Abstract
Methanogenic archaea occupy a unique and functionally important niche in the microbial ecosystem inhabiting the gut of mammals. The purpose of this work was to quantitatively characterize the dynamics of methanogenesis by integrating microbiology, thermodynamics and mathematical modelling. For that, in vitro growth experiments were performed with key methanogens from the human and ruminant gut. Additional thermodynamic experiments to quantify the methanogenesis heat flux were performed in an isothermal microcalorimeter. A dynamic model with an energetic-based kinetic function was constructed to describe experimental data. The developed model captures efficiently the dynamics of methanogenesis with concordance correlation coefficients between observations and model predictions of 0.93 for CO2, 0.99 for H2 and 0.97 for CH4. Together, data and model enabled us to quantify species-specific metabolism kinetics and energetic patterns within the group of cytochrome-lacking methanogenic archaea. Using a theoretical exercise, we showed that kinetic information only cannot explain ecological aspects such as microbial coexistence occurring in gut ecosystems. Our results provide new information on the thermodynamics and kinetics of methanogens. This understanding could be useful to (i) construct novel gut models with enhanced prediction capabilities and (ii) devise feed strategies for promoting gut health in mammals and mitigating methane emissions from ruminants.
Introduction
Methanogenic archaea inhabit the gastro-intestinal tract of mammals where they have established syntrophic interactions within the microbial community (1–3) and thus play a critical role in the energy balance. In the human gut microbiota, implication of methanogens in organism homeostasis or diseases is poorly studied, but of growing interest. Methanobrevibacter smithii (accounting for 94% of the methanogen population) and Methanosphaera stadtmanae are specifically recognized by the human innate immune system and contribute to the activation of the adaptive immune response (4). Decreased abundance of M. smithii was reported in inflammatory bowel diseases patients (5), and it has been shown that methanogens may contribute to obesity (6). In the rumen, the methanogens community is more diverse though still predominated by Methanobrevibacter spp., followed by Methanomicrobium spp., Methanobacterium spp. (7) and Methanomassillicoccus spp (8). However, the proportion of these taxa could vary largely, with Methanomicrobium mobile and Methanobacterium formicium being reported as major methanogens in grazing cattle (9). Though methanogens in the rumen are essential for the optimal functioning of the ecosystem (by providing final electron acceptors), the methane they produce is emitted by the host animal and contributes to global greenhouse gas emissions. Livestock sector is responsible for 14.5 of the anthropogenic greenhouse gas emissions (10). Some Methanobrevibacter-related taxa, as M. smithii, M. gottschalkii, M. milerae and M. thaueri correlated with higher methane production, whereas M. ruminantium was 1.3 fold more abundant in low emitters (11). Methanogens, in general, are phylogenetically and metabolically diverse, but could be separated in two groups based on the presence or absence of cytochromes (12). Most methylotrophic and few hydrogenotrophic methanogens possess membrane-associated cytochrome receiving reducing equivalents from a methanogen specific electronic shuttle, which creates a membrane potential for ATP generation. Major rumen methanogens (13) and the dominant human archaeon, M. smithii (14), are hydrogenotrophic without cytochrome. Cytochrome-lacking methanogens exhibit lower growth yields than archaea with cytochromes (e.g. aceticlastic methanogens) (12). However, this apparent energetic disadvantage has been counterbalanced by a great adaptation to the environmental conditions (15), and by the establishment of syntrophic interactions with other microbes within the orchestration of the degradation and further fermentation of feed. This syntrophic cooperation centred on the transfer and utilization of hydrogen makes possible anaerobic reactions of substrate conversion to take place close to thermodynamic equilibrium (16,17) (that is with Gibbs free energy change close to zero).
