioenergetics andkinetics is proposed.

Are existing models adequate?Existing mathematical models of open mixed microbialcommunities have mostly been applied to biological aer-obic and anaerobic wastewater treatment systems[13,14]. These models typically consist of several mass-balance-based differential equations (one for each chemi-cal compound and physiological group of microorganismsconsidered). The mass balances include terms for theinfluent, effluent and the reaction in the system (i.e.the bioreactor). Each microbial activity can thereby bedescribed with an overall growth reaction with constantbiomass and product yield values, as well as with aMonod-type kinetic equation for defining the rate of thisparticular metabolic reaction as a function of a limitingsubstrate. Microbial and other chemical reactions occurin parallel, and all their contributions are added inthe net reaction term. The dynamics of the systemwith regard to all species present can be obtained bysolving the entire set of mass-balance-based differentialequations for the system.

Several such models have been considerably improvedover the previous decades and now present adequate toolsfor the description of the dynamic performance of aerobic,anoxic and methanogenic processes. These models havefound broad application in the wastewater treatmentindustry and have significantly improved the control andoptimum operation of these systems [13,15]. However, sofar they have failed to describe anaerobic, fermentative,non-methanogenic processes in a satisfactory manner andwere also not able to determine the dependence of productformation on the environmental conditions imposed on themicrobial community.

Questions on the applicability of existing kinetic-based models for the investigation of anaerobic mixed-culture fermentations arise for the following three mainreasons:

(i) M

ost of the existing kinetic-based models assumeconstant values for product and biomass yields.However, anaerobic fermentative microorganismsare known to produce a variable range of products,and their production is dependent on several factors,including the thermodynamics of the reactions [8].Variability in the product spectrum also affects thebiomass growth yield and, therefore, the prediction ofthe overall substrate conversion rates observedbecause the biomass is the catalyst of these conver-sions.

(ii) E

xisting models often segregate the microbial com-munity into several species or groups depending ontheir function. This segregation has proved to besuccessful when aerobic activated sludge systems areconsidered in which the different microbial activitiesact on different elemental cycles and are therefore

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368

clearly distinguishable. Furthermore, the segregationof different physiological groups has been adopted forthe sequential degradation of organic substrates formethanogenic systems. This has also been successfulbecause methanogenesis can be clearly distinguishedas the limiting reaction [16]. However, such asegregation can cause problems in anaerobic (non-methanogenic) fermentative systems in which thepresent microorganisms have similar growth ratesand yields and several fermentative reaction path-ways are catalysed (shared) by several differentmicroorganisms in parallel. If numerous competingmicrobial groups are to be considered in a model,extensive kinetic and stoichiometric parameter esti-mations are required in order to describe theirexperimental behaviour. This causes identificationproblems due to the problematic quantification of thedifferent microbial groups in a mixed microbialcommunity.

(iii) E

xisting kinetic-based models often neglect energeticand thermodynamic limitations because they havebeen based on aerobic processes that entail large DGvalues. In anaerobic systems this might lead tounrealistic predictions, such as the catalysis ofendergonic reactions (i.e. with DG>0) that areimpossible according to the second law of thermo-dynamics [17]. These unrealistic predictions mightoccur because reactions in these systems proceedclose to thermodynamic equilibrium (i.e. with verysmall DG values), and accumulation of products caneasily result in positive DG values and might evenreverse the reaction fluxes.

Taken together, the characteristics discussed above

make existing kinetic-based mathematical models unsui-table for adequate description of the conversions occurringin anaerobic microbial communities. This seriously com-promises their use for the development of the emergingprocesses for production of energy carriers and valuablechemicals. For this reason, we believe that there is a needfor a new mathematical modelling approach that will beable to deliver models that are better equipped to inves-tigate anaerobic microbial communities in detail.

What would a suitable model look like?The extrapolation of models that are not adequate fordescribing a specific system to fit experimental obser-vations via extensive parameter calibrations constitutesa bad modelling habit and should be avoided. Only ad-equate mechanistic descriptions enable knowledge-basedprocess development and methods to enhance and/orrepress specific reactions of interest.

