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Rheological Properties and Cutting Time of Rennet Gels. Effect of pH and Enzyme Concentration
PII : S0958-6946(98)00055-7
Int. Dairy Journal 8 (1998) 289—293 ( 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0958-6946/98/$19.00#0.00
Rheological Properties and Cutting Time of Rennet Gels. Effect of pH and Enzyme Concentration M. B. Lo´ peza, S. B. Lomholtb* and K. B. Qvistb aDepartment of Food Technology, Veterinary Faculty, University of Murcia, E-30071 Murcia, Spain bDepartment of Dairy and Food Science, The Royal Veterinary and Agricultural University, Rolighedsvej 30, DK-1958 Frederiksberg, Denmark (Received 10 July 1997; accepted 12 April 1998) ABSTRACT The subjectively evaluated cutting time of rennet gels was compared to the rheological moduli measured by oscillation at different rennet concentrations and different milk pHs. We found no unique value of the rheological moduli at cutting time but a linear correlation between the cutting time and the time of the maximum rate of increase of G@ indicating that the properties evaluated empirically by the cheesemaker are related to fundamental rheological properties. G* was 7—10 Pa at the cutting time at pH 6.7 and decreased with decreasing pH. Plotting the maximum rate of increase of G@ vs. the enzymatic reaction rate we found a linear relationship with a positive intercept at the y-axis. This shows that the rate of gelfirming is not determined by the enzymatic reaction rate alone. Both the slope and the intercept increased with decreasing pH, demonstrating that the effect of pH on the rate of gelfirming was not only caused by the change in the enzymatic reaction rate. The results indicated that the rate of structural rearrangements of the gel increased when the pH was lower. ( 1998 Elsevier Science Ltd. All rights reserved Keywords: rheology; rennet; cutting time
increase in the rate of gelfirming (Zoon et al., 1988a). Horne (1995) found that curves of G* vs time for individual milks during renneting could be reduced to a single master curve by scaling the time axis with gelation time for each experiment and the gel strengths by the value of G* at a fixed multiple of the reactions gel time. This suggests that two parameters can describe the time course of renneting and the rate of gelfirming: the clotting time and the maximal gel strength. Lomholt and Qvist (1997) found that curves of G* during renneting with different rennet concentrations could not be reduced to a single curve by scaling with the enzymatic reaction rate constant and argued that a more complex description was needed to describe the rate of gel firming taking both the rate of proteolysis of i-casein and the rate of aggregation into account. An objective of this study was to examine more closely the relation between the enzymatic rate and the rate of gelfirming at different values of milk pH, in order to get a better understanding of the mechanisms determining the time course of rennet coagulation.
INTRODUCTION The coagulation of milk by rennet is an essential step during cheesemaking and is the result of two processes: the proteolysis of i-casein by the rennet enzyme leading to destabilisation of the casein micelles, and the aggregation of the destabilised micelles leading to the formation of a gel. After coagulation the firmness of the gel increases for several hours (e.g. Bohlin et al., 1984, Zoon et al., 1988a). During cheesemaking the curd is cut when the firmness is sufficient, judged by empirical evaluation, to promote whey drainage without excessive loss of curd fines. A useful method for monitoring the increase of gel firmness in the laboratory is the measurement of rheological moduli by mechanical oscillation at small deformation. When comparing such data to actual cheesemaking conditions it would be useful to establish correlations between measured rheological properties and the empirically determined cutting time. In this work we studied relations between measured values of the elastic modulus (G@) and an empirically determined cutting time at different rennet concentrations and different values of milk pH. It is well known that the clotting time is reduced when the concentration of rennet is increased, caused by an increase in the rate of proteolysis of i-casein, though there is no direct proportionality between the values (e.g. Foltman, 1959). This has also been shown to lead to an
MATERIAL AND METHODS Milk Skim milk was prepared by dissolving 10 g of low heat skim milk powder (MD Foods, Akafa, Denmark) in 100 g of distilled water at 50°C and stirring for 30 min. The reconstituted milk was kept at 4°C overnight and
