Some physical, functional and antinutrients of breakfast cereals from blends of guinea corn, pigeon pea and mango flour using mixture-process design

Abstract

Some functional, physical and anti-nutritional factors of breakfast cereals from blends of sorghum (X₁), pigeon pea (X₂) and mango (X₃) flours were evaluated using mixture-process design. The flours were blended in ratios of 1:0:0, 0:1:0, 0:0:1, 05:0.5:0, 0.5:0:0.5, 0:0.5:0.5, and 1/3:1/3:1/3, for sorghum, pigeon pea, and mango flour, respectively. Twenty-eight samples were generated from a multiplicative (2³–1) simplex centroid mixture design and a (2, 2) full factorial design. The samples were roasted at varying temperatures (Z₁) (250 and 270 °C) and times (Z₂) (4 and 7 min). The water absorption capacity (WAC), pH, bulk density (BD), foam capacity (FC), haemagglutinin, phytates, and tannins were evaluated. Significant (p < 0.05) regression models were generated to explain these responses. The temperature time-combination did not significantly (p > 0.05) affect pH changes. For WAC, BD, FC, and the antinutrients, there was no clear trend to describe the effect of mixture components and process variables. Experimental runs with the same mixture formulation, processed at different temperature–time combinations had different values for these attributes with the degree of reduction of antinutrients being a simultaneous effect of these variables. Cross interactions between the mixture and process variables showed that the selected properties were dependent both on the mixture and processing conditions.

Introduction

Breakfast cereals have been defined by Stan (2006) as products consisting of cereals that can be consumed with milk or other appropriate nutritious liquids. These cereal-based foods are prepared primarily from one or more milled cereal products such as wheat, rice, barley, oats, rye, maize, millet, sorghum and buckwheat. They may also contain legumes (pulses) for protein complementation and nutrient diversification (Mbaeyi-Nwaoha and Uchendu 2016), starchy roots (such as arrowroot, yam or cassava) or starchy stems, oilseeds in smaller proportions, or fruit powders to improve nutritional quality and attractiveness (Bolanho et al. 2015).

The most popular cereals in the production of breakfast cereals are corn, wheat, oats, and rice (Cablevey 2021). The utilization of sorghum is still limited even though is the fifth most produced cereal in the world with over 58.4 million metric tons produced in 2019 (Shabandeh 2020). On the other hand, Olurin et al. (2021) has reported that its use can be diversified in the production of ready-to-eat breakfast cereals. Sorgum, like other cereals, is limited in lysine which is an essential amino acid needed by humans. In the production of breakfast cereals, this limiting amino acid can be introduced by complementing sorghum with a legume such as pigeon pea (Okafor and Usman 2014).

Again, cereal-based foods are often deficient in bioactive components such as carotenoids, vitamins C, and K (Bolanho et al. 2015). Nigeria is the leading producer of mangoes in Africa with over 860, 000 million tons (UNCTAD 2016). This fruit is seasonal and highly perishable. Incorporating it in breakfast cereals will increase bioactive components, reduce postharvest losses during the harvesting season, increase the organoleptic quality, and modify the physical and functional properties.

The physical and functional properties of breakfast cereals are essential for scientists and engineers who have to solve appropriate challenges in processing, preservation, packaging,, storage, marketing, and consumption (Rahman and McCarthy 1999). These functional properties can also be important in developing process conditions for breakfast cereals from an engineering point of view.

Cereal-based foods whether produced exclusively with a cereal or complemented with a legume, are often associated with some anti-nutritional factors (Mbaeyi-Nwaoha and Uchendu 2016). While polyphenols, cyanogenic glycosides, and phytic acid are anti-nutritional factors present in sorghum, protein inhibitors (Trypsin and Chymotrypsin) and amylase inhibitors have been reported by Popova and Mihaylova (2019) to be present in pigeon pea. Polyphenols (tannins) interfere with bio-availability of major nutrients, while phytic acid usually forms insoluble complexes with minerals like calcium, iron, magnesium, and zinc thus making them unavailable These anti-nutritional factors can be reduced to tolerant levels by further processing as reported by Popova and Mihaylova (2019).

Many scientists have carried out intensive research on the physical, functional, and anti-nutritional contents of breakfast cereals and other snacks. Chandra et al. (2014) evaluated functional properties of biscuits from composite flours, while Okafor and Usman (2014) evaluated the physical and functional properties of breakfast cereals from blends of maize, African yam bean, and coconut cake. Borah et al. (2016) optimized the physicochemical properties of mineral and fibre-rich breakfast cereals from low amylose rice banana and carambola pomace, while Meza et al. (2019) optimized the physical properties of gluten-free breakfast cereals from red and black rice.

However, these studies have concentrated on the single effects of either mixture or processing conditions to study and optimize the physical, functional, and antinutrients of the breakfast cereals. Ideally, during processing, both the mixture and process variables simultaneously interact to affect the physicochemical and antinutritional factors of food products (Snee et al. 2015). The mixture-process experimental design approach has been used to simultaneously study the effects of mixture and processing conditions during food formulation and processing but its usage is still limited in studying the physical, functional and antinutrients of breakfast cereals. This study was therefore aimed at using mixture-process design to evaluate some physical, functional, and anti-nutritional factors of breakfast cereals produced from blends of sorghum, pigeon pea and mango flours.

