Team:Toulouse INSA-UPS/Model

Flux Balance Analysis (FBA)

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Basic principle of Flux Balance Analysis

Flux balance analysis is a mathematical approach for analyzing the flow of metabolites through a metabolic network [29]. This constraint-based modeling technique is used to analyze metabolic networks at the whole-cell level and study the intracellular fluxes in a microorganism. Flux balance analysis (FBA) is based on a Genome Scale Model (GSM) containing all the biochemical reactions of a microorganism. FBA aims to determine the flux distribution that results in an optimal objective (e.g. maximal growth rate) while complying with (pseudo-)steady-state conditions and experimental constraints (e.g. measurement of uptake and production fluxes), as briefly detailed below.

Figure 1. Basic principle of constraint-based modeling [29]

The GSM of a microorganism is constructed based on its genome, from which all reactions are identified based on the genes encoding for metabolic enzymes (Fig 1a). GSMs are used to create a stoichiometric matrix S, in which each row represents a metabolite and each column represents a reaction, and with each cell containing the corresponding stoichiometric coefficient (Fig 1b). The flux through each reaction is given by solving the equation S.v = 0, where v is the flux vector (Fig 1c). This equation represents steady-state assumption, with stable concentrations of intracellular metabolites. In a large model there are more reactions than metabolites leading to an undetermined equation system, i.e. with an infinite number of solutions. Without any constraints, the flux distribution can lie at any point in this infinite solution space. The use of directionality constraints (based on thermodynamics) and of upper bound for nutrient uptake reaction rates (based on experimental measurements of the extracellular uptake and production fluxes) further constraints the solution space (Fig 1d). Finally, linear optimization allows us to determine a unique flux solution that corresponds to an optimal functioning of a given process of interest (e.g. growth or production rates) (Fig 1e). Representative examples illustrating the value of FBA in our project are provided below.

Example 1: Evaluation of acetate production capabilities by Clostridium ljungdahlii.

We evaluated the capabilities of Clostridium ljungdahlii to produce acetate during growth on a mixture of CO₂ and H₂. When optimizing growth on these substrates, our model predicts that Clostridium ljungdahlii would produce acetate at the highest growth rate, which is a function often optimized through evolution ([32], [33]). This situation is highly similar to the illustrative example provided in Fig. 1e. Consistently with the literature ([3], [5], [6], [7], [8], [9], [10], [11]), our model thus predicts the coupling between growth and acetate production in Clostridium ljungdahlii (Fig 2).

Figure 2. Acetate production by Clostridium ljungdahlii as function of growth rate on CO₂ + H₂.

Example 2: Improvement of model predictions for Saccharomyces cerevisiae by integration of experimental data

As a starting point, we used the GSM of Saccharomyces cerevisiae to predict its maximal growth rate on ethanol and acetate, using arbitrary values of acetate and ethanol uptake rates. This predicted growth rates (0.17 h^-1 on acetate and 0.22 h^-1 on ethanol) were significantly higher than the growth rates we observed experimentally on these carbon sources. We thus measured the uptake rates in our conditions (Fermentation results). The optimal growth rates estimated from these refined parameters were in excellent agreement with measurements (Table 1).

Table 1. Comparison between experimentals growth rate and predictions with refined parameters.

Algorithm explanation step by step

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Our model combines several processes, each of them being represented using the most relevant mathematical formalism (e.g. constraint-based genome scale modeling for metabolism, Henry’s law for physical transfer through hollow fiber membranes, etc). Due to this heterogeneity, the different parts of the complete model cannot be directly coupled. We have thus designed and implemented an original algorithm to combine the different modules into an integrated dynamic model, as detailed in this section. This integrated model brings together each of these modules under a single ODE system, thereby allowing to simulate, predict, understand and finally optimize the dynamics of the complete system.

This algorithm takes as input i) the concentration of each species (list below) and ii) model parameters. It then calculates all fluxes (for transfer reactions and metabolism), and returns the derivative of each concentration. This function was used to simulate the system dynamics by numerical integration, using the "odeint" ODE solver included in the Scipy package of Python (v3.6). For the most daring of you, our original algorithm code and its detailed description are presented just below.

List of species of interest:

(\( H_{2,g} ; CO_{2,g} ; O_{2,g} ; H_{2,l,C} ; CO_{2,l,C} ; O_{2,l,C} ; EtOh_{C} ; ace_{C} ; H_{2,l,S} ; CO_{2,l,S} ; O_{2,l,S} ; EtOh_{S} ; ace_{S}\)

\( \text{and } X_{C} ; X_{S} ; \beta \text{-} carotene ; geraniol ; limonene ; brazzein \))

Figure 1. Algorithm explanation

Summary

Modeling was a cornerstone of our iGEMINI project. As detailed in this section, we built a model of our production system to verify that our project was feasible, i.e. that our system can produce sufficient nutritional supplements (ꞵ-carotene and yeast) for astronauts, as well as suggesting rational strategies to optimize nutrient production. Our model describes the kinetics of the gas-liquid exchanges and of metabolic fluxes between the two microorganisms, Clostridium ljungdahlii and the Saccharomyces cerevisiae modified strains to produce β-carotene, geraniol, brazzein and limonene. First, the model showed that β-carotene can be produced by a coculture of Clostridium ljungdahlii and Saccharomyces cerevisiae, hence demonstrating the feasibility of the project. To optimize the system, we identified the parameters that control production in order to minimize i) the time needed to produce β-carotene and ii) the utilization of resources required for an efficient production. Finally, we used the model to dimension our production system (reactor volumes).

