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Milk Coagulation Time: Linear Relationship with Inverse of Rennet Activity1
TECHNICAL
NOTES
Milk Coagulation Time:. Linear Relationship with Inverse of Rennet Activity 1 D. J. McMAHON and R. J. BROWN Department of Nutrition and Food Sciences Utah State University Logan 84322
ABSTRACT
where tc is coagulation time, E is enzyme activity, and k is a constant. Holter (9) observed that this equation is only valid for a narrow range of enzyme concentration (variations of 1:4) and concluded that deviations from the Storch and Segelcke relationship are due to a time lag in the aggregation phase during the coagulation process. He introduced a correction factor into the equation:
The extent to which time for milk coagulation is linear with the inverse of enzyme activity was investigated. The Formagraph can be used to measure time for coagulation of milk over a range of rennet activity. Linearity of coagulation time versus inverse of enzyme activity exists within the range of concentration .0011 RU/ml to .16 RU/ml, which represents relative variation in rennet activity of 1:140.
E(t c -- x) = k
where x represents the time required to allow enzymically converted casein to aggregate. To facilitate statistical analysis, Foltmann (6) rearranged the Holter equation into the form:
INTRODUCTION Milk-clotting enzyme activity commonly is calculated by comparing coagulation time o f an unknown relative to a standard of known activity. Because of deviations from linearity of the relationship between coagulation time and the inverse of enzyme activity, it has been suggested that unknown and standard samples should have approximately the same enzyme concentration (5). In (12) this relationship was linear over coagulation time ranging from 5 to 30 rain when clotting time was measured with the Formagraph or the Sommer and Matsen apparatus (20). The linear relationship between milk coagulation time and the inverse of enzyme concentration first was postulated by Storch and Segelcke (21), who stated that the product of enzyme concentration and coagulation time is constant: tcE = k
k+ tc = ~ x
[31
Observing that k remained constant whereas x varied for several fresh milk samples, he concluded that differences in coagulability were a consequence of the nonenzymic aggregation phase of the overall coagulation process. Various mathematical models have been proposed to describe enzymic coagulation of milk. Payens (14, 16) derived an expression for changes in weight average molecular weight of coagulating milk by yon Smoluchowski's rate theory (13) for the production of multiple particles in bimolecular flocculation:
Mw M--o=
[11
1 -- M o ( l - - f ) (
) 1/2 {f(t) _
(1-f)(t)3/3)/C O Received April 26, 1982. ~Utah Agricultural Experiment Station Journal Article No. 2709. Approved by the director. 2From New Zealand Cooperative Rennet Co., Eltham, New Zealand. Rennin activity units as described by Ernstrom (4). 1983 J Dairy Sci 66:341--344
[2]
341
[4]
where Mo is the average molecular weight of casein micelles in milk, ks is the aggregation rate constant, V is the enzymic velocity, f is the ratio of the molecular weight of released peptide to Mo, Co is the substrate concentration,
342
McMAHON AND BROWN
and r is the parameter governing the kinetics of the clotting process, is defined as: r = (k s v ) - 1 1 2 -2-
[51
in which V is proportional to enzyme concentration and r is assumed to approximate t c (18, 19). The r can be visualized as the time needed for the enzyme to produce a minimum number of hydrolyzed particles in the absence of any flocculation. Measured t c depends on the technique chosen to monitor coagulation and according to Foltmann (6) is only an empirical approximation, because the aggregation stage begins as soon as the first casein is hydrolyzed. The lag time is merely the result of different orders of enzymic and aggregation reactions (19). Equation [5] has an advantage over the Storch and Segelcke equation in that it states explicitly that the lag period is dependent on aggregation rate to the same extent as on enzymic velocity (10). If k s is constant, equation [5] predicts a plot of log tc versus log E - 1 to be a straight line with slope .5. Payens (15, 19) postulated that not every collision between para-casein micelles leads to permanent contact but only those in which para-K-casein sites are involved. Because k s is a measure of repulsion between flocculating particles, it can be considered a function of the amount of macropeptide split from K-casein (15). Clotting starts before the maximal number of peptides are proteolysed b y the enzyme, and the fraction of sites available for permanent contact (and, hence, ks) increases in proportion to the enzyme concentration (19). A t a first approximation, equation [5] reduces to the linear form of equation [ 3 ]. Another mathematical model for milk coagulation was described by Darling and Van H o o y d o n k (2) from which an equation expressing tc was derived: 1 (S O + l-e x p ( - CmSo ) - 1 ) + tc =~V
