Optimization of Culture Conditions in a Bioreactor for the Production of Biomass and Metabolites of the Macromycete Lentinula Edodes

Lentinula edodes is an edible mushroom known for its medicinal properties attributed to different secondary metabolites. In this article, the effect of glucose concentration, aeration and agitation on the production of biomass and intrametabolites in submerged fermentation was evaluated. By means of a Box-Behnken design, these variables were optimized to obtain a multifunctional biomass. It was determined that both glucose concentration and agitation had a significant effect on the response variables (biomass, sterols and polysaccharides). Under the evaluated conditions, the values of the variables that optimize biomass production were 1.2 vvm, 60 rpm and 21.97 g / L of glucose. Subsequently, the sterols and total carbohydrates extracted from the biomass were quantified through a spectrophotometric analysis. To optimize these two response variables, similar values are required for aeration (1.2 vvm) and agitation (60 rpm), while the glucose concentration was 16.32 g / L and 19.6 g / L for sterols and total polysaccharides respectively.


Introduction
The Lentinula edodes (Shitake) mushroom is one of the most widely used basidiomycetes in traditional Chinese medicine and in East Asian countries, due to its medicinal and nutritional properties (1), it also has potential use in the production of pharmaceuticals, functional foods and dietary supplements, among others (2). These properties are attributed to different compounds that may be present in the fruiting body, the mycelium, or be excreted to the culture medium (3). Among the main bioactive compounds are polysaccharides, sterols, terpenoids, polyphenolic compounds, and flavonoids that gives a wide spectrum of use based on their biological activities such as antioxidant, hypercholesterolemic, anticancer, antibiotic, antiparasitic, and immunomodulatory. In addition, these compounds generally cause less toxic effects in the human body than the products obtained by synthesis (4)(5).
The traditional cultivation of mushrooms to obtain the fruiting body was initially developed to provide a nutrient-rich food source.
However, it has several disadvantages that make it inefficient, for example, it is a slow process and the variables that favor the growth of the fungus are very difficult to control, which significantly affects the standardization of the final product (5). For these reasons, biotechnological fermentation techniques have grown in popularity due to their low-cost and environmental advantages, modifying and refining old techniques to maximize productivity (6). Additionally, the isolation of secondary metabolites produced by these organisms have made Solid State Fermentation (SSF) and Liquid State Fermentation (LSF) the most suitable techniques for the production of this class of bioactive compounds. Due to these drawbacks and in order to increase the production of biomass and fungimetabolites, controlled culture was developed in bioreactors using submerged and solid-state fermentation (7). Despite having several advantages compared to submerged fermentation such as low energy consumption and high volumetric production from low-cost substrates; solid-state fermentation presents problems associated with the control of variables (pH, temperature, aeration, water content and oxygen transfer), which has not allowed working with larger-scale bioreactors as a result of the complexity in their design (8)(9). On the other hand, in submerged fermentation these factors can be controlled more efficiently, a fact that allows standardizing and optimizing the production of biomass and metabolites of interest. Taking into account the bioprospective potential that the fungus 3 L. edodes has, it is possible to develop new products in search of benefits for the treatment of different diseases through bioreactor culture (7)(8).
There are some studies focused on optimizing the conditions for the production of biomass and metabolites of fungi (10)(11)(12)(13)(14)(15)(16)(17)(18). However, there are few reports about the cultivation of this fungus in bioreactors, and most of them have focused on obtaining a particular type of compounds (10,11,13). Considering that, it was possible to determine the optimal operating conditions (aeration, agitation and glucose concentration) for the fermentation in liquid state of the fungus Lentinula edodes in a stirred bioreactor, taking into account the importance of obtaining a balance between biomass production and its composition.

Materials and methods
The biomass obtained by LSF of Lentinula edodes in a bioreactor under each of the different combinations of agitation, aeration and glucose content, was subjected to exhaustive extraction processes with solvents of different polarity (dichloromethane, ethanol and water) to subsequently quantify the metabolites of interest by colorimetric tests

Fungal material and strain conditioning
The strain of the fungus L. edodes was bought from the company Mushroom Shroom Supply (USA). The activation was carried out in Petri dishes using Potato Dextrose Agar (PDA) medium, in conditions of total darkness and maintaining a temperature of 25 ± 1 ° C for a period of 10 to 15 days (2), in a WISD incubator model WIG-155.

