Optimizing Docosahexaenoic Acid (DHA) Production by Schizochytrium sp. Grown on Waste Glycerol

: The aim of this study was to optimize biomass and docosahexaenoic acid (DHA) production by Schizochytrium sp. grown on waste glycerol as an organic carbon source. Parameters having a signiﬁcant effect on biomass and DHA yields were screened using the fractional Plackett–Burman design and the response surface methodology (RSM). Schizochytrium sp. growth was most significantly inﬂuenced by crude glycerin concentration in the growth medium (150 g/dm 3 ), process temperature (27 ◦ C), oxygen in the bioreactor (49.99% v / v ), and the concentration of peptone as a source of nitrogen (9.99 g/dm 3 ). The process parameter values identiﬁed as optimal for producing high DHA concentrations in the biomass were as follows: glycerin concentration 149.99 g/dm 3 , temperature 26 ◦ C, oxygen concentration 30% ( v / v ), and peptone concentration 2.21 g/dm 3 . The dry cell weight (DCW) obtained under actual laboratory conditions was 66.69 ± 0.66 g/dm 3 , i.e., 1.27% lower than the predicted value. The DHA concentration obtained in the actual culture was at 17.25 ± 0.33 g/dm 3 , which was 3.03% lower than the predicted value. The results obtained suggest that a two-step culture system should be employed, with the ﬁrst phase focused on high production of Schizochytrium sp. biomass, and the second focused on increasing DHA concentration in the cells.


Introduction
The properties of microalgae make them a useful resource for environmental engineering technologies, including wastewater treatment, bio-sequestration of carbon dioxide, manufacture of biofuels, and sorption of contaminants [1,2]. Microalgal biomass is also a source of value-added products useful in medicine, pharmaceuticals, fertilizer industry, animal feed industry, and the food sector [3,4]. The potential of the widespread industrial use of microalgae is limited by the lack of technologies that are process-efficient, simple in terms of design/technology, cost-effective to build and operate, and environmentally friendly [5]. One of the major drivers of operating cost for microalgal biomass production systems are the chemical components of the growth medium [6]. Therefore, there is a real need to seek, develop, and optimize methods that could serve as a competitive alternative to the current solutions. One of the most promising and encouraging options is found in the development of technologies that use waste substrates as the main growth medium ingredient [7,8], a method consistent with the idea of the circular economy and the principles of an integrated biorefinery approach [9]. With the use of biorefinery complexity index (BCI) as an indicator of technical and economic risk, algal-and waste-based bio-refinery platforms are considered to be one of the most promising approaches for producing fuel, food, animal feed, food supplements, fertilizers, and pharmaceuticals [10].
The aim of this research was to use a fractional Plackett-Burman design and the response surface methodology (RSM) to optimize docosahexaenoic acid (DHA) production by heterotrophic Schizochytrium sp., with waste glycerol used as a source of organic carbon.

General Design
The study aimed to identify and quantify the key process parameter values that affect the growth and DHA production of Schizochytrium sp. cultures, using glycerol as an external carbon source. The values were determined through a series of experiments structured using a Plackett-Burman design. After screening the most significant parameters having an effect on the performance, the parameter values resulting in highest dry cell weight (DCW) and DHA levels were determined using the response surface methodology. The modeled parameter values and predicted performance were then experimentally verified using a batch Schizochytrium sp. culture.

