Bioregenerative life support systems (BLSS) will be a key component of future long-duration space exploration, as they can reduce mission mass and volume (Imhof et al, 2017; Audas et al, 2022). A BLSS recycles human waste by feeding it to an artificial ecosystem consisting of a range of different organisms, such as higher plants, microalgae, and bacteria. These organisms gradually break down the waste and in the process provide fresh food, generate oxygen, and clean water for the crew (Nelson et al, 2010; Escobar and Nabity, 2017; Pannico et al, 2022). As a result, there is less reliance on constant resupply from Earth, which greatly reduces the material footprint needed for extended missions in space (Macelroy and Averner, 1978; Häder, 2020; Audas et al, 2022). Because of its constant fresh food provision, a BLSS also solves the problem that essential nutrients in processed and prepackaged food are deficient and degrade over time (Cooper et al, 2017; Carillo et al, 2020). Biological systems are also capable of self-repair, unlike mechanical systems that need separate systems to be repaired. Surviving organisms and tissues in a damaged BLSS can potentially recover to their original size on their own, even after significant damage (Bartsev et al, 1996).

MELiSSA is a BLSS concept developed by ESA with a consortium of 15 international partners and the involvement of approximately 50 organizations (MELiSSA Foundation, 2023). It is an artificial ecosystem consisting of five interconnected compartments inhabited by higher plants, microalgae, microorganisms, and humans (abbreviated as C1 to C5, Figure 1; Table 1). Each of the compartments has its own specific metabolic function within the entire MELiSSA loop. First, all human waste is broken down through a sequence of three bioreactor types: a thermophilic anaerobic compartment (C1), photoheterotrophic compartment (C2) and nitrifying compartment (C3). This results in nutrients and CO₂ for microalgae and plants (C4a and C4b) that, in turn, provide food, oxygen, and fresh water for the crew (C5), thus closing the loop (Hendrickx and Mergeay, 2007; Clauwaert et al, 2017; Vermeulen et al, 2020a). The operational pilot plant at Universitat Autònoma de Barcelona consists of a number of connected MELiSSA compartments and demonstrates a part of the system’s entire metabolic loop (Gòdia et al, 2004; Garcia-Gragera et al, 2021). Mathematical models of the MELiSSA loop have been developed and improved since the beginning of the MELiSSA project in 1989 (MELiSSA, 1989; Dussap and Gros, 1991). Some of these models are used for predictive control, to be run alongside the actual physical system. The MELiSSA models help in understanding the dynamics of mass flow fluctuations and achieving long-term reliability of the system (Cornet et al, 2001; Ciurans Molist et al, 2020; Poulet et al, 2020). Such ecosystem models can also be used to simulate the impact of unforeseen perturbations, deliberate interventions, or design changes in the system (Volk and Rummel, 1987; Pilo Teniente, 2015; Vermeulen et al, 2019).

To describe the material flows in an ecosystem model, the stoichiometric relations governing these flows need to be developed (Volk and Rummel, 1987; Begon and Townsend, 2021). Several authors have described mass flow models of biological life support systems (Volk and Rummel, 1987; Garland, 1989; Loader et al, 1997; Finn, 1998), but not all studies contain the underlying chemical stoichiometric equations. The stoichiometric equations describing mass flows in the MELiSSA BLSS have been published in publicly-available MELiSSA literature, both in peer-reviewed papers and research reports disseminated by the MELiSSA Foundation (Table 1). In less than half of the listed studies, all five MELiSSA compartments were modeled. The other studies describe either a smaller number of compartments, or just one. The loop is never fully closed in any of the listed studies. There are a number of reasons for this. First of all, it may indicate that certain compounds are not part of the regenerative logic of the system and are not generated within the loop, and therefore need to be fully supplied from the outside (Dussap et al, 1993; Poughon et al, 2009). Secondly, it may indicate an output that does not get regenerated, such as a residual indigestible material (Fulget et al, 1999; Poughon et al, 2000). Because of the resulting accumulation of that material, external supply is required to keep the system running. And thirdly, it may be a deliberate system design choice that only a fraction of a particular compound or resource is generated by the BLSS. Several MELiSSA studies, for example, explicitly specify that only a part of the needed food is generated by the loop (Poughon et al, 2000; Guirado and Podhajsky, 2008; Thiron, 2020). The rest is supplied externally. One of the main motivations for such a choice is the limited space that is available in common spacecraft and habitat designs to integrate bioreactors and plant growth chambers (Johnson et al, 2021; Gorce et al, 2022).