Liquid State Fermentation (LSF)
The LSF was carried out in the following phases; preinoculum, inoculum and bioreactor culture. GPY medium (Glucose-Peptone-Yeast Extract) was used in each of them, based on previous studies carried out by 2 and 19. The GPY medium was composed of (g / L) glucose (20), peptone (2.5), yeast extract (2.5) and the pH was adjusted to 5.0 (Feng et al., 2010). To obtain the preinoculum and inoculum, 100 mL of medium served in 250 mL flasks were used, while 2100 mL of medium were needed for the culture in the bioreactor.
The fermentation conditions such as temperature, initial pH, growth period, peptone concentration and yeast extract were kept constant at 25 ° C, 5.0, 5 days and 2.5 g / L respectively (10,11,20).

Preinoculum
The preinoculum was obtained by adding 15 discs of 0.5-1.0 cm in diameter to each of the flasks, maintaining the conditions previously established by (21) for submerged fermentation. The disks were made up of mycelium and agar (22) from the Petri dishes from the conditioning stage. The flasks were placed on an orbital shaker at 120 rpm and 25 °C for a period of 10 days to favor the formation of pellets (23, 24).

4
The biomass produced in the pre-inoculum was filtered, 1.5 g of wet mycelium produced in the pre-inoculum were weighed, transferred to flasks with GPY culture medium and cultured under the same pre-inoculum conditions for a period of 5 days.
The content of four flasks was used as inoculum for the bioreactor, the others were filtered and lyophilized to determine the amount of biomass added.

Bioreactor
The culture was carried out in a 3 L Applikon bioreactor, with agitation and a flute aeration system. The bioreactor was fed with 400 mL of the inoculum (16% v / v) and was kept at a temperature of 25 ± 1 ° C for a period of 5 days. The assembly and inoculation were carried out in an ESCO model LHS-5CG-F9 laminar flow cabinet, to ensure aseptic conditions, and both the culture medium and the bioreactor were sterilized in an autoclave at a temperature of 121°C. The specific conditions of each of the treatments are presented in table 1. A total of 15 experiments with three replicas at the central point were performed and carried out randomly.

Biomass and metabolites optimization process
A response surface methodology (RSM) was used to maximize the production of biomass and intrametabolites (sterols and total polysaccharides) using three factors (agitation, aeration and glucose concentration). A Box-Behnken design was selected to analyze the effect of the three factors with three levels (Error! Reference source not found.), it is described in Error! Reference source not found..
The relationship between the factors and the response variables was adjusted to the following second-order polynomial equation: where Yi is the predicted response, the subscripts i and j takes values from 1 to the number of variables, β0 is a constant, βi is the linear coefficient, βii is the quadratic coefficient, βij is the cross product coefficient, k is the number of factors, and Xi and Xj are the dimensionless coded values of the investigated variables.