To our knowledge, the impact of thermodynamics on human gut metabolism has been poorly addressed in existing mathematical models (18–21). For the rumen, due to the important role of thermodynamic control on the fermentation, research teams have been motivated in addressing the question of incorporating thermodynamic principles into mathematical models (22–27). Despite these relevant efforts, much work remains to be conducted for attaining a predictive thermodynamic-based model that allows for quantitative assessment of the impact of the thermodynamics on fermentation dynamics. Theoretical frameworks have been developed to allow stoichiometric and energetic balances of microbial growth from the specification of the anabolic and catabolic reactions of microbial metabolism (28,29), and advances have been done to link thermodynamics to kinetics (30–32). These works constitute a solid basis for tackling the thermodynamic modelling of gut metabolism. In this respect, new knowledge on the extent of methanogenesis could help to improve existing gut models. Accordingly, our purpose was to quantitatively characterize the dynamics of hydrogen utilization, methane production, growth and heat flux of three hydrogenotrophic methanogens by integrating microbiology, thermodynamics, and mathematical modelling. We investigated the rate and extent of methanogenesis by performing in vitro experiments with three methanogenic species representing major human and ruminant genera: M. smithii, M. ruminantium and Methanobacterium formicium. To interpret and get the most out of the resulting data, a mathematical model with thermodynamic basis was developed to describe the dynamics of the methanogenesis.
Material and Methods
In vitro growth experiments
Archaeal strains and growth media
Archaeal strains used in the study were Methanobrevibacter ruminantium DSM 1093, M. smithii, and Methanobacterium formicium. The growth media was prepared as previously described (33) and composition is summarized in Table S1 of the Supplementary material. Rumen fluid, that was the main constituent of the culture medium, was sampled through the rumen cannula from a grazing dairy cow prior to the beginning of the experiment. Sampled rumen contents were firstly strained through a monofilament cloth and then centrifuged at 5 000 g for 15 min. Supernatant was autoclaved and then centrifuged again in the same conditions. Clarified rumen fluid was stored at −20°C and centrifuged again after thawing prior to media preparation. Media was boiled to expel dissolved oxygen, a reducing agent (L-cystein) and a redox indicator (resazurin) were added to keep a low redox potential and indicate the oxidative state of the medium respectively. Growth media was distributed in Balch tubes (6 ml per tube), tubes were sealed and sterilized by autoclaving at 121°C for 20 min. Media preparation and distribution was realized under CO2 flushing to assure anoxic conditions. Oxygen traces from commercial gases were scrubbed using a heated cylinder containing reduced copper (33).
Experimental design and measures
Starter cultures were grown until reaching optical density at 660 nm (OD660) of 0.400 ± 0.030. Optical density was measured on a Jenway spectrophotometer. Then, exactly 0.6 ml were used to inoculate one experimental tube. Commercially prepared high purity H2/CO2 (80%/20%) gas mix was added to inoculated tubes by flushing for 1 min at 2.5 Pa. Mean initial OD660 and pressure values are summarized in Table S2 of the Supplementary material. Growth kinetics for each strain were followed over 72 h. The experiment was repeated twice. Each kinetics study started with 40 tubes inoculated in the same time. At a given time point, two tubes with similar OD660 values were sampled. One of the tubes was used for measuring gas parameters: pressure was measured using a manometer and composition of the gas phase was analysed by gas chromatography on a Micro GC 3000A (Agilent Technologies, France).
Microcalorimetry
Microcalorimetric experiments as described by Bricheux et al. (34) were performed to determine the heat flux pattern of each methanogen. Metabolic activity and microbial growth were monitored by using isothermal calorimeters of the heat-conduction type. A TAM III (TA Instruments, France) equipped with two multicalorimeters, each holding six independent microcalorimeters, allowed continuous and simultaneous recording as a function of time of the heat flux produced by 12 samples. The bath temperature was set at 39°C; its long-term stability was better than ± 1×10-4 °C over 24h. Each microcalorimeter was electrically calibrated. The specific disposable 4 mL microcalorimetric glass ampoules capped with butyl rubber stoppers and sealed with aluminum crimps were filled with 1.75 mL of Balch growth media and overpressed with 2.5 Pa of H2/CO2 80%/20% gas mixture for 30 s. They were sterilized by autoclave and stored at 39°C until the beginning of the microcalorimetric measurements. Actively growing cultures of methanogens (OD660 of 0.280±0.030 for M. smithii, 0.271±0.078 for M. ruminantium and 0.142±0.042 for M. formicium) were stored at −20°C prior to their injection into the microcalorimetric ampoules. Inoculation was carried out by injecting 0.25 mL of the culture through the septum just before insertion of the overpressed ampoule containing Baltch media into the minicalorimeter. After insertion of the ampoule the sample took about two hours to reach the bath temperature and yield a heat flux equilibrated at zero. Blank experiments were also carried out by inserting ampoules that were not inoculated and, as expected, no heat flux was observed confirming the medium sterility. Each experiment was repeated five times.
