Application of experimental design as a statistical approach to recover bioactive peptides from different food sources

Abstract

Bioactive peptides (BAPs) derived from samples of animals and plants have been widely recommended and consumed for their beneficial properties to human health and to control several diseases. This work presents the applications of experimental designs (DoE) used to perform factor screening and/or optimization focused on finding the ideal hydrolysis condition to obtain BAPs with specific biological activities. The collection and discussion of articles revealed that Box Behnken Desing and Central Composite Design were the most used. The main parameters evaluated were pH, time, temperature and enzyme/substrate ratio. Among vegetable protein sources, soy was the most used in the generation of BAPs, and among animal proteins, milk and shrimp stood out as the most explored sources. The degree of hydrolysis and antioxidant activity were the most investigated responses in obtaining BAPs. This review brings new information that helps researchers apply these DoE to obtain high-quality BAPs with the desired biological activities.

Introduction

Bioactive peptides (BAPs) are fragments of parental proteins that typically contain two up to 20 amino acid units and play physiological functions that benefit human health (Maqsoudlou et al., 2019). The BAPs have attracted the attention of consumers and researchers because of their several functional activities, such as antioxidant, antimicrobial, anticarcinogenic, hypocholesterolemic, antihypertensive, immunomodulatory, and opioid (Hajfathalian et al., 2018).

Recent research has isolated BAPs from animal origin samples such as milk (Ballatore et al., 2020), meat (Arihara et al., 2021; Ryder et al., 2016), eggs (Yuan et al., 2020), fish (Rivero-Pino et al., 2020), and seafood (Zhang et al., 2020a, 2020b), and from vegetal origin such as plants (Xu et al., 2022), fruits (Sosalagere et al., 2022), vegetables (Ding et al., 2020), and almonds (Wu et al., 2014).

The peptides are inactive in the parental protein. Otherwise, they are activated when released through reactions during food processing such as acidification, acylation, phosphorylation, glycosylation, fermentation, and changes by heat treatments. Although different methods have been proposed to obtain BAPs, microbial fermentation and enzymatic hydrolysis are the most widely studied protocols (Marciniak et al., 2018; Toldrá et al., 2018).

The produced peptides’ functional characteristics primarily guide the enzymatic hydrolysis method. This process is affected by variables such as the type of peptidase, its hydrolytic conditions, specificity, stability, and catalytic efficiency (Tavano, 2013). Additionally, reaction time, enzyme concentration, and substrate nature can interfere in the quality of the generated peptides (Singh et al., 2019).

Therefore, there is no standard protocol in the literature for enzymatic hydrolysis of matrices aiming to produce peptides with specific bioactivities. Furthermore, there is no consensus regarding which response to define the ideal hydrolytic condition.

Recent studies with proteases have some drawbacks. It can be cited that their use is based on mass (g) or volume (mL) instead of normalized enzymatic activity unit (U); different pH and temperature conditions for each protease significantly influence the enzyme catalytic potential and the generation of peptides. The type of response considered to define the ideal peptidase, considering the studies published thus far, generally considers the degree of hydrolysis and the in vitro activity of the hydrolysates rather than in vivo functions as a response (Zhang et al., 2020a, 2020b).

Li-Chan (2015) discusses the challenges faced by the commercialization of BAPs, such as their high production cost, selection of the best protein source, isolation and purification procedures, and the conditions of enzymatic hydrolysis to achieve the best activity and yield. As a strategy, experimental designs are required to optimize production cost parameters and obtain BAPs with better quality attributes.

In this context, Design of Experiments (DoE) have been widely used in the development of analytical methods (Fig. 1) for screening and reaching the ideal hydrolytic condition with the minimum number of experiments, that is, to investigate the combination of factors that provides the desirable answer (Azcarate et al., 2020). Some experimental designs, such as Full Factorial Design (FFD), Fractional Factorial Design (FrFD), Box–Behnken Design (BBD), Central Composite Design (CCD), and Simplex-Centroid Mixture Design (SCD), have been used in multivariate analysis considering different types of responses to obtain BAPs (Aguilar et al., 2020; Maqsoudlou et al., 2019; Marson et al., 2019, 2020; Yuan et al., 2020).

Fig. 1.

Main experimental designs used to obtain BAPs. BAPs bioactive peptides, DoE design of experiments, FFD full factorial design, FrFD fractional factorial design, PBD Plackett–Burman design, CCD central composite design, BBD Box–Behnken design, SCD simplex centroid design, SLD simplex lattice design

So, the present work reviews and summarizes recent applications and proposes future directions using DoE in the production of bioactive peptides. Instead of being a comprehensive review, this work discusses the application of multivariate approaches in developing analytical methods to obtain bioactive peptides from different food matrices to guide future research and accelerate the industrial production of BAPs. The following sections will address some research articles produced from 2010 to 2022.

Obtaining bioactive peptides

Enzymatic hydrolysis consists of a chemical reaction catalyzed by a proteolytic enzyme that occurs in an aqueous medium, breaking the peptide bonds of the parental proteins, cleaving them into fragments of peptides and smaller amino acids. While in microbial fermentation, the production of peptides and amino acids occurs through the cleavage of parental proteins using microorganisms (Sanjukta and Rai, 2016).

The use of protease in food applications has been known since ancient Greece, where enzymes from micro-organisms were used in the preservation and baking of foods and the production of alcohol, cheese, and beer, among others. Nowadays, proteases are versatile in the food, chemical, pharmaceutical, detergents, and bioethanol production industries, accounting for ca. 60% of total global enzyme sales (Sharma et al., 2017). Proteases can be classified according to (i) their source: animal, plant, or microbial, (ii) catalytic action: endo or exopeptidases, and (iii) physicochemical properties: molecular size, charge, or substrate specificity. Moreover, the Enzyme Commission recently released a new classification: serine and serine carboxyl proteases, cysteine proteases, aspartic proteases, metalloproteases I, and metallocarboxy proteases (Sharma et al., 2017).

Digestive and microbial proteases have been used to obtain BAPs. New peptides have been found through enzymatic hydrolysis and microbial fermentation of different food matrices using digestive proteases: bromelain, pancreatin, pepsin, papain, and trypsin (Aguilar et al., 2020; Azcarate et al., 2020; Singh et al., 2019; Tavano, 2013), and microbial ones: flavourzyme, alcalase, neutrase, protamex (Azcarate et al., 2020; Maqsoudlou et al., 2019; Marciniak et al., 2018; Marson et al., 2019, 2020).

The use of enzymes for protein cleavage has several advantages such as high reaction speed, region and stereoselectivity, and the use of moderate temperatures and pHs (Cruz-Casas et al., 2021). These characteristics reduce costs and provide desired peptide sequences due to the high specificity of the enzymes. Despite this, the factors already mentioned such as pH, temperature, hydrolysis time and also the type and concentration of enzyme can directly influence the bioactivity of the generated peptides. Functional properties of these peptides depend directly on the structure and conformation of their parental proteins and it is also important to consider that the specificity of the enzyme and excessive proteolysis can affect functionality and cause unfavorable effects on the peptides generated by altering their bioactivity (Cruz-Casas et al., 2021; Mune 2015). Another critical point is that in this approach it is common to pre-treat the substrate to improve hydrolysis efficiency, considering that the cleavage regions of the enzyme are exposed. For this purpose, heat treatments are an alternative, however, it can denature proteins, which can damage amino acids such as tryptophan, lysine, arginine, serine, threonine, among others, which in turn, can be decomposed, dehydrated or cycled, directly impacting the generated peptide sequence and its functionality.

At the end of the hydrolysis procedures, the inactivation of enzymatic activity is carried out through heat treatment, which limits excessive hydrolysis. Furthermore, it is essential to control the time and degree of hydrolysis in order to obtain reproducible and ideal peptide size distribution so that peptide sequences with desired activities are generated (Yin et al., 2008). Therefore, the use of experimental designs proves to be an assertive alternative to control these parameters in a way that provides insights and significant correlations between the different experimental conditions (pH, hydrolysis time, temperature, enzyme/substrate ratio, type of enzyme), the degree of hydrolysis and bioactivity of the generated peptides.

Design of experiments used to obtain bioactive peptides

A quantitative analysis of the articles published from 2010 to 2022 was performed in six different databases: Google Scholar, PubChem, Science Direct, Scielo, Scopus, and Web of Science. There was no refinement regarding languages or countries. However, it is worth that there was delimitation only for the time interval of the last 12 years. “Design of Experiments” was the first topic researched, and it provided 396,916 works with applications in different areas: Engineering Electrical Electronic, Materials Science Multidisciplinary, Chemistry Multidisciplinary, and Engineering Chemical. Subsequently, “Bioactive Peptides” was filtered during this period. Were found 13,682 works with applications in food science technology, Biochemistry, Molecular Biology, Medicinal Chemistry, and Multidisciplinary Chemistry. Combining these two topics resulted in a total of 148 published articles. Figure 2 correlates the number of publications related to “Bioactive Peptides” and your production with “Design of Experiments” in the 12 years of evaluated papers. Despite being a recent topic, there has been a considerable increase in the number of articles published in recent years.

Fig. 2.

Advanced search in the Web of Science database related to works involving DoE and bioactive peptides from 2010 to 2022. Data obtained from the https://www.webofscience.com/wos/woscc/basic-search

Different DoEs have been reported to generate bioactive peptides, as shown in Tables 1, 2, 3, and 4. Experimental designs evaluate the system under analysis from dependent variables (responses) and independent variables (factors or parameters at different levels). Typically, the investigated parameters depend on the level of knowledge, criteria, objectives outlined by the researchers, and other aspects such as availability of samples, supplies, analytical frequency, and apparatus (Tavares Luiz et al., 2021).

Table 1.

