## 3 Results and Discussion
### Regression Modeling and Statistical Analysis
#### 3.2.5 Validation of RSM-CDD Based Models  
The results obtained from various models were validated, and the corresponding values were shown in Tables 1-3. The quantification of biomass, lipids, and carotenoids was performed using spectrophotometric and gravimetric methods. Based on model analysis and the prediction of optimal culture conditions, the optimum cultivation conditions were found to be N (5000 mg\(\cdot\)L\({}^{-1}\)), P + K (250 mg\(\cdot\)L\({}^{-1}\)), S (70 mg\(\cdot\)L\({}^{-1}\)), PP (24 h), and LI (137.5 umol m\({}^{-2}\)s\({}^{-1}\)). To confirm the accuracy of the regression model used in the response surface approach, the maximum development efficiency under optimal conditions was examined. The actual values of biomass, lipid, and caroten development efficiencies were 75.4 mg\(\cdot\)L\({}^{-1}\)d\({}^{-1}\), 40.28%, and 16.2 ug\(\cdot\)mL\({}^{-1}\), respectively. These findings confirmed the applicability of the obtained models, and the experimental values corresponds to the predicted values. Based on the aforementioned experimental findings, it was demonstrated that the model was reliable. Effect of Distinctive Abiotic Factors on the Yield of Biomass, Lipids, Chlorophylls, and Carotenoids  
Under the photoautotrophic (BBM) conditions, which served as the control, _Monoraphidium_ sp. exhibited a dynamic growth pattern, with a maximal biomass production of 576.6 mg\(\cdot\)L\({}^{-1}\), biomass productivity of 28.3 mg\(\cdot\)L\({}^{-1}\)d\({}^{-1}\), lipid production of 106 mg\(\cdot\)L\({}^{-1}\), and total carotenoid production of 3.76 ug\(\cdot\)mL\({}^{-1}\) during the stationary phase. In contrast, under optimized cultivation conditions, the highest biomass production was 1357.36 mg\(\cdot\)L\({}^{-1}\), the highest biomass productivity was 75.4 mg\(\cdot\)L\({}^{-1}\)d\({}^{-1}\), the highest lipid production was 542.8 mg\(\cdot\)L\({}^{-1}\), and the highest total carotenoid production was 16.25 ug\(\cdot\)mL\({}^{-1}\), all of which were achieved during the stationary phase. Both the control and optimized conditions were used for harvest on the 18 th day of culture, as this day resulted in the highest biomass, lipid, and carotenoid yields under the optimized conditions. These results supported our hypothesis that abiotic factors, such as nutrients and light, play a crucial role in the accumulation of value-added metabolites in _Monoraphidium_ sp. Previous studies have shown that single abiotic factors can affect the synthesis of metabolites and microalgal growth [32]. However, not much research has been conducted on the effects of multiple abiotic factor combinations on microalgal development [33,34]. In this study, a wide range of abiotic factors were studied with an emphasis on boosting carotenoid synthesis while enhancing the ability to produce biomass and lipid levels. Carotenoid and lipid production were directly correlated with biomass production, irrespective of various external factors, including light, nutrition, temperature, etc. As shown in Table 4, N, P + K, S, LI, and PP promoted the accretion of biomass, carotenoids, and lipids. Several abiotic factors are combined to trigger biomass, fatty acid, and carotenoid production compared to the control (autotrophic cultivation under BBM medium). In _D. salima_ cultivated under light and nitrogen deprivation stress conditions, a concomitant rise in \(\beta\)-carotene and TAG accumulation has been reported [35]. [PERSON] et al. (2021) reported that _Monoraphiidium_ sp. SP03 increased astaxanthin concentration under UV-A (0.476 \(\upmu\)g\(\cdot\)mL\({}^{-1}\) biomass) compared to the control (0.363 ug\(\cdot\)mL\({}^{-1}\) biomass) [36]. Nitrogen stress has been widely used to improve lipid formation in microalgae such as _Chorella vulgaris_ and _Scenadesmus_ sp. [37]. These studies suggest that nutrient and illumination stress constitute a feasible paradigm that can be employed in _Monoraphiidium_ sp. for industrial applications, as it triggers the synthesis of significant quantities of carotenoids and lipids.