The heat flux , also called thermal power output P, was measured for each methanogen and the blank samples with a precision ≥ 200 nW. The heat flux data of each sample were collected every 5 minutes during more than 10 days. The total heat Q was obtained by integrating the overall heat flux– time curve using the TAM Assistant Software and its integrating function (TA Instruments, France).
Classically, the heat flux-time curve for a growing culture starts like the S-shaped biomass curve (a lag phase followed by an exponential growth phase) but differs beyond the growth phase, the heat flux being then modulated by transition periods (34). Heat flux data can be used to infer the microbial growth rate constant. Such inference must be done with caution, since under certain conditions detailed by Braissant et al. (35) lack of correlation occurs between heat flux and microbial growth. The authors suggest that the correlation between isothermal microcalorimetry data and microbiological data (e.g., cell counts) exist at early growth. During the exponential growth phase, microbial growth follows a first-order kinetics defined by the specific growth rate constant μc(h−1). Analogously, the heat flux follows an exponential behaviour determined by the parameter μc as described by (34,35).
The growth rate constant μc can be determined by fitting the exponential part of the heat flux-time curve using the fitting function of the TAM Assistant Software. In our case study, careful selection of the exponential phase of heat flux dynamics was performed to provide a reliable estimation of the maximum growth rate constant from calorimetric data.
Mathematical model development
Modelling in vitro methanogenesis
The process of in vitro methanogenesis is depicted in Figure 1. The H2/CO2 mixture in the gas phase diffuses to the liquid phase. The H2 and CO2 in the liquid phase are further utilized by the mono-culture of rumen methanogens producing CH4. Methane in the liquid phase diffuses to the gas phase.
Model construction was inspired on our previous dynamic model of rumen in vitro fermentation (36) followed by certain simplifications. Due to the low solubility of hydrogen and methane (37), liquid-gas transfer was only accounted for carbon dioxide. To allow thermodynamic analysis, instead of using the Monod equation in the original formulation, we used in the present work the kinetic rate function proposed by Desmond-Le Quéméner and Bouchez (38). The resulting model is described by the following ordinary differential equations Where is the concentration (mol/L) of carbon dioxide in the liquid phase and is the biomass concentration (mol/L) of hydrogenotrophic methanogens. The number of moles in the gas phase are represented by the variables . The gas phase volume Vg = 20 mL and the liquid phase volume VL = 6 mL. Liquid-gas transfer for carbon dioxide is described by a non-equilibria transfer rate which is driven by the gradient of the concentration of the gases in the liquid and gas phase. The transfer rate is determined by the mass transfer coefficient kLa (h-1) and the Henry’s law coefficients (M/bar). R (bar∙(M ∙ K)-1) is the ideal gas law constant and T is the temperature (K). Microbial decay is represented by a first-order kinetic rate with kd (h-1) the death cell rate constant. Microbial growth was represented by the rate function proposed by Desmond-Le Quéméner and Bouchez (38) using hydrogen as the limiting reactant where μ is the growth rate (h-1), μmax (h-1) is the maximum specific growth rate constant and Ks(mol/L) the affinity constant. Equation (7) is derived from energetic principles following Boltzmann statistics and uses the concept of exergy (maximum work available for a microorganism during a chemical transformation). The affinity constant has an energetic interpretation, since it is defined as where Edis (kJ/mol) and EM (kJ/mol) are, respectively, the dissipated exergy and stored exergy during growth, Ecat (kJ/mol) is the catabolic exergy of one molecule of energy-limiting substrate, and υharv is the volume at which the microbe can harvest the chemical energy in the form of substrate molecules (38). Ecat is the absolute value of the Gibbs energy of catabolism (ΔGr,c) when the reaction is exergonic (ΔGr,c<0) or zero otherwise. The stored exergy EM is calculated from a reaction (destock) representing the situation where the microbe gets the energy by consuming its own biomass. EM is the absolute value of the Gibbs energy of biomass consuming reaction (ΔGr,destock) when the reaction is exergonic (ΔGr,destock<0) or zero otherwise. Finally, the dissipated exergy Edis is the opposite of the Gibbs energy of the overall metabolic reaction, which is a linear combination of the catabolic and destock reactions. This calculation follows the Gibbs energy dissipation detailed in Kleerebezem and Van Loosdrecht (39).
