KINETIC MODEL OF COMMERCIAL GLUCOSE-AFFECTED GROWTH AND MICROBIAL OIL PRODUCTION OF OLEAGINOUS YEAST Pseudozyma parantarctica CHC28

This research proposed to study the effect of commercial glucose concentration in a nitrogen-limiting medium on the growth of Pseudozyma parantarctica CHC28 and to estimate the kinetic parameters of fermentation. The biomass, microbial oil, biomass production rate (Qx), and oil production rate (Qp) increased dramatically and reached 22.10±1.95 g/L, 10.99±1.31 g/L, 0.184±0.016 g/L h, and 0.092±0.011 g/L h, respectively, when glucose concentration was increased to 100 g/L (C/N ratio = 333). In contrast, these results showed a decrease when glucose and C/N ratio were higher than 100 g/L and 333, respectively. Concurrently, the oil content showed a continuous rise as the glucose and C/N ratio increased. Furthermore, the maximum specific growth rate (μmax) declined sharply when P. parantarctica was cultivated under high glucose concentration. It was therefore suggested that the glucose concentration could affect the growth of oleaginous yeast because of osmotic pressure and C/N ratio. For the bioreactor scale, biomass, microbial oil, and oil content were enhanced to 29.92 g/L, 15.13 g/L, and 50.57 %w/w, respectively, at 120 hrs of cultivation. The mathematical models could describe the effect of glucose concentration on both yeast growth and microbial oil production. Thus, the kinetic model satisfactorily fitted the experimental data relating to oleaginous growth, microbial oil production, and substrate consumption.


INTRODUCTION
The energy crisis is one of the most critical issues in current times. Due to the limited reserves of fossil fuels, high energy demand, and environmental impact, meeting the future energy demand is a matter of great concern (Ma et al., 2018). Renewable energy has emerged as one of the most feasible solutions to overcome this challenge. Biodiesel obtained from energy crops and their derivatives reduces undesirable effects on the environment, such as acid rain and the greenhouse effect caused by fossil fuel combustion. In addition, it offers an advantage over fossil fuels because it is biodegradable and renewable (Soccol et al., 2017). However, the amount of vegetable oils available for biodiesel production is insufficient in case of increase in demand. Currently, single-cell oil or microbial oil has been reported to be a fascinating alternative source for biodiesel production. The cultivation of microorganisms producing microbial oil can be carried out through an uncomplicated process with low-cost raw materials. The microorganism which accumulates more than 20 percent of intracellular oil is identified as an oleaginous microorganism (Qin et al., 2017). The various oleaginous microorganisms which can produce microbial oil include bacteria, yeasts, molds, and microalgae (Qasim and Sultan, 2020; Saenge et al., 2011). Previous research has shown that yeast has an advantage over other oleaginous microorganisms, in growing and producing oil at a higher rate (Saenge et al., 2011). The fatty acid compositions of yeasts are similar to that of vegetable oils such as palm, coconut, jatropha, and rapeseed oils (Ong et al., 2011;Satyanarayana and Muraleedharan, 2011;Areesirisuk et al., 2015;Sutanto et al., 2018). Oleaginous yeast is cultured in order to extract intracellular oil from microbial cells. The microbial oils thus obtained are used as a feedstock for biodiesel production, thus offering an interesting alternative (Li et al., 2007). Previous research has found that oleaginous microorganisms could be induced to produce and accumulate oil in media containing an excess of carbon, with limitation in the quantities of some elements such as phosphorus, sulfate, or nitrogen (Gill et al., 1977;Jakobsen et al., 2008;Wu et al., 2010Wu et al., , 2011Bonturi et al., 2017). For instance, phosphorus is an important component of microbial growth. It is used to determine the composition of biomolecules, i.e., nucleic acid, phospholipids, and coenzymes. Studies show that phosphate limitation could lead to oil production in oleaginous yeast (Granger et al., 1993;Wu et al., 2010). Further, nitrogen deficiency was also proposed as a master regulator of oil synthesis (Ratledge and Wynn, 2002; Bonturi et al., 2017). Moreover, it has been observed that the application of nitrogen starvation strategy in microbial oil production, provides higher intracellular oil content when compared to oil content generated by the limitation of other elements (Wu et al., 2010). In this context, a mathematical model of the microbial fermentation process may be applied to understand and predict the fermentation profile. Moreover, such models could be used to estimate the kinetic parameters of fermentation. For instance, a practical model could be used to at least indicate parameters such as microbial growth, substrate consumption, and characteristics of product formation during fermentation (Yang et al., 2011;Farias et al., 2014). Therefore, given all of the above-mentioned factors, in this study, kinetic modeling was used to evaluate the effect of glucose-based nitrogen-limiting media on growth, microbial oil production, and substrate consumption of oleaginous yeast Pseudozyma parantarctica CHC28. This research aimed to study the influence of commercial glucose concentration on the growth of oleaginous yeast and to employ a mathematical model for predicting yeast growth and microbial oil production profiles.

