Dependence of cyanobacterium growth and Mars-specific photobioreactor mass on total pressure, pN2 and pCO2

Model organism and routine growth conditions

Anabaena sp. PCC 7938 (hereafter, Anabaena sp.) was obtained from the Pasteur Culture Collection of Cyanobacteria (Paris, France). Prior to experiments, cultures were grown inside a poly klima PK 520-LED photo-incubator at 25 °C, in BG11₀ medium, with a light intensity of 15–20 μmol_ph m⁻² s⁻¹ (16 h/8 h day/night cycle), on a rotary shaker set at 100 rpm.

Setup for cultivation under artificial atmospheres

During experiments, Anabaena sp. was grown inside Atmos, a photobioreactor developed in-house for the cultivation of phototrophic microorganisms under low pressure². This hardware was modified to integrate a system (shown in Fig. 1 and outlined hereafter) which enables taking samples without affecting the atmospheric conditions inside the vessels. An injector nut with support and ¼” low bleed septum (Vici Valco Instruments, Houston, TX) was fitted, with a straight male connector (Swagelock Company, Solon, OH), to one of the G1/4” holes in the lid of each vessel. Prior to liquid sampling, the culture was stirred vigorously, and 1.3 ml was lifted to within centimetres of the lid, by using a Teflon sample container placed inside the vessel and manually controlled with an outer piece (3D-printed in-house). This container was designed in-house and manufactured by Spanflug Technologies GmbH (Munich, Germany). One millilitre of culture was then sampled with a syringe (Model 1002; Hamilton Company, Reno, NV) and a needle (23 gauge, 100 mm, removable; Hamilton Company) inserted through the septum. To reduce the risks of inward biological contamination, the needle and the top of the injector nut were sterilized prior to sampling by, respectively, passing through a flame or wiping with 70% ethanol. During this sterilization step and until the needle had been fully inserted, the flame of a Bunsen burner was maintained above the lid.

Left: Close-up of the sample lifting system, composed of a Teflon sample container (a) placed inside the vessel and of an outer piece (b) connected to it by two pairs of neodymium magnets. Right: View of one vessel. Liquid samples can be brought to within a few centimetres of the lid by using the sample lifting system, then collected with a syringe and a needle inserted through a sampling port (c) integrated into the lid.

Full size image

Cultivation under various partial pressures of carbon dioxide and dinitrogen

Atmos was used to assess the relationship between the growth rates of Anabaena sp. and the partial pressures of CO₂ and N₂. In each vessel, 70 ml of BG11₀ was inoculated to an optical density at 750 nm (OD₇₅₀) of 0.05 with precultures in late exponential phase (one preculture was used for all vessels within one experimental run). When the partial pressure of CO₂ was varied across samples, the medium was buffered with 20 mM HEPES to avoid large changes in pH.

At the onset of experiments, the air in the vessels was replaced with a gas mixture – provided by either Linde Gas (Dublin, Ireland; standard gas mixture class 1) or Air Liquide S.A. (Paris, France; CYSTAL mixture) – containing either 1% CO₂ and one among various fractions of N₂ (0, 2, 10, 20 or 80%), or 80% N₂ and one among various fractions of CO₂ (0, 0.05, 0.5, 1, 2 or 5%), and Ar as a balance gas. Six replicate vessels (across at least two separate experimental runs) were used per gas mixture. The pressure in the gas phase was set to 1000 hPa and automatically reset to this value when deviations exceeded 10 hPa. The gas in the headspace was renewed (by flushing at constant pressure) 2 h after starting the experiment, then every 12 h throughout the experiment. The light intensity was set to 50 μmol photons m⁻² s⁻¹ per side (measured at the inner side of the vessel, where it is closest to the LED strips, at culture mid-height), temperature to 30 °C and stirring to 100 rpm.

Anabaena sp. was grown in these conditions for four days. Every 24 h, samples were taken to measure the OD₇₅₀.