Materials
The study used Schizochytrium sp., a strain of single-cell heterotrophic microalgae from the family Thraustochytriaceae. The inoculum was obtained from the ATCC (American Type Culture Collection). Schizochytrium sp. cells were maintained in sterile agar slants of ATCC790By+ medium containing 2% agar (w/w). The cells were spread into new agar slants on a monthly basis. To obtain enough inoculum for the experiment, the cells were transferred from the agar slants to 50 cm 3 Erlenmeyer flasks, containing 15 cm 3 of the agarless ATCC790By+ liquid medium with a pH of 6.5, with the composition given in Tables 1 and 2. The medium was autoclave-sterilized before use (Systec V-95 autoclave, parameters: 121 • C, 15 min, 2 bars, automatic demineralized water feed for steam generation was used). The flasks were agitated in a temperature-controlled orbital shaker (Excella E24R, New Brunswick/Eppendorf) set to 170 rpm at 25 • C. After 120 h, 10 cm 3 of the culture (Schizochytrium sp. inoculum) was transferred into a 250 cm 3 Erlenmeyer flask containing 90 cm 3 of fresh ATCC790By+. The resultant 100 cm 3 culture was inoculated into 500 cm 3 bioreactors (with optimization performed using the Plackett-Burman design and response surface methodology) and a Biostat B Twin (Sartorius Stedim) bioreactor with a working capacity of 2.0 dm 3 (for the verification step).
Crude glycerin sourced from the PKN Orlen Południe S.A. plant in Trzebinia (Poland) was used as the substrate and the sole carbon source in the cultures. During the production of biodiesel, pressed rapeseed oil is filtered and transesterified with the use of NaOH catalyst in the amount of 1.2% to the weight of the oil (process temperature is 25 • C, reaction time 45 min). The ester and glycerol phases are separated by gravity or by centrifugation and the methanol is recovered from both phases by distillation. The substrate contained at least 80% (w/w) glycerol, up to 5% (w/w) ash, up to 6% (w/w) MONG (matter organic non glycerol), and trace water, according to its safety data sheet. The liquid had pH = 5, a light-brown coloration, and a characteristic odor.

Experimental Equipment
Batch photobioreactors (Erlenmeyer flasks) with an active volume of 500 cm 3 were used for the optimization step. The flasks were agitated in a temperature-controlled orbital shaker (Excella E24R, New Brunswick/Eppendorf) set to 170 rpm. During the validation step, the Schizochytrium sp. biomass was grown in a Biostat B Twin (Sartorius Stedim) bioreactor with a working capacity of 2 dm 3 . The bioreactor was fitted with acid, base, antifoaming agents, and organic substrate pumps. The system had a gas module for monitoring dissolved oxygen (DO), a system for stabilizing pH based on injecting acid or base via peristaltic pumps, and a temperature measurement/stabilization system. The vessels were stirred by a six-bladed Rushton turbine (53 mm diameter).

Analytical Methods
The crude glycerin concentration in the culture medium was determined by precentrifugation (8000× g, 4 min, 10 • C; UNIVERSAL 320 R centrifuge, Hettich, Westphalia, Germany). The supernatant was then filtered (pore size = 0.2 mm), and the filtrate was assayed for glycerol levels using a Glycerol GK Assay Kit (Megazyme). The test involved phosphorylating the glycerol with adenosine 5 -triphosphate (ATP), with the reaction product, adenosine 5 -diphosphate (ADP) then used to further phosphorylate d-glucose, which oxidizes producing nicotinamide adenine dinucleotide (NADH). The concentration of NADH was measured spectrophotometrically (Multiskan GO Microplate, Thermo Scientific, Waltham, MA, USA) at a wavelength of 340 nm.
The dry cell weight (DCW) of the microalgae was determined according to the method described by Chang et al., (2013) [45]. It was done by transferring a 50 cm 3 sample of the culture to a pre-weighed centrifuge tube, which was then centrifuged (8000 g for 15 min, UNIVERSAL 320 R centrifuge, Hettich). The supernatant was discarded and the concentrated biomass was washed twice with distilled water, then dried at 60 • C for 12 h in a moisture balance (MAR, Radwag, Radom, Poland) to stabilize the biomass.
The lipid content of the biomass was determined by adding 7 cm 3 of a 20% hydrochloric acid solution to 1.0 g of freeze-dried biomass (ALPHA 1-4 LD plus freeze dryer, Christ), which was then placed in a water bath (GFL 1003) at 75 • C for 40 min. The sample was treated with 20 cm 3 of n-hexane to extract the lipids and placed in a vacuum evaporator (Hei-VAP Advantage G3, Heidolph, Schwabach, Germany) to evaporate the solvent. The lipid content of the sample was measured gravimetrically. The determination of fatty acids in the microalgal biomass was done using a modified direct transmethylation process by Grayburn (1992) [46]. The freeze-dried microalgal biomass (ALPHA 1-4 LD plus, Christ, Bethlehem, Palestine) of 20-100 mg was transferred to a reaction vial, enriched with 2 mg of triheptadecanoylglycerol as an internal standard, and spiked with 2 cm 3 of a 1% solution of H 2 SO 4 in methanol. The vial was then thoroughly mixed and heated to a temperature of 80 • C for 2 h (MKR 13 blockthermostat-Ditabis, Pforzheim, Germany). After cooling, 2 cm 3 of chloroform and 1 cm 3 of distilled water were added. The vial was mixed at 1250 rpm (Vortex Reax top, Heidolph), and centrifuged at 1500× g (UNIVERSAL 320 R, Hettich). The organic phase containing fatty acid methyl esters (FAME) was harvested and analyzed by chromatography. A Clarus 680 GC (Perkin Elmer, Waltham, MA, USA) gas chromatograph was used for FAME analysis, with helium used as the carrier gas. The column temperature was raised from 150 • C to 250 • C at 10 • C/min, then kept at 250 • C for 10 min. The injector was kept at 275 • C with an injection volume of 1 µL. Detection was made using a flame ionization detector (FID) at 280 • C. The peak areas were identified by comparing their retention times with those of standard mixtures.

