In Silico Geobacter sulfurreducens Metabolism and Its Representation in Reactive Transport Models

Microbial activity governs elemental cycling and the transformationof many anthropogenic substances in aqueous environments. Throughthe development of a dynamic cell model of the well-characterized,versatile, and abundant Geobacter sulfurreducens, we showedthat a kinetic representation of key components of cell metabolismmatched microbial growth dynamics observed in chemostat experimentsunder various environmental conditions and led to results similarto those from a comprehensive flux balance model. Coupling thekinetic cell model to its environment by expressing substrateuptake rates depending on intra- and extracellular substrateconcentrations, two-dimensional reactive transport simulationsof an aquifer were performed. They illustrated that a properrepresentation of growth efficiency as a function of substrateavailability is a determining factor for the spatial distributionof microbial populations in a porous medium. It was shown thatsimplified model representations of microbial dynamics in thesubsurface that only depended on extracellular conditions couldbe derived by properly parameterizing emerging properties ofthe kinetic cell model.

INTRODUCTION

Top

INTRODUCTION

Microbes control the breakdown of organic matter in low-temperaturesubsurface environments. Their activities affect the physicochemicalnature of the local environment, drive elemental cycling, anddetermine the fate of many contaminants (9, 49). Effects canbe direct (for example, by altering the local chemical compositionthrough the utilization of substrates and terminal electronacceptors for energy production and growth or cometabolism)or indirect (for example, by affecting the presence and thechemical nature of solid iron phases, which determines sorptionand coprecipitation of transition metals and contaminants) (4,6, 17, 51). In addition, hydrological factors such as groundwaterflow patterns and velocities can impact cell metabolism throughnutrient delivery, with possible feedbacks through bioclogging(46).

To predict how bacteria regulate their activity and grow insitu, it is necessary to quantitatively understand the complexand dynamic interactions between the numerous concurrent biogeochemicalprocesses involved, which requires the use of mathematical models.While subsurface reactive transport models generally containa comparatively sound description of the physical transportprocesses (3, 34), they often do not explicitly account forthe dynamics of microbial populations that mitigate the majorityof biogeochemical processes (18, 48). When included, microbesare typically represented as functional groups, with growthdynamics depending linearly on substrate availability or followingMonod kinetics (27, 38, 44), an approach that has been successfulin describing geochemical contaminant plume dynamics (7). However,lacking a realistic representation of microbial metabolism,such models are limited in their capability of reflecting microbialdynamics and forecasting the response to changing environmentalconditions, which restricts their predictive power at the macroscaleand their usefulness, for example, in the assessment of conditionsthat optimize in situ bioremediation (22).

With the advent of genome sequencing, over the last decade,the biological revolution has led to the characterization ofcellular metabolic networks and to the development of mathematicalmodels at the cell scale (41), ranging from descriptions ofnetwork topology (20, 45) to constraint-based models for differentorganisms (13, 33, 42) and fully kinetic approaches (e.g., seereferences 2, 30, and 50). Integration of such models of environmentallyimportant groups of bacteria in reactive transport simulationswould clearly benefit forecasting biogeochemical responses tochanging macroscopic conditions. The gammaproteobacteria Geobacteraceaeconstitute such an abundant and environmentally important groupin both pristine and contaminated sediment environments (22).Geobacter species are metabolically diverse and can grow withnumerous electron donors and acceptors, including acetate orH₂, and Fe(III), fumarate, or malate, respectively (8, 23).They have been shown to be enriched when Fe(III) reduction ispromoted in a petroleum-contaminated sandy aquifer (39) andto mediate the reduction of U(VI) to U(IV) (25), convertingthe soluble form to the insoluble form and effectively removingthe uranium from the groundwater (51). Geobacter shapes biogeochemicalcycling directly through its metabolic activity, as well asindirectly, such as via the effect of iron (hydr)oxide reductionon the motility of sorbed trace metals and on pH.