Mathematical models that are suitable for the quanti-tative description of substrate and product fluxes inmixed-culture communities of microorganisms must incorporatethe stoichiometry and kinetics of the relevant metabolicreactions that occur within these communities. Theymust contain a mechanistic description of the processoccurring and incorporate the fundamental laws that needto be obeyed while minimising the number of processparameters that need to be identified by calibration.

A mathematical model that is well equipped to inves-tigate the activity of any microbial community must alsoprovide reliable expressions for the rate-limiting reac-tions, which can be either kinetically of thermodynami-cally controlled. In energy-limited anaerobic microbialecosystems, fermentative reactions occur that have DGvalues very close to zero and that are limited by thermo-dynamics. These reactions are therefore only feasiblewithin narrow concentration ranges of substrates andproducts. However, the rates of reactions that havemuch larger energy dissipation (i.e. strongly negativeDG values) are kinetically controlled. This is the casefor oxidation reactions with strong electron acceptors likeoxygen or nitrate.

Including thermodynamicsIn addition to mass conservation laws, thermodynamicsprovide additional boundary conditions that must beobeyed by any reaction that is described by a realisticmodel. However, such boundary conditions are currentlynot included in most of the existing models, which con-sequently might unrealistically predict the catalysis ofreactions with a positive DG value.

Thermodynamic laws always apply, and they can beverified using the same experimental concentrationmeasurements as used for mass balances. Thermodynamiclaws must be systematically incorporated in environmen-tal biotechnology models because they neither limit themodel applicability nor increase the number of parametersfor estimation (thermodynamic properties are in generalavailable in the literature).

Thermodynamic limitations could, in theory, be easilyincorporated into the kinetic equations of existing modelsof mixed microbial cultures without having to drasticallychange their main structure. Some of the inconsistenciesidentified above, such as the catalysis of endergonic reac-tions, could be eliminated by incorporating a thermodyn-amic threshold term in the kinetic expressions, and this isillustrated in Box 1.

Although such modifications might address some of thethermodynamic inconsistencies, the main reasons whykinetic-based mathematical models are unsuitable forinvestigating anaerobic mixed microbial ecosystemsremain, including the constant product yields and themicrobial-group segregation that most of these modelsare based on. Therefore, we believe that different model-ling approaches are necessary to accurately describe theactivity of anaerobic microbial ecosystems, and such next-generation models require a methodology that is based onmore-profound energetic considerations.

Several studies are available in the literature for theestimation of biomass growth yields based on Gibbs energybalancing [18–20]. These approaches have demonstratedthat the anabolic reaction for biomass synthesis is basicallyindependent of the catabolic reaction for energy generationand is mainly a function of the carbon and nitrogen source.The maintenance concept proposed by Pirt can also bedescribed in terms of Gibbs energy requirements [21], aswell as other very useful methods for estimating biomassyield that are also based on Gibbs energy calculations [22].Numerous studies also exist on the relation between the

Box 1. Relationship between energy and biomass growth

In the absence of external sources of energy, such as light,

microorganisms depend on catabolic redox reactions for growth

and cell maintenance. Energy, typically in the form of ATP, is

conserved and made available for growth and maintenance purposes.

Consequently, the overall Gibbs energy change of any catabolic

reaction (DGcatab) is partly conserved for growth purposes and partly

used for maintenance purposes, but to some extent it is also

dissipated to maintain a non-equilibrium situation that is required

to establish a flux through the catabolic system.

