Functional properties of foods. Database and model prediction

Functional Properties of Foods. Database and Model Prediction
Nikolaos A. Oikonomou a , Magda Krokida b
a Department of Chemical Engineering, National Technical University of Athens, Athens, Greece
(nikosoik@central.ntua.gr)
b Department of Chemical Engineering, National Technical University of Athens, Athens, Greece
(mkrok@chemeng.ntua.gr)
ABSTRACT
A food system is characterized by several physicochemical properties. Some of those physicochemical
properties affecting the food system during preparation, processing, storage and consumption are defined
functional properties. A wide range of functional properties are delivered mainly by proteins, due to their
structural characteristics and amphiphilic nature. Additionally, protein functionality is affected by extrinsic
factors such as temperature, pH, ionic strength, and interaction with other components. The novelty of the
present study was the collection of experiment data in a database from the available scientific journals,
regarding the values of water absorption index, water solubility index, protein dispersibility index, nitrogen
solubility index, gluten index and wet gluten and secondly the investigation of statistical models for optimum
correlation of the retrieved data. The published data was then organized based on the experimental factors.
For the water absorption index and water solubility the main experimental factors were the leading extrusion
parameters such as die temperature, screw speed, feed moisture content. The extrinsic factors concerning the
protein dispersibility index and nitrogen solubility index was the pH, the amount of heat treatment, the total
time of treatment and the level of enzymatic hydrolysis. Finally, for gluten index and wet gluten the
correlated factors were the wheat genotype, fertilization level, crop location, and the exist subunits of
genotype. Furthermore, mathematical models were developed to describe the relationship between functional
variables and the main experimental factors. The statistical models fit the experimental data as closely as the
experimental variance (literature noise) would allow. The estimation of parameters of power low regression
models was conducted by the Levenberg–Marquardt algorithm and the regression diagnostic shows a good fit
of datasets to functional properties. The investigation of food functional properties is of great importance for
food industry as they affect the quality and acceptance of the final product.
Keywords: Extrusion; Cereals; Soybean products; Database
INTRODUCTION
Functionality is a term used to describe those characteristics of a food that have been correlated to quality
attributes identified by the human senses. Proteins play important roles in the functional properties of many
foods, and thus contribute to the quality and sensory attributes of many food products. Protein functional
properties have traditionally been defined as physical or chemical properties of proteins that affect their
behaviour in food systems during preparation, processing, storage, and consumption [1,2,3,4,5]. The novelty
of the present study was firstly the investigation and proper classification of the effect of various parameters
on six typical functional properties such as water absorption index (WAI), water solubility index (WSI),
protein dispersibility index (PDI), nitrogen solubility index (NSI), gluten index (GI) and wet gluten (WG) of
several food products and secondly the investigation of statistical models for optimum correlation based on
the retrieved data.
MATERIALS & METHODS
For model purposes an extensive literature search was contacted through the most popular food engineering
and food science journals of recent years. The compiled data, approximately 10,000 values, of the previous
functional properties were organized into a database developed in Microsoft Excel 2003.
Extrusion is a technological process, commonly used in the field of the human and animal feed industry,
applied successively on a broad spectrum of commercially manufactured products. It is observed that WAI
and WSI are related to the extrusion process variables such as extruder type, die temperature, feed moisture

content, feed rate, screw speed, screw configuration. Other affecting factors may include raw material
formulation, pre-processing treatments, initial particle size of milled materials, and the milling procedure. A
preliminary statistical investigation shows that we have a strong relationship between WAI or WSI and 4
independent variables such as die temperature, feed moisture content of food product in wet base %, screw
speed of extruder and blend level% mainly for starchy and proteinaceous extruded food products. It is found
from the modelling exercise that using a model, which considers power law dependency of all independent
variables, provides the best performance in the model:
WAI or WSI
a
T
T o
where WAI: water absorption index (dimensionless), WSI: water solubility index (%), T: die temperature of
extruder ( o C), X: feed moisture content of food product in wet base %, S: screw speed of extruder (rpm), M:
mixture of blend %, variables with subscripts: reference steady average values of independent variables,
a,b,c,d,e: dimensionless adjustment parameters.
