A bioenergetic model to predict habitability, biomass and biosignatures in astrobiology and extreme conditions

1. Introduction

Astrobiology has the challenge of studying life on Earth in environments which are poorly characterized or extreme, usually both, and predicting the habitability of extraterrestrial environments. A habitable environment can allow an organism to undergo metabolic activity and hence maintain itself and grow or reproduce [1]. Locations of interest across the field vary: from extreme conditions on Earth [2], to the Martian surface [3] and subsurface [4–7], icy moons (e.g. Enceladus [8]) and even exoplanets [9]. The extreme conditions expected in these targets are typically under-studied and often difficult to replicate in the laboratory. We set out to create a computational model which can help take steps towards answering three key questions in astrobiology using a minimal number of input assumptions:

Biogeochemical modelling has been used extensively in an attempt to understand regions of the Earth that are not easily accessible, such as hydrothermal vents (e.g. [13–16]), the marine subsurface (e.g. [17–19]), drylands (e.g. [20]) and the atmosphere (e.g. [21]). These modern ecological models can provide very effective results, but have high specificity and still require a large number of potentially complex input parameters and knowledge of the systems they aim to replicate.

Alternatively, there are many routes to estimating biomass yields from a more theoretical basis (e.g. [4,22,23]), but often little attention is paid to differing environments and the effect of extremes such as temperature and salinity. In geomicrobiology and environmental microbiology, many of these extremes are more commonplace. A comprehensive method of modelling growth energetically in these natural settings is described by LaRowe and Amend [17,24], in which the rate of change in total biomass is calculated by considering the balance between energetic supply and demand. Such a general approach is required for astrobiology, albeit more agnostic and requiring fewer known variables because often little is known about astrobiological targets. Furthermore, extraterrestrial life, if it exists at all, may not necessarily behave in the same way as Earth life. Nonetheless, it must be bound by the laws of thermodynamics and we could reasonably take this as a starting point to assess the biological potential of any extraterrestrial environment.

This study focuses on assessing habitability using an energetic and kinetic approach. The energetic approach to habitability [10,25] parametrizes the way in which biology interacts with its environment in terms of energy, based on the notion that an appropriate supply of energy and nutrients is necessary for life to synthesize the complex structures required for metabolism, growth and reproduction. A multitude of energy sources are possible, but when one thinks of energy as a fuel for life the most common method of uptake is through chemical pathways featuring redox couples, occasionally involving the absorption of radiation [10]. This energetic uptake can be quantified by calculating the free energy $\mathrm{\Delta }G\hspace{0.17em}[\text{J}\hspace{0.17em}{\text{mol}}^{-1}]$ of the relevant process(es). ΔG is a measure of the spontaneity of a chemical reaction, demonstrating whether it is a net source or sink of energy. A negative ΔG describes a spontaneous process—one in which energy is released—such as in the break down of polymers or simple metabolisms, and a positive ΔG requires net energetic input, such as building new biomacromolecules. Free energies vary with the local composition, temperature and pressure [26].

Organisms grow and reproduce by using overall energy-yielding reactions with negative ΔG to drive energy-consuming reactions with positive ΔG [10]. More important, however, is the rate at which the organisms can access this energy—the available power P [W] [11]. To calculate this one must also be aware of the kinetics of these biologically mediated interactions, which are strongly dependent on the energetic availability and physio-chemical environment [27]. Principally, the metabolic reaction must provide enough power to overcome the energetic costs of survival [11] (for example, overcoming rates of amino acid racemization with temperature [28]).

A simple organism can direct its energy supply into either growth or maintenance processes [24]. For this work, growth processes are those concerning the energetic cost of biosynthesis (i.e. building new biomass), and all other mechanisms of energetic loss are considered maintenance processes. In reality, the computation of both these contributions is complex, with the compounding effects of temperature (e.g. [29,30]), pressure (e.g. [31]), salinity (e.g. [32]), pH (e.g. [33]), nutrient availability (e.g. 34]) etc. each contributing to the organism’s ultimate fate [10,35,36]. The actual power organisms use for maintenance also varies with growth phase and substrate availability [37].