Here, a generalised quantitative description of the catabolic flux in

terms of the biomass-specific substrate-uptake rate and the biomass

growth rate is derived. First, a fraction of the catabolic Gibbs energy

(DGcatab) is assumed to be dissipated to establish a flux through the

catabolic enzyme system ( fdis), and this dissipated fraction of Gibbs

energy is entitled DGdis. The remaining Gibbs energy change of the

catabolism is available for growth and maintenance purposes (DGm/m)

[48]. According to this, DGdis = fdis DGcatab and DGm/m = (1 � fdis)

DGcatab

The amount of dissipated Gibbs energy (DGdis) can be regarded as

the actual driving force for the catabolic reaction. This term can

readily be implemented in a Hill-like equation [49] that describes the

actual biomass-specific substrate-uptake rate (qS) as a function of the

DGdis value according to the following equation:

qs ¼ qmaxS � ½1� expðDGdisÞ�

¼ qmaxS � ½1� expð f dis � DGcatabÞ�; if DGdis < 0 [Equation I]

In this equation, qmaxS represents the maximum biomass-specific sub-

strate-uptake rate. Evidently, the value for qS decreases when the

values for fdis or DGcatab are closer to thermodynamic equilibrium.

Using a Gibbs energy balance, the catabolic flux can be coupled to

the anabolic flux using the Gibbs-energy-based Pirt equation [48]:

m ¼ 1

ð�DGanabÞ� ðqS � DGm=m �mGÞ

¼ 1

ð�DGanabÞ� ½qS � ð1� f disÞ � DGcatab �mG � [Equation II]

where DGanab is the overall Gibbs energy dissipation for growth in kJ/

molC-X and mG is the Gibbs energy dissipation rate for growth-indepen-

dent maintenance purposes in kJ/(molC-X�h). The value for the growth

rate (m) increases at increasing values for qS but decreases at increasing

values for fdis, suggesting that a maximum value for m is established at a

certain value for fdis. This is further clarified in Figure I below.

Negative growth rates as indicators for biomass decay are found

both at fdis = 0, because in this situation no catabolic flux occurs

(qS = 0), and at fdis = 1, because no Gibbs energy is available for

growth and maintenance purposes (DGm/m = 0). In this specific

example, the maximum value for the specific growth rate is found

at a value for fdis of �0.2. One can argue that an optimisation criterion

for microbial fluxes would be the maximisation of the specific growth

rate and that, consequently, an equilibrium between catabolic and

anabolic fluxes will be established at fdis ffi 0.2. The optimum value for

fdis depends strongly on DGcatab, and the considerations described

here are only of importance at small driving forces with values of

DGcatab close to zero.

Figure I. Relationship between the specific biomass growth rate and the fraction

of catabolic energy dissipated for establishment of a catabolic flux. The following

parameter values were chosen solely for the purpose of generating numerical

output: qmaxS ¼ 1 molS=molC-X � h; mG = �1 kJ/(molC-X�h); DGcatab = �10 kJ/molS;

DGanab = 300 kJ/molC-X.

Opinion Trends in Biotechnology Vol.26 No.7

thermodynamic driving forces (which are a function of thecomposition of the medium) and reaction rates [23–27].These studies do not focus on the prediction of productformation as a function of the medium composition inmixed microbial communities, but they provide an excel-lent basis for a bioenergetic approach to this problem.

An energetics frameworkGibbs energy calculations allow the identification of theenergy niches that are needed for redox reactions to occur.A key characteristic of anaerobic fermentations is thatmetabolic reactions occur very close to thermodynamicequilibrium and have small DG values [28], meaning thatseveral anaerobic bioreactions of interest are only thermo-dynamically feasible if the concentrations of the reactantsand products fall within a narrow range. An example of thisis the hydrogen transfer between producer and consumermicroorganisms that usually occurs in methanogenic sys-tems. Hydrogen producers and consumers can only ther-modynamically coexist if the hydrogen concentration ismaintained at a very low value by the methanogenichydrogen consumers [29–31].

The amount of energy that can be obtained from acatabolic reaction, which is typically conserved in theform of ATP, depends on the concentrations of substratesand products in the medium. By converting substratesinto products, the microbial activity changes the respect-ive concentrations in the medium, and this mightresult in other reactions becoming feasible and energe-tically sufficient to sustain the growth of other microor-ganisms.