Optimization Design
A Plackett-Burman based experimental design was used to screen the factors having significant effects on the DCW increase and DHA production (Design-Expert software by Stat-Ease Inc.). The evaluated parameters were as follows: temperature ( • C), initial growth medium pH, volumetric air flow rate (L area /min·L cont .), oxygen in the growth medium (%), initial inoculum level (% v/v), concentration of crude glycerin (g/dm 3 ), salinity (psu), concentration of yeast extract (g/dm 3 ), turbine speed (rpm), and concentration of peptone (g/dm 3 ). A design matrix of experiments with specific parameters was generated using the method. Parameters that significantly affected the values of: the rate of DHA production by microalgae-r DHA (g/dm 3 ·h) and the growth rate of the microalgal biomass-r DCW (g/dm 3 ·h), were identified in the course of the study.
Each independent variable was investigated at a low (−) and a high (+) level. The values of parameters for both levels were selected through the analysis of the available literature data. The low levels (−) of a variable always corresponded to the lowest parameter value at which Schizochytrium sp. growth and DHA production were possible. A high (+) level of a variable was taken as the lowest parameter value at which these parameters were not inhibited. Each experiment was conducted in triplicate. Table 3 shows a list of the analyzed parameters and their values for each of the levels. Twelve experiments were established, as shown in Table 4. To determine the significant level for each parameter, as prescribed by the Analytical Methods Committee method, an additional "dummy" variable, "d 1 ", was added to the design matrix. The resultant effects of dummy variables reflected the standard error of the experiments, which was used to derive the significant level for each of the parameters. Parameters at p < 0.10 were taken as significant factors, which were further optimized using response surface methodology. For the experiments designed using the response surface methodology matrix, the levels of non-significant parameters were maintained at −1. The effects of each variable (E (xi) ), the significant (P) levels, and the F-test results for the obtained data are presented herein.
The effect of each variable (E (xi) ) was derived using the equation: where E (xi) is the effect of the variable, M i+ is theDCW or DHA concentration for the high (+) level of the variable, M i− is the DCW or DHA concentration for the low (−) level of the variable, and N is the number of runs. In order to determine how significant the effect of each parameter was on the technological process, ANOVA-derived calculations were used, i.e., the sum of squares of the effects (SS) of each parameter (with the exception of the dummy variable). The parameter was calculated according to the equation: where SS is the sum of the squares of the effects of each variable, E (xi) is the effect of the variable, and N is the number of runs. The most significant parameters affecting the DCW and DHA concentration were screened, followed by the determination of the parameter values resulting in the highest DCW and DHA levels. This was achieved by using a statistical response surface methodology to formulate a list of experiments with Design-Expert software by Stat-Ease Inc. The method involved testing the parameters at five levels: −2, −1, 0, 1, and 2, and establishing an experimental design with central and axial points (Table 5). Other parameters previously identified as non-significant were maintained at a constant level. The experimental design matrix consisted of a 2 4 full factor design combined with six central points, and eight axial points, where one variable was set at an extreme level while the others were set at the central point level (Table 6).  Table 6. Experimental matrix designed using response surface methodology, with coded levels of significant parameters.