DoE studies for the generation of bioactive peptides using screening designs

Fractional factorial designs 2k−p (FrFD)
Substrate	Dependent variable	Independent variables	Ideal condition	BAPs found	References
Yeast (Brewer)	Degree of hydrolysis Antioxidant activity Physicochemical parameters	pH Substrate concentration E/S ratio Temperature	5.5 100% 10% 60 ºC	Not found	Marson et al. (2019)
Full Factorial Design (FFD)
Bovine collagen	Degree of hydrolysis	pH Temperature Substrate concentration	8 25 °C 7.5 mg mL−1	3 sequences identified: GDKGETGEQGDR, FLPQPPQEKAHDGGR, and FGGDFYR MW: 1264.60 kDa, 1676.97 kDa, and 919.41 kDa	Lima et al. (2015)
Whey Protein Concentrate	Antioxidant activity	E/S ratio Time	0.100 m/m 24 h	Not found	Contreras et al. (2011)
Plackett–Burman design (PBD)
Corn gluten meal	Yield of generated peptides	Temperature Inoculation size Initial pH Moisture Time Glucose Peptone	–	Not found	Jiang et al. (2020)
Goat’s milk casein	Antioxidant activity	Temperature pH Substrate concentration E/S ratio Ratio of compound protease (Alc/Pap) Time	–	Not found	Shu et al. (2018)
Shrimp	Degree of hydrolysis	pH Temperature E/S ratio Time Substrate concentration Denaturation of substrate protein	–	Not found	Cao et al. (2012)

Table 2.

DoE studies for the generation of bioactive peptides using Central Composite Design (CCD)

Central composite design (CCD)
Substrate	Dependent variable	Independent variables	Ideal condition	BAPs found	References
Corn	Degree of hydrolysis Antioxidant yield Antioxidant activities	Ratio E/S Time	5.2% w/w 9.3 h	420 sequences identified 48 new peptides MW: 372.2372–1191.6975 Da	Sharma et al. (2022)
Bovine skin gelatin	Cooking loss	Ingredient concentration in the meat sample Concentration of peptide fraction in the ingredient	3.0 g 100g−1 0.0 g 100g−1	Not found	Nuñez et al. (2021)
Mushroom	Degree of hydrolysis	Enzyme loading Temperature Time	0.15% 50 °C 120 min	Not found	Goswami et al. (2021)
Pea protein concentrate	Antioxidant activity	pH Enzyme Concentration	10 100 U mL−1	Not found	Aguilar et al. (2020)
α-lactalbumin from whey protein	Antidiabetic activity	Temperature Substrate concentration Enzyme Concentration Time	41.5 °C 7% 4539 U g−1 129 min	201 sequences identified: MW: 1035–1798 Da	Jia et al. (2020)
Tilapia fish by-products	Physicochemical properties Antioxidant activity	Time Applied pressure	Different conditions for each dependent variable	Not found	Hemker et al. (2020)
Whey protein	Antioxidant activity	E/S ratio Temperature Time	0.017 41.1 °C 4.31 h	3 sequences identified: ALC (carbamidomethyl)SEK, ELKDLK, and ALPMHIR MW: 707.34, 745.44, 837.48	Ballatore et al. (2020)
Shrimp	Iron-binding capacity	E/S ratio Time	27.4 U g−1 4.8 h	2 sequences identified: DSVNFPVHGL and FKVGQENTPILK	Vo et al. (2020)
Egg white	Antioxidant activity	Time Sample/solution ratio E1/E2 ratio	3.16 h 10% 1.7:1	Not found	Yuan et al. (2020)
Pollen protein and royal jelly	Antioxidant activity Antihypertensive activity	Enzyme Concentration Time	Different conditions for each dependent variable	195 sequences identified MW: 500–3000 Da	Maqsoudlou et al. (2019)
Rice bran protein	Degree of hydrolysis	Temperature Time pH E:S ratio	50 °C 2.5 h 7 0.035 m/m	Not found	Singh et al. (2019)
Raw wheat germ protein	Antioxidant activity	Temperature Time E:S ratio	37 °C 285 min 0.54 g 100 g−1	42 sequence identified MW: 866.47- 2,857.27 Da Greater AA: MDATALHYENQK and SGGSYADELVSTAK	Karami et al. (2019)
Cottonseed protein	Degree of hydrolysis Antihypertensive activity	Temperature pH E:S ratio	38.9 °C 7.5 1.04%	1 sequence identified: FPAIGMK MW: 763.4 Da	Gao et al. (2019)
Cheese whey discarded	Degree of hydrolysis Soluble protein Antioxidant activity Antihypertensive activity Hydrophilic fraction	pH Temperature	Different conditions for each dependent variable	Not found	Martín-del-Campo et al. (2019)
Okara protein concentrate	Degree of hydrolysis	Temperature E/S ratio pH Alcalase/flavourzyme ratio	40 °C 5% 7.1 90:10%	Not found	Pereira et al. (2019)
Proteins from sea snail	Degree of hydrolysis Antioxidant activity	Temperature Time pH	51 °C 4.1 h 7.7	193 sequences identified MW: 699–2560 Da	He et al. (2019)
Shrimp head meat	Degree of hydrolysis Antioxidant activity	Alcalase concentration Flavourzyme Concentration Temperature pH Time	19.43 U g−1 32.09 U g−1 54.94 °C 7.01 2.96 h	Not found	Vy et al. (2018)
Chicken blood corpuscle	Antioxidant activity	E/S ratio Temperature Time	2% 50 ºC 6 h	1 sequence identified: AEDKKLIQ MW: 943.5 Da	Zheng et al. (2018)
Scad residue proteins	Degree of hydrolysis Iron-binding capacity	Temperature Time E/S ratio	46 °C 66 min 3. 60.40 U g−1	Not found	Zhang et al. (2016a, 2016b)
Eggshell membrane by-product	Degree of hydrolysis Antihypertensive activity Antioxidant activity	E/S ratio Time	Different conditions for each dependent variable	Not found	Santana et al. (2016)
Shrimp waste	Degree of hydrolysis	E/S ratio Time pH Temperature	1.64% 3.59 h 9 52.57 ºC	Not found	Zhang et al. (2016a, 2016b)
Egg white protein	Antioxidant activity	Substrate concentration Protease concentration	3% 20 U mL−1	Not found	de Castro and Sato (2015a)
Fish protein	Degree of hydrolysis Iron-binding capacity	pH Temperature Time Enzyme concentration	9.0 50 ºC 120 min 160 mg 100 mL−1	Not found	Yang et al. (2015)
Leucena tree seeds	Yield Antioxidant activity	Temperature Time E/S ratio pH	55 ºC 90 min 2% 9	Not found	Rafi et al. (2015)
Isolated soy protein	Antioxidant activity Foaming activity Emulsifying activity	Temperature pH E/S ratio	Different conditions for each dependent variable	Not found	de Oliveira et al. (2015)
Pumpkin oil cake protein	Degree of hydrolysis	Pepsin E/S α-Chymotrypsin E/S Trypsin E/S Time	0.039 mg mg protein−1 0.02 mg mg protein−1 0.08 mg mg protein−1 89 min	Not found	Vaštag et al. (2013)
Palm kernel cake protein	Degree of hydrolysis	pH Temperature Substrate concentration E/S ratio	Different conditions for each degree of hydrolysis	Not found	Ng et al. (2013)
Soy whey protein	Antioxidant activity	Temperature Salt concentration Surfactant concentration Time E/S ratio	40 ºC 0.05 mol L−1 0.0075% 80 min 164 IU g−1	Not found	Singh and Banerjee (2013)
Rice dregs protein (RD)	Degree of hydrolysis Protein recovery	E/S ratio (w/w) RD/H2O ratio pH Temperature Time	0.89:1000 w/w 0.22 g mL−1 7.6 52.8 ºC 2.4 h	Not found	Li et al. (2012)
Purple sea urchin	Degree of hydrolysis TCA soluble peptide index (TCA-SPI)	Temperature pH E/S ratio Substrate concentration	48.83 ºC 6.92 3143 U g−1 83.5 g L−1	Not found	Zhou et al. (2012)
Bovine whey protein concentrate, α-lactalbumin, and caseinomacropeptide	Degree of hydrolysis Antioxidant activity Total antihypertensive activity for the < 3 kDa fraction	E/S ratio Time	Different conditions for each dependent variable	22 sequences identified Greater ACE inhibitory activity: MAIPPKKNQD and AIPPKKNQD	Tavares et al. (2011)
Whey Protein Concentrate	Antioxidant activity	E/S ratio Time Temperature	0.10 w/w 8 h 80 ºC	21 sequences identified MW: 287.3–1097.3 Da	Contreras et al. (2011)
Porcine hemoglobin	Degree of hydrolysis Antioxidant activity	Temperature pH E/S ratio	40.4 ºC 1.6 1.6%	Not found	Sun et al. (2011)

Table 3.

