A Response Surface Methodology for Sustainable Production of GABA from Black Soybean Okara Using Solid-State Collaborative Fermentation of Rhizopus oligosporus and Yarrowia lipolytica

Abstract

Black soybean okara is a common food byproduct in Asia. This study conducted collaborative fermentation with Rhizopus oligosporus and Yarrowia lipolytica to produce a GABA-enriched okara product. Two black soybean varieties, TN3 and TN5, were used, and optimal fermentation conditions were predicted using response surface methodology (RSM). After 24 h of Rhizopus oligosporus incubation, Yarrowia lipolytica was inoculated under 20 trial conditions with variations in temperature, incubation time, and inoculation size. The model predicted that the highest GABA content would be achieved at 34–35 °C, 47–49 h incubation, and 3–4 log CFU/mL inoculation. Under these optimal conditions, the maximum GABA yields achieved were 868.3 µg/g for TN3 and 853.1 µg/g for TN5. Fermentation conditions had minimal influence on protease activity, which may be attributed to the distinct roles of Rhizopus oligosporus and Yarrowia lipolytica in the fermentation process. The solid-state collaborative fermentation technology supports food waste recycling and enhances product functionality, contributing to the circular economy.

1. Introduction

According to statistics from the Food and Agriculture Organization (FAO) of the United Nations (UN), approximately 1.05 billion tons of food are lost or wasted each year along global production and supply chains [1], accounting for one-third of total food production. In 2015, the UN proposed 17 Sustainable Development Goals (SDGs) for 2030. Among them, SDG 12.3 aims to reduce food waste at the retail and consumer levels as well as food losses at the production level (including post-harvest losses) by promoting the 3Rs (reduce, reuse, and recycle) to address the issue of severe food insecurity faced by 864 million people worldwide [2,3].

In recent years, many research efforts have aimed to incorporate food processing by-products into food as a strategy for value addition and reuse to reduce the excessive consumption of raw materials and contribute to the circular economy. In Asian countries with high soybean consumption, large amounts of soybean residues (okara) are produced each year as a by-product. Although okara has been reused in foods such as baked goods, the energy cost of drying okara far exceeds the protein value of doing so. Therefore, the microbial conversion of okara into the by-products of soybean processing provides an alternative for value addition [4]. Microbial fermentation converts high molecular weight okara proteins, carbohydrates, and lipids into peptides, amino acids, and fatty acids of low molecular weight, increasing the solubility of okara proteins and producing bioactive compounds [5]. Studies have shown that the fermentation of okara by Saccharomyces cerevisiae increases total protein content, while reducing the total content of crude fiber, thereby improving digestibility [6].

Solid-state collaborative fermentation (SSCF) refers to a fermentation process consisting of two or more microorganisms. Different microorganisms may be used simultaneously or sequentially under different conditions to obtain a variety of fermentation outcomes. The advantages of such methods are simple operation and low cost with improved product nutrition and diverse functional ingredients [7]. The traditional fermented food tempeh in Southeast Asian countries is produced by the SSCF of soybean residue by R. oligosporus and A. oryzae. The protein in legumes or grains is hydrolyzed by microbial proteases to produce peptides and free amino acids, which are then subject to food processing procedures to produce fermented foods with unique flavors [8]. Studies have shown that compared to single-microbe cultures, the SSCF of okara with R. oligosporus and Y. lipolytica, as well as SSCF of okara with B. subtilis and A. oryzae, improves the digestibility, nutritional value, and flavor of okara. This process also significantly increased total phenolic content and minimizes the reduction in total dietary fiber, confirming the presence of synergistic metabolism [9,10]. On the other hand, collaborative fermentation also reduces the content of anti-nutritive factors in okara, such as antigenic proteins, trypsin inhibitors, phytic acid, and soybean oligosaccharides [11].