Experiment No.
Temperature

Concentration of Crude Glycerin (g/dm 3 )
Oxygen Concentration (%) Based on the experimental results, the DCW and DHA values were correlated by the second-order polynomial equation: where Y is the predicted response of the design, β is the coefficient of the equation, and x i and x j are coded levels of parameters i and j, respectively. The variable matrix equation was generated using Design-Expert software by Stat-Ease Inc. The significance level for the model was confirmed with an F-test. The selected cultural conditions resulting in highest DCW and DHA levels were verified through two experiments. The first experiment was to compare the experimental data with the predicted DCW levels, the other was to compare the experimental data with the predicted DHA concentrations.

Statistical Analysis
Each experimental variant was conducted in triplicate. The statistical analysis of experimental results was conducted using the STATISTICA 13.1 PL package. The hypothesis concerning the normality of distribution of each analyzed variable was verified using a W Shapiro-Wilk test. One-way analysis of variance (ANOVA) was conducted to determine differences between variables. Homogeneity of variance in groups was determined using a Levene test. The Tukey (HSD) test was applied to determine the significance of differences between the analyzed variables. In the tests, results were considered significant at α = 0.05.

Screening Significant Culture Factors According to the Plackett-Burman Design
The dry cell weight (DCW) of Schizochytrium sp. microalgae varied between 16.1 and 65.4 g/dm 3 , DHA concentration ranged from 3.6 to 14.7 g/dm 3 , depending on the culture parameters. Mean DCW and DHA concentrations were 35.72 ± 4.36 g/dm 3 and 8.09 ± 0.62 g/dm 3 , respectively ( Figure 1). The lowest DCW and DHA concentrations were observed in experiment 12 with all culture parameters at low (−1) levels. Conversely, the highest DCW and DHA concentrations were observed in experiment 8, which had high (+1) levels of parameters designated X 1 , X 2 , X 3 , X 4 , X 6 , X 8 , and X 9, and low (−1) levels of parameters X 5 , X 7 , and X 10 . Therefore, an inoculum level of 10% (v/v), salinity of 17.5 psu, and peptone concentration of 2 g/dm 3 were sufficient to obtain the highest levels of Schizochytrium sp. biomass and DHA across the experiments. A screening of physicochemical cultural parameters was performed with Design-Expert software by Stat-Ease Inc. Table 7 shows the significance levels for those parameters that were highly correlated with DCW level and DHA concentration (p < 0.10), namely: crude glycerin concentration, temperature, oxygen concentration, and peptone concentration. The selected parameters were optimized using the response surface methodology.

Quantification of Culture Parameter Values Using the Response Surface Methodology
The objective of this step was to define those values of the Schizochytrium sp. batch culture parameters that resulted in the highest DCW and DHA levels. The results are presented in Figure 2. The DCW of Schizochytrium sp. microalgae varied between 38.9 and 65.4 g/dm 3 , whereas DHA levels in the culture ranged from 8.43 to 16.00 g/dm 3 , depending on the culture parameters ( Figure 2). The lowest DCW and DHA levels were almost 2.5 times higher than the lowest values obtained in the first part of this experimental step. Mean DCW and DHA concentrations were 56.07 ± 4.68 g/dm 3 and 13.49 ± 1.72 g/dm 3 , respectively, and were 1.6 times higher than the mean Plackett-Burman design results. The highest biomass concentration was recorded for experiment 20, with the crude glycerin concentration set at level +2 (187.5 g/dm 3 ) and other significant parameters at 0 (oxygen concentration 40%, peptone concentration 3.5 g/dm 3 , temperature 26.5 °C). The highest increase in DHA levels (experiment 12) occurred with the crude glycerin

