Antioxidant Protein Hydrolysates from Hemp Seed Oil Cake—Optimization of the Process Using Response Surface Methodology

Abstract

Hemp seed oil cake, a by-product of hemp seed oil extraction, is characterized by its high protein content and bioactive components, making it a valuable resource for the development of functional products through enzymatic hydrolysis. Hemp seed oil itself is renowned for its rich content of essential fatty acids, vitamins, and antioxidants, contributing to its widespread use in health and wellness products. Consequently, the residual cake presents significant potential for the food, pharmaceutical, and cosmetic industries as a source of high-quality protein ingredients. The optimization of enzymatic hydrolysis conditions is crucial for maximizing the efficiency and quality of the resulting protein hydrolysates. This study aims to optimize the hydrolysis process of hemp seed oil cake with bromelain, focusing on three key factors: enzyme concentration (E/S ratio), temperature, and time, to achieve hydrolysates with superior antioxidant activity. Response Surface Methodology (RSM) was applied using a Box–Behnken design to model and optimize the hydrolysis conditions. The experimental design involved three levels for each factor: 1%, 2%, and 3% for bromelain concentration; 20 °C, 30 °C, and 40 °C for temperature; and 60, 120, and 180 min for hydrolysis duration, resulting in 21 experimental runs. The antioxidant activity was assessed via DPPH and ABTS radical scavenging assays (%RSA), and the derived regression models were statistically analyzed and validated. The findings indicate that the optimal conditions for obtaining protein hydrolysates with the highest antioxidant activity are a bromelain concentration of 3.0%, a temperature of 40 °C, and a hydrolysis time of 60 min.

1. Introduction

Food waste is among the main sources of environmental pollution, and its utilization is challenging due to its biological instability. Effective food waste management is crucial for ensuring economic, social, and environmental sustainability [1,2].

The production of oils from various oilseed crops, vegetables, and fruits generates about 350 million tons of waste (meal or cake) annually. The most common use of these cakes and meals is for animal feeding or as organic fertilizers. The waste obtained from the vegetable oil industry are rich in proteins and various biologically active compounds. Common vegetable oil by-products include meals from soybeans, rapeseeds, sunflowers, and sesame, which are rich in compounds such as phenolics, tocopherols, and phytosterols [3]. By-products from the processing of grape and citrus oils are being studied as sources of bioactive substances with health benefits and applications in food, cosmetics, and pharmaceuticals [4,5,6].

Olive oil production also generates a large amount of residue, which is typically discarded into the environment. These resources can be valorized into value-added products for use in the food and cosmetic industries [7].

The proper utilization of plant waste and their transformation into valuable products with practical applications is beneficial from both economic and environmental perspectives [8,9].

Hemp (Cannabis sativa L.) is a versatile and cost-effective cultivated plant resource for producing textiles, food, paper, biofuel, medicine, and hygiene products [10]. Hemp seed has a unique phytochemical composition and various applications, including in the pharmaceutical and food industries. Hemp seeds contain approximately 20–25% protein with a good balance of essential amino acids, unsaturated fatty acids, mineral nutrients, and fiber. Hemp seed proteins generally consist of two main fractions—edestin (globulin) and albumin. Hemp proteins used in the food industry originate from the species Cannabis sativa L., which, unlike marijuana (Cannabis indica), contains only traces of δ-9-tetrahydrocannabinol (THC) [1].

Hemp seeds are gaining attention as a high-value raw material due to their excellent nutritional properties, and research into developing functional food products using hemp seeds is actively progressing [11,12,13].

After cold pressing and separating the hemp seed oil, the remaining cake is a protein-rich by-product. Enzymatic hydrolysis is a widely used method for the valorization of hemp cake and obtaining plant proteins with improved functional properties. Through hydrolysis, peptide bonds in proteins are broken down, releasing peptides of different sizes and free amino acids [14,15].

Specific hemp seed peptides have been identified as having functional activities including antioxidant [16,17], immunomodulatory [18,19], hypocholesterolemic [20,21], antihypertensive [22,23], and antihyperglycemic activity [24,25].

These properties make hydrolyzed hemp seed proteins valuable ingredients in functional foods aimed at improving human health.

Enzymatic hydrolysis is a method that takes place under gentle conditions—pH (6–8), temperature (30–60 °C)—and minimizes side reactions. In enzymatic hydrolysis, the nature and extent of treatment can be controlled due to the inherent specificity of the different proteases. The most commonly used proteolytic enzymes to obtain bioactive peptides from hemp seed cake with antioxidant potential are alcalase, pancreatin, pepsin, flavourzyme [26,27].

