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Original citation: Großkopf, Tobias and Soyer, Orkun S.. (2016) Microbial diversity arising from thermodynamic constraints. The ISME Journal. 10.1038/ismej.2016.49 Permanent WRAP URL: http://wrap.warwick.ac.uk/77434 Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes this work of researchers of the University of Warwick available open access under the following conditions. This article is made available under the Creative Commons Attribution 4.0 International license (CC BY 4.0) and may be reused according to the conditions of the license. For more details see: http://creativecommons.org/licenses/by/4.0/ A note on versions: The version presented in WRAP is the published version, or, version of record, and may be cited as it appears here. For more information, please contact the WRAP Team at: wrap@warwick.ac.uk

OPEN

ORIGINAL ARTICLE

Microbial diversity arising from thermodynamicconstraints

Tobias Großkopf and Orkun S SoyerSchool of Life Sciences, University of Warwick, Coventry, UK

The microbial world displays an immense taxonomic diversity. This diversity is manifested also in amultitude of metabolic pathways that can utilise different substrates and produce different products.Here, we propose that these observations directly link to thermodynamic constraints that inherentlyarise from the metabolic basis of microbial growth. We show that thermodynamic constraints canenable coexistence of microbes that utilise the same substrate but produce different end products.We find that this thermodynamics-driven emergence of diversity is most relevant for metabolicconversions with low free energy as seen for example under anaerobic conditions, where populationdynamics is governed by thermodynamic effects rather than kinetic factors such as substrate uptakerates. These findings provide a general understanding of the microbial diversity based on the firstprinciples of thermodynamics. As such they provide a thermodynamics-based framework forexplaining the observed microbial diversity in different natural and synthetic environments.The ISME Journal advance online publication, 1 April 2016; doi:10.1038/ismej.2016.49

Introduction

There is an immense diversity of microbes in thenatural environment (Curtis et al., 2002). One majorchallenge for microbial ecology, besides achievingmore complete enumeration of the total diversity(Bunge et al., 2013), is to explain how this diversityis generated and maintained over evolutionary time.In particular, understanding the set of environmen-tal, biochemical and evolutionary conditions thatcan lead to the generation and maintenance ofmicrobial diversity is a prerequisite to understandand control natural microbial populations (Gudeljet al., 2010; O’Brien et al., 2013) and engineersynthetic microbial communities (Großkopf andSoyer, 2014).

In ecology, a historically dominant idea in thestudy of diversity is the ‘competitive exclusionprinciple’, which states that at equilibrium no twospecies can coexist occupying the same niche(Hardin, 1960). This principle is shown theoreticallyin the context of microbial ecology using mathema-tical models of the well-mixed, single substratechemostat environment. In such environments, thetheory predicts that coexistence of two species canonly be possible for a unique combination of kineticparameters, and outside this combination onlya single species, that has the highest substrateaffinity, can survive at steady state (Hsu et al., 1977).Thus, it is expected that a single organism should

monopolise each substrate; and the number ofobserved species in the environment should notsurpass the number of limiting nutrients or substrates.This exclusion theory led to the proposition of the‘paradox of the plankton’ as the problem of how a highbiological diversity can be maintained on a relativelylimited number of niches (Hutchins, 1961). One way toresolve this paradox is to invoke spatial and temporalvariations in substrate levels (Hsu et al., 1977;Pfeiffer et al., 2001; Kerr et al., 2002; MacLean andGudelj, 2006).

Although spatial and temporal variation in a singlesubstrate can certainly contribute to microbialdiversity, it cannot explain species harbouringdifferent metabolic pathways that enable conversionof the same substrate into different end products(Rodríguez et al., 2008). Even a common substratesuch as glucose can be converted into a variety ofend products by different species or even withina single species (Gupta and Clark, 1989). Thiscatabolic diversity contributes to the observedspecies diversity in the environment; and it ispossible that these two observations of diversity arelinked. For example, it is proposed that metabolicbyproducts (Schink, 1997) as well as specificproduction of toxic substances (Lenski andHattingh, 1986) could differentially inhibit compet-ing species or result in autoinhibition (De Freitas andFredrickson, 1978). When such inhibition affectsspecies competing for a given substrate in adifferential way, it can allow coexistence on thatsingle substrate (De Freitas and Fredrickson, 1978;Lenski and Hattingh, 1986).