*Corresponding author. 289
290
M. B. Lo´ pez et al.
Table 1. Enzymatic rate constant at different values of milk pH pH
Rennet conc. (%)
Ke (s~1)
6.74 6.74 6.74 6.50 6.50 6.50 6.25 6.25 6.25
0.04 0.03 0.02 0.03 0.02 0.01 0.02 0.01 0.005
2.4]10~3 1.8]10~3 1.2]10~3 3.2]10~3 2.1]10~3 1.1]10~3 2.6]10~3 1.3]10~3 0.7]10~3
used the day after preparation. Before use the milk was equilibrated at 30°C for 45 min. Milk was acidified with 1.0 M HCl and tempered for 30 min, and the pH was checked just before renneting. Rennet The rennet preparation used was Chymogen 100 (Chr Hansens Laboratorium, H+rsholm, Denmark) with a strength of 66 CHU mL~1 (2.45 10~5 M chymosin). The stock rennet dilution was diluted in 0.075 M ammonium acetate buffer at pH 6.2 to give the desired concentration (Table 1). Determination of enzymatic rate constant The amount of Casein Macro Peptide was determined as described by van Hooydonk and Olieman (1982). For each pH the amount of CMP was plotted versus the product of time and enzyme concentration and the firstorder reaction and Michaelis—Menten rate constants were determined by least-squares fitting to the data. Two repetitions were done at each combination of pH and rennet concentrations. Dynamic rheological measurements
surface that split easily. For each pH and enzyme concentration this test was repeated at least three times.
RESULTS Van Hooydonk et al. (1984), Hyldig (1993) and Lomholt and Qvist (1997) found that the proteolysis of icasein is adequately described as a first-order reaction at the normal pH of milk. At pH 6.2 van Hooydonk et al. (1986) observed that the first-order equation could not satisfactorily describe the data but the Michaelis—Menten equation was needed. We found that both first order and Michaelis—Menten kinetics described our results equally well at all pH values used in this study and preferred to use the simpler first-order equation. The reaction rate constants are shown in Table 1. During milk coagulation the elastic modulus (G@) started to increase at some time after rennet addition as seen in Fig. 1. The first derivative of G@ is also shown, and it can be seen that the rate of increase of G@@ initially increased, reached a maximum value and decreased steadily thereafter. The change from sol to gel was accompanied by a decrease of the tangent of the phase angle (tan d) to a constant value of approximately 0.26 in the curd. This behaviour was found in all experiments in accordance with the results of others (e.g. Bohlin et al., 1984; Hyldig, 1993; Zoon et al., 1988a). The cutting time and the degree of i-casein proteolysis, the complex modulus (G*), storage modulus (G@) and tan d at the cutting time are shown in Table 2. At normal pH almost all i-casein is proteolysed at the cutting time and as pH is lowered the degree of proteolysis at the cutting time decreases. There is no clear effect of the enzyme concentration on the degree of proteolysis at the cutting time. At normal pH the cutting time occurred at a value of G* of 7—10 Pa; the value being lower at the lower pH values. There was a tendency for G* to increase with increasing enzyme concentration, though this effect was not significant. At the cutting time tan d had almost reached its plateau value of 0.27 indicating that a gel was formed and decreased only little during the rest of the
Measurements of the storage modulus, G@, the loss modulus, G@@, and the complex modulus, G*, were performed continuously during renneting at 30°C using a Bohlin CVO rheometer (Bohlin Rheology, Gloucestershire, UK) equipped with the DG 40/50 double-gap concentric cylinder measuring system. The oscillation frequency was 1 Hz and the rheometer was programmed to automatically adjust the stress to give a strain of 0.01 which was found to be within the linear viscoelastic region for rennet milk gels (Hyldig 1993). Cutting time determination 300 mL of milk was tempered at 30°C in a glass vessel for 30 min and 3 mL of the enzyme dilution was added. The determination was done by a cheesemaker trainer when the curd could be pulled from the surface of the glass vessel with a spatula without tearing. At least three strokes were made with a sharp knife in different regions. The strokes were made at different time intervals of at least 1 min. It was observed that the curd was weak and soft, and crumbled prior to the cutting time. The cutting time is the time when a cut through the gel gave a smooth
Fig. 1. The elastic modulus (G@), (——), and dG@/dt, ( . . . . . . ), as a function of time after rennet addition. pH 6.25, 0.02% rennet.
