Modelling gelation and cutting times using light backscatter parameters at different levels of inulin, protein and calcium

LWT - Food Science and Technology 91 (2018) 505–510

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Modelling gelation and cutting times using light backscatter parameters at different levels of inulin, protein and calcium

T

O. Arangoa,b,∗, A.J. Trujilloa, M. Castilloa a

Centre d’Innovació, Recerca i Transferència en Tecnologia dels Aliments (CIRTTA), XaRTA, TECNIO-CERPTA, Departament de Ciència Animal i dels Aliments, Facultat de Veterinària, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain b Facultad de Ingeniería Agroindustrial, Universidad de Nariño, Ciudad Universitaria Torobajo, Pasto, Nariño, Colombia

A R T I C L E I N F O

A B S T R A C T

Keywords: Cutting time Prediction models NIR light backscatter Optical sensor Inulin

Optical sensors based on light backscatter are being used by important cheese industries worldwide for predicting cutting time, but predictions can be affected by factors influencing coagulation such as milk composition or ingredients addition. Enzymatic coagulation of reconstituted milk with inulin as a fat substitute was monitored in parallel using a rheometer and an optical sensor, in order to obtain and validate models for predicting rheological gelation time (tG′1) and cutting time (tG′30). Prediction models were fitted using data from a factorial design with three factors: inulin (2, 5, 8 g/100 g), protein (3, 4, 5 g/100 g) and calcium (100, 200 mg/L) concentrations, and afterwards were validated with data from a central composite design experiment, where the same factors, but with different levels were evaluated. The addition of inulin to milk decrease tG′1 and tG′30 due to the inulin water retention capability. The increase in protein and calcium concentrations also produced a decrease in the curd firming phase. Optical parameters were sensitive enough to account variations in milk composition or ingredients addition and allowed obtaining and validating good prediction models for gelation and cutting times.

1. Introduction

nutritive products such as those enriched with prebiotics (Balthazar et al., 2015). Prebiotics are recognized as important food ingredients to keep and improve the human health (Rolim, 2015; Saad, Delattre, Urdaci, Schmitter, & Bressollier, 2013). The worldwide market demand for prebiotics is estimated to reach $4.5 billion in 2018, and it is dominated by inulin, accounting for over 40% overall in 2011 (Transparency Market Research, 2015). Inulin can be used as a thickener and a fat substitute in low-fat foods because, in the presence of water, inulin forms microcrystals which interact with each other, forming small aggregates that can occlude a great amount of water and create a particulate gel (Arcia, Navarro, Costell, & Tarrega, 2011). For previous reason, inulin has been evaluated as a fat substitute in several types of cheeses (Alnemr, Abd El–Razek, Hasan, & Massoud, 2013; Cardarelli, Buriti, de Castro, & Saad, 2008; Juan, Zamora, Quintana, Guamis, & Trujillo, 2013; Salvatore, Pes, Mazzarello, & Pirisi, 2014). In cheese industry, addition of calcium is a common practice, in order to compensate the migration of calcium to the casein micelle during milk pasteurization and also to accelerate coagulation reaction and to improve the texture and cheese yield (Hallén, Lundén, Tyrisevä, Westerlind, & Andrén, 2010; Landfeld, Novotna, & Houska, 2002). Gelation time and cutting time predictions based on near infrared

In cheese manufacture, a simple and non-destructive technology for determining the right moment to cut the curd has been looked for a long time, with the aim of avoiding the use of subjective methods and to achieve a complete automatization of the process. Payne, Madangopal, Hicks, and Shearer (1990) developed an inline sensor (CoAguLite, Reflectronics Inc., Lexington, Ky.) based on direct light backscatter measurements. That sensor has been demonstrated to be one of the most proper inline, nondestructive methods for monitoring milk coagulation and predicting cutting time and nowadays it is used in important cheese industries, mainly in the United States. Payne, Hicks, and Shen (1993) predicted cutting time multiplying the time from enzyme addition to the inflection point of the near infrared light backscatter ratio profile by a coefficient selected to replicate the cheese maker's judgment of the cutting time. Previous predicting model is accurate only if protein is constant, but when protein concentration vary significantly, it is necessary to include a protein term in the model with the aim of improving predictions (Castillo, Payne, Hicks, Laencina, & López, 2003). Nowadays, dairy industry is concerned about developing high