Quantification of Culture Parameter Values Using the Response Surface Methodology
The objective of this step was to define those values of the Schizochytrium sp. batch culture parameters that resulted in the highest DCW and DHA levels. The results are presented in Figure 2. The DCW of Schizochytrium sp. microalgae varied between 38.9 and 65.4 g/dm 3 , whereas DHA levels in the culture ranged from 8.43 to 16.00 g/dm 3 , depending on the culture parameters ( Figure 2). The lowest DCW and DHA levels were almost 2.5 times higher than the lowest values obtained in the first part of this experimental step. Mean DCW and DHA concentrations were 56.07 ± 4.68 g/dm 3 and 13.49 ± 1.72 g/dm 3 , respectively, and were 1.6 times higher than the mean Plackett-Burman design results. The highest biomass concentration was recorded for experiment 20, with the crude glycerin concentration set at level +2 (187.5 g/dm 3 ) and other significant parameters at 0 (oxygen concentration 40%, peptone concentration 3.5 g/dm 3 , temperature 26.5 • C). The highest increase in DHA levels (experiment 12) occurred with the crude glycerin concentration set at level −1 (75 g/dm 3 ) and other parameters at +1 (temperature 28 • C, oxygen concentration 50%, and peptone concentration 5 g/dm 3 ). This means that the concentrations of cell biomass and DHA were most significantly influenced by the same parameters, though at different values.
It was shown that the parameters having a statistically significant (p < 0.10) effect on DCW and DHA levels were: crude glycerin concentration, temperature, oxygen concentration, and peptone concentration ( Table 8). The data analysis was followed by the determination of coefficients for the second-order polynomial equation, indicating the correlation of the most significant variables and their effect on DCW/DHA levels ( Table 9). These values of coefficients for the second-order polynomial equation served as the basis for deriving the predicted DCW/DHA levels in relation to the significant parameters screened by the response surface methodology. The predicted parameter values for the biomass-optimized culture were DCW 67.55 g/dm 3 and DHA 15.53 g/dm 3 ; whereas the predicted parameter values for the DHA-optimized culture were DHA 17.79 g/dm 3 and DCW 63.59 g/dm 3 . The DCW estimation model was characterized by an estimation error on the level of ±4.075 g/dm 3 , and reflected 89.45% of changes in the process (coefficient of determination R2 = 0.8945). The DHA estimation model reflected 90.92% of changes in the process (coefficient of determination R2 = 0.9092), with an estimation error at the level of ±2.061 g/dm 3 . The ANOVA calculation shows that the p-value was 0.0035 for the DCW estimation model and 0.0010 for the DHA estimation model, which means the relationship between the independent variables and the response values investigated in this experiment were significant and the scheme was reliable.     The correlation between the DCW and DHA values and the parameter values shows that increasing temperature and crude glycerin concentration (up to 27.25 • C and 150 g/dm 3 , respectively) caused the DCW to increase as well. The opposite was found to be true at higher values ( Figure 3). Raising the oxygen concentration (up to a value of 30%) and temperature (up to a value of 26.37 • C) increased DHA concentration in the biomass. As previously, the trend was reversed at higher values ( Figure 4).  The correlation between the DCW and DHA values and the parameter values shows that increasing temperature and crude glycerin concentration (up to 27.25 °C and 150 g/dm 3 , respectively) caused the DCW to increase as well. The opposite was found to be true at higher values ( Figure 3). Raising the oxygen concentration (up to a value of 30%) and temperature (up to a value of 26.37 °C) increased DHA concentration in the biomass. As previously, the trend was reversed at higher values ( Figure 4).