We present a novel computational model which can estimate maintenance costs in extreme and/or nutrient limited environments from theory or empirical data. It can predict theoretical biomass levels and rates of biosignature production from as little as an overall catabolic reaction in poorly characterized, extreme (extra)terrestrial environments and other locations of astrobiological interest. A collection of organisms and their local environment are considered as self-contained objects communicating only via energy and nutrient exchange. The notion of modelling certain bioenergetic processes such as metabolism in a modular fashion has been suggested before [38] although it has also been recognized that modelling life in extreme environments, for which there is little information, is difficult [10]. The model’s simplicity does come with some caveats and these will be discussed.

2. Methods

2.1. An efficiency based model for microbial growth (the core concept)

For any given organism, the power going into growth processes must be a fraction of the power supply from metabolism, as other energetic processes necessary for maintenance must take precedence [10,27]. Beyond this primary limitation due to maintenance, the ability of an organism to grow new biomass can also be restricted by the availability of key nutrients. The majority of biological matter is made up of six elements: carbon, hydrogen, nitrogen, oxygen, phosphorus and sulfur, hitherto referred to as ‘CHNOPS’ elements [35].

We have developed nutrients, maintenance, energy and growth (NutMEG),¹ an open source Python module for predicting growth behaviour of life in poorly characterized environments. To do so, it estimates the free energy ΔG of internal cellular processes corresponding to: metabolism (§5.2); growth (§5.4) and optionally maintenance, and the rate of these processes (§5.3). This novel schema offers several benefits. The use of kinetics allows for more realistic consideration of the thermodynamics at play governing metabolic rates [27] rather than simply using static total energetic availability to predict biomass. By monitoring metabolic rates and nutrient uptake, ΔG is dynamically corrected as the organism(s) interact with the environment (via equation (5.3), §5.2). This allows us to also consider external effects on the metabolic energy yield with time, such as an abiotic source or sink of substrate. The minimum required input parameters for a growth prediction are shown in table 1.

Table 1. Minimal organism and environment parameters required to initialize a growth prediction and default parameters for NutMEG to output in time series. There are many more parameters included in the model for organisms which allow for fine tuning of a well-characterized species or an exploration of possible parameter spaces for others. Further information on what can be changed can be found in NutMEG’s documentation. By default, E. coli-like parameters are chosen unless otherwise specified. Where these are unavailable, other model organisms are used and these are noted in the documentation. Using inheritance, one can increase specificity for organisms or environments allowing new parameters or adaptations to be introduced.

Collapse

organism parameter	symbol	unit
rate constant of catabolism	kcat	${\text{M}}^{1-z}\hspace{0.17em}{\text{s}}^{-1\hspace{0.17em}\mathrm{a}}$
rate constants of nutrient uptake	kx	${\text{s}}^{-1}$
catabolic reaction	—	—
environment parameter	symbol	unit
composition activities or molarities	[x]	— or M
temperature	T	K
pressure	p	Pa
volume	V	${\text{m}}^3$
pH	pH	—
NutMEG output	symbol	unit
population	N	cells
population volume	VBM	${\text{m}}^3$
free energy of catabolism	−ΔGA	$\text{J}\hspace{0.17em}{(\text{mol}\hspace{0.17em}{\text{CO}}_2)}^{-1}$
free energy of ATP production	ΔGC	$\text{J}\hspace{0.17em}{(\text{mol}\hspace{0.17em}\hspace{0.17em}{\text{CO}}_2)}^{-1}$
rate of catabolism	r	(M ${\text{CO}}_2$) ${\text{s}}^{-1}$
available power supply	PS	$\text{W}\hspace{0.17em}{\text{cell}}^{-1}$
maintenance as a fraction of supply	1 − εM	—
power available for growth	PG	W ${\text{cell}}^{-1}$
growth rate	rG	${\text{s}}^{-1}$
composition activities or molarities	[x]	— or M
rates of nutrient uptake	rx	M ${\text{s}}^{-1}$

^a z is the order of the catabolic reaction.