∗

Corresponding author. Universidad de Nariño, calle 18 carrera 50 Pasto, Nariño, Colombia. E-mail address: [email protected] (O. Arango).

https://doi.org/10.1016/j.lwt.2018.01.081 Received 26 September 2017; Received in revised form 22 January 2018; Accepted 29 January 2018 Available online 03 February 2018 0023-6438/ © 2018 Elsevier Ltd. All rights reserved.

LWT - Food Science and Technology 91 (2018) 505–510

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corresponding amount of powdered milk was dissolved in distilled water at a temperature of ∼43 °C by using a heating plate with stirring and then inulin was added slowly in order to avoid agglomeration. The required quantity of cream was weighed in a beaker and added to the milk by making a spill of it in the beaker in two stages. The reconstituted milk sample was left in stirring for one hour and then it was kept in a dark place for another one hour to achieve a complete rehydration of the casein micelles. For each trial, 300 mL of milk were reconstituted, after which the required concentration of calcium from a solution prepared using dehydrate calcium chloride (CaCl2 2H2O; Panreac Química S.A., Montcada i Reixac, Barcelona, Spain) was added. The milk was left in a thermostatic bath until it reached the coagulation temperature of 32 °C. In that moment 100 μL/L of chymosin (CHY-MAX extra; EC 3.4.23.4, isozyme B, 600 IMCU/mL, Chr. Hansen Inc.) was added. It was vigorously stirred with a spatula and then, two aliquots of ∼80 mL were quickly placed in the optical sensor vessels and a third aliquot of ∼40 mL was placed in the rheometer. The contents of protein and fat of reconstituted milk and cream were determined through Dumas (IDF, 2002) and Gerber (AOAC, 2000) methods, respectively.

(NIR) light backscatter ratio, can be affected by factors that influence milk coagulation such as variation in protein concentration, added calcium or the use of ingredients like inulin as a fat replacer or as a fiber source. In previous research conducted by our group, models for predicting gelation and cutting times using optical parameters have been developed (Castillo, Payne, Hicks, & López, 2000; Castillo et al., 2003). But previous models might require validation, adaptation, or even rejection before they can be used by the industry, when inulin is added to the milk as a new raw material. For previous reasons, the aim of this work was to evaluate the effect of inulin, protein and calcium on modelling gelation and cutting times using light backscatter parameters. 2. Materials and methods 2.1. Experimental design and statistical analysis Two experiments were carried out in this work to obtain and validate models for predicting the rheological gelation time (tG′1) and the rheological cutting time (tG′30) of enzymatic milk gels added with inulin. Prediction models were obtained using a complete randomized factorial design replicated three times and with three factors: inulin (2, 5 and 8 g/100 g), protein (3, 4, and 5 g/100 g) and calcium (100 and 200 mg/L, equivalent to 0.90 and 1.80 mmol/L). The effect of previous factors on the rate of aggregation and curd firming reactions during milk coagulation were monitored in parallel using oscillatory rheology and a NIR light backscatter optical sensor. Optical parameters derived from the NIR light backscatter ratio were used to develop the models. In order to validate the prediction algorithms, a second and independent experiment was carried out. It consisted of a central composite design (CCD) without replications, where the same factors of previous experiment, but with different levels were evaluated (Table 1). The CCD consisted of a 2k factorial (k = 3), with 2k axial points and 4 central point tests, for a total of 18 tests. All data were processed and analyzed using “Statistical Analysis System” (SAS version 2009, SAS Institute Inc., Cary, NC, USA). The analysis of variance (ANOVA) was performed using the General linear model (GLM) procedure. The maximum R2 procedure was utilized to obtain the best one, two- and three-parameter models for predicting the rheological gelation time (tG′1) and the rheological cutting time (tG′30) of enzymatic milk gels added with inulin. Complementary regression analysis to obtain and select simpler and more effective models was performed using either the “GLM” (linear regression) or the “NLIN” (non-linear regression) procedures.