291
Rheology and cutting time of rennet gels Table 2. Gel properties at curd cutting time pH
Rennet conc. (%)
Cutting time (s)
i-casein proteolysed (%)
G* (Pa)
G@ (Pa)
tan d
6.74 6.74 6.74 6.50 6.50 6.50 6.25 6.25 6.25
0.04 0.03 0.02 0.03 0.02 0.01 0.02 0.01 0.005
2885 3498 4002 1078 1477 2321 800 1320 2904
100 100 99 97 96 92 88 82 87
9.96 8.77 7.65 3.46 2.37 1.07 6.54 4.53 4.82
9.82 8.21 7.37 3.32 2.27 1.01 6.28 4.34 4.63
0.27 0.28 0.29 0.29 0.30 0.36 0.29 0.30 0.30
($231) ($260) ($135) ($75) ($17) ($15) ($20) ($84) ($65)
($6.93) ($5.28) ($6.59) ($0.06) ($0.15) ($0.05) ($1.01) ($0.06) ($1.93)
($6.58) ($4.74) ($6.37) ($0.06) ($0.14) ($0.04) ($0.98) ($0.06) ($1.87)
Table 3. Rheological properties of milk gels at the maximum value of the first derivative of the storage modulus, and tan d at 5400 s Ph
Rennet conc. (%)
Time for max dG@/dt (s)
i-Casein proteolysed (%)
Max dG@/dt (mPa s~1)
G* (Pa)
G@ (Pa)
tan d
tan d 5400
6.74
0.04
3970 ($22)
100
11.00 ($3.00)
22.30 ($5.80)
21.57 ($5.64)
0.27
0.26
6.74
0.03
4680 ($419)
100
9.70 ($4.00)
18.93 ($8.81)
18.27 ($8.51)
0.27
0.26
6.74
0.02
5235 ($624)
100
6.90 ($3.60)
19.72 ($4.70)
19.05 ($4.53)
0.26
0.26
6.50
0.03
1755 ($190)
100
31.50 ($2.00)
24.35 ($1.34)
23.55 ($1.34)
0.26
0.26
6.50
0.02
2590 ($93)
100
26.00 ($2.00)
27.75 ($1.85)
26.63 ($1.79)
0.26
0.25
6.50
0.01
4065 ($21)
99
19.00 ($0.00)
28.15 ($0.07)
27.25 ($0.07)
0.26
0.26
6.25
0.02
1096 ($90)
94
77.00 ($8.00)
35.37 ($0.83)
34.01 ($0.83)
0.26
0.25
6.25
0.01
1860 ($127)
91
53.00 ($3.00)
34.40 ($1.70)
33.25 ($1.63)
0.27
0.26
6.25
0.005
3990 ($212)
94
33.00 ($7.00)
36.90 ($6.65)
35.65 ($6.43)
0.26
0.26
experiment as seen by the value at 5400 s. Tan d was independent of pH and rennet concentration. Table 3 shows the time and the value of dG@/dt at the maximum. In Fig. 2 the cutting time is plotted vs this time. Within the range of our experiments a good linear correlation between the values was found independent of enzyme concentration and pH. It can be noted that the cutting time in all cases was found before the maximum increase of G@. To examine the effect of rennet concentration and pH on the rate of gelfirming we have plotted the maximum of dG@/dt as a function of the enzymatic reaction rate constant in Fig. 3. A straight line could be fitted to the results for each pH, but the regression lines have a positive intercept at the y-axis, meaning there is no proportionality between the rate of the enzymatic reaction and the rate of gelfirming. The experiments at different pH did not show the same relationship between the rate of enzymatic proteolysis and maximum rate of gelfirming, showing that the effect of decreasing pH on the rate of gelfirming cannot be explained by the increase in the enzymatic reaction rate alone. DISCUSSION During cheesemaking the time for cutting the curd is normally determined manually by the cheesemaker by
Fig. 2. The time for the maximum of dG@/dt as a function of cutting time. pH 6.74 (s), pH 6.50 (h) and pH 6.25 (n). Solid line found by linear regression.
a simple empirical evaluation of the rheological properties of the curd and its visual appearance. From experience the cheesemaker recognises the time when the curd has the optimum properties for cutting. Numerous
292
M. B. Lo´ pez et al.
Fig. 3. The maximum value of dG@/dt as a function of the enzymatic reaction rate constant (K ). Points are experimental % values, lines found by linear regression. pH 6.74 (s, ——), pH 6.50 (h, - - - - - - ) and pH 6.25 (n, . . . . . . ).