NutMEG considers cells as small engines whose growth is throttled by a maintenance efficiency ε_M ∈ [0, 1] (equivalent to 1 − the fractional energetic cost of maintenance versus the energetic supply). Hence, with an instantaneous power supply P_S(t) and maintenance cost P_M(t), both in W ${\text{cell}}^{-1}$, the net power available as fuel for growth, P_F(t) [W ${\text{cell}}^{-1}$] is

$$P_F=P_S-P_M={ϵ}_M{P}_S.$$2.1

Growth also necessitates the availability of nutrients to build the new biomass. If nutrient uptake can also be characterized as an efficiency ε_UT ∈ [0, 1] then the final power which can be used for biomass production, P_G(t) [W ${\text{cell}}^{-1}$], is

$$P_G(t)={ϵ}_{UT}[{ϵ}_M[P_S(t)]].$$2.2

Further details on how these efficiencies are parametrized and calculated can be found in §5. This schema is shown in figure 1.

• Download figure
• Open in new tab
• Download PowerPoint

To convert this growth power into new biomass, one must know the energy required to synthesize each cell from the nutrients available $E_{\text{syn}}\hspace{0.17em}[\text{J}\hspace{0.17em}{\text{cell}}^{-1}]$ (§5.4). Then, if either the energy or nutrient supply is the limiting factor in growth and not the rate of biomass production, for a suitably small time step dt [s], the total biomass N(t) [cells] is

$$N(t+\text{d}t)=N(t)(1+\frac{E_G(t,\text{d}t)}{E_{\mathrm{syn}}}),$$2.3

where $E_G(t,\text{d}t)=P_G(t)\hspace{0.17em}\text{d}t\hspace{0.17em}[\text{J}\hspace{0.17em}{(\text{cell s})}^{-1}]$ is the total energy each cell can contribute to growth per time step.

At first glance, the simplicity of this model may give the impression of limited applicability. We argue that sorting processes into groups concerning supply, maintenance, nutrient uptake and growth is useful for determining how these factors could affect habitability. One can introduce unique traits of organisms without compromising computational efficiency (allowing for trivial inclusion of: life spans; unique rates for nutrient uptake, growth, metabolism; competition between organisms etc. (§§4, 5)). At the same time, NutMEG allows flexibility in input for conditions which have limited data or large uncertainties (e.g. extraterrestrial environments), and can highlight areas in which a given environment or organism requires better understanding. For example, in keeping with the concepts outlined above, one could define upper and lower efficiencies required for life in various environments, i.e. best-case and worst-case habitability assessments.

3. Results

3.1. Maintenance costs of methanogens

Values of P_M were selected which yielded the empirical growth rates for each empirical methanogen (figure 2, blue crosses). While the different methanogen species clearly have different maintenance powers, an exponential trend upwards with increasing temperature can be seen, consistent with previous studies [43]. The maintenance power of the TOM follows a similar trend (figure 2, orange bar).

• Download figure
• Open in new tab
• Download PowerPoint

Below temperatures of 280 K, one bound of the TOM’s maintenance power range (corresponding to an ATP yield of 0.5 mol per mol ${\text{CO}}_2$) drops significantly (i.e. ε_M → 1, P_M → 0). A P_M of 0 is non-physical, and this reflects a scenario in which NutMEG predicts that the P_S is less than the P_G required to match the target growth rate. This suggests that methanogens at low temperatures must be metabolically efficient and able to metabolize more moles of ATP per mole of ${\text{CO}}_2$ or have lower energies of cell synthesis. It should be noted, however, that this occurs outwith the temperature range for which methanogen data were available (288–371 K) [40] and our logarithmic extrapolation of target growth rates (electronic supplementary material, figure S2) could be unreliable.

