Integration of mathematical and experimental modeling for sustainable phycobiliprotein production via fed-batch cultures

• The utilization of mathematical models was assessed to optimize C-phycocyanin (C-PC) production employing a thermotolerant strain of Potamosiphon sp., focusing on overcoming nutrient limitations and enhancing process efficiency. • C-PC production exhibited critical dependence on optimal phosphorus and nitrogen concentrations, underscoring the importance of adjusting the nutrient feeding rates to maximize conversion and yield. • The Tessier model was identified as the most suitable for accurate prediction and optimization of operational conditions, achieving growth rates of 1.23 g/L and a C-PC concentration of 37 mg/L, which is essential for industrial applications. The production of phycobiliproteins, such as cyanobacterial phycocyanins, is a growing interest due to their diverse industrial and biotechnological applications. This study focuses on optimizing phycocyanin production using the strain Potamosiphon sp. through experimental techniques and mathematical modeling in fed-batch cultures. The methodology applied includes determining the kinetic constants by linearizing the Monod equation evaluating the concentrations of biomass, C-phycocyanin (C-PC), nitrates (NO 3 ), and phosphates (PO 4 ). A mathematical model of periodic fed-batch feeding was subsequently established, applying mass conservation principles and evaluating the accuracy of the Monod, Contois, Moser, and Tessier models. The results indicate that phycocyanin production is highly dependent on phosphorus and nitrogen concentrations, with optimal conversion observed at specific levels of these elements (0.832 for phosphorus and 0.805 for nitrogen in terms of C-PC and biomass, respectively). The Tessier model demonstrated the highest accuracy in predicting production and optimizing operational conditions, with a Mean Squared Error (MSE) of 0.005000 for biomass production, 0.200000 for C-PC production, and 0.000010 for substrate consumption. It also achieved high R² values of 0.980 for biomass, 0.999 for C-PC production, and 0.997 for substrate consumption. It presented the lowest Akaike Information Criterion (AIC) scores, indicating its robustness and reliability in modeling these processes and manipulating cultivation conditions and providing adequate nutrition allowed for achieving growth rates of 1.23 g/L and a C-PC concentration of 37 mg/L, which are essential for industrial applications such as natural colorants and antioxidants, among others.