In our model, the stoichiometry of methanogenesis is represented macroscopically by one catabolic reaction (R1) for methane production and one anabolic reaction (R2) for microbial formation. It was assumed that ammonia is the only nitrogen source for microbial formation. The molecular formula of microbial biomass was assumed to be C5H7O2N (37).
In the model, the stoichiometry of the reactions is taken into account via the parameters Y, , , which are the yield factors (mol/mol) of microbial biomass, CO2 and CH4. The fraction of H2 utilized for microbial growth (reaction R2) is defined by the yield factor Y. Now, let f be the fraction of H2 used for the catabolic reaction R1. It follows that
The yield factors of CO2 and CH4 can be expressed as functions of the microbial yield factors:
The model has two physicochemical parameters (kLa, ) and four biological parameters (μmax, Ks, Y, kd). The initial condition for is unknown and was also included in the parameter vector for estimation. The Henry’s law coefficients are known values calculated at 39°C using the equations provided by Batstone et al. (37).
Theoretical model to study interactions among methanogens
To investigate the ecology of methanogens in the gut ecosystem, we considered a toy model based on the previous model for in vitro methanogenesis. Let us consider the following simple model for representing the consumption of hydrogen by the methanogenic species i under an in vivo scenario of continuous flow where is the flux of hydrogen produced from the fermentation of carbohydrates. The kinetic parameters are specific to the species . The parameter Di (h-1) is the dilution rate of the methanogens and b (h-1) is an output rate constant. Extending the model to n species with a common yield factor Y, the dynamics of hydrogen is given by where the sub index i indicates the species. In our case study, n = 3.
Parameter identification
Before tackling the numerical estimation of the model parameters, we addressed the question of whether it was theoretically possible to determine uniquely the model parameters given the available measurements from the experimental setup. This question is referred to as structural identifiability (40). Structural identifiability analysis is of particular relevance for model whose parameters are biologically meaningful, since knowing the actual value of the parameter is useful for providing biological insight on the system under study (41). Moreover, in our case, we are interested in finding accurate estimates that can be further used as priors in an extended model describing the in vivo system.
We used the freely available software DAISY (42) to assess the structural identifiability of our model. Physical parameters (kLa, ) were set to be known. The model was found to be structurally globally identifiable. In practice, however, to facilitate the actual identification of parameters and reduce practical identifiability problems such as high correlation between the parameters (43), some model parameters were fixed to values reported in the literature. The transport coefficient kLa, the Henry’s law coefficient , and the dead cell rate constant kd were set to be known and were extracted from Batstone et al. (37). Analysis of the data led us to consider the microbial yield factor Y to be the same for all the methanogens. The yield factor was set to be known and its value was taken from Thauer et al. (12) for cytochrome lacking methanogens. Therefore, only the parameters μmax, Ks were set to be estimated. To capitalize on the calorimetric data, we further assumed that the specific rate constant (μc) estimated from the heat flux-time curve is close to the maximal growth rate constant μmax of the kinetic function developed by Desmond-Le Quéméner and Bouchez (38). By this, only the affinity constant for each strain was left to be estimated.