These maintenance power predictions can be compared with previous theoretical and empirical estimations. Tijhuis et al. [43] used empirical data to estimate the maintenance power requirement with temperature for E. coli. Shown in black in figure 2 is the Tijhuis prediction for a cell with the same size as the TOM. Also shown in figure 2 are theoretical estimates generated using Lever et al.’s method whereby minimum thermodynamic maintenance predictions are based on protein replacement after racemization [28]. The lines on figure 2 represent the cost of protein replacement to the TOM after 2% or 10% racemization of the amino acids in an average protein.

3.2. Energy and nutrient limitation of the typical optimal methanogen

NutMEG was used to artificially limit the availability of energy and nutrients to explore the effect they would have on the predicted growth rates, biomass levels and total ${\text{CH}}_4$ produced by the TOM. Figure 3 shows growth curves for the TOM with its calculated maintenance cost at 280 K, 300 K and 330 K. Figure 4 shows the peak growth rate, final biomass and total ${\text{CH}}_4$ production for temperatures between 280 K and 330 K. For both figures, each column represents the effect of a specific limiting factor on the organism. These include reducing the initial concentration of dissolved metabolic substrates ${\text{CO}}_2$ and ${\text{H}}_2$, or nutrient sources P (the sole phosphorus source), or limiting the rate constant with which the organism can access phosphorus (§5.5). All simulations were performed in 1 l ‘vessels’ saturated in nutrients apart from the phosphorus limiting simulations.

• Download figure
• Open in new tab
• Download PowerPoint

• Download figure
• Open in new tab
• Download PowerPoint

3.2.1. Growth curves

When the concentration of either ${\text{CO}}_2$ or ${\text{H}}_2$ is restricted with no other changes to the organism or environment, growth curves become more characteristic of inhibited microbial growth as shown in figure 3. For higher temperatures, the effect of limiting ${\text{CO}}_2$ and ${\text{H}}_2$ becomes more pronounced, with little to no growth at 90% optimal [${\text{CO}}_2$] at 330 K compared to almost optimum growth at 280 K. This is due to the higher maintenance power at higher temperatures (figure 2).

Limiting the concentration of available nutrients places a cap on the growth curves when all of the available phosphorus is locked in biomass for the cooler environments with slower growth (figure 3, centre-right, top and middle). This demonstrates that the rate of uptake of phosphorus is not the key limiting factor until there is too little remaining to sustain exponential growth of a large culture. At 330 K, the growth rate is also limited by a lower [P], due to the overall uptake rate (below, §5.5) running slower than the metabolism.

If instead of changing the concentration of available phosphorus the uptake rate constant k_P was changed (parametrizing phosphorus bioavailability and microbial adaptation to its uptake), the growth rate slows but there is little impact on biomass levels. This is because the growth rate becomes nutrient limited, i.e. phosphorus uptake rather than the metabolism is determining the rate of biomass production, but there remains enough phosphorus to continue building large cultures. The final biomass is still lower than the optimal alternative because the methanogens are surviving for a longer period of time and hence more of the available energy in the system has been diverted to maintenance costs before reaching the limit of microbial growth.

Specific characteristics of the growth curves and how they change with temperatures can be examined in further detail.

3.2.2. Growth rates

There is an exponential increase in peak growth rate with temperature for the TOM in its optimal conditions (figure 4, top row). When restricting substrate concentration to a fraction of the optimal dissolved amount, the effect on growth rate becomes more pronounced at higher temperatures. This is due to the higher maintenance power predicted for the TOM at higher temperatures (figure 2). The initial ε_M value decreases with increasing temperature because maintenance costs become a larger fraction of power supply. As ε_M → 0 the TOM can tolerate smaller deviations in substrate concentration before maintenance power exceeds power supply and the growth rate → 0.