Almost three-quarters of the researched MELiSSA studies list all the stoichiometric equations of their models. The other studies limit themselves to a few selected equations as examples. The stoichiometric coefficients in the chemical equations can either be fixed beforehand, or dynamically calculated on the fly, during the simulation run. For example, in simulating the production of Limnospira indica in C4a, the elementary composition of its biomass is determined by the variable light irradiation inside the photobioreactor (Guirado and Podhajsky, 2008; Poughon et al, 2009). This then necessitates the recalculation of all subsequent stoichiometric equations that contain this dynamic empirical biomass formula.

Whenever creating a stoichiometry to describe mass flows in an ecosystem, choices need to be made about which compounds will be considered, and which level of detail will be used to describe the ecosystem’s biochemical processes (Dubitzky et al, 2011; Begon and Townsend, 2021). This choice is influenced by the level of knowledge about the individual metabolism of the different species in the ecosystem, but ultimately depends on the objective and scope of the study. In light of this, the reviewed MELiSSA studies contain varying assumptions concerning the role of different compounds such as lipids, VFAs, and CO₂. This is partially due to the fact that over time the MELiSSA models became more detailed, incorporating more processes. Early MELiSSA papers assume that all lipids consumed by the astronauts are oxidized and no traces of lipids are found in the feces (Dussap and Gros, 1991; Dussap et al, 1993). This is later adjusted, and lipids become an explicit part of the feces input in C1 (Poughon et al, 2000). The mix of VFAs that is generated as output of C1 varies quite significantly between the different studies. In the earliest studies only acetic acid and butyric acid are considered (Dussap and Gros, 1991; Dussap et al, 1993), but in later studies, a broader range of VFAs is included in the stoichiometry (Poughon, 2007b).

The stoichiometric model presented in this paper provides the basis for an agent-based model (ABM) of the MELiSSA loop to study the interactions and emergent behavior of the MELiSSA system from a theoretical perspective. MELiSSA is fundamentally a complex system, and properties such as nonlinearity, stochasticity and chaos may play an important role in the overall behavior of the system, just like in any ecosystem (Bjørnstad, 2015). Because all functions in the MELiSSA loop are tightly coupled and since there are no large buffers in space (e.g., no large atmosphere or water bodies), slight variations in any of the loop’s pathways can have dramatic consequences for the entire loop (Macelroy and Averner, 1978; Poulet et al, 2018). It is precisely such tightly coupled systems that are potentially susceptible to irregular fluctuations (Bjørnstad, 2015). ABMs offer a modeling approach that helps to gain insight in such dynamics and helps to explore different design strategies for improved system robustness. ABMs are used to understand those aspects of the behavior of a system, that are not easily represented in population-level differential equations, such as variation among individuals or variation of individuals during their life cycle (Deangelis and Grimm, 2014). Such exploratory models of complex systems lead to insights about essential mechanisms and principles, a use of modeling that is different from modeling aimed at making accurate predictions (Forrest and Mitchell, 2016). MELiSSA modeling studies to date focus on predictive modeling because this is a critical step to develop a durable and reliable BLSS. The MELiSSA modelling approach is mechanistic, allowing for better understanding and improved predictions. With its exploratory approach, this study can be considered as being complementary to the existing MELiSSA modeling efforts. In order to build an ABM of MELiSSA, a stoichiometric model is needed that describes essential mass flows between all involved agents (bacteria, microalgae, higher plants and humans). The key metabolic processes in all MELiSSA compartments need to be described with enough detail to enable studying the interactions. At the same time, they need to remain abstracted enough to tlead to an efficient model and retain relevance for the objectives of the ABM which are centered around investigating the impact of heterogeneity in the system and capturing nonlinear dynamics.

The research objective of this paper is to develop a stoichiometric model of a hypothetical BLSS that provides a crew with fresh food and oxygen during long-duration space missions, without the need for any resupply. The envisioned stoichiometric model should conform to the following requirements:

• The system provides 100% of all the food and oxygen needed by the crew, and 100% of the resources needed by every other organism in the loop.

The current literature (listed in Table 1) has, to the authors’ knowledge, not included such a stoichiometric model of the MELiSSA loop. As described above, the loop is always considered to be partially open, primarily for practical reasons. The research reported in this paper is more theoretical in nature, focusing on the internal dynamics of hypothetically fully closed systems.

This section describes the empirical formulas, stoichiometric equations, and the setup of a static spreadsheet model.

This section describes the general assumptions behind the model and those per compartment.

This section describes the results of the stoichiometry development, and the simulation results.