W o e x p ( _ C m S o ) ( 1 _ 1_ ) Ks nc no
[61
where So is the micellar surface K-casein concentration at time zero, W o is the stability factor at time zero, n o is the particle concenJournal of Dairy Science Vol. 66, No. 2, 1983
tration at time zero, nc is the particle concentration at time tc, and Cm is a proportionality constant. For this model, coagulation time can be visualized as the time required to reduce the number of micelles from n o to n o If k s is a function of enzyme concentration or a constant, this equation also reduces to equation [ 3 ]. From either of these models of milk coagulation, it appears that the inverse linear relationship between coagulation time and enzyme activity is valid for use in measuring enzyme activity. A study was made of the extent to which it remains valid when coagulation time is measured by Formagraph. Linearity between coagulation time and inverse of enzyme activity over an extensive range would indicate it is not necessary to dilute samples to approximately the same coagulation times in comparing enzyme activities. The ability to work with the Formagraph at low enzyme concentrations also may provide new possibilities for studying mechanism of milk coagulation. EXPERIMENTAL PROCEDURES
The Formagraph was used to measure coagulation time as in (12) at a temperature of 35°C. A purified rennet solution 2 of known activity (80 RU/ml) 3 was used to prepare dilutions ranging from .055 RU/ml to 8 RU/ml. Aliquots of 200 /A were added to 10 ml of substrate giving a final activity of enzyme in the milk of .0011 RU/ml to .16 RU/ml. Three replicates were prepared at each activity. By Tektronix 4052 microcomputer (22), data were fitted to plots of t c versus E - ~ and log(tc) versus log(E) - 1 by linear least squares regression. Marquardt's nonlinear least squares regression (11) was used to fit the data to equation [ 3] without transformation. R ESU LTS
Measured coagulation times covered the range from .7 to 66 min corresponding to a relative variation in enzyme activity of 1:140. For the simple ratio estimation of the Storch and Segelcke equation to be valid, the linear regression of t c versus E - 1 must cross the origin. This was not observed. The data were, instead, described by Foltmann's equation, in which the intercept approximates the minimum
TECHNICAL NOTE
343
method used to measure coagulation time (12). Linearity between coagulation time and enzyme concentration is affected by substrate composition. Such variations are largely due to changes in the calcium phosphate equilibrium between ionic and colloidal states and can be eliminated by using nonfat dry milk reconstituted in .01M CaC12 (1). The time that: reconstituted milk is held at the experimental temperature also can cause variation in coagulation time (1, 7). It is recommended that the substrate be aged for 20 h at 2°C then
70
t-
g
ooOOZ/i16 /2010
,,i
5O
k-
200
400
600
800
1000
(ENZYME ACTIVITY) "1 (mLIRU)
Figure 1. Linear regression of coagulation time on inverse rennet activity. Triplicate samples at each activity.
70
.E E v
60
w 50
time required for the enzyme to produce coagulable material (6) under the finite constraints of the experimental conditions. The linear transformation (Figure 1) and the nonlinear method (Figure 2) produced identical k and x: i.e., t c = .685 + .0754 / E
Z
40 30
-J
O
20
o o
10
[7] 0
If this relationship is linear, then the slope of a double logarithmic plot should equal unity. An experimental slope was .94 (Figure 3). This agrees with other slopes (10) and shows that a marginally better fit (R 2 = .999) is obtained compared with equation [7] (R 2 = .996). This difference is so small, however, that in determining enzyme activity equation [3] gives results comparable to those of a logarithmic plot and is easier to use routinely.