With limiting nutrients, different effects are seen depending on the extent to which we restrict [P]. For this example, when restricted to ${10}^{-8}\hspace{0.17em}\text{M}$ there is no slow down in growth rate meaning the TOM remains energy limited at all temperatures while in its exponential phase. When restricted instead to ${10}^{-10}\hspace{0.17em}\text{M}$ the growth is nutrient limited for temperatures greater than 300 K meaning the rate of uptake of phosphorus cannot meet the demands for biosynthesis made by P_F (§5.1). For all temperatures above 300 K, the growth rate is then restricted by this uptake rate. Changing the phosphorus uptake rate constant more explicitly limits the nutrient availability for reasons discussed above.

3.2.3. Biomass levels

With increasing temperature the final expected biomass in the vessel decreases exponentially. This is due to the effects on ε_M described above. Reducing substrate availability exacerbates this by decreasing net power supply while maintenance power remains constant, decreasing ε_M further until the energy limitation renders the environment uninhabitable to the TOM at these maintenance powers. It has been postulated, however, that in extreme energy-limited systems some organisms focus on other processes at the expense of repairing non-fatal protein degradation, reducing the maintenance by up to 95% [28,37].

The availability of phosphorus also affects the final biomass levels. When $[\mathrm{P}]={10}^{-8}\hspace{0.17em}\text{M}$, while growth rates in the exponential phase are the same as the optimum, growth arrest begins sooner, but not until phosphorus is completely exhausted at lower temperatures (figure 3, centre-right top). At temperatures greater than 315 K, growth stops before all of the phosphorus has been consumed, hence there is only energy limitation in this scenario. When $[\text{P}]={10}^{-10}\hspace{0.17em}\text{M}$, there is a gentle increase in final biomass with temperature because at lower temperatures there is slower growth and more energy overall is used for maintenance before nutrient limitation becomes important. However, there is a peak in biomass at approximately 310 K after which the energy limitation also becomes important, as above for the 10⁻⁸ simulation. When decreasing k_P the final biomass falls with temperature at an increased rate due to a larger amount of energy being used for maintenance in total throughout the lifetime of the simulation.

3.2.4. ${\text{CH}}_4$ production

The total ${\text{CH}}_4$ production has a qualitatively similar trend to total biomass production with temperature: at increased temperature the final methane concentration decreases exponentially. This suggests that net biosignature production of thermophilic methanogens in closed systems could be lower than their psychrophilic counterparts. It is important to note though that the faster metabolism and growth rate with temperature means that the rate of ${\text{CH}}_4$ production is higher at higher temperatures but growth arrest occurs sooner leading to this lower overall ${\text{CH}}_4$ production. In natural systems with substrate replenishment this may not be the case (e.g. hydrothermal vents).

Restricting [P] reduces total ${\text{CH}}_4$ production at lower temperatures (figure 4, centre-right bottom). At the lower P_M at these temperatures, the organism is nutrient limited because less energy is required for maintenance. The ${\text{CH}}_4$ production increases for these nutrient limited organisms with temperature until energy becomes limiting (at 285–295 K for $[\mathrm{P}]={10}^{-8}\hspace{0.17em}\text{M}$ and 300–305 K for $[\mathrm{P}]={10}^{-10}\hspace{0.17em}\text{M}$) and total ${\text{CH}}_4$ production begins to decrease again, for reasons discussed above. These results show that as extreme environments require more energy to survive, biosignatures produced by the overall metabolism (methane in this case) will be produced at a higher rate per unit biomass.