DoE studies for the generation of bioactive peptides using Box–Behnken Design (BBD)

Box–Behnken design (BBD)
Substrate	Dependent variable	Independent variables	Ideal condition	BAPs found	References
Whey protein	Antifungal ability Peptide content	Nitrogen sources Inoculum size Lactose	28.44 g L−1 3.72% v/v 26.69 g L−1	156 sequences identified MW: 683.36–3225.53 Da	XIE et al. (2022)
Millet bran	Antioxidant activity	pH Temperature Concentration of Papain Time	7.8 51.6 ºC 8.17 mg g−1 5.9 h	3 sequences identified: CFMTY, CTGTPYC and RGLLLPSMSNAP MW: 663.86, 743.93, and 1255.64 Da	Xu et al. (2022)
Casein	Degree of hydrolysis	E/S ratio pH Temperature	5.45% 7.13 51.9 ºC	13 sequences identified Greater AA: LHSMK	Liu et al. (2021)
Rice husk	Protein concentration	pH Temperature Flow rate	10 60 ºC 2 mL min−1	Not found	Ilhan-Ayisigi et al. (2021)
Fish protein	Antihypertensive activity	Temperature pH Enzyme addition amount	55 ºC 9 5%	54 sequences identified Greater ACE inhibitory activity: LPGPGP and EYFR MW: 160–8770 Da	Ma et al. (2021)
Pea protein	Antioxidant activity	Temperature Concentration E/S ratio	55 ºC 3.15% 9.2%	40 sequences identified Antioxidant activity: YSSPIHIW, ADLYNPR, and HYDSEAILF	Ding et al. (2020)
Corn gluten meal	Yield of generated peptides	Inoculation size Moisture Glucose	5.8 × 109 spores g−1 46% 10.7 mg g−1	Not found	Jiang et al. (2020)
Egg white protein	Antioxidant activity	Time E/S ratio Enzyme dosage	2.51 h 4.13% 4500 U g−1	Not found	Chi et al. (2020)
Whey protein	Antioxidant activity Antihypertensive activity	Temperature E/S ratio pH Time	58.2 ºC 2.5% 7.5 6.03 h	Not found	Hussein et al. (2020)
Shrimp	Antioxidant activity	Temperature E/S ratio Concentration	59.55 ºC 6.09% 1.76%	2 sequences identified: MTTNI and MTTNL	Wu et al. (2020)
Soybean meal	Antihypertensive activity Peptide content Biomass content	Power density Temperature Time	0.8 W mL−1 36.70 ºC 1.0 h	Not found	Ruan et al. (2020)
Shrimp	Degree of hydrolysis	pH E/S ratio Temperature	8 1.53% 53.5 ºC	Not found	Dhanabalan et al. (2020)
Freshwater mussel meat	Degree of hydrolysis	Ratio of liquid to material Power Processing time Enzymolysis time	1:10.36 360.52 W 6.91 h 4 h	Not found	Zhou et al. (2018)
Egg white protein	Antioxidant activity	Impeller speed E/S ratio Permeate flow rate	300 rpm 22.5 g 2.05 cm3 min−1	Not found	Jakovetić Tanasković et al. (2018)
Mackerel protein	Antioxidant activity	Enzyme concentration Extraction time pH Water/material ratio Extraction temperature	1000 U g−1 4 h 7 5:1 v/w 40 ºC	2 sequences identified: LDIQKEV and TAAIVNTA MW: 843.5 Da and 759.4 Da	Wang et al. (2018)
Wheat gluten	Degree of hydrolysis Antioxidant activity	Gluten concentration Temperature pH E/S ratio	5 w/w 50 ºC 8 0.5 AU g−1	Not found	Elmalimadi et al. (2017)
Walnut protein meal	Degree of hydrolysis Reducing power	Time Inoculum concentration Water content	82.01 h 10.40% 1.50 mL g−1	Not found	Wu et al. (2014)
Pumpkin seeds	Antioxidant activity	Enzyme amount Substrate concentration Time	6000 U g−1 0.5 g mL−1 5 h	Not found	Fan et al. (2014)
Silkworm Protein	Antioxidant activity	E/S ratio pH Temperature	7.38% 7.97 60 ºC	Not found	Yang et al. (2013)
Anchovy protein	Antioxidant activity	E/S ratio Temperature Reaction time	3.27% 55.4 ºC 2.7 h	Not found	He et al. (2014)

Table 4.

DoE studies for the generation of bioactive peptides using Simplex Centroid Design (SCD) and Simplex Lattice Design (SLD)

Substrate	Dependent variable	Independent variables	Ideal condition	BAPs found	References
Simplex Centroid design (SCD)
Lentil	Antioxidant activity Antidiabetic Activity Reducing power	Neutrase Termamyl Optimase	Binary mixture of Neutrase and Termamyl Binary mixture of Optimase and Termamyl Pure Neutrase and Optimase	Not found	Casarin et al. (2021)
Spent brewer’s yeast	Degree of hydrolysis Antioxidant activity Physicochemical parameters	Alcalase Brauzyn Protamex	Binary mixture of brauzyn and protamex Ternary mixture	Not found	Marson et al. (2020)
Chicken viscera protein concentrate	Antioxidant activity Total antioxidant activity Antihypertensive activity	Flavourzyme Alcalase Neutrase	Binary mixture of flavourzyme and alcalase	Not found	Aguilar et al. (2019a)
Black bean protein concentrate	Antioxidant activity Total antioxidant activity Reducing power	Flavourzyme Alcalase Neutrase	Binary mixture of flavourzyme and alcalase	Not found	Aguilar et al. (2019b)
White bean protein concentrate	Antioxidant activity Total antioxidant activity Reducing power	Flavourzyme Alcalase Neutrase	Binary mixture of flavourzyme and alcalase	Not found	de Castro et al. (2017)
Soy protein isolate (SPI), bovine whey protein (BWP), and egg white protein (EWP)	Degree of hydrolysis Relative lipid accumulation (RLA%) RLA suppression (%)	SPI BWP EWP	Different conditions for each dependent variable	Not found	de Castro et al. (2016)
Soy protein isolate	Antioxidant activity Inhibition of linoleic acid autoxidation Reducing power assay Total antioxidant activity TCA-SPI	Flavourzyme Alcalase YeastMax A	Binary mixture of flavourzyme and alcalase Ternary mixture Pure flavourzyme Pure YeastMax A	Not found	de Castro and Sato (2015b)
Soy protein isolate (SPI), bovine whey protein (BWP), and egg white protein (EWP)	Antioxidant activity Inhibition of linoleic acid autoxidation (%) TCA-SPI Physicochemical parameters	SPI BWP EWP	Different conditions for each dependent variable	Not found	Castro and Sato (2014)
Simplex Lattice Design (SLD)
Anchovy protein	Antioxidant activity Degree of hydrolysis	Protamex Flavourzyme Alcalase	1.1:1.0:0.9	Not found	He et al. (2014)

DoEs have two main functions: factor screening and optimization of the investigated system. Screening is generally the initial research stage and aims to examine potentially significant parameters directly influencing a studied system with a minimum number of experiments and to determine the ranges in which these should be investigated (Myers et al., 2009). Designs that result in linear and interaction models, such as two-level full factorials (FFD), two-level fractional factorials (FrFD), and Plackett–Burman Designs, are the most commonly used for this purpose (Table 1). Comparatively, screening designs are less used than optimization methodologies, mainly because factors such as pH, temperature, E/S ratio, and hydrolysis time are the variables known that most influence enzymatic hydrolysis for the production of bioactive peptides.

On the other hand, optimization seeks to identify the ideal operating conditions for a given purpose, increasing the yield of a reaction or maximizing a desirable response, among other purposes. Optimization can be performed by evaluating the significant factors obtained in a previous screening study or by investigating the most influential parameters in a given system in the literature (Jiang et al., 2020; Montgomery, 2012). In this case, the most used are Response Surface Methodology (RSM) methods such as three-level complete factorial designs, three-level fractional factorial designs, Box–Behnken (BBD), Central Composite (CCD), and mixture designs.

Jiang et al. (2020) first performed a screening using Plackett–Burman Design to investigate the most significant factors affecting the yield of peptide formation of corn gluten meal (CGMP). After that, a Box–Behnken design was applied to optimize the CGMP yield increase based on the most significant independent variables provided by the Plackett–Burman Design (PBD).

Therefore, the following sections will discuss some papers based on the main objectives of applying experimental designs to obtain bioactive peptides: screening and optimization.

Screening design to obtain bioactive peptides

2^k full factorial design (FFD)

Together with the fractional factorials, these designs are usually applied in the initial stage of the analytical experiments. These experiments provide a broad idea concerning the behaviour of the studied system, that is, how the responses vary according to the change in the levels chosen for each investigated factor (Mousavi et al., 2018). This design allows the evaluation of all the variables of interest and their interactions in the desired response. The number of experiments is given by N = 2^k (Narenderan et al., 2019). The number of levels is 2, and 2 to 5 factors are chosen for this design. A more significant number makes its execution difficult due to the many experiments required and the loss of efficiency (Mousavi et al., 2018). The selected factors can be quantitative or qualitative, and for the levels evaluated, codes such as + (high), −(low) are used (Narenderan et al., 2019).

The main effects and interactions (e.g., secondary, tertiary, quaternary, depending on the number of factors) are calculated and evaluated to determine whether they have statistical significance in the generated mathematical model (Teófilo and Ferreira, 2006). Significance analysis can be performed using a Pareto chart, which represents the estimate of the effect of each factor and its statistical significance. Typically, Pareto charts are shown by a bar graph consisting of standardized effects, dividing each coefficient by its standard deviation. Also, a straight line draws the confidence limit at a certain percentage, usually 95%. The length of each bar is proportional to the magnitude of the factor coefficient, and if it is statistically significant, the bar exceeds the line (Marrubini et al., 2020).

The effects of a 2^k FFD can be converted into a regression model that can predict the response at any point in the experimental space domain. The generated regression model is a first-order and may contain mixed second-order terms, and is given by:

$$\text{y}={\mathrm{\beta }}_0{\sum }_{\text{i}=1}^{\text{k}}{\mathrm{\beta }}_{\text{i}}{\text{x}}_{\text{i}}+{\sum }_{\text{i}=1\le \text{i}\le \text{j}}^{\text{k}}{\mathrm{\beta }}_{\text{ij}}{\text{x}}_{\text{i}}{\text{x}}_{\text{j}}+\epsilon$$ 1

where β₀ represents a constant, β_i represents the coefficients of the linear parameters, x_i represents the variables, β_ij represents the coefficients of the interaction terms, and ε represents the residual associated with the experiments (Teófilo and Ferreira, 2006).