2.3. Monitoring NIR light backscatter NIR light backscatter during milk coagulation was monitored using a fibre optic sensor (Coagulab, Reflectronics, Inc., Lexington, KY, USA). The apparatus has two vats in order to monitoring two samples simultaneously and to make precise comparisons feasible. A detailed description of the equipment was presented by Tabayehnejad et al. (2012). Sample temperature in the two milk sample vats was controlled using a circulating water bath (Lauda RM 20, Brinkmann Instrument Inc., Westbury, NY, USA) and was measured with a precision thermistor thermometer. A fiber optic unit (Model 5, Reflectronics, Inc., Lexington, KY) was used to measure near infrared light backscatter at 880 nm. The fiber optic units directed near infrared light from a LED (Model L2791, Hamamatsu Corp., Bridgewater, NJ, USA) into the milk sample and returned the backscattered light to a detector (Model TSL250, TAOS, Plano, TX). A light backscatter ratio (R) was calculated starting immediately after enzyme addition, by dividing the voltage output from the sensor by the average of the first 10 voltage data points collected, according to the procedure described by Castillo et al. (2000). Using an algorithm, the first (R′) and second (R´´) derivatives of the light backscatter ratio (R) were obtained, as described by Castillo, Lucey, and Payne (2006) and two optical time parameters (min), which were used as predictors in the models, were defined by the maxima and minima of the derivatives as follows: tmax was the elapsed time from enzyme addition to the first maximum of the first derivative and t2min was the time to the minimum of the second derivative.

2.2. Milk sample preparation and testing procedures

2.4. Monitoring rheological parameters

Reconstituted milk prepared from low heat skim milk powder with 34 g/100 g protein and 0.9 g/100 g fat (Chr. Hansen, Barcelona, Spain) was used to reduce the variability inherent to the composition of fresh milk. Mass balances were carried out to adjust the proportions of protein and inulin (Frutafit® Tex, Brenntag Química S.A., Barcelona, Spain), according to the experimental design. Cream extracted from fresh milk was utilized to obtain a constant proportion of 1.6 g/100 g fat. The method for milk reconstitution was adapted from IDF Standard 157: 2007 and Tabayehnejad, Castillo, and Payne (2012). The

The coagulation process was monitored using small amplitude oscillatory rheology (SAOR) with a ThermoHaake rheometer RS1 (Thermo-Haake GmbH, Karlsruhe, Germany) equipped with a concentric-cylinders sensor according to the procedure describe by Arango, Castillo, and Trujillo (2013). Rheological gelation time (tG′1) and rheological cutting time (tG′30) were defined as the time when the gels had a G´ = 1 and G´ = 30 Pa, respectively (Everard et al., 2008; Hussain, Bell, & Grandison, 2011; Jaros, Seitler, & Rohm, 2008). In order to estimate the firming time, the parameter tF30 was used, which referred to the elapsed time between G´ = 1 Pa and G´ = 30 Pa.