3.3. Alternative explanation: synthesis energy

One input variable to NutMEG which is difficult to estimate is the energy required to synthesize a cell $E_{\text{syn}}$. For this study, it was estimated by combining the energetic cost of amino acid synthesis [46] in anoxic environments and the cost of protein synthesis from these amino acids [47,48] (§5.4), and increases with the local temperature (electronic supplementary material, figure S1). Were $E_{\text{syn}}$ larger, a lower maintenance power would be required for NutMEG’s output to match the empirical growth data (§3.1). Figure 5 shows the proportion with which $E_{\text{syn}}$ needs to be increased such that the maintenance power required to match empirical growth rates would be zero—a scenario classically considered by Monod kinetics [49], though thermodynamically unrealistic [10]. At temperatures exceeding 320 K $E_{\text{syn}}$ would need to be corrected by an order of magnitude or more to minimize P_M, but in these conditions the maintenance cost would be non-zero [10,28,43,50]. At less extreme temperatures, such as 300 K, a correction of less than 10× would minimize the maintenance contribution required. Even if this were the case, one would expect that the growth curves and biosignatures in figures 3 and 4 would be similar—perhaps with more ${\text{CH}}_4$ production if ε_M → 0 after more substrate usage due to the lower maintenance power.

• Download figure
• Open in new tab
• Download PowerPoint

4. Discussion and conclusion

A common problem for astrobiologists is investigating the habitability of extreme environments on Earth or extraterrestrial environments for which we have very little information. We have developed a simple bioenergetic model for the dynamic monitoring of both organism and environment as they interact with one another, allowing for the study of growth rates, biomass production, biosignature (e.g. gas) production and other parameters. By matching the model predictions to laboratory observations we have investigated how placing a theoretical methanogen under either energy or nutrient limitation can affect the rates of microbial growth, total biomass production and total ${\text{CH}}_4$ production in closed, well-mixed systems. Increased energy and nutrient limitation restrict the total biomass expected—an important measure of habitability—increasingly at higher temperatures owing to the low energy yield of the methanogenesis metabolism and higher maintenance power. They also limit the total ${\text{CH}}_4$ production, which would be an important biosignature for detecting methanogens on other planets, such as on exoplanets. The model’s simplicity does mean that these results come with some caveats.

First, our results rely on the assumption that in optimal conditions the uptake of ${\text{CO}}_2$ and ${\text{H}}_2$ is the rate-determining step in the metabolism; a reasonable assumption for such a low-energy reaction. When calculating the effects of energy limitation there are two major effects on the simulation parameters. First is the free energy yield of the metabolism (equation (5.3)), second is the rate of the metabolism r = r₊F_T, where r₊ is the forwards rate of the metabolic pathway’s rate-determining step, and F_T is a thermodynamic scaling factor [27] (§5.3). Here, we assume that the rate-determining step is the uptake of ${\text{H}}_2$ or ${\text{CO}}_2$, e.g. $r_{+}=k_M[\hspace{0.17em}{\text{CO}}_2]{[{\text{H}}_2]}^4$ where k_M is the rate constant of methanogenesis, but it could be from another step in the metabolism such as the phosphorylation of ATP or an enzyme-controlled interaction in the pathway [27]. If this were the case, and in our optimal conditions [${\text{CO}}_2$] and/or [${\text{H}}_2$] were well above the value at which their uptake would be the rate-limiting step, they could be lowered without effect until this were reached and energy limitation becomes important. From that point on, one would achieve results qualitatively similar to those reported in this paper. Further laboratory experiments are required to help better understand at which [${\text{CO}}_2$] and [${\text{H}}_2$] accessing these substrates will become the rate-determining step, but in the meantime our results provide a qualitative view of what will happen at that stage.

The maintenance power was used as a single temperature-dependent value, whereas in reality it would reflect the energy change from a series of chemical transactions the organism has made. For extreme conditions, the maintenance power should be computed explicitly for each adaptation to every given extreme [10] and NutMEG does allow for this. For example, the energetic cost of maintaining cellular pH against a gradient $\mathrm{\Delta }\text{pH}$ could be estimated as $\mathrm{\Delta }G=-2.3RT\mathrm{\Delta }\text{pH}$ where R is the universal gas constant [10,33]. The power cost can then be computed, if the rate of the mechanism is known. This knowledge is not available for many extremes, and different organisms will use different pathways with varying efficiencies. As a result, further understanding of microbial adaptations to extremes is required—either by predicting such pathways or finding their net minimum thermodynamically viable energetic cost [10,36].