In energy-limited ecosystems, thermodynamic calcu-lations can provide an interesting picture of the energeticscenario of the system and help locate thresholds thatmight change the whole microbial ecosystem behaviour.Figure 2 illustrates this through two example energeticscenarios in a hypothetic anaerobic microbial ecosystem inwhich the oxidation and reduction of butyrate to acetateand butanol, respectively, can be catalysed, as well as thedirect electron transfer into a solid electrode that wouldoccur in a microbial fuel cell [6]. Scenarios analogous tothose in Figure 2 can be studied by calculating the Gibbsfree energy change of any catabolic reaction at differentsubstrate or product concentrations and/or electrode

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Figure 2. Example of two energetic scenarios where the Gibbs free energy exchange of different catabolic reactions (selected for illustrative purposes only) is presented as a

function of controllable variables in a reactor. The (-DGcatab) value of each reaction is calculated according to the general equation shown in the box and using the

concentration values indicated in each panel. The scenario in (a) presents the effect of pH and hydrogen partial pressure (PH2) on a system where only reactions R1 and R2

can be biocatalysed. In a reactor operating at the PH2 and pH conditions of point (i), only butyrate oxidation (R1) could thermodynamically proceed. If this is the case, and in

absence of external control measures, after some time the pH will decrease and the PH2 will increase. The system will therefore evolve towards different energetic

conditions where butyrate reduction (R2) might not only become thermodynamically feasible, but even bioenergetically more attractive than R1. The opposite would occur

if starting from point (ii). In the scenario in (b), electroactive microorganisms are present and, in addition to R1 and R2, electrons can also be directly transferred to an

electrode (R3) at a given electrical potential (Ee). The effect of the Ee and PH2 on the Gibbs energy change of the reactions is presented. The same general Gibbs energy

equation is applied by considering electrons as a product whose activity is a function of the electrode potential according to ½e�� ¼ expððF=R � T Þ � Ee Þ.

Opinion Trends in Biotechnology Vol.26 No.7

potential values according to the well known Equation 1:

DGcatab ¼ DGocatabR � T

� 1n ½P1�p1 � ½P2�p2 � . . .

½S1�s1 � ½S2�s2 � . . .ðkJ-molÞ [Equation 1]

where, for a reaction in which stoichiometry is givenby s1S1 þ s2S2 þ . . . !p1P1 þ p2P2 þ . . ., DGcatab is theactual Gibbs free energy change of the catabolic reactionand DGo

catab the value under standard conditions (i.e.T = 298 K; [Si] = [Pi] = 1 mol/L).

In Figure 2, the existence of energetically equivalentregions in the scenario described in part (a) and the pathsfollowed from point (i) (or (ii)) towards a lower (higher) pHand/or higher (lower) PH2 will depend on the medium(reactor configuration) and on the implementation of exter-nal control measures (e.g. pH controller, gas sparging).Analogously, the scenario in part (b) shows how thresholdvalues exist (for PH2 and Ee in this case) at which reactionsbecome thermodynamically feasible or bioenergeticallymore attractive.

Although the interdependence between the energeticniches (which determine the redox reactions that arethermodynamically favourable) and the microbial activi-ties (i.e. the catalytic potential of themicroorganisms in thesystem) is not completely understood [32], valuable infor-mation can be obtained from studies of energetic scenariossuch as the one represented in Figure 2. There are alsoexamples of microbial reactions that were first predicted

370

thermodynamically and subsequently confirmed exper-imentally in natural and man-made ecosystems, such asanaerobic ammonium oxidation [33,34] and methane oxi-dation with sulphate [35] or nitrate [36]. The advantages ofthis approach have also started to be recognised by otherscientific disciplines, such as astrobiology [37].

An energetic framework can be very useful for develop-ing processes in which specific reactions need to befavoured to obtain the specific desired products. Reactorexperiments might be also designed to investigate whethera microbial community might or could be forced to operatein specific energetic regions.

