A predictive growth model for Yarrowia lipolytica ATCC 9773 in wastewater

This study focuses on the development of a secondary model for Yarrowia lipolytica in a sewage treatment process. The raw data of Y. lipolytica growth were adjusted to the Buchanan model in order to obtain growth parameters such as initial count cells (Y0), maximum specific growth rate (μmax), latency phase (λ) and maximum cell population (Ymax). The μ values obtained at different pH levels (5.0 to 8.0) were used to build the secondary model based on a linear equation. The results showed a significant effect of pH on μmax values. The validation process of the developed models displays accuracy (Af) and bias factor (Bf) values close to one, while the values of root mean square error (RMSE) were low, confirming that such models can predict the growth of Y. lipolytica in dairy wastewater. This can be interesting to optimize sewage treatments that involve this kind of microorganism. Moreover, the dairy wastewater was a good substrate to support the Yarrowia lipolytica's growth and could be used to produce enzymes.


INTRODUCTION
Predictive microbiology is an interdisciplinary area defined as: "the quantitative description of the microbial response in various ecosystems by employing mathematical models". A model is the description of a system or phenomenon that accounts for its known or inferred properties and might be used to further study its characteristics. Usually, predictive models have been built using raw data obtained from a pure culture in microbiological media. The composition and characteristics (broth, solid or semi-solid) of the medium are important factors that affect the behavior of microorganisms in foods. Mathematical models are developed to describe the effect of environmental conditions on microbial growth, thus allowing accurate predictions of microbial behaviors (Ding et al., 2011). Furthermore, the models can be valuable for estimating shifts in microbial concentrations (Fakrudding et al., 2011;Lee et al., 2014). In the area of predictive microbiology, there are primary and secondary models: (i) primary models describe a microbial response as a function of time for a single set of environmental conditions; and, (ii) secondary models quantify the effect of environmental variations on primary model parameters (Whiting, 1995).
Essentially, the function of a primary model is to obtain the growth or inhibition parameters of the microorganisms for each of the treatments established in the experimental design, whereas secondary models are built with parameters estimated from primary models. They are also employed to predict the response of microorganisms against new combinations of the environmental factors included in the experimental design. Once the secondary model has been constructed, it is necessary to corroborate the accuracy of its predictions. Statistical indices such as root mean square error (RMSE), bias (Bf) and accuracy factors (Af) have been proposed for estimating the accuracy of the model (Geitenes et al., 2013;Slongo et al., 2009). However, most of the predictive models have been developed on different food matrices (Antunes-Rohling et al., 2019;Schlei et al., 2020). Little research has been focused on modeling microbial growth in wastewater. The benefit of creating a secondary model relies on the ability to predict and optimize the duration of the sewage treatment processes.
The food industry has an elevated incidence of environmental contamination, for example, dairy industries produce large quantities of wastewater (Porwal et al., 2015). These wastes are impurities discharged into the environment without any previous decontamination treatment (Liu et al., 2015;Kumari et al., 2017); which significantly impacts public health and environmental sustainability. Hence, dairy waste requires decontamination treatments before it is discharged into sewer systems (Kumari et al., 2017). The principal substances in wastewater are oils, fats and long-chain fatty acids, which are contaminants of aquatic ecosystems (Becerra-Gutiérrez et al., 2015). Biological treatments have been employed as an alternative to decontaminate wastewater (González et al., 2012;Tarón-Dunoyer et al., 2020). Some yeasts are well-known for their ability to grow and decompose post-industrial wastes. Yarrowia lipolytica has been used as a biological agent for biodegradation of pollutant substrates. Additionally, this yeast is recognized as GRAS (Generally Recognized As Safe) in several industrial processes (Groenewald et al., 2014). This non-pathogenic, aerobic and dimorphic fungus has been studied in biodegradation processes and can be used for multiple biotechnological applications related to the production of enzymes and other compounds of