The parameter identification of the affinity constant for each methanogen was performed with the IDEAS Matlab® toolbox (44), which is freely available at http://genome.jouy.inra.fr/logiciels/IDEAS. IDEAS uses the maximum likelihood estimator that minimizes the following cost function. where ny is the number of measured variables and nt, kthe number of observation times for the kth variable yk, and is the kth variable predicted by the model. The model output is function of the parameter vector p. The measured variables are the number of moles in the gas phase (H2, CH4, CO2). The Lin’s concordance correlation coefficient (CCC) (Lin, 1989) was computed to quantify the agreement between the observations and model predictions.
Results
Calorimetric pattern of methanogens
Figure 2 displays a representative isothermal calorimetric curve for each methanogen. The five measured heat flux dynamics of each methanogen were found to follow similar energetic patterns. M. smithii and M. formicium exhibited a lag phase of a few hours, while M. ruminantium was already metabolically active when introduced into the minicalorimeter though several attempts were made to obtain a lag phase by changing storage conditions and thawing the culture just before inoculating the microcalorimetry vials. The pattern of heat flux for all tested methanogens is characterized by one predominant peak which was observed at different times for each methanogen. M. smithii exhibited a second metabolic event occurring at 60 h with an increase of heat flux. The same phenomenon is observed for M. formicium but at lower intensity at 140 h. One possible explanation for this event is cell lysis (35). At the end of the process, heat flux ceased as result of the end of the metabolic activity. Figure 2 shows a small peak for M. formicium at 14 h (a similar peak, but of much smaller size, was observed on the four other curves obtained with this methanogen). M. smithii also exhibits a small peak at 7 h that is difficult to visualize at the scale of Figure 2 (the occurrence of this tiny peak was 5 out 5). For M. ruminantium, we do not know whether the tiny peak exists since the initial part of the curve is missing. This small peak translates in a metabolic activity that remains to be elucidated.
The total heat (Qm) produced during the methanogenesis process that took place under the present experimental conditions was, on average, −5.5 J for the three methanogens (for M. ruminantium, the missing initial part of the heat flux-time curve was approximately estimated by extrapolating the exponential fit). As we shall see below, this experimental value is consistent with the theoretically expected value.
Estimation of thermodynamic properties
Enthalpies
We defined two macroscopic reactions to represent the catabolism (R1) and anabolism (R2) of the methanogenesis (see Material and Methods). The heat produced during methanogenesis results from the contribution of both catabolic and anabolic reactions. So, first, we calculated the standard enthalpies of the catabolic and anabolic reactions using the standard enthalpies of formation given in Table 1 for the different compounds involved in methanogenesis. The standard enthalpy of the catabolic reaction was calculated as follows
A similar equation was used for the calculation of the standard enthalpy of the anabolic reaction
These results are at 25°C since this is the temperature of the standard enthalpies of formation reported in Table 1. A correction could be made to get results at 39°C but the heat capacities reported by Wagman et al. (45) show that the temperature correction can be neglected. Next, we considered the fact that the heat of a given reaction can be calculated at any state along the reaction pathway via the determination of the reaction coordinate or degree of advancement ε (46). At constant temperature and pressure, the heat produced or consumed by a particular reaction during a given interval can indeed be calculated as follows
For our two reactions, at the instant t we have where is the number of moles of hydrogen at the instant t, is the initial number of moles of hydrogen, and f is the fraction of H2 used for the catabolic reaction. Our calorimetric experiments started with mol in all cases. At the final time tf, all the hydrogen was consumed, so that . As indicated in section Parameter Identification, we use the microbial yield factor Y given by Thauer et al. (12) for cytochrome lacking methanogens, that is Y=0.006 which implies that f =0.94. Accordingly, εc = 2.075 ∙ 10−5 mol and εa = 5.30 ∙ 10−7 mol. It thus follows that the overall heat produced during the methanogenesis process (Qm) can be calculated using the following equation where Qc, Qa are the heat produced during catabolism and anabolism respectively. Equation (21) can also be written as
Under the experimental conditions, this yields
This shows that the anabolic reaction contributes to only 7% of the metabolic heat. It is also interesting to note that there is a very good agreement between the theoretical value calculated above and the overall heat experimentally determined by microcalorimetry (−5.5 J).