Yoon et al. [28] evaluated the antioxidant properties of hemp seed protein hydrolysates obtained by enzymatic hydrolysis using five different proteases (alcalase, bromelain, flavourzyme, neutrase, and papain). The presented results prove that the obtained hemp seed protein hydrolysates showed higher antioxidant activity than the non-enzyme control group. In addition, the potential for the use of hemp proteins in the development of natural antioxidant products has been confirmed.

In most published articles aiming for enzymatic hydrolytic degradation of seed proteins and obtaining hydrolysates with antioxidant activity, the concentration of enzymes is between 1 and 3% [1,28].

The process of enzymatic hydrolysis requires specific conditions that are optimal for the action of the enzymes. In this context, the protein substrate, the enzymes used, and the hydrolysis conditions (pH, temperature, and time) lead to the production of protein hydrolysates with different profiles and a spectrum of functional activities.

Tang et al. investigated the process of enzymatic hydrolysis of hemp protein isolate by six proteases (alcalase, Flavourzyme^®, neutrase, protamex, pepsin, and trypsin) and the antioxidant activities of the resulting hydrolysates [29]. They found that the hydrolysates exhibited distinct differences in DPPH radical scavenging ability depending on the type of protease used and the hydrolysis time. When increasing the time for hydrolysis from 2 to 4 h and using the proteases neutrase and trypsin, the radical scavenging ability was significantly increased, while that for flavourzyme, pepsin, and protamex was on the contrary decreased.

Assuming that the proteins in hemp oilseed cakes can be converted into bioactive peptides, the aim of this study was to optimize the enzymatic hydrolysis process with respect to three factors: temperature, time, and enzyme concentration (E/S ratio) to obtain hydrolysates with the highest antioxidant activity. From the perspective of waste utilization and maximum economic efficiency, experiments were conducted using direct enzymatic hydrolysis of HSC without prior protein extraction. The enzymatic hydrolysis of hemp seed cake was investigated using the Response Surface Methodology (RSM). The Box–Behnken design was applied to predict the model and optimize the hydrolysis conditions. Preliminary experiments by our group on the enzymatic hydrolysis of hemp seed proteins with papain and bromelain found that with bromelain treatment the degree of hydrolysis was higher, reaching 30.71% (unpublished data). For this reason, the enzyme bromelain was used in the present study.

2. Materials and Methods

2.1. Materials

Cold-pressed hemp seed (Cannabis sativa L., ssp. sativa) oil cake (HSC) with particle sizes smaller than 0.500 mm was obtained from ViM Production Ltd., Stryklevo village, Bulgaria. Bromelain (EC 3.4.22.32) with an activity of 256,475 U/g was sourced from SERVA Electrophoresis GmbH, Germany. DPPH (1,1-diphenyl-2-picrylhydrazyl), ABTS (2,2′-azino-bis (3-ethylbenzothiazoline-6-sulfonic acid)), and methanol were purchased from Merck KGaA, (Darmstadt, Germany). All reagents and chemicals used were of analytical grade.

2.2. Physicochemical Analysis of HSC

Moisture Content: Measured using a Moisture Analyzer DBS 60-3 (Kern&Sohn GmbH, Balinger, Germany). Total Protein Content: Determined in accordance with ISO 1871:2009 [30] using a Kjeldahl protein determination apparatus (UDK-129 Distillation Unit, VELP Scientifica, Usmate (MB), Italy).

Total Fat Content: Determined using a Soxtec Avanti 2055 apparatus (Foss Analytical A/S, Hillerød, Denmark), following EN ISO 659:2009 and the manufacturer’s instructions [31]. Total Ash Content: Determined according to ISO 936:1998 [32].

2.3. Enzymatic Hydrolysis of HSC

HSC samples were suspended in 0.1 M phosphate buffer (pH 6.5) to prepare a mixture with protein concentration of 6.25 g/100 mL. Bromelain was added at concentrations of 1%, 2%, or 3% relative to the protein content. Hydrolysis was performed at 20 °C, 30 °C, or 40 °C for 60, 120, or 180 min in a shaking water bath (VLSB18, VWR International, Vienna, Austria). Post-hydrolysis, the samples were heated to 85 °C for 15 min to deactivate the bromelain, cooled to room temperature, and centrifuged at 4250× g for 15 min at 4 °C. The supernatant was collected, filtered, frozen, and lyophilized using a laboratory freeze-dryer (LYOBETA 6PL, Telstar, Barcelona, Spain). The lyophilized hemp protein hydrolysate (LHPH) samples were stored at −28 °C until further analysis.

