This part built on the COBRApy computational framework.

Two primary objectives:

1、Maximize protein secretion flux：

max_v v_prot^exp

2、Optimize a weighted objective combining growth rate and protein secretion flux：

max_v w₁·v_prot^exp + w₂·v_growth

We first configured the model medium to an H₂/CO₂ regime, using these as the primary carbon and energy sources, while urea and ammonium were opened as nitrogen sources.

Under this configured H₂/CO₂ medium, we ran pFBA on the unmodified (no-knockout) model to obtain its maximum biomass production rate (solution_initial.objective_value) and milk-protein (lactoalbumin) synthesis flux (lactoprotein_flux_initial). These serve as the baseline for subsequent knockout comparisons.

We then iterated knockouts for all reactions in the list and re-optimized with pFBA. A reaction knockout was implemented by setting the upper and lower flux bounds to 0.

14 genes, when knocked out, significantly increased biomass (>0.01%). Top five:

1. H16_A2325
   • Reaction: 2-oxoglutarate decarboxylase (2-oxoglutarate → succinyl–DH–lipoyl)
   • Pathway: TCA cycle / α-ketoglutarate metabolism
2. H16_A3146 / H16_B1386 / PHG418
   • Reaction: GAPDH (glyceraldehyde-3-phosphate dehydrogenase)
   • Pathway: Glycolysis (central metabolism)
3. H16_A1083 + H16_A1081 + H16_A1084
   • Reaction: Urease (urea → 2 NH₄⁺ + CO₂)
   • Pathway: Nitrogen metabolism
4. H16_A3013 / H16_A1306 / H16_A3649 / H16_A1109
   • Reaction: N-formylglutamate amidase
   • Pathway: Glutamate-derivative metabolism
5. H16_A2227 / H16_A2211
   • Reaction: Isocitrate lyase
   • Pathway: Glyoxylate cycle (glyoxylate shunt)

• Genes in glycolysis and the TCA cycle constitute the central metabolic backbone; their knockout tends to stall growth or be lethal, which is unfavorable for maintaining a protein-producing background.
• Genes in nitrogen/amino-acid metabolism exert indirect effects on protein synthesis and are potential targets.
• For bypass carbon metabolism, impacts on protein synthesis are also indirect, and knockout risk is lower than in central metabolism—making them more suitable for experimental attempts.

Taking all factors into account, we knocked out H16_A3598, corresponding to R_GLYOCARBOLIG_RXN (glyoxylate carboligase reaction), to reduce glyoxylate-branch flux and divert more carbon into the TCA cycle and into energy/amino-acid supply.

Using FBA under specified media where urea serves as the nitrogen source, we quantitatively evaluated metabolism for producing the target protein (lactoprotein). The analysis covers conversion efficiency from feedstock to product, the impact of key reaction knockouts, and a theoretical yield estimate.

The nitrogen mass fraction of urea is wᵤᵣₑₐ_N ≈ 46.6%.

The average nitrogen mass fraction of protein (Kjeldahl) is wᵖʳᵒᵗᵉⁱⁿ_N ≈ 16%.

Hence, neglecting losses, the maximum protein mass producible per unit mass of urea is:

mₚᵣₒₜₑᵢₙ,ₘₐₓ = (wᵤᵣₑₐ_N ⋅ mᵤᵣₑₐ) / wᵖʳᵒᵗᵉⁱⁿ_N = 0.466 / 0.16 ⋅ mᵤᵣₑₐ = 2.9125 ⋅ mᵤᵣₑₐ

Convert the FBA-derived protein synthesis flux, together with a given dry cell weight (DCW), into the volumetric productivity P (g·L⁻¹·d⁻¹):

P = vₚᵣₒₜₑᵢₙ × MWₚᵣₒₜₑᵢₙᵉᶠᶠ × DCW × 24

Here:

• P is the daily, per-liter protein yield
• MWₚᵣₒₜₑᵢₙᵉᶠᶠ is the effective molecular weight of the protein (0.5 g/mmol in this study)
• DCW is the cell dry weight concentration (this study set to 0.20 g/L based on OD₆₀₀ = 0.4)

Despite supplying H₂ and CO₂ in the medium, the model preferentially adopts heterotrophic or mixotrophic growth on fructose and ammonium. Key exchange fluxes are:

Exchange (Metabolite)	Reaction ID	Flux (model units)	Note
Fructose uptake	EX_BETA_D_FRUCTOSE_e	-100.00	Major carbon & energy source
Ammonium uptake	EX_AMMONIUM_e	-100.00	Major nitrogen source
Urea uptake	EX_UREA_e	-24.41	Auxiliary nitrogen source
O₂ uptake	EX_OXYGEN_MOLECULE_e	-20.00	Respiratory electron acceptor
H₂O secretion	EX_WATER_e	224.68	Metabolic product
CO₂ secretion	EX_CARBON_DIOXIDE_e	54.99	Respiration product

Under these simulation conditions, cells do not exhibit autotrophic (Knallgas) metabolism, but rather typical heterotrophy. Based on FBA fluxes, the model’s nitrogen efficiency is 1.4% and carbon efficiency is 4.5%, indicating that much of the nutrients are directed to biomass formation and energy maintenance rather than directly to target-protein synthesis.

At the optimal growth state in this regime:

• Maximum biomass production rate (R_Biomass): 2.4337 h⁻¹
• Target-protein synthesis flux (SYNTHESIS_lactoprotein): 0.1188 mmol·gDW⁻¹·h⁻¹

Assuming the culture reaches at steady phase OD₆₀₀ = 0.4 (corresponding DCW ≈ 0.20 g/L), the estimated daily volumetric protein yield is:

Daily protein titer:

0.2852 g·L⁻¹·d⁻¹

When the production of lactose protein increases, the biomass growth rate significantly decreases, proving that the synthesis of lactose protein imposes a substantial metabolic burden on cell growth. Cells must make trade-offs and allocate resources between growth (biomass accumulation) and the production of target proteins. To enhance lactose protein yield, cells have to sacrifice their own proliferative capacity.