Biomass production optimization
The results obtained in the experimental design for biomass production are presented in Error! Reference source not found..
In the data, a significant variation in biomass can be observed from 1.3463 g dry biomass / g BAB to 8.1534 g dry biomass / g BAB, depending on the fermentation conditions in the bioreactor. To evaluate the optimal conditions and the effect of significant factors on biomass production, a statistical analysis of variance (ANOVA) was carried out. Additionally, the P-value was used as a tool to determine the significance of the factors and their interactions, the smaller the P-value, the more significant the corresponding factor 5 was (Li et al., 2012). As shown in Error! Reference source not found., the experimental data fit a quadratic model. The ANOVA indicated that the quadratic regression model for the response surface was statistically significant ( = 0.008) with an F value of 11.00, for a significance level of 95%. The multiple regression equation that describes the behavior of biomass (Y) as a function of (x1) glucose concentration, (x2) aeration and (x3) agitation, obtained from the experimental data, was given by the following expression: A higher absolute value of the coefficient in the regression equation indicates that the factor has a greater effect on biomass production, in contrast, a value close to zero represents a low or no effect of the independent variable on the response (32).
According to the ANOVA, the terms that have a high significant effect on biomass production were 1 and 2 2 ( = 0.003), 1 2 ( = 0.018), 2 ( = 0.029) and 2 3 ( = 0.035). Through the regression analysis of the data, it is observed that the coefficient of determination (R2) for equation (1) was 0.9519, which indicates that 95.19% of the variation for biomass production can be explained by the model and only 4.81% is attributed to experimental error. Additionally, the statistical results suggest that the previous regression model can adequately predict the biomass values within the range of the variables studied (R = 0.9756). This validity of the model is confirmed with the lack of fit, whose P-value was 0.109 (> 0.05), which implies that the lack of fit is not significant and therefore the pure error is not due to noise. in order to determine the optimal conditions to maximize the response. The 3D surfaces and their respective level curves (Fig 1(a)) represent the effect of the interaction between glucose concentration and aeration on biomass production, when stirring is maintained at 60 rpm. From this graph, it can be inferred that by increasing the glucose concentration and maintaining aeration at values close to or greater than 1.2 vvm, the biomass yield could be significantly increased. A similar behavior is observed in Fig 1(b) where it is appreciated that slight changes in glucose concentration favor the mycelial growth of the fungus. It is expected for an aerobic organism, considering the low solubility of oxygen in aqueous media, the possible limitation to the mass transfer from the gas phase to the culture medium, and from this to the interior of the mycelium. It could limit not only the growth rate of the fungus but also the production of metabolites of interest (33). In contrast, a study revealed that aeration values between 1 and 1.5 vvm cause a considerable decrease in the cell growth of P. ostreatus (34). This could indicate that, as mentioned by (33), depending on the fermentation conditions, the microorganism establishes a metabolic route for the production of a particular compound, being necessary to guarantee a certain oxygen transfer rate under certain operating conditions. Meanwhile, it is evident that the agitation in the analyzed interval does not have an important effect on the biomass production (Fig 1b) and (c)). These results showed that the maximum amount of biomass (7.48 g) for L. edodes was obtained with a glucose concentration of 21.97 g / L, aeration of 1.2 vvm and a stirring of 60 rpm.

Fig 1 Effect of variables on biomass production
Glucose appreciably promotes mycelial growth, a result that coincides with that reported by (11) who indicate that this is the most effective carbon source for L. edodes in submerged fermentation. These authors used a similar experimental design to analyze the glucose concentration, the yeast extract concentration and the pH in an airlift reactor (100 L), finding that a glucose concentration of 15.4 g / L maximizes the production of mycelial biomass. This difference can be attributed to many factors, including strain, operating conditions, reactor type, and culture medium. (35) who worked with Pleurotus ostreatus agree that the highest biomass production is found when the glucose concentration increases (> 25 g / L), however, they observed an inverse effect on the production of phenolic compounds, since the maximum values of these metabolites were reached at concentrations lower than 20 g / L.

Sterol production optimization
Sterols are triterpenoidal compounds commonly present in edible macromycete fungi to which a wide variety of proven biological activities are attributed (36). The regression model that predicts the production of sterols is given by the following equation: According to the results of the ANOVA, only two factors have a significant effect on this response ( < 0,05); 1 2 ( = 0.033), 2 2 ( = 0.040). Additionally, the multiple correlation coefficient R2 was 0.8402, which indicates that 84.02% of the variation in the production of sterols can be explained by the variation between treatments. Meanwhile, since the multiple correlation coefficient R (0.9166) has a value close to 1, the experimental concentration of sterols can be predicted by the regression model. As can be seen, the biosynthesis of sterols responds to both glucose concentration and aeration, since slight changes in any of these variables can generate a drastic increase or decrease in its production (Error! Not a valid bookmark self-reference. (a)).

Fig 2 Effect of variables on sterols production
In Glucose appreciably promotes mycelial growth, a result that coincides with that reported by (11) who indicate that this is the most effective carbon source for L. edodes in submerged fermentation. These authors used a similar experimental design to analyze the glucose concentration, the yeast extract concentration and the pH in an airlift reactor (100 L), finding that a glucose concentration of 15.4 g / L maximizes the production of mycelial biomass. This difference can be attributed to many factors, including strain, operating conditions, reactor type, and culture medium. (35) who worked with Pleurotus ostreatus agree that the highest biomass production is found when the glucose concentration increases (> 25 g / L), however, they observed an inverse effect on the production of phenolic compounds, since the maximum values of these metabolites were reached at concentrations lower than 20 g / L.