instruments have been proposed for determining the cutting time based on different principles. Mechanical methods based on the resistance exerted by the milk gel on an oscillatory deformation (Richardson et al., 1985, Ustunol and Hicks, 1990b). Thermal methods based on the work reported by Hori (1985), correlating the temperature changes with the kinematic viscosity of the coagulating milk. Optical methods related to the changes occur during milk coagulation determined by NIR diffuse reflectance (Payne et al., 1990; Bellon et al., 1988; Ustunol et al., 1991; 1993; Lo´pez et al., 1997). Other methods recently incorporated are ultrasonic ones (Gunasekaran and Ay, 1994; 1996), in which the ultrasonic attenuation measurements provided a useful indicator for predicting milk coagulation time nondestructively. It would be logical to assume that most of the properties empirically evaluated by the cheesemaker correspond to fundamental rheological properties of the gel at the cutting time, but we are not aware of any studies of such relations. When conducting fundamental rheological measurements during rennet coagulation, knowledge about such relations will be of great value in order to relate experimental results to cheesemaking conditions. Our measurements showed that G* had a value of 7—10 Pa at the manually determined cutting time in milk at normal pH, and that this value was lower at lower pH values. There was a slight, though not significant, effect of the rennet concentration on the rheological moduli at cutting. It thus seemed that there was no unique values of the rheological moduli corresponding to the empirically determined cutting time. This indicates that the empirical determination includes other properties than the rheological properties determined at the same point in time and at small deformation. Nevertheless, we found a high correlation between the empirically determined cutting time and the time of the maximum of dG@/dt even when varying pH, showing that the empirical determination of cutting time is related to fundamental rheological
properties. Payne et al. (1990) found that the inflection point of the diffuse reflectance profile was highly correlated to the cuting time determined by the Formagraph response K . These results could indicate that the rate of 20 change of gel properties is more important in determining cutting time than the actual value at the cutting time. At normal pH practically all i-casein has been proteolysed at the maximum of dG@/dt, nevertheless, the rate of gelfirming (dG@/dt) is higher with the higher enzyme concentration. This means that even though the enzymatic reaction is practically over, the enzyme concentration has an effect on the rate of the process. It is clear, however, that there is not just a simple proportionality between the enzymatic rate and the maximal rate of gel firming as demonstrated by the intercept seen in Fig. 3. An explanation could be that the structure of the aggregates formed during the initial aggregation varies with the enzyme concentration, and that this affects the rate of gel firming. In agreement with van Hooydonk et al. (1986) and Hyldig (1993) we observed that a decrease in the pH of milk caused an increase in the rate of the enzymatic proteolysis of i-casein in the pH-range used. As seen from Fig. 3 the effect of lowering pH is not only to increase the enzymatic reaction rate, the maximum rate of gelfirming is increased above what can be explained by the effect on the enzymatic reaction rate constant. The firming of the gel is a result of structural rearrangements and during cheesemaking these rearrangements continue after the gel has been cut and results in syneresis (Walstra and van Vliet, 1986). A decrease in pH leads to reduced electrostatic repulsion between micelles as well as an increase in Ca2` activity caused by the solubilisation of calcium phosphate which is expected to lead to a faster rate of micelle aggregation and bond formation (Zoon et al., 1988b; 1989). This is in accordance with the fact that the initial rate of syneresis is higher with lower pH in the pH range investigated here, indicating that the rate of rearrangement is higher. The effect of pH on the rate of gelfirming at a constant enzymatic rate can thus be explained by an increased rate of structural rearrangements. Our results show that the rate of gelfirming is a useful parameter for describing the kinetics of gelfirming as demonstrated by varying pH and enzyme concentration, and that it is affected by the rate of enzymatic proteolysis of i-casein and probably, the rate of rearrangement of the gel network. Both these factors should be included in a mechanistic description of gelfirming.
REFERENCES Bellon, J. L., Quiblier, J. P., Durier, C. and Noel, Y. (1988) Un noveau capteur industrial de mesure du temps de coagulation du lait. ¹echnique ¸aitiere 1031, 29—32. Bohlin, L., Herr, P. and Ljusberg-Wahren, H. (1984) Viscoelastic properties of coagulating milk. Journal of Dairy Science 67, 729—734. Foltmann, B. (1959) On the enzymatic and coagulation stages of the renneting process. Proceedings of the 15th International Dairy Congress »ol. 2 pp. 655—661. Gunasekaran, S. and Ay, Ch. (1994) Evaluating milk coagulation with ultrasonics. Food ¹echnology 48, 74—78 Gunasekaran, S. and Ay, Ch. (1996) Milk coagulation cut-time determination using ultrasonics. Journal of Food Process Engineering 19, 63—73.
Rheology and cutting time of rennet gels Hori, T. (1985) Objective measurements of the process of curd formation during rennet treatment of milks by the hot-wire method. Journal of Food Science 50, 911—917. Horne, D. S. (1995) Scaling behaviour of shear moduli during the formation of rennet milk gels. In Food Macromolecules and Colloids, eds E. Dickinson and D. Lorient. Royal Society of Chemistry, Cambridge, pp. 456—461. Hyldig, G. (1993) Rennet coagulation. Effect of technological parameters on the enzymatic reaction and gel formation in milk and UF concentrates. Ph.D. thesis, Royal Veterinary and Agricultural University, Copenhagen. Lomholt, S. B. and Qvist, K. B. (1997) The relation between rheological properties and degree of i-casein proteolysis during renneting of milk. Journal of Dairy Research 64, 541—549. Lo´pez, M. B., Jorda´n, M. J., Luna, A., Banon, S., Garrido, M. D. and Laencina, J. (1997) Diffuse reflectance profiles of goat’s milk during coagulation by various enzymes. Food Science and ¹echnology International (in press). Payne, F. A., Madangopal, S. and Hicks, C. L. (1990). Fiber optic coagulation sensor for cut-time detection. Proceedings of the Food Processing Automation Conference AEAE, ºSA. Richardson, G. H., Okigbo, L. M. and Thorpe, J. D. (1985) Instrument for measuring milk coagulation in cheese vats. Journal Dairy Science 68, 32—36. Ustunol, Z. and Hicks, C. L. (1990b) Effect of a coagulation monitoring device on experimental cheese yield. Journal Dairy Science 73, 1—10. Ustunol, Z. and Hicks, C. L. (1991) Diffuse reflectance profiles of eight milk clotting enzyme preparations. Journal of Food Science 56, 441—415.