Table 1 Central composite design used to validate the prediction models. Factors

Inulin (g/100 g) Protein (g/100 g) Calcium (mg/L)

Levels

Axial points

Low

Medium

High

1.5 3.0 100

3.0 3.3 150

4.5 3.6 200

0.0 2.7 50

3. Results and discussion Final means and standard deviations for protein concentration obtained in experimental milk samples for each one of the target levels fixed in the experimental design (i.e., 3, 4, and 5 g/100 g) were 2.95 g/ 100 g ± 0.05, 3.95 g/100 g ± 0.06 and 4.92 g/100 g ± 0.05,

6.0 3.9 250

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Table 2 Analysis of variance and F statistics of the effect of inulin, protein, calcium and their interactions on the optical and rheological parameters. Model

Variation source

R2

Parameters

F ∗∗∗

0.852 0.856 0.880 0.940 0.948

tmax t2min tG′1 tG′30 tF30

In (DF = 2)

P (DF = 2)

Ca (DF = 1)

InxP (DF = 4)

InxCa (DF = 2)

PxCa (DF = 2)

F

F

F

F

F

F

∗∗∗

17.7 18.4∗∗∗ 22.6∗∗∗ 48.2∗∗∗ 55.7∗∗∗

∗∗∗

29.3 35.0∗∗∗ 54.9∗∗∗ 31.8∗∗∗ 20.3∗∗∗

∗∗∗

39.3 30.9∗∗∗ 7.03∗ 184.5∗∗∗ 254.6∗∗∗

61.5 70.7∗∗∗ 102.9∗∗∗ 79.9∗∗∗ 58.7∗∗∗

ns

1.89 2.20ns 2.27ns 7.27∗∗ 8.57∗∗∗

11.1∗∗∗ 12.7∗∗∗ 23.5∗∗∗ 33.4∗∗∗ 31.5∗∗∗

ns

0.58 1.16ns 5.41∗ 9.28∗∗ 8.95∗∗

N = 54; In, inulin; P, protein; Ca, calcium; InxP, inulin-protein interaction; InxCa, inulin-calcium interaction; PxCa, protein-calcium interaction; R2, coefficient of determination; F, ANOVA F-statistic; DF, degree of freedom; ∗P < 0.05, ∗∗P < 0.001, ∗∗∗P < 0.0001; ns, not significant. Dependent variables explained in the text.

increase in number and strength of the bonds between the coagulated casein micelles (Anema, 2008). Least-square means of the rheological parameters tG′1, tG′30 and tF30 decreased significantly with the addition of calcium chloride, which means that the firming phase was faster as a result of the increase in CaCl2 concentration. The effect of calcium on milk gels firming has been attributed to the reduction in the global ζ potential of the casein micelles and, consequently, the decrease in the electrostatic repulsion and the increase of bounds among micelles (Choi, Horne, & Lucey, 2007; Udabage, McKinnon, & Augustin, 2001).

respectively, while the fat content was 1.57 g/100 g ± 0.09. For the calcium level of 100 mg/L, the average final pH in samples was 6.64 ± 0.004, while for the level of 200 mg/L it was 6.61 ± 0.004. An analysis of variance (ANOVA) was conducted to determine the main sources of variation in the dependent variables (Table 2) and least square means of the studied parameters for inulin, protein and calcium main treatments are presented in Table 3. It was observed that, with the lowest levels of the factors (3 g/100 g inulin, 3 g/100 g protein and 100 mg/L calcium), coagulations were abnormally, too long compared with other tests, so the analysis of variance was carried out considering all data, but for model calibration it was necessary to removed that extreme data (3 data points). Significant effects of the inulin, protein and calcium concentrations were observed on all optical and rheological variables. The effect of PxCa interaction was also significant on all the evaluated response parameters, while the InxP and InxCa interactions showed significant effects especially on the rheological firming indices. The addition of inulin to milk, especially when moving from a level of 2–5 g/100 g, produced a significant decrease in the gelation time (tG′1), the rheological cutting time (tG′30) and in the firming time (tF30). This could be attributed to the inulin water retention capability, which would produce a relative increase in the solutes concentration and thereby a greater interaction between the casein micelles. The gelation time significantly decreased when increasing the protein level from 3 to 4 g/100 g, however it remained constant when going from 4 to 5 g/100 g, according with what was observed by Guinee et al. (1997). Rheological cutting time at 30 Pa (tG′30) as well as the curd firming time (tF30) significantly decreased when protein increased. At a protein concentration of 3 g/100 g, tF30 was 28.1 min, but with 5 g/100 g tF30 was just 6.8 min. Since the casein micelle is the structure responsible for the formation of the three-dimensional network in milk gels, it is expected that the increase in its concentration may cause an increase in the rates of aggregation and firming as a result of the increment in collisions and contact points per unit of area, and the