Verification of Process Parameter Optimization
Optimization using the response surface methodology (RSM) showed that a culture optimized for DCW concentration could yield DCW levels of 67.55 g/dm 3 ( Figure 5). The DCW levels obtained under actual laboratory conditions were 66.69 ± 0.66 g/dm 3 , being 1.27% lower than the predicted value. When cell DHA levels are compared between the DHA-optimized culture (17.25 ± 0.33 g/dm 3 ) and the value predicted using RSM (17.79 g/dm 3 ), the former is found to be lower by 3.03% ( Figure 5).
The culture optimized for high DCW levels produced rDCW of 0.56 ± 0.005 g/dm 3 ·h and rDHA of 0.12 ± 0.006 g/dm 3 ·h. While the rDCW value was the same as predicted using RSM (0.56 g/dm 3 ·h), the rDHA was 7.7% lower than predicted (0.13 g/dm 3 ·h). The culture optimized for DHA concentration resulted in a rDCW value of 0.51 ± 0.014 g/dm 3 ·h, whereas the rDHA equaled 0.14 ± 0.003 g/dm 3 ·h. In this case, rDCW deviated from the predicted value by 3.77%, whereas the rDHA was 6.67% lower ( Figure 5).
The experiments confirmed that the significant culture parameters must be adjusted differently depending on whether the culture is intended to produce high biomass growth or high DHA yields. With cultural parameters set for high biomass growth (temperature 27 °C, crude glycerin concentration 150 g/dm 3 , oxygen concentration 49.99%, and peptone concentration 9.99 g/dm 3 ), the dry cell weight was 66.69 ± 0.66 g/dm 3 , and the DHA level was 14.60 ± 0.76 g/dm 3 . On the other hand, cultural conditions optimized for higher cell DHA levels (temperature 26 °C, crude glycerin concentration 149.99 g/dm 3 , oxygen concentration 30%, and peptone concentration 2.21 g/dm 3 ) produced DCW levels of 61.73 ± 1.70 g/dm 3 and DHA levels of 17.25 ± 0.33 g/dm 3 ( Figure 5). These results suggest that a two-step culture system should be employed, with the culture process divided into two phases. The first phase would target a higher cell concentration, while the second, higher DHA yields from the biomass.

Verification of Process Parameter Optimization
Optimization using the response surface methodology (RSM) showed that a culture optimized for DCW concentration could yield DCW levels of 67.55 g/dm 3 ( Figure 5). The DCW levels obtained under actual laboratory conditions were 66.69 ± 0.66 g/dm 3 , being 1.27% lower than the predicted value. When cell DHA levels are compared between the DHA-optimized culture (17.25 ± 0.33 g/dm 3 ) and the value predicted using RSM (17.79 g/dm 3 ), the former is found to be lower by 3.03% ( Figure 5).
The culture optimized for high DCW levels produced r DCW of 0.56 ± 0.005 g/dm 3 ·h and r DHA of 0.12 ± 0.006 g/dm 3 ·h. While the r DCW value was the same as predicted using RSM (0.56 g/dm 3 ·h), the r DHA was 7.7% lower than predicted (0.13 g/dm 3 ·h). The culture optimized for DHA concentration resulted in a r DCW value of 0.51 ± 0.014 g/dm 3 ·h, whereas the r DHA equaled 0.14 ± 0.003 g/dm 3 ·h. In this case, r DCW deviated from the predicted value by 3.77%, whereas the r DHA was 6.67% lower ( Figure 5). (a) (b) Figure 5. Comparison of (a) obtained levels of biomass (DCW) and DHA; and (b) biomass growth rate and microalgal DHA production with the parameters set using the response surface methodology and experimental data (by culture purpose).

Discussion
The present experiments are part of larger pioneer research efforts on the use of waste organic substrates to grow heterotrophic microalgae Schizochytrium sp. for industrial purposes [47,48]. As these microalgae are able to grow on a variety of carbon sources, they may reasonably be grown on waste glycerol [49]. The biomass of Schizochytrium sp. heterotrophic microalgae contains high amounts of DHA and no heavy metals (e.g., mercury), making it highly suitable for use in food supplements, food products, and animal feed [50,51]. To ensure an optimum growth rate of Schizochytrium sp. biomass and, above all, to enable scale-up of production for commercial purposes, a variety of factors  The experiments confirmed that the significant culture parameters must be adjusted differently depending on whether the culture is intended to produce high biomass growth or high DHA yields. With cultural parameters set for high biomass growth (temperature 27 • C, crude glycerin concentration 150 g/dm 3 , oxygen concentration 49.99%, and peptone concentration 9.99 g/dm 3 ), the dry cell weight was 66.69 ± 0.66 g/dm 3 , and the DHA level was 14.60 ± 0.76 g/dm 3 . On the other hand, cultural conditions optimized for higher cell DHA levels (temperature 26 • C, crude glycerin concentration 149.99 g/dm 3 , oxygen concentration 30%, and peptone concentration 2.21 g/dm 3 ) produced DCW levels of 61.73 ± 1.70 g/dm 3 and DHA levels of 17.25 ± 0.33 g/dm 3 ( Figure 5). These results suggest that a two-step culture system should be employed, with the culture process divided into two phases. The first phase would target a higher cell concentration, while the second, higher DHA yields from the biomass.