In Asian countries, black soybeans (Glycine max (L.) Merr.) are often made into soy sauce or black soybean milk, and a large amount of okara by-products are also produced during the manufacturing process. Many studies have suggested that the fermentation products of black soybeans may be used to produce highly functional ingredients, where antioxidant activity, total phenolic compounds, and anthocyanin content are increased, while polysaccharides, soluble proteins, and short-chain fatty acid levels are decreased. In addition, fermentation also induces the bioconversion of glycosidic isoflavones and saponin into more bioactive forms [12]. Tainan No. 3 (TN3, green kernel) and No. 5 (TN5, yellow kernel) black soybeans are varieties developed by the Taiwan Agricultural Research Institute and are suitable for making soybean powder, fermented soy sauce, tofu, and soy milk. Locally grown black soybeans are fresher and have a richer flavor than imported ones. Due to the shorter transportation distance, they also help reduce carbon emissions, aligning with both environmental protection goals and farmers’ interests. Furthermore, locally grown black soybean varieties are non-GMO, avoiding the potential health risks associated with genetically modified foods. TN3 offers a more distinctive flavor compared to imported varieties, while TN5 is rich in protein, providing an excellent substrate for nutrient transformation during subsequent fermentation processes. However, few studies have focused on enhancing the value of okara from TN3 and TN5 through microbial fermentation in a sustainable manner. Therefore, the SSCF of okara could be explored as a means to enhance its value and achieve sustainability.

γ-aminobutyric acid (GABA) is a non-protein amino acid with four carbon atoms. It is considered a bioactive compound that is widely found in animals, plants, and microorganisms, with anti-hypertension, anti-depression, anti-diabetes, anti-obesity, and immunity-enhancing effects [13]. GABA used in commercial nutritional supplements is mainly produced through chemical synthesis or enzymatic methods. However, these approaches often involve high production costs or the use of organic solvents. In contrast, microbial fermentation enables the natural and safe production of GABA, allowing its direct application in foods and aligning with the current trend toward sustainable food development. Legumes are good substrates for GABA production. Soybeans and adzuki beans have all been used for fermentation to produce fermented beverages with high GABA contents. Animal experiments have confirmed that these products have a significant effect on relieving mild depression in mice [14,15]. Although studies have produced functional ingredients, such as isoflavones, from the SSCF of soybean residues with R. oligosporus and Y. lipolytica [10,16], there have been no reports concerning the production of GABA to date. Furthermore, it is necessary to compare the differences between the okara of the two black soybean varieties in terms of their effectiveness for GABA production. Therefore, in this study, these two varieties were used for SSCF, optimizing using the response surface methodology (RSM) to produce black soybean okara with high GABA content.

2. Materials and Methods

2.1. Activation and Cultivation of Microbial Strains

The method described by Zhang et al. was referred to with modifications [17]. R. oligosporus (BCBC 31631) and Y. lipolytica (BCRC 21252) were purchased from the Food Industry Research and Development Institute (Hsinchu City, Taiwan). R. oligosporus was inoculated from frozen vials onto potato dextrose agar (PDA, St Bio, HiMedia Laboratories Pvt. Ltd., Mumbai, India) containing 10% tartaric acid and cultured at 30 °C for 48 h. After activation with potato dextrose broth (PDB, HiMedia Laboratories), the fungus was cultured on PDA plates containing 10% tartaric acid at 30 °C for 5 days. Then, the surface was rinsed with sterile water, and a spore suspension was collected. The spores were counted and stored at 7 °C for subsequent use in okara fermentation experiments. Frozen Y. lipolytica was activated twice by shaker-flask culture at 100 rpm and 30 °C for 20 h in yeast malt broth (YMB, HiMedia Laboratories) and then counted for later use in okara fermentation experiments.

2.2. Okara Fermentation

Tainan No. 3 (TN3) and Tainan No. 5 (TN5) black soybeans were washed and soaked in water at a 1:5 (w/v) soybean-to-water ratio in a refrigerator for 7 h. After soaking, 5 times the quantity of water was added, and the soybeans were ground using a soybean and rice grinder (model CH-102, Cheng Huei Machinery Co., Ltd., Taichung, Taiwan). Then, the okara was separated using an automatic soybean milk filter (Chang Shern Machinery Industrial Co., Ltd., Taoyuan, Taiwan). Okara was vacuum-packed into 200 g packages and subjected to high-pressure sterilization at 121 °C for 15 min in a Hot Water Shower Spray Sterilizer (CY-3000H-RD-770-1P, Chang Yu Machinery Works, Changhua, Taiwan).