2.4. Antioxidant Activity of Lyophilized Hemp Protein Hydrolysate (LHPH)

Samples of 0.400 g of LHPH from each test group were dissolved in 10 mL of distilled water. The resulting solutions were analyzed for antioxidant activity by DPPH and ABTS methods. Additionally, the radical-scavenging activity towards DPPH and ABTS of the aqueous extract from HSC, without enzyme addition, and the lyophilized hydrolysate (LHPH), obtained under the experimentally determined optimal parameters for bromelain treatment, were determined. These results are presented as mg Trolox equivalent per g of cake or lyophilizate (mg TE g⁻¹).

2.4.1. DPPH Radical Scavenging Capacity

The DPPH radical scavenging capacity was measured following the Brand-Williams method [33], with minor modifications [34], and the percentage of DPPH radical inhibition (%RSA) was calculated. The absorbance measurement at 517 nm was carried out at using a UV–VIS spectrophotometer (Libra S22, Biochrom, Holliston, MA, USA).Trolox standard solutions (concentrations ranging from 1.0 to 15 μg/mL) were used as positive controls and for constructing a calibration curve.

2.4.2. ABTS Radical Scavenging Capacity

The ABTS radical scavenging capacity was determined according to the method of Re et al. [35], with slight modifications [34], and the percentage of ABTS radical inhibition (%RSA) was calculated. The absorption was measured at 734 nm. Trolox standard solutions (concentrations ranging from 6.25 to 125 μg/mL) were used as positive controls and for constructing a calibration curve.

2.5. Experimental Design and Statistical Analysis

To investigate the effects of three independent variables on the radical scavenging activity of LHPH, the Response Surface Methodology (RSM) was utilized, applying the Box–Behnken design (BBD). The variables analyzed included bromelain concentration (X₁), temperature (X₂), and hydrolysis time (X₃), all of which influence the radical scavenging activities as measured by DPPH and ABTS assays. The coded and actual levels of these independent variables are detailed in

Table 1. Independent variables: coded and actual levels applied in the RSM design.

Independent Variables	Symbols	Levels
		−1	0	+1
Bromelain concentration (%)	X1	1.0	2.0	3.0
Temperature (°C)	X2	20	30	40
Hydrolysis time (min)	X3	60	120	180

.

The dependent variables, denoted as Y₁ and Y₂, represent the DPPH and ABTS radical scavenging activities, respectively, and were modeled using a second-order polynomial Equation (1). The application of RSM in conjunction with the Box–Behnken design facilitates the efficient optimization of the process by minimizing the number of experiments required to achieve precise and reliable results. This is particularly critical in complex biochemical processes where multiple factors may interact in unpredictable ways.

$$Y_j={\beta }_0+{\displaystyle \sum }_{i=0}^k{\beta }_i{X}_i+{\displaystyle \sum }_{i=1}^k{\beta }_{ii}{X}_i^2+{\displaystyle \sum }_{i>0}^k{\beta }_{ij}{X}_i{X}_j+E,$$

(1)

In this model (1), Yj (where j = 1, 2) denotes the responses being modeled. The term β₀ represents the constant coefficient, β_i is the coefficient of the linear effect, β_ij signifies the coefficient of the interaction effect, and β_ii corresponds to the coefficient of the squared effect. The variable k stands for the number of variables, while X_i and X_j define the independent variables, specifically bromelain concentration (X₁), temperature (X₂), and hydrolysis time (X₃). The statistical significance of the coefficients was assessed using the Student’s t-test at a significance level of α = 0.05. The model’s goodness-of-fit was evaluated using the determination coefficient (R²), and its consistency was verified by the Fisher F test, also at α = 0.05.

Design-Expert software (version 13.0.5.0, State-Ease Inc., Minneapolis, MN, USA) was used to carry out the experimental design and statistical analysis. The experiment involved a total of 21 runs, which were conducted in random order to minimize potential bias. To facilitate the estimation of the pure error sum of squares, five center points per block were included in the design. This approach not only ensures the accurate estimation of pure error but also enhances the reproducibility and stability of the experimental process, thereby contributing to the robustness and reliability of the results.