Cultivation under various total pressures

Cultivation assays were used to test whether relying on a low total pressure (down to 80 hPa) has effects which are independent of pN₂ and pCO₂ on Anabaena sp.’s growth rates. They were performed as described above but for the following modifications. Anabaena sp. was cultivated in 80 ml of BG11 (BG11₀ supplemented with 1.5 g l⁻¹ NaNO₃) buffered with 20 mM HEPES and supplemented with 10 g l⁻¹ NaHCO₃. The air in the culture vessels was evacuated down to 1000, 100 or 80 hPa and replaced with Ar (Argon 6.0, Linde Gas). The gas in the headspace was renewed 2 h after starting the experiment, then every 24 h throughout the experiment. The pressure was automatically reset to its target value when it deviated by more than 10 or (for vessels under 80 hPa) 5 hPa.

Assessment of growth rates as a function of gas composition and pressure, assuming liquid-gas equilibrium

As no total pressure-dependent effect was found over the tested range (80–1000 hPa), the growth rates of Anabaena sp. were determined as a function of the partial pressures of CO₂ and N₂ (over 0–50 hPa and 0–800 hPa, respectively). Growth rates were determined based on OD₇₅₀ values in exponential phase and fitted to a Monod equation using the non-linear curve fitting function of Prism (GraphPad Software, Boston, MA; version 10.2.0 for Windows). As CO₂ appeared to be limiting in some of the experimental conditions aimed at assessing the effect of pN₂, a Monod equation for pN₂ in the absence of CO₂ limitation was obtained by excluding these conditions and including the 2%-CO₂, 80%-N₂ condition (R² = 0.995). Growth rates under given sets of atmospheric conditions were then determined as the minima between the growth rates predicted based on pN₂ and these predicted based on pCO₂.

Assessment of the minimum gas pressure required to sustain given growth rates, assuming liquid-gas equilibrium

The minimum gas pressure (P_gas, hPa) required to sustain given specific growth rates of Anabaena sp. was determined as the sum of pCO₂, pN₂, and the partial pressures of water vapour (pH₂O) and of gases injected alongside nitrogen (pOthers):

The O₂ produced by cyanobacteria was neglected as we assume a constant gas flow which prevents its accumulation. pCO₂ and pN₂ were calculated based on equations analogous to Monod’s (see above). pOthers accounts for gases present in the source of N₂, which we assume to be derived from pressurized Martian atmosphere by removal of CO₂ but not of other gases. We also assume that the ambient (unprocessed) atmosphere has the following composition¹³: 94.9% CO₂, 2.79% N₂, 2.08% Ar, 0.174% O₂, and 0.075% CO. Assuming ideal gas behaviour (a reasonable approximation given the low pressure range and the temperature around 30 °C), it follows that:

pH₂O was determined as follows. The water vapour pressure that would be saturating if no other gases were present (({p}_{H2O,{pure},s}), hPa) was first calculated as a function of the system’s temperature²³ (T, K):

The water vapour pressure in the absence of other gases (({p}_{H2O,{pure}}), hPa) is dependent on relative humidity (%RH, %):

Here we assume a relative humidity of 100%, hence ({p}_{H2O,{pure}}={p}_{H2O,{pure},s}).

({p}_{H2O,{pure}}) pertains to a system where water vapour is the only gas. To account for the impact of other gases, a dimensionless enhancement factor, f_w, was applied:

This factor was calculated as follows²⁴ (where P_Earth [hPa] is the ambient pressure on Earth at sea level):

The constants in Eq. (6) were determined by others, empirically, for a terrestrial atmospheric composition. Their use in the present work was deemed acceptable given the similar elemental composition of the expected gas phase (an N₂-dominated mixture of the same main components, though at different concentrations) and the low relative impact (<10% increase) of the enhancement factor on the calculated vapour pressure. ({t}_{{dp}}) (K) is the dew point temperature, which we determined with an empirical equation²⁵:

Assessment of the minimum inner pressure under constrained superficial velocity of sparged gases

The partial pressures calculated as described above assume an equilibrium between the liquid and gas phases, and that the dissolved inorganic carbon and nitrogen are replenished as they are consumed by cyanobacteria. Maintaining these conditions requires gases to be sparged with high enough a superficial velocity. However, superficial velocity can be increased to only some extent before inducing excessive shear stress (it is common practice not to exceed 0.08 m s⁻¹). Keeping growth rates constant as productivity goes up may therefore require enhancing the input of dissolved gases by increasing pCO₂ and pN₂. This effect – as well as that of the medium’s hydrostatic pressure – on the minimum inner pressure of a photobioreactor was accounted for as described below.