The methods described by Zhang et al. and Shih et al. were referenced with modifications [17,18]. Thirty grams of sterilized okara was mixed with 1.8 mL of the R. oligosporus spore suspension (5.05 × 10⁵ CFU/mL) in a glass culture dish. A sterile spoon was used to stir evenly before the culture dish was covered with a lid and placed in a 30 °C incubator for 24 h. After 24 h of incubation, the surface of the okara was covered with a thin layer of white hyphae. The okara in the dish was gently disrupted using a sterile scalpel to partially break up the surface hyphae and improve the distribution and penetration of Y. lipolytica during the subsequent co-fermentation. The disruption was performed under aseptic conditions in a biosafety cabinet and standardized across all samples to ensure consistency. Following this, 1.8 mL of Y. lipolytica culture was added to the glass culture dish to continue fermentation. The fermentation conditions of Y. lipolytica were designed using RSM. The fermented okara was then freeze-dried and ground into powder to analyze GABA content.

2.3. Optimizing of GABA Production

The inoculum level of Y. lipolytica as well as the temperature and time ranges for co-fermentation were set based on the conditions reported by Zhang et al. [17]. This experiment utilized a rotated central composite design (RCCD) with three independent variables related to fermentation: temperature (X₁, 20–40 °C), time (X₂, 24–72 h), and the amount of Y. lipolytica inoculated (X₃, 10³–10⁷ CFU/mL) across five levels (−2, −1, 0, 1, 2). The operating conditions and levels of response surface design are shown in

Table 1. Okara fermentation by Y. lipolytica: independent variables and their levels in RCCD experiments.

Independent Variables	Code	Levels
		−2	−1	0	1	2
Incubation temperature (°C)	X1	20	25	30	35	40
Incubation time (h)	X2	24	36	48	60	72
inoculation amount of Y. lipolytica (CFU/mL)	X3	103	104	105	106	107

. A total of 20 experimental runs were conducted, with the center point assessed in six trials.

The experimental data were fitted to a second-order polynomial model (Equation (1)), where $y$ represents the response variable, $x_i$ and $x_j$ are the independent variables, and ${\beta }_0$, ${\beta }_i$, ${\beta }_{ii}$, and ${\beta }_{ij}$ are regression coefficients for the intercept, linear, quadratic, and interaction terms, respectively. To visualize the relationship between the independent variables and the response variable, contour plots and response surface 3D plots were generated based on the fitted second-order polynomial model by Origin software 9.1 (OriginLab, Northampton, MA, USA). Analysis of variance (ANOVA) was performed to assess the statistical significance of the model terms, with results reported at significance levels of p < 0.05, 0.01 or 0.001.

$$y={\beta }_0+{\sum }_{i=1}^3{\beta }_i{x}_i+{\sum }_{i=1}^3{\beta }_{ii}{x_i}^2+{\sum }_{i=1}^2{\sum }_{j=i+1}^3{\beta }_{ij}{x_{i}x}_j+\mathsf{ϵ}$$

(1)