Materials and methods

Sourcing of raw materials

The principal raw materials used in the research were flour from guinea corn, pigeon pea, malted guinea corn and Tommy Adkins specie of mango. Guinea corn and pigeon pea were purchased from Ogige market, Nsukka, Enugu State, Nigeria and firm ripe mangoes were plucked from mango trees in the University of Nigeria, Nsukka (UNN).

Production of mango flour

Mango flour was produced using the method described by FAO (2015) on dried fruits with slight modifications. Firm ripe mangoes (30 kg) were carefully selected, washed and rinsed in clean water and manually peeled with a stainless steel knife. The mango pulp was sliced with a knife into thicknesses ranging from 6 to 8 mm and blanched in boiling water for 5 min. It was dried in a passive solar dryer for 18 h at 48 °C ± 5 °C and milled in the Department of Food Science and Technology (FST) milling laboratory, UNN using a hammer mill (Viking Hammer mill, Horvick manufacturing model No. IG.01.09.2H.H3), sieved with 4.2 µm mesh sieve (Brabender OHG Duisburg type) to flour and packaged in airtight polypropylene containers and tightly covered. The processes were summarized in Fig. 1.

Fig. 1.

Production of breakfast cereals from sorghum flour, pigeon pea, and mango flour

Production of sorghum flour

Sorghum flour was produced using the method described by Mbaeyi (2005) with slight modifications. White sorghum grains (5 kg) were cleaned, dry-milled into flour using a hammer mill, sieved with 4.2 µm mesh sieve (Brabender OHG Duisburg type) and packaged in an airtight polypropylene container and tightly covered. This process is summarized in Fig. 1.

Production of pigeon pea flour

Pigeon pea flour was produced using the method described by Singh and Jambunathan (1982) with slight modifications. Five (5) kg were cleaned and tempered with 3% water for 12 h to allow for easy removal of the hulls. Pigeon pea seeds were cracked using a disc attrition mill (Bentall Superb Model 200L, 090) and hulls were separated by manual winnowing prior to milling with same hammer mill (Viking Hammer mill, Horvick manufacturing model No. IG.01.09.2H.H3), sieved with 4.2 µm mesh sieve and packaged in an airtight polypropylene container and tightly covered. This process is summarized in Fig. 1.

Production of corn malt

Corn malt was produced using the method described by Okafor and Usman (2014) with slight modifications. Five kilograms (5 kg) of sorghum grains were steeped in tap water (1:3) for 18 h and germinated on wet jute bag floor for 3 days at room temperature (28 ± 2 °C). The green malt was oven-kilned in FST Food Chemistry lab at 55 °C for 8 h and further at 65 °C for 16 h to get friable rootlets. The rootlets were separated by robing the grains between the hands after allowing it to cool. The grains were milled using a hammer mill in FST milling lab to obtain malt powder and packaged in airtight polypropylene containers. It was stored for later use. This process is summarized in Fig. 1

Mixture-process design of experiments

Having produced the components to be used, a mixture-process design of experiments approach was used to formulate the breakfast cereal (Snee et al. 2015). The factors were: X₁ = guinea corn flour, 0.5 ≤ X₁ ≤ 0.85, X₂ = pigeon pea flour, 0.1 ≤ X₂ ≤ 0.45, X₃ = mango flour, 0.05 ≤ X₃ ≤ 0.15, Z₁= roasting temperature, -1 ≤ Z₁ ≤ 1 and Z₂ = roasting time, -1 ≤ Z₂ ≤ 1. The responses were bulk density, water absorption capacity, pH, foam capacity, haemagglutinins (lectins), phytates, and tannins. Table 1 gives the experimental layout of the formulation.

Table 1.