A metabolic network modelling approach based onenergyThe environmental conditions imposed on a givenmicrobial community in a reactor determine the totalamount of Gibbs energy that the microorganisms canharvest for growth. Furthermore, the environmental con-ditions affect the spectrum ofmetabolic products generatedif the microorganisms are assumed to catalyse the reactionpathways that yield the maximum energy possible fromsubstrate. From a set of possible catabolic reaction path-ways, the set of reaction fluxes that will yield the highestamount of energy can be calculated. For this purpose, anoptimisation problem can be defined in which the reactionfluxes are the decision variables and the total energy yieldis the objective to be maximised while satisfying several

Figure 3. Representation of the modelling approach proposed to predict the activity of an anaerobic mixed microbial ecosystem. If the ecosystem follows a maximum

energy yield criterion and the most relevant fermentative reactions are included in the metabolic network used, the maximisation of the energy yield as a function of the

possible reaction fluxes returns a prediction of the product formation.

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constraints (i.e. mass conservation and thermodynamiclaws). A similar energetic optimisation approach is widelyused in metabolic engineering to predict the metabolicactivity of pure microbial cultures [38]. We have used thisapproach for predicting the product spectrum as a functionof the environmental conditions in anaerobic mixed-cul-ture fermentation processes [39]. It is plausible that inthese ecosystems the energy limitation imposes a selectivepressure that favours the product formation reactions thatare associated with the maximised Gibbs energy yield. Theenvironment will subsequently select for the microorgan-isms that are capable of catalysing this optimised set ofreactions.

Previous studies have used a thermodynamic-equi-librium-based approach to predict the formation of pro-ducts in anaerobic fermentations [40,41]. However, thepredictionsmade by thesemodels could never be validated,and more recent models are based on a constant fermenta-tion product spectrum. Recently, a conceptual model wasproposed [39] that assumed the whole anaerobic microbialecosystem to be a single microorganism that could bedescribed by a simplified metabolic network of the mosttypical fermentative reactions. The fluxes in the networkwere defined by optimisation of the net energy yield, asillustrated in Figure 3.

The seemingly overwhelming task of modelling complexmicrobial ecosystems that involve hundreds of differentmicroorganisms and mechanisms is facilitated by twocharacteristics specific to anaerobic systems. The firstfactor is the close proximity of anaerobic catabolic reac-tions to the thermodynamic equilibrium, as discussedabove. This enables the estimation of the concentrationsof intermediate metabolites by assuming quasi equi-librium (i.e. DGcatab ffi 0, see Equation 1). The secondimportant factor is the limited number of fermentativemetabolic reactions or pathways that are actually relevantin anaerobic fermentative systems [42]. A recent study onEscherichia coli has demonstrated that the overall meta-bolic activity appeared to be dominated by only a small setof high-flux reactions, whereas most of the remaining low-

flux reactions did not contribute significantly [43].Responses to changes in environmental conditionsappeared to manifest themselves in a reorganisation ofthese fluxes. So far, this has only been demonstrated for E.coli, but it is likely that this represents a more universalfeature of the metabolic activity of microorganisms.

These factors facilitated the approximation of a wholemicrobial ecosystem into a simplifiedmetabolic network byfocusing only on a limited set of relevant high-flux reac-tions [39]. This approach is basically equivalent to remov-ing microbial speciation from the common metabolic fluxmodels and relying instead on the tight energy niches todefine the activities. On the one hand, this might beregarded as an extreme simplification of highly complexmicrobial ecosystems but, on the other hand, it is based onsound assumptions, such as well-known reaction stoichi-ometries and thermodynamics and a plausible selectivepressure based on energy limitation. Another advance ofsuch an approach is its highly flexible modelling frame-work, into which detailed physiology, biochemistry andmicrobial ecology variables can easily be incorporated.The initial, highly simplifiedmodel returned an estimationof the product spectrum and the biomass yield as a functionof environmental conditions in a chemostat reactor fedwith glucose [39]. Although this first version of the modelhas subsequently been proved to be insufficient, the incorp-oration of new mechanisms has already demonstrated theflexibility of the approach [44,45].