In this study, we present a kinetic cell model of Geobactersulfurreducens metabolism and its application in the simulationof a subsurface contaminant plume with the following goals:(i) to assess the kinetic description of central cellular metabolismand the growth efficiencies emerging under a range of substrateconditions by comparing them to observational data; (ii) toquantify the sensitivity of model results to the parameterizationof the enzymatic reactions of the tricarboxylic acid (TCA) cycleand gluconeogenesis considered here; (iii) to compare and contrastdifferent cell model approaches; (iv) to introduce a couplingapproach between cell metabolic expressions and macroscopicreactive transport models; and (v) to assess the potential andthe limits of macroscopic models that parameterize microscopicintracellular processes. Our cell model is validated againstgrowth efficiencies obtained in chemostat experiments (12) andis compared to the flux balance (FB) model developed by Mahadevanet al. (26) who—based on an extensive genome analysis—useda constraint-based modeling approach to estimate steady-stateintracellular fluxes and metabolite exchange with the environment.To assess the role of microbial dynamics in the environment,an acetate plume is studied in a heterogeneous porous medium,for which simulations with a full coupling between the environmentand the cell model are contrasted with several simplified parameterizations,including commonly used Monod approximations.

MATERIALS AND METHODS

Top

MATERIALS AND METHODS

Dynamic cell model.
The dynamic cell model was implemented in the kinetic cell modelsimulator Karyote (31), which divides metabolic reactions intothose that occur at equilibrium (fast reactions) or at a finiterate (slow reactions). For example, a single-substrate isomerizationreaction occurs by the fast formation of an enzyme-substratecomplex ( Formula

) followed by a slow dissociation ( Formula

), where Q_f isthe equilibrium constant for the fast reaction and k and kQ_sare the backward and forward rate constants for the slow reactions,respectively.

Under typical natural subsurface conditions, the oxidation ofacetate in Geobacter—initially activated through the combinedactions of acetate kinase (AK; EC 2.7.2.1) and phosphate acetyltransferase(10)—is coupled to the reduction of Fe(III) (24), whichis believed to take place on the extracellular membrane (21).Thus, the kinetic cell model encompassed the uptake of acetateand its incorporation into biomass via gluconeogenesis or itscomplete oxidation in the TCA cycle (10, 14) (Fig. 1). Two compartments—oneextracellular and the other intracellular—were considered.The extracellular compartment accounted for species concentrationsthat represented environmental conditions, while the intracellularone accounted for enzymatic reactions and resource allocationin cellular metabolism. Reactions were formulated using massaction kinetics:

Formula 1 (1)
where c_i is the concentration of species i, Q_l is the equilibriumconstant, k_l is the backward rate constant for reaction l, ${upsilon}$ _ldenotes stoichiometric coefficients, and N_p and N_r are the numberof products and number of reactants, respectively. Model parameterswere derived from the literature and are given in Table A1.As the literature rarely contains enzymatic forward and reverserate constants, model parameters were typically derived fromenzyme turnover numbers, specific activities, and substrateaffinities. Details of the procedures and sources for modelparameterization are given in the Appendix.

View larger version (68K):
[in this window]
[in a new window]

FIG. 1. Structure of the kinetic cell model and FB models. The kinetic model focuses on the fate of acetate in the metabolism of Geobacter sulfurreducens through incorporation into biomass from gluconeogenesis or energy production from the TCA cycle. All reactions are assumed to be intrinsically reversible, and the rates are computed using the parameter values listed (for data sources, see the Appendix). The FB model is described in a study by Mahadevan et al. (26) and encompasses some 500 reactions and species.

View this table:
[in this window]
[in a new window]

TABLE A1. Values used for the parameterization of the reaction network^f

Sensitivity analysis.
The effect of the uncertainties in reaction rate parametersk and Q on the predicted growth efficiencies was quantifiedover a range of extracellular acetate concentrations by performingcell model simulations with perturbed parameter sets. Parametersk and Q were selected at random from a normal distribution centeredat the literature-derived base value with a 5.7% standard deviation.Sensitivity coefficients, s_j, which constitute a measure ofthe response of the growth efficiency to a change in parameterj, were determined via a multivariate linear regression using

Formula 2 (2)
where g_eff is the growth efficiency,i indicates the i^th random realization, base denotes the baselinesimulation, and j identifies the parameter p_j, set here to thebackward and forward rate constants (k, kQ) and equilibriumconstants for fast reactions (Q_f; see Appendix).

