Mathematical Model of a Bubble Column for the Increased Growth of Arthrospira platensis and the Formation of Phycocyanin

The objective of this research was to develop a mathematical model for batch photoautotrophic cultivation of Arthrospira platensis and to validate it against data obtained in experiments. All trials were carried at 30°C, under a light intensity of 60 or 120 µmol m^-2s^-1. The purpose of the model was to determine the optimal concentration of carbon dioxide, as well as to investigate the formation of phycocyanin. For the experimental conditions in this study, the optimal concentration carbon dioxide (0.8% CO₂, v/v) was predicted using the model according to the initial bicarbonate level, the carbon uptake by the microalga, the pH, and the mass transfer process. The use of this optimal value in the gas inlet seems to be a suitable option for maintaining the optimal pH (9.5), thereby eliminating the need for a pH controller in the bioreactor system. According to the simulations, the mass fraction of the phycocyanin formation rate seems to depend on the internal light level. The percentage of adjustment obtained (R²) was ?75%. The velocity of phycocyanin formation was enhanced at intensities up to 120 µmol m^-2s^-1. However, the actual internal irradiance values were lower than the light compensation point (4.5 µmol m^-2s^-1), so phycocyanin formation ceased. The mathematical model may facilitate the examination of optimal carbon delivery, as well as the light input, in several A. platensis culture conditions aimed at phycocyanin production.

Arthrospira platensis; Carbon dioxide; Light intensity; Mathematical model; Phycocyanin

        Arthrospira platensis is a prokaryotic photoautotrophic cyanobacterium characterized by high levels of lipids that are currently being used as a fuel source (Jamilatun et al., 2019; Sukarni et al., 2019; Jamilatun et al., 2020). Its biomass also contains protein and other valuable substances, so A. platensis is now also cultivated to market it as complete biomass. Among the valuable compounds found in this microalga is phycocyanin, a protein of great interest to the food industry for its antioxidant capacity and to the cosmetic interest for its bright blue color. Other potential compounds of interest include ?-linoleic acid, which is an important unsaturated fatty acid, and spirulan calcium, which is a sulfated exopolysaccharide with promising biological functions (Borowitzka, 2013). A. platensis is cultivated in open cropping systems, but this cultivation method has a low biomass productivity (0.04 g DW L^-1d^-1) (Jiménez et al., 2003) and produces a low-quality phycocyanin compared to cultivation in photobioreactors.

        Open cropping systems have a 20-fold lower biomass production than photoreactors (Bezerra et al., 2011; Chen et al., 2013) because the environment in open ponds cannot be controlled for the variables that determine the productivity of microalgae (temperature, pH, light intensity, nutrient levels, carbon, etc.) (Borowitzka, 2013). This control is possible in bioreactors, but the cultivation of microalgae in photobioreactors is only economically feasible if it produces an optimal yield with low investment costs, including the operation of the facility (Bertucco et al., 2014). The important aspects needed for bioreactor technology to be successful and efficient are the use of optimal strategies for carbon delivery and precision in the use of light.

A. platensis is a filamentous cyanobacterium capable of naturally forming colonies in waters that contain high levels of carbonates and bicarbonates (Binaghi et al., 2003). Therefore, increasing the production of A. platensis is possible by avoiding carbon limitations and taking advantage of carbon dioxide capture, since the main source of inorganic carbon of A. platensis is the bicarbonate ion (HCO₃^-) (Cornet et al., 1998). Naturally occurring bicarbonate present in the medium, which is approximately 117 mM, is taken up by the cyanobacteria and used in photosynthesis to support growth (de Morais and Costa, 2007). This uptake also controls the pH (Pawlowski et al., 2014), because the loss of dissolved carbon dioxide due to uptake into cyanobacterial cells is partly compensated by regeneration from carbonates and bicarbonates, so carbon dioxide uptake is accompanied by changes in pH (Rubio et al., 1999). In bubble column photobioreactors, a carbon dioxide line is opened or closed automatically according to an established pH set point. This implies that these reactors require pH sensors (Doucha et al., 2005; Spalding, 2008), thereby increasing investment and operating costs. However, a mathematical model for the control of CO₂ supply could overcome this challenge.

One of the main functions of phycocyanin in microalgae is the capture of light; therefore, the intensity of light has an important influence on the accumulation of this phycobiliprotein (Chen et al., 2013). However, the reported optimal light intensity values required to achieve a high production of phycocyanin show no consistency, which could reflect different intensities of internal light within the culture. This discrepancy may also be a consequence of different bioreactor configurations and culture conditions (Xie et al., 2015). Again, the use of a mathematical model could aid in identifying the optimal light intensity for a particular cyanobacterial crop.

The biomass growth and pH variations predicted with the model agree with the experimental measurements. Cultivations with either 3% or 0.035% CO₂ led to a suboptimal pH, so the model was used to determine a CO₂ concentration that results in an optimal pH of 9.5. For the experimental conditions in this work (60 µmol m^-2s^-1), a 0.8% CO₂ concentration was selected. A sensitive analysis with higher light intensity (120 µmol m^-2s^-1) showed an increment in the biomass productivity, as well as in the optimal CO₂ concentration (1.2% CO₂). The mass fraction of phycocyanin was produced at a rate that was mainly controlled by the internal light in the photobioreactor before nitrate limitations appeared. At light intensities of 120 µmol m^-2s^-1, the biomass productivity was two times greater than the experimental results at 60 µmol m^-2s^-1. According to the simulations, the average internal light should be between 140 µmol m^-2s^-1 and 4.5 µmol m^-2s^-1 (the CO₂ compensation point for A. platensis). Lower or higher values seem to have an adverse effect on the phycocyanin mass fraction.

In summary, the mathematical model proposed here can help to eliminate the need for pH sensing in cyanobacterial cultivation by forecasting the CO₂ level required to regulate the pH. The results showed a good adjusted R² (coefficient of determination) between the model data and the experimental data (R² ? 75%). The model can support the investigation of other culture conditions (i.e., light intensity) or photobioreactor modifications (i.e., light path) and their influence on phycocyanin production.

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