3.1. Obtaining the prediction models Using maximum R2 and NLIN procedures of SAS the best one, two and three parameters models for prediction of the rheologically-determined gelation (tG′1) and cutting times (tG′30) were obtained. They are presented in Table 4. The best predictor for the rheological gelation time (tG′1) was the parameter t2min, even though, when this was used as the single explanatory variable, the obtained model (model 1 in Table 4) had an R2 of only 0.626. This was probably due to that the variation in t2min is not sufficient to account for the effect of all the experimental factors over the gelation time. The above was proved when analyzing the best twovariable model found (model 2 in Table 4), which included the effect of the protein. Such effect resulted in a remarkable improvement in the prediction, by reducing the SEP value to less than half (0.58 min) and increasing the R2 value to 0.871. The incorporation of InxCa interaction in the previous algorithm allowed to obtain the best three-parameter model, with R2 and SEP values of 0.92 min and 0.53 min respectively, reflecting the effect of these two factors on the hydrolysis and Table 4 Algorithms for prediction of rheological gelation time (tG′1) and rheological cutting time (tG′30) in milk gels with different levels of inulin, protein and added calcium. Model

Table 3 Effect of inulin, protein and calcium on optical and rheological coagulation parameters1,2.

1 2

tG′1 = β1t2min tG′1∗∗∗ = β1t2min(1 + γP)

3

tG′1∗∗∗ = β1t2min(1 + γP) + β2InxCa

Main effects Inulin (g/100 g)

tmax t2min tG′1 tG′30 tF30

∗∗∗

Calcium (mg CaCl2/L)

Protein (g/100 g)

2

5

8

3

4

5

100

200

4

tG′30∗∗∗ = β1t2min(1 + γP)

10.4a 12.0a 15.3a 34.3a 19.0a

9.23b 10.6b 13.0b 27.3b 14.3b

8.66c 10.1c 11.8c 24.9b 13.1b

8.38a 9.93a 14.1a 42.3a 28.1a

9.50b 11.0b 13.0b 24.4b 11.4b

10.4c 11.8c 13.0b 19.8c 6.8c

10.1a 11.7a 14.8a 33.3a 18.6a

8.69b 10.1b 12.0b 24.3b 12.3b

5

tG′30∗∗∗ = β1t2min(1 + γP) + β2tmax

6

tG′30∗∗∗ = β1t2min(1 + γ1P + γ2P2)

Coefficients

R2

SEP (min)

β1 = 1.192 β1 = 1.7271 γ = −0.0737 β1 = 1.782 γ = −0.1331 β2 = −0.00046 β1 = 6.7429 γ = −0.1546 β1 = −6.303 γ = 11.80 β2 = −0.9458 β1 = 15.584 γ1 = −0.3573 γ2 = −0.0358

0.626 0.871

1.23 0.58

0.919

0.53

0.781

3.50

0.792

3.43

0.939

1.93

1

Least squares means (LSM) with the same letters were not significantly different (P < 0.05), comparisons are only for each factor; number of replications = 3; number of observations, N = 54. 2Dependent variables explained in the text.

N = 51. β1, β2, γ, γ1, γ2, coefficients of regression. R2, coefficient of determination (corrected for means). SEP, standard error of prediction. ∗∗∗ P < 0.0001.