This study presents a stoichiometric model of the MELiSSA BLSS, which describes the main metabolic processes in all compartments using a series of static chemical equations. In steady state, 100% of the necessary food and oxygen for the crew, as well as 100% of the compounds required for all other organisms in the loop, are generated. Using the assumption that all waste compounds in the loop can be broken down again, full closure was achieved in the static model by balancing the size of each compartment relative to all the other compartments. This is the first time a fully closed static MELiSSA model is described that can provide all the food and oxygen for astronauts. The model is a useful tool for theoretical research on autonomous BLSSs for long-duration space exploration, allowing tracing of the elements over the entire cycle.

However, in practice, no system can be 100% closed. There are always potential outfluxes from the system, for example, through a buildup of recalcitrant organic matter (Hendrickx and Mergeay, 2007; Lasseur et al, 2010; Zhang et al, 2018) or the accumulation of different precipitates such as carbonates and phosphates (De Paepe et al, 2018; Christiaens et al, 2019). Recalcitrant organic matter consists mainly of plant fibers that do not rapidly biodegrade. Plant cell walls are composed of cellulose, hemicellulose, pectin, and lignin and are among the least degradable polymers in a BLSS (Hendrickx and Mergeay, 2007; Zhang et al, 2018). As a result, up to about 70% of the organic waste could be digested in MELiSSA lab experiments (Farges et al, 2008; Lasseur et al, 2010). The MELiSSA community has investigated additional methods to break down the remaining recalcitrant matter using hydrothermal and chemical oxidation, and anaerobic and hyperthermophilic cellulose-degrading bacteria (Hendrickx & Mergeay, 2007; Lasseur et al, 2010). The most efficient results were obtained by using supercritical water oxidation (SCWO) in which up to 98% of all organic matter could be broken down (Hendrickx and Mergeay, 2007; Zhang et al, 2018). Hydrogen peroxide was used as an oxidizer in these tests, which is a compound that can be generated within a BLSS loop (Tikhomirov et al, 2011; Vijapur et al, 2017; Nelson et al, 2020). Nevertheless, it is safe to assume that, in reality, there will always be some level of material loss in any BLSS loop. It would therefore be interesting to investigate what accumulates over a long period of time and then calculate the dimensions of the reserve storage required to mitigate the resulting material shortages.

The interaction between compartments C1 and C2 represents a subcycle in this model. The Rhodospirillum biomass generated in C2 is fed back into C1 as organic waste. The goal of this subcycle is to produce a surplus of CO₂, H₂, and NH₃ that is needed in the other compartments of the MELiSSA loop. Steady state of this subcycle is reached gradually until enough biomass from C2 is sent back to C1 to ensure that the exact amount of VFAs is produced to sustain a stable Rhodospirillum culture. If too few VFAs are provided, C2 will underperform due to a lack of Rhodospirillum growth. If too many VFAs are provided, the Rhodospirillum culture will not be able to process all of them, leading to accumulation and negative impacts on the mass flows and efficiency of the entire loop. At steady state, this subcycle generates the following surplus (per day, for a crew of six): 213 mol CO₂, 434 mol H₂, and 126 mol NH₃. The subcycle also explains the dominant amount of protein present in the loop, despite the food provided to the crew containing much less protein (Table 4). Due to the need for a significant mass of Rhodospirillum to process the VFAs and their high protein content (72%), a lot of protein is present in the loop in general. Bio-electrochemical oxidation is a potentially more efficient approach to convert the VFAs into CO₂. In a study by Luther et al, 2018, using bio-electrochemical oxidation within a microbial electrolysis cell, 80%–100% of the VFAs in the effluent of MELiSSA’s C1 were converted into CO₂ in 7 days. With further process development and optimization, bio-electrochemical oxidation can potentially entirely replace the use of Rhodospirillum in C2.

(Jiang et al, 2013) conducted a series of experiments on anaerobic digestion of food waste. At a pH of 5.0, the resulting VFA spectrum consisted of 60.40% acetic acid, 8.32% propionic acid, 31.13% butyric acid, and 0.15% valeric acid, which falls within the same range as the results achieved in our model at steady state. Another study by Lim et al, 2008 also involved anaerobic digestion of food waste. At a pH of 5.5, the resulting VFA spectrum had a more variable composition, but acetic acid was generally the dominant VFA. These reported results are consistent with the results of our static model, which suggests that the theoretical VFA outcome is a potentially realistic scenario. However, it must be noted that VFA spectra generated during anaerobic fermentation are highly variable and depend on various factors such as substrate composition and inoculum (Poughon et al, 2013; Khan et al, 2016), pH and temperature (Shin et al, 2004; Jiang et al, 2013; Khan et al, 2016), and bioreactor design and operation (Lim et al, 2008; Bharathiraja et al, 2016). For instance, in experiments using food waste by Shin et al (2004), and in MELiSSA experiments using a synthetically composed organic waste (Luther et al, 2018; Zhang et al, 2019), both acetic acid and butyric acid were the main VFAs, with butyric acid being dominant.