.0S
.10
.15
ENZYME ACTIVITY (RU/mL) Figure 2. Nonlinear regression of coagulation time on rennet activity. Triplicate samples at each activity.
2.0
1.8 A W
1.6 1.4
DISCUSSION
Enzymically induced coagulation of milk is a continuous process. Coagulation time, therefore, is not an integral part of the coagulating system. Its determination by turbidity or rheological methods results in t c that correspond to attainment of a particular degree of coagulation (14). Some arbitary point in the overall coagulation process is chosen as the endpoint. For the Formagraph, this point occurs when the substrate gel is of sufficient viscosity to inhibit movement of an immersed pendulum. Consequendy, k and x vary according to the
Z
o
1.2
1.0
R2=
.999
.8 ,6 .4 .2 0 .2
.6
.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
(ENZYME ACTIVrPO-1 Figure 3. Linear regression of log(coagulation time) on log(inverse rennet activity). Triplicate samples at each activity. LOG
Journal o f Dairy Science Vol. 66, No. 2, 1983
344
McMAHON AND BROWN
e q u i l i b r a t e d at t h e e x p e r i m e n t a l t e m p e r a t u r e f o r 30 m i n (3). Provided that conditions under which m e a s u r e m e n t s are m a d e ( s u b s t r a t e c o m p o s i t i o n , t e m p e r a t u r e , a n d e n z y m e c o m p o s i t i o n ) can be c o n t r o l l e d , t h e n r e n n e t a c t i v i t y can be c a l c u l a t e d accurately from Formagraph milk coagulation d a t a . T h e p r o c e d u r e s d e s c r i b e d in this p a p e r f o r p r e p a r i n g t h e s u b s t r a t e a n d m e a s u r i n g coa g u l a t i o n t i m e allow e n z y m e a c t i v i t y t o b e m e a s u r e d a c c u r a t e l y in c o m p a r i s i o n t o a s t a n d a r d curve, w i t h o u t h a v i n g t o d i l u t e t h e u n k n o w n t o t h e same c o n c e n t r a t i o n as t h e reference. T h e s t a n d a r d curve c a n c o v e r a range t h a t e x t e n d s a t least f r o m .0011 R U / m l t o .16 R U / m l . By m o d i f y i n g t h e p r o c e d u r e t o allow a d d i t i o n o f a larger a m o u n t o f e n z y m e , this m e t h o d can m e a s u r e m i l k - c l o t t i n g e n z y m e a c t i v i t y w i t h i n t h e range o f t h e gel d i f f u s s i o n test o f H o l m e s e t al. (8). REFERENCES
1 Berridge, N. J. 1952. Some observations on the determination of the activity of rennet. Analyst 77:57. 2 Darling, D. F., and A.C.M. Van Hooydonk. 1981. Derivation of a mathematical model for the mechanism of casein micelle coagulation by rennet. J. Dairy Res. 48:189. 3 Ernstrom, C. A. 1956. Studies on rennet and rennin. Ph.D. thesis, Univ. Wisconsin, Madison. 4 Ernstrom, C. A. 1958. Heterogeneity of crystalline rennin. J. Dairy Sci. 41:1663. 5 Ernstrom, C. A. 1974. Milk-clotting enzymes and cheese chemistry, Part 1. Milk-clotting enzymes and their action. Page 691 in Fundamentals of dairy chemistry. B. H. Webb, A. H. Johnson, and J. A. Alford, ed. 2nd ed. Avi Publ. Co., Westport, CT. 6 Foltmann, B. 1959. On the enzymatic and the coagulation stages of the rennetting process. Proc. XV Int. Dairy Congr. 2:655. 7 Foltmann, B. 1962. Studies on rennin. VI. The heterogeneity of prorennin and its transformation