Arguably the most fundamental inhibitoryconstraint on microbial growth is that arising from

Correspondence: OS Soyer, School of Life Sciences, The Uni-versity of Warwick, Coventry CV4 7AL, UK.E-mail: O.Soyer @warwick.ac.ukReceived 22 November 2015; revised 25 February 2016; accepted1 March 2016

The ISME Journal (2016), 1–9© 2016 International Society for Microbial Ecology All rights reserved 1751-7362/16www.nature.com/ismej

thermodynamics of metabolism. As microbialgrowth depends on energy harvested from substratesconverted into end products, it is governed by thethermodynamics of such metabolic conversions.Here, we consider this relation between the thermo-dynamic constraints placed on growth sustainingmetabolic conversions and the resulting population-level dynamics. Using thermodynamic models ofmicrobial growth, we show that the inevitableslowing down of microbial growth ensuing fromproduct built-up can lead to coexistence of differentspecies implementing different metabolic conver-sions and consuming the same substrate. As eachmetabolic conversion operates with different ther-modynamics, species utilising these are governed bydifferent growth and product-inhibition dynamicsthat result in their coexistence. We find this‘thermodynamics inhibition’ effect to be strongestfor reactions leading to a low change in free energy,where it dominates over kinetic factors such assubstrate uptake rates. In line with this fundamentalobservation, we find that several biologically rele-vant microbial conversions as well as theoreticallypossible metabolic conversions of glucose fit in theregime of strong thermodynamic effects and readilylead to coexistence of different species on a singlesubstrate. These findings provide a thermodynamicbasis to evaluate observed microbial diversity.

Materials and methodsThermodynamic model for microbial growthThe change of free energy generated by a metabolicconversion under non-standard conditions can becalculated according to Equation 1;

DGrxn ¼ DG00rxn þ R ´T ´ ln

Piam;ii

Pjam;jj

!ð1Þ

where R is the gas constant, T is the temperature,a and m are the chemical activity and stoichiometriccoefficient of each compound involved in thereaction, i and j are indices over products andsubstrates, respectively, and DG00

rxn is the changein free energy under biological standard conditions(1 M concentration of all solutes, 1 atm, 25 °C,and pH 7).

We use here a previously proposed thermodynamicmodel (Hoh and Cord-Ruwisch, 1996) that captures theobserved microbial growth dynamics under anaerobic,low-energy conditions. Utilising the results fromreversible enzyme kinetics (Haldane, 1930), this modelderives a rate function for microbial growth asfollows;

n ¼ nmax ´ ½S� ´ 1� expðDGrxnÞð ÞK þ ½S� ´ 1þ kr ´ expðDGrxnÞð Þ ð2Þ

Here DGrxn is the thermodynamic energy available inthe reversible reaction for a given set of substrate andproduct concentrations, as given in its generic form

in Equation 1. The constants K and kr are the halfsaturation constant for substrate turnover and theratio of maximum forward over maximum reversereaction rate, respectively (Hoh and Cord-Ruwisch,1996).

Note that by modelling microbial growth as areversible enzymatic reaction, this model makes theassumption that the rate of such an equation can betaken as the growth rate. In reality, the availablethermodynamic energy in the reaction would haveto be invested in driving the reaction, as well asin growth and cellular maintenance. Subsequentstudies have tried to address this point by proposingalternative models that consider the connectionbetween the energetics of catabolic and anabolicmetabolism (Kleerebezem and Stams, 2000; Jin andBethke, 2003,2007; Rodríguez et al., 2008). In thecontext of the present study, any of these morecomplex models could be utilised without affectingthe key conclusion that thermodynamic inhibitioncan lead to microbial diversity on a single substrate(see Supplementary Text). Implementing these mod-els, we find that conclusions regarding the interplayof kinetic and thermodynamic factors counteractingeach other (Figure 5) are affected only quantitativelyby the exact model choice on how much of the freeenergy available from a reaction is invested ingrowth rate vs biomass production. The presentedresults provide a conservative estimate.

Kinetic, non-thermodynamic model for microbialgrowthFor comparison with the thermodynamic model,we also use a solely kinetic model first developed byMonod (1949). This model uses an empiricallyderived kinetic equation to describe microbialgrowth and does not include the effects arising fromthermodynamics. The reaction rate for microbialmetabolism is given by

n ¼ nmax ´ ½S�K þ ½S� ð3Þ

Note that this equation results also from the thermo-dynamic model (Equation 2) when the change in freeenergy available from the growth reaction is verynegative (that is, exp(ΔGrxn)≈0).