Cellular energy dynamics.
Cellular energy dynamics were accounted for through reactionsutilizing and producing AMP, ADP, and ATP. In addition to theenergy used in the phosphorylation of acetate and pyruvate (Fig.1, reactions 2 and 9), ATP is also produced through the reactionsof the TCA cycle and consumed through cell growth and reactionsrequired for cell maintenance according to the following equation:

Formula 3 (3)
where R_TCA is the overall rateof the TCA cycle, in which every acetate that cycles throughwill ultimately produce 0.5 ATP molecules (26). R_g is the growthrate, and a converts the rate of growth into ATP usage and isset to 19 mol_ATP mol_acetate^–1. It was based on ATP usagein the growth reaction of Mahadevan et al. (26) and modifiedto exclude the growth reactions explicitly accounted for inthe reaction network (Fig. 1). R_m represents ATP consumptionfor cell maintenance, set to 0.45 mmol_ATP per gram of dry weight(g_dw) h^–1 (26), and ${delta}$ _T and ${delta}$ _D reflect the presence of ATPand ADP, respectively (1 if present, 0 otherwise). ATP, ADP,and AMP values were further constrained through a fast exchangeof ATP + AMP = 2ADP that mimicked the balance between adenosinephosphates not modeled at the process level (29). Levels ofother substances involved in intracellular energy regulation,such as NAD-NADH, NADP-NADPH, CO₂, and phosphates (P_i, PP),were assumed to be constant (Fig. 1).

Acetate uptake.
Acetate uptake rates for the kinetic cell model were formulatedusing the four-state model for a facilitated diffusion carrierkinetics (2), in which the flux of acetate across the cell membrane,J_ac (mol liter^–1 s^–1), is described by

Formula 4 (4)
where C_in and C_out are the intracellularand extracellular concentrations (mol liter^–1) of acetate,respectively, V is the cellular volume (liters), A is the cellsurface area (dm²), and h (dm s^–1) describes the transportof acetate across the cell membrane, as described by the followingequation:

Formula 5 (5)
whereK_t is a half-saturation constant (10 µM) (12), Y is themaximum exchange of acetate (dm s^–1), and the symmetryindex ${alpha}$ is set to 0 for symmetric cross-membrane transport ofacetate. Cell area was calculated based on G. sulfurreducenscell size (37), assuming a cylindrical shape. Maximum acetateexchange (Y = 1.20 x 10^–4 dm s^–1) was set to matchthe results from Geobacter chemostat experiments (12).

Growth efficiency was calculated from the acetate uptake fluxand the flux of acetate through phosphoenolpyruvate (PEP) withthe following equation: g_eff = ${alpha}$ _pepβ/J_ac, where ${alpha}$ _pep is themolar concentration of PEP produced per unit of time and βdescribes the grams of dry weight of biomass produced per moleof PEP created. β was calculated from a growth efficiencyof 4.4 x 10^–3 g_dw mmol_acetate^–1 at a cell-specificgrowth rate, µ, of 0.06 h^–1 and an acetate fluxto gluconeogenesis (Q) of 0.30 mol_acetate g_dw^–1 h^–1(26). Taking into account the 2-to-3 acetate-to-PEP carbon ratio,β = 2µ/3Q = 0.3 g_dw mmol_PEP^–1.