Model

Overview

The production system is composed of several entities (including hollow fiber membranes, reactors, cells and metabolites) into different compartments and involves many physical and biological processes such as gas exchanges, growth, metabolite production, diffusion, etc. A standardized synthetic biology representation of our system, using the Systems Biology Graphical Notation (SBGN), was thus a necessary starting point to formalize the design and to visualize our complete system (Figure 1).

Figure 1. Representation of the model in Systems Biology Graphical Notation ([30] ; Moodie et al.). Hollow fiber membranes are represented in red and the bioreactors are represented in yellow. The carbon fixation module (Clostridium ljungdahlii) is in greyish blue and the production module (Saccharomyces cerevisiae) is in purple.

Based on this representation, we identified three independent modules:

• a transfer module, that provides resources (CO₂, H₂ and O₂) to the coculture

• a carbon fixation module, to convert CO₂ and H₂ into nutrients (acetate and ethanol) that can feed the production module

• a production module, which uses nutrients supplied by the carbon fixation module to produce yeasts and provitamin A

Consistently, these modules were implemented and coupled in the integrated model, as described in the following sections.

Transfer Module

To supply resources (CO₂ and H₂) to the coculture, we chose to use multiple hollow fiber membranes that can dissolve gas in the aqueous medium even in microgravity. This transfer module is crucial to understanding the gas exchanges and their distribution in our system, which is necessary to dimension the system (e.g. amount of resources that must be injected in the system, surface of hollow fibers, volume of bioreactors). This module describes the exchange between the gas and the soluble phase as well as the exchange of resources (CO₂, H₂, O₂, acetate and ethanol) between the two bioreactors.

Figure 2. SBGN representation of transfer into our reactors.

Gas input rate in the system (I) where \(Q_{X,g}\) is the flow rate of the compound at gas state in the entry of hollow fiber membrane and \(X_{e}\) its concentration

\(I_{X} = Q_{X,g} \cdot X_{e}\)

Transfer terms: the equation which describes the action of our hollow fiber membranes. It is the diffusivity of the compounds through the membrane surface multiplied by the difference between the saturation of the compound in the medium (calculated with Henry's law) and the concentration of our dissolve compound. It represents the transfer between the gas state and the dissolved state of the compounds. Following the concentration gradient, this transfer will be effective from the gas state in the hollow fiber membrane to the liquid state in the medium.

\( T_{X_{l}} = k_{L}a \cdot \left( X^{*} - X_{l} \right) \)

\( X^{*} = \alpha \cdot X_{g} \)

Output rate in the system, \( X_{g} \) is the concentration of our compound at gas state.

\( O_{X} = Q_{X,g} \cdot X_{g} \)

These equations for each compound allow us to model the gas transfer inside our reactor and give us information on their availability and diffusion via the hollow fiber membrane. The transfer model allows us to better understand the dynamics of our gases; bearing in mind that their concentrations is also crucial to fully understand their distribution and impacts on our system as their properties change.

These equations were defined for each substrate (CO₂, H₂ and O₂). Beside gas transfer, all compounds are exchanged between the two bioreactors via a pump. Hence, the rates of exchange are represented by a mass action law:

\( rt_{X,C\rightarrow S} = X_{l,C} \cdot Q_{pump} \)

\( rt_{X,S\rightarrow S} = X_{l,S} \cdot Q_{pump} \)

Where \( Q_{pump} \) is the pump flow rate, \(X_{l,C}\) and \(X_{l,S}\) are respectively the concentration of the dissolved substrate in the reactor of Clostridium ljungdahlii and Saccharomyces cerevisiae.

Metabolic modules

Carbon fixation module

Clostridium ljungdahlii was chosen as a carbon fixation module because this microorganism is able to use the scarce resources available in a spaceship. C. ljungdahlii fixes the carbon dioxide of the ambient air by using H₂ as an energy source. A part of CO₂ is used by anabolism to sustain growth, while another part is used by catabolism and excreted into the medium as acetate, a carbon product that can be used by Saccharomyces cerevisiae as substrate. This carbon fixation process is a succession of reactions catalyzed by a specific metabolic pathway, namely the Wood-ljungdahl pathway. The Genome Scale Model (GSM) iHN637 [1] which contains 785 reactions and 698 metabolites is used to simulate the metabolism of C. ljungdahlii.