Hereafter, the concentrations of dissolved inorganic carbon and dissolved CO₂ are used interchangeably. While this is not formally correct as the former is also composed of carbonate and bicarbonate, inorganic carbon is entirely replenished by CO₂, and the half-velocity constant determined as described above already accounts for it.

Assuming ideal gas behaviour, the required partial pressure of gas i (p_i, hPa) – i standing for either CO₂ or N₂ – can be expressed as a function of its molar concentration in the gas phase (({C}_{i,G}), mol_i m^–3):

({C}_{{i,G}}) is dependent on the gas transfer rates (({iTR}), mol_i,L m^–3 s^–1) and gas-liquid mass transfer coefficients (({k}_{{iL}}a), s^–1) of CO₂ and N₂. This relationship is shown in Eq. (9), where m_i (mol_i,G mol_i,L^–1) is the partition coefficient – the ratio of the concentrations of gas i in the liquid and gas phases at equilibrium – calculated based on Henry’s law, and ({C}_{i,L}) (mol_i,L m^–3) is the concentration of CO₂ or N₂ in the medium.

The iTR required to replenish the dissolved CO₂ and N₂ was assessed based on the mass balance, shown in Eq. (10), over the liquid phase. The concentration of each dissolved gas is determined by the following elements: the ingoing and outgoing liquid flows (({F}_{L,{in}},{rm{and}},{F}_{L,{out}}), m³ s^–1) per culture volume (({V}_{{culture}}), m³); the gas concentrations in the ingoing and outgoing liquids (({{C}_{i,L,{in}},{rm{and}},{C}}_{i,L,{out}}), mol_i m^–3); the gas-liquid mass transfer (({iTR}cdot {V}_{{culture}}), mol_i,L s^–1); and the gas consumption rate by cyanobacteria. The latter was calculated as the product of biomassproductivity ((frac{{{dC}}_{x}}{{dt}}), mol_x m^–3 s^–1) and molar coefficient per mol of carbon in the biomass – i.e., the number of moles of gas i consumed for producing an amount of biomass that contains one mole of carbon (({i}_{{rm{COEFF}}}), mol_i mol_x^–1; here we assume²⁶ values of 1 for CO₂ and 0.0873 for N₂).

The concentrations of dissolved gases are assumed to remain constant, hence (frac{{dCi},{L}}{{dt}}=0). Assuming batch cultivation (and therefore, that ({{F}_{L,{in}}}={{F}_{L,{out}}}=0)), ({{iTR}}={{{i}_{rm{COEFF}}}}cdot frac{{dC}_{x}}{dt}).

({k}_{{iL}}a) (used in Eq. (9)) can be calculated from the gas-liquid mass transfer coefficient of O₂ (({k}_{O2L}a), s⁻¹) through Eq. (11), where D_i (cm² s⁻¹) is the diffusion coefficient of gas i and D_O2 (cm² s⁻¹) that of O₂ (here we assume D_O2 = 2.42 ×10⁻⁵, D_CO2 = 1.91 ×10⁻⁵, and D_N2 = 2.00 ×10⁻⁵):

While diffusivity coefficients vary with pressure, at a given temperature, their ratio does not. ({k}_{O2L}a) was calculated using Eq. (12):

In Eq. (12), a factor is applied to the superficial velocity of the incoming gas (v_gs, here assumed to be 0.08 m s⁻¹) to account for a variation in velocity along the height of the liquid phase. ({P}_{{gasR}}) (hPa) is the gas pressure at culture mid-height. As shown in Eq. (13), its value depends on hydrostatic pressure (({P}_{{hyd}}), hPa), which itself depends on Martian gravity (g_Mars, equal to 3.7278 m s^–2), medium density (ρ_L, here assumed to be 1000 kg m⁻³) and culture height (({h}_{L}), m).