Since the substrate was totally consumed, the enthalpy of the methanogenesis process per mole (or C-mol) of biomass formed, ΔHm, can be calculated as follows which yields
Gibbs energies and entropies
Following a procedure analogous to the one used above for the enthalpies, the standard Gibbs energies of the catabolic () and anabolic () reactions were calculated using the standard Gibbs energies of formation listed in Table 1.
The free energy of the methanogenesis process per mole (or C-mol) of biomass formed, ΔGm, can then obtained from the following equation which yields
Knowing that, at constant temperature and pressure, it follows that the entropic contribution to the methanogenesis process is equal to which gives, at 39°C, the following value for the entropy of the methanogenesis process per mole (or C-mol) of biomass formed
In Table 2, the changes in Gibbs energy, enthalpy and entropy observed here during methanogenesis of M. ruminantium, M. smithii and M. formicium on H2/CO2 are compared with values found in the literature for other methanogens grown on different substrates.
Dynamic description of in vitro kinetics
The developed mathematical model was calibrated with the experimental data from in vitro growth experiments in Balch tubes. Table 3 shows the parameters of the dynamic kinetic model described in Equations 2-6. The reported value of μmax for each methanogen corresponds to the average value obtained from five heat flux-time curves. From Table 3, it is concluded that M. smithii exhibited the highest growth rate constant, followed by M. ruminantium and finally M. formicium. In terms of the affinity constant Ks, while M. smithii and M. ruminantium have a similar value, the affinity constant for M. formicium is lower in one order of magnitude.
Figure 3 displays the dynamics of the compounds in the methanogenesis for the three methanogens. Experimental data are compared against the model responses. Table 4 shows standard statistics for model evaluation. The model captures efficiently the overall dynamics of the methanogenesis. Hydrogen and methane are very well described by the model with concordance correlation coefficients (CCC) of 0.99 and 0.97 respectively. For carbon dioxide, CCC = 0.93.
Figure 4 displays the dynamics of OD600 for the methanogens. To infer microbial biomass produced in the anabolic reaction, we used to the data from methane instead of OD600 to avoid possible bias due to species-specific absorbance properties of the methanogens. The maximal production of methane among the three microbes was 0.36 mmol for M. smithii and 0.33 mmol for M. ruminantium and M. formicium, which gives an average value of 0.35 ±0.017 mmol (the standard deviation is 3.7% of the mean). This value is fully in agreement with the theoretical value of 0.37 mmoles derived from 1.48 mmol of H2 (average number of moles at t0) and a yield factor of 0.006. The agreement between the actual methane produced and the theoretical one confirms our hypothesis of considering the same yield factor for all the three methanogens. For our experiment in Balch tubes, approximately 0.009 mmol (1.02 g) of microbial biomass were produced.
Discussion
Our objective in this work was to quantitatively characterize the dynamics of hydrogen utilization, methane production, growth and heat flux of three hydrogenothropic methanogens by integrating microbiology, thermodynamics and mathematical modelling. Our model developments were instrumental to quantify energetic and kinetic differences between the three methanogens studied, strengthening the potentiality of microcalorimetry as a tool for characterizing the metabolism of microorganisms (34,35,47).