Modelling growth of two species in a chemostat on thesame substrateWe consider two species X1 and X2 in a chemostat,where they are consuming the same substrate,S. Species X1 and X2 are assumed to process thesubstrate to produce different end products, P1 and P2,respectively. The feed-in rates of the species to thechemostat are considered to be zero, while thesubstrate concentration in the feed is given by S0.The dilution rate (per hour) of the chemostat isconsidered to be λ. Using these notations, and a givenmicrobial growth model, we can construct ordinary

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differential equations (ODEs) to model the dynamicsin a chemostat as follows:

d½S�dt

¼ ½S0� � ½S�ð Þ ´ l� ½X1� ´ n1 � ½X2� ´ n2d½X1�dt

¼ Y1 ´ ½X1� ´ n1 � l ´ ½X1�d½X2�dt

¼ Y2 ´ ½X2� ´ n2 � l ´ ½X2�d½P1�dt

¼ ½X1� ´ n1 � l ´ ½P1�d½P2�dt

¼ ½X2� ´ n2 � l ´ ½P2� ð4Þ

where Y is a biomass yield parameter and vi representsthe reaction rates of species i as given by Equations 2or 3. To understand the species concentrations atsteady state, we can solve Equation 4 by setting theleft side of each of the ODEs equal to zero. Inparticular, we can use the steady-state condition forsecond and third ODEs to obtain:

l ´ X1� � ¼ Y1 ´ X1

� �´nmax;1 ´ S

� �K1 þ S

� �l ´ X2� � ¼ Y2 ´ X2

� �´nmax;2 ´ S

� �K2 þ S

� � ð5Þ

where the bar notation indicates steady-stateconcentrations. For the non-thermodynamic model,this condition can only be satisfied if ν1 ×Y1 = ν2 ×Y2,which can be achieved only by a unique combinationof the yield, maximal growth and uptake parameters orwhen all these parameters are the same (that is, X1 andX2 are the same species) (Hsu et al., 1977). Under anyother set of parameters, the species with the loweraffinity for the substrate will be washed out of thechemostat (Hsu et al., 1977).

For the thermodynamic model, the steady-statecondition leads to

l ´ X1� � ¼ Y1 ´ X1

� �´

nmax;1 ´ S� �

´ 1� expðDGrxn;1Þ� �

K1 þ S� �

´ 1þ kr;1 ´ expðDGrxn;1Þ� �

l ´ X2� � ¼ Y2 ´ X2

� �´

nmax;2 ´ S� �

´ 1� expðDGrxn;2Þ� �

K2 þ S� �

´ 1þ kr;2 ´ expðDGrxn;2Þ� �

ð6Þ

Assuming that kr1,2=1 (equal maximum forward andbackward conversion rates) and parameters K1 andK2 are much larger compared with the steady-statesubstrate concentration, we can re-arrange thisequation to derive a condition for the steady state as

A� 1 ¼ A ´ exp DGrxn;2� �� exp DGrxn;1

� � ð7Þ

where A is a composite parameter given byY2 ´ vmax:2 ´K1=Y1 ´ vmax:1 ´K2. Thus, steady-statecondition can be satisfied with the two species

coexisting, for the correct combination of theirkinetic parameters and metabolic free energychanges. Since metabolic free energies are a functionof substrate and product concentrations, coexistenceis possible in a larger dynamical regime comparedwith the kinetics-only model. To get a sense on howspecies frequencies at steady state depend onproduct concentrations, we can make the strictassumption that yield, maximal growth and uptakeparameters of the two species are the same (thiscould be the case right after a speciation event), thatis, A=1. In this case, we can substitute Equation1 into the simplified Equation 7 to derive a relationbetween the end product concentrations at steadystate as a function of the standard free energychanges of the metabolic conversions:

expDG0

rxn;2 � DG0rxn;1

R ´T

!¼ P1� �P2� � ð8Þ

Since the product concentrations at steady staterelate to species concentrations at steady state (seeEquation 4 and Supplementary Text), the relationgiven by Equation 8 extends to the species concen-trations. We conclude that the two species withequal kinetic parameters will coexist at steady stateat frequencies that are determined by the standardfree energy changes of the metabolic conversionsthat they utilise as given in Equation 8.

Sampling of metabolic reactions from glucoseTo analyse the prevalence of reactions with lowGibbs free energy change, we consider stoichiome-trically balanced, fermentation reactions startingfrom glucose and involving 12 additional commoncompounds. We generate all possible reactionsamong these compounds, where each reaction mustfeature glucose as a substrate. To automatethis reaction generation, we define stoichiometriccoefficient ranges for each compound, where nega-tive and positive coefficients indicate compoundstaking part in a reaction as product or substrate,respectively. We then computationally iteratethrough these stoichiometric coefficient ranges togenerate all possible reactions within these limits.The 13 compounds used in this analysis and theirstoichiometric ranges are (lower bound; upperbound): glucose (−1;− 1), lactate (0;2), acetate (0;3),CO2 (−6;6), formate (0;3), pyruvate (0;2), acetalde-hyde (0;2), ethanol (0;2), H2 (0;6), H+ (0;12), water(−6;6), butyrate (0;2) and methane (0;6).