Experimental layout of the design in pseudo, coded, and real values

Run	Sample	Sorghum (X1) (g)	Pigeon pea (X2) (g)	Mango flour (X3) (g)	Roasting temperature (Z1) (oC)	Roasting time (Z2) (s)
1	1a	0.5 = 67.5	0.5 = 27.5	0 = 5.0	− 1 = 150	1 = 7
25	1b	0.5 = 67.5	0.5 = 27.5	0 = 5.0	1 = 270	− 1 = 4
2	1c	0.5 = 67.5	0.5 = 27.5	0 = 5.0	− 1 = 150	− 1 = 4
22	1d	0.5 = 67.5	0.5 = 27.5	0 = 5.0	1 = 270	1 = 7
6	2a	0 = 50.0	0 = 10.0	1 = 40.0	1 = 270	− 1 = 4
14	2b	0 = 50.0	0 = 10.0	1 = 40.0	− 1 = 150	− 1 = 4
24	2c	0 = 50.0	0 = 10.0	1 = 40.0	1 = 270	1 = 7
3	2d	0 = 50.0	0 = 10.0	1 = 40.0	− 1 = 150	1 = 7
7	3a	1 = 85.0	0 = 10.0	0 = 5.0	− 1 = 150	− 1 = 4
4	3b	1 = 85.0	0 = 10.0	0 = 5.0	− 1 = 150	1 = 7
16	3c	1 = 85.0	0 = 10.0	0 = 5.0	1 = 270	− 1 = 4
18	3d	1 = 85.0	0 = 10.0	0 = 5.0	1 = 270	1 = 7
5	4a	0 = 50.0	0.5 = 27.5	0.5 = 22.5	− 1 = 150	− 1 = 4
13	4b	0 = 50.0	0.5 = 27.5	0.5 = 22.5	1 = 270	− 1 = 4
11	4c	0 = 50.0	0.5 = 27.5	0.5 = 22.5	− 1 = 150	1 = 7
21	4d	0 = 50.0	0.5 = 27.5	0.5 = 22.5	1 = 270	1 = 7
8	5a	0.33 = 61.7	0.33 = 21.7	0.33 = 16.6	1 = 270	1 = 7
19	5b	0.33 = 61.7	0.33 = 21.7	0.33 = 16.6	− 1 = 150	1 = 7
20	5c	0.33 = 61.7	0.33 = 21.7	0.33 = 16.6	1 = 270	− 1 = 4
9	5d	0.33 = 61.7	0.33 = 21.7	0.33 = 16.6	− 1 = 150	− 1 = 4
10	6a	0 = 50.0	1 = 45.0	0 = 5.0	1 = 270	1 = 7
12	6b	0 = 50.0	1 = 45.0	0 = 5.0	− 1 = 150	1 = 7
15	6c	0 = 50.0	1 = 45.0	0 = 5.0	1 = 270	− 1 = 4
17	6d	0 = 50.0	1 = 45.0	0 = 5.0	− 1 = 150	− 1 = 4
23	7a	0.5 = 67.5	0 = 10.0	0.5 = 22.5	− 1 = 150	− 1 = 4
26	7b	0.5 = 67.5	0 = 10.0	0.5 = 22.5	− 1 = 150	1 = 7
27	7c	0.5 = 67.5	0 = 10.0	0.5 = 22.5	1 = 270	1 = 7
28	7d	0.5 = 67.5	0 = 10.0	0.5 = 22.5	1 = 270	− 1 = 4

Twenty-eight samples were obtained from the combined mixture-process linear multiplication model. The samples were mixed with corn malt, water, salt and sugar and roasted at different process conditions, cooled to room temperatures and packaged. Figure 1 summarizes the flow diagram of the production process.

The combined mixture-process modelling equation for the formulation was as presented in Eq. 1.

$$Y={\gamma }_1^0{X}_1+{\gamma }_2^0{X}_2+{\gamma }_3^0{X}_3+{\gamma }_{12}^0{X}_1{X}_2+{\gamma }_{13}^0{X}_1{X}_3+{\gamma }_{23}^0{X}_2{X}_3+{\gamma }_{123}^0{X}_1{X}_2{X}_3+{\gamma }_1^1{X}_1{Z}_1+{\gamma }_2^1{X}_2{Z}_1+{\gamma }_3^1{X}_3{Z}_1+{\gamma }_{12}^1{X}_1{X}_2{Z}_1+{\gamma }_{13}^1{X}_1{X}_3{Z}_1+{\gamma }_{23}^1{X}_2{X}_3{Z}_1+{\gamma }_{123}^1{X}_1{X}_2{X}_3{Z}_1+{\gamma }_1^2{X}_1{Z}_2+{\gamma }_2^2{X}_2{Z}_2+{\gamma }_3^2{X}_3{Z}_2+{\gamma }_{12}^2{X}_1{X}_2{Z}_2+{\gamma }_{13}^2{X}_1{X}_3{Z}_2+{\gamma }_{23}^2{X}_2{X}_3{Z}_2+{\gamma }_{123}^2{X}_1{X}_2{X}_3{Z}_2+{\gamma }_1^{12}{X}_1{Z}_1{Z}_2+{\gamma }_2^{12}{X}_2{Z}_1{Z}_2+{\gamma }_3^{12}{X}_3{Z}_1{Z}_2+{\gamma }_{12}^{12}{X}_1{X}_2{Z}_1{Z}_2+{\gamma }_{13}^{12}{X}_1{X}_3{Z}_1{Z}_2+{\gamma }_{23}^{12}{X}_2{X}_3{Z}_1{Z}_2+{\gamma }_{123}^{12}{X}_1{X}_2{X}_3{Z}_1{Z}_2$$ 1

where “γ” is the regression constant for the combined mixture-process model.

Experimental layout of the formulation is presented in Table 1.

Determination of bulk density

Bulk density was determined by the method described by Onwuka (2005). The samples were gently filled into l0 ml measuring cylinder to the mark. The bottom of the cylinder was gently tapped on a laboratory bench 20 times until there was no further reduction in volume. Bulk density was estimated as mass per unit volume (g/ml) of the sample.