Energetic and kinetic differences between methanogens
Methanogenesis appears as simple reaction with a single limiting substrate (H2). The microcalorimetry approach we applied revealed that this simplicity is only apparent and that hydrogenotrophic methanogens exhibit energetic and kinetic differences. Methanogenesis is indeed a complex process that could be broken down in several stages. The dominant metabolic phase is represented by one peak that occurs at different times. The magnitude of the peak differs between the methanogens and also the slope of the heat flux trajectories. The return time of the heat flux to the zero baseline was also different. The energetic difference is associated to kinetic differences that translate into specific kinetic parameters, namely affinity constant (Ks) and maximum growth rate constant (μmax). Energetic differences between methanogens has been ascribed by the presence/absence of cytochromes (12). These differences are translated into different yield factors, H2 thresholds, and doubling times. The kinetic differences revealed in this study for three cytochrome lacking methanogens might indicate that other mechanisms than the presence of cytochromes might play a role on the energetics of methanogenesis. Interestingly, calorimetric experiments show that M. ruminantium was metabolically active faster than the other methanogens, suggesting a great adaptation capability for M. ruminantium which could be linked to its predominance in the rumen (48).
Looking at the expression of the affinity constant (Equation (8)), and given that we have assumed that all the three methanogens have the same yield factors, it follows that the exergies E dis, E M, E cat (kJ/mol) are common for all the three species, suggesting that the harvest volume υharv is responsible for the differences between the affinity constants. Note that in the kinetic function developed by Desmond-Le Quéméner and Bouchez (38), the maximum growth rate did not have any dependency on the energetics of the reaction. Our experimental study revealed that μmax is species-specific and reflects the dynamics of the heat flux of the reaction at the exponential phase. Since our study is limited to three species, it is important to conduct further research on other methanogens to validate our findings.
Thermodynamic analysis
Regarding the energetic information for different methanogens summarized in Table 2, it is observed that the thermodynamic behaviour of our three methanogens is analogous to that observed for Methanobacterium thermoautotrophicum (49) The values reported in Table 3 show indeed that the methanogenesis on H2/CO2 is characterized by a large heat production. The growth is highly exothermic, with a ΔHm value that largely exceeds the values found when other energy substrates are used. The enthalpy change ΔHm, which is more negative than the Gibbs energy change ΔGm, largely controls the process. Growth on H2/CO2 is also characterized by a negative entropic contribution TΔSm which, at first sight, may look surprising since entropy increases in most cases of anaerobic growth (50). However, this can be understood if one remembers that TΔSm corresponds in fact to the balance between the final state and the initial state of the process, that is
Methanogenesis on H2/CO2 is particular because the final state of its catabolic reaction (1 mol CH4 + 2 mol H2O) involves a smaller number of moles than the initial state (4 mol H2 + 1 mol CO2), which results in a significant loss of entropy during the process. For spontaneous growth in such a case, the ΔHm must not only contribute to the driving force but must also compensate the growth-unfavourable TΔSm, which means that ΔHm must be much more negative than ΔGm (51). For this reason, methanogenesis on H2/CO2, which is accompanied by a considerable decrease of entropy and a large production of heat, has been designed as an entropy-retarded process (52). More generally, (von Stockar and Liu) (51) noticed that when the Gibbs energy of the metabolic process is resolved into its enthalpic and entropic contributions, very different thermodynamic behaviours are observed depending on the growth type: aerobic respiration is clearly enthalpy-driven (ΔHm << 0 and TΔSm > 0) whereas fermentative metabolism is mainly entropy-driven (ΔHm < 0 and TΔSm >> 0); methanogenesis on H2/CO2 is enthalpy-driven but entropy-retarded (ΔHm << 0 and TΔSm < 0) whereas methanogenesis on acetate is entropy-driven but enthalpy-retarded (ΔHm > 0 and TΔSm >> 0). In the present case, the highly exothermic growth of M. ruminantium, M. smithii and M. formicium on H2/CO2 is largely due to the considerable decrease of entropy during the process: in fact, 50% of the heat produced here serves only to compensate the loss of entropy. A proportion of 80% was found for M. thermoautotrophicum (49), which results from the fact that their TΔSm and ΔHm values are, respectively, 2.7 and 1.7 times larger than ours. This difference might be due to the differences of temperature of the studies, namely 39°C in our study vs 60°C in the study by (49).