This topic will address two papers that used FFD to screen factors to obtain bioactive peptides (Table 1).

In an experiment developed by Contreras et al. (2011), a typical 2² with replicated center point was chosen to investigate the effect of enzyme/substrate (E/S) ratio and time on the antioxidant activity (AA) of the Corolase PP® and thermolysin hydrolizates from whey protein concentrate enriched in β-lactoglobulin. The repetitions in the central point made it possible to determine the size of the experimental variation, known as the replicate error. AA was determined by Oxygen Radical Absorbance Capacity employing Fluorescein (ORAC-FL) as a fluorescence probe. The results showed that the estimated model for thermolysin hydrolysis was adequate to describe the antioxidant activity under these conditions, and the hydrolysis time was more significant than E/S ratio.

Lima et al. (2015) obtained bioactive peptides from bovine collagen hydrolysates with antimicrobial and radical scavenging properties produced by the action of the Penicillium aurantiogriseum URM 4622 collagenase. A 2³ FFD with replicated center point was performed to evaluate the effect of the variables pH, temperature, and substrate (collagen) concentration, using the degree of hydrolysis (DH) as the dependent variable. The results showed pH exerted the highest significant positive effect followed by collagen concentration and temperature exerted the lowest and negative effect. Furthermore, the significant synergistic interaction between pH and collagen concentration improved DH. Additionally, the generated peptides were characterized by MALDI-TOF MS, and those with mass < 2 kDa exhibited antioxidant and antibacterial activity.

Fractional 2^k−p factorial designs (FrFD)

The 2^k−p FrFD designs are performed to screen the most critical factors and levels to be studied before conducting a complete analysis. The number of levels is 2, k is the number of evaluated factors, and p is the fraction size, which can vary according to the chosen resolution (Vera Candioti et al., 2014).

These designs are advantageous mainly when working with a reduced sample, reagents, and time, or even with a large number of variables, as the required tests are reduced by half or by an even smaller fraction when p = 1 or higher, respectively. It is almost always possible to reach the same conclusions one would obtain using a FFD because the higher-order interactions tend to become negligible and can therefore be disregarded (Teófilo and Ferreira, 2006).This means that higher-order interactions may be assigned to other factors, reducing the number of trials. In these cases, the effects are said to be confounded which it can no longer be computed completely free of one another (Montgomery, 2012).

The subset of trials from the FFD is determined by generators that lead to the defining relation of a design. The defining relation is useful in that it directly gives the confounding pattern and additionally the resolution of a FrFD (Montgomery, 2012).

The research revealed only one paper that reports the use of this DoE to perform factor screening (Table 1). In the study developed by Marson et al. (2019), a 2^4–1 FrFD was employed to investigate the effect of pH, substrate concentration ([S]), (E/S) ratio, and temperature on some physicochemical characteristics and antioxidant properties of peptides generated from the hydrolysis of brewer’s yeast proteins (Saccharomyces pastorianus) using the Brauzyn® enzyme and sequential hydrolysis. The experimental design indicated a positive influence of higher (E/S) ratio and smaller pH on the solids and protein yield. High temperature values resulted in the reduction of the antioxidant properties of the hydrolysate. The protein hydrolysate obtained by sequential hydrolysis using Brauzyn® and Alcalase™ resulted in the material with the highest antioxidant properties and total solids content.

Plackett–Burman design (PBD)

Plackett–Burman designs are very compact and efficient for screening when only the main effects are of interest, once the main effects are, in general, heavily confounded by two-factor interactions. A PBD in twelve trials may, for example, be used for an investigation containing up to eleven factors. PBD have number of experimental trials that are multiples of four, rather than powers of two as is the case for FrFD, and the number of factors that the screening can examine is one less than the number of experimental trials (Eriksson et al., 2008; Jacyna et al., 2019; Myers et al., 2009).

All PBD are at resolution III. They are sometimes referred to as saturated main effect designs because all degrees of freedom which are utilized to examine the main effects. Moreover, PBD do not have a defining relation, since the interactions that may be involved in the study are not equal to main effects (Eriksson et al., 2008).

Shu et al. (2018) applied a PBD to investigate of bioactive peptides generated through the hydrolysis of goat milk casein using the proteases (Table 1). First, it was investigated six variables using One-factor-at-a-time (OFAT): temperature, pH, substrate concentration, E/S ratio, the ratio between proteases (alcalase/papain), and time. After the univariate study, a PBD matrix with eight trials was created based on the results of the single-factor experiments and each factor was fixed at two levels; the higher level was approximately 1.25 times the lower level.

Each activity was evaluated separately. The most significant factors were antioxidant activity (AA) using the DPPH method, temperature, E/S ratio, and ratio between proteases. For AA using metal-chelating activity, the factors time, temperature, and E/S ratio were the most significant, indicating that these three factors had the greatest influence on this antioxidant activity. For AA by superoxide radical scavenging activity, the time, the ratio between the proteases, and the substrate concentration were the most significant variables. Peptides generated in hydrolysis were not identified.

Another work, the obtained bioactive peptides from samples of Acetes chinensis produced by the action of the enzyme pepsin (Table 1). A PBD with eight assays was performed to evaluate the effect of pH, hydrolysis temperature, E/S ratio, hydrolysis time, substrate concentration ([S]), and substrate protein denaturation, using the degree of hydrolysis (DH) as the dependent variable. The results demonstrate that the E/S ratio, protein denaturation, and hydrolysis time significantly affected the evaluated response. The analyzed parameters follow the order of significance: E/S ratio > protein denaturation > hydrolysis temperature > pH > hydrolysis time > substrate concentration. Substrate concentration was a non-significant variable and was disregarded. The generated peptides were not identified. After the screening study, it was used a CCD to optimize the investigated system, considering the most significant effects: I/S ratio, hydrolysis temperature, and pH. The least significant factors such as hydrolysis time and substrate concentration were fixed at 3 h and 200 g kg^–1, respectively. The protein denaturation, although significant, was also fixed as it was not quantifiable (Cao et al., 2012).

Optimization design focused on obtaining bioactive peptides

Central composite design (CCD)

The CCD is an experimental design divided into three parts: a factorial part, an axial part (star), and a central part. The number of designs is given by: 2^k + 2k + n_c, where 2^k refers to the designs of the factorial part, 2^k the axial part, and n_c to the number of central point. Axial and central points are used to estimate the effect of curvature (Stalikas et al., 2009).

CCD has several advantages over other designs. Its number of trials is not as high as a 3^k factorial. The axial points, called α, can have their distances adjusted according to the particular experimental conditions of each work. In the factorial part, a fractional factorial can be used. Each piece of the design can be done separately, blocking or not the other experiments if necessary. The sequential experimentation method with ascending climb can be performed. The number of levels used can be 3 or 5 without increasing the number of experiments (Myers et al., 2009). As for the disadvantages, depending on its α value, they can contain extreme, very high, or very low levels, which may not be viable due to experimental restrictions. Furthermore, CCD requires more experiments than Box–Benhken Design, which reduces its efficiency for some applications (Okolie et al., 2021).

Its regression model has linear, mixed second-order, and quadratic terms and is given by:

$$\text{y}={\mathrm{\beta }}_0{\sum }_{\text{i}=1}^{\text{k}}{\mathrm{\beta }}_{\text{i}}{\text{x}}_{\text{i}}+{\sum }_{i=1}^k{\mathrm{\beta }}_{\text{ii}}{\text{x}}_{\text{i}}^2+{\sum }_{\text{i}=1\le \text{i}\le \text{j}}^{\text{k}}{\mathrm{\beta }}_{\text{ij}}{\text{x}}_{\text{i}}{\text{x}}_{\text{j}}+\epsilon$$ 2

where β_ii represents the coefficient of the quadratic term. In this research, 33 works used this design to obtain bioactive peptides making this the most used DoE. This fact demonstrates the preference of this design over the others, due to its advantages already mentioned above.

Among the papers that use this design, 10 of them evaluated 2 factors simultaneously, 11 evaluated 3 factors, 9 evaluated 4 factors, and 3 evaluated 5 factors simultaneously. A preference for investigating 2 and 3 variables is perceived, possibly because the number of tests required is not so high. The smaller number of studies that use 5 variables can be justified by the need for a larger number of tests, besides, sometimes not all factors are significant.

The factors explored are those most reported in the literature, as these parameters directly influence the enzymatic hydrolysis by different mechanisms, generating peptides with specific structures, sizes, and biological activities (Halim and Sarbon, 2017; Sharma et al., 2022). The most evaluated factors were time (23 works), temperature (22), E/S ratio (21), and pH (15). In addition to these, some studies have chosen to investigate substrate concentration (4), enzyme concentration (7), and the ratio between proteases (2). Many dependent variables or responses were evaluated in the following order: antioxidant activity (19) and degree of hydrolysis (18), followed by antihypertensive activity (5), iron-binding capacity (IBC) assay (3), and antidiabetic activity (1).

The protein sources studied were the most diverse: peas (Aguilar et al., 2020), cotton seeds (Gao et al., 2019), corn (Sharma et al., 2022), soybeans (de Oliveira et al., 2015; Singh and Banerjee, 2013), rice (Li et al., 2012; Singh et al., 2019), fish (Hemker et al., 2020; Yang et al., 2015; Zhang et al., 2016a, 2016b), milk (Ballatore et al., 2020; Contreras et al., 2011; Jia et al., 2020; Tavares et al., 2011), bee pollen and royal jelly (Maqsoudlou et al., 2019), raw wheat germ (Karami et al., 2019), cheese (Martín-del-Campo et al., 2019), okara (Pereira et al., 2019), shrimp (Vy et al., 2018; Vo et al., 2020; Zhang et al., 2016a, 2016b), sea urchin (Zhou et al., 2012), egg (Santana et al., 2016), egg white (de Castro and Sato, 2015a; Yuan et al., 2020), chicken blood corpuscles (Zheng et al., 2018), pumpkin pie (Vaštag et al., 2013), palm oil (Ng et al., 2013), among other samples (Table 2).