The model established a relationship between the med-ium concentrations and their bioenergetic consequencesfor the microorganisms and, subsequently, to shifts in thenet fluxes that led to different products driven by a maxi-mum-energy-yield selective force. One of the most import-ant factors included in the model is how the medium pHinfluences the system by changing the energetics of thetransport of products [39]. This is discussed in greaterdetail in Box 2, where it is demonstrated that includingthe Gibbs energy production or consumption for transportof acidic products has a significant impact on the biomassyield obtained and on product formation. Both Box 1 and

371

Box 2. Effect of pH on energetics and biomass growth

Microorganisms conserve energy by coupling the transport of solutes

to the generation or consumption of ATP [50,51]. Consequently, the

amount of Gibbs energy available for growth is dependent on the pH

of the medium; therefore, pH levels directly affect the microbial

growth yield. The bioenergetic properties of lactate fermentation are

used below to clarify this.

Glucose fermentation to lactate is assumed to generate one ATP per

mol lactate produced (YATP,Lac = 1 molATP/molLac) by substrate level

phosphorylation. The Gibbs energy conserved by production of ATP

(DGATP) corresponds to �50 kJ/molATP under physiological conditions.

Therefore, if a chemostat is considered, the Gibbs energy produc-

tion rate associated to glycolysis is:

RG;Gly ¼ D � CextLacT � Y ATP ;Lac � DGATP ðkJ=L � hÞ [Equation I]

where D (h�1) is the dilution rate in the chemostat and CextLacT (mol/L) is

the total extracellular concentration of lactate.

All lactate produced must be extruded from the cell, but whether or

not this is an energetically favourable process depends on the intra-

and extracellular pH values, as shown in Figure I. The actual driving

force for extrusion of lactic acid can be calculated according to:

DGLacHTr ¼ R � T � 1n

CextLacH

CintLacH

[Equation II]

where C intLacH and Cext

LacH are the intra- and extracellular concentrations of

undissociated lactic acid, respectively, as can be calculated from the

intra- and extracellular total lactate concentrations (C intLacT and Cext

LacT ),

the corresponding pH values and the acid constant for lactate

( pKa = 3.8).

Furthermore, considering the passive diffusion of lactic acid across

the cytoplasmic membrane, the overall Gibbs energy production or

consumption rate associated with transport equals:

RG;Tr � ðK Dif � ðCintLacH � Cext

LacHÞ � X � CextLacT � DÞ � DGLacH

Tr [Equation III]

where CextLacT � D equals the net lactate production rate and

K Dif � ðCintLacH � Cext

LacH Þ � X equals the passive diffusion rate for undisso-

ciated lactic acid, as characterised by the biomass specific rate constant

KDif (L�molC-X�1�h�1) and the biomass concentration X (mol/L).

The net Gibbs energy production now equals RG,Net = RG,Gly + RG,Tr.

In a chemostat, and therefore in steady state, the catabolic Gibbs

energy production equals the anabolic Gibbs energy consumption for

growth. By defining a DGanab (kJ/molC-X) value, the steady state

lactate and biomass concentrations can be calculated if the concen-

tration of glucose fermented (DCGlu) is defined. A numerical example

is shown in Figure II. Note how the biomass yield values are linearly

related to the net Gibbs energy production according to:

Y X ;Glu ¼RG;Net

DGanab � DCGlu � D[Equation IV]

The results show that at pH values higher than�7.5, transport-related

product extrusion contributes to the catabolic Gibbs energy production,

resulting in a biomass yield that is higher than the yield that can be

estimated from RG,Gly. At lower pH values, the unfavourable gradient

created (see Figure I) requires both more energy per lactate transported

and additional energy expenditure in a futile cycle for active extrusion

of the lactic acid passively diffused inside the cells. This causes a

negative value for RG,Tr. Consequently, RG,Net values and the corre-

sponding biomass yield values are significantly lower than RG,Gly.