To ensure that the model responds to changes of extracellular nutrient concentrations, the constraints on hydrogen and carbon dioxide uptake rates required by FBA (Cosmos will explain you what is a FBA) are defined by Monod equations which cap the consumption kinetics based on the (maximal) uptake capacities and a half velocity constant:

\( q_{CO_{2}} = q_{CO_{2},max} \cdot (\frac{CO_{2,l,C}}{K_{CO_{2}}+CO_{2,l,C}}) \)

\( q_{H_{2}} = q_{H_{2},max} \cdot (\frac{H_{2,l,C}}{K_{H_{2}}+H_{2,l,C}}) \)

Production module

The production of nutrients (β-carotene, limonene, geraniol and brazzein) is achieved by Saccharomyces cerevisiae, which uses acetate and ethanol produced by Clostridium ljungdahlii as carbon sources. The production is modeled using the GSM of Saccharomyces cerevisiae iAZ900 [2], which contains 1234 metabolites and 1597 reactions. Since S. cerevisiae was engineered to produce different products of interest, 15 metabolites and 14 reactions that represent the production pathways were added.

In the same way as for Clostridium ljungdahlii, the uptake rates of acetate and ethanol are constrained by the Monod kinetics laws:

\( q_{O_{2}} = q_{O_{2},max} \cdot (\frac{O_{2,l,S}}{K_{O_{2}}+O_{2,l,S}}) \)

\( q_{ace} = q_{ace,max} \cdot (\frac{ace_{S}}{K_{ace}+{ace_{S}}}) \)

\( q_{EtOh} = q_{EtOh,max} \cdot (\frac{EtOh_{S}}{K_{EtOh}+{EtOh_{S}}}) \)

Here again, these equations ensure that S. cerevisiae will respond to changes in nutrient concentrations of the environment. Importantly, some parameters ( \( q_{ace,max} \) and \( q_{EtOh,max} \)) have been determined by our own experiments (Coculture experiments and parameters). These parameters correspond to the maximal uptake capacity of each carbon source by the microorganism. Regarding the production pathways, we assumed a constant production yield, which were thus determined from the uptake rates.

Coupled model

Our complete model couples the three modules described above by defining a system of 19 differential equations which describe the dynamics of concentration of each metabolite in our integrated production system.

The final model contains 1947 species (proteins, metabolites, and cells) and 2415 reactions from a broad range of processes (growth of each microorganism, metabolite production and utilization, transport between compartments, diffusion, etc). The dynamics of our microbial consortium was summed up in 19 differential equations as a system of ODEs which represents the mass balance of each compound.

Each model is described using the most appropriate modeling formalism, thereby these heterogeneous models cannot be directly coupled together. We thus developed an original algorithm to couple the models into a unified, consistent modeling framework (see here). And for the braves that may want to read more, the pdf of our complete mathematical model and demonstration can be found here: Our Complete model.

The final set of ODEs is briefly described below.

Dynamics of input (CO₂, H₂, O₂) and intermediary (ethanol, acetate) resources:

\( \frac{d H_{2,g}}{d t} = I_{H_{2}} - T_{H_{2}} \cdot \frac{V_{R}}{nV_{F}} - O_{H_{2}} \)

\( \frac{d CO_{2,g}}{d t} = I_{CO_{2}} - T_{CO_{2}} \cdot \frac{V_{R}}{nV_{F}} - O_{CO_{2}} \)

\( \frac{d O_{2,g}}{d t} = I_{O_{2}} - T_{O_{2}} \cdot \frac{V_{R}}{nV_{F}} - O_{O_{2}} \)

\( \frac{dH_{2,l,C}}{dt} = T_{H_{2}} - q_{H_{2},upd} \cdot X_{C} + \frac{rt_{H_{2} , S \rightarrow C } - rt_{H_{2} , C \rightarrow S } }{V_{C}} \)

\( \frac{dCO_{2,l,C}}{dt} = T_{CO_{2}} - q_{CO_{2},upd} \cdot X_{C} + \frac{rt_{CO_{2} , S \rightarrow C } - rt_{CO_{2} , C \rightarrow S } }{V_{C}} \)

\( \frac{dO_{2,l,C}}{dt} = \frac{rt_{O_{2} , S \rightarrow C } - rt_{O_{2} , C \rightarrow S } }{V_{C}} \)

\( \frac{dEtOH_{C}}{dt} = q_{EtOH,C} \cdot X_{C} + \frac{rt_{EtOH , S \rightarrow C } - rt_{EtOH , C \rightarrow S } }{V_{C}} \)

\( \frac{dace_{C}}{dt} = q_{ace,C} \cdot X_{C} + \frac{rt_{ace , S \rightarrow C } - rt_{ace , C \rightarrow S } }{V_{C}} \)

\( \frac{dH_{2,l,S}}{dt} = \frac{rt_{H_{2} , C \rightarrow S } - rt_{H_{2} , S \rightarrow C } }{V_{S}} \)

\( \frac{dCO_{2,l,S}}{dt} = q_{CO_{2}, S, upd2} \cdot X_{S} + \frac{rt_{CO_{2} , C \rightarrow S } - rt_{CO_{2} , S \rightarrow C } }{V_{S}} \)