Discussion
The present experiments are part of larger pioneer research efforts on the use of waste organic substrates to grow heterotrophic microalgae Schizochytrium sp. for industrial purposes [47,48]. As these microalgae are able to grow on a variety of carbon sources, they may reasonably be grown on waste glycerol [49]. The biomass of Schizochytrium sp. heterotrophic microalgae contains high amounts of DHA and no heavy metals (e.g., mercury), making it highly suitable for use in food supplements, food products, and animal feed [50,51]. To ensure an optimum growth rate of Schizochytrium sp. biomass and, above all, to enable scale-up of production for commercial purposes, a variety of factors need to be optimized and controlled for, including physicochemical parameters of the culture, properties of the waste substrate, presence of potential growth inhibitors, substrate availability and cost, culture productivity, investment costs, and the choice of the microalgae strain [52]. Therefore, more advanced research is needed on this issue.
The present study showed that DCW and DHA levels in Schizochytrium sp. microalgae are most significantly influenced by: temperature, crude glycerin concentration in the medium, oxygen concentration, and peptone concentration in the bioreactor. A temperature of 26 • C favored DHA production in the cells, whereas higher temperatures promoted biomass growth. These findings are corroborated by the authors of [53,54], who reported that temperature was the primary driver of cell concentration in the culture medium and the accumulation of bioactive compounds in the biomass. The optimal value for producing the highest biomass levels varies with the microalgae strain and its source environment. Many authors [55][56][57][58], have noted that fatty acid production in Chlorella minutissima, Pythium irregulare, and Crypthecodinium cohnii cells consistently occurred at low temperatures, as opposed to temperature levels most favorable to biomass growth in process systems. According to [59,60], the increased PUFA content in the investigated microalgae cells at low culture temperatures was linked to increased cell membrane elasticity in the microorganisms, triggered as a defense mechanism. The increase might also be attributed to the higher availability of intracellular molecular oxygen at low temperatures, leading to the activation of oxygen-dependent enzymes that desaturate and elongate PUFAs in cells [61,62].
The present study demonstrated that a crude glycerin concentration of 150 g/dm 3 led to the highest DCW levels at 67.55 g/dm 3 , as well as an increase of DHA concentration in Schizochytrium sp. cells to 17.25 g/dm 3 . Comparable results were obtained by Huang et al. (2012). Their study results indicated that at 100 g/dm 3 glycerol, Aurantiochytrium limacinum SR21 achieved a biomass at 61.76 g/dm 3 and DHA concentration at 20.3 g/dm 3 [63]. A lower production was observed by Chi et al. (2007), according to whom the optimal range of crude glycerol concentration is lower to support the growth of Schizochytrium limacinum algae and DHA production, and amounts to 75-100 g/dm 3 . A highest DHA yield of 4.91 g/dm 3 with 22.1 g/dm 3 DCW was obtained [50]. Moreover, Scott et al. (2011) achieved less efficient results. Using 64.7 g/dm 3 of crude glycerol, they achieved 31.66 g/dm 3 biomass of Thraustochytrium sp. ONC T18 and 4.41 g/dm 3 DHA [64]. Other researchers have also noted how the type and level of the external carbon source affected microalgal cultures [65,66]. These authors reported that the carbon source affected biomass growth and might influence PUFA synthesis. Glycerol-based cultures produced higher yields than processes based on glucose, coconut oil, brewery wastes, or wastewater from soymilk production. Thraustochytriacae microalgae biomass (Y) grown on crude (waste) glycerol was found to produce higher DHA yields (166-550 mg/g) than a pure glycerol-based culture (110-223 mg/g) [50,67]. It is worth noting, however, that the final cell DHA levels are mainly determined by the cell growth phase at the time of DHA extraction.
Previous scientific reports have optimized the oxygen level in microalgae cultures for the production of PUFAs, including DHA. The study described in patent [68] proposed the induction of higher DHA concentrations by lowering oxygen in the growth medium. Oxygen limitation caused a decrease in monounsaturated fatty acids and activated oxygen-dependent PUFA synthase, thus increasing cell DHA and DPA [69,70]. A study by Chi et al. (2009) [71] showed that cultures grown at 10% oxygen exhibited low microalgal growth in favor of an increasing concentration of fatty acids in the biomass, whereas the reverse was true at 50% oxygen. These findings are corroborated by the present results, where the 30% oxygen concentration was found to favor DHA production in the cells, (DCW = 63.59 g/dm 3 , C DHA = 17.79 g/dm 3 ), and the highest biomass concentration was obtained when the system was oxygen-saturated to 50% (DCW = 67.55 g/dm 3 , C DHA = 15.53 g/dm 3 ). This can be explained by the fact that biomass growth necessitates the production of large quantities of primary metabolites, such as nucleic acids, enzymes, and proteins. The production of these compounds requires high oxygen in the process system [71,72].
The dry mass of Schizochytrium sp. microalgae contains 14-20% nitrogen (w/w), mainly incorporated into the structure of proteins and nucleic acids [53,73]. In order to meet cellular nitrogen demand, growth mediums are spiked with various nitrogen sources, such as corn steep, peptone, ammonium sulfate, or mixtures thereof [74,75]. Other alternatives to cheap nitrogen sources include fish waste hydrolysate, silkworm larvae, and wheat bran extract [76]. It is important to note that different nitrogen sources are preferred for different strains to ensure rapid cell growth and the accumulation of metabolites (such as DHA) in technological processes [77,78]. The present study confirms that a 9.99 g/dm 3 dose of peptone is required for an increased concentration of Schizochytrium sp. cells in the growth medium, whereas only 2.21 g/dm 3 is needed at the lipid (DHA) accumulation stage. This observation supports the thesis that the generation of new cells and biomass requires a supply of primary metabolite components, such as enzymes, proteins, or nucleic acids. The nitrogen demand is less pronounced in cultures designed for secondary metabolite (Omega-3 acids) synthesis [71,79]. It is worth noting that peptone is a complex nitrogen source, meaning that it contains proteins, peptides, and free amino acids, while being low in carbohydrates, lipids, inorganic ions, vitamins, and growth factors. In addition to its primary function of supplying nitrogen to cell biomass, peptone also promotes overall cell development, granting an advantage over industrial nitrogen sources [80,81].