This example demonstrates the impact of including Gibbs energy

change of acidic products transport on the overall microbial kinetics

obtained. Furthermore, relating the KDif value to the specific cell-

surface area might also provide insight into diffusion rates over the

cytoplasmic membrane.

Figure I. Representation of the effect of pH on the energetics of lactic acid

transport at acidic (a) and alkaline (b) pH values in the medium.

Figure II. Glycolytic, transport-associated and resulting net Gibbs energy

production rates as a function of the medium pH. Numerical values used are:

D = 0.1 h�1, DCGlu = 20 mM, CintLacT ¼ 10 mM, pHint = 7, KDif = 200 L�molC-X

�1�h�1,

DGanab = 250 kJ/molC-X.

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Box 2 constitute specific examples of how to link thermo-dynamics and kinetics, and these equations can be easilyincorporated into mathematical models.

Perspective for applicationsThe most immediate application of such a proposed mod-elling approach is the prediction of product formation in

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anaerobic mixed-culture fermentations as a function of theenvironmental conditions imposed in a reactor. Knowledgeof this dependence would bring immediate advantages forthe development of robust processes for producing biofuelsor other valuable chemicals (see Figure 1). The develop-ment of reliable models will also help to define the oper-ation conditions required in reactors to obtain specific

Opinion Trends in Biotechnology Vol.26 No.7

products, as well as to integrate these reactors into morecomplex processes, such as those in biorefineries.

Another interesting application is the study of bioelec-trochemical systems, such as microbial fuel cells, in whichelectrons are transferred to solid electrodes [6]. This reac-tion can be easily incorporated in the modelling approachin the form of an additional metabolic pathway in whichelectrons can be treated as products whose energeticsdepend on the electrical potential of the electrode (seeFigure 2b). The energetics (chemical and electrical) ofthe different possible mechanisms of electron transportto electrodes could then be investigated using such anadapted model. Further understanding of the energeticsof the microbial community might also enable researchersto control its activity and products by modifying the poten-tial or the current of the electrode [46,47].

ConclusionsAnaerobicmixedmicrobial ecosystems catalysemany reac-tions of interest for environmental biotechnology, such asthe production of valuable energy carriers and chemicalsfrom wastes, but there is currently only a limited under-standing of the mechanisms that favour some reactionsover others. Mathematical modelling has proven very use-ful in describing complex systems, but most of the existingmathematical models, which were originally conceived foraerobic systems, are not adequate for these anaerobicecosystems.

Anaerobic fermentative reactions proceed close tothermodynamic equilibrium, and anaerobic microbial eco-systems are in general energy-limited. These character-istics make it possible to consider the energetics ofreactions and transport processes, allowing these systemsto be studied in detail. We believe that the systematicanalysis of energetic scenarios will help in understandingthe factors that determine reaction fluxes and might con-tribute to answering important ecological questions, suchas how the composition and activity of a microbial com-munity might evolve when competing for the limitedenergy available.

We propose here a modelling approach that is based on asimplified but flexible representation of anaerobicmicrobialecosystems as a single metabolic network, as well as onusing a maximum-energy-yield selective force to define thereaction fluxes as a function of environmental factors.

This has opened a path for the integration of microbialecology and environmental biotechnology with the help ofenergy-based modelling approaches and the incorporationof biological information into these models. This integra-tive approach is expected to translate into significantadvances in the development of environmental biopro-cesses for the production of valuable energy carriers andchemicals.

AcknowledgementsThe authors wish to acknowledge the anonymous reviewers for theirinvaluable contribution to improving this manuscript. The authorsacknowledge the support of the European Commission under the MarieCurie Host Fellowship Transfer of Knowledge scheme (MTKD-CT-2004–509821) and the Spanish Ministry of Education and Science(NOVEDAR_Consolider, CSD2007–00055).

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