Flux balance model.
Cellular metabolic rates under a range of acetate uptake fluxeswere calculated using the FB model of G. sulfurreducens metabolismby Mahadevan et al. (26), which estimated intracellular fluxesand metabolite exchange with the environment for a given acetateuptake. The metabolic fluxes (reaction rates f) were sought,where for a network described by a stoichiometric matrix S,

Formula 6 (6)
implying steady state. The fluxeswere determined via optimizing a specific objective function,which is subjected to physiological constraints on the magnitudeof the fluxes, as follows: lower bound $≤$ f $≤$ upper bound. Maximizationof biomass production rate was used as an objective function,which had been shown to lead to results in agreement with experimentaldata (26). The FB model was implemented in MATLAB, and growthefficiencies were calculated from the ratio of growth rate (f_growth)and acetate uptake (f_ac) as g_eff = f_growth/f_ac.

Coupled environment-cell model.
Representations of Geobacter metabolism were coupled to simulationsof a dynamic environment through incorporation into a reactivetransport model. The two models were connected such that thereactive transport model was used to evaluate the transportof substrate and biomass while the cell model provided the cell-specificreaction rates under the environmental conditions at a giventime and location. These cell-specific rates were then usedto compute the reaction rates in the macroscopic reactive transportmodel. For dissolved constituents, the governing equation is

(7)
where ${phi}$ is porosity, t is time, C is concentration,v is pore water velocity, D* is the dispersion tensor implementedwith dependence on v as described by Scheidegger (36), and ${Sigma}$ Ris the net reaction rate. Flow velocities were computed froman imposed pressure gradient using a Darcy model (40).

In our implementation, the cell model was driven by the availabilityof acetate as the substrate, whose spatiotemporal dynamics proceededvia

(8)

(9)
where T_ac and T_BM denote the transport ofacetate (C_ac) and biomass (C_BM), respectively, due to convectionand dispersion, g_eff is the growth efficiency, Formula 6 is the rate of acetate uptake, and R_ferm is asource of acetate from the breakdown of high-molecular-weightorganics. The model was solved numerically using sequentialnoniterative operator splitting. In each time step, ${Delta}$ t, firstthe pressure and flow field were determined, which were thenused to calculate the net transport for each of the chemicalspecies. Subsequently, concentration changes due to reactionswere evaluated by solving a set of coupled ordinary differentialequations at each node. Reaction parameters that depend on thecell model (i.e., g_eff, Formula 6 ) were computed for a given environmental condition and cell state,reflected by the intracellular concentrations, and were assumedconstant over a time step. Cell death was considered throughnegative growth efficiencies, which were obtained when the ATPproduced did not completely account for cell maintenance demandsand the existing pool of ATP was insufficient to meet the cellularenergy requirements. In that case, the use of biomass resourceswas considered to meet ATP demands (a · R_g; see equation3).

RESULTS AND DISCUSSION

Top

RESULTS AND DISCUSSION

Model comparison and validation.
Experimentally determined growth efficiencies under acetate-limitingconditions are on the order of 4 g_dw mol_acetate^–1 at uptakefluxes of >10 mmol acetate g_dw^–1 h^–1, and theydecrease to 0 at 0.91 mmol g_dw^–1 h^–1 (12). Underreplete substrate conditions, growth efficiencies were similarin the FB model and the kinetic description, yielding resultsconsistent with data at high acetate uptake rates (Fig. 2).The fluxes are consistent with those of ¹³C tracer experimentsobserved in the isotopic data of Tang et al. (43), which showedthat the TCA cycle encompassed $~$ 90% of the acetate uptake flux,with an additional $~$ 8% of acetate flowing through the TCA cyclebeing used for amino acid and lipid production, and the remainderof the acetate uptake flux passed through the pentose-phosphatepathway and gluconeogenesis. Along with the FB model, the kineticmodel predicted that for lower acetate uptake rates, acetateis channeled preferentially into the TCA cycle, leading to lowgrowth efficiency. Both the kinetic and the FB models showednearly identical responses of the TCA cycle to acetate uptake,with a nearly linear increase in the TCA cycle with increasingacetate uptake rates (not shown). Both models reproduced thegeneral trend in growth efficiencies seen in the literatureas a function of the acetate uptake rate (Fig. 2), reflectingthat at elevated uptake rates, the portion of acetate followingthe growth reaction pathway increased relative to that for theTCA cycle.