Preparation of the inoculum and obtaining the crude enzymatic extract (CEE)
The activation of Y. lipolytica was carried out through incubation at 25°C in Petri dishes with PDA (potato dextrose agar) agar and olive oil as a lipid source for three days. Then, Y. lipolytica was suspended in a saline solution (0.9% w/v) until reaching 6×10 8 CFU/mL and then stored at 4°C until use. The dairy wastewater (DWW) was collected from a dairy industry located in Valledupar (Colombia) following the protocol mentioned by Taron-Dunoyer et al. (2020). Then, DWW volume (3 L) was divided into three subsamples with pH values of each subsample adjusted to 5.0; 6.5 and 8.0, respectively. It is important to note that pH was controlled by addition of acid (1 N H2SO4) or base (1 N KOH) taking into account pH-metro readings, which were taken every 10 minutes. In order to obtain each growth curve, each subsample was added to an inoculum of Y. lipolytica (6×10 8 CFU/mL). Likewise, 200 mL of a synthetic wastewater (SW) based on saltwater (30% SW), sodium chloride (5.0%), yeast extract (0.5%), olive oil (1.0%) and Triton X-100 (0.1%) (Taron-Dunoyer et al., 2020) was inoculated with a similar amount of Y. lipolytica. The subsamples were aerated with filtered air at 2L/min and stirred at 300 rpm. Approximately every 20 minutes after inoculation, 1 mL was taken from each subsample and SW to carry out appropriate dilutions in peptone water and plated onto PDA agar. The petri dishes were incubated at 25°C for three days and then colonies were counted to obtain viable cell numbers (CFU/mL). Experiments lasted between 40 and 50 hrs.

Primary modeling
Growth curves of Y. lipolytica were constructed by plotting the logarithm of the number of microorganisms versus time at the different pH investigated. Each point of the growth curve corresponds to the average value of the entire set of samples assessed (at least three replicates of each was used to allow for statistical analysis). For growth curve fitting, the Buchanan model (Huang, 2013) was used to encounter the optimum fit for the growth curve (Equations 1 and 2).
Where y0, ymax and y(t) are the bacterial concentration in natural logarithm at initial, maximum, at time t; µmax represents the maximum growth rate [(log CFU/g)/h], and λ represents the latency phase. The latency phase coefficient is α 4.

Secondary modeling
The secondary model establishes a linear relationship between the natural logarithm (Ln) of μmax and pH (Equation 3).
Where, x is the growth rate, m is the slope and b is the y-intercept.

Validation of the secondary model
The bias factor (Bf), accuracy factor (Af), and root mean square error (RMSE) were employed to evaluate the performance of the generated secondary model (Ross, 1996). The Equations for 4,5 and 6 are the following: Where, the variable factors obs, pred, and n are the observed value, predicted value, and repetition number of the observed data, respectively.

Statistical analysis
The results for growth parameters of Y. lipolytica were expressed as means ± standard deviation. The influence of pH levels on maximum specific growth rate (µmax) was evaluated through an analysis of variance (ANOVA one way); whereas, post hoc tests (LSD test) were used to determine statistical differences (P < 0.05) using SPSS software version 23.0 for windows. It is important to note that all tests were repeated at least three times to allow for statistical evaluation.

RESULTS AND DISCUSSION
Growth curves of Yarrowia lipolytica investigated in DWW at different pH levels (5, 6.5 and 8.0) were obtained as described in the Materials and Methods section. The growth curves of Y. lipolytica ATCC 9773 were fitted using the Buchanan model and kinetic parameters were obtained. Figure 1 depicts the growth phases (lag, exponential and stationary phase) of Y. lipolytica in DWW. Similar behavior was observed for Y. lipolytica in SW (data not shown). These findings show the capability of Y. lipolytica of using some compounds present in the wastewater as a source of carbon, nitrogen and energy. Y. lipolytica is a non-conventional yeast due to its diverse biosynthetic potential (Egermeier et al., 2017). Dairy residues are considered highly biodegradable due to Y. lipolytica's ability to reduce BOD5 and COD to 43.32% and 44.30%, respectively (Taron-Dunoyer et al., 2020). Hence, it could be an interesting model to predict the growth of Y. lipolytica in wastewater.  The suitability of primary models employed for developing predictive models is based on two factors: (i) environmental conditions and (ii) the microorganisms involved (Yoon, 2010). In the current study, Buchanan's primary predictive model was applied to model the growth of Y. lipolytica in a biodegradation treatment. Fitting the growth curves to the Buchanan model allows for determining growth parameters such as initial count cells (Y0), maximum growth rate (μ), latency phase (λ) and maximum cell population (Ymax) as illustrated Table 1. Y0 values were not modified significantly (P>0.05) by the substrate (DWW and SW) or its pH level. Y0 had values between 8.630 and 8.930 log CFU indicating that Y0 can be controlled at the beginning of the biodegradation process, that is when the microorganisms are incorporated into the sewage treatment system. λ, represents the time that microorganisms take to adapt to new environmental or nutritional conditions (Swinnen et al., 2004). This variable showed a tendency to increase with increasing pH of the substrates (DWW and SW) from 5.0 to 8.0. The highest values were found in SW at different pH levels: at pH 8.0-λ-14.302 h; at pH 6.5 -λ -10.711h and at pH 5.0 -λ-9.985 h. This result suggests that the λ parameter was directly proportional to pH levels. Similar results were obtained with Y. lipolytica in DWW; where, the highest value (11.325 h) was obtained at pH of 8.0, while the lowest value, 8.635h, was obtained at pH of 5.0. Ymax is another parameter calculated by the Buchanan model, which corresponds to the maximum microbial concentration reached at the end of the exponential phase. In DWW, the highest Ymax value (14.020 log CFU) was reached at pH 5.0 followed by pH 6.5 and 8.0 with 12.000 and 11.340 log CFU, respectively. On the other hand, in regard to SW, the highest value was obtained at pH of 5.0 (13.540 log CFU), while the lowest value was reached at pH 8.0 (10.210 log CFU). Generally, the Ymax values were higher in DWW than SW indicating that DWW is a good substrate to support Y. lipolytica growth and it could be used for biotechnological applications.
μmax is a key parameter because it represents the growth rate of microorganisms. Although it must be highlighted that μmax values mainly depend on the environmental conditions (Arroyo- López et al., 2012). This parameter was inversely proportional to the pH levels. The lowest values were obtained at pH 8.0 for both DWW and SW corresponding to 0.094 and 0.048 (h -1 ), respectively. Similar findings were published by da Costa et al. (2020), who cultivated Y. lipolytica in yeast peptone media at 29°C, calculating values of μ close to 0.1114 h -1 . Skandamis and Jeanson (2015) mentioned that μ reduction is caused mainly by limitations of nutrients, oxygen and production of some metabolites.