Sterol production optimization
Sterols are triterpenoidal compounds commonly present in edible macromycete fungi to which a wide variety of proven biological activities are attributed (36). The regression model that predicts the production of sterols is given by the following equation: 7 = 3.10 + 1.266 1 + 1.103 2 − 0.195 3 − 1.66 1 2 + 3.05 2 2 + 1.62 3 2 − 3.11 1 2 + 0.73 1 3 − 0.06 2 3 According to the results of the ANOVA, only two factors have a significant effect on this response ( < 0,05); 1 2 ( = 0.033), 2 2 ( = 0.040). Additionally, the multiple correlation coefficient R2 was 0.8402, which indicates that 84.02% of the variation in the production of sterols can be explained by the variation between treatments. Meanwhile, since the multiple correlation coefficient R (0.9166) has a value close to 1, the experimental concentration of sterols can be predicted by the regression model. As can be seen, the biosynthesis of sterols responds to both glucose concentration and aeration, since slight changes in any of these variables can generate a drastic increase or decrease in its production (Error! Not a valid bookmark self-reference. (a)).

Sterol production optimization
Sterols are triterpenoidal compounds commonly present in edible macromycete fungi to which a wide variety of proven biological activities are attributed (36). The regression model that predicts the production of sterols is given by the following equation: According to the results of the ANOVA, only two factors have a significant effect on this response ( < 0,05); 1 2 ( = 0.033), 2 2 ( = 0.040). Additionally, the multiple correlation coefficient R2 was 0.8402, which indicates that 84.02% of the variation in the production of sterols can be explained by the variation between treatments. Meanwhile, since the multiple correlation coefficient R (0.9166) has a value close to 1, the experimental concentration of sterols can be predicted by the regression model. As can be seen, the biosynthesis of sterols responds to both glucose concentration and aeration, since slight changes in any of these variables can generate a drastic increase or decrease in its production (Error! Not a valid bookmark self-reference. (a)).

Fig 2(b) and (c).
Regarding to a comparison of these results with previous studies, there are no similar reports for the culture of Lentinula edodes in a bioreactor. Results can only be contrasted with studies carried out with other types of macromycete fungi in which the agitation is considered an important parameter for the production of exometabolites, the transfer of oxygen and heat, as well as the shear stress, are relevant aspects to determine the morphology of the mycelium (7,8,14,37).
Meanwhile, the maximum sterol production predicted by the model was 10.12 mg / g BAB under the following conditions: glucose concentration 16.32 g / L, aeration of 1.2 vvm and stirring at 60 rpm.

Optimization of polysaccharide production
According to the results, there is a considerable variation in the amount of polysaccharides obtained in each of the treatments. The following expression describes the interaction between the factors on total polysaccharides: The value of R 2 was 0.9315, only 6.85% of the total variation cannot be explained by the model. On the other hand, because the Pvalue for the quadratic regression model was less than 0.05 (P = 0.019), it is possible to ensure that the equation model adequately predicts the production of polysaccharides over the studied region. The only terms that had a significant effect were 1 2 ( < 0.025) and 2 3 ( < 0.002).

Fig 3 Effect of variables on polysaccharides production
In Glucose appreciably promotes mycelial growth, a result that coincides with that reported by (11) who indicate that this is the most effective carbon source for L. edodes in submerged fermentation. These authors used a similar experimental design to analyze the glucose concentration, the yeast extract concentration and the pH in an airlift reactor (100 L), finding that a glucose concentration of 15.4 g / L maximizes the production of mycelial biomass. This difference can be attributed to many factors, including strain, operating conditions, reactor type, and culture medium. (35) who worked with Pleurotus ostreatus agree that the highest biomass production is found when the glucose concentration increases (> 25 g / L), however, they observed an inverse effect on the production of phenolic compounds, since the maximum values of these metabolites were reached at concentrations lower than 20 g / L.

Sterol production optimization
Sterols are triterpenoidal compounds commonly present in edible macromycete fungi to which a wide variety of proven biological activities are attributed (36). The regression model that predicts the production of sterols is given by the following equation: According to the results of the ANOVA, only two factors have a significant effect on this response ( < 0,05); 1 2 ( = 0.033), 2 2 ( = 0.040). Additionally, the multiple correlation coefficient R2 was 0.8402, which indicates that 84.02% of the variation in the production of sterols can be explained by the variation between treatments. Meanwhile, since the multiple correlation coefficient R 9 (0.9166) has a value close to 1, the experimental concentration of sterols can be predicted by the regression model. As can be seen, the biosynthesis of sterols responds to both glucose concentration and aeration, since slight changes in any of these variables can generate a drastic increase or decrease in its production (Error! Not a valid bookmark self-reference. (a)).