View larger version (18K):
[in this window]
[in a new window]

FIG. 2. Growth efficiency in g_dw mol_acetate^–1 at a given acetate uptake rate (R_ac^cell) for the cell model, FB model, and measured chemostat data (12). Error bars for the kinetic cell model represent the 25% and 75% quartile ranges, as determined in the sensitivity analysis (see the text). Inset: Acetate uptake flux at a given extracellular acetate concentration computed with the kinetic model along with measured data (chemostat data depicted with filled rectangles indicate measured acetate concentrations below the detection limit of 10 µM).

In contrast to the FB approach, which does not contain informationon intracellular concentrations or provide an explicit connectionto extracellular substrate levels, the kinetic model mechanisticallyrelates intracellular process rates to extracellular concentrationsof acetate. Its results can therefore be parameterized as afunction of acetate availability and provide an explicit linkbetween intracellular processes and extracellular conditions.At low extracellular acetate concentrations (µM), acetateuptake responds strongly to changes in substrate availability(Fig. 2, inset). Assuming Michaelis-Menten kinetics, Formula 6 , and using steady-state cell modelresults, one obtained v_max = (19.54 ± 0.04) mmol_ac g_dw^–1h^–1 and K_m(acetate) = (10.24 ± 0.11) x 10^–6mol liter^–1, consistent with half-saturation constantsand maximum uptake rates derived from experimental data (12).

The kinetic model also provides estimates of intracellular metaboliteconcentrations, which can be used as diagnostics to experimentallyassess its validity and limitations. Under steady-state conditions,the cell model predicted malate concentrations in the mM range,consistent with predictions of high malate concentrations basedon the thermodynamics of the malate dehydrogenase reaction (5).Several other substances, including oxaloacetate, citrate, isocitrate,and succinate were predicted—depending on growth conditions—tobe present in the micro- to millimolar range and to increaseby a factor of 10 to 30 between no-growth and maximum-growthconditions. Succinyl coenzyme A (CoA) concentration was predictedto be relatively constant, while significant variations underchanging growth conditions were computed for pyruvate and ${alpha}$ -ketoglutarate,with lower concentrations at higher growth rates.

Model sensitivity.
The sensitivity analysis based on $≥$ 1,000 realizations for a givenextracellular acetate concentration, which was sufficient toestablish the probability distribution of the model response,allowed the identification of the reactions affecting growthefficiency most strongly (Fig. 3). The extent to which a parameteraffected growth efficiency varies with the acetate uptake rate.For example, at low acetate uptake rates, growth efficiencywas most sensitive toward parameters describing the acetate-CoAtransferase (ACT; EC 2.8.3.8) reaction. In general, however,growth efficiency, over the range of acetate uptake rates, wasmost sensitive to cell model parameters associated with theactivation of acetate to acetyl-P catalyzed by AK (Fig. 3),a reaction essential to the use of acetate in biomass production,as all acetate incorporated into cell biomass must go throughthis reaction (26). Increasing the forward rate constant k_f—correspondingto an increase in enzyme concentration (E_T), maximum enzymeactivity (v_max), or higher substrate affinity (lower K_m)—involvedin the reaction catalyzed by citrate synthase (CS; EC 2.3.3.1)decreased growth efficiencies as more acetyl-CoA is shiftedto the TCA cycle. For the same reason, increasing the parametersassociated with the reaction catalyzed by succinate dehydrogenase(SDH; EC 1.3.99.1) resulted in a decrease in growth efficiency,and increasing parameters associated with pyruvate ferredoxinoxidoreductase (PFO; EC 1.2.7.1), a reaction involved in growth,resulted in an increase in growth efficiency. The variationin growth efficiency due to small—on the order of 5%—variationsin forward and backward reaction rate constants can largely(>95%) be explained by the linear model (equation 2). Uncertaintiesin E_T, v_max, and K_m, however, tend to result in larger uncertaintiesin growth efficiencies due to error propagation, but the samereactions are found to have the most decisive impact (not shown).