Among the papers that identified the bioactive peptides generated, 11 used the CCD to investigate the factors that most influence bioactive peptide generation, representing ca. 58% of the total. Five of them were selected for further discussion. This choice covered a greater diversity of samples, factors, and chemical responses evaluated.

The most explored sample for optimizing factors to obtain BAPs using CCD as an experimental design was protein derived from bovine whey protein concentrate (WPC) (Table 2). Despite using the same experimental design, some initiatives were different, such as: (i) pre-screening the substrate by heating to cause slight denaturation and a conformational change of the globular proteins in the serum (Ballatore et al., 2020) (ii) initially carrying out a full factorial (FF) design to explore the most significant factors (Contreras et al., 2011) (iii) carry out a one-factor experiments to define the central point to be explored in optimization design (Jia et al., 2020). In most studies, enzymes of animal origin were used, such as trypsin, corolase, thermolysin, and only in one of them was an aqueous extract of C. cardunculus used to carry out enzymatic hydrolysis (Tavares et al., 2011). Factors such as substrate concentration (S), hydrolysis time (t), temperature (T), enzyme concentration (E), and E/S ratio were investigated. For the antioxidant activity, the effects of the variables temperature (T), hydrolysis time (t), and E/S ratio significantly influenced the response (Contreras et al., 2011). The type of enzyme is also an important factor to be considered, when producing antioxidant peptides from WPC, Contreras et al. (2011) chose thermolysin instead of corolase as it provided the best results in univariate experiments. The optimization design indicated that among the factors evaluated, the E/S ratios and T had significantly higher effects on the response to the scavenging activity of ABTS⋅+ radical and the absorption of oxygen radicals (ORAC-FL) by the generated peptides, indicating high antioxidant activity (Contreras et al., 2011; Ballatore et al., 2020). The independent variables T and E/S ratio significantly influenced the dependent variables antioxidant activity and ACE inhibitory activity of peptides generated through enzymatic hydrolysis such as Cynara cardunculus. The E/S ratio was the one that most influenced the antioxidant activity and the T was the one that most significantly influenced the ACE inhibitory activity. In the generation of antidiabetic peptides, the magnitude of the effects of the independent variables the following order: substrate concentration (S) > hydrolysis time (t) > temperature (T) > enzyme concentration (E) (Jia et al., 2020). A CCD with three factors, four factors, ten independent experiments, and central composite circumscribed (CCC) were used. Despite the common objective of producing bioactive peptides from the same or similar food matrix, the definition of the experimental design can be influenced mainly by the desired activity, followed by the type of enzyme and the factors that influence the use of this enzyme for enzymatic proteolysis, given that define the number of factors that can be determined by experimental screening through literature consultations, single-factor experiments, and even appropriate screening designs.

Another group of samples widely explored in the production of bioactive peptides using CCD as an experimental design was made up of fish and shrimp products and by-products. To produce antioxidant peptides from shrimp head meat (Litopenaeus vannamei) alcalase and flavourzyme were used for enzymatic hydrolysis in a sequential manner and the concentration of the enzymes was previously optimized using the orthogonal method. The CCD was used to explain the influence of pH, time, and temperature factors, all of which significantly influenced the DH responses and DPPH radical scavenging activity. A pertinent observation from this study is that the combination of exo- and endopeptidases positively influenced the hydrolysis efficiency (Vy et al., 2018).

Hemker et al. (2020) also utilized BBD to study the effects of pressure-assisted enzymatic hydrolysis on the production of peptides with antioxidant activity from fish by-product samples (head, tail, and fins). The evaluated factors were time and applied pressure, and the dependent variables were antioxidant activity, reducing power, and peroxide value. The latter variable is not commonly assessed in conventional enzymatic hydrolysis, but it is a parameter to be considered in pressure-assisted enzymatic hydrolysis. The results indicated that peroxide value was significantly influenced by time and applied pressure, and antioxidant activity was also affected by both factors, where moderate pressures and an extended time provided the highest antioxidant activity values. The reduction in power is a relevant response as it indicates the hydrogen-donating capacity of the hydrolysates; therefore, this dependent variable is directly correlated with AA, and time and pressure significantly influenced the hydrolysate’s ability to interact and donate electrons to the ferric ion.

Iron-binding peptides were generated from shrimp (Acetes japonicus) and fish (Trachurus japonicus and Decapterus maruadsi) by enzymatic hydrolysis (Table 2) using respectively the following enzymes: Alcalase, Neutrase, Protamex, Corolase, Flavourzyme and Trypsin, Alcalse, Protamex, Flavourzyme (Vo et al., 2020; Yang et al. 2015; Zhang et al. 2016a, 2016b). One-factor experiments showed that flavourzyme provided the shrimp proteolysate with the highest iron-binding capacity (IBC) value (Acetes japonicus) while alcalase, flavourzyme and trypsin provided fish waste hydrolysates with good IBC values (Trachurus japonicus) and only alcalase provided the Decapterus maruadsi peptides with higher IBC values. Despite this, for both cases, alcalase was chosen for two different reasons: to present the best hydrolysis efficiency estimated by DH and the highest IBC value (Trachurus japonicus) and because the IBC of the hydrolyzate with alcalase hydrolysis was significantly higher than the other three enzymes (Decapterus maruadsi). Vo et al. (2020) also used a single-factor experiment to evaluate the four factors pH, temperature, time and E/S ratio, and chose to optimize just two factors through design CCD (time and E/S ratio) and evaluated the significance of the factors only in relation to the IBC value, while Zhang et al. (2016a, 2016b) carried out preliminary studies and chose to evaluate the significance of the factors temperature, time, and E/S ratio. On the contrary, Yang et al. (2015) evaluated the four factors mentioned above using a CCD and degree of hydrolysis and IBC as responses (dependent variables). The results showed that time and E/S ratio significantly influenced the IBC value of shrimp peptides (Vo et al., 2020) while pH, temperature and their interactions significantly influenced an increase in the IBC value of fish waste peptides, which was achieved with a decrease in pH and at average temperature values (Yang et al., 2015). Contrary to the aforementioned observations, Zhang et al. (2016a, 2016b) pointed out that the factors temperature, time and E/S ratio and the interactive items did not significantly affect the IBC value, that is, the influence of various factors on the IBC was not a simple linear relationship. Despite this, the model was able to predict the optimal hydrolysis conditions with good accuracy.

It was used the CCD to optimize the conditions for generating bioactive peptides with specific desired activities in all the works mentioned above. It was possible to evaluate two to four factors simultaneously. Thus, the versatility and effectiveness of this design are evident when generating bioactive peptides. It provided diverse optimal conditions using different samples, conditions, factors, number of parameters, and evaluated responses. In all the works discussed here, the model generated by the CCD was significant and showed no lack of adjustment. There is a preference for optimizing factors such as time and temperature of hydrolysis and the ratio of the concentration of enzyme and substrate, as these variables are the most significant in the enzymatic hydrolysis process for the supply of BAPs.

Box–Behnken design (BBD)

Box–Behnken Design is a second-order analytical optimization statistical design developed in the 1960s by Box and Behnken. It assesses the nonlinear interaction between indices and factors to optimize operating conditions for responses affected by multiple variables (Montgomery, 2012).

The BBD is a rotatable design when its number of factors (k) equals four or seven; for the other values of k, it is almost rotatable. The number of experiments (N) performed by this design is given by, N = 2k(k−1) + C₀ where k is the number of factors and C₀ is the number of central points (Zhang et al., 2020a, 2020b). This design does not have points at the vertices of the cubic region created by each variable’s upper and lower limits, implying a reduction in the number of experiments needed. That can be advantageous when the points on the cube’s vertices represent combinations at a factor level that have physical or economic limitations and avoid experiments under extreme conditions (Jacyna et al., 2019; Zhang et al., 2020a, 2020b).

BBD is an advantageous method compared to factorial design, as it allows using three levels for each factor, minimizing the number of tests and samples. In addition, it makes it possible to perform the lack of fit test in a regression model. This design comprises three incomplete factorial levels, which is more efficient than the 3^k complete factorial design. The latter requires many more trials, which can be economically unfeasible in many cases (Aslan and Cebeci, 2007; Ferreira et al., 2007b). However, this design also has some disadvantages, such as: being impossible to perform tests in extreme conditions when necessary and not being applicable in a two-variable matrix since the k factors must be ≥ 3, which is possible in the CCD, for example. Furthermore, the BBD has limitations regarding a rigorous analysis, as the value of α will be low, and its experimental region becomes restricted (Ferreira et al., 2007b). Its second-order polynomial regression model is given by:

$$\text{y}={\beta }_0+\sum _{i=1}^k{\beta }_i{X}_i+\sum _{i=1}^k{\beta }_{\mathit{ii}}{X}_i^2+\sum _{i=1}^{k-1}\sum _{j=2}^k{\beta }_{\mathit{ij}}{X}_i{X}_j+\epsilon$$ 3

where X_i and X_j are the independent variables β₀, β_i, β_ii, β_ij e ε are the regression coefficients for the intercept, the linear term, the quadratic term, the interaction term, and the residual associated with the experiments, respectively (Myers et al., 2009).