Sterol production optimization
Sterols are triterpenoidal compounds commonly present in edible macromycete fungi to which a wide variety of proven biological activities are attributed (36). The regression model that predicts the production of sterols is given by the following equation: According to the results of the ANOVA, only two factors have a significant effect on this response ( < 0,05); 1 2 ( = 0.033), 2 2 ( = 0.040). Additionally, the multiple correlation coefficient R2 was 0.8402, which indicates that 84.02% of the variation in the production of sterols can be explained by the variation between treatments. Meanwhile, since the multiple correlation coefficient R (0.9166) has a value close to 1, the experimental concentration of sterols can be predicted by the regression model. As can be seen, the biosynthesis of sterols responds to both glucose concentration and aeration, since slight changes in any of these variables can generate a drastic increase or decrease in its production (Error! Not a valid bookmark self-reference. (a)).

Fig 2(b) and (c).
Regarding to a comparison of these results with previous studies, there are no similar reports for the culture of Lentinula edodes in a bioreactor. Results can only be contrasted with studies carried out with other types of macromycete fungi in which the agitation is considered an important parameter for the production of exometabolites, the transfer of oxygen and heat, as well as the shear stress, are relevant aspects to determine the morphology of the mycelium (7,8,14,37).
Meanwhile, the maximum sterol production predicted by the model was 10.12 mg / g BAB under the following conditions: glucose concentration 16.32 g / L, aeration of 1.2 vvm and stirring at 60 rpm.

Optimization of polysaccharide production
According to the results, there is a considerable variation in the amount of polysaccharides obtained in each of the treatments. The value of R 2 was 0.9315, only 6.85% of the total variation cannot be explained by the model. On the other hand, because the Pvalue for the quadratic regression model was less than 0.05 (P = 0.019), it is possible to ensure that the equation model adequately predicts the production of polysaccharides over the studied region. The only terms that had a significant effect were 1 2 ( < 0.025) and 2 3 ( < 0.002). This difference can be attributed to many factors, including strain, operating conditions, reactor type, and culture medium. (35) who worked with Pleurotus ostreatus agree that the highest biomass production is found when the glucose concentration increases (> 25 g / L), however, they observed an inverse effect on the production of phenolic compounds, since the maximum values of these metabolites were reached at concentrations lower than 20 g / L.

Sterol production optimization
Sterols are triterpenoidal compounds commonly present in edible macromycete fungi to which a wide variety of proven biological activities are attributed (36). The regression model that predicts the production of sterols is given by the following equation: According to the results of the ANOVA, only two factors have a significant effect on this response ( < 0,05); 1 2 ( = 0.033), 2 2 ( = 0.040). Additionally, the multiple correlation coefficient R2 was 0.8402, which indicates that 84.02% of the variation in the production of sterols can be explained by the variation between treatments. Meanwhile, since the multiple correlation coefficient R (0.9166) has a value close to 1, the experimental concentration of sterols can be predicted by the regression model. As can be seen, the biosynthesis of sterols responds to both glucose concentration and aeration, since slight changes in any of these variables can generate a drastic increase or decrease in its production (Error! Not a valid bookmark self-reference. (a)).

Fig 2 it
is observed that at glucose concentrations between 16 and 22 g / L and aeration levels higher than 1.2 vvm, a maximum of sterols can be produced, while values outside these ranges cause an appreciable decrease. Stirring, on the other hand, has a less marked effect, since the increase in the amount of sterols is reached at low values of this factor, as indicated in Glucose appreciably promotes mycelial growth, a result that coincides with that reported by (11) who indicate that this is the most effective carbon source for L. edodes in submerged fermentation. These authors used a similar experimental design to analyze the glucose concentration, the yeast extract concentration and the pH in an airlift reactor (100 L), finding that a glucose concentration of 15.4 g / L maximizes the production of mycelial biomass. This difference can be attributed to many factors, including strain, operating conditions, reactor type, and culture medium. (35) who worked with Pleurotus ostreatus agree that the highest biomass production is found when the glucose concentration increases (> 25 g / L), however, they observed an inverse effect on the production of phenolic compounds, since the maximum values of these metabolites were reached at concentrations lower than 20 g / L.