2.4. Determination of GABA Content in Fermented Okara

This experiment was conducted based on the method of Rossetti and Lombard [16]. A total of 100 mg of fermented okara powder was added to 1 mL of 70% ethanol, extracted by shaking for 30 min, and centrifuged at 1530× g for 20 min to collect the supernatant. Next, 200 μL of the extract was dried using a centrifugal concentrator (Genevac, miVac DUO, Warminster, PA, USA), and 40 μL of the mixed reagent (99% ethanol: triethylamine: water = 2:1:1) was added. After ensuring complete dissolution, the mixture was centrifuged and dried again. Then, 60 μL of phenyl isothiocyanate (PITC) derivatization reagent (99% ethanol: triethylamine: water: PITC = 7:1:1:1) was added, and the mixture was left in the dark for 20 min before being centrifuged and dried. The dried sample was then re-dissolved to 200 μL with a mobile phase consisting of 80% solvent A (0.1 M sodium acetate solution containing 0.05% triethylamine, 0.07% acetic acid, and 0.5% acetonitrile) and 20% solvent B (60% acetonitrile aqueous solution (pH 5.8)) and filtered through a 0.22 μm nylon filter (Basic Life Bioscience Inc., 0.22 µm, Boston, MA, USA) before being subject to high-performance liquid chromatography (HPLC) using an Inertsil ODS-2 C18 column (4.6 × 250 mm, 5 μm, GL Sciences Inc., Yamagata, Japan). The elution phase was a mixture of 80% solvent A and 20% solvent B, which was used to elute for 30 min at a flow rate of 0.6 mL/min. The eluate was analyzed using a UV/VIS detector (Waters 2489, Waters Corporation, Milford, MA, USA) at a wavelength of 254 nm.

2.5. Determination of Protease Activity in Fermented Okara

The methods of Benimana et al. and Chen et al. were used with slight modifications [19,20]. In this study, 0.1 g of fermented okara powder was added to 1.0 mL of 0.2 M phosphate buffered saline (PBS) at pH 7.0, and extraction was carried out at room temperature for 20 min. The mixture was centrifuged at 13,800× g for 10 min to obtain the supernatant as a crude protease extract. Then, 100 μL of the crude protease extract and 500 μL of 0.65% casein (prepared with 50 mM potassium phosphate solution) were mixed and incubated at 37 °C for 60 min (the reaction time of the control group was 0 min). Then, 500 μL of 110 mM trichloroacetic acid was added to terminate the reaction. After the mixture was centrifuged at 13,800× g for 10 min, 200 μL of the supernatant was mixed with 500 μL of 500 mM sodium carbonate and 100 μL of 0.5 mM Folin–Ciocalteu reagent (Folin–Ciocalteu reagent and water were mixed at a ratio of 1:2). The reaction was performed in a dark room at 37 °C for 30 min, and optical absorbance was measured at 660 nm. A standard curve was generated by replacing the sample with tyrosine (0.0275, 0.055, 0.11, 0.22, and 0.275 mM) at different concentrations and performing the same reaction under identical conditions. Protease activity is defined as the number of activity units per gram of solid dry weight (DW), using the formula (Equation (2)) as follows, and one activity unit (U) is defined as the amount of tyrosine released every 60 min at 37 °C.

Protease activity = tyrosine concentration (mM)/1 h/g dry weight = U/g DW

(2)

2.6. Statistical Analysis

All fermentation trials and GABA determinations were conducted in triplicate. Data are presented as means ± standard deviation (SD). The Statistical Analysis System software (Version 9.4, SAS Institute Inc., Cary, NC, USA) was used to perform response surface regression.

3. Results and Discussion

3.1. Solid-State Collaborative Fermentation of Black Soybean Okara

According to the findings of Medwid and Graut and Barth and Gaillardin, the optimal growth temperatures of R. oligosporus and Y. lipolytica are 25–30 °C and 35–42 °C, respectively [21,22]. Therefore, a culture temperature of 30 °C was adopted in this study to measure the growth curves of these two microorganisms within 24 h. As R. oligosporus is a fungus, the dry weight of its fermentation product usually reflects its growth rate. Cultivation experiments showed that R. oligosporus entered the logarithmic growth phase after 18 h of incubation, and that the maximum microbial count (0.031 g DW/mL) was seen at 24 h. Moreover, the pH during incubation was maintained at approximately 3.0. Y. lipolytica entered the stationary phase after 12 h of culture, and the maximum yeast count (~10⁷ CFU/mL) was seen at 21 h. The pH value was maintained between 4.0 and 5.0 during the incubation. As the two strains grew at different pH values and can both grow stably within 24 h, they are suitable for the co-fermentation of okara. As the maximum growth of R. oligosporus was seen after 24 h of culture, solid-state inoculation and the fermentation of R. oligosporus were performed first before co-cultivation with Y. lipolytica.