\( \frac{d O_{2,l,S}}{dt} = T_{O_{2}} + \frac{rt_{O_{2} , C \rightarrow S } - rt_{O_{2} , S \rightarrow C } }{V_{S}} \)

\( \frac{dEtOH_{S}}{dt} = -q_{EtOH,S,upd2} \cdot X_{S} + \frac{rt_{EtOH , C \rightarrow S } - rt_{EtOH , S \rightarrow C } }{V_{S}} \)

\( \frac{dace_{S}}{dt} = -q_{ace,S,upd2} \cdot X_{S} + \frac{rt_{ace , C \rightarrow S } - rt_{ace , S \rightarrow C } }{V_{S}} \)

Dynamics of biomass concentrations:

\( \frac{dX_{C}}{dt} = X_{C} \cdot \mu_{C} \)

\( \frac{dX_{S}}{dt} = X_{S} \cdot \mu_{S,upd2} \)

Dynamics of products:

\( \frac{d \beta \text{-} carotene}{dt} = q_{\beta \text{-} carotene\_e , upd} \cdot X_{S} \)

\( \frac{d geraniol}{dt} = q_{geraniol , upd} \cdot X_{S} \)

\( \frac{d limonene}{dt} = q_{limonene , upd} \cdot X_{S} \)

\( \frac{d brazzein}{dt} = q_{brazzein} \cdot X_{S} \)

Parameters

Overall, our model contains 27 biochemical and physical parameters. The values of most parameters (25/27) were collected from publications, since they were already available and we could not have performed the hundreds of complex experiments that would be required to determine their experimental values in our conditions during this project. Still, some experimental results were exploited to determine important parameters of the model and verify its predictive capabilities. For instance, we measured the maximal uptake capacity of ethanol and acetate by S. cerevisiae, and we tested whether the production module of our model could predict the corresponding growth rate of S. cerevisiae on these carbon sources. The excellent agreement between predictions and measurement (example 2 in the FBA box) demonstrates that our model yields fairly accurate predictions, hence validating the proposed approach. The complete list of parameters is given below.

Table 1. Model parameters.

Simulation and feasibility analysis

To assess the feasibility of our project, we simulated the dynamics of our complex metabolism network and its production of ꞵ-carotene, limonene, geraniol and brazzein. Each physical and biological process has been mathematically defined using the appropriate kinetics rate laws. As seen above, they were all assembled into a single system of ordinary differential equations. This ODEs system was solved using the "odeint" solver of the SciPy package of Python (odeint.html), using parameters and initial conditions that correspond to realistic conditions of our system environment.

Figure 3. Dynamics of the concentration of each species considered in the model

Figure 4. Dynamics of Clostridium ljungdahlii (blue), Saccharomyces cerevisiae (purple), ꞵ-carotene (orange) and limonene (black --) concentrations.

The predictions show consistent dynamics of our system (Fig 3,4). Importantly, model simulations indicate that our system may produce a daily dose of ꞵ-carotene in 16.1 hours. Assuming a negligible delay following the activation of the optogenetic regulations, the sweet rose flavor appears after 15.1 hours and the lemon flavor after 77.1 hours. Overall, these model simulations demonstrate the feasibility of our project and encouraged us to continue in this direction!

Understanding and optimizing

Global sensitivity analysis

With a time-limited project and a model of nearly thirty parameters, all parameters cannot be measured experimentally. Our experiments to estimate some parameters confirm this fact. As an additional concern, many sources of variability may perturb parameters and ultimately impact the efficiency of the system. Variability could emerge from the system itself (living systems exert some variability by nature) or during each step of the process (manufacturing, gas flow rates, etc). Facing this problem, a global sensitivity analysis approach was applied to evaluate the impact of random parameters fluctuations on the response time to reach non-pathogenic concentrations [25].

To perform this analysis, we generated 200 sets of parameters randomly sampled (from a uniform distribution) within ± 5% of their reference values, and the production time of the system was calculated for each of these sets.

Figure 5. Frequency histogram of the ꞵ-carotene production time

The distribution of production times indicates that our system is robust. Production times range from 14.3 to 19.4 hours for ꞵ-carotene, 13.6 to 17.6 hours for sweet rose flavor and 69.3 to 86.9 hours for the lemon flavor, indicating that our system will remain efficient even under a reasonable degree of uncertainty.

Metabolic control analysis

Metabolic Control Analysis (MCA) is a mathematical tool widely used in biotechnology to quantify the influence of a specific parameter on the functioning of a system, in terms of fluxes and concentrations [26]. Working with a system governed by a large number of parameters, MCA allows to quantify the influence of each of them towards each variable of the system.