As an example, the homolactic fermentation ofGlucose would be represented by the followingvector of stoichiometric coefficients for thesecompounds: [� 1,2,0,0,0,0,0,0,0,2,0,0,0]. All reactionvectors within the search space are generated(that is, all combinatory permutations) and are thenevaluated for chemical and stoichiometric balance.To do so, we multiply each reaction vector with amass- and charge-balance matrix that holds the

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number of carbon, hydrogen and oxygen atomsas well as the charge of each molecule (seeSupplementary Table S1). For a reaction to bebalanced, this operation must yield zero. Balancedreactions are then considered as biochemically feasibleand their Gibbs free energy change is computed,assuming biological standard conditions (1 M, 1 atm,298.13 °K, pH=7) and using tabulated formationenergies (Thauer et al., 1977). The full list of reactionsresulting from this analysis is given in SupplementaryTable S2. A MATLAB script that implements theabove algorithm is provided in Supplementary Fileand can also be found at http://osslab.lifesci.warwick.ac.uk/?pid= resources.

Results

To analyse the relation between cellular metabolismand microbial ecology, we consider the thermody-namic basis of microbial growth. Microbes achievecellular growth through harvesting of free energychange available from metabolic conversions.As with any other chemical reaction, these conver-sions are governed by thermodynamics whereby thefree energy change for the reaction is given by thedifference between the free energy of formationof the products ðDG00

fproductsÞ and the substratesðDG00

f substratesÞ in that reaction. This is the maximumtheoretical amount of energy that microbes canutilise from the degradation of a substrate forbuilding up their own cell biomass under standardbiochemical conditions. If the concentrations deviatefrom standard conditions (1 M concentration of allsolutes, 1 atm, 25 °C, and pH 7), the apparentthermodynamic energy ΔGrxn available for microbialgrowth can be calculated according to Equation 1.In reality, energy available for growth would be lessthan this maximum amount, due to energy invest-ments in driving anabolic reactions leading tobiomass and other maintenance requirements(Thauer et al., 1977; Hoh and Cord-Ruwisch, 1996;Jin and Bethke, 2007; Rodríguez et al., 2008)(see further discussion below).

Thermodynamic constraints allow for coexistence ofmultiple species on a single substrateTo account for the inherent thermodynamicconstraints on microbial metabolism givenby Equation 1, we use here a thermodynamicgrowth model (Hoh and Cord-Ruwisch, 1996)(see Materials and methods). This model is shownto provide a better explanation of microbial growthunder anaerobic, low-energy conditions, wherethermodynamic effects are expected to be moreprofound, compared with models that are solelybased on empirical, kinetic formalisms (Hoh andCord-Ruwisch, 1996). Within this model, thegrowth rate of each species is described by afunction that contains kinetic and thermodynamic

factors that are governed by the substrate uptakedynamics and the free energy of the reactionconverting substrates to products respectively(see Equation 2). Considering alternative thermo-dynamic models does not alter qualitative conclu-sions of the presented study (see Materials andmethods and Supplementary Text).

Using this thermodynamic growth model, wefirst consider the simplest and most idealisedecological case of two species living on a singlesubstrate in a homogenous environment. Thisscenario can be realised in an ideal chemostat,where influx of substrate, dilution of metabolitesand cells can be taken into account and modelledthrough appropriate ODEs (see Materials andmethods). Chemostat models that consider micro-bial growth solely as a function of substrate uptakekinetics have been used to derive the exclusionprinciple; under the assumption of species havingthe same maximal growth rate and growth yield,there can only be one species existing in achemostat with a single substrate and this specieswould be the one with the most favourable substrateuptake kinetics (Hsu et al., 1977) (Figures 1a and b).When kinetic parameters of species are allowed tovary, there exists only a unique combination ofmaximal growth and kinetic uptake rates that wouldallow coexistence (Hsu et al., 1977). When we modelthe scenario of two species with the same growth,uptake and yield parameters using the thermody-namic growth model, we find that coexistence oftwo species on a single substrate is a possible stablestate, provided that these species produce differentend products from the substrate (Figures 1c and d).