Determination of water absorption capacity (WAC)

WAC was determined by the method described by Kanu et al. (2009) with slight modifications. Ten (10) g of each sample was weighed into a 100 ml beaker. A known volume (5 ml) of water was pipetted into the beaker, carefully stirred manually and allowed to equilibrate for one hour at room temperature (28 ± 2 °C). After complete water absorption, the samples were further treated with 2 ml water portion at 10 min interval before visual observation. The volume that gave a complete absorption of water (no visible free water) was recorded and WAC calculated as the ratio of the maximum amount of water in grams absorbed by 10 g dry material.

Determination of pH

pH was determined using the method described by Onwuka (2005) with slight modifications. Two grams (2 g) of the samples were homogenized in 20 ml of deionized water. The mixture was filtered and the pH of the filtrate measured with the help of a Mettler Delta 350 pH meter. Duplicate readings were taken for each sample.

Determination of foam capacity

Foam capacity was determined by the method described by Usman (2012). The sample (0.2 g) was mixed with 10 ml distilled water in a warring blender and whipped at 1600 rpm for 5 min. The mixture was poured into a 25 ml cylinder and the volume recorded after 30 s.

$$Foamcapacity=\left(\frac{Volumeafterwhipping-volumebeforewhipping}{volumebeforewhipping}\right)\times 100$$ 2

Determination of Anti-nutrients

Phytates and haemagglutinins were determined by the spectrophotometric methods described by AOAC (2010) while tannins were determined by the method described by Pearson (1976) as follows: One gram (1 g) of the sample was put into a flask and 10 ml distilled water added. The mixture was allowed to stand for 30 min at room temperature with gentle shaking at 5 min intervals. After this 30 min, the mixture was centrifuged. Two and a half (2.5) ml of the supernatant and 2.5 ml of standard tannin solution was measured into separate 50 ml volumetric flasks. One millilitre (1 ml) of Folin-Dennis reagent added into each flask followed by 2.5 ml of saturated Na₂CO₃. The solution was made up to the mark and incubated for 90 min at room temperature. The absorbance was read at 250 nm and tannin content calculated using Eq. 3.

$$\%Tannin=\frac{A_n}{A_s}\times \frac{C}{V_a}\times V_f\times \frac{100}{W}$$ 3

where, A_n = Absorbance of test sample, A_s = absorbance of the standard, C = Concentration of standard, W = Weight of sample used, V_f = Total volume of extract, and V_a = Volume of extract used for the analysis.

Statistical analysis

The obtained data were subjected to statistical analysis using design expert software version 7 to evaluate the validity of the model proposed for the responses. The backward elimination method was used to select the fitting significant model terms. Means for duplicate analysis were separated using Duncan multiple range test using Statistical Product and Service Solution (IBM SPSS Statistics) version 20.0.

Results and discussion

The functional properties of breakfast cereals from blends of sorghum flour, pigeon pea and mango flour are presented in Table 2.

Table 2.

Functional properties of breakfast cereals from blends of sorghum flour, pigeon pea and mango flour

Sample	Run	Water absorption capacity (WAC) g/g	pH	Bulk density (B.D) g/ml	Foam capacity (F.C) %
1a	1	2.50gh ± 0.00	5.3hi ± 0.00	0.64f ± 0.00	5.84fgh ± 0.02
1c	2	2.40 fg ± 0.00	5.4i ± 0.07	0.62def ± 0.02	6.33fghi ± 0.01
2d	3	2.53 h ± 0.01	4.3b ± 0.14	0.55a ± 0.02	1.43ab ± 0.02
3b	4	2.65i ± 0.01	5.1f ± 0.00	0.59abcd ± 0.00	1.92ab ± 0.00
4a	5	1.50a ± 0.02	4.7d ± 0.00	0.60abcde ± 0.03	3.39bcd ± 0.00
2a	6	2.45gh ± 0.00	4.1a ± 0.07	0.56ab ± 0.00	0.94a ± 0.01
3a	7	1.50a ± 0.01	5.2fgh ± 0.00	0.60bcdef ± 0.01	5.84fgh ± 0.04
5a	8	2.40 fg ± 0.00	4.8de ± 0.00	0.59abcd ± 0.04	4.37cdef ± 0.02
5d	9	2.30ef ± 0.00	4.9e ± 0.07	0.69 g ± 0.06	3.39bcd ± 0.02
6a	10	1.95b ± 0.00	5.3ghi ± 0.07	0.61def ± 0.01	9.76 k ± 0.01
4c	11	2.10 cd ± 0.06	4.7d ± 0.00	0.63def ± 0.02	8.29hij ± 0.00
6b	12	2.00bc ± 0.04	5.4i ± 0.07	0.62def ± 0.00	5.35efgh ± 0.01
4b	13	2.30ef ± 0.02	4.7d ± 0.00	0.62def ± 0.01	5.35efgh ± 0.01
2b	14	2.20de ± 0.00	4.3b ± 0.00	0.61def ± 0.02	2.41abc ± 0.01
6c	15	2.25e ± 0.02	5.3hi ± 0.00	0.61cdef ± 0.01	6.82ghij ± 0.01
3c	16	2.30ef ± 0.02	5.2 fg ± 0.07	0.57abc ± 0.01	9.76 k ± 0.02
6d	17	1.60a ± 0.00	5.3ghi ± 0.07	0.63def ± 0.02	6.82ghij ± 0.01
3d	18	2.45gh ± 0.00	5.2 fg ± 0.07	0.61def ± 0.00	5.35efgh ± 0.04
5b	19	2.25e ± 0.01	4.9e ± 0.07	0.62def ± 0.01	7.31hij ± 0.02
5c	20	2.25e ± 0.00	4.9e ± 0.07	0.64ef ± 0.01	2.90abc ± 0.02
4d	21	2.40 fg ± 0.02	4.8de ± 0.14	0.60bcdef ± 0.01	6.33fghi ± 0.01
1d	22	2.45gh ± 0.04	5.2fgh ± 0.00	0.59abcde ± 0.00	8.78jk ± 0.00
7a	23	2.25e ± 0.03	4.5c ± 0.00	0.64ef ± 0.01	0.94a ± 0.00
2c	24	2.40 fg ± 0.05	4.2b ± 0.00	0.64ef ± 0.01	4.86defg ± 0.01
1b	25	2.40 fg ± 0.01	5.2 fg ± 0.07	0.61def ± 0.02	6.82ghijj ± 0.01
7b	26	2.45gh ± 0.03	4.5c ± 0.00	0.61cdef ± 0.00	7.31hij ± 0.01
7c	27	2.50gh ± 0.00	4.5c ± 0.00	0.59abcd ± 0.01	7.31ijj ± 0.00
7d	28	2.30ef ± 0.00	4.6c ± 0.07	0.64f ± 0.02	3.39bcd ± 0.02