• Per-capita daily urine volume: 1.4 L·d⁻¹
• Mean urea concentration: 25.745 g·L⁻¹
• Crew size: 6
• Per-capita daily protein requirement: 80 g·d⁻¹
• System-level nitrogen conversion efficiency (includes urea recovery and biotransformation): 0.8

Based on nitrogen conservation, we relate urea supply to protein production.

1. Total daily urea available — this is the nitrogen input to the system:

   Mᵤᵣₑₐ = n ⋅ Vᵤᵣᵢₙₑ × Cᵤᵣₑₐ

   Substituting values: Mᵤᵣₑₐ = 6 × 1.4 × 25.745 = 216.26 g/d

2. Total daily protein demand — the production target for the life-support system:

   P_dₑₘₐₙd = n ⋅ X

   Substituting values: P_dₑₘₐₙd = 6 × 80 = 480 g/d

3. Theoretical protein supply — using the maximum urea→protein conversion coefficient (2.9125) and system efficiency:

   Pₛᵤₚₚₗᵧ = 2.9125 ⋅ η_N ⋅ Mᵤᵣₑₐ

   Substituting values: Pₛᵤₚₚₗᵧ = 2.9125 × 0.8 × 216.26 = 502.92 g/d

Pₛᵤₚₚₗᵧ ≥ P_dₑₘₐₙd

Supply meets and exceeds demand.

From a theoretical material-balance perspective, at 80% system nitrogen conversion efficiency, urea generated by six astronauts is sufficient to meet their daily protein requirement, with a small surplus. Genome-scale FBA simulations further corroborate that, under specified culture conditions, the model grows effectively and synthesizes the target protein. This provides key biological feasibility evidence for a urea-recycling–based bioregenerative life support system (BLSS); future optimization of culture conditions could enable more efficient autotrophic protein production.

To quantify the upper bounds and operating ranges for utilizing N, C, and H resources, we combined stoichiometric balance calculations with Flux Balance Analysis (FBA) and defined a calculate_efficiencies function to compute nitrogen efficiency (η_N), carbon efficiency (η_C), and hydrogen efficiency (η_H₂).

η_N = (The nitrogen mass in the produced protein) / (The mass of nitrogen in the ingested urea) = (vₗₐcₜₒₚᵣₒₜₑᵢₙ × MWₗₐcₜₒₚᵣₒₜₑᵢₙ × Nₚᵣₒₜₑᵢₙ_fᵣₐc) / (abs(vᵤᵣₑₐ) × MWᵤᵣₑₐ_N)

η_C = (The carbon mass in the produced protein) / (The mass of carbon in the ingested CO₂) = (vₗₐcₜₒₚᵣₒₜₑᵢₙ × MWₗₐcₜₒₚᵣₒₜₑᵢₙ × Cₚᵣₒₜₑᵢₙ_fᵣₐc) / (abs(v_CO₂) × MW_CO₂_C)

η_H₂ = (Quality of produced protein) / (The mass of H₂ intake) = (vₗₐcₜₒₚᵣₒₜₑᵢₙ × MWₗₐcₜₒₚᵣₒₜₑᵢₙ) / (abs(v_H₂) × MW_H₂)

Before analysis, we printed the fluxes of all exchange reactions in the metabolic model to directly compare differences under distinct media.

Exchange Reaction	Flux under H₂/CO₂ medium (mmol·gDW⁻¹·h⁻¹)	Flux under custom medium (mmol·gDW⁻¹·h⁻¹)	Description
EX_HYDROGEN_MOLECULE_e (H₂)	-79.911	0.633	Hydrogen
EX_CARBON_DIOXIDE_e (CO₂)	-18.916	802.587	Carbon dioxide
EX_BETA_D_FRUCTOSE_e	0	-970.015	Fructose
EX_UREA_e	0	-100.000	Urea
EX_AMMONIUM_e	-4.577	-100.000	Ammonium
EX_OXYGEN_MOLECULE_e (O₂)	-20.000	-20.000	Oxygen
EX_WATER_e	72.574	720.495	Water
EX_PROTON_e	4.076	1000.000	Proton
EX_Pi_e	-0.217	-12.460	Phosphate
EX_SULFATE_e	-0.170	-9.790	Sulfate
EX_L_ALPHA_ALANINE_e	0	-1.000	L-Alanine
EX_D_LACTATE_e	0	821.524	D-Lactate
EX_ACET_e	0	107.067	Acetate
EX_ETOH_e	0	576.197	Ethanol
EX_CH33ADO_e	0.002	0.100	CH33ADO
EX_FE2_e	-0.001	0	Ferrous ion

Efficiency Metric	H₂/CO₂ medium	Heterotrophic medium
Nitrogen efficiency (η_N)	0.017	0.020
Carbon efficiency (η_C)	0.015	0.003
Hydrogen efficiency (η_H₂)	0.037	267.832

From the fluxes and efficiency conversions, the heterotrophic condition exhibits a marked advantage in converting urea → protein. The heterotrophic model not only shows higher nitrogen conversion efficiency, but also effectively uses urea as the primary nitrogen source. This strongly supports that, with appropriate organic carbon supplementation, microorganisms can more efficiently transform astronaut-derived urea into valuable protein—offering a promising protein production route for bioregenerative life-support systems.