Figure 1 Population dynamics of two species living on a singlesubstrate in a chemostat, modelled using an empirical, kineticmodel (a, b) and a thermodynamic model (c, d) (see Materialsand methods). Panels (b and d) show relative biomass of species X1

(dashed line), with vmax = 1, K=0.1 and DG0‘rxn ¼ �25kJmol�1 and

species X2 (continuous line) with vmax = 1, K=0.01 andDG0‘

rxn ¼ �20kJmol�1. Total biomass is scaled to 1. Chemostatmodel parameters are λ=0.1 and S0 = 1000.

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This result can be understood simply by the factthat growth dynamics in the thermodynamic modelis a function not only of yield and uptakeparameters, but also of the free energy changeavailable from the metabolic conversion. As freeenergy change of a specific reaction changes withthe concentration of substrates and products(Equation 1), it dynamically affects the growth rateof each species according to the concentration oftheir metabolic products. In particular, the build-up of products reduces the free energy available forinvesting in growth rate. The result of this effect issimilar to each species having a self-inhibition ontheir growth rate, which ultimately leads to thebalancing of substrate consumption among differ-ent species producing different end products(Figure 1d). This results in a dynamical steadystate, where the abundance of each species isgoverned by the free energy of the substrate–product pair (that is, catabolic metabolism) thatthey utilise. More specifically, we can show that forthe simple case of two species living on a singlesubstrate and assuming that all kinetic parametersgoverning substrate uptake, maximal growth rateand growth yield are equal, the ratio of speciesabundances at steady state is related to the DG0‘

rxn oftheir catabolic reactions (see Materials and meth-ods and Equation 8). This result can be readilyextended to multiple species coexisting on a singlesubstrate within a chemostat, provided thatthey can utilise different and chemically feasiblecatabolic reactions.

Thermodynamics-driven coexistence is most significantamong conversions with low free energy change andsuch conversions are prevalent in natureWe explore what happens to species abundances asthe difference in the DG00

rxn values between thetwo reactions that they utilise increases. As expectedfrom Equation 8, this reveals that the ratio of thespecies abundances increases exponentially infavour of the species utilising the reaction with ahigher change in free energy (more negative DG00

rxn) asthe difference in DG00

rxn values increases (Figure 2).Thus, while coexistence due to thermodynamics isalways possible theoretically, the abundance ofspecies with metabolic reactions producing thesmaller change in free energy becomes increasinglynegligible as the differences in the free energychanges of the two reactions increase beyond~50 kJ (mol Substrate)− 1 (Figure 2). Here, it isimportant to note that the thermodynamic modelwe use ignores energy investments in anabolicreactions and maintenance and thus provides aconservative estimate of this energy range. Also,more complex biochemical reactions leading tothe production of multiple products can increasethe range of allowed coexistence (see SupplementaryText).

Although Figure 2 provides a conservative esti-mate of the energy difference in catabolic reactionsthat would sustain coexistence of species at signifi-cant frequencies for the above reasons, it is stilluseful to consider the relevance of this energy regimein nature. In particular, are there chemically feasiblecatabolic reactions that are available for differentspecies to utilise for the conversion of the samesubstrate, and that have DG0‘

rxn values within~50 kJ (mol Substrate)− 1 of each other? To answerthis question, we collect the DG0‘

rxn of known growth-supporting microbial catabolic reactions using tabu-lated free energy changes, with particular focus onmicrobial reactions occurring in anaerobic environ-ments like sediments, animal guts and anaerobicdigesters (Table 1) (Thauer et al., 1977; Conrad et al.,1986; Seitz et al., 1988; Schink, 1997; Kleerebezemand Stams, 2000; Walker et al., 2009; Dolfing, 2013;Worm et al., 2014). As seen from Table 1, many ofthese reactions are within 20–100 kJ of each other(Figure 3). To further extend this analysis andaccount for any possible biases in the knownmetabolic conversions supporting microbial growth,we generated all chemically feasible reactions withina bounded search space. The aim was to get an ampleset of reactions utilising glucose as a substrate in afermentative manner (see Materials and methods).This exhaustive exploration of thermodynamicallyand stoichiometrically feasible metabolic conver-sions from glucose revealed that most of thesereactions have DG0‘

rxn values within 50–100 kJ (molSubstrate)− 1 of each other (Figure 3).

An example of thermodynamics-driven coexistenceamong propionate degraders further illustrates producteffects on coexistenceTo further demonstrate the thermodynamic inhibi-tion effect with an example, we consider three

Figure 2 Double logarithmic plot showing the effect of thermo-dynamic energy difference (dΔG) on the steady-state biomass ratioof the two species X1 and X2 growing in a chemostat with sharedsubstrate but differing waste products (according to Equation 8).