View larger version (30K):
[in this window]
[in a new window]

FIG. 3. Sensitivity, s_j, of growth efficiencies to perturbations in the cell model parameters as a function of acetate uptake rates (equation 2). Labels AK, CS, ACT, SDH and PFO along the bottom of the figure denote the reactions promoted by the respective enzymes (see Fig. 1). k_b, k_f, and Q values denote the model parameters. Large absolute values of s_j indicate a strong impact of a model parameter on resulting growth efficiencies (see the text for details).

Environmental setting.
Reactive transport models often do not—or only in a simplisticmanner—reflect microbial population dynamics (22). Toassess the importance of dynamically resolving cellular metabolism,where the rates depend on both extracellular and intracellularconcentrations, reactive transport simulations with the fullkinetic cell model (model I) were compared with three parameterizedversions. The first used a lookup table established from steady-stateruns of the kinetic cell model so that cell-specific rates wereexpressed as a function of extracellular conditions, but itdid not take into account intracellular dynamics and assumedthat intracellular metabolite concentrations have reached asteady state. Because computed intracellular metabolite concentrations(at least at the level resolved in the kinetic cell model) adjustedto changes in substrate availability over timescales in seconds,consistent with observed intracellular dynamics in bacteria(e.g., see reference 35), the results from the steady-statecell model were virtually indistinguishable from those of modelI and are hence not shown separately. The second implementation(model II) simplified the approach further, to a level typicallyused in reactive transport models, assuming that cell-specificgrowth efficiency (g_eff; equations 8 and 9) is constant andthat acetate uptake ( Formula 6 ; equations 8 and 9) can be expressed by Monod kinetics, with K_m(acetate)= 10.24 µM and v_max = 19.54 mmol g_dw^–1 h^–1,as derived above. Finally, a third approximation employed botha constant growth efficiency and a constant acetate uptake rateas long as acetate was present (model III), with a cell-specificacetate uptake rate of 9 x10^–3 mol_acetate g_dw^–1h^–1 and a growth efficiency of 3.3 g_dw mol_acetate^–1(12).

In order to quantify the impact of microbial dynamics and thesubstrate dependence of growth efficiencies under environmentalconditions, simulations were performed in a domain that was10 cm long and 6 cm high. The porous medium consisted of permeablesand (k = 10^–11 m²) into which a less permeable sectionwas embedded (k = 10^–13 m²) as depicted in Fig. 4. No-flowconditions were set at the upper and lower domain boundaries,and a positive pressure gradient was imposed across the horizontalx-direction. The inflowing fluid was set to contain 0.76 µMacetate and 0.03 g_dw m^–3 biomass. After a period of constantinput that allowed the establishment of a steady substrate andbiomass distribution, the concentrations in the inflowing fluidwere ramped up over a duration of 1 h to an inflow concentrationof 1 mM acetate and 0.3 g_dw m^–3 biomass, reflecting aplume of dissolved organic carbon (16), and were held constantat high levels thereafter.

View larger version (46K):
[in this window]
[in a new window]

FIG. 4. Results of reactive simulations utilizing different representations of bacterial growth and acetate uptake. Steady-state acetate and biomass distributions under low (panels A to F) and high (panels G to L) input conditions for the dynamic cell model (panels A, B, G, and H), the Monod parameterization (panels C, D, I, and J), and simulations with fixed growth efficiency and acetate uptake rate (panels E, F, K, and L). The low-permeability zone is indicated by the boxes with dashed-line borders, and the arrows in panel A indicate the direction and magnitude of flow.