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aggregation times. However the improvement of the model is quite light and the new algorithm is not practical given the number of coefficients included. Castillo et al. (2006) using an optical method similar to that used in this study, found that gelation time (tgel) determined by oscillatory rheometry in Cottage cheese, was predicted by the equation tgel = β1 t2min (R2 = 0.988, SEP = 11.30 min). Previous model was obtained for a constant protein level while, in this study, 3 concentrations of protein were used, so it was necessary to include a protein parameter in the model with the aim of improving the goodness of fit. Variations in the protein content of the milk samples had significant effect on the hydrolysis and micellar aggregation phases; this will be discussed in deep in an independent paper derived from this research. For prediction of cutting time at 30 Pa, it was not possible to obtain a single parameter model with acceptable values of R2 and SEP. The model number 4 of Table 4 was the best two-parameter model obtained, with R2 = 0.781 and SEP = 3.50 min, respectively, being identical to that found for tG′1 (model 2). When entering the optical parameter tmax in the previous algorithm, the improvement in R2 and SEP values was slight. However, when including the quadratic effect of protein, model 6 was obtained, which allowed predicting rheological cutting time with an R2 of 0.939 and a SEP of 1.93 min. These were acceptable values if it is considered that the other two experimental factors (inulin and calcium) also have significant effects on the different phases of the coagulation process. Castillo et al. (2003) used the same type of optical sensor to monitor the coagulation of skimmed goat's milk without inulin, with adjustment of the protein levels at 3, 5 and 7 g/100 g. They found the next model for the prediction of visual cutting time, tcut = β0t2min(1 + γ% Protein), with R2 = 0.98 and SEP = 2.42 min, which is equal to model 4 (Table 4) of this study. Note that Castillo et al. (2003) found a smaller SEP as compared to model 4 in our study, which had a SEP of 3.50 min. Thus, in the presence of inulin, reducing the SEP to ∼2 min (i.e., similar to Castillo et al., 2003 study) required incorporating a quadratic term for protein. Experimental data showed that firming time (tF30 = tG′30 – tG′1) decreases more than proportionally with the increase in protein concentration. In addition, when analyzing the rheological data, it was found that the increase in the slope of the elastic modulus was greater when protein concentration changed from 4 to 5 g/100 g compared when it changed from 3 to 4 g/100 g. Coinciding with this results, Guinee et al. (1997) found, through oscillatory rheology, that gelation time (G´ > 0.2 Pa) and cutting time at G´ = 20 Pa, increased with protein concentration in a relationship directly proportional to Pn, where P is the protein concentration and n > 1.0. This would justify the inclusion of a quadratic protein term in the model for the prediction of rheological cutting time. With this modified model (model 6 in Table 4) there was a reduction in the SEP of ∼45% and an increase in R2 of ∼20%. Fig. 1 shows the comparative effect of the inclusion of P2 in the fitting of the model for the prediction of tG′30. In Fig. 2, it can be observed an almost linear relationship between

Fig. 2. Effect of the concentration of protein on the relationship t2min vs. tG′30. ◊3, □4, ⧍5 g/100 g protein.

the predictor t2min (the elapsed time from enzyme addition to the minimum of the second derivative) and the cutting time at 30 Pa (tG′30), in the tests with different concentrations of inulin and calcium. The variation in the protein level had a considerable effect on the slope of the relationship between the two variables. That is how at a low level of protein (3 g/100 g) the variations in tG′30 due to inulin and calcium are more pronounced, resulting in an increase in tG′30 greater than the observed at higher levels of protein. Therefore, the presence of inulin and calcium seems not to have affected the behavior of the relationship between cutting time and the predicting variable t2min. 3.2. Validating the prediction models The fitting of the best models for predicting tG′1 and tG′30 obtained previously, was validated using a new, independent set of the experimental data where the same variables, but with different levels, were evaluated. The best model for predicting the gelation time was tG′1 = β1t2min(1 + γP), with R2 = 0.871 and SEP = 0.58 min. Fitting this model to the new data set, the R2 and SEP values obtained were not good (0.598 and 1.60 min respectively). Similarly to the observed behavior in the calibration experiment, it was observed that the fit was poor only in the tests with the lowest levels of the factors, where coagulation times were abnormally long. After eliminating that extreme data (4 data), the fitting of the model improved substantially, obtaining R2 and SEP values much better that the initial ones (R2 = 0.936, SEP = 0.47 min). For prediction of cutting time at 30 Pa (tG′30), the best model obtained previously was tG′30 = β1t2min(1 + γ1P + γ2P2), with R2 = 0.939 and SEP = 1.93 min. Fitting that model to the new data set, prediction of tG′30 was poor (R2 = 0.220 and SEP = 10 min), due to the effect of the same bad coagulation conditions mentioned before, where tG′30 values were very long (Fig. 3 a). When the model was validated without including the extreme data, the fit improvement was evident, with