According to the literature, BBD is the second most used DoE to obtain peptides. This research revealed 20 works that use this design, which represents ca. 29% of the evaluated works. One of these works assessed five factors simultaneously, five assessed four factors, and 14 assessed three factors. The samples used were varied, highlighting: fish (He et al., 2014; Ma et al., 2021), egg white (Chi et al., 2020; Jakovetić Tanasković et al., 2018), shrimp (Dhanabalan et al., 2020; Wu et al., 2020), animal protein-silk (Yang et al., 2013), pumpkin seeds (Fan et al., 2014), rice husks (Ilhan-Ayisigi et al., 2021), walnuts (Wu et al., 2014), wheat gluten (Elmalimadi et al., 2017), mackerel protein (Wang et al., 2018), freshwater mussel meat (Zhou et al., 2018), concentrate whey protein (Hussein et al., 2020; XIE et al., 2022), soy meal (Ruan et al., 2020), millet bran (Xu et al., 2022), casein (Liu et al., 2021) and pea protein (Ding et al., 2020) (Table 3). The most investigated chemical response was the antioxidant activity. Only one study reported the lack of adjustment (Elmalimadi et al., 2017), indicating that the model generated and tested in this case was inadequate. Alcalase was the most used protease to obtain bioactive peptides.

Samples of marine origin such as fish and shrimp were the most explored for generating BAPs using BBD experimental design (Table 3). Despite their similar origins, researchers had different initial approaches such as: (i) screening the most suitable protease to hydrolyze Channa striatus muscle and anchovy minced fish (Engraulis japonicus) (He et al., 2014; Ma et al., 2021); (ii) One-factor experimental design to define the type of enzyme and levels of factors to be investigated in subsequent optimization design (BBD) (He et al., 2014; Ma et al., 2021; Wu et al., 2020). Dhanabalan et al. (2020) used Box–Behnken design as a single step to optimize the factors that influenced the enzymatic hydrolysis of shrimp proteins (Acetes indicus). One-factor experiments to choose the appropriate protease were carried out at different temperatures and pHs (Ma et al., 2021; Wu et al., 2020) while He et al. (2014) combined an endogenous enzyme with six commercial proteases (Protamex, Flavourzyme, Alcalase, Neutrase, Bromelain and Papain) at fixed temperature and pH values for the different proteases, which may imply a questionable result when considering that proteolytic enzymes individually have ideal pHs and temperatures for their catalytic activity. The results of one-factor experiments showed that temperature, pH and enzyme concentration added significantly influenced the inhibition of angiotensin-converting enzyme (ACE) by the generated BAPs, and for this reason they were chosen for further optimization using BBD (Ma et al., 2021). The results obtained by He et al. (2014) showed that the hydrolysates resulting from combinations with the proteases protamex, flavourzyme and alcalase exhibited the greatest capacity to eliminate the DPPH radical and, therefore, greater antioxidant activity (He et al., 2014). From this point onwards, simplex lattice design was used to study the influence of adding different compositions of proteases on the DPPH and DH radical scavenging activity of anchovy hydrolysates (Engraulis japonicus). The most important linear contribution was through the addition of protamex, followed by the addition of flavourzyme and alcalase and the binary combination of flavourzyme and alcalase resulted in the best DPPH radical scavenging activity. The BBD combined with RSM indicated that the independent variables pH, temperature and E/S ratio had a significant influence. The BBD was used to optimize the hydrolysis conditions by varying three factors and the results showed that the ones that contributed most to the antioxidant activity were the hydrolysis time (t), temperature, and E/S ratio. BBD was also used to produce bioactive peptides from fish and shrimp and for both cases single-factor screening indicated that alcalase provided the most antioxidant peptides with the greatest capacity to inhibit ACE. The optimization results using BBD indicated that the factors pH, temperature and E/S ratio significantly influenced the production of ACE inhibitor peptides, while temperature, E/S ratio and substrate concentration were the factors that most influenced the production. of shrimp antioxidant peptides (Ma et al., 2021; Wu et al., 2020). BBD combined with RSM was used to evaluate the effects of pH, temperature and E/S ratio on the hydrolysis efficiency of shrimp peptides (Acetes indicus) and the results indicated that the temperature and E/S ratio had a significant effect on the degree of hydrolysis and the physicochemical and functional properties of the hydrolysates generated (Dhanabalan et al., 2020).

Samples of dairy products such as whey protein, casein, and bovine whey were also explored by BBD to produce peptides with different activities (antifungal, antioxidant, and ACE inhibitory) (Hussein et al., 2020; Liu et al., 2021; XIE et al., 2022). Antifungal peptides have been produced from whey protein. Factors influencing antifungal activity were pre-screened by one-factor experiments. The independent variables chosen to optimize the fermentation medium by BBD were: nitrogen source (g/L), inoculum size (%) and lactose (g/L). The results showed that the three factors significantly influenced the peptide yield and maximum antifungal activity (XIE et al., 2022). Antioxidant peptides and ACE inhibitors were produced by enzymatic hydrolysis from casein and bovine whey, where the influence of four factors was investigated: pH, E/S ratio, time and temperature (Hussein et al., 2020; Liu et al., 2021). One of the studies chose to perform a one-factor screening (Liu et al., 2021) and the other (Hussein et al., 2020) chose to optimize the conditions by employing a BBD without screening the factors experimentally. One study chose to optimize the hydrolysis conditions by evaluating only the degree of hydrolysis as a response and using trypsin as a proteolytic enzyme (Liu et al., 2021) while the other estimated the significant factors for four dependent variables (DH, inhibition of ACE, DPPH⋅ radical scavenging and ferrous ion chelating) and used alcalase for enzymatic hydrolysis (Hussein et al., 2020). The one-factor experiments combined with the response surfaces generated by the mathematical model indicated that among the factors mentioned above, E/S ratio, pH and temperature were those that most influenced the degree of hydrolysis of the bioactive milk casein peptides that were subsequently purified and additionally, the measurement of antioxidant activity was carried out (Liu et al., 2021). The optimization results obtained by Hussein et al. (2020) showed that the dependent variable degree of hydrolysis was greatly influenced mainly by temperature and also by pH, time and E/S ratio. The ACE inhibitory activity was influenced by the four factors and their combinations and a positive correlation was observed between DH and ACE inhibitory activity, that is, the higher the DH value, the greater the activity achieved. While the antioxidant activity of the generated peptides was estimated by the responses to the DPPH⋅ radical scavenging activity and ferrous ion chelating capacity and the results showed that the two dependent variables were influenced by the four factors and their interactions and the temperature had a pronounced influence on the activity DPPH⋅ radical scavenging. Despite coming from the same protein source, the generated peptides showed different activities in which their hydrolytic conditions were optimized by using the BBD experimental design.

It was used the BBD to optimize the conditions to generate bioactive peptides with specific desired activities in the works mentioned above. It was possible to evaluate between three and five factors simultaneously. The more outstanding application was observed by optimizing factors such as time and temperature of hydrolysis, which shows the importance of these variables in obtaining BAPs.

Simplex centroid design (SCD)

Centroid Simplex (SCD) design and Simplex Lattice Design are part of mixture designs, which investigate the variables (components). In these designs, the properties of the mixtures depend on the proportions of the components. Therefore, they are used to optimize the composition of a mixture (Myers et al., 2009; Sahu et al., 2018).

In a Simplex Centroid Design, a mixture of 3 components can be, for example, chemical solvents for the extraction of some compound of interest (Mendes et al., 2019), or a mixture of proteases to generate bioactive peptides (Marson et al., 2020), which can be represented by an equilateral triangle. For a 4-component mixture, the design can be represented by a regular tetrahedron (Bezerra et al., 2020). The sum of the proportions between the components must always equal 1 or 100%. In this way, for any mixture with q components, one can have the equation:

$${\sum }_{i=1}^q{X}_1=100\%=1$$ 4

where X_i represents the proportion of the i-th component, for polynomial mathematical models developed to describe the behavior of the mixture as a function of the proportions of their components, the condition X₁ + X₂ = 1 and X₁ + X₂ + X₃ = 1 must be considered for a mixture of two and three components, respectively. Thus, for a mixture of two components, the equation that describes the experimental region is given by:

$$\text{y}={\text{b}}_1^{\prime }{\text{x}}_1+{\text{b}}_2^{\prime }{\text{x}}_2+{\text{b}}_{12}^{\prime }{\text{x}}_1{\text{x}}_2$$ 5

where y represents the chemical response of interest, b′ = b₀ + b_i + b_ii (for i = 1,2) and b′₁₂ = b₁₂ − b₁₁ − b₂₂ (Ferreira et al., 2007a). The mathematical models to be used in an SCD can be linear, quadratic, cubic, or special cubic, depending on the number of components of the mixture, the significance of the tested model, and its lack of fit or not (Barros Neto et al., 2001).

The effect of the mixture of components can be synergistic or antagonistic. For a synergistic effect, the response obtained with the mix of elements is always more significant than the individual sum of their responses. For an antagonistic effect, the response obtained by the mixed components is always smaller than the sum of their responses duly weighted by their respective proportions (Myers et al., 2009).

The eight papers that used this mixture design evaluated three components (Table 4). In six studies, the investigated components were some protease (Aguilar et al., 2019b, 2019a; Casarin et al., 2021; de Castro et al., 2017; de Castro and Sato, 2015b; Marson et al., 2020), given that proteolytic enzymes satisfactorily cleave proteins are the main ones responsible for generating hydrolysates rich in bioactive peptides. While in two of them, the investigated components were protein isolates and their hydrolysates obtained by some protease (de Castro and Sato, 2014; de Castro et al., 2016). The most evaluated chemical response was antioxidant activity. The diversity of samples studied was very wide: brewer’s yeast (Marson et al., 2020), lentils (Casarin et al., 2021), protein concentrate from chicken offal (Aguilar et al., 2019a), protein concentrate from black beans (Aguilar et al., 2019b) and common white beans (de Castro et al., 2017), and isolates and hydrolysates of soy, bovine whey and egg white (de Castro and Sato, 2014; de Castro et al., 2016) (Table 4).