293
Ustunol, Z., Hicks, C. L., Payne, F. A. and Milton, K. (1993) Effect of pH, temperature and enzyme concentration on diffuse reflectance profiles of coagulating milk. Italian Journal of Food Science 2, 107—114. van Hooydonk, A. C. M., Boerrigter, I. J. and Hagedoorn, H. G. (1986) pH-induced physicochemical changes of casein micelles in milk and their effect on renneting. 2. Effect of pH on renneting of milk. Netherlands Milk Dairy Journal 40, 297—313. van Hooydonk, A. C. M. and Olieman, C. (1982) A rapid and sensitive HPLC method for following the action of chymosin in milk. Netherlands Milk Dairy Journal 36, 153—158 van Hooydonk, A. C. M., Olieman, C. and Hagedoorn, H. G. (1984) Kinetics of the chymosin-catalysed proteolysis of kappa-casein in milk. Netherlands Milk Dairy Journal 38, 207—222 Walstra, P. and van Vliet, T. (1986) The physical chemistry of curd making. Netherlands Milk and Dairy Journal 40, 241—259 Zoon, P., van Vliet, T. and Walstra, P. (1988a) Rheological properties of rennet-induced skim milk gels. 1. Introduction. Netherlands Milk Dairy Journal 42, 249—269. Zoon, P., van Vliet, T. and Walstra, P. (1988b) Rheological properties of rennet-induced skim milk gels. 3. The effect of calcium and phosphate. Netherlands Milk Dairy Journal 42, 295—312. Zoon, P., van Vliet, T. and Walstra, P. (1989) Rheological properties of rennet-induced skim milk gels. 4. The effect of pH and NaCl. Netherlands Milk Dairy Journal 43, 17—34.
Int. Dairy Journal 8 (1998) 289—293 ( 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0958-6946/98/$19.00#0.00
Rheological Properties and Cutting Time of Rennet Gels. Effect of pH and Enzyme Concentration M. B. Lo´ peza, S. B. Lomholtb* and K. B. Qvistb aDepartment of Food Technology, Veterinary Faculty, University of Murcia, E-30071 Murcia, Spain bDepartment of Dairy and Food Science, The Royal Veterinary and Agricultural University, Rolighedsvej 30, DK-1958 Frederiksberg, Denmark (Received 10 July 1997; accepted 12 April 1998) ABSTRACT The subjectively evaluated cutting time of rennet gels was compared to the rheological moduli measured by oscillation at different rennet concentrations and different milk pHs. We found no unique value of the rheological moduli at cutting time but a linear correlation between the cutting time and the time of the maximum rate of increase of G@ indicating that the properties evaluated empirically by the cheesemaker are related to fundamental rheological properties. G* was 7—10 Pa at the cutting time at pH 6.7 and decreased with decreasing pH. Plotting the maximum rate of increase of G@ vs. the enzymatic reaction rate we found a linear relationship with a positive intercept at the y-axis. This shows that the rate of gelfirming is not determined by the enzymatic reaction rate alone. Both the slope and the intercept increased with decreasing pH, demonstrating that the effect of pH on the rate of gelfirming was not only caused by the change in the enzymatic reaction rate. The results indicated that the rate of structural rearrangements of the gel increased when the pH was lower. ( 1998 Elsevier Science Ltd. All rights reserved Keywords: rheology; rennet; cutting time
increase in the rate of gelfirming (Zoon et al., 1988a). Horne (1995) found that curves of G* vs time for individual milks during renneting could be reduced to a single master curve by scaling the time axis with gelation time for each experiment and the gel strengths by the value of G* at a fixed multiple of the reactions gel time. This suggests that two parameters can describe the time course of renneting and the rate of gelfirming: the clotting time and the maximal gel strength. Lomholt and Qvist (1997) found that curves of G* during renneting with different rennet concentrations could not be reduced to a single curve by scaling with the enzymatic reaction rate constant and argued that a more complex description was needed to describe the rate of gel firming taking both the rate of proteolysis of i-casein and the rate of aggregation into account. An objective of this study was to examine more closely the relation between the enzymatic rate and the rate of gelfirming at different values of milk pH, in order to get a better understanding of the mechanisms determining the time course of rennet coagulation.