Fig. 1. Actual vs. predicted values of tG′30 without a) and with b) inclusion of a quadratic protein term in the model. N = 51. R2, coefficient of determination (corrected for the means).

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Fig. 3. Validation of the prediction model for cutting time at 30 Pa: a) fitting with all data set (N = 18), b) fitting after eliminating extreme data (N = 14).

CCD experiment data. The rate of increase of the elastic modulus (ΔG'/ Δt) for protein concentration between 2.7 and 3.9 g/100 g was almost linear (R2 = 0.995) and maybe because of that, it was not necessary to include a quadratic term for protein in the prediction model. 4. Conclusions Models for prediction of the rheological gelation and cutting times in milk gels with variations in inulin, protein and added calcium content were developed using near infrared light backscatter parameters. The optical parameter t2min (the elapsed time from enzyme addition to the minimum of the second derivative of the light backscatter ratio) was the best predictor for both the gelation time and the cutting time. This parameter was affected by milk protein concentration but not by inulin and calcium addition, so it was necessary to include a protein term in the algorithms to obtain acceptable predictions. Rheological data showed that the increase in milk protein concentration from 4 to 5 g/ 100 g produced an increase in the rate of the elastic modulus (ΔG'/Δt) more than proportional. Maybe due to this, when protein level was between 3.0 and 3.9 g/100 g the best model for prediction of rheological cutting time at 30 Pa (tG′30) was tG′30 = βt2min(1 + γP), but when protein was between 3.0 and 5.0 g/100 g, the best model obtained was tG′30 = β1t2min(1 + γ1P + γ2P2), in which it was necessary to include a quadratic term for the protein with the aim of improving the fit. The results showed that using parameters from NIR light backscatter ratio, it is possible to predict gelation and cutting times in milk gels with variations in protein, inulin and calcium concentrations.

Fig. 4. Correlation between tG′30 and (tG′30 – t2min), N = 18.

Acknowledgements The authors wish to thank the Animal and Food Science Department, Universitat Autònoma de Barcelona. During this research O. Arango was supported by a FI-DGR grant from Generalitat of Catalunya (Catalunya, Spain) and by Universidad de Nariño (Pasto, Colombia).

Fig. 5. Prediction of tG′30 vs. actual data obtained using the model: tG′30 = βt2min (1 + γP). N = 14.

R2 = 0.884 and SEP = 2.1 min (Fig. 3 b). A very linear relationship between tG′30 and (tG′30 – t2min) was observed as it is shown in Fig. 4. It means that previous relationship can be expressed as tG′30 = βt2min, where β = tG′30/t2min and is a function of all factors affecting curd firming, as coagulation temperature and protein, fat, inulin and calcium concentrations. If there is a cheese process where all previous factors except protein concentration are constants, for cutting time prediction using the optical sensor, it is only necessary to know the effect of protein on β. Using data from CCD experiment where protein concentrations varied between 3.0 and 3.9 g/100 g, it was determined that β variation was almost linear (R2 = 0.98), therefore, rheological cutting time could be predicted with the algorithm tG′30 = βt2min (1 + γP). The advantage of previous model is its larger simplicity, requiring less calibration effort for in-plant implementation. Fig. 5 shows the fit of previous model to

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