Conclusions
The experiments presented in this study showed the high potential of using the waste fraction of glycerol from biodiesel production to produce biomass and DHA by Schizochytrium sp. microalgae. In the course of designing and executing the study, as well as analyzing the results of optimization and experimental work, the theses made prior to the experiments were verified.
In the course of the study, parameters having a significant effect on Schizochytrium sp. cell growth and DHA accumulation were screened using the Plackett-Burman design and quantified using the response surface methodology.
The study has shown that the growth and DHA production of Schizochytrium sp. microalgae was most significantly influenced by the following physicochemical parameters: crude glycerin concentration in the growth medium (150 g/dm 3 ), process temperature (27 • C), oxygen concentration in the bioreactor (49.99% v/v), and peptone concentration as a source of nitrogen (9.99 g/dm 3 ). Other parameters, such as initial pH, volumetric air flow rate, inoculum level, salinity, turbine speed, and concentration of yeast extract, were not statistically significant and were therefore eliminated from further analyses.
The optimization methods used in the study identified the following physicochemical parameter values as optimal for producing high DHA concentrations in the biomass: temperature 26 • C, crude glycerin concentration 149.99 g/dm 3 , oxygen concentration 30% (v/v), and peptone concentration 2.21 g/dm 3 .
Laboratory verification produced DCW levels of 66.69 ± 0.66 g/dm 3 , i.e., 1.27% lower than the predicted value. When cell DHA levels are compared between the DHAoptimized culture (17.25 ± 0.33 g/dm 3 ) and the value predicted using the response surface methodology (17.79 g/dm 3 ), the former is found to be lower by 3.03%.
The results suggest that a two-step culture system should be employed, with the culture process divided into two phases. The first phase would target higher cell concentration, while the second, higher DHA yields from the biomass.

Conflicts of Interest:
The authors declare no conflict of interest.