After black soybean okara was initially cultured with R. oligosporus at 30 °C for 24 h, it was co-cultivated with Y. lipolytica (10⁵ CFU/mL) at three temperatures (25 °C, 30 °C, and 39 °C). Internal codes used throughout the manuscript and in Figure 1 are defined as follows: “3R” and “5R” represented TN3 and TN5 okara fermented solely with R. oligosporus, respectively, while “3RY” and “5RY” refer to TN3 and TN5 okara subjected to co-cultivation of R. oligosporus and Y. lipolytica. Figure 1a shows the white hyphae observed on the surface of okara (3R and 5R) after fermentation with R. oligosporus at 30 °C for 24 h. Figure 1b presents the results after Y. lipolytica inoculation at three fermentation temperatures. For both TN3 and TN5 okara (3RY and 5RY), the fewest hyphae were observed at 25 °C incubation. However, for co-cultivation at 30 °C and 39 °C, hyphae growth increased with prolonged fermentation.

The pH changes in TN3 okara and TN5 okara after fermentation with R. oligosporus and Y. lipolytica for 72 h are shown in Figure 2a,b. The initial pH values of TN3 and TN5 okara were between 6.22 and 6.38. After the addition of R. oligosporus, the pH declined to 6.11–6.14. After adding Y. lipolytica, an increase was seen in pH values with increasing temperature. The pH value of TN3 okara was between 6.38 and 7.04, and that of TN5 okara was between 6.23 and 6.78. During the fermentation process, the pH of the samples increased. This phenomenon may be attributed to microbial protein metabolism, leading to the release of free amino acids and ammonia, which possess basic properties. Similar pH-increasing trends during tempeh fermentation have also been reported by Tojang et al. [23].

3.2. Response Surface Analysis of GABA Production in TN3 and TN5 Okara Fermentation

Following confirmation that the two microorganisms (R. oligosporus and Y. lipolytica) could successfully grow under the set culture conditions, the experiment employed an RSM-RCCD experimental design to investigate the effects of time, temperature, and Y. lipolytica inoculum size on GABA production and protease activity. The experimental design consisted of 20 trials, with the independent variable levels (lower, central, and upper) being temperature (20–40 °C), time (24–72 h), and Y. lipolytica inoculum size (10³–10⁷ CFU/mL).

Table 2. Operating conditions for three-factor and five-level response surface design of the fermented black soybean okara test.

	Code and Decoded Variables			Output Responses
	X1	X2	X3	Y1 GABA (μg/g)		Y2 Protease Activity (U/g)
	Temperature (°C)	Incubation Time (h)	Inoculation Size (log CFU/mL)	TN3	TN5	TN3	TN5
1	1 (35)	1 (60)	1 (6)	118.63	294.27	1.59	1.88
2	1 (35)	1 (60)	−1 (4)	171.39	189.63	0.41	1.29
3	1 (35)	−1 (36)	1 (6)	262.20	181.58	1.33	1.77
4	1 (35)	−1 (36)	−1 (4)	235.80	230.16	1.33	1.48
5	−1 (25)	1 (60)	1 (6)	234.80	132.12	1.55	1.38
6	−1 (25)	1 (60)	−1 (4)	210.98	203.08	0.75	2.43
7	−1 (25)	−1 (36)	1 (6)	751.31	811.10	1.30	0.88
8	−1 (25)	−1 (36)	−1 (4)	746.40	588.50	2.10	1.25
9	2 (40)	0 (48)	0 (5)	189.43	97.89	0.28	0.64
10	−2 (20)	0 (48)	0 (5)	730.36	595.68	2.44	1.73
11	0 (30)	2 (72)	0 (5)	272.36	175.62	1.71	1.66
12	0 (30)	−2 (24)	0 (5)	594.72	666.26	0.28	1.09
13	0 (30)	0 (48)	2 (7)	176.72	349.50	2.40	1.04
14	0 (30)	0 (48)	−2 (3)	147.63	274.70	2.85	3.46
15	0 (30)	0 (48)	0 (5)	840.65	787.13	0.22	1.28
16	0 (30)	0 (48)	0 (5)	884.56	828.07	0.23	1.14
17	0 (30)	0 (48)	0 (5)	912.08	794.86	0.23	0.89
18	0 (30)	0 (48)	0 (5)	790.76	826.55	0.25	1.25
19	0 (30)	0 (48)	0 (5)	781.04	852.88	0.16	1.25
20	0 (30)	0 (48)	0 (5)	801.18	777.65	0.22	1.21

presents the independent parameters along with the corresponding output responses. The optimal coefficient values can be identified by optimizing both the input variables (culture conditions) and the output responses (experimental results).