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different anaerobic oxidation reactions for propio-nate (Table 1). Two of these reactions are identifiedto be taking place in anoxic paddy soils in asimultaneous manner (Gan et al., 2012), indicatingthat the mediating microbes are coexisting in theseenvironments. Although each reaction has a differentstandard thermodynamic energy change they alsodiffer in the stoichiometry of their waste products,and in particular H2, produced. At standard condi-tions, that is, P(H2) = 1 atm, none of the reactions isenergy yielding. However, when applying morerealistic conditions of milli molar concentrations ofsubstrates and products, there is a H2 pressure atwhich any of the three reactions will be exothermic.

Interesting here is that when we consider the fullrange of biologically feasible H2 pressures, we findthat the reaction that can generate the highestamount of energy per propionate gets inhibited at alower ambient H2 pressure than the other tworeactions (Figure 4). This is underpinned by thestoichiometry of the reactions, where the reactionthat can yield the highest energy at low H2 pressureshas also the highest H2 yield (propionate:H2 stoi-chiometry = 1:7). In other words, the thermodynamicadvantage at low H2 pressures for the highest energyyielding reaction is removed by the rapid accumula-tion of H2 from its own reaction turnover. Thisexample further highlights the fact that microbialgrowth will be dominated by the thermodynamics ofthe supporting reactions, which can then lead to newregimes of coexistence and diversity among compet-ing reactions due to product accumulation.

Thermodynamics effects dominate for low-energymetabolic conversions, but can be readily overridden bykinetic factors for high-energy metabolic conversionsIn the above analyses, we considered species coex-istence solely due to differences in their metabolicconversions and resulting thermodynamic effects. Inreality, species can diversify in many different traitsgoverning their metabolism and growth. Amongsuch traits, those relating to kinetic properties suchas substrate uptake rates could be particularlyrelevant for the maintenance of species diversity ashighlighted by the mathematical studies on theexclusion principle (Hsu et al., 1977). To addressthis possibility, we re-consider the case of twospecies living on a single substrate by relaxingthe assumption that these species have the samesubstrate uptake kinetics. Assuming a scenariowhere one species uses a slightly more energy-richmetabolic conversion, we consider alterations in

Table 1 Thermodynamic energy under standard conditions (ΔG°Rxn) for selected catabolic reactions

Name Reaction dG° (KJ mol−1, pH 7) Citation

Glucose oxidation/Respiration C6H12O6+6O2 −4 6HCO3− +6H+ −2843.8 Thauer et al. (1977)a

Homoacetic fermentation of glucose C6H12O6 −4 3C2H3O2−+3H+ −310.9 Thauer et al. (1977)a

Ethanol fermentation of glucose C6H12O6+2H2O −4 2C2H6O+2HCO3−+2H+ −225.6 Thauer et al. (1977)a

Butyric acid fermentation of glucose C6H12O6+2H2O −4 2HCO3−+2H++2H2+C4H7O2

− −214.6 Thauer et al. (1977)a

Lactic acid fermentation of glucose C6H12O6 −4 2 C3H5O3−+2H+ −198.2 Thauer et al. (1977)a

Pyruvate fermentation of glucose C6H12O6 +2H2O −4 C3H3O3−+C2H3O2

−+HCO3−+3H++3H2 −159 Thauer et al. (1977)a

Methanogenesis (hydrogenotrophic) 4H2+HCO3−+H+ −4 CH4+3H2O −135.6 Seitz et al. (1988)

Lactate oxidation C3H5O3−+H2O −4 C2H3O2

−+2H2+CO2 −8.8 Walker et al. (2009)Lactate oxidation with sulphate C3H5O3

−+H++0.5SO42− −4 0.5H2S+H2O+CO2+C2H3O2

− −87.8 Thauer et al. (1977)a

Ethanol oxidation C2H6O+H2O −4 C2H3O2−+H2+H+ 9.6 Thauer et al. (1977)a

Butyrate degradation C4H7O2−+H2O −4 2C2H3O2

−+H++2H2 48.3 Rodríguez et al. (2008)C4H7O2

−+2H2+H+ −4 C4H10O+H2O −56.4 Rodríguez et al. (2008)Propionate degradation 2C3H5O2

−+2H2O −4 3C2H3O2−+H++2H2 48.4 Dolfing (2013)

C3H5O2−+3H2O −4 C2H3O2

−+HCO3−+3H2+H+ 76.5 Dolfing (2013)

C3H5O2−+7H2O −4 3HCO3

−+7H2+2H+ 181.1 Thauer et al. (1977)Glycolate degradation C2H3O3

−+H++H2O −4 2CO2+3H2 19.3 Schink (1997)Acetate degradation C2H3O2

−+H++2H2O −4 2CO2+4H2 94.6 Schink (1997)Methanogenesis (acetoclastic) C2H3O2

−+H2O −4 CH4+HCO3− −31.1 Schink (1997)

aComputed according to listed formation energies.