INTRODUCTION The coagulation of milk by rennet is an essential step during cheesemaking and is the result of two processes: the proteolysis of i-casein by the rennet enzyme leading to destabilisation of the casein micelles, and the aggregation of the destabilised micelles leading to the formation of a gel. After coagulation the firmness of the gel increases for several hours (e.g. Bohlin et al., 1984, Zoon et al., 1988a). During cheesemaking the curd is cut when the firmness is sufficient, judged by empirical evaluation, to promote whey drainage without excessive loss of curd fines. A useful method for monitoring the increase of gel firmness in the laboratory is the measurement of rheological moduli by mechanical oscillation at small deformation. When comparing such data to actual cheesemaking conditions it would be useful to establish correlations between measured rheological properties and the empirically determined cutting time. In this work we studied relations between measured values of the elastic modulus (G@) and an empirically determined cutting time at different rennet concentrations and different values of milk pH. It is well known that the clotting time is reduced when the concentration of rennet is increased, caused by an increase in the rate of proteolysis of i-casein, though there is no direct proportionality between the values (e.g. Foltman, 1959). This has also been shown to lead to an
MATERIAL AND METHODS Milk Skim milk was prepared by dissolving 10 g of low heat skim milk powder (MD Foods, Akafa, Denmark) in 100 g of distilled water at 50°C and stirring for 30 min. The reconstituted milk was kept at 4°C overnight and
*Corresponding author. 289
290
M. B. Lo´ pez et al.
Table 1. Enzymatic rate constant at different values of milk pH pH
Rennet conc. (%)
Ke (s~1)
6.74 6.74 6.74 6.50 6.50 6.50 6.25 6.25 6.25
0.04 0.03 0.02 0.03 0.02 0.01 0.02 0.01 0.005
2.4]10~3 1.8]10~3 1.2]10~3 3.2]10~3 2.1]10~3 1.1]10~3 2.6]10~3 1.3]10~3 0.7]10~3
used the day after preparation. Before use the milk was equilibrated at 30°C for 45 min. Milk was acidified with 1.0 M HCl and tempered for 30 min, and the pH was checked just before renneting. Rennet The rennet preparation used was Chymogen 100 (Chr Hansens Laboratorium, H+rsholm, Denmark) with a strength of 66 CHU mL~1 (2.45 10~5 M chymosin). The stock rennet dilution was diluted in 0.075 M ammonium acetate buffer at pH 6.2 to give the desired concentration (Table 1). Determination of enzymatic rate constant The amount of Casein Macro Peptide was determined as described by van Hooydonk and Olieman (1982). For each pH the amount of CMP was plotted versus the product of time and enzyme concentration and the firstorder reaction and Michaelis—Menten rate constants were determined by least-squares fitting to the data. Two repetitions were done at each combination of pH and rennet concentrations. Dynamic rheological measurements
surface that split easily. For each pH and enzyme concentration this test was repeated at least three times.
RESULTS Van Hooydonk et al. (1984), Hyldig (1993) and Lomholt and Qvist (1997) found that the proteolysis of icasein is adequately described as a first-order reaction at the normal pH of milk. At pH 6.2 van Hooydonk et al. (1986) observed that the first-order equation could not satisfactorily describe the data but the Michaelis—Menten equation was needed. We found that both first order and Michaelis—Menten kinetics described our results equally well at all pH values used in this study and preferred to use the simpler first-order equation. The reaction rate constants are shown in Table 1. During milk coagulation the elastic modulus (G@) started to increase at some time after rennet addition as seen in Fig. 1. The first derivative of G@ is also shown, and it can be seen that the rate of increase of G@@ initially increased, reached a maximum value and decreased steadily thereafter. The change from sol to gel was accompanied by a decrease of the tangent of the phase angle (tan d) to a constant value of approximately 0.26 in the curd. This behaviour was found in all experiments in accordance with the results of others (e.g. Bohlin et al., 1984; Hyldig, 1993; Zoon et al., 1988a). The cutting time and the degree of i-casein proteolysis, the complex modulus (G*), storage modulus (G@) and tan d at the cutting time are shown in Table 2. At normal pH almost all i-casein is proteolysed at the cutting time and as pH is lowered the degree of proteolysis at the cutting time decreases. There is no clear effect of the enzyme concentration on the degree of proteolysis at the cutting time. At normal pH the cutting time occurred at a value of G* of 7—10 Pa; the value being lower at the lower pH values. There was a tendency for G* to increase with increasing enzyme concentration, though this effect was not significant. At the cutting time tan d had almost reached its plateau value of 0.27 indicating that a gel was formed and decreased only little during the rest of the
Measurements of the storage modulus, G@, the loss modulus, G@@, and the complex modulus, G*, were performed continuously during renneting at 30°C using a Bohlin CVO rheometer (Bohlin Rheology, Gloucestershire, UK) equipped with the DG 40/50 double-gap concentric cylinder measuring system. The oscillation frequency was 1 Hz and the rheometer was programmed to automatically adjust the stress to give a strain of 0.01 which was found to be within the linear viscoelastic region for rennet milk gels (Hyldig 1993). Cutting time determination 300 mL of milk was tempered at 30°C in a glass vessel for 30 min and 3 mL of the enzyme dilution was added. The determination was done by a cheesemaker trainer when the curd could be pulled from the surface of the glass vessel with a spatula without tearing. At least three strokes were made with a sharp knife in different regions. The strokes were made at different time intervals of at least 1 min. It was observed that the curd was weak and soft, and crumbled prior to the cutting time. The cutting time is the time when a cut through the gel gave a smooth
Fig. 1. The elastic modulus (G@), (——), and dG@/dt, ( . . . . . . ), as a function of time after rennet addition. pH 6.25, 0.02% rennet.