Similarly, concerning the property of PDI the intended model is:
b
PDI a
T
T
o
t
t
where PDI: protein dispersibility index (%), T: is the temperature of the product which was exposed during
preparation ( o C), t: is the corresponding residence time (10 3 *s), variables with subscripts: reference steady
average values of independent variables, a,b,c: dimensionless adjustment parameters.
The parameter estimation was performed by the Levenberg–Marquardt (LM) algorithm. The LM algorithm is
an iterative technique that locates the minimum of a multivariate function that is expressed as the sum of
squares of nonlinear real-valued functions. The software package Stargraphics Centurion v. XV (Manugistics
Inc. Rockville, MD, USA) was used for the nonlinear regression analysis.
RESULTS & DISCUSSION
b c
X
X
o
c
o
Table 1 presents, in a compact form, the main information concerning the examinee properties. The
minimum, maximum, average values and the standard deviation for each of six properties are presented in the
first four columns. The main food systems and the factors which altered the value of properties are presented
in the fifth and sixth columns respectively. Finally, the total number of experimental data which was
retrieved is presented in the final column.
Table 1. Data compiled from literature about examinee functional properties used in statistical analysis
Property MIN MAX AVG SD a Food System Main Factor N b
WAI 0.3 14.4 4.8 1.9 Corn, Wheat,
Rice Flours
WSI 0.2 94.8 22.4 15.4 Corn, Wheat,
Rice Flours
PDI 1.3 100.0 42.0 42.0 Soybean
Products
NSI 2.5 94.0 40.7 19.4 Soybean
Products
Extrusion parameters,
blends
Extrusion parameters,
blends
pH, Heat, Enzymatic
Hydrolysis
pH, Heat, Enzymatic
Hydrolysis
GI 1.0 100.0 71.0 25.1 Wheat Products Genotype, Fertilization,
Location, Subunits
WG 0.2 60.9 29.6 9.2 Wheat Products Genotype, Fertilization,
Location, Subunits
a Standard Deviation; b Number of retrieved data
S
S o
d e
M
M
o
Due to the large number of replicates, a fundamental prerequisite for the least squares fitting of the models to
the corresponding data sets is equal variance of the different observations. The results of these tests show that
the variance was almost steady. The results of the nonlinear regression analysis of fitting the equation 1 to the
experimental points are shown in Table 2. In this table the standard experimental error and the standard
deviation between experimental and calculated values are also presented. In most cases the values of the
1268
1083
1067
780
3400
2354
(1)
(2)

standard experimental error are slightly smaller (or slightly bigger in the cases of corn starch:WPC and rice
starch:SPI) than the values of the standard deviation between experimental and calculated values indicating
that the model (Eqn. 1) is satisfactory in predicting the WAI of products. In the cases of wheat, wheat:DDG
and potato:DDG the difference in the values was slightly bigger than that in the above cases showing that
there is an adequate fit to the equation 1.