Secondary modeling
The µmax values calculated by applying the Buchanan model were employed to develop the secondary model using a linear equation. Besides µmax was significantly affected by pH values and type of substrate. The secondary model describes the effect of pH on Y. lipolytica behavior in a biodegradation process. The changes in µ of Y. lipolytica, according to pH levels, is illustrated in Figure 2. Where, a reduction in µ values is observed when pH increases. Considering that most of the secondary models are developed under real and abusive environmental conditions, a validation process must be carried out in order to verify the predictive accuracy of the models. Therefore, statistical indices such as accuracy (Af) and bias (Bf) have been suggested for validating secondary models (Baranyi et al., 1999;López et al., 2006).
Af is the sum of absolute differences between observed and predicted values of one parameter calculated in the secondary model. Bf represents the relative deviation among observed and predicted; moreover, this parameter allows for determining whether the model over or under-predicts microbial growth (Dalgaard and Jorgensen, 1998). For instance, a Bf value outside the range 0.7 to 1.5 indicates that the model is unsuitable (Choi et al., 2019;Ross, 1996;1999). A perfect agreement between predictions and observations must have values of Af and Bf equal to 1.0 (Choi et al., 2019;Ross, 1999). Another parameter in a validation process is RSME, which compares observed values in the experiment with those calculated by the predictive model. A good validation process has values of RSME close to zero (Baranyi et al., 1996). The mathematical validation of Y. lipolytica growth is summarized in Table 2; where values of Af and Bf close to 1 were obtained based on secondary models. This indicates that both linear models developed herein can optimally simulate Y. lipolytica's growth in both dairy wastewater and synthetic wastewater at different pH levels (5.0 to 8.0). Regarding RSME, low values were achieved, corroborating that lineal models were suitable for predicting Y. lipolytica's growth in a sewage treatment. It is important to emphasize that real wastewater was used to develop a secondary model to predict Yarrowia lipolytica's growth. Interestingly, when microbial growth is carried out in artificial microbiological culture, models usually overestimate the predictions (Pérez and Valero, 2013). Hence, the models constructed herein could be considered consistent for practical use and improve the sewage treatment processes.

CONCLUSIONS
In the present article, a secondary model was developed to simulate the growth of Yarrowia lipolytica in both dairy wastewater (DWW) and synthetic wastewater at different pH levels. This model established a linear relationship between μmax and pH. The validation process yielded accuracy and bias factors of approximately 1; while values of RSME were low. These results indicate that the secondary model developed can predict Y. lipolytica growth in wastewater; hence proving highly valuable for optimizing sewage treatment processes that include this kind of microorganism. Furthermore, DWW proved to be a good substrate to support the growth of Yarrowia lipolytica and could be used for biotechnological approaches such as the production of enzymes.