291
Rheology and cutting time of rennet gels Table 2. Gel properties at curd cutting time pH
Rennet conc. (%)
Cutting time (s)
i-casein proteolysed (%)
G* (Pa)
G@ (Pa)
tan d
6.74 6.74 6.74 6.50 6.50 6.50 6.25 6.25 6.25
0.04 0.03 0.02 0.03 0.02 0.01 0.02 0.01 0.005
2885 3498 4002 1078 1477 2321 800 1320 2904
100 100 99 97 96 92 88 82 87
9.96 8.77 7.65 3.46 2.37 1.07 6.54 4.53 4.82
9.82 8.21 7.37 3.32 2.27 1.01 6.28 4.34 4.63
0.27 0.28 0.29 0.29 0.30 0.36 0.29 0.30 0.30
($231) ($260) ($135) ($75) ($17) ($15) ($20) ($84) ($65)
($6.93) ($5.28) ($6.59) ($0.06) ($0.15) ($0.05) ($1.01) ($0.06) ($1.93)
($6.58) ($4.74) ($6.37) ($0.06) ($0.14) ($0.04) ($0.98) ($0.06) ($1.87)
Table 3. Rheological properties of milk gels at the maximum value of the first derivative of the storage modulus, and tan d at 5400 s Ph
Rennet conc. (%)
Time for max dG@/dt (s)
i-Casein proteolysed (%)
Max dG@/dt (mPa s~1)
G* (Pa)
G@ (Pa)
tan d
tan d 5400
6.74
0.04
3970 ($22)
100
11.00 ($3.00)
22.30 ($5.80)
21.57 ($5.64)
0.27
0.26
6.74
0.03
4680 ($419)
100
9.70 ($4.00)
18.93 ($8.81)
18.27 ($8.51)
0.27
0.26
6.74
0.02
5235 ($624)
100
6.90 ($3.60)
19.72 ($4.70)
19.05 ($4.53)
0.26
0.26
6.50
0.03
1755 ($190)
100
31.50 ($2.00)
24.35 ($1.34)
23.55 ($1.34)
0.26
0.26
6.50
0.02
2590 ($93)
100
26.00 ($2.00)
27.75 ($1.85)
26.63 ($1.79)
0.26
0.25
6.50
0.01
4065 ($21)
99
19.00 ($0.00)
28.15 ($0.07)
27.25 ($0.07)
0.26
0.26
6.25
0.02
1096 ($90)
94
77.00 ($8.00)
35.37 ($0.83)
34.01 ($0.83)
0.26
0.25
6.25
0.01
1860 ($127)
91
53.00 ($3.00)
34.40 ($1.70)
33.25 ($1.63)
0.27
0.26
6.25
0.005
3990 ($212)
94
33.00 ($7.00)
36.90 ($6.65)
35.65 ($6.43)
0.26
0.26
experiment as seen by the value at 5400 s. Tan d was independent of pH and rennet concentration. Table 3 shows the time and the value of dG@/dt at the maximum. In Fig. 2 the cutting time is plotted vs this time. Within the range of our experiments a good linear correlation between the values was found independent of enzyme concentration and pH. It can be noted that the cutting time in all cases was found before the maximum increase of G@. To examine the effect of rennet concentration and pH on the rate of gelfirming we have plotted the maximum of dG@/dt as a function of the enzymatic reaction rate constant in Fig. 3. A straight line could be fitted to the results for each pH, but the regression lines have a positive intercept at the y-axis, meaning there is no proportionality between the rate of the enzymatic reaction and the rate of gelfirming. The experiments at different pH did not show the same relationship between the rate of enzymatic proteolysis and maximum rate of gelfirming, showing that the effect of decreasing pH on the rate of gelfirming cannot be explained by the increase in the enzymatic reaction rate alone. DISCUSSION During cheesemaking the time for cutting the curd is normally determined manually by the cheesemaker by
Fig. 2. The time for the maximum of dG@/dt as a function of cutting time. pH 6.74 (s), pH 6.50 (h) and pH 6.25 (n). Solid line found by linear regression.