3. Results and Discussion

3.1. Physicochemical Analysis of HSC

Hemp cake used as substrate for hydrolysis is characterized by a protein content of 29.72% (

Table 2. Physicochemical analysis of HSC.

Composition	Content (g/100 g)
Moisture	7.63 ± 0.30
Protein	29.72 ± 0.24
Fat	10.50 ± 0.01
Ash	5.82 ± 0.58

Values represent means ± standard deviations (n = 3).

). Similar values were also reported by Kasula et al. [36]. Depending on the hemp variety, hemp seed meal contains between 24–32% protein, 29–37% fiber, and 5–6% ash [37].

Although hemp cake is a waste material from the production of cold-pressed oil and is obtained after the extraction of hemp seed oil, the biomass retains between 9–20% total lipids. The measured content of total lipids in the raw material used in this study was also within these limits, namely 10.50%. In a study conducted by Banskota et al. [38], hemp seed meal was reported to have a rich profile of polyunsaturated fatty acids, including omega-3 (ω-3) and omega-6 (ω-6) fatty acids.

3.2. Optimization of the Enzymatic Hydrolysis Process

The experimental data were analyzed using a Box–Behnken design (BBD), which is a central element of Response Surface Methodology (RSM) [39]. RSM encompasses a set of statistical and mathematical techniques aimed at process development, enhancement, and optimization. Among the principal designs within RSM, BBD and the central composite design (CCD) are most notable. BBD, however, was selected for this study due to its efficiency, requiring fewer experimental runs and employing only three levels per factor, compared to the five levels used in CCD [40]. This efficiency made BBD particularly suitable for the objectives of this research.

All experiments were performed in triplicate to ensure precision, with the means and standard deviations calculated to enhance accuracy. The experimental data were then subjected to statistical analysis using Design-Expert software (version 13.0.5.0). The findings, as presented in

Table 3. Effects of bromelain concentration (A), temperature (B), and hydrolysis time (C) on DPPH (Y₁) and ABTS (Y₂) radical scavenging activity in LHPH.

Factor 1		Factor 2		Factor 3		Y1	Y2
A: Bromelain Concentration		B: Temperature		C: Hydrolysis Time		DPPH	ABTS
−1	1%	−1	20 °C	0	2 h	51.48	33.81
0	2%	0	30 °C	0	2 h	60.50	49.60
0	2%	0	30 °C	0	2 h	62.16	55.77
0	2%	0	30 °C	0	2 h	63.60	49.6
0	2%	−1	20 °C	1	3 h	55.94	34.51
1	3%	0	30 °C	1	3 h	67.13	50.15
1	3%	−1	20 °C	0	2 h	55.74	52.27
−1	1%	0	30 °C	−1	1 h	58.11	46.00
1	3%	1	40 °C	0	2 h	69.18	63.03
0	2%	0	30 °C	0	2 h	60.63	49.60
0	2%	0	30 °C	0	2 h	60.50	51.84
0	2%	−1	20 °C	−1	1 h	51.36	40.20
−1	1%	0	30 °C	1	3 h	57.82	57.01
−1	1%	1	40 °C	0	2 h	60.31	62.73
0	2%	1	40 °C	−1	1 h	62.24	64.28
1	3%	0	30 °C	−1	1 h	64.82	67.64
0	2%	0	30 °C	0	2 h	60.63	55.77
0	2%	1	40 °C	1	3 h	65.15	64.32
0	2%	0	30 °C	0	2 h	62.16	51.69
0	2%	0	30 °C	0	2 h	63.60	51.84
0	2%	0	30 °C	0	2 h	60.50	55.77

, provide a detailed overview of the radical scavenging activity of the hydrolysates, specifically against DPPH and ABTS radicals. This comprehensive analysis underscores the reliability of the experimental outcomes and supports the study’s conclusions.

The experimental design involved three levels for each factor: 1%, 2%, and 3% for bromelain concentration; 20 °C, 30 °C, and 40 °C for temperature; and 60, 120, and 180 min for hydrolysis duration. The selection of levels for each factor was determined based on economic efficiency (low energy consumption) and ensuring enzyme stability throughout the hydrolysis period (up to 180 min). At 60 °C, bromelain has the highest activity but is highly unstable. Ref. [41] found that bromelain loses 50% of its activity after just 20 min of heating at 60 °C. Ref. [42] reported that after incubation at 50 °C for 60 min, bromelain activity decreases to 83% of the initial value.