Values are mean ± standard deviation of duplicate analysis. Means within a column that do not share a common letter are significantly (p < 0.05) different

Water absorption capacity (WAC)

As presented in Table 2, WAC ranged from 1.5 ± 0.01 to 2.65 ± 0.01 g/g. Mango flour had the highest influence on the WAC followed by sorghum flour and then, pigeon pea as presented in Fig. 2a. Sorghum flour also had a positive influence on WAC. This increase could be due to a high degree of starch gelatinization as reported by Serna Saldívar (2012). The hydrophilic nature of these starches that bind water could also be a reason for this high WAC values. These values were lower than the range (7.00 g/g to 8.50 g/g) reported by Mbaeyi (2005) from formulations of treated and untreated sorghum and pigeon pea breakfast cereals. They were however, higher than values obtained by Okafor and Usman (2014) for African yam beans based ready-to-eat breakfast cereals.

Fig. 2.

Response surface plot displaying the effect of mixture-process on physical and functional properties. a Water absorption capacity (WAC) b pH c bulk density d Foam Capacity (A) Sorghum flour (X1) (B) Pigeon pea flour (X2) (C) Mango flour (X3)

A combined quadratic-linear model (Eq. 4) fitted the data and showed significance (p < 0.05). There were both synergestic and antagonistic interactions between the mixture and process variables to affect the WAC. R² was 0.99 and adjusted R² was 0.91, while adequate precision value was 14.27 indicating that the model could be used to navigate the design space.

$$\mathrm{WAC}=+2.2{\mathrm{X}}_1+1.95{\mathrm{X}}_2+2.40{\mathrm{X}}_3+1.36{\mathrm{X}}_1{\mathrm{X}}_2+0.22{\mathrm{X}}_1{\mathrm{X}}_3+0.15{\mathrm{X}}_1{\mathrm{Z}}_1+0.33{\mathrm{X}}_1{\mathrm{Z}}_2-0.43{\mathrm{X}}_2{\mathrm{X}}_3+0.15{\mathrm{X}}_2{\mathrm{Z}}_1+0.030{\mathrm{X}}_2{\mathrm{Z}}_2+0.035{\mathrm{X}}_3{\mathrm{Z}}_1+0.075{\mathrm{X}}_3{\mathrm{Z}}_2-0.74{\mathrm{X}}_1{\mathrm{X}}_2{\mathrm{Z}}_1-0.64{\mathrm{X}}_1{\mathrm{X}}_2{\mathrm{Z}}_2-0.35{\mathrm{X}}_1{\mathrm{X}}_3{\mathrm{Z}}_1-0.48{\mathrm{X}}_1{\mathrm{X}}_3{\mathrm{Z}}_2-0.25{\mathrm{X}}_1{\mathrm{Z}}_1{\mathrm{Z}}_2+0.56{\mathrm{X}}_2{\mathrm{X}}_3{\mathrm{Z}}_1+0.42{\mathrm{X}}_2{\mathrm{X}}_3{\mathrm{Z}}_2-0.18{\mathrm{X}}_2{\mathrm{Z}}_1{\mathrm{Z}}_2-0.099{\mathrm{X}}_3{\mathrm{Z}}_1{\mathrm{Z}}_2+0.87{\mathrm{X}}_1{\mathrm{X}}_2{\mathrm{Z}}_1{\mathrm{Z}}_2+0.67{\mathrm{X}}_1{\mathrm{X}}_3{\mathrm{Z}}_1{\mathrm{Z}}_2+0.11{\mathrm{X}}_2{\mathrm{X}}_3{\mathrm{Z}}_1{\mathrm{Z}}_2$$ 4