The regression coefficients of the second-order polynomial model for GABA content are shown in

Table 3. Quadratic polynomial regression model coefficients for GABA content in TN3 and TN5 fermented black soybean okara.

Parameter Intercept	GABA Content
	TN3	TN5
intercept	−10754 *	−7221.245 *
X1	443.679 ***	272.262 *
X2	133.335 *	105.133 *
X3	586.905	481.306
X12	−5.517 **	−3.987 *
X22	−1.199 ***	−1.266 ***
X33	−21.296	−34.234
X1X2	−0.559	0.528
X1X3	−12.786	−7.180
X2X3	−0.540	0.139
R2	0.8539	0.8318
lack of fit p-value	0.0037	0.0002

Level of significance: * significant at p ≤ 0.05. ** significant at p ≤ 0.01. *** significant at p ≤ 0.001.

. This study aimed to evaluate the effects of the fermentation variables on each reaction and determine the significance of each coefficient based on p-values (<0.05, <0.01, <0.001). Lower p-values indicate stronger associations between independent variables and responses. The predicted regression model for GABA content, based on the independent variable, is shown in (Equation (3)):

Y₁ (TN3) = −10754 + 443.679X₁ + 133.335X₂ + 586.905X₃ − 5.517X₁² − 1.199X₂² − 21.296X₃² − 0.559X₁X₂ − 12.786X₁X₃ − 0.540X₂X₃

(3)

where X₁ (temperature) and X₂ (incubation time) positively and significantly affected GABA production. However, although X₃ (inoculation size) had a positive effect on GABA production, this was not statistically significant. On the other hand, it can be found that the second-order interaction effects (X₁X₂, X₁X₃, and X₂X₃) all exerted a negative impact on GABA production, indicating that no synergistic effect exists between the process variables. A second-order quadratic model was generated, and the coefficient of determination (R²) of the regression Equation was 0.8539 (R² > 0.8), indicating that the model can predict 85.39% of the quadratic equation of the response surface.

According to the output value of TN5 in Table 3, the regression equation obtained is shown in (Equation (4)), which is obviously similar to the results of TN3. The R² value of the regression Equation was 0.8318 (R² > 0.8), indicating that while 16.82% of the total variation in the model cannot be explained, there is still more than an 80% probability that it can be predicted by the quadratic equation of the reaction surface. However, the significant lack-of-fit observed in TN3 and TN5, particularly concerning the inoculum variable, suggests that the model may not fully explain the observed variation in the response. This limitation implies that the model’s predictive capability should be interpreted with caution. Future improvements may involve refining the model structure or incorporating additional variables to enhance its fit and reliability.

Y₂ (TN5) = −7221.245 + 272.262X₁ + 105.133X₂ + 481.306X₃ − 3.987X₁² − 1.266X₂² − 34.234X₃² + 0.528X₁X₂ − 7.180 X₁X₃+ 0.139X₂X₃

(4)

3.3. RSM Model Plot Showing the Effect of Variables on GABA Production

The changes in GABA production across various processing variables were plotted using Equations (3) and (4), as presented in Figure 3. Figure 3a,d displays the response surface plots of fermentation temperature (X₁) and fermentation time (X₂) on GABA content when the Y. lipolytica inoculum size was fixed at 5 log CFU/mL (X₃ = 0). Figure 3b,e shows the response surface plots of fermentation temperature (X₁) and Y. lipolytica inoculum size (X₃) on GABA content, with fermentation time fixed at 48 h (X₂ = 0). Figure 3c,f illustrates the response surface plots of fermentation time (X₂) and Y. lipolytica inoculum size (X₃) on GABA content, with fermentation temperature fixed at 30 °C (X₁ = 0).

