## 3 Results and Discussion
### Effect of Nitrogen Starvation on Carotenoids and Astaxanthin Production by H. pluvialis
pluvialis_ grown in BWW is illustrated in Figure 7.  
The fast transition to the inductive stage under N starvation is evident from Figure 7d, where the highest astaxanthin content of 1.59 %dw was observed in the raw BWW (N1), where no external N was added. This condition not only yielded the highest astaxanthin content but also resulted in the lowest biomass content (0.07 g L\({}^{-1}\)) and biomass productivity (8 mg L\({}^{-1}\) day\({}^{-1}\)). A clear proportional relationship can be seen between the increasing N concentrations added to the BWW and the gradual decrease in astaxanthin content. The same trend can be obviously detected for TC. This trend aligns with the literature findings [17], wherein a proportional decline in astaxanthin production was reported when N concentrations were increased from 0- to 3-fold in terms of nitrate under low light (30 \(\mu\)mol m\({}^{-2}\) s\({}^{-1}\)) for 10 days. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline \(\mu_{max}\) & 0.503 \(\pm\) 0.181 & day\({}^{-1}\) \\ k\({}_{\text{m}}\) & 1.172 \(\pm\) 0.784 & mM \\ k\({}_{\text{i}}\) & 9.726 \(\pm\) 7.508 & mM\({}^{2}\) \\ Reduced x\({}^{2}\) & 425.65 & - \\ R\({}^{2}\) & 0.936 & - \\ Adjusted R\({}^{2}\) & 0.905 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameters of the Haldane kinetics and main statistical analysis of fitting performance. Figure 6: Experimental specific growth rate of _H. pluvialis_ under mixotrophy as a function of N concentration in BWW medium and fitting with the model by [PERSON] for growth with substrate inhibition. In our study, there was also a slight but consistent increase in biomass content and productivity as the N concentration increased, particularly within the N range 0 to 1.76 mM. Beyond this range, further additions of nitrate led to a slight decline in both biomass content and productivity. This behavior is consistent with the literature [47], wherein the highest astaxanthin content was reported (2.3 % dW) with the addition of 0.18 mM nitrate to the BG11 control medium during _H. pluyuilis_ cultivation in the attached systems. Previous research has demonstrated that N deficiency suppresses chlorophyll biosynthesis in _H. pluyuilis_, accelerates chlorophyll \(b\) degradation, enhances plastoquinol terminal oxidase (PTOX) activity, and increases cyclic electron transport [50]. The reduction in chlorophyll levels diminishes the photosynthetic capacity of the cells [51]. Under these stress conditions, _H. pluyuilis_ tends to accumulate substantial amounts of carbon, primarily in the form of lipids and carotenoids [52]. In our study, lower N concentrations were strongly correlated with increased astaxanthin levels, while total carotenoids were higher in BWW with both high N concentrations (3.52-17.56 mM) and in the raw BWW (0 mM N). Future work should expand this analysis to higher light intensities to fully understand the combined effects of light and N on astaxanthin synthesis. Finally, a deeper analysis of the upscaling potential of this technique will be carried out in the next steps of this research activity. The main challenges when upscaling the proposed technique would be to maintain a high biomass productivity while ensuring the efficient induction of astaxanthin synthesis, since the latter one is typically produced when cells are stressed and the growth rate is lower. So, a trade-off set of operating conditions should be identified that is capable of ensuring good biomass productivity and a simultaneous good intracellular content of astaxanthin. A deep understanding  
Figure 7: Effect of N starvation on (**a**) biomass content (g L\({}^{-1}\)), (**b**) productivity (mg L\({}^{-1}\) day\({}^{-1}\)), (**c**) total carotenoids (mg g\({}^{-1}\)\({}_{\text{dw}}\)) and (**d**) astaxanthin content (%DW) of _H. pluyuilis_ grown for 9 days in BWW using a light intensity of 35 \(\upmu\)mol m\({}^{-2}\) s\({}^{-1}\). N1 = 0 mM, N2 = 0.18 mM, N3 = 0.35 mM, N4 = 0.88 mM, N5 = 1.76 mM, N6 = 3.52 mM, N7 = 8.82 mM, N8 = 17.56 mM.