pH

The pH values of the breakfast cereals presented in Table 2, ranged from a pH of 4.1 ± 0.07 to 5.4 ± 0.07. The sample with least pH value had formulation 0, 0, 1 (run 6) for sorghum, pigeon pea and mango flour, respectively. The sample with the highest value of pH was that containing 0, 1, 0 (runs 2 and 12) for sorghum flour, pigeon pea, and mango flour, respectively. Increasing substitution with pigeon pea flour increased pH, while increasing substitution with mango flour decreased pH values, as presented in Fig. 2b. These values were lower than those obtained by Usman (2012) (4.7 to 6.6) for African yam bean based ready-to-eat breakfast cereal and the range of values (4.25 and 5.87) obtained by Mbaeyi (2005) for breakfast cereals from pigeon pea and sorghum.

A combined quadratic-mean model (Eq. 5) was found significant (p < 0.05). The R² and the adjusted R² values were 0.98 and 0.97, respectively, while adequate precision value was 35.23, indicating that the model could be used to navigate the design space. Though, the process conditions had no significant (p > 0.05) effect on the pH, there were interactions between mixture variables to affect the pH change.

$$\mathrm{pH}=+5.17{\mathrm{X}}_1+5.32{\mathrm{X}}_2+4.22{\mathrm{X}}_3+0.18{\mathrm{X}}_1{\mathrm{X}}_2-0.62{\mathrm{X}}_1{\mathrm{X}}_2-0.12{\mathrm{X}}_2{\mathrm{X}}_3$$ 5

Bulk density (BD)

Bulk density values ranged from 0.55 to 0.69 g/ml with the lowest values recorded for formulations with a high proportion of mango flour. The most influencial factor was pigeon pea whose increasing inclusion in the formulation led to an increase in bulk density as presented in Fig. 2c. Increase in the inclusion of sorghum and mango flour in the formulation increased the bulk density but not as much as pigeon pea flour. The mixture interactive terms also had synergistic effects on the bulk density but this effect was insignificant (p > 0.05). This could be due to the fact that the flour particle sizes used in the formulation were passed through the same mesh size (4.2 µm mesh sieve). Raigar and Mishra (2015) has reported an increase in bulk density with an increase in particle size of Bengal Flour. Similar values (0.55 to 1.53 g/ml) were obtained by Kanu et al. (2009) for breakfast cereals from rice, sesame, and pigeon pea for adults.

A combined quadratic-linear model (Eq. 6) was proposed but the model terms were not significant (p > 0.05). The value of R² was 0.25, while the adequate precision value was 2.86. Adequate precision measures the signal to noise ratio. A ratio of 2.86 indicates an inadequate signal, implying that this model should not be used to navigate the design space. Value ratio greater than 4 could have been desirable.

$$\mathrm{B}.\mathrm{D}=+0.59{\mathrm{X}}_1+0.62{\mathrm{X}}_2+0.059{\mathrm{X}}_3+0.063{\mathrm{X}}_1{\mathrm{X}}_2+0.13{\mathrm{X}}_1{\mathrm{X}}_3+0.039{\mathrm{X}}_2{\mathrm{X}}_3$$ 6

Foam capacity (FC)

Values for foam capacity presentd in Table 2, ranged from 0.94 ± 0.01 to 9.76 ± 0.01%. The highest influencing factor on foam capacity was pigeon pea as shown in Fig. 2d and from the corresponding regression constant in Eq. 7. These values were higher than those obtained by Usman (2012) for African beans based ready to eat breakfast cereals. The lowest value of 0.94 ± 0.01% was obtained from run 6 (0, 0, and 1). High values of FC could be due to increase solubilization of proteins in pigeon pea. Foamability has been reported by Foegeding et al. (2006) to be related to the amount of solubilized proteins and the amount of polar and non-polar lipids in the sample. There were both positive and negative interactions between the mixture components and temperature and time of processing. Wang and Wang (2009) reported on the reduction of foam capacity by holding temperatures and times of processing.

A combined linear–linear model (Eq. 7) was proposed as the model terms were significant (p < 0.05). Though R² adjusted R² were just 0.33 and 0.28 respectively, adequate precision value was 6.67. This indicated that the model could be used to navigate the design space.

$$\mathrm{F}.\mathrm{C}=+5.3{\mathrm{X}}_1+7.44{\mathrm{X}}_2+2.74{\mathrm{X}}_3+1.33{\mathrm{X}}_1{\mathrm{Z}}_1-0.72{\mathrm{X}}_1{\mathrm{Z}}_2+0.50{\mathrm{X}}_2{\mathrm{Z}}_1+0.80{\mathrm{X}}_2{\mathrm{Z}}_2-0.092{\mathrm{X}}_3{\mathrm{Z}}_1+1.97{\mathrm{X}}_3{\mathrm{Z}}_2$$ 7

Antinutritional factors

The antinutrients of the breakfast cereals are presented in Table 3.

Table 3.