Usually applied to study the control of concentrations and fluxes under steady state conditions, we have extended the concepts of MCA to quantify the control exerted by each parameter on i) the production time and ii) the utilization of resources, which depends on the system dynamics. For each parameter (p), the control coefficients (C_time and C_resources) were calculated as:

\( C_{p}^{time} = \left ( \frac{p}{time}\frac{\Delta time}{\Delta p} \right ) \Delta p\rightarrow 0 \)

\( C_{p}^{resources} = \left ( \frac{p}{resources}\frac{\Delta resources}{\Delta p} \right ) \Delta p\rightarrow 0 \)

If the controlled parameter (production time or resource utilization) is not impacted by the parameter p, the corresponding coefficient will be zero. A positive (negative) value indicates that an increase in p increases (reduces) the response time. A coefficient of 1 indicates that a change in x % of the parameter results in a change of x % of the response time. All control coefficients were calculated by numerical differentiation (using a relative perturbation of each parameter of 1%). MCA results are shown as a heatmap in Figure 6.

Figure 6. Heatmap of the control coefficients of each parameter on production time and resource utilisation.

Significant conclusions can be reached from this analysis. In our model, the most controlling parameters listed in Table 2 and detailed below.

Table 2. Parameters with the highest control coefficients on production time and resource utilization.

\( q_{H_{2},max} \) & \( q_{CO_{2},max} \)

The uptake capacity of substrates by C. ljungdahlii (\( q_{H_{2},max} \) and \( q_{CO_{2},max} \) ) greatly influence the production time. The greater the amount of acetate produced by C. ljungdahlii and the faster the yeast will grow and produce ꞵ-carotene, limonene, geraniol and brazzein. As one would expect, the faster the production, the lower the resources utilization will be, because the system use time will be shorter. Therefore explaining why these parameters are also critical when it comes to resource usage. Although these parameters are controlling, we can hardly optimize them because they are intrinsic, systemic properties of Clostridium ljungdahlii metabolism.

Production yield

Beside the uptake capacity of C. ljungdahlii, an important parameter is the production yield of ꞵ-carotene by S. cerevisiae. This parameter impacts both the production time and resources usage because it is the part of the flux that will be distributed into the ꞵ-carotene production. The higher it will be, the faster it will be produced. This result has thus driven us towards the optimization of our system by engineering the production pathway of S. cerevisiae. The strategy we designed consisted in i) increasing the expression of mevalonate pathway genes that form geranylgeranyl pyrophosphate, the precursor of ꞵ-carotene, before ii) adding the carotene synthase (Cloning and coculture results).

\( Q_{pump} \)

An increase of the flow rate between the two reactors leads to a decrease of the production time and resource utilization. The greater the exchanges between the two reactors, the more homogeneous the medium and the faster the exchange of substrates between the two microorganisms. Thus, production will be faster and the resources used will therefore be lower. The flow rate of the pump between the two reactors is a parameter that we can control easily.
These graphs show that once the flow rate reaches 0.2 L/h the production time and resource usage hardly varies. It means that we can save a lot of resources and time by adjusting this flow rate. It is not necessary to set the pump to its maximal flow rate and lose energy because a plateau is reached from 0.2 L/h.

Figure 7. Resource utilization (red) and production time (blue) as a function of the flow rate between the two reactors.

\( H_{2}ge \) & \( CO_{2}ge \)

The higher the hydrogen concentration at the input of our model into the hollow fiber membranes, the lower the production time, the less resources used. By increasing the concentration we increase the gradient between the hollow fiber membrane and the medium and so we increase the exchange of hydrogen. Thus, there will be more hydrogen in the medium, available for Clostridium ljungdahlii which will grow faster and will be able to use more carbon dioxide, which will reduce the waste of resources. Whereas, the higher the carbon dioxide concentration will be, the higher its waste and its exchange in the medium will be. But the carbon dioxide uptake will be limited by the hydrogen uptake leading to a waste of resources.

Figure 8. Resource utilisation (left) and production time (right) in function of the hydrogen and carbon dioxide concentration.

Results indicate that, in order to minimize resource utilization and production time, we must set a high concentration of hydrogen and a low concentration of carbon dioxide. Respectively 50 and 15 mmol will lead to a minimal resource utilization (2.147 mol) and production time (15.76 hours).

\( QgCO_{2} \)

The higher the flow rate of carbon dioxide, the higher the waste and therefore the resources used for our system. Since this parameter has no control over the production time, it is worthy to decrease its value to reduce the amount of resources wasted during the production process.

Figure 9. Resource utilization (left) and production time (right) as a function of the flow rate of carbon dioxide.

Thus, by setting the flow rate to the minimum the production time will not be impacted but we will save consequent resources. In this tested range of carbon dioxide flow rate, the production time is stable at 16.1 hours.

Summary of MCA results

Overall, MCA helped us to better understand the functioning of the system. Moreover, we identified two types of parameters that influence the functioning of our production system. Some parameters can hardly be controlled or even optimized (e.g. \( q_{H_{2},max} \)) using rational design strategies, though they could potentially be improved using alternative strategies (e.g. directed evolution). We thus focused on determining the optimal parameters that can be controlled directly (e.g. gas flow and flow rate of the pump) or by engineering the microorganisms (e.g. beta-carotene production in S. cerevisiae) to optimize the system.