Growing enough plants to meet the food requirements of a human crew typically results in the production of more oxygen than the crew needs. This is because the harvest index of the crops is often less than 100%, meaning that only a portion of the grown biomass is used for food (Jones, 2003). However, the unused biomass still generates oxygen. In a closed loop system, this could lead to an accumulation of excess oxygen (as e.g., observed in Poughon et al, 2000; Gros et al, 2003) and, eventually, the collapse of the system. In our model, the excess oxygen is used to hydrolyze solid waste in C1, in the form of H₂O. The hydrogen-burning auxiliary helps to transform any remaining oxygen gas into H₂O. Since oxygen originates from splitting H₂O during photosynthesis, the amount of surplus oxygen matches the amount of surplus hydrogen in the system.

In our model, the human crew consumes 21.51 mol/person/day of CO₂, which is very close to the target value of 22.72 mol/person/day used for calculating the stoichiometry. However, the human crew only uses 24.29 mol/person/day of oxygen, much lower than the target value of 52.50 mol/person/day. The proportion between consumed oxygen and produced CO₂ should be 2.31, but in our model, this proportion is 1.13, precisely because of the lower oxygen consumption. Remarkably, other BLSS modeling studies show the same tendency. In MELiSSA studies, the proportion is 1.20 (Fulget, 1996; Thiron, 2020) and in Lunar Palace studies, it ranges from 1.13 to 1.38 (Hu et al, 2010; Fu et al, 2016). This suggests that the description of the O₂ consumption in all of these studies is not entirely complete. This could be due to the fact that in reality, more compounds are oxidized than represented in the simplified stoichiometric equation for human metabolism. The total mass of consumed food per person per day corresponds to 781 g DW/day. This is slightly higher than the range of baseline values used in MELiSSA studies and reference documents. Adjusted to a daily food intake of 3,000 kcal/person, the values in these studies and documents range from 509 to 748 g DW/day (e.g. (Dussap et al, 1993; Poughon et al, 2000; Thiron, 2020)).

The composition of feces was calculated by solving the stoichiometric equation for human metabolism, using the general characterization of feces reported in the literature as a starting point (Rose et al, 2015). After solving the equation for human metabolism, the resulting feces composition was found to be 66% carbohydrates, 28% proteins, and 6% lipids, corresponding to the empirical formula CH_1.6676O_0.6028N_0.07715. This formula is similar to the one used in BLSS studies by Hu et al, 2010 and Fu et al, 2016, which is CH_1.70O_0.60N_0.05. Because the MELiSSA diet is a vegan diet, it is expected that there is a high fiber intake and a resulting high amount of fiber in the feces (Brodribb et al, 1980; Kay, 1982; Forsum et al, 1990). As a result, the overall carbohydrate fraction could be quite significant. It should be noted that the fraction of protein in the feces could be an underestimation, as bacteria can compose up to half of the fecal solids and may have a significant protein content (Cummings, 2001; Rose et al, 2015). Intestinal bacterial growth is not included in the human stoichiometry, which is justifiable as it means more digestion is done by the same groups of microbes in C1. The amount of feces produced is 253 g DW/person/day. Jenkins et al, 2001 measured 160 ± 24 g DW/person/day for a vegetarian diet. It should be noted that no other solid body wastes have been included in the stoichiometry, and as such the ‘feces’ in the equation represent a more general representation of all wastes combined.

Further development of the stoichiometric model could focus on increasing its granularity. This could involve expanding the model to include more elements beyond CHON, incorporating a greater diversity of crops, and using a more detailed description of human metabolism. Nitrogen, phosphorus, and potassium are the three major macro-elements for plants (Usherwood and Segars, 2001; Kanazawa et al, 2008). Therefore, including the latter two elements in the next version of the model seems like a logical step. Fertilizers typically contain these three elements, but it is crucial that they are applied in the correct ratio (Usherwood and Segars, 2001; Chun et al, 2017), which must also be factored into the model. Diverse plant crops could be used instead of the concept of an ‘ideal plant’, allowing for a more detailed description of the crew’s daily diet. Integrating water usage beyond it's role as a metabolite will result in a more accurate description of the entire water budget. For example, water transpiration, water excretion, and free water inside the plant could be factored in. By integrating solid body wastes other than feces, the stoichiometry of human metabolism could also be further refined.