Anti-nutritional factors of breakfast cereals from sorghum, pigeon pea and mango flour

Sample	Run	Lectins in mg/100 g	Phytates in mg/100 g	Tannins in mg/100 g
1a	1	0.07de ± 0.01	0.52abcdef ± 0.03	0.09bcdefghi ± 0.01
1c	2	0.07de ± 0.00	0.47abcdef ± 0.01	0.08bcdefgh ± 0.00
2d	3	0.03b ± 0.00	0.39f ± 0.01	0.07bcdef ± 0.02
3b	4	0.09f ± 0.01	0.54bcdef ± 0.15	0.08bcdefg ± 0.01
4a	5	0.09f ± 0.01	0.56cdef ± 0.13	0.08bcdefg ± 0.01
2a	6	0.08ef ± 0.03	0.38abcdef ± 0.02	0.10efghij ± 0.01
3a	7	0.08ef ± 0.01	0.43abcde ± 0.03	0.08bcdefgh ± 0.01
5a	8	0.12gh ± 0.04	0.40ab ± 0.02	0.06bcd ± 0.02
5d	9	0.02a ± 0.01	0.49abcdef ± 0.09	0.11ghijk ± 0.01
6a	10	0.117gh ± 0.02	0.40ab ± 0.03	0.12hijk ± 0.04
4c	11	0.05 cd ± 0.05	0.42abc ± 0.05	0.07bcdefg ± 0.01
6b	12	0.12 h ± 0.02	0.42abcd ± 0.01	0.06bcd ± 0.00
4b	13	0.09f ± 0.01	0.44abcde ± 0.02	0.07bcdef ± 0.01
2b	14	0.09f ± 0.01	0.34 g ± 0.08	0.10efghij ± 0.00
6c	15	0.15 h ± 0.01	0.41ab ± 0.10	0.06bcd ± 0.01
3c	16	0.02a ± 0.00	0.39ab ± 0.02	0.08bcdefgh ± 0.01
6d	17	0.13 h ± 0.00	0.39a ± 0.03	0.06bc ± 0.02
3d	18	0.10f ± 0.00	0.39a ± 0.04	0.05b ± 0.01
5b	19	0.09f ± 0.02	0.45abcdef ± 0.03	0.10defghi ± 0.00
5c	20	0.11 g ± 0.01	0.57def ± 0.06	0.09cdefghi ± 0.01
4d	21	0.09f ± 0.02	0.45abcdef ± 0.09	0.10fghijk ± 0.01
1d	22	0.01a ± 0.00	0.43abcde ± 0.03	0.06bcde ± 0.02
7a	23	0.12gh ± 0.02	0.52abcdef ± 0.04	0.16 lm ± 0.02
2c	24	0.04bc ± 0.01	0.34bcdef ± 0.07	0.01a ± 0.00
1b	25	0.08ef ± 0.03	0.47abcdef ± 0.00	0.12jkl ± 0.00
7b	26	0.08ef ± 0.00	0.52abcdef ± 0.06	0.14jk ± 0.01
7c	27	0.07de ± 0.02	0.48abcdef ± 0.01	0.17 m ± 0.003
7d	28	0.06de ± 0.01	0.57ef ± 0.09	0.14ijk ± 0.01

Values are mean ± Standard Deviation of duplicate analysis. Means within a column that do not share a common letter are significantly (p < 0.05) different

Haemagglutinins (Lectins)

The values for the lectin content, ranged from 0.01 ± 0.00 to 0.15 ± 0.01 mg/100 g. Increasing the inclusion of pigeon pea increased the lectin content, while increased inclusion of mango flour reduced the lectin content. As presented in Fig. 3a and Eq. 8, the interaction between pigeon pea and the other mixture components had an antagonistic effect on the lectin content, while the interaction between mango flour and sorghum had a synergistic effect on the lectin content in the breakfast cereals. Temperature and time also had an interaction with mixture components on the haemagglutinin content. The interaction between sorghum, pigeon pea, mango flour, temperature and time reduced the haemagglutinin content, while the interaction between sorghum, pigeon pea, and mango flour without temperature and time increased the haemagglutinin content. Thompson et al. (1983) has described haemagglutinins as heat liable glycoproteins and can easily be destroyed by heat. The level of destruction in this case was depended on mixture and temperature–time combination. The two-factor interaction term and the special cubic model term in the regression equation were dropped because they made the model insignificant (p > 0.05). Higher values (0.10 to 0.29 mg/100 g) were recorded by Usman (2012) for breakfast cereals produced from maize, African yam bean, and defatted coconut.

Fig. 3.