Table 2. Standard experimental error (Se), standard deviation between experimental and calculated values (Sr) and the
parameters of the model for the WAI and WSI prediction respectively
Property Food System Se Sr a b c d e
WAI Barley cv. 0.60 1.29 4.62 -0.69 0.44 0.86 0
Corn 0.42 0.69 5.23 0.07 0.16 0.35 0
Oat 0.24 0.55 2.26 -0.68 -0.14 -0.06 0
Rice cv. 1.12 1.21 5.97 0.09 0.60 0.01 0
Wheat 0.26 1.88 4.63 -1.07 -0.46 0.46 0
Beans & Chickpeas cv. 0.42 1.51 4.07 0.11 0.49 0.05 0
Starch 1.08 3.06 7.54 1.23 0.91 -0.06 0
Blends
Corn : DDG a 0.40 0.74 0.04 0.11 -0.06 -7.46 -0.17
Corn : Lentil 0.28 0.53 4.39 0.28 0.15 1.00 -0.00
Rice : DDG 0.41 1.21 7.54 0.17 0.32 1.00 -0.08
Wheat : DDG 0.40 1.78 4.07 -0.60 -0.13 0.34 -0.12
Corn starch : WPC b 1.55 1.21 5.37 0.30 0.54 0.14 -0.08
Rice starch : SPI c 1.02 0.51 19.40 0.15 -0.33 1.00 -0.29
Potato : DDG 0.53 2.07 9.40 0.03 0.19 1.00 -0.12
WSI Corn 5.96 11.99 19.76 -0.16 -0.34 -0.20 0
Oat 0.18 1.20 6.24 -0.08 -0.51 -0.07 0
Rice cv. 2.53 18.70 23.17 1.36 0.10 -0.04 0
Wheat 3.34 9.96 10.42 2.57 0.02 1.45 0
Beans & Chickpeas cv. 2.96 16.58 33.98 -1.48 1.12 0.26 0
Starch 7.91 27.30 27.80 0.70 -0.41 -1.09 0
Blends
Corn : Lentil 6.23 7.57 12.76 0.52 -0.72 1.00 -0.11
Corn starch : WPC d 10.00 15.48 27.18 -0.20 0.02 0.60 -0.11
a Dried Distillers Grains from corn & wheat; b Whey protein concentrate; c Soy protein isolate; d Whey protein concentrate; cv: cultivar
The plot, which relate the WAI (left figure) with die temperature of extruded products at X=15 % and S=180
rpm are presented in figure 1. The various dots shapes represent the experimental values of materials, while
the lines are calculated model values. Increase in die temperature does not have a consistent effect on
experimental and predicted WAI for all raw materials examined. In the case of WSI (right figure) at X=15 %
and S=200 rpm we conclude that there is not a general tendency for the various extruded materials with
respect to the die temperature. Figure 2 presents typical chart of the standard experimental error (Se) and lack
of fit (Sr) as a function of the number of parameters for WAI model in the case of rice.
The confidence intervals (=0.05) for parameters of food products (data not shown), for WAI and WSI show
that all the calculated parameters are required in the equation 1. The products such as wheat, beans,
wheat:DDG with two or more parameters having 0 within the range of their confidence intervals are also
those products where the differences in the values of Se and Sr was great. In these cases the number of
parameters for accurate prediction of the model may be smaller.
The values of Se, Sr and parameters for PDI (Eqn. 2), obtained by curve fitting using lack of fit regression
diagnostic with Levenberg–Marquardt algorithm are presented in Table 3, showing that the performance of
the proposed regression model, was satisfactory for the case of beans and canola meal. The results presented
in Table 3 suggest that, for soy flour and soybean components, a power low nonlinear relationship between
PDI and the two predictor variables (exposing temperature, corresponding residence time) is moderate; a

Standard Deviation
WAI .
different relationship concerning more predictor variables is more appropriate. In general, the agreement
between the experimental data and the estimated values is reasonably good.
10
Χ = 20 % (wb) S = 180 (rpm)
9
Starch
8
7
Rice
6
5
Corn
Beans
4
3
Barley
Wheat
2
1
Oat
0
80 110 140 170 200 230 260
Die Temperature ( o C)
WSI % .