The data presented in Table 3 indicate that all LHPH samples exhibit antioxidant activity by inhibiting both DPPH and ABTS radicals, though the extent of this inhibition varies depending on the specific enzymatic hydrolysis parameters applied. The % Radical Scavenging Activity (%RSA) for DPPH ranges from 49.47% to 69.18%, while for ABTS, it spans from 33.81% to 67.64%. In these experimental conditions, the IC₅₀ values—the concentration needed to inhibit 50% of the radical—were determined for the standard antioxidant Trolox, with values of 13.07 µg/mL for the DPPH assay and 64.70 µg/mL for the ABTS assay.

Table 4. Dependent variable models used in the RSM framework.

Dependent Variables	Symbols	Model
DPPH	Y1	${\mathrm{Y}}_1=61.58+3.64{\mathrm{X}}_1+5.30{\mathrm{X}}_2+1.19{\mathrm{X}}_3-2.85{\mathrm{X}}_2^2$
ABTS	Y2	${\mathrm{Y}}_2=51.61+4.88{\mathrm{X}}_1+10.52{\mathrm{X}}_2-4.64{\mathrm{X}}_1{\mathrm{X}}_2-8.46{\mathrm{X}}_1{\mathrm{X}}_3+1.21{\mathrm{X}}_1^2$$+1.09{\mathrm{X}}_3^2$

provides a summary of the models developed in this study. These models were assessed based on the lack of fit and the coefficient of determination (R²). The significance of each coefficient within the models was evaluated using an F-test derived from the analysis of variance (ANOVA). Additionally, numerical optimization was performed to determine the optimal conditions for the enzymatic hydrolysis process, ensuring maximum efficiency and effectiveness. These optimizations and evaluations underscore the robustness and predictive accuracy of the developed models, providing a strong foundation for further research and practical application.

The software product Design-Expert identified a quadratic relationship between the DPPH radical scavenging activity and the input variables, as shown in

Table 5. Analysis of variance for the quadratic model of DPPH (output 1).

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Model	388.74	9	43.19	24.37	<0.0001	significant
A—Bromelain concentration	106.17	1	106.17	59.90	<0.0001
B—Temperature	224.40	1	224.40	126.61	<0.0001
C—hydrolysis time	11.31	1	11.31	6.38	0.0282
AB	5.30	1	5.30	2.99	0.1118
AC	1.68	1	1.68	0.9487	0.3510
BC	0.7055	1	0.7055	0.3981	0.5410
A2	0.9200	1	0.9200	0.5191	0.4863
B2	37.82	1	37.82	21.34	0.0007
C2	0.0162	1	0.0162	0.0092	0.9255
Residual	19.50	11	1.77
Lack of Fit	5.37	3	1.79	1.01	0.4356	not significant
Pure Error	14.12	8	1.77
Cor Total	408.23	20

. Although the model includes some terms with statistically insignificant coefficients, the overall model remains robust. The F-value of 24.37 suggests that the model is statistically significant, with a mere 0.01% probability that such a high F-value could be attributed to random noise. p-values below 0.0500 further confirm the significance of the model terms, with factors A, B, C, and B² being particularly noteworthy.

The accuracy assessments of the model, presented in

Table 6. Model accuracy metrics for DPPH (output 1).

Std. Dev.	1.33	R2	0.9522
Mean	60.64	Adjusted R2	0.9132
C.V. %	2.20	Predicted R2	0.7457
		Adeq Precision	19.4608

, show that the high R² and adjusted R² values effectively capture the variability in DPPH activity. Additionally, the Adeq Precision value, which measures the signal-to-noise ratio, is 19.46—well above the threshold of four—indicating a strong and reliable signal. This adequacy suggests that the model is well-suited for navigating the design space, allowing for reliable predictions and optimizations within the defined parameters. The robustness of this model facilitates a deeper understanding of the factors influencing DPPH activity and provides a solid foundation for future studies seeking to optimize antioxidant activity through enzymatic hydrolysis. The model’s high predictive accuracy and signal strength make it a valuable tool for guiding experimental design and process optimization in related research.