Steady-state biomass and acetate distributions under pristineconditions showed distinct differences between the various models.For all representations, relatively low, uniform biomass distributionswere observed (Fig. 4B, D, and F). However, the fixed uptakeand growth efficiency formulation (model III) predicted spatiallyvarious acetate concentrations, with lower levels in the low-permeabilityzone (Fig. 4E). This drawdown was caused by the slightly elevatedbiomass concentrations in that region (Fig. 4F), because thisapproximation contains no feedback between substrate level andthe allocation of acetate to growth versus catabolism that wouldlower uptake rates at low substrate availability. Results frommodel II (Fig. 4A and C) closely matched those from model I(Fig. 4B and D), despite that at low acetate concentrations,the Monod approximation and cell model differed in their growthefficiency. This is because at low acetate levels, cell-specificacetate uptake rates are low. In addition, the Monod model doesnot take into account cell death, which, when included, becameimportant for regulating biomass levels in the pristine settingat cell death rates on the order of 10% of the growth rate (notshown).

Steady high substrate input stimulated microbial growth, reflectedin the elevated biomass levels in both high- and low-permeabilityregions (Fig. 4H, J, and L). A clear distinction was visiblebetween the results obtained with the dynamic cell model andthe Monod approximations compared to the fixed growth efficiencydescription. The latter predicted biomass levels ranging from0.3 to 1.2 g_dw m^–3 in the low-permeability zone (Fig.4L), while the kinetic models suggested a region of higher biomassin the low-permeability zone adjacent to the more-permeableone (Fig. 4H and J). In the models that represented the cellin more detail, the maximum growth efficiencies exceeded theconstant average value in the "fixed" model, leading to a buildupof biomass and the depletion of acetate in the low-permeabilityzone. The Monod parameterized model suggested acetate levelsthat are similar to those for the cell model (Fig. 4G and I).The cell model predicted the depletion of biomass in those low-permeabilityregions that exhibited low acetate concentrations (Fig. 4H).This pattern was less pronounced in the Monod model, which asa result of the missing feedback of substrate availability ongrowth efficiencies showed elevated biomass levels even whereacetate levels approached zero (Fig. 4I and J).

Conclusion.
The kinetic representation of Geobacter sulfurreducens centralmetabolism, encompassing its TCA cycle and the use of pyruvatein gluconeogenesis, successfully reproduces measured growthefficiencies, with iron as electron acceptor over a wide rangeof extracellular acetate concentrations. Despite its limitedscope, it predicts process rates that are in good agreementwith results from a comprehensive FB model (26), as it includesfeedback between metabolite levels and transformation rateswhich can accurately regulate the response over a range of substrateconditions.

The two main differences between these two modeling approachesare the extents of the network considered and the fact thatthe kinetic description provides explicit estimates of intracellularmetabolite concentrations. The more comprehensive descriptioninherent in FB models—possible because they do not requireextensive parameterization—is an advantage as, intrinsically,it extends the range of applicability well beyond the acetate-limitedenvironmental settings discussed here. However, the computationof metabolite levels in the kinetic approach allows for a mechanisticprocess description linking intracellular conditions to environmentalconditions. In contrast, the FB approach requires a priori knowledgeof uptake fluxes, which may restrict its use to settings atwhich they are constrained by experimental data.

While comparison of the fully coupled reactive transport modelwith the Monod type simulations shows that it is possible toapproximate microbial distribution patterns without the explicitincorporation of cell models into reactive transport simulations,the parameterization has to reflect the response of intracellularprocesses. Process-level descriptions of microbial metabolismgive rise to emerging properties, such as growth efficiencies,that are critical in the incorporation of microbial dynamicsin reactive transport models. Hence, models aiming at describingin situ microbial functioning and at accounting for environmentalfeedbacks can benefit substantially from reflecting the growingknowledge on cellular metabolism, which in turn will bolsterthe predictive power necessary for their broad application.