Figure 3 Histogram of the difference in thermodynamic energyavailable (dΔG°Rxn) between 85, algorithmically generated, stoi-chiometrically balanced anaerobic reactions starting from glucose(grey bars, see Materials and methods for details) and between allcombinations of the reactions displayed in Table 1 (black bars, thecase of glucose oxidation is excluded from these combinations andthe number of the cases is scaled by 10 to fit the same graph as thedata from algorithmic case).

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the uptake kinetics of this species. In otherwords, we explore the possibility of kinetic effectscounteracting the effects arising from thermody-namics in the context of species competition andcoexistence. As expected, kinetic effects can counter-act thermodynamic effects in a way such thata species utilising a more energy-rich metabolicconversion can become the rare species if ithas weaker substrate uptake dynamics (Figure 5).We find that this counteracting effect of kinetics overthermodynamics becomes more dominant as theDG0‘

rxn values of the metabolic conversions consid-ered for the different species increases. This resultcan be understood directly from the thermodynamicgrowth model (Equation 2); as the DG00

rxn valuesincrease, the thermodynamic effects arising fromproduct accumulation become negligible and thegrowth dynamics are increasingly governed bysubstrate uptake kinetics (for further analyses,see Supplementary Text).

Discussion

We have considered a thermodynamic model formicrobial growth and analysed the ensuing popula-tion dynamics in the context of competition andcoexistence. The model is derived from the funda-mental principles of conservation of energy andthermodynamics in metabolic conversions fuellingmicrobial growth. The key result from this first-principles model is that utilisation of differentmetabolic conversions by different species can allowfor their coexistence on a single substrate under ahomogenous environment. We find that the

abundance of different species under this circum-stance is governed by the change in standard freeenergy of the reaction that they utilise, and thatspecies utilising reactions that are within ~ 50 kJ (molSubstrate)− 1 of the reaction with highest change infree energy would coexist at significant frequency.An analysis of known and chemically possiblemetabolic conversion reactions shows that this isa biologically relevant regime, where many biochem-ical reactions known to sustain microbial growth arefound. This indicates that significant amounts ofmicrobial diversity on a single substrate could haveinitially emerged from, or are being sustained bythermodynamic constraints.

As the change in standard free energy of theutilised metabolic conversion reactions increases,however, we find that kinetic effects such asdifferences in substrate uptake rates overcome thethermodynamics effects on microbial growthdynamics. As a result, it can be expected that anychange in kinetic parameters (for example, byevolutionary change) would easily disruptthermodynamic-driven diversity emerging undermetabolic conversions with large change in freeenergy. The same is not true for metabolic conver-sions with small change in Gibbs free energy, wherewe find that species utilising metabolic pathwayswith DG00

rxn of − 20 vs − 25 kJ (mol Substrate)− 1 canstill coexist even with a 10-fold difference in theirsubstrate half saturation constants (Figure 5).We emphasise that these predictions on the energyranges leading to coexistence are conservativeestimates, as the thermodynamic model used hereconsiders that all of the free energy available fromthe metabolic conversion is invested into growth rate

Figure 4 Thermodynamic energy of three propionate degradingreactions (from Table 1), normalised per propionate, at differentambient H2 pressures. Each reaction produces H2 as a byproduct,and the line type indicates the reaction stoichiometry between thepropionate and hydrogen (as shown in the legend). The conditionsused to calculate the reaction thermodynamics are pH=7,1 mmol l− 1 of ambient propionate, acetate and HCO3

− and varyingambient H2 pressures as shown on the x axis.

Figure 5 Numerical simulation showing the effect of substrateaffinity (parameter K in Equation 2) and free energy values on thesteady-state biomass composition. The colour mapping indicatesbiomass of species X2 as fraction of total biomass. The y axis showsthe K1 of species X1, while K2 for species X2 is fixed at 10×10−6.The x axis shows the free energy of metabolic conversion reactionfor species X1, while that of species X2 is always set to be 5 kJ (molSubstrate)−1 lower (i.e, thermodynamically more favourable) thanthat for species X1.

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(Hoh and Cord-Ruwisch, 1996). In reality, some ofthis free energy would need to be invested in drivinganabolic reactions and other cellular maintenanceprocesses (Kleerebezem and Stams, 2000; Jin andBethke, 2003; Rodríguez et al., 2008). As a result,even metabolic conversions with higher free energychange could enter a regime of thermodynamicinhibition, and offer a window for the emergence ofthermodynamics-driven diversity.