The maintenance power can also vary with the organism’s growth phase and the local energetic availability (e.g. [37]). Most empirical data, including those used in this study, are based on measurements made in the exponential phase which are not representative of life in natural systems. In energy-limited systems, maintenance costs could be substantially lower than those calculated here [37]; for example, a recent study suggests that in Earth’s deep subsurface most methanogens could be surviving on energy fluxes between approximately ${10}^{-19}\text{ and }{10}^{-21}\hspace{0.17em}\text{W}\hspace{0.17em}{\text{cell}}^{-1}$ [51]. For NutMEG to successfully simulate natural systems, better understanding of how organisms can survive on such low energy fluxes is required.

The synthesis energy was calculated by combining the cost of amino acid and protein synthesis, but our analyses would benefit from a more comprehensive complement of biomacromolecules. Proteins account for approximately 55% the dry mass content of E. coli in the exponential growth phase [48,52], and the inclusion of other biomolecules such as RNA and lipids will improve the quality of this estimation. Similarly, protein repair is a key factor in maintenance costs but the cost of RNA repair becomes more important with increasing cell size [50]. Biomolecular content also varies significantly between species and growth phase and this should also be accounted for [52,53].

NutMEG primarily predicts growth arrest when the maintenance power exceeds the supply power among other criteria, but there are other explanations of what could cause growth to stop. An example is the potential role of quorum sensing in some bacteria (e.g. [54]), which means that some microbes will not grow until a critical cell density is achieved, even though theoretically the energy and substrates for growth are available. The problem with the specifics of growth arrest is that it is often tied to the specific physiology of particular species. NutMEG’s philosophy in part relies on having minimal ties to the peculiarities of particular terrestrial organisms and instead opts for a general approach. Nevertheless, these specificities could be included if one was modelling organisms in which one wished to investigate the influence of such characteristics on biomass or biosignature production.

While the simulations we performed did predict growth, none reached a steady state with the environment. This is because there was no cell death or net inflow of substrates to sustain the methanogen population after ε_M → 0. This would, inevitably, lead to the death of all of the organisms. This issue is mitigated in this study, as we explicitly considered laboratory-like ‘vessels’ as well-mixed closed systems for analysis. Mixing and diffusion effects will also need to be considered in wider astrobiological applications which would aim to achieve a steady state, such as the simulation of hot springs or oceans. Some small steps can be made with NutMEG to mitigate these issues, such as including net inflows or outflows of substrates. Omission of a cell death rate is common in simulations of cell dynamics, but it has been shown to be an important factor in maintenance considerations. Characterizing its effects along with other kinetic factors such as growth rate are some of the major problems in the current understanding of maintenance requirements [36].

Other parameters within NutMEG can be altered and have a significant effect on growth rates, biomass and biosignature production. To explore them we also trialled some simulations including: varying the maintenance power to see how less well-adapted organisms could be quantified or to what extent a new extreme could be tolerated; including a life span for the methanogens after which they become inactive; and including net sources/sinks of ${\text{CO}}_2$ and ${\text{H}}_2$ to dynamically change the energetic availability with time (electronic supplementary material, animation). Increasing the maintenance power by up to 20% has a similar effect to the energy limitation across different temperatures. Inclusion of a lifespan reduces peak biomass values (and final active biomass falls to zero) but it did not significantly affect ${\text{CH}}_4$ production.

