## 3 Results and Discussion
### Effect of Nitrogen Starvation on Carotenoids and Astaxanthin Production by H. pluvialis  
While light intensity and organic carbon from BWW are critical factors influencing carotenoid synthesis, N availability is another key determinant [46]. In this section, we explore how N starvation under low light conditions influences astaxanthin production, aiming to identify optimal conditions for pigment accumulation under minimal light stress. In various studies, light intensities used for _H. pluvialis_ cultivation in flasks or columns typically range between 30 and 60 \(\upmu\)mol m\({}^{-2}\) s\({}^{-1}\)[16]. N is the primary nutrient influencing both _H. pluvialis_ growth and astaxanthin accumulation [47]. N starvation is a consolidated strategy to enhance the astaxanthin content within the cells [17]. In this study, when _Haematococcus_ was cultivated in BWW under all the three light regimes, the content of chlorophyll \(a\) and \(b\) and total chlorophyll was lower compared to the other systems blended with the control medium and the control itself (Table 4). Furthermore, when comparing the mixotrophic systems (excluding growth under 140 \(\upmu\)mol m\({}^{-2}\) s\({}^{-1}\)), the total carotenoid content in BWW was higher than in other systems. These findings suggest that N starvation, a condition likely present in BWW (as shown in Table 3), may trigger a metabolic shift within the cells, promoting astaxanthin formation at the expense of chlorophyll production. The literature supports the idea that low light intensity coupled with N starvation can enhance astaxanthin accumulation in _Haematococcus_. Under these stress conditions, microalgae shift their metabolic processes towards producing secondary metabolites like astaxanthin, which serves as a protective mechanism against environmental stress [48]. To corroborate these observations, _H. pluvialis_ was cultivated under the lowest light regime (35 \(\upmu\)mol m\({}^{-2}\) s\({}^{-1}\)) for an extended period (9 days) while applying the N starvation strategy. To this aim, eight different concentrations of N (ranging from 0 to 17.56 mM) were selected, with corresponding amounts of sodium nitrate added to the BWW medium. Figure 5 illustrates the growth kinetics of _Haematococcus_ under N starvation. Haematococcus_ exhibited an average lag phase of around 3 days, after which fast accumulation of biomass occurred in systems with N concentrations between 1.76 and 8.82 mM. Systems with lower N contents (0.35-0.88 mM) and with the highest concentration (17.56 mM) experienced a longer lag phase, with biomass accumulation starting around the sixth day. The system with the lowest N concentration (0.18 mM) and the raw BWW (0 mM) showed a lag phase persisting for 9 days. Biomass accumulation ranged from 0.07 g L\({}^{-1}\) with 0 mM of N to 0.9 g L\({}^{-1}\) with 17.56 mM of N, with a maximum value of 2.54 g L\({}^{-1}\) observed at 1.76 mM of N. The specific growth rates \(\mu\) obtained under the different N concentrations were calculated using Equation (2) and are shown in Figure 6.  
Figure 5: Growth kinetics of _H. pluvialis_ during 9 days under mixotrophy at different N concentration (mM) in BWW medium and a low light regime of 35 \(\upmu\)mol m\({}^{-2}\) s\({}^{-1}\). Since the specific growth rate showed an optimum N value and then decreased for higher N concentrations, the data could be theoretically interpreted through the Haldane kinetic model for substrate inhibition [49] reported in Equation (9). \[\mu=\mu_{\text{max}}\,\cdot\,\frac{C_{N}}{k_{m}+C_{N}+\frac{C_{N}^{2}}{k_{i}}} \tag{9}\]  
It can be observed that the model matched the experimental data well when the parameters were tuned to the values reported in Table 5.  
Such a model can be viably used to eventually model the growth of _H. pluvialis_ in different devices operating in continuous or fed-batch mode. The impact of N starvation on biomass productivity (mg L\({}^{-1}\) day\({}^{-1}\)), total carotenoids (mg g\({}^{-1}\)dw), and astaxanthin content (%dw) in _H.