Can we use our results to say something about species coexistence?
The competitive exclusion principle states that coexistence cannot occur between species that occupy the same niche, that is that perform the same function (53), only the most competitive will survive. Recently, by using thermodynamic principles, Großkopf & Soyer (32) demonstrate theoretically that species utilizing the same substrate and producing different compounds can coexist by the action of thermodynamic driving forces. Since in our study, the three methanogens perform the same metabolic reactions, the thermodynamic framework developed Großkopf & Soyer (32) predicts, as the original exclusion principle (53), the survival of only one species. For continuous culture of microorganisms, it has been demonstrated that at the equilibrium (growth rate equals the dilution rate) with constant dilution rates and substrate input rates, the species that has the lowest limiting substrate concentration wins the competition. From Eq. (12), the number of moles of hydrogen of the species at the steady state is
Using the model parameters of Table 3, we studied in silico three possible competition scenarios, assuming a constant environment (constant dilution rate D). Two dilution rates were evaluated: D = 0.021 h-1 (retention time = 48 h) and D = 0.04 h-1 (retention time = 25 h). For D= 0.021 h-1, we obtained that , , where the subindex Ms, Mr, Mf stand for M. smithii, M. ruminantium and M. formicium. From these results, it appears that under a constant environment, M. formicium will win the competition. Since , M. ruminantium will be extinguished before M. smithii. For D = 0.04 h-1, we obtained that , , , and thus M. smithii wins the competition. In a third hypothetical scenario, with D = 0.04 h-1, we ascribed to M. ruminantium better adhesion properties (it is known that both M. ruminantium and M. smithii genes encode adhesin-like proteins (54,55)). This enhanced adhesion property of M. ruminantium was translated mathematically by a factor modulating the microbial residence time as we proposed in our mathematical model of the human colon (18). We then assigned to M. ruminantium a 40% of the dilution rate of M.smithii and M. formicium. We obtained , and thus M. ruminantium wins the competition. To illustrate these aspects, we built a multiple-species model with the three methanogens using Eq. (12) and Eq. (14). The parameter b was set to 0.5 h-1 and the hydrogen flux production rate was set to 0.02 mol/min. Figure 5A displays the dynamics of the three methanogens for the first scenario (D = 0.021 h-1). It is observed that at 50 d only M. formicium survives. In the rumen context, this result however is not representative of what occurs in reality where the three methanogens coexist (56,57). It is intriguing that in our toy model it is M. formicium that wins the competition, bearing in mind that M. ruminantium and M. smithii are more abundant than M. formicium (48,57). Figure 5 shows that selective conditions favour the survival of one species. Similar results can be obtained for the human gut by including the effect of pH on microbial growth (21) and setting the gut pH to select one of the species. On the basis of the competitive exclusion principle, it is thus intriguing that having a very specialized function, methanogens are a diverse group that coexist. In the case of the rumen, our modelling work suggest that in addition to kinetic and thermodynamic factors, other forces contribute to the ecological shaping of the methanogens community in the rumen favouring the microbial diversity. Indeed, methanogenic diversity in the rumen results from multiple factors that include pH sensitivity, the association with rumen fractions (fluid and particulate material), and the endosymbiosis with rumen protozoa (48,57). For the human gut, ecological factors enable methanogens to coexist to competitive environment where hydrogenotrophic microbes (acetogens, methanogenic archaea and sulfate-reducing bacteria) utilize H2 via different pathways (58–60).
Finally, mathematical modelling is expected to enhance our understanding of gut ecosystems (61,62). It is then key that in addition to metabolic aspects, mathematical models of gut fermentation incorporate the multiple aspects that shape microbial dynamics to provide accurate predictions and improve insight on gut metabolism dynamics and its potential modulation.
Conflict of interest
No conflict.
Acknowledgements
We are grateful to Dominique Graviou (UMRH, Inra) for her skilled assistance on the in vitro growth experiments.