Dimensioning the system

Dimensioning the system was a crucial aspect of our project because of the very limited space in the spaceship (see our guide to start a space project). The physical size of our production system mainly depends on the reactor volume of Clostridium ljungdahlii and Saccharomyces cerevisiae. MCA showed that their volumes impact both production time and resource utilization, hence the reactor dimensions must be minimized while ensuring a sufficient production. To determine the optimal volume, we varied the reactor volume of C. ljungdahlii and S. cerevisiae and computed the production time.

Figure 10. Production time as a function of the reactor volume of Clostridium ljungdahlii and Saccharomyces cerevisiae.

Results shown in Fig 10 indicate that the production time may be kept within an appropriate range provided the reactors volume for Clostridium ljungdahlii and Saccharomyces cerevisiae are higher than to 0.5 and 0.3 L, respectively. To minimize space utilization and production time, a compromise of about 1 L seems to be optimal.

Our system has been designed, dimensioned and optimized to produce a daily dose in 11h for one astronaut. Interestingly, a second dose can be produced more rapidly (in 8h) since a sufficiently high cell density is already reached once the first daily dose is produced. Hence, based on the proposed strategy, our system has the potential to produce almost three daily doses in 24h. Should more doses be produced to feed a larger crew, our model is ready to scale up the production system, hence stressing the flexibility of our synthetic microbial consortium to fit the needs of tomorrow’s missions.

Impact on the project

The synthetic microbial consortium at the core of our project is complex, with many entities interacting in a dynamic way. Modeling was thus vital to ensure the system feasibility, simulate its behavior, understand its properties and ultimately optimize its design. More broadly, we used the model as an integrative platform to support several aspects of the project, as detailed below. Importantly, we provide the code as an open source Jupyter notebook ( Download the Jupyter notebook of the iGEMINI model) to ensure reproducibility and reusability by any teams interested in modeling synthetic consortia behavior.

• Project feasibility: when starting the project, we truly believed modeling was a perfect tool to test different aspects of the strategy, hence enhancing our chances of success. We first developed a visual representation of the system, which helped to organize the lab work and the parts we had to construct. When running the first simulations, the model highlighted the feasibility of iGEMINI, which enthusiastically encouraged us to go further down that route.

• Use of experimental data and design of experiments: following an iterative systems biology approach, our model has been initially built from data collected in the literature, and has been updated with some preliminary results from wet lab experiments to improve its predictive capabilities. As an example, based on a first run of metabolic control analysis carried out on the initial model, we decided in early summer to measure the growth and uptake rates of Saccharomyces cerevisiae cells during growth on acetate and ethanol. These experimental uptake rates were directly updated in the model, and we verified that some model predictions (e.g. growth rate of S. cerevisiae) were improved when using these refined parameters.

• Integrated design of the production system: in a close relationship with our Implementation effort, model predictions rationally guided the development of a prototype (see below our 3D model). As an example, with the estimation of 16.1 hours to produce a daily dose of nutritional supplements, it has been possible to dimension our device (bioreactors volume of 1 L) and evaluate the efficacy in terms of resources.





• Implementation & Entrepreneurship: predicting optimal reactors volume of 1 L allowed to complete the product life-cycle (Implementation). It was essential to ensure the reliability of our project in front of stakeholders and show them that our project was anchored in reality. For instance, the feasibility and robustness analyses helped us convince some of the sponsors to invest time and money in our project.

• Human practices & communications: developing a system that aims to be embarked in space requires many technical discussions. Our project raises various processes and engineering issues (e.g. resources consumption, material used, functioning time needed, etc.) responding to these issues involved consulting with various experts. Many questions could be addressed using model predictions (Interview), which also guided discussions with experts. More generally, the model was key in order to facilitate discussions with all the scientific and non-scientific interlocutors.

References

Reference for Clostridium ljungdahlii model :

1. Characterizing Acetogenic Metabolism Using a Genome-Scale Metabolic Reconstruction of Clostridium Ljungdahlii by Harish Nagarajan, Merve Sahin, Juan Nogales, Haythem Latif, Derek R Lovley, Ali Ebrahim, Karsten Zengler ; DOI: 10.1186/1475-2859-12-118

Reference for Saccharomyces cerevisiae model :

2. Genome-scale metabolic models of Saccharomyces cerevisiae. by Nookaew, Olivares-Hernández, Bhumiratana, Nielsen J. ; Methods Mol Biol. 2011 ; doi:10.1007/978-1-61779-173-4_25

References on Clostridium ljungdahlii :

3. Enhancing CO₂-valorisation using Clostridium autoethanogenum for sustainable fuel and chemicals production by James K. Heffernan, Kaspar Valgepea, Renato de Souza Pinto Lemgruber, Isabella Casini, Manuel Plan, Ryan Tappel, Sean D. Simpson, Michael Köpke, Lars K. Nielsen, Esteban Marcellin ; doi: https://doi.org/10.1101/2020.01.23.917666

4. A novel MXene-coated biocathode for enhanced microbial electrosynthesis performance by Khurram Tahira, Waheed Miranc, Jiseon Jangd, Asif Shahzada, Mokrema Moztahidaa, Bolam Kima, Dae Sung Leea ; August 2019 ; Chemical Engineering Journal 381 ; https://doi.org/10.1016/j.cej.2019.122687