Journal of Dairy Science Vol. 66, No. 2, 1983
into rennin. C. R. Tray. Lab. Carlsberg. 32:425. 8 Holmes, D. G., J. W. Duersch, and C. A. Ernstrom. 1977. Distribution of milk clotting enzymes between whey and curd and their survival during Cheddar cheese making. J. Dairy Sci. 60:862. 9 Holter, H. 1932. Uber die Labwirkung. Biochem. Z. 255:160--188. Cited by B. Foltmann in Proc. XV Int. Dairy Congr. 2:655. 10 Hyslop, D., T. Richardson, and D. S. Ryan. 1979. Kinetics of pepsin-initiated coagulation of K-casein. Biochim. Biophys. Acta 566: 390. 11 Marquardt, D. W. 1963. An algorithm for leastsquares estimation of non-linear parameters. J. Soc. Ind. Appl. Math. 2:431. 12 McMahon, D. J., and R. J. Brown. 1982. Evaluation of the Formagraph for comparing rennet solutions. J. Dairy Sci. 65:1639. 13 Overbeek, J.Th.G. 1952. In Colloid science. Vol 7, Ch. 7. H. R. Kruyt, ed. Elsevier, Amsterdam-New York. Cited by T.A.J. Payens. 1976. On the enzyme-triggered clotting of casein; a preliminary account. Netherlands Milk Dairy J. 30:55. 14 Payens, T.A.J. 1976. On the enzyme-triggered clotting of casein; a preliminary account. Netherlands Milk Dairy J. 30:55. 15 Payens, T.A.J. 1977. On enzymatic clotting processes. II. The colloidal instability of chymosintreated casein micelles. Biophys. Chem. 6:263. 16 Payens, T.A.J. 1978. On different modes of casein clotting; the kinetics of enzymatic and nonenzymatic coagulation compared. Netherlands Milk Dairy J. 32:170. 17 Payens, T.A.J. 1978. On enzymatic clotting processes. III. Flocculation rate constants of paracasein and fibrin. Disc. Faraday Soc. 65:164. 18 Payens, T.A.J., and P. Both. 1979. Enzymatic clotting processes. IV. The chymosin-triggered clotting of p-K-casein. Adv. Chem. Ser. 13:129. 19 Payens, T.A.J., A. K. Wiersma, and J. Brinkhuis. 1977. On enzymatic clotting processes. I. Kinetics of enzyme-triggered coagulation reactions. Biophys. Chem. 6:253. 20 Sommer, H. H., and H. Matsen. 1935. The relation of mastitus to rennet coagulability and curd strength of milk. J. Dairy Sci. 18:741. 21 Storch, V., and Th. Segelcke. 1874. Milchforsch, Milchprax. 3:997. Cited by B. Foltmann. 1959. Proc. XV Int. Dairy Congr. 2:655. 22 Tektronix Plot 50 Statistics. 1977. Vol 4. Tektronix, Inc., Beaverton, OR.
NOTES
Milk Coagulation Time:. Linear Relationship with Inverse of Rennet Activity 1 D. J. McMAHON and R. J. BROWN Department of Nutrition and Food Sciences Utah State University Logan 84322
ABSTRACT
where tc is coagulation time, E is enzyme activity, and k is a constant. Holter (9) observed that this equation is only valid for a narrow range of enzyme concentration (variations of 1:4) and concluded that deviations from the Storch and Segelcke relationship are due to a time lag in the aggregation phase during the coagulation process. He introduced a correction factor into the equation:
The extent to which time for milk coagulation is linear with the inverse of enzyme activity was investigated. The Formagraph can be used to measure time for coagulation of milk over a range of rennet activity. Linearity of coagulation time versus inverse of enzyme activity exists within the range of concentration .0011 RU/ml to .16 RU/ml, which represents relative variation in rennet activity of 1:140.