The presented model considers the thermody-namics of microbial growth, by considering a overallgrowth-supporting metabolic reaction (for example,glucose to acetate). In reality, cellular metabolismtakes place over many reactions that finally reach ametabolic end product. Thus, the reaction Gibbs freeenergy change from the overall reaction is splitamong all the individual reactions and some of itneeds to be invested to achieve an appropriate fluxfor these reactions (Flamholz et al., 2013). Theconsequence of this is that not all of the Gibbs freeenergy change from the overall reaction can beinvested in growth rate, as we assume here. There-fore, our estimates for the effects of thermodynamicinhibition could act in a larger parameter regime,that is, even for overall reactions with larger Gibbsfree energies than studied here. In future work, itcould be possible to consider different reactionpathways in different species to get a more accuratemodel of their thermodynamic growth dynamics.Indeed, studies in this direction are already beingemployed to compare different pathways (Flamholzet al., 2013) and assess pathway feasibility underdifferent conditions (González-Cabaleiro et al., 2013;Cueto-Rojas et al., 2015).

Although the thermodynamic constraints high-lighted here act similar to inhibition driven bymetabolic byproducts (De Freitas and Fredrickson,1978; Lenski and Hattingh, 1986), it is important tonote that the former does not inhibit microbialgrowth per se, but emerge from the drive towardschemical equilibrium in the given metabolic reactionsustaining growth. Therefore, each given species isspecifically affected by the build-up of its ownproducts. The inherent thermodynamic mechanismis thus to punish specifically the fastest growingorganisms the earliest, and thereby favouring thecoexistence of a high number of different metabolicconversions in the environment. The products ofthese diverse metabolic conversions can then beutilised by the same species or different ones asenergy source, resulting in an example of ‘nichecreation’, and potentially leading to the emergence offurther microbial diversity and interactions throughadaptation. Indeed, anaerobic microbial commu-nities are frequently characterized by abundanceof such interlinked metabolic conversions (Schink,1997, 2002).

The findings of this study suggest that microbialcoexistence can readily arise under metabolicgrowth-supporting reactions with low freeenergy change. A direct experimental test for this

proposition for this would be to grow two differentspecies, or synthetically tagged variants of thesame species, on a single substrate. The choice ofthe species and substrate should be such that eachspecies can only utilise metabolic growth-supportingreactions with low free energy change. Such anexperiment can be run under chemostat conditions,as well as under batch conditions that test mutualinvasion from low frequency. Examples wouldinclude anaerobic growth on propionate or glycerol,where different metabolic pathways are known toexist. A broader suggestion from this study is thatenvironments that mainly allow for growth-supporting metabolic reactions with low free energychange should harbour more metabolic diversitycompared with environments that allow for meta-bolic reactions with high free energy change.This proposition could potentially be tested throughthe use of increasingly available metagenomics datafrom different environments. Examples for formertype of environments would include anaerobicdigesters, animal guts, wet soils and ocean sedimentsof highly productive regions. In these environments,high concentrations of substrates along with the lackof strong oxidising agents like oxygen or nitrate leadto accumulation of high concentrations of wastecompounds. Thus, we expect microbial growth inthese environments to be mainly limited by the lackof free energy available from the specific metabolicconversions a given species utilises. Microbes canovercome this limitation by evolving an ability toproduce different waste products from the samesubstrate molecule. This way they can maintaingrowth by producing those products that are onlypresent at very low concentrations in the environ-ment, and overcoming any thermodynamic inhibi-tion from accumulated products. This situation isanalogous to a river flowing from the mountains tothe sea, at its steeper parts the river is maintained ina single basin, while running over the flat surfaceclose to the coast it starts to meander and form manylittle rivers in a delta.

Conflict of Interest

The authors declare no conflict of interest.

AcknowledgementsWe acknowledge the generous support of the Isaac NewtonResearch Institute (INI) and the Wissenschaft Kollege zuBerlin (WIKO), where parts of this study were conductedduring fellowships held by OSS and TG. We acknowledgefruitful discussions with fellow colleagues at the INI andWIKO and in particular with Qusheng Jin, Steve Frankand Chris Quince. We thank Wolfram Liebermeisterand Carsten Wiuf for valuable comments on an earlierversion of this manuscript. We thank two anonymousreviewers for their comments and suggestions of improval.This work is funded by a research grant from Biotechno-logical and Biological Research Council (BBSRC) of the UK(grant ID: BB/K003240/2).

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