5. Characterizing acetogenic metabolism using a genome-scale metabolic reconstruction of Clostridium ljungdahlii by Harish Nagarajan, Merve Sahin, Juan Nogales, Haythem Latif, Derek R Lovley, Ali Ebrahim and Karsten Zengler ; Nagarajan et al. Microbial Cell Factories 2013 ; https://doi.org/10.1186/1475-2859-12-118

6. Ethanol and acetate production by Clostridium ljungdahlii and Clostridium autoethanogenum using resting cells by Jacqueline L. Cotter, Mari S. Chinn and Amy M. Grunden ; Published online: 26 August 2008 ; Bioprocess Biosyst Eng (2009) 32:369–380 ; DOI 10.1007/s00449-008-0256-y

7. Understanding the interdependence of strain of electrotroph, cathode potential and initial Cu(II) concentration for simultaneous Cu(II) removal and acetate production in microbial electrosynthesis systems by Jiaxin Hou, Liping Huang, Peng Zhou, Yitong Qian, Ning Li ; 6 November 2019 ; ScienceDirect Chemosphere 243 (2020) ; https://doi.org/10.1016/j.chemosphere.2019.125317

8. Traits of Selected Clostridium Strains for Syngas Fermentation to Ethanol by Michael E. Martin, Hanno Richter, Surya Saha, Largus T. Angenent ; 9 September 2015 in Wiley Online Library ; DOI 10.1002/bit.25827

9. CONCEPTION D’UN PROCEDE D’ELECTROSYNTHESE MICROBIENNE ; Mme ELISE BLANCHET le vendredi 1 avril 2016.

10. Formic acid Formation by Clostridium ljungdahlii at elevated Pressures of carbon Dioxide and hydrogen by Florian Oswald, I. Katharina Stoll, Michaela Zwick, Sophia Herbig, Jörg Sauer,Nikolaos Boukis and Anke Neumann ; Frontiers in Bioengineering and Biotechnology ; February 2018 doi: 10.3389/fbioe.2018.00006

11. Kinetic Studies on Fermentative Production of Biofuel from Synthesis Gas Using Clostridium ljungdahlii by Maedeh Mohammadi, Abdul RahmanMohamed, Ghasem D. Najafpour, Habibollah Younesi, andMohamad Hekarl Uzir ; 30 January 2014 ; Volume 2014, Article ID 910590 ; http://dx.doi.org/10.1155/2014/910590

References on Saccharomyces cerevisiae:

12. Redox responses in yeast to acetate as the carbon source by Karyl I. Minard and L. McAlister-Henn ; Arch Biochem Biophys. 2009 March ; DOI: 10.1016/j.abb.2008.12.014

13. Analysis of the yeast short-term Crabtree effect and its origin by Hargman, Torbjörn and Piskur ; The Febs Journal ; August 2014 ; doi:10.1111/febs.13019

14. Effects of Oxygen Supply on Yeast Growth and Metabolism in Continuous Fermentation by HIROSHI KURIYAMA AND HARUMI KOBAYASHI National Institute of Bioscience and Human-Technology ; February 1998

15. Kinetic Parameters of Saccharomyces cerevisiae Alcohols Production Using Nepenthes mirabilis Pod Digestive Fluids-Mixed Agro Waste Hydrolysates by Nkosikho Dlangamandla, Seteno K. O. Ntwampe, Justine O. Angadam, Boredi S. Chidi and Maxwell Mewa-Ngongang ; 17 January 2019 ; Fermentation 2019, 5, 10; doi:10.3390/fermentation5010010

16. Role of Transcriptional Regulation in Controlling Fluxes in Central Carbon Metabolism of Saccharomyces cerevisiae, a Chemostat Culture Study by Pascale Daran-Lapujade, Mickel L.A. Jansen, Jean-Marc Daran, Walter van Gulik, Johannes H. de Winde, Jack T. Pronk ; Transcript levels and metabolic fluxes in S. cerevisiae ; J. Biol. Chem. published online November 20, 2003

17. Overproduction of Geranylgeraniol by Metabolically Engineered Saccharomyces cerevisiae by Kenro Tokuhiro, Masayoshi Muramatsu, Chikara Ohto, Toshiya Kawaguchi Nobuhiko Muramoto, Masana Hirai, Haruo Takahashi, Akihiko Kondo, Eiji Sakuradani, Sakayu Shimizuand Shusei Obata ; APPLIED AND ENVIRONMENTAL MICROBIOLOGY ; Sept. 2009 ; doi:10.1128/AEM.00277-09

18. Evolutionary Engineering of Saccharomyces cerevisiae for Anaerobic Growth on Xylose by Marco Sonderegger and Uwe Sauer ; APPLIED AND ENVIRONMENTAL MICROBIOLOGY ; Apr. 2003 ; DOI: 10.1128/AEM.69.4.1990–1998.2003