E(t c -- x) = k
where x represents the time required to allow enzymically converted casein to aggregate. To facilitate statistical analysis, Foltmann (6) rearranged the Holter equation into the form:
INTRODUCTION Milk-clotting enzyme activity commonly is calculated by comparing coagulation time o f an unknown relative to a standard of known activity. Because of deviations from linearity of the relationship between coagulation time and the inverse of enzyme activity, it has been suggested that unknown and standard samples should have approximately the same enzyme concentration (5). In (12) this relationship was linear over coagulation time ranging from 5 to 30 rain when clotting time was measured with the Formagraph or the Sommer and Matsen apparatus (20). The linear relationship between milk coagulation time and the inverse of enzyme concentration first was postulated by Storch and Segelcke (21), who stated that the product of enzyme concentration and coagulation time is constant: tcE = k
k+ tc = ~ x
[31
Observing that k remained constant whereas x varied for several fresh milk samples, he concluded that differences in coagulability were a consequence of the nonenzymic aggregation phase of the overall coagulation process. Various mathematical models have been proposed to describe enzymic coagulation of milk. Payens (14, 16) derived an expression for changes in weight average molecular weight of coagulating milk by yon Smoluchowski's rate theory (13) for the production of multiple particles in bimolecular flocculation:
Mw M--o=
[11
1 -- M o ( l - - f ) (
) 1/2 {f(t) _
(1-f)(t)3/3)/C O Received April 26, 1982. ~Utah Agricultural Experiment Station Journal Article No. 2709. Approved by the director. 2From New Zealand Cooperative Rennet Co., Eltham, New Zealand. Rennin activity units as described by Ernstrom (4). 1983 J Dairy Sci 66:341--344
[2]
341
[4]
where Mo is the average molecular weight of casein micelles in milk, ks is the aggregation rate constant, V is the enzymic velocity, f is the ratio of the molecular weight of released peptide to Mo, Co is the substrate concentration,
342
McMAHON AND BROWN
and r is the parameter governing the kinetics of the clotting process, is defined as: r = (k s v ) - 1 1 2 -2-
[51
in which V is proportional to enzyme concentration and r is assumed to approximate t c (18, 19). The r can be visualized as the time needed for the enzyme to produce a minimum number of hydrolyzed particles in the absence of any flocculation. Measured t c depends on the technique chosen to monitor coagulation and according to Foltmann (6) is only an empirical approximation, because the aggregation stage begins as soon as the first casein is hydrolyzed. The lag time is merely the result of different orders of enzymic and aggregation reactions (19). Equation [5] has an advantage over the Storch and Segelcke equation in that it states explicitly that the lag period is dependent on aggregation rate to the same extent as on enzymic velocity (10). If k s is constant, equation [5] predicts a plot of log tc versus log E - 1 to be a straight line with slope .5. Payens (15, 19) postulated that not every collision between para-casein micelles leads to permanent contact but only those in which para-K-casein sites are involved. Because k s is a measure of repulsion between flocculating particles, it can be considered a function of the amount of macropeptide split from K-casein (15). Clotting starts before the maximal number of peptides are proteolysed b y the enzyme, and the fraction of sites available for permanent contact (and, hence, ks) increases in proportion to the enzyme concentration (19). A t a first approximation, equation [5] reduces to the linear form of equation [ 3 ]. Another mathematical model for milk coagulation was described by Darling and Van H o o y d o n k (2) from which an equation expressing tc was derived: 1 (S O + l-e x p ( - CmSo ) - 1 ) + tc =~V
W o e x p ( _ C m S o ) ( 1 _ 1_ ) Ks nc no
[61
where So is the micellar surface K-casein concentration at time zero, W o is the stability factor at time zero, n o is the particle concenJournal of Dairy Science Vol. 66, No. 2, 1983