Three types of diagnostics were used to evaluate the model: the normal probability plot, the plot of residuals versus ascending predicted response values, and the plot of predicted response values versus actual response values, as depicted in Figure 1. The normal probability plot (Figure 1a) was used to assess whether the residuals follow a normal distribution. The plot reveals that the residuals generally align with a straight line, with only minor deviations, indicating that the residuals are normally distributed. The plot of residuals versus predicted values (Figure 1b) shows that the residuals are randomly dispersed around the line where residual = 0, suggesting that the model is adequate and free from significant biases. Additionally, the absence of any residuals that deviate markedly from the random pattern indicates that no outliers are influencing the model. Lastly, the plot of actual versus predicted values (Figure 1c) illustrates that while the points do not perfectly align with the diagonal line, they remain within reasonable bounds, which is expected given an R² value of 0.9132. This suggests that the model has a strong predictive capability, albeit with some inherent variability.

The series of model plots presented in Figure 2 illustrates the effects of the input factors on the output variable. In Plot 2a, the influence of the input factors on DPPH radical scavenging activity is highlighted, with factor B (temperature) exerting the most significant impact, followed by factor A (bromelain concentration). The line for factor C (hydrolysis time) is nearly parallel to the x-axis, indicating that it has little to no significant effect on DPPH activity.

The response surface plots (Figure 2b–d) provide a visual representation of how two independent variables interact within the experimental range, while the third variable remains constant. Figure 2b shows that the maximum DPPH value can be achieved when both the temperature and bromelain concentration are maintained above 30 °C and 3.0%, respectively, with hydrolysis time set at a maximum of 180 min. In Figure 2c, it is evident that the highest DPPH value is attainable with a hydrolysis time exceeding 120 min, a bromelain concentration above 2.5%, and the maximum temperature. Figure 2d demonstrates that the optimal DPPH radical scavenging activity is achieved at maximum levels of both bromelain concentration and temperature, while hydrolysis time does not play a significant role in this scenario.

These plots provide valuable insights into the conditions necessary to maximize DPPH activity, emphasizing the critical role of temperature and bromelain concentration in the process while suggesting that hydrolysis time is less influential under the conditions tested.

Design-Expert software identified the relationship between ABTS radical scavenging activity and the input variables as quadratic, as shown in

Table 7. Analysis of variance for the quadratic model of ABTS (output 2).

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Model	1465.21	9	162.80	164.76	<0.0001	significant
A—Bromelain concentration	190.69	1	190.69	192.98	<0.0001
B—Temperature	884.94	1	884.94	895.60	<0.0001
C—Hydrolysis time	0.9748	1	0.9748	0.9865	0.3419
AB	86.05	1	86.05	87.08	<0.0001
AC	286.12	1	286.12	289.56	<0.0001
BC	0.7854	1	0.7854	0.7949	0.3917
A2	6.76	1	6.76	6.84	0.0240
B2	0.0003	1	0.0003	0.0003	0.9865
C2	5.54	1	5.54	5.61	0.0373
Residual	10.87	11	0.9881
Lack of Fit	4.71	3	1.57	2.04	0.1871	not significant
Pure Error	6.16	8	0.7700
Cor Total	1476.08	20

. Although some added terms have statistically insignificant coefficients, the model as a whole remains robust. The model’s F-value of 164.76 indicates a high level of statistical significance, with only a 0.01% likelihood that such a large F-value is due to random noise. p-values below 0.0500 confirm the significance of specific model terms, particularly A (bromelain concentration), B (temperature), AB (interaction between bromelain concentration and temperature), AC (interaction between bromelain concentration and hydrolysis time), A², and C².

The accuracy of the model is further supported by the assessments presented in

Table 8. Model accuracy metrics for ABTS (output 2).

Std. Dev.	0.9940	R2	0.9926
Mean	52.49	Adjusted R2	0.9866
C.V. %	1.89	Predicted R2	0.9437
		Adeq Precision	50.7486

. The high R² and adjusted R² values demonstrate that the model effectively captures the variability in ABTS radical scavenging activity. Additionally, the Adeq Precision value, which measures the signal-to-noise ratio, is 50.7486, far exceeding the minimum threshold of four. This indicates a strong and reliable signal, confirming that the model is well-suited for navigating the design space and making accurate predictions.

The robustness and precision of this model make it a valuable tool for optimizing ABTS radical scavenging activity in future studies, providing reliable guidance for process adjustments and enhancements.

Model diagnostics were conducted using three key plots: the normal probability plot, the plot of residuals versus ascending predicted response values, and the plot of predicted response values versus actual response values, as shown in Figure 3. The normal probability plot (Figure 3a) was used to determine whether the residuals followed a normal distribution. In this instance, the residuals align closely with a straight line, with only minor deviations, indicating that they are normally distributed.