19. RNAi expression tuning, microfluidic screening, and genome recombineering for improved protein production in Saccharomyces cerevisiae by Guokun Wuang, Sara M. Björkb, Mingtao Huanga, Quanli Liua, Kate Campbella, Jens Nielsena, Haakan N. Joenssonb, and Dina Petranovica ; May 7 2019, vol. 116 ; www.pnas.org/cgi/doi/10.1073/pnas.1820561116

20. Modeling of batch kinetics of aerobic carotenoid production using Saccharomyces cerevisiae by M. Carolina Ordonez, Jonathan P. Raftery, Tejasvi Jaladi, Xinhe Chen, Katy Kao,M. Nazmul Karim ; Biochemical Engineering Journal ; 2016 Elsevier B.V. ; http://dx.doi.org/10.1016/j.bej.2016.07.004

21. Cloning and Disruption of a Gene Required for Growth on Acetate but not on Ethanol: the Acetyl-Coenzyme A Synthetase Gene of Saccharomyces cerevisiae by CLAUDIO DE VIRGILIO, NIELS BURCKERT. GEROLD BARTH. JEAN-MARC NEUHAUS, THOMAS BOLLER AND ANDRES WIEMKEN ; 1992 YEAST ; https://doi.org/10.1002/yea.320081207

22. Regulation of Cell Size in the Yeast Saccharomyces cerevisiae by G. C. JOHNSTON, C. W. EHRHARDT,A. LORINCZ AND B. L. A. CARTER ; JOURNAL OF BACTERIOLOGY ; Jan. 1979 ;

Henry’s law solubility coefficient:

23. Compilation of Henry’s law constants (version 4.0) forwater as solvent by R. Sander ; 30 April 2015 ; Atmos. Chem. Phys., 15, 4399–4981 ; doi:10.5194/acp-15-4399-2015

Hollow fiber membrane properties:

24. BIOETHANOL PRODUCTION VIA SYNGAS FERMENTATION OF CLOSTRIDIUM LJUNGDAHLII IN A HOLLOW FIBER MEMBRANE SUPPORTED BIOREACTOR by Irika Devi Anggraini, Keryanti, Made Tri Ari Penia Kresnowati, Ronny Purwadi, Reiji Noda, Tomohide Watanabe, Tjandra Setiadi1 ; International Journal of Technology 10(3): 481-490 ; https://dx.doi.org/10.14716/ijtech.v10i3.2913

Reference for the global sensitivity analysis:

25. Global analysis of night marine air temperature and its uncertainty since 1880: The HadNMAT2 data set by Elizabeth C. Kent, Nick A. Rayner, David I. Berry, Michael Saunby, Bengamin I. Moat, John J. Kennedy, and David E. Parker ; OURNAL OF GEOPHYSICAL RESEARCH: ATMOSPHERES ; 2013 ; doi:10.1002/jgrd.50152

Reference for the MCA:

26. A. Cornish-Bowden (1995) Metabolic control analysis in theory and practice. Adv. Mol. Cell. Biol. 11, 21-64 and https://en.wikipedia.org/wiki/Metabolic_control_analysis

References for vitamin A treatment :

27. https://www.pharmanity.com/medicaments/a-313-50-000-u-i-capsule-molle-n7lbji5

28. https://en.wikipedia.org/wiki/International_unit

Reference for the FBA:

29. What is flux balance analysis? by Jeffrey D. Orth, Ines Thiele and Bernhard Ø. Palsson ;. Nat Biotechnol. ; 2010 March ; doi:10.1038/nbt.1614

Reference for the SBGN:

30. Systems Biology Graphical Notation: Process Description language Level 1 by Stuart Moodie, Nicolas Le Novère, Emek Demir, Huaiyu Mi and Falk Schreiber ; Nature Precedings ; Feb 2011 ; doi:10.1038/npre.2011.3721.3

Reference for limonene threshold:

31. Optical Isomers and Odor Thresholds of Volatile Constituents in Citrus sud achi by Areeya PADRAYUTTAWAT, Takumi YOSHIZAWA, Hirotoshi TAMURA and Tadashi TOKUNAGA ; Food Sci. Technol. Int. Tokyo ; 1997

Other references:

32. Optimal control of bacterial growth for the maximization of metabolite production by Yegorov Ivan, Mairet Francis , De Jong Hidde, Gouze Jean-Luc ; Journal Of Mathematical Biology ; March 2019 ; https://doi.org/10.1007/s00285-018-1299-6

33. Optimality and sub-optimality in a bacterial growth law by Benjamin D. Towbin , Yael Korem , Anat Bren, Shany Doron, Rotem Sorek & Uri Alon ; NATURE COMMUNICATIONS ; Jan 2017 ; DOI: 10.1038/ncomms14123

34. https://www.boconline.co.uk/en/legacy/attachment?files=tcm:t410-116758,tcm:410-116758,tcm:10-116758

35. https://www.boconline.co.uk/en/legacy/attachment?files=tcm:t410-54560,tcm:410-54560,tcm:10-54560

36. https://www.boconline.co.uk/en/legacy/attachment?files=tcm:t410-54571,tcm:410-54571,tcm:10-54571

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