Sterol production optimization
Sterols are triterpenoidal compounds commonly present in edible macromycete fungi to which a wide variety of proven biological activities are attributed (36). The regression model that predicts the production of sterols is given by the following equation: According to the results of the ANOVA, only two factors have a significant effect on this response ( < 0,05); 1 2 ( = 0.033), 2 2 ( = 0.040). Additionally, the multiple correlation coefficient R2 was 0.8402, which indicates that 84.02% of the variation in the production of sterols can be explained by the variation between treatments. Meanwhile, since the multiple correlation coefficient R (0.9166) has a value close to 1, the experimental concentration of sterols can be predicted by the regression model. As can be seen, the biosynthesis of sterols responds to both glucose concentration and aeration, since slight changes in any of these variables can generate a drastic increase or decrease in its production (Error! Not a valid bookmark self-reference. (a)).

Fig 2(b) and (c).
Regarding to a comparison of these results with previous studies, there are no similar reports for the culture of Lentinula edodes in a bioreactor. Results can only be contrasted with studies carried out with other types of macromycete fungi in which the agitation is considered an important parameter for the production of exometabolites, the transfer of oxygen and heat, as well as the shear stress, are relevant aspects to determine the morphology of the mycelium (7,8,14,37).
Meanwhile, the maximum sterol production predicted by the model was 10.12 mg / g BAB under the following conditions: glucose concentration 16.32 g / L, aeration of 1.2 vvm and stirring at 60 rpm.

Optimization of polysaccharide production
According to the results, there is a considerable variation in the amount of polysaccharides obtained in each of the treatments. The following expression describes the interaction between the factors on total polysaccharides: The value of R 2 was 0.9315, only 6.85% of the total variation cannot be explained by the model. On the other hand, because the Pvalue for the quadratic regression model was less than 0.05 (P = 0.019), it is possible to ensure that the equation model adequately predicts the production of polysaccharides over the studied region. The only terms that had a significant effect were 1 2 ( < 0.025) and 2 3 ( < 0.002) .   Fig 3 (a)), the production of these compounds tends to increase for glucose values between 18 and 24 g / L and aerations greater than 1 vvm. From In Glucose appreciably promotes mycelial growth, a result that coincides with that reported by (11) who indicate that this is the most effective carbon source for L. edodes in submerged fermentation. These authors used a similar experimental design to analyze the glucose concentration, the yeast extract concentration and the pH in an airlift reactor (100 L), finding that a glucose concentration of 15.4 g / L maximizes the production of mycelial biomass. This difference can be attributed to many factors, including strain, operating conditions, reactor type, and culture medium. (35) who worked with Pleurotus ostreatus agree that the highest biomass production is found when the glucose concentration increases (> 25 g / L), however, they observed an inverse effect on the production of phenolic compounds, since the maximum values of these metabolites were reached at concentrations lower than 20 g / L.

Sterol production optimization
Sterols are triterpenoidal compounds commonly present in edible macromycete fungi to which a wide variety of proven biological activities are attributed (36). The regression model that predicts the production of sterols is given by the following equation: = 3.10 + 1.266 1 + 1.103 2 − 0.195 3 − 1.66 1 2 + 3.05 2 2 + 1.62 3 2 − 3.11 1 2 + 0.73 1 3 − 0.06 2 3 According to the results of the ANOVA, only two factors have a significant effect on this response ( < 0,05); 1 2 ( = 0.033), 2 2 ( = 0.040). Additionally, the multiple correlation coefficient R2 was 0.8402, which indicates that 84.02% of the variation in the production of sterols can be explained by the variation between treatments. Meanwhile, since the multiple correlation coefficient R (0.9166) has a value close to 1, the experimental concentration of sterols can be predicted by the regression model. As can be seen, the biosynthesis of sterols responds to both glucose concentration and aeration, since slight changes in any of these variables can generate a drastic increase or decrease in its production (Error! Not a valid bookmark self-reference. (a)). promotes mycelial growth, a result that coincides with that reported by (11) who indicate that this is the most effective carbon source for L. edodes in submerged fermentation. These authors used a similar experimental design to analyze the glucose concentration, the yeast extract concentration and the pH in an airlift reactor (100 L), finding that a glucose concentration of 15.4 g / L maximizes the production of mycelial biomass. This difference can be attributed to many factors, including strain, operating conditions, reactor type, and culture medium. (35) who worked with Pleurotus ostreatus agree that the highest biomass production is found when the glucose concentration increases (> 25 g / L), however, they observed an inverse effect on the production of phenolic compounds, since the maximum values of these metabolites were reached at concentrations lower than 20 g / L.