Yeast strain and inoculum preparation
P. parantarctica CHC28, an oleaginous yeast, was used in this study (Areesirisuk et al., 2015). The stock culture of oleaginous yeast CHC28 was recultured in Yeast Malt broth (YM broth) at 30°C, 150 rpm of shaking speed, for 24 hrs. Subsequently, 5 mL volume of activated yeast (with an optical density of approximately 0.7-0.8 at 600 nm) culture was transferred to a 100 mL seed medium containing (in g/L): glucose 20, yeast extract 0.5, (NH4)2SO4 5.0, MgSO4·7H2O 0.5, and KH2PO4 1.0. It was cultured as per the above-mentioned procedure for 20 hrs. This cultured yeast was used as a starter in the following experiment.

Glucose-affected growth of oleaginous yeast
Five milliliters of yeast starter were aseptically inoculated into 100 mL of nitrogen-limiting medium containing (in g/L): yeast extract 0.1, (NH4)2SO4 0.5, MgSO4·7H2O 0.15, and KH2PO4 7.0. Commercial glucose produced from cassava starch (cassava starch-based glucose, WGC, Co. Ltd.) was used as the primary carbon source. This glucose was added as the sole carbon source and its concentration was varied between 20 to 300 g/L. The batch fermentation was performed at 30°C and 150 rpm of shaking speed. The culture was withdrawn aseptically from the experimental flask and the biomass, oil, and glucose concentration were determined as described below. The experiments were run in triplicates. The bioreactor scale experiment was performed using 5 L of nitrogen-limiting medium containing glucose 100 g/L in a 10-L fermenter (Major Science, MS-F1, Taiwan). Fifteen milliliters of the re-cultured oleaginous strain were aseptically transferred to 300 mL of seed medium and cultured at 30°C and 150 rpm of shaking speed for 20 hrs. Five hundred milliliters of seed culture were aseptically inoculated to the bioreactor and cultivated at 30°C, a stirring speed of 300 rpm, and 1.0 vvm of aeration rate. The sample was withdrawn throughout cultivation to determine glucose, biomass, and oil concentration.

Analytical method
The yeast cells were harvested by centrifugation at 12,000 rpm for 10 min and washed twice with water. The cleaned cells were dried at 60°C to a constant weight, usually for 24 hrs. The biomass was determined gravimetrically and expressed as the gram of biomass per liter (Xue et al., 2008). The oil concentration was analyzed with a mixture of chloroform and methanol, according to the method proposed in Bligh and Dyer (1959). Glucose was determined using 3,5-dinitrosalicylic colorimetric method (Miller, 1959).

Kinetic model
The growth rate of oleaginous yeast was investigated by the Logistic equation in (1) (Zajšek and Goršek, 2010; Laopaiboon et al., 2016), as follows: where µmax was the maximum specific growth rate, X was the biomass at specific times (t) of yeast growth, and Xmax was maximum biomass concentration.
The rate of substrate consumed (dS/dt) was used to explain the cell growth rate (including the intracellular oil) and the biomass concentration following the equation (2): where Yx/s was the biomass yield on substrate and ms was the biomass maintenance coefficient. The rate of production of oil (dP/dt) was dependent on the biomass concentration, following the Luedeking-Piret equation given below: In Eq. (3) α was a growth-associated oil formation coefficient, and β was a nongrowth-associated oil formation coefficient. If α≠0 and β=0, the oil formation was directly coordinated to microbial growth; if α≠0 and β≠0, the oil formation was partially dependent on microbial growth; and if α=0 and β≠0, the oil formation was unrelated to microbial growth (Gaden, 2000; Yang et al., 2011).