For the six experiments that used proteases as components, there was a preference for alcalase and flavourzyme, possibly because both are already widely used in studies with this focus (Hajfathalian et al., 2018; Marciniak et al., 2018) and the combination generated between them. Alcalase is a non-specific, high-spectrum endopeptidase with an affinity for hydrophobic amino acids. At the same time, the flavourzyme is a complex mixture of endo and exopeptidases capable of releasing minimal peptides and free amino acids (Rivero-Pino et al., 2020). Many studies reported that combining these proteases enhances hydrolysis, generating peptides with reduced molecular weight, which are generally associated with a greater antioxidant capacity (Marson et al., 2020).

Marson et al. (2020) investigated the DH, AA (DPPH, FRAP, and ORAC), and some other physicochemical parameters of peptides generated from hydrolysis with alcalase brauzyn and protamex, and your spent brewer’s yeast mixes (waste). For ORAC, the models tested showed a lack of adjustment, so the AA of this method was discarded. For each response, there was an optimal condition provided by the model. For FRAP, there was a synergistic effect between the binary mixture of brauzyn and protamex, generating the best results for this method. As for DPPH, the interaction between the three enzymes increased antioxidant properties. The ternary mixture of enzymes was chosen as the optimal condition to generate peptides with the desired characteristics. The bioactive peptides were then fractionated by ultrafiltration using 10 and 30 kDa molecular weight cut-off (MWCO) membranes and characterized by gel electrophoresis. Fractionation separated the peptides, resulting in a concentrated fraction of ca. 30 kDa of peptides and another with fewer than 35 kDa.

The antioxidant activity (DPPH and total AA) and the antihypertensive activity of peptides generated from hydrolysis with flavourzyme, alcalase, neutrase, and their chicken offal protein concentrate mixtures were investigated (Aguilar et al., 2019a). The binary mixture of flavourzyme and alcalase in the same proportions was defined as an optimal condition to obtain peptides with bifunctional properties (antioxidant and antihypertensive), showing the synergistic effect of the mixture of using both enzymes. Fractionation of protein hydrolysates with 30, 10, and 3 kDa MWCO ultrafiltration membranes was performed. The results showed that ultrafiltration did not favor the increased antioxidant and antihypertensive properties of the generated peptides. The antioxidant capacity results showed values ranging from 59.31 to 70.70% for DPPH and 142.90 to 189.00 Trolox EQ g^–1 for total antioxidant capacity. While for antihypertensive activity, the values ranged from 70.53 to 83.72%.

A protein concentrate of standard black and white beans (Phaseolus vulgaris L.) was used to obtain bioactive peptides with antioxidant activity (Aguilar et al., 2019b; de Castro et al., 2017). Flavorenzyme, alcalase, and neutrase and their mixtures were used to carry out the enzymatic hydrolysis. The mixture of flavourzyme and alcalase in equal proportions generated a synergistic effect and, this was defined as an optimal condition. Enzymatic hydrolysis increased the antioxidant activity of both white and black beans. The ultrafiltration was performed with 30, 10, and 3 kDa membranes resulting in a relationship between lower antioxidant activity and lower molecular weight peptide species for both types of beans.

The antioxidant activities (DPPH assay, Inhibition of linoleic acid auto-oxidation, reducing power, and total AA) and the TCA-soluble peptide index (TCA-SPI) of peptides generated from hydrolysis with flavourzyme, alcalase, YeastMax A and their soybean protein isolate mixtures was investigated (de Castro and Sato, 2015b). The model provided the binary mixture with flavourzyme and alcalase as an optimal condition for DPPH wich it had a synergistic effect with increases in antioxidant activity compared to the hydrolysates produced with individual enzymes. For the inhibition of linoleic acid autooxidation, the ternary mixture of the three enzymes proved the best condition. For determination of reducing power and AA trial, flavourzyme alone generated the peptides with the best results, similar to TCA-SPI, in which the best condition was shown with pure YeastMax A enzyme. The generated peptides were not characterized. These results demonstrate the high capacity of mixture design to optimize different conditions for each dependent variable with few experiments and evaluating different responses.

Aguilar et al. (2019b) and Castro et al. (2017) used SCD design to evaluate the influence of the combination of three enzymes: alcalase, flavourzyme and neutrose in obtaining hydrolysates from protein concentrates of black beans and white beans with greater antioxidant activity, which were estimated by the dependent variables DPPH radical-scavenging, total antioxidant activity, and reducing power assay. To evaluate the modulation of proteases under the substrate, kinetic analyzes of the reactions were carried out based on reactive conditions (in the presence of the substrate) and non-reactive conditions (in the absence of the substrate) aiming to obtain a response in relation to the best hydrolytic conditions from of the protease mixture. Kinetic parameters are considered important, as they serve to define and model the use of enzymes in certain industrial applications, the alcalase and flavourzyme combination showed a reduction in half-life in reactive conditions (black bean substrate) and most mixtures enzymes in the presence of white bean substrate also showed a reduction in half-life. In both cases, the binary mixture of alcalase and flavourzyme enzymes generated a synergistic effect and was defined as an ideal combination as it is very effective in the production of black and white bean peptides with antioxidant activities. The ultrafiltration was performed with 30, 10, and 3 kDa membranes resulting in a relationship between lower antioxidant activity and lower molecular weight peptide species for both types of beans.

de Castro et al. (2016) investigated the effect of component interactions on the inhibition capacity of relative lipid accumulation (RLA). The hydrolyzed mixture containing BWP and EWP in equal proportions showed increases of up to 220 and 27% in their activities, respectively, compared to the isolated substrates, reaching a maximum suppression of RLA of 15.5%. Ultrafiltration was performed with 30, 10, and 3 kDa membranes, and the results indicated that the unfractionated sample of BWP (1/2) and EWP (1/2) was the most active for anti-adipogenic activity and stated that there is a critical contribution of fractions with various molecular sizes in the suppression of RLA. On the other hand, de Castro and Sato (2014) observed synergistic effects between formulations containing binary or ternary mixtures for several dependent variables. The binary mixture in the same proportions between SPI and EWP generated the optimal condition for the DPPH antioxidant activity and the emulsion activity index, which exhibited increases of up to 45.0 and 1200.0%, respectively, after enzymatic hydrolysis concerning isolated substrates. The generated peptides were not characterized.

Simplex lattice design (SLD)

This design is equivalent to the FFD mentioned above (“2^k full factorial design (FFD)” section) for process variables since the experimental points are performed at the ends of the experimental domain, using more than two levels, uniformly spaced together with the coordinates representing the variables (Ferreira et al., 2007a). This design is also known as simplex network design, as it consists of a network of the type (q, m) for q components, in which proportions taken by each component are the values m + 1 equally spaced from 0 to 1, according to the Eq. (6) (Myers et al., 2009):

$$x_i=0,\frac{1}{m},\frac{1}{m},\frac{m-1}{m},fori=1,2,\dots ,q$$ 6

Simplex Lattice designs have some disadvantages: as the polynomial degree increases, the number of experimental points becomes high, often making its application unfeasible. Another issue, the coefficients estimated by the adjusted mathematical model are obtained based only on experimental data; that is, only the points that correspond to pure components and binary mixtures are involved. Thus, contributions to tertiary mixtures are underestimated (Ferreira et al., 2007a).

He et al. (2014) investigated the antioxidant activity and the degree of hydrolysis of peptides generated from anchovy protein (Engraulis japonicus) using OFAT, SLD, and BBD (Table 4). An OFAT was performed to determine the hydrolysis time and the proteases used later in the DoE. Six enzymes were investigated, protamex, flavor enzyme 500MG, 2.4 L alcalase, 0.8 L neutrase, bromelain, and papain. The analyzed hydrolysis times were 0.5, 1, 2, 3, 4, 5, 6, and 8 h. Antioxidant activity (DPPH) was used as a response. The results demonstrate that hydrolysis for 3 h using the enzymes protamex, flavourzyme, and alcalase generate the best results. Thus, an SLD was performed to determine the optimal condition for mixing these proteases to obtain peptides with better antioxidant activity and a higher degree of hydrolysis.

The SLD results revealed that the optimal composition for the two responses was a 1.1:1.0:0.9 ternary mixture of protamex, flavourzyme, and alcalase. Then, this mixture was used in a BBD to evaluate the E/S ratio, temperature, and hydrolysis time factors, using antioxidant activity (DPPH) as a response. The generated peptides were not characterized. In this work, it is possible to observe that the combination of DoE can be an alternative for the complete optimization of the evaluated system. Using SLD followed by a BBD allowed the investigation of all parameters’ effects with a relatively small number of trials.

Identity of BAPS generated with DoE

Identity and CHARACTERISTICS

This topic presents a discussion on the identity and characteristics of the known bioactive peptides. The general characteristics of the BAPs are described in Fig. 3. The number of BAPs identified in each work ranged from 1 to 420 bioactive peptides from different biological matrices. Fourteen articles identified peptides with antioxidant activity, followed by antihypertensive (5 articles), antidiabetic, iron chelation, antimicrobial, and antifungal activity, with only one paper each. Purification, ultrafiltration, and separation techniques were effective and capable of providing low molecular weight peptides in which were obtained from fractions containing BAPs with molecular weight ≤ 3 kDa. Furthermore, the BAPs found are primarily hydrophobic and consist of short chains of amino acids. Such characteristics are desirable and attributed to the bioactivity of these compounds, as reported below.

Fig. 3.