APPENDIX

Top

APPENDIX

To derive estimates of rate and equilibrium constants requiredin the model, literature data were mined and converted intothe format required for the cell model. Whenever available,enzyme turnover numbers were used, as they represent a measurementof kQ_s (s^–1). However, this parameter was not often available,so kQ_s values were derived from reported Geobacter enzymaticspecific activities. Specific activity from pure enzyme extractwas converted into a forward rate constant, kQ_s (s^–1),by

Formula A1 (A1)
where SA_pure(mol^–1 g_enzyme^–1) is the specific activity measuredfrom the pure enzyme extract and MW is the molecular weightof an enzyme subunit (g mol^–1). Specific activity measuredfrom the crude enzyme fraction was converted into an in situv_max (mol liter^–1 s^–1) value, as described by Albeet al. (1) by using

Formula A2 (A2)
where SA_crude (mol s^–1 g_protein^–1) is measured fromthe crude enzyme fraction, f_prot is the fraction of cell biomassthat is protein, determined to be 0.46 (26), g_bm is grams ofdry weight of biomass per cell, determined to be 40 fg, andV_cell is the cell volume, determined to be 4.91 x 10^–16liters, calculated based on G. sulfurreducens cell size (37)assuming a cylindrical shape. This v_max value was convertedto kQ_s for implementation into Karyote (31) according to

Formula A3 (A3)
where E_T is the total enzymeconcentration. The parameter, kQ_s, was converted into k andQ_s values for implementation of the slow reaction dynamics intothe cell model. Values of Q_s were calculated according to

Formula A4 (A4)
where Q_T is the equilibriumconstant for the overall net reaction based on thermodynamicdata, obtained from a study by Goldberg et al. (15), and Q_fiis the equilibrium constant for the ith fast reaction in eachmechanism. Equilibrium constants for the fast reactions—andslow reactions when no thermodynamic data were available toestimate Q_T—were determined from

Formula A5 (A5)
where C_k represents the equilibrium concentrationof species k in reaction i in the enzyme mechanisms below, andv_ik is its stoichiometric coefficient (positive for products,negative for reactants).

Concentrations of enzyme substrate complexes used in equationA5 are not measured directly and were calculated according toeach enzyme's mechanism, which is separated into several fastcomponents and one slow component (32):

Formula A5

The enzyme substrate concentrations in the slow reactions werecalculated following Purich and Allison (32):

isomerization reaction

Formula A6 (A6)

ordered bi-bi reaction

Formula A7 (A7)

ping-pong reaction

Formula A8 (A8)

tri-ping-pong reaction

Formula A9 (A9)
where [S₁], [S₂], and [S₃] are the typical cell concentrationsof the first, second, and third substrates to bind with theenzyme, respectively, and Km₁, Km₂, and Km₃ are the half-saturationconstants for substrates 1, 2, and 3, respectively. The enzymesubstrate complexes involved in the fast reactions were thencalculated according to equations A10 to A16, as follows:

for enzymes that employ an ordered bi-bi mechanism,

Formula A10 (A10)

for enzymes that employ a ping-pong mechanism,

Formula A11 (A11)

Formula A12 (A12)

for a tri-ping-pong mechanism,

Formula A13 (A13)

Formula A14 (A14)

Formula A15 (A15)

Formula A16 (A16)
where ES represents the enzyme substratecomplexes, Km_i the half-saturation constant of the ith substrate,Km_p₁ the half-saturation constant for the ith product released,S_j the jth substrate in the enzymatic reaction, and P_j the jthproduct released. As the determination of Q_s values is subjectto considerable uncertainties and does not take into accountchemical speciation in the highly complex intracellular fluid,all values were adjusted by a factor of 100, which led to TCAcycle rates consistent with observations.

The values used for the parameterization of the reaction networkare shown in Table A1.

ACKNOWLEDGMENTS

This work was supported by the Department of Energy Office ofScience grant DE-FG02-05ER25676.

We thank two anonymous reviewers, whose comments significantlyimproved the manuscript.

FOOTNOTES

* Corresponding author. Mailing address: Department of Marine Sciences, University of Georgia, Athens, GA 30602-3636. Phone: (706) 542-6549. Fax: (706) 542-5888. E-mail: cmeile{at}uga.edu

Published ahead of print on 14 November 2008.

REFERENCES

Top