Estimation of model parameters
The kinetic parameters of the Logistic model (µmax and Xmax) were calculated to fit the model and the experimental data. The fitting was performed using Berkley Madonna™ software for curve fitting (Marudkla et al., 2018). The coefficient of determination (R 2 ) was applied to measure the model fitting quality between the predicted and the experimental data (Wannawilai and Sirisansaneeyakul, 2015). R 2 was calculated using the following equation: In Eq. (4), Cpred was the value of a predicted variable using the mathematical model. Cexp and C ̅ exp were the corresponding experimental values and the average of all the experimented values of the critical variable, respectively. The nonnormalized root means square (NRMS) value was employed to investigate the actual error for each determination (Wannawilai and Sirisansaneeyakul, 2015).
The NRMS was expressed as follows: where N is the number of determinations.

Statistical method
The experimental data were examined for statistical significance using a one-way analysis of variance (ANOVA). Duncan's multiple range test (DMRT) was used to compare the effect of glucose on fermentation parameters. Statistical analysis was performed using SPSS 15.0 software (SPSS Inc., USA).

Glucose-affected growth and oil production of oleaginous yeast
The glucose-affected growth of P. parantarctica CHC28 was studied. The batch fermentations were operated in a shaking flask with glucose variation between 20 g/L and 300 g/L. Figure 1 represents the biomass concentration of P. parantarctica CHC28 against cultivation time. The results showed that the growth of P. parantarctica CHC28 was affected by glucose concentration as the primary carbon source. The yeast growth increased with an increase in glucose and then decreased slightly when glucose was increased to 120 g/L. This result suggested that P. parantarctica CHC28 could grow well without substrate inhibition under a wide range of substrate concentrations, especially from 20 to100 g/L. Table 1 presents the microbial oil production of yeast following 120 hrs of cultivation. The biomass and oil production were enhanced following the increase in the glucose concentration until 100 g/L. Subsequently, they clearly dropped when yeast was cultured in glucose over 100 g/L. The oil content increased continuously in accordance with the increasing C/N ratio, and the maximum oil content of 59.70±2.51% was obtained at 300 g/L of glucose (C/N ratio = 999). Simultaneously, the biomass production rate (Qx) and oil production rate (Qp) rapidly reached the highest values of 0.190±0.019 and 0.092±0.011 g/L at glucose levels of 80 and 100 g/L, respectively. Furthermore, the Qx and Qp reduced dramatically when glucose was higher than 100 g/L. Thus, it was found that when P. parantractica CHC28 was cultured in glucose 100 g/L (C/N ratio = 333), it produced the maximum biomass, oil, Qx, and Qp, at the rate of 22.10±1.95 g/L, 10.99±1.31 g/L, 0.184±0.016 g/L h, and 0.092±0.011 g/L h, respectively. These results suggested that oil accumulation occurred most frequently, when the nutrient source, particularly the nitrogen source, was limited, while the excess carbon source was offered at the required levels (Bonturi et al., 2017). Typically, it occurred concurrently with the stationary phase. Thus, nitrogen limitation has proved to be one of the most practical methods to induce oil production because it can easily control media composition. Eventually, oil synthesis pathways of microorganisms were positively regulated to balance cell growth with energy storage (   Legend: The data indicate mean ± standard deviation (SD). The different letters alongside the values in the same column indicate significant differences (pvalue < 0.05).