Response surface plot displaying the effect of mixture-process variables on antinutrients. a Haemaglutinin or lectins b Phytates c Tannins (A) Sorghum flour (X1) (B) Pigeon pea flour (X2) (C) Mango flour (X3)

The model proposed to monitor the haemagglutinin content was a combined quadratic-mean model. This model was significant (p < 0.05). The R² and adjusted R² were 0.38 and 0.24, respectively. This model could be used to navigate the design space since adequate precision value was 4.78.

$$\mathrm{lectins}=0.071{\mathrm{X}}_1+0.13{\mathrm{X}}_2+0.059{\mathrm{X}}_3-0.15{\mathrm{X}}_1{\mathrm{X}}_2+0.083{\mathrm{X}}_1{\mathrm{X}}_3-0.039{\mathrm{X}}_2{\mathrm{X}}_3$$ 8

Phytates

The phytate contents presented in Table 3, ranged from 0.34 ± 0.07 to 0.57 ± 0.06 mg/100 g. Values were high in samples with a high proportion of sorghum and the concentration decreased with increased inclusion of mango flour in the formulation. The presence of vitamin C in mango flour could be the reasons for this decrease in phytate content. When vitamin C is added to foods containing phytates the two components compete for the binding of non-haem iron. The non-haem iron will form soluble complexes with vitamin C and can be readily absorbed in the small intestines. This will result to a reduction in phytates activity (Siegenberg et al. 1991). This could be the reason why the addition of mango powder in the breakfast cereals reduced the phytate content.

Figure 3b presents the response surface for the phytates content. Interaction between the mixture components had a positive influence on the response and the highest effect was from the special cubic term in the proposed model (Eq. 9). This term was dropped as the model term was not significant (p > 0.05). Mbaeyi (2005) reported lower phytates (0.01 to 0.06 mg/100 g) in breakfast cereals from sprouted and untreated sorghum and pigeon pea. Phytate level in the breakfast cereals was reduced below the maximum tolerable limits in food (250 to 500 mg/100 g).

A combined quadratic-mean model to monitor the phytate content was proposed and this model showed a level of significance (p < 0.05). The values of R² and adjusted R² were 0.53 and 0.42, respectively. The proposed model could be used to navigate the design space since adequate precision was 6.23, a value greater than 4.

$$\mathrm{Phytates}=+0.44{\mathrm{X}}_1+0.41{\mathrm{X}}_2+0.36{\mathrm{X}}_3+0.16{\mathrm{X}}_1{\mathrm{X}}_2+0.43{\mathrm{X}}_1{\mathrm{X}}_3+0.28{\mathrm{X}}_2{\mathrm{X}}_3$$ 9

Tannins

The tannin contents presented in Table 3, ranged from 0.01 ± 0.00 to 0.17 ± 0.01 mg/100 g sample. Increasing inclusion of sorghum and pigeon pea flours in the formulation increased the tannin content, while mango flour reduced the tannin content. This could be due to a dilution effect of mango flour on sorghum and pigeon pea. There was antagonism between mango flour and pigeon pea as their interactive effect reduced the tannin content. On the other hand, the interaction between sorghum and the other components had a synergy as an interaction between them increased the tannin content (Fig. 3c). The interaction between the mixture and process variables and most especially, temperature also affected the tannin content, negatively. Higher values (34.67 to 76.62 mg/100 g) were reported by (Edima-Nyah et al 2020) for breakfast cereals from yellow maize, soybeans and banana. Low values in the formulation could imply a high potential of this product to increase protein digestibility as tannins interact with proteins to reduce digestibility (Watrelot and Norton 2020). Tannin level was reduced below the maximum tolerable limits in food (100–400 mg/day).

A combined quadratic-mean model (Eq. 10) to monitor tannin content was found significant (p < 0.05). R² and adjusted R² were 0.53 and 0.42, respectively, while adequate precision was 5.88. This showed the validity of this model to predict values of tannin content for other formulations which were not included in the design.

$$\mathrm{Tannin}=+0.08X_1+0.07X_2+0.02X_1{X}_2+0.28X_1{X}_3-0.003X_2{X}_3$$ 10

Conclusion

The results of this study revealed that the physical and functional properties as well as  the antinutrients of the breakfast cereals does not only depend on the mixture components used in the formulation but also, on the different processing conditions given to the breakfast cereals. For the water absorption capacity, bulk density, and foam capacity, there was no clear trend to describe the effect of mixture components and process variables. Experimental runs with the same mixture formulation, processed at different temperature–time combinations had different values for these quality attributes. On the other hand, different formulations processed at the same temperature–time combination also had different values of these quality attributes. For the pH, variation in temperature and the duration of processing had no significant (p > 0.05) changes in pH. The pH values varied as a function of the mixture formulation.

For the antinutrients, increasing the temperature–time combination reduced the antinutrients with the degree of reduction dependent on the mixture combination of sorghum, pigeon pea, and mango flours in the samples. The same formulation treated at different processing conditions had different values for the antinutrients, while different formulations that were processed using the same processing conditions also had different values for these antinutrients. This can also be justified through the various cross-interactions in the modeling equations proposed to navigate the design spaces. Both the mixture and process variables interacted with each other to affect these properties. Hence, the mixture-process approach can be a useful tool to understanding how food formulation and processing can simultaneously affect the overall quality.

Author contribution

OGI contributed in research conception, supervised the research work, and revised the manuscript prior to submission. AMM designed the study, analyzed and interpreted the data and drafted the manuscript.

Funding

The German Academic Exchange Service (DAAD).

Availability of data and material

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Code availability

Not Applicable.

Declarations

Conflict of interest

The authors declare that they have no competing interests.

Ethics approval

Not applicable.

Consent to participate

Not applicable.