The 0.32 factor and 0.7 exponent in Eq. (12) are empirical constants for a bubble column with normal bubble aeration²⁷. Equation (12) also includes the following two correction factors. One ((sqrt{frac{{P}_{{Earth}}}{{P}_{{gasR}}}})) accounts for an increase in gas-liquid mass transfer with decreasing pressure, which is due to an increase in gas diffusivity. This correction was defined by considering that, in all of the various models which have been proposed to assess ({k}_{L}a), the latter varies proportionally to the square root of the diffusion coefficient²⁸, which itself is inversely proportional to pressure²⁹. It is only applicable because the empirical constants pertain to a photobioreactor under Earth’s ambient pressure at sea level. It is worth noting that the effects of diffusivity on gas-liquid mass transfer coefficients are usually not considered when modelling bioprocesses. This is mostly because they are not as significant as the associated change in bubble volume. As the bubble volume is here assumed to be constant, these effects are more relevant. The second correction factor addresses the lower gas-transfer efficiency in low gravity environments (({g}_{{corr}})), calculated as described by others³⁰. It accounts for the decrease in bubble velocity, which results in lower turbulent mixing, and is only valid when the bubble volume remains constant across the compared gravity levels.

Assessment of a photobioreactor’s wall mass as a function of total inner pressure

Increasing the difference between the inner and outer pressures increases the stress on the photobioreactor’s walls, and thereby the minimum thickness required of these walls to withstand it. To illustrate the impact this would have on payload mass, rough calculations were performed based on a simple structure which approximates that of a bubble column photobioreactor: a cylinder closed by plates at both ends, with a liquid phase of one cubic metre and whose diameter is twice its height, with a headspace increasing the height by one tenth, and under a constant temperature of 30 °C.

The shear forces acting on the cylinder are dependent on the inside-outside pressure difference ((Delta {P}_{{cyl}}), hPa). The inner pressure is the sum of the inner gas pressure (({P}_{{gas}})) and the hydrostatic pressure (({P}_{{hyd}})), and the outer pressure is that of the ambient atmosphere (P_Mars, here assumed to be 6 hPa):

The forces acting on the on the upper plate – the lid – are dependent on the difference between ({P}_{{gas}}) and ({P}_{{Mars}}) ((Delta {P}_{{top}}), hPa).

The minimum t hickness of the cylindrical wall necessary to withstand ({Delta P}_{{cyl}}) (({s}_{{cyl},min }), m) was calculated for different materials – poly(methyl methacrylate) (PMMA), polyethylene terephthalate (PET), polycarbonate (PC), aluminium (alu) and steel – using Eq. (16) (based on the maximum shear stress theory)³¹:

In Eq. (16), d (m) is the cylinder’s inner diameter, R_m is the tensile strength of material m (hPa; here we assume^32,33 R_PMMA = 73 ×10⁴; R_PET = 80 ×10⁴; =; R_PC = 66 ×10⁴; R_Alu = 250 ×10⁴; and R_Steel = 650 ×10⁴) and S is a safety factor (here set to 2).

A lower boundary on material thickness (s_min,m, m; here assumed to be 2 ×10⁻³ for steel and 3 ×10⁻³ for the other materials^32,33) was set to account for constraints on manufacturing and handling. The thickness of the cylindrical wall (s_cyl, m) is therefore assumed to be the minimum between s_cyl,min and s_min,m.

Based on (varDelta {P}_{{top}}) (Eq. (15)), the minimum thickness of the lid (s_top,min, m) was calculated according to Eqs. (17)–(20)^34,35:

As the bottom plate is assumed to be resting on a surface (and thus not to be directly impacted by the inner-outer pressure difference), its thickness is assumed to be equal to ({s}_{min ,m}).

The mass of the photobioreactor’s walls was determined as the sum of the masses of the cylinder, lid and bottom plate. These individual masses were obtained by multiplying the volume (m³) of each component by the density of the material it is made of (ρ_m, kg m⁻³; here we assume^32,33 ρ_PMMA = 1190; ρ_PET = 1400; ρ_PC = 1200; ρ_Alu = 2700; and ρ_Steel = 7900).

• SEO Powered Content & PR Distribution. Get Amplified Today.
• PlatoData.Network Vertical Generative Ai. Empower Yourself. Access Here.
• PlatoAiStream. Web3 Intelligence. Knowledge Amplified. Access Here.
• PlatoESG. Carbon, CleanTech, Energy, Environment, Solar, Waste Management. Access Here.
• PlatoHealth. Biotech and Clinical Trials Intelligence. Access Here.
• Source: https://www.nature.com/articles/s41526-024-00440-1