The residuals versus predicted values plot (Figure 3b) reveals that the residuals are randomly dispersed around the line where residual = 0. This random scatter suggests that the model is well-fitted and free from significant bias. Moreover, the absence of any residuals that significantly deviate from the overall pattern indicates that no outliers are affecting the model’s accuracy.

The actual versus predicted values plot (Figure 3c) shows that while the points do not align perfectly with the diagonal line, they remain within acceptable limits. This slight deviation is reasonable given the high R² value of 0.9926, which indicates that the model has an excellent fit and strong predictive power. These diagnostic plots collectively confirm the adequacy and reliability of the model, ensuring its robustness in predicting the response variable accurately across the design space.

Figure 4 presents a series of model plots that illustrate the effects of the input factors on the output. Plot 4a highlights the influence of the input factors on ABTS radical scavenging activity, with factor B (temperature) exerting the most significant impact, followed by factor A (bromelain concentration). The line representing factor C (hydrolysis time) is nearly parallel to the x-axis, indicating that it has little to no significant influence on the ABTS activity.

The response surface plots (Figure 4b–d) provide a visual representation of how two independent variables interact within the experimental range while the third variable is held constant. Figure 4b reveals that the maximum ABTS value can be achieved when both temperature and bromelain concentration are maintained above 30 °C and 3.0%, respectively, while the hydrolysis time is minimized to 60 min. In Figure 4c, two distinct zones for achieving maximum ABTS values are identified. The first zone requires a maximum bromelain concentration above 2.5% combined with minimal hydrolysis time, while the second zone achieves maximum ABTS activity with maximum hydrolysis time but minimal bromelain concentration. Both scenarios assume maximum temperature.

Figure 4d demonstrates that the optimal ABTS radical scavenging activity can be obtained by simultaneously maximizing both bromelain concentration and temperature while keeping the hydrolysis time to a minimum. These findings provide valuable insights into the critical factors and their interactions that drive ABTS activity, offering a clear pathway for optimizing conditions to achieve the highest antioxidant potential in the enzymatic hydrolysis process. The response surface plots underscore the importance of precise control over temperature and bromelain concentration while suggesting that hydrolysis time plays a secondary role under these optimal conditions.

An optimization process was conducted to simultaneously achieve maximum values for both DPPH and ABTS radical scavenging activities. The constraints applied during this optimization are outlined in

Table 9. Optimization constraints.

Name	Goal	Lower Limit	Upper Limit	Lower Weight	Upper Weight	Importance
A: Bromelain concentration	is in range	−1	1	1	1	3
B: Temperature	is in range	−1	1	1	1	3
C: Hydrolysis time	is in range	−1	1	1	1	3
DPPH	maximize	51.3567	80.1767	0.794328	1	5
StdErr(DPPH)	none	0.443767	1.15294	1	1	3
ABTS	maximize	33.6725	75.7325	1	1	5
StdErr(ABTS)	none	0.331345	0.860859	1	1	3

. The optimization yielded 100 potential solutions, of which only the top 10 are presented in

Table 10. Results of numerical optimization.

Number	Bromelain Concentration	Temperature	Hydrolysis Time	DPPH	StdErr (DPPH)	ABTS	StdErr (ABTS)	Desirability
1	1.000	1.000	−1.000	67.789	1.541	73.039	1.151	0.774	Selected
2	1.000	1.000	−1.000	67.788	1.541	73.035	1.151	0.774
3	1.000	1.000	−0.992	67.801	1.534	72.959	1.146	0.773
4	1.000	0.992	−1.000	67.780	1.534	72.996	1.145	0.773
5	1.000	0.992	−1.000	67.780	1.534	72.992	1.145	0.773
6	1.000	1.000	−0.985	67.811	1.527	72.880	1.140	0.773
7	1.000	0.981	−1.000	67.766	1.524	72.936	1.138	0.773
8	0.992	1.000	−1.000	67.751	1.534	72.955	1.146	0.772
9	1.000	1.000	−0.973	67.831	1.516	72.752	1.132	0.772
10	1.000	0.965	−1.000	67.746	1.510	72.850	1.127	0.771

for clarity and brevity. Analysis of these results identified the optimal conditions for enzymatic hydrolysis as follows: a bromelain concentration of 3.0%, a temperature of 40 °C, and a hydrolysis time of 60 min. These conditions were found to produce the highest levels of DPPH and ABTS radical activity. These findings are consistent with previous studies, such as the research by Yoon et al. [28], which also found that bromelain is one of the most effective enzymes for enhancing the antioxidant activity of hemp proteins.