We used the Excel optimization tool to estimate the optimal SSCF conditions for Equations (3) and (4). The best predicted variables for fermenting TN3 okara were a temperature of 35 °C, a time of 47 h, and a Y. lipolytica inoculum size of 3 log CFU/mL. For fermenting TN5 okara, the best predicted variables were a temperature of 34 °C, a fermentation time of 49 h, and a Y. lipolytica inoculum size of 4 log CFU/mL. Under these conditions, the maximum GABA yields were 868.3 µg/g for TN3 and 853.1 µg/g for TN5. From the response surface plots in Figure 3, it can be observed that the predicted values align closely with the 3D curve, showing a good fitness for the fermentation temperature and time. However, there is a significant deviation in Y. lipolytica inoculum size (X₃), especially at the edges of the experimental design range (3–6 log CFU/mL).

By analyzing Figure 3b,c,e,f, the inoculation level (X₃) does not fit perfectly with the GABA content (Y), which may be due to the regression model not adequately capturing the trend within the range of X₃ variables. Although the X₃² and the X₁X₃ interaction parameters are statistically insignificant (Table 2), their larger coefficients still have a significant impact on the model’s predictions, resulting in the optimal X₃ values to fall at the edge of the design range. This phenomenon is reflected on a lack of fit p-values in the model, which may be attributed to insufficient data or limitations in the design range of the variables. Future research could improve the model’s accuracy and reliability by adding more data points within the X₃ variable range or conducting additional experiments to further explore the impact of X₃ on the response.

3.4. Response Surface Analysis of Protease Activity in TN3 and TN5 Okara Fermentation

The inclusion of protease activity as a response variable was based on its potential role in enhancing GABA production during fermentation. Zhang et al. reported that R. oligosporus RT-3 secreted abundant proteases during the SSF of soybeans, leading to a significant increase in small peptides (<10 kDa) and amino acids after 60 h of fermentation [24]. These hydrolyzed amino acids, particularly glutamate, serve as direct precursors for GABA biosynthesis. Furthermore, the black soybean varieties used in this study, TN3 and TN5, have high protein contents of 41.7 and 44.3 g/100 g, respectively [25], providing a plentiful substrate for protease activity and subsequent glutamate release. Notably, okara, a by-product of soymilk production, undergoes high-temperature cooking during processing, resulting in the loss of endogenous enzymatic activity, including proteases. As such, the role of microbial proteases becomes critical in catalyzing protein hydrolysis and increasing free glutamate levels. Previous research has also shown that unfermented soybeans contain very low levels of GABA (e.g., 27 μg/g) and protease activity [24,26], highlighting the importance of fermentation in enhancing GABA accumulation. Our results (Table 2) suggest that increased protease activity could be associated with enhanced availability of GABA precursors, supporting the inclusion of enzymatic parameters in the optimization process.

The effects of each independent variable on the protease activity in TN3 and TN5 fermented okara were evaluated from the regression equation in the coded level (Equations (5) and (6)):

Y₃ (TN3) = 42.885 − 0.942X₁ − 0.295X₂ − 8.251X₃ + 0.011X₁² + 0.001X₂² + 0.600X₃² + 0.001X₁X₂ + 0.029 X₁X₃ + 0.029X₂X₃

(5)

Y₄ (TN5) = 13.1668 − 0.1510X₁ +0.1081X₂ − 4.6010X₃ + 0.0003X₁² + 0.0004X₂² + 0.2746X₃² − 0.0037X₁X₂ + 0.0572X₁X₃ − 0.0041X₂X₃

(6)

The regression coefficients for independent variables were obtained by multiple linear regressions, as shown in

Table 4. Quadratic polynomial regression model coefficients for protease activities in TN3 and TN5 fermented black soybean okara.