General characteristics of the identified BAPs

According to Sharma et al. (2022), the antioxidant activities of BAPs are related to their amino acid sequences, molecular weight, electronic characteristics, stericity of amino acids at the N- and C-terminal, hydrophobicity at the carbon terminus, side-chain residues, and hydrogen bonding characteristics of amino acids. It was also demonstrated that low MW BAPs have a higher solubility and lower viscosity as well as higher absorption than amino acids (AAs) or free proteins. Furthermore, hydrophobic and/or aromatic AAs such as Leu, Ile, Pro, Val, Tyr, Trp, Gly, Ala, and Phe can offer their profuse electrons or hydroxyl groups to quench radicals which are lipid soluble performing antioxidant activity against fat-soluble radical species. For example, Zheng et al. (2018) obtained a new AEDKKLIQ chicken blood corpuscle peptide with the aforementioned characteristics. Wu et al. (2020) also found two peptides (MTTNL and MTTNI) and presented high antioxidant activity and attribute the presence of the amino acids leucine and isoleucine as determinants for stronger antioxidant activity.

In work developed by Lima et al. (2015), it was obtained BAPs with antioxidant and antimicrobial activity. In this case, low molecular mass and hydrophobic BAPs were desirable considering that peptides with these characteristics better expose their amino acid residues and their charges, as well as facilitate the entry of peptides into the bacterial membrane. Three peptides of molecular weight ≤ 2 kDa that were hydrophobic were identified (GDKGETGEQGDR, FLPQPPQEKAHDGGR, and FGGDFYR) and exerted antibacterial activities against Escherichia coli, Bacillus subtilis, and Staphylococcus aureus.

Jia et al. (2020) generated BAPs with DPP-IV inhibiting activity, characteristic of BAPs with antidiabetic activity. In general, the DPP-IV inhibitory peptide structure has Pro or Ala at the penultimate N-terminal to interact with the substrate and cleave the peptide bond. Other hydrophobic AAs at the N- or C-terminal position such as Leu, Ile and Phe may also exhibit DPP-IV inhibitory activity. The hydrophobic amino acids located at these positions of the peptides facilitate interaction with the hydrophobic pocket found in the active site of DPP-IV. For example, in this work, a new DPP-IV inhibitor peptide was identified (LDQWLCEKL) and did not bind to the catalytically active center of DPP-IV. Instead, it exhibited a typical mode of non-competitive inhibition and formed an inactive complex, preventing the catalytic reaction of the enzyme. The new peptide was considered a potent inhibitor of DPP-IV.

In work reported by Maqsoudlou et al. (2019), it was sought to generate bioactive peptides with ACE inhibitory activity, typically BAPs with antihypertensive activity. ACE-inhibitory peptides have been reported to be typically < 20 amino acids and MW < 3 kDa (Karami et al., 2019). ACE inhibitory activity is typically related to the number of hydrophobic amino acids present in the peptide sequences, probably because the ACE active site is more accessible by hydrophobic peptides (Maqsoudlou et al., 2019), which have greater solubility in lipid environments, such as cell membranes—vide that ACE is membrane bound—and can engage in hydrophobic interactions, eventually interrupting ACE activity and lowering blood pressure (Karami et al., 2019). ACE-inhibitory peptides have also been described as containing lysine, proline, or aromatic AAs residues preferentially in the three positions closest to the C-terminal site (Maqsoudlou et al., 2019). For example, the experimental design applied to the generation of antihypertensive peptides from fish of the Channa striatus fish generated BAPs of low molecular mass ranging from 25 to 8770 Da. Among the identified peptides, EYFR and LPGPGP exhibited the highest ACE inhibition with IC₅₀ values of 179.2 and 186.3 µM, respectively. In silico molecular docking studies indicated that the peptide EYFR established 10 hydrogen bonds while LPGPGP presented only 3 hydrogen bonds. It was indicated that electrostatic interactions, hydrogen bonds, and hydrophobic interactions were the main driving forces between LPGPGP and ACE, while for EYFR and ACE, hydrogen bonds and electrostatic interactions were more determinant (Ma et al., 2021).

The work developed by Vo et al. (2020) aimed to generate BAPs with iron-chelating activity from the shrimp species Acetes japonicus. Regarding the composition of AAs, the presence of Asn and Phe in the peptides generated during hydrolysis may facilitate the binding to iron. The Asn revealed fourth-strongest interaction residue with a ferrous ion, followed by Glu, His and Asp. Furthermore, the Phe amino acid is related to the binding potential of iron due to the effects of its aromatic ring and the adjacent nitrogen of the amide group. Smaller-sized peptides are also reported to have a greater ability to migrate and chelate ferrous ions and to have greater stability than high-molecular-mass peptides during gastrointestinal digestion. It is worth mentioning that in this case, the presence of hydrophobic peptides is favorable which they are more easily absorbed through PepT1-mediated transport and transcytosis due to their high affinity for this transporter and cell membrane as well as great bioavailability in vitro. DSVNFPVHGL and FKVGQENTPILK were identified and presented a molecular weight of 1083.53 Da and 1372.77 Da, respectively. These present in their composition the aforementioned amino acids: Asn, Phe, Glu, His, and Asp that, contribute to a stronger interaction with the ferrous ion. Therefore, the low molecular weight and the amino acids that make up the peptide sequence were determinants for these peptides’ high metal chelating activity.

Identification of BAPs vs DoE

Considering the DoE applied in the works analyzed in this manuscript, only 27.5% of the studies identified the BAPs produced. It should be note that 11 studies used CCD while seven applied BBD, and only one using FFD to produce bioactive peptides that were later identified. Thus, it can be stated that the optimization experiment process to obtain and determine the BAPs is independent. However, identifying BAPs strongly correlates with the instrumental advances of each research group/institution and the year in which the work was developed. Of the 19 works that identified the bioactive peptides, 16 were published in the last five years. This fact can be associated with researchers’ access to modern techniques (MALDI-TOF–MS and Nano LC–MS/MS) with high detectability compared to instruments available in previous years. The modernization and improvement of instrumentation are essential to advances in the structural characterization of BAPs, making it easier to understand the relationship between the identity and function of these biomolecules in biological systems.

Future perspective

Considering all the highlighted points in the manuscript, the relevance of applying experimental designs in the screening and optimization of analytical methods to obtain bioactive peptides in different types of food samples is clear, which are relevant information for the production of BAPs and their subsequent commercialization in the food industry. Although the present study highlights a diversity of experimental designs, the Box–Behnken design (BBD) and the Central Composite Design (CCD) were the most applied. This fact can be associated with the advantages of these methodologies over the others, mainly due to their optimization capabilities with the reduced need for experiments and the possibility of exploring the response surface. There is no consensus regarding the dependent variables to be evaluated. Degree of hydrolysis and antioxidant activity were the most investigated responses in all applied DoE.

Furthermore, few studies identify the bioactive peptides obtained, which may be related to limited access to adequate instrumentation. It is also important to emphasize that the careful choice of the type of experimental design appropriate to the study objective is crucial and decisive for obtaining BAPs with the desired bioactivity and depends on the instrumental conditions, and the availability of reagents and samples. In this sense, experimental design has much to contribute to understanding the effects of variables and standardizing the production methods of BAPs. Additionally, the application of experimental design can be extended to future and innovative studies on: (i) Bioinformatic studies of the peptide sequences present in the parental proteins that can be found substantially in protein sequence databases, (ii) In silico approaches for selection of proteases based on the hydrolytic specificity of proteins, (iii) The bioavailability of bioactive peptides aimed at developing transport and delivery systems for these biomolecules, improving their activities under human physiological conditions, and iv) Apply novel green technologies such as ultrasound, microwaves, hydrostatic pressure, among others during enzymaticB hydrolysis to increase the yield of bioactive peptides.

Abbreviations

BAPs

Bioactive peptides

DoE

Design of experiments

RSM

Response surface methodology

OFAT

One-factor-at-a-time

FFD

Full factorial design

FrFD

Fractional factorial design

PBD

Plackett–Burman design

CCD

Central composite design

BBD

Box–Behnken design

SCD

Simplex centroid design

SLbD

Simplex lattice design

DH

Degree of hydrolysis

E/S

Enzyme/substrate ratio

Da

Dalton

MW

Molar weight

MWCO

Molecular weight cut-off

AAs

Amino acids

AA

Antioxidant activity

DPPH

Diphenyl-picrylhydrazyle

ABTS

2,2′-Azino-bis(3-ethylbenzothiazoline-6-sulfonic acid)

FRAP

Ferric reducing antioxidant power

ORAC

Oxygen radical absorbance capacity

RP

Reducing power

DPP-IV

Dipeptidyl peptidase-IV

IBC

Iron-binding capacity

TCA

Trichloroacetic acid

TCA-SPI

Trichloroacetic acid soluble peptide index

MALDI-TOF–MS

Matrix-assisted laser desorption/ionization-time of flight mass spectrometry

RP–HPLC–MS/MS

Reverse-phase high-performance liquid chromatography coupled with tandem mass spectrometry

HPLC-SEC

Size-exclusion high-performance liquid chromatography

RP-HPLC

Liquid chromatography and reverse-phase separation

Author contributions

Mikael Kélvin de Albuquerque Mendes: conceptualization, investigation, writing of the original article. Christian Bremmer dos Santos Oliveira: conceptualization, investigation, writing of the original article. Carla Mariana da Silva Medeiros: conceptualization, investigation, writing of the original article. Clecio Dantas: editing the final version of the article and reviewing the design of the experiments topic. Ana Rita de Araújo Nogueira: rationale, supervision, editing, and correction of the final version of the article. Emanuel Carrilho: rationale, supervision, editing, and revision of the final version of the article. Cícero Alves Lopes Júnior: supervision, acquisition of financing, editing, and correction of the article's final version. Edivan Carvalho Vieira: supervision, acquisition of financing, editing, and correction of the article’s final version.

Declarations

Conflict of interest

The authors declare that no personal or financial interests may interfere with the work written in this article. We, CALJ and ECV, as the corresponding authors and on behalf of the staff, certify that there is no conflict of interest.