Sterol production optimization
Sterols are triterpenoidal compounds commonly present in edible macromycete fungi to which a wide variety of proven biological activities are attributed (36). The regression model that predicts the production of sterols is given by the following equation: According to the results of the ANOVA, only two factors have a significant effect on this response ( < 0,05); 1 2 ( = 0.033), 2 2 ( = 0.040). Additionally, the multiple correlation coefficient R2 was 0.8402, which indicates that 84.02% of the variation in the production of sterols can be explained by the variation between treatments. Meanwhile, since the multiple correlation coefficient R (0.9166) has a value close to 1, the experimental concentration of sterols can be predicted by the regression model. As can be seen, the biosynthesis of sterols responds to both glucose concentration and aeration, since slight changes in any of these variables can generate a drastic increase or decrease in its production (Error! Not a valid bookmark self-reference. (a)).

Fig 2(b) and (c).
Regarding to a comparison of these results with previous studies, there are no similar reports for the culture of Lentinula edodes in a bioreactor. Results can only be contrasted with studies carried out with other types of macromycete fungi in which the agitation is considered an important parameter for the production of exometabolites, the transfer of oxygen and heat, as well as the shear stress, are relevant aspects to determine the morphology of the mycelium (7,8,14,37).
Meanwhile, the maximum sterol production predicted by the model was 10.12 mg / g BAB under the following conditions: glucose concentration 16.32 g / L, aeration of 1.2 vvm and stirring at 60 rpm.

Optimization of polysaccharide production
According to the results, there is a considerable variation in the amount of polysaccharides obtained in each of the treatments. The following expression describes the interaction between the factors on total polysaccharides:

14
The value of R 2 was 0.9315, only 6.85% of the total variation cannot be explained by the model. On the other hand, because the Pvalue for the quadratic regression model was less than 0.05 (P = 0.019), it is possible to ensure that the equation model adequately predicts the production of polysaccharides over the studied region. The only terms that had a significant effect were 1 2 ( < 0.025) and 2 3 ( < 0.002) .   Fig 3 (b) it can be deduced that to maximize polysaccharide biosynthesis, low stirring conditions (<60 rpm) and glucose values similar to those of sterols should be maintained, as long as the aeration remains constant at 0.85 vvm. Finally, In Glucose appreciably promotes mycelial growth, a result that coincides with that reported by (11) who indicate that this is the most effective carbon source for L. edodes in submerged fermentation. These authors used a similar experimental design to analyze the glucose concentration, the yeast extract concentration and the pH in an airlift reactor (100 L), finding that a glucose concentration of 15.4 g / L maximizes the production of mycelial biomass. This difference can be attributed to many factors, including strain, operating conditions, reactor type, and culture medium. (35) who worked with Pleurotus ostreatus agree that the highest biomass production is found when the glucose concentration increases (> 25 g / L), however, they observed an inverse effect on the production of phenolic compounds, since the maximum values of these metabolites were reached at concentrations lower than 20 g / L.

Sterol production optimization
Sterols are triterpenoidal compounds commonly present in edible macromycete fungi to which a wide variety of proven biological activities are attributed (36). The regression model that predicts the production of sterols is given by the following equation: According to the results of the ANOVA, only two factors have a significant effect on this response ( < 0,05); 1 2 ( = 0.033), 2 2 ( = 0.040). Additionally, the multiple correlation coefficient R2 was 0.8402, which indicates that 84.02% of the variation in the production of sterols can be explained by the variation between treatments. Meanwhile, since the multiple correlation coefficient R (0.9166) has a value close to 1, the experimental concentration of sterols can be predicted by the regression model. As can be seen, the biosynthesis of sterols responds to both glucose concentration and aeration, since slight changes in any of these variables can generate a drastic increase or decrease in its production (Error! Not a valid bookmark self-reference. (a)). promotes mycelial growth, a result that coincides with that reported by (11) who indicate that this is the most effective carbon source for L. edodes in submerged fermentation. These authors used a similar experimental design to analyze the glucose concentration, the yeast extract concentration and the pH in an airlift reactor (100 L), finding that a glucose concentration of 15.4 g / L maximizes the 15 production of mycelial biomass. This difference can be attributed to many factors, including strain, operating conditions, reactor type, and culture medium. (35) who worked with Pleurotus ostreatus agree that the highest biomass production is found when the glucose concentration increases (> 25 g / L), however, they observed an inverse effect on the production of phenolic compounds, since the maximum values of these metabolites were reached at concentrations lower than 20 g / L.