Adding a net inflow of ${\text{CO}}_2$ or ${\text{H}}_2$ increased all three of the peak growth rates, biomass levels and biosignature production as this is fundamentally the opposite of energy limitation. However, reservations must be made when considering these predictions, as the growth of real methanogens is likely limited by the rate-determining step, such that decreasing the availability of nutrients may slow growth down, but increasing nutrients will not necessarily enhance growth any further. Adding a sink of ${\text{CO}}_2$ or ${\text{H}}_2$, for example by abiotic processes or a competing organism, has a similar effect to energy limitation. There are examples of natural systems exhibiting higher cell concentrations than those achievable in the laboratory (e.g. [55]). Properly including sources and sinks of potential substrates and nutrients could help explain these observations; our results suggest that sometimes slower peak growth rates could produce higher concentrations of biomass given enough time.

As some of the results presented in §3.2 predict growth on the scale of years, resupply of substrates will be of particular importance when estimating how much biomass such an environment could sustain for these long periods of time. There could also be a significant influence from other CHNOPS elements, nutrients and micro-nutrients, which should be included if they act as a significant limiting factor. For example, observations from the Cassini spacecraft suggest Enceladus’ subsurface ocean may contain the major ingredients of methanogenesis in an energy-yielding configuration (e.g. [8]). Phosphorus is the only CHNOPS element yet to be directly detected [8,56], but a recent study suggests it could be as low as approximately ${10}^{-10}\hspace{0.17em}\text{M}$ [57], a level at which our results suggest nutrient limitation could be important. This tenuous energetic and nutrient landscape provides a salient example of how NutMEG could be applied to astrobiological problems.

When attempting to model extraterrestrial environments, existing studies generally infer possible energetic habitability from the free energy values alone (e.g. [8]), or predict maximum biomass values from the total free energy available (e.g. [7]). NutMEG can offer valuable additions to such calculations by dynamically calculating the kinetics of metabolism, maintenance costs and variation in free energy yield as the local composition changes with time. Monitoring of the organisms and environment also allows us to see the trends in biomass and biosignatures with time.

In conclusion, NutMEG offers a new computational technique to investigate habitability and potential growth, biomass and biosignature production in little understood terrestrial and extraterrestrial environments. It was used to predict that in energy and nutrient saturated conditions, there is an exponential drop in final biomass (${10}^9-{10}^6\hspace{0.17em}\text{cells}\hspace{0.17em}{\text{l}}^{-1}$) and total methane production ($62-3\hspace{0.17em}\mu \text{M}$) despite an increase in peak growth rates ($0.007-0.14\hspace{0.17em}{\text{h}}^{-1}$) as temperature rises from 280 to 330 K for methanogens in ideal conditions. When placed in energy or nutrient limiting environments, all three parameters are further reduced.

In the future, NutMEG’s credibility can be bolstered by comparing its first-order predictions with empirical evidence from real extreme environments on the Earth. In extraterrestrial environments, it can provide a basis for prioritizing locations to be studied. Example applications could be to explore energy and nutrient availability on Saturn’s moon Enceladus or in the subsurface of Mars. Given the minimal observations and inferences available from exoplanets, NutMEG can also be used to explore the possible parameter space for expected biomass and gas production which can impact, and therefore be used to explain, exoplanetary spectra.

5. Extended methods

NutMEG has been developed as a wide-ranging model to assess the key requirements of energetic habitability and a full complement of its applicability with further examples is available in its documentation. Here, we will summarize the key calculations performed for the results in this work.

Data accessibility

All of the code required to replicate these results, as well as data files containing the data plotted in all figures are available in the NutMEG-Implementations GitHub repository, in the TOM directory: https://github.com/pmhiggins/NutMEG-Implementations. NutMEG itself is available in the NutMEG public GitHub repository: https://github.com/pmhiggins/NutMEG.

Authors' contributions

P.M.H. and C.S.C. conceived the core concepts of the model. P.M.H. developed the methodology and code, performed the simulations and analysis and drafted the manuscript. C.S.C. offered astrobiology and microbiology insight and guidance throughout the study and helped with the structure and editing of the manuscript.

Competing interests

We declare we have no competing interest.

Funding

This work was supported through the Science and Technology Facilities Council (STFC) grant no. ST/R000875/1 and an STFC studentship to P.M.H.