Parameter Intercept	Protease Activity
	TN3	TN5
intercept	42.885 ***	13.1668
X1	−0.942 *	−0.1510
X2	−0.295 *	0.1081
X3	−8.251 ***	−4.6010 **
X12	0.011 *	0.0003
X22	0.001	0.0004
X32	0.600 ***	0.2746 **
X1X2	0.001	−0.0037
X1X3	0.029	0.0572
X2X3	0.029	−0.0041
R2	0.8474	0.7477
lack of fit p-value	<0.0001	0.0037

Level of significance: * significant at p ≤ 0.05. ** significant at p ≤ 0.01. *** significant at p ≤ 0.001.

. For protein activity in TN3 okara, three independent variables (X₁, X₂, and X₃) have negative regression coefficients and are significant, indicating that they have a significant negative impact on protease activity. The effect of Y. lipolytica inoculation size (X₃) on protease activity is particularly pronounced. In contrast, the three independent variables had no significant effect on protease activity in TN5 okara.

The interaction of the three independent variables did not reach the level of significance (p > 0.05), indicating that their impact on protease activity is minimal and may not be sufficient to significantly affect protease activity. This suggests that the interactions between the independent variables do not play an important role in protease activity.

The regression coefficient X₃² represents the quadratic term of Y. lipolytica inoculation size. For protease activity in both TN3 and TN5 okara, it reflects the nonlinear effect of inoculation size on both response values. In these results, X₃² is significant for protease activity, with positive coefficients, indicating that as the inoculation size increases, the responses will follow an increasing trend in a quadratic manner. Furthermore, this effect is more significant (p ≤ 0.001) in TN3.

The coefficients of determination (R²) were between 0.85 (TN3) and 0.75 (TN5), indicating that these models can explain 85% and 75% of the variability in the response variables, respectively. In addition, the lack-of-fit of all models is very small (p < 0.05), indicating that there is a significant lack of fit in these models.

3.5. RSM Model Plot Showing the Effect of Variables on Protease Activity

The changes in protease activity across various processing variables were plotted using Equations (5) and (6), as shown in Figure 4. From the response surface plots, it can be observed that both TN3 (Figure 4a–c) and TN5 (Figure 4d–f) exhibit bowl or inverted saddle shapes. The fit between the three fermentation experimental variables (X₁, X₂, and X₃) and protease activity (Y) was weak, likely because Y. lipolytica mainly produces lipases; whereas, R. oligosporus is more characterized by protease production. A previous study showed that significant amino acid production only occurred after 72 h of culture with R. oligosporus alone [26]. The relatively low protease activity observed could be attributed to the metabolic preference of Y. lipolytica for lipase production over proteases. Bankar et al. also showed that Y. lipolytica primarily produces lipases, favoring lipid metabolism rather than protein degradation [27]. However, further enzymatic analysis is needed to confirm this hypothesis.

Analysis of the 20 operating conditions listed in Table 2 indicated that the central points of the experimental design (trials 15 to 20) were associated with the highest GABA content, as predicted in Figure 3. Notably, these trials exhibited relatively low protease activity, suggesting that the relationship between GABA accumulation and protease activity remains to be further clarified through additional research.

4. Conclusions

In this study, an RSM-RCCD experimental design was employed to predict the optimal GABA production conditions for TN3 and TN5 black soybean okara. The results indicated that the optimal fermentation conditions of both were similar, with the exception that the inoculation size of Y. lipolytica could be further optimized. The highest GABA content was achieved when the fermentation temperature was 34–35 °C, and the fermentation time was 47–49 h. This study explores the use of the mold R. oligosporus and the yeast Y. lipolytica in a collaborative process to produce GABA-rich black soybean okara, providing new insights into the potential of this fermentation combination. Although protease activity was included as a potential indicator based on previous studies, it did not exhibit a clear correlation with GABA accumulation. Future study should incorporate more direct indicators associated with GABA accumulation, such as glutamic acid content or amino acid profiling, to gain a more comprehensive understanding of the metabolic mechanism during the fermentation process. The optimized SSCF conditions predicted in this study not only enhance the functionality of black soybean okara but also provide a new direction for promoting by-product recycling in the food industry.