Sterol production optimization
Sterols are triterpenoidal compounds commonly present in edible macromycete fungi to which a wide variety of proven biological activities are attributed (36). The regression model that predicts the production of sterols is given by the following equation: According to the results of the ANOVA, only two factors have a significant effect on this response ( < 0,05); 1 2 ( = 0.033), 2 2 ( = 0.040). Additionally, the multiple correlation coefficient R2 was 0.8402, which indicates that 84.02% of the variation in the production of sterols can be explained by the variation between treatments. Meanwhile, since the multiple correlation coefficient R (0.9166) has a value close to 1, the experimental concentration of sterols can be predicted by the regression model. As can be seen, the biosynthesis of sterols responds to both glucose concentration and aeration, since slight changes in any of these variables can generate a drastic increase or decrease in its production (Error! Not a valid bookmark self-reference. (a)).

Fig 2(b) and (c).
Regarding to a comparison of these results with previous studies, there are no similar reports for the culture of Lentinula edodes in a bioreactor. Results can only be contrasted with studies carried out with other types of macromycete fungi in which the agitation is considered an important parameter for the production of exometabolites, the transfer of oxygen and heat, as well as the shear stress, are relevant aspects to determine the morphology of the mycelium (7,8,14,37).
Meanwhile, the maximum sterol production predicted by the model was 10.12 mg / g BAB under the following conditions: glucose concentration 16.32 g / L, aeration of 1.2 vvm and stirring at 60 rpm.

Optimization of polysaccharide production
According to the results, there is a considerable variation in the amount of polysaccharides obtained in each of the treatments. The following expression describes the interaction between the factors on total polysaccharides: The value of R 2 was 0.9315, only 6.85% of the total variation cannot be explained by the model. On the other hand, because the Pvalue for the quadratic regression model was less than 0.05 (P = 0.019), it is possible to ensure that the equation model adequately predicts the production of polysaccharides over the studied region. The only terms that had a significant effect were 1 2 ( < 0.025) and 2 3 ( < 0.002) .  Fig 3(c) depicts the variation of polysaccharide production when slight changes are made in the aeration and agitation; it indicates that high air flows (> 1.2 vvm) and slow agitation (<60 rpm) are required in order to improve the production of these compounds.
These results coincide with a study in which the effect of aeration on the production of IPS was evaluated for the Ganoderma lucidum fungus, in which it was found that high percentages of oxygen saturation (> 25%) are optimal for the production of these compounds (38). Likewise, Hsieh, Liu, Tseng, Lo, & Yang (2006) determined that with 21% oxygen the maximum concentration of IPS is reached when working with Grifola frondosa (39).
The optimal value of total polysaccharides predicted by the model (243.58 mg / g BAB) is reached with 19.6 g / L of glucose, 1.2 vvm of aeration and 60 rpm of agitation. Similar results were obtained by (10) who used a genetic algorithm coupled to an artificial neural network (GA-ANN) as an optimization method, and found that the maximum amount of EPS extracted from L. edodes mycelium was generated with a glucose concentration of 22.5 g / L, exposing the culture to UV radiation.

Conclusions
Glucose and aeration were the factors that most influenced the three response variables studied. According to the results obtained in the Box-Behnken experimental design, aeration (1.2 vvm), agitation (60 rpm) and glucose concentrations of 21.97, 16.32 and 19.6 g / L were the conditions that optimized biomass (7.48 g / g BAB), sterols (10.12 mg / g BAB) and total polysaccharides (243.58 mg / g BAB) respectively.
The results of this research provide useful information that can serve as a reference for optimizing the culture conditions of other macromycete fungi. Additionally, these results demonstrate that the submerged fermentation of L. edodes in a bioreactor is a promising technique for the production of biomass and secondary metabolites with potential biological activities.
In addition to this, the products obtained from this cultivation method could be used to make functional foods or other products for the medical or pharmaceutical industry. The optimization method used in this research was reliable and could also be applied efficiently in other fermentation systems to increase the production of biomass and metabolites with biological activities. Figure 1 Effect of variables on biomass production Effect of variables on sterols production Figure 3 Effect of variables on polysaccharides production