50
Χ = 15 % (wb) S = 200 (rpm)
45
40
35
Beans
Rice
30
Starch
25
20
15
10
5
0
Wheat
Corn
Oat
80 110 140 170 200 230 260
Die Temperature ( o C)
Figure 1. Effect of die temperature ( o C) on WAI (left) and WSI (right) for barley (▲), corn (●), oat (■), rice (x), wheat
(◊), beans (○) and starch (□). Lines are calculated model values using parameters given in Table 2
16
12
8
Lack of fit
4
0
Experimental
error
0 1 2 3 4 5
Number of Parameters
Figure 2. The standard experimental error (Se) and lack of fit (Sr) as a
function of the number of parameters for WAI model; case of rice
Table 3. Standard experimental error (Se), standard deviation between experimental and
calculated values (Sr) and the parameters of the model for the PDI prediction
Food System Se Sr a b c
Beans (P. vulgaris L.) meal 2.83 3.23 16.58 -0.98 -0.05
Canola meal 1.55 1.98 21.57 -2.08 0.11
Soy flour 3.34 14.45 16.22 -3.26 -0.10
Soybean 0.62 3.18 27.08 -0.01 -0.06
The variety of experimental PDI values ranges from 6.2 to 96.8 while, PDI predicted vary from 6.6 to 46.8
for all products. The smaller range of predicted values compared to experimental values may be explained by
the low ability of the model to predict accurate values mainly at high values of independent variables. The
scatter plot, which relates the PDI with residence time of products at three different temperatures for beans

100
110
120
130
140
PDI %
PDI %
PDI %
meal is presented in figure 3 (left). Incremental increase in residence time does not have a consistent effect
on experimental and predicted values of PDI for all examined products. Figure 3 (right) presents the scatter
plot of PDI versus temperature at three different residence times for beans meal. In general, an increase in
temperature leads to a decrease of PDI value, for all products. A possible explanation for this situation is that
when the protein is heated rapidly, denatures. The quaternary or tertiary structure is destroyed and the protein
molecules break up into several subunits, of which some slowly form a soluble and later on insoluble
aggregate, whereas the rest remains in solution. Simultaneously other factors such as pH, salt content and
additives concentration can affect the protein solubility; however we don't take them into consideration for
practical reasons.
25
23
20
18
15
13
10
0 1 2 3 4 5 6 7
t x10^3 (s)
T=102
T=113
T=136
Figure 3. The graphical correlation between experimental (dots) and calculated (lines) values of PDI versus residence
time (left) and temperature (right) for beans meal
The effect of temperature and residence time on predicted PDI values for the beans meal is presented in
figure 4. The minimum and maximum values of the independent variables are based on the corresponding
experimental values. At high temperatures, the PDI of all products decreased considerably with increasing
residence time, while at high residence times, the decrease in temperature resulted in only a slight decrease in
PDI (Fig. 3).
25
23
20
18
15
13
10
100 105 110 115 120 125 130 135 140
T ( o C)
t=0.09
t=3.65
t=7.2
24
22
20
18
16
14
12
10
0.09
2 468
t x10^3
(s)
CONCLUSION
T ( o C)
Figure 4. Contour plots showing the effect of temperature and
residence time on calculated PDI values for beans meal
The present study proposes a mathematical model that investigates the effects of the main extrusion variables
on the WAI and WSI properties for some food products. The model is fitted to literature data and the model
parameters were estimated for every category of food products. The method used for curve fitting was a
nonlinear regression that was based on the Levenberg–Marquardt algorithm. In most cases, the modelling
showed that the power law equation is fitted satisfactory to the available experimental values. Furthermore,
modelling of a solubility index (PDI) for food products which contain protein or starch showed that power

low equations is fitted adequately to the available experimental values, which allows theoretical prediction so
that important information can be withdrawn without experimental procedures.
REFERENCES
[1] Maroulis, Z.B.; Saravacos, G.D. 2007. Food Plant Economics. CRC Press: Boca Raton, pp.70-99.
[2] Maroulis, Z.B.; Saravacos, G.D. 2003. Food Process Design. Marcel Dekker: USA, pp. 2-13.
[3] Oikonomou N.A. & Krokida M. 2011. Literature Data Compilation of WAI and WSI of Extrudate Food Products.
International Journal of Food Properties, 14(1), 199-240.
[4] Oikonomou N.A. & Krokida M. 2011. Water Absorption Index and Water Solubility Index Prediction for Extruded
Food Products. International Journal of Food Properties, In Press.
[5] Oikonomou N.A. & Krokida M. 2011. Protein Dispersibility Index: Data Compilation from Published Research for
1065 Foods Classified into Seven Product Categories. International Journal of Food Science and Technology,
Submitted.