Modeling the growth kinetic
A growth kinetic model was used to predict the behavior of the microbial cultivation process. Equation (1) was deployed to model the biomass growth in nitrogen-limiting media, which contained glucose as the major carbon source. During cultivation, the lag phase was observed during 6-11 hours of fermentation. Subsequently, the P. paranrarctica CHC28 presented a classical growth trend corresponding to the sigmoid curve. Moreover, it was found that the final biomass concentration also depended on the initial glucose concentration. At the end of fermentation, the microbial oil was produced at an increasing rate when the initial substrate was enhanced to 100 g/L and decreased slightly when glucose levels were raised higher than 120 g/L. As shown in figures 2A-2H, the Logistic model fitted the experimental data well (determination coefficients (R 2 ) ≥ 0.9907 and NRMS ≤ 0.4920). The biomass of P. parantarctica CHC28 could be satisfactorily modeled. As can be seen, the R 2 values obtained from the Logistic model were very high. All R 2 values were higher than 0.99. This result demonstrated that the Logistic model was suitable for describing the experimental biomass profile. However, it should be noted carefully that the Logistic equation could not explain the lag time and maximum biomass productivity. Further, the Logistic model is ideal for estimating the growth kinetics, i.e., the maximum specific growth rate (μmax, h -1 ) (Phukoetphim et al., 2017). Table 2 shows the kinetic values in the Logistic model. The μmax was used to define the glucose-affected growth of P. parantarctica CHC28. It revealed that the highest μmax was obtained by using glucose 20g/L for 0.333±0.022 h -1 . Subsequently, the μmax decreased dramatically upon cultivation in the nitrogen-limiting medium containing high initial glucose concentration, though the μmax of yeast cultivated in glucose 60-120 g/L was not significantly different (p-value < 0.05). The cultivation of P. parantarctica in glucose 300 g/L provided the lowest μmax for 0.146±0.004 h -1 . These results suggested that glucose concentration and C/N ratio could affect oleaginous yeast growth because of osmotic pressure.

Scale-up of microbial oil production in bioreactor and its kinetic modeling
The fermentation profile of oleaginous yeast in a bioreactor (glucose 100 g/L, C/N ratio = 0.333) was illustrated in figure 3. The lag time was verified using the online DMFit software (http://browser.combase.cc/DMFit.aspx) to fit a curve to the experimental biomass value. The result presented a lag phase of 8.14 hrs, which was shorter than that in a flask scale experiment (9.65 hrs for glucose 100 g/L), following which it entered the log and stationary phase. The maximum biomass was provided at 18.96 g/L for 48 hrs, which was higher than that in the flask scale (17.19 g/L). Besides, at 120 hrs of cultivation, the biomass and oil levels reached 29.92 g/L and 15.13 g/L, respectively. At the same time, the intracellular oil accumulation reached 50.57 %w/w. A comparison of the growth rate and oil production efficiency demonstrated that the biomass, oil, and oil content in the bioreactor scale were higher than those in the flask scale. The cause for this difference may be aeration. Previous studies have reported the influence of different aeration supplies in flask and bioreactor scale experiments on oleaginous yeast growth and microbial oil production (Yen and Zhang, 2011; Yen and Liu, 2014; Karamerou et al., 2016). It was demonstrated that the growth and oil yield of Rhodotorula glutinis showed an apparent increase in baffled bioreactor compared with a non-baffled bioreactor, indicating that air supply plays a key role in the growth of R. glutinis. However, when the aeration rate was increased higher than 0.5 L/min, the cell and oil concentrations were reduced. According to these findings, higher aeration did not improve growth or oil production. Although the impacts of aeration rates are still unclear, the size of air bubbles in the bioreactor might be a possible influencing factor. Higher airflow rates produce larger air bubbles with a smaller specific surface area, resulting in less oxygen mass transfer (Karamerou et al., 2016). However, the effect of oxygen supply on the growth and oil production of P. parantarctica CHC28 should be further investigated.
Time ( The values of the best-fit model parameters (i.e., μmax, Xmax, Yx/s, ms, α, and β) in the bioreactor were shown in Table 3. The μmax was 0.137 h -1 , which is lower than the flask scale. However, the Xmax was higher than the shaking flask scale (27.03 g/L). The ms value was nearly zero, indicating that the almost substrate was used to form the oleaginous biomass, which was higher than that used for cell maintenance. The α and β were very similar, which demonstrated that the oil production of P. parantarctica CHC28 was partially dependent on microbial growth (Yang et al., 2011).  Table 4 presents a comparison of different carbon sources and C/N ratios for microbial oil production. In this study, the biomass and oil concentrations were

CONCLUSION
A glucose concentration composed in a nitrogen-limiting medium affected the growth and microbial oil production of P. parantarctica CHC28. The increase in glucose concentration along with the C/N ratio enhanced biomass and oil concentration. However, the maximum specific growth rate was decreased in a high glucose concentration due to the osmotic pressure in the solution. The oil content of 50.57 %w/w was obtained in the bioreactor. The mathematical model employed in this study could efficiently describe the experimental data in both flask and bioreactor scales. The R 2 and NRMS values were higher and lower than 0.9056 and 2.9693, respectively.