The data from the analysis of the radical-scavenging activity of LHPH after enzymatic hydrolysis of HSC under the established optimal conditions are presented in

Table 11. Radical-scavenging activity of LHPH after enzymatic hydrolysis of HSC under the established optimal conditions.

Sample	Radical Scavenging Activity (mg TE/g)
	DPPH	ABTS
HSC	0.323 ± 0.057	2.357 ± 0.181
LHPH	6.227 ± 0.064	26.378 ± 0.411

. The results are expressed as mg TE/g lyophilizate and compared to those of aqueous extracts from the raw material without enzyme treatment (mg TE/g hemp cake). A significant increase in antioxidant activity was observed—11 times higher by the ABTS method and 19 times higher by the DPPH method.

When comparing these results with studies on other plant proteins, such as soy [43] and pea proteins [44], it is observed that hemp proteins demonstrate similar or even higher antioxidant activity under comparable hydrolysis conditions. For example, in [43] it was found that the antioxidant activity of soybean hydrolysates prepared with alcalase or protamex peaked at relatively higher temperatures and hydrolysis times, but remained below the levels recorded in the present study for hemp proteins hydrolysates.

The analysis of the significance of the results shows that the combination of high bromelain concentration and moderate temperature is crucial for achieving optimal outcomes. Interestingly, increasing the hydrolysis time beyond 60 min does not significantly increase antioxidant activity, suggesting that certain hydrolysis parameters play a more significant role than others.

All of this highlights the importance of properly adjusting process parameters in enzymatic hydrolysis, especially in the development of functional foods and supplements that aim to maximize antioxidant activity. Therefore, the present study contributes to a deeper understanding of the interaction between enzymes and plant proteins, offering new opportunities for the utilization of hemp proteins in various industries.

The results of this study have significant potential for application in various industries, including food, cosmetics, and pharmaceuticals. The hydrolysates obtained from hemp proteins, characterized by high antioxidant activity, can be utilized as functional ingredients in a variety of food products aimed at improving health and well-being. For instance, these hydrolysates can be incorporated into the production of functional beverages, energy bars, and dietary supplements focused on antioxidant protection and immune system support.

In the cosmetics industry, hemp protein hydrolysates can be used in the development of anti-aging products and skin protection creams due to their antioxidant properties. These ingredients could play a role in reducing skin damage caused by free radicals and ultraviolet radiation, making them attractive for skincare formulations.

From an economic perspective, the use of hemp proteins as a raw material is particularly appealing due to the availability of hemp cake as a by-product of hemp oil production. This by-product, often considered waste, can be transformed into high-value protein hydrolysates. This reduces waste and enhances the economic viability of the entire production process. Manufacturers can integrate the enzymatic hydrolysis process into their existing production lines, resulting in minimal additional investment and maximizing return on investment.

Furthermore, the global market for functional foods and nutraceuticals continues to grow, creating favorable conditions for the commercialization of new products based on hemp protein hydrolysates. This provides manufacturers not only access to new market segments but also the opportunity to create high-margin products that meet the growing consumer demand for natural and sustainable health solutions.

4. Conclusions

The comprehensive analysis and optimization of the enzymatic hydrolysis process for hemp oilseed cake using bromelain have yielded significant insights into achieving maximum antioxidant activity as measured by DPPH and ABTS assays. The quadratic models developed for DPPH and ABTS, as defined by the Design-Expert software, demonstrated high accuracy with R² values of 0.9132 and 0.9926, respectively. These models were validated through extensive diagnostic plots, including normal probability plots, residuals versus predicted values, and actual versus predicted values, confirming their adequacy and reliability.

Optimization results indicate that the ideal hydrolysis conditions for maximizing both DPPH and ABTS activities are a bromelain concentration of 3.0%, a temperature of 40 °C, and a hydrolysis time of 60 min. This was supported by high Adeq Precision values (19.46 for DPPH and 50.7486 for ABTS), suggesting strong signal-to-noise ratios and robust model performance. The sample of hemp protein hydrolysates obtained under the established optimal parameters exhibited significantly stronger antioxidant activity compared to the raw material—HSC.

These findings underscore the potential of using response surface methodology (RSM) combined with robust statistical tools for optimizing complex biochemical processes.