a simple empirical evaluation of the rheological properties of the curd and its visual appearance. From experience the cheesemaker recognises the time when the curd has the optimum properties for cutting. Numerous
292
M. B. Lo´ pez et al.
Fig. 3. The maximum value of dG@/dt as a function of the enzymatic reaction rate constant (K ). Points are experimental % values, lines found by linear regression. pH 6.74 (s, ——), pH 6.50 (h, - - - - - - ) and pH 6.25 (n, . . . . . . ).
instruments have been proposed for determining the cutting time based on different principles. Mechanical methods based on the resistance exerted by the milk gel on an oscillatory deformation (Richardson et al., 1985, Ustunol and Hicks, 1990b). Thermal methods based on the work reported by Hori (1985), correlating the temperature changes with the kinematic viscosity of the coagulating milk. Optical methods related to the changes occur during milk coagulation determined by NIR diffuse reflectance (Payne et al., 1990; Bellon et al., 1988; Ustunol et al., 1991; 1993; Lo´pez et al., 1997). Other methods recently incorporated are ultrasonic ones (Gunasekaran and Ay, 1994; 1996), in which the ultrasonic attenuation measurements provided a useful indicator for predicting milk coagulation time nondestructively. It would be logical to assume that most of the properties empirically evaluated by the cheesemaker correspond to fundamental rheological properties of the gel at the cutting time, but we are not aware of any studies of such relations. When conducting fundamental rheological measurements during rennet coagulation, knowledge about such relations will be of great value in order to relate experimental results to cheesemaking conditions. Our measurements showed that G* had a value of 7—10 Pa at the manually determined cutting time in milk at normal pH, and that this value was lower at lower pH values. There was a slight, though not significant, effect of the rennet concentration on the rheological moduli at cutting. It thus seemed that there was no unique values of the rheological moduli corresponding to the empirically determined cutting time. This indicates that the empirical determination includes other properties than the rheological properties determined at the same point in time and at small deformation. Nevertheless, we found a high correlation between the empirically determined cutting time and the time of the maximum of dG@/dt even when varying pH, showing that the empirical determination of cutting time is related to fundamental rheological
properties. Payne et al. (1990) found that the inflection point of the diffuse reflectance profile was highly correlated to the cuting time determined by the Formagraph response K . These results could indicate that the rate of 20 change of gel properties is more important in determining cutting time than the actual value at the cutting time. At normal pH practically all i-casein has been proteolysed at the maximum of dG@/dt, nevertheless, the rate of gelfirming (dG@/dt) is higher with the higher enzyme concentration. This means that even though the enzymatic reaction is practically over, the enzyme concentration has an effect on the rate of the process. It is clear, however, that there is not just a simple proportionality between the enzymatic rate and the maximal rate of gel firming as demonstrated by the intercept seen in Fig. 3. An explanation could be that the structure of the aggregates formed during the initial aggregation varies with the enzyme concentration, and that this affects the rate of gel firming. In agreement with van Hooydonk et al. (1986) and Hyldig (1993) we observed that a decrease in the pH of milk caused an increase in the rate of the enzymatic proteolysis of i-casein in the pH-range used. As seen from Fig. 3 the effect of lowering pH is not only to increase the enzymatic reaction rate, the maximum rate of gelfirming is increased above what can be explained by the effect on the enzymatic reaction rate constant. The firming of the gel is a result of structural rearrangements and during cheesemaking these rearrangements continue after the gel has been cut and results in syneresis (Walstra and van Vliet, 1986). A decrease in pH leads to reduced electrostatic repulsion between micelles as well as an increase in Ca2` activity caused by the solubilisation of calcium phosphate which is expected to lead to a faster rate of micelle aggregation and bond formation (Zoon et al., 1988b; 1989). This is in accordance with the fact that the initial rate of syneresis is higher with lower pH in the pH range investigated here, indicating that the rate of rearrangement is higher. The effect of pH on the rate of gelfirming at a constant enzymatic rate can thus be explained by an increased rate of structural rearrangements. Our results show that the rate of gelfirming is a useful parameter for describing the kinetics of gelfirming as demonstrated by varying pH and enzyme concentration, and that it is affected by the rate of enzymatic proteolysis of i-casein and probably, the rate of rearrangement of the gel network. Both these factors should be included in a mechanistic description of gelfirming.
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