tration at time zero, nc is the particle concentration at time tc, and Cm is a proportionality constant. For this model, coagulation time can be visualized as the time required to reduce the number of micelles from n o to n o If k s is a function of enzyme concentration or a constant, this equation also reduces to equation [ 3 ]. From either of these models of milk coagulation, it appears that the inverse linear relationship between coagulation time and enzyme activity is valid for use in measuring enzyme activity. A study was made of the extent to which it remains valid when coagulation time is measured by Formagraph. Linearity between coagulation time and inverse of enzyme activity over an extensive range would indicate it is not necessary to dilute samples to approximately the same coagulation times in comparing enzyme activities. The ability to work with the Formagraph at low enzyme concentrations also may provide new possibilities for studying mechanism of milk coagulation. EXPERIMENTAL PROCEDURES
The Formagraph was used to measure coagulation time as in (12) at a temperature of 35°C. A purified rennet solution 2 of known activity (80 RU/ml) 3 was used to prepare dilutions ranging from .055 RU/ml to 8 RU/ml. Aliquots of 200 /A were added to 10 ml of substrate giving a final activity of enzyme in the milk of .0011 RU/ml to .16 RU/ml. Three replicates were prepared at each activity. By Tektronix 4052 microcomputer (22), data were fitted to plots of t c versus E - ~ and log(tc) versus log(E) - 1 by linear least squares regression. Marquardt's nonlinear least squares regression (11) was used to fit the data to equation [ 3] without transformation. R ESU LTS
Measured coagulation times covered the range from .7 to 66 min corresponding to a relative variation in enzyme activity of 1:140. For the simple ratio estimation of the Storch and Segelcke equation to be valid, the linear regression of t c versus E - 1 must cross the origin. This was not observed. The data were, instead, described by Foltmann's equation, in which the intercept approximates the minimum
TECHNICAL NOTE
343
method used to measure coagulation time (12). Linearity between coagulation time and enzyme concentration is affected by substrate composition. Such variations are largely due to changes in the calcium phosphate equilibrium between ionic and colloidal states and can be eliminated by using nonfat dry milk reconstituted in .01M CaC12 (1). The time that: reconstituted milk is held at the experimental temperature also can cause variation in coagulation time (1, 7). It is recommended that the substrate be aged for 20 h at 2°C then
70
t-
g
ooOOZ/i16 /2010
,,i
5O
k-
200
400
600
800
1000
(ENZYME ACTIVITY) "1 (mLIRU)
Figure 1. Linear regression of coagulation time on inverse rennet activity. Triplicate samples at each activity.
70
.E E v
60
w 50
time required for the enzyme to produce coagulable material (6) under the finite constraints of the experimental conditions. The linear transformation (Figure 1) and the nonlinear method (Figure 2) produced identical k and x: i.e., t c = .685 + .0754 / E
Z
40 30
-J
O
20
o o
10
[7] 0
If this relationship is linear, then the slope of a double logarithmic plot should equal unity. An experimental slope was .94 (Figure 3). This agrees with other slopes (10) and shows that a marginally better fit (R 2 = .999) is obtained compared with equation [7] (R 2 = .996). This difference is so small, however, that in determining enzyme activity equation [3] gives results comparable to those of a logarithmic plot and is easier to use routinely.
.0S
.10
.15
ENZYME ACTIVITY (RU/mL) Figure 2. Nonlinear regression of coagulation time on rennet activity. Triplicate samples at each activity.
2.0
1.8 A W
1.6 1.4
DISCUSSION
Enzymically induced coagulation of milk is a continuous process. Coagulation time, therefore, is not an integral part of the coagulating system. Its determination by turbidity or rheological methods results in t c that correspond to attainment of a particular degree of coagulation (14). Some arbitary point in the overall coagulation process is chosen as the endpoint. For the Formagraph, this point occurs when the substrate gel is of sufficient viscosity to inhibit movement of an immersed pendulum. Consequendy, k and x vary according to the
Z
o
1.2
1.0
R2=
.999
.8 ,6 .4 .2 0 .2
.6
.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
(ENZYME ACTIVrPO-1 Figure 3. Linear regression of log(coagulation time) on log(inverse rennet activity). Triplicate samples at each activity. LOG
Journal o f Dairy Science Vol. 66, No. 2, 1983
344
McMAHON AND BROWN
e q u i l i b r a t e d at t h e e x p e r i m e n t a l t e m p e r a t u r e f o r 30 m i n (3). Provided that conditions under which m e a s u r e m e n t s are m a d e ( s u b s t r a t e c o m p o s i t i o n , t e m p e r a t u r e , a n d e n z y m e c o m p o s i t i o n ) can be c o n t r o l l e d , t h e n r e n n e t a c t i v i t y can be c a l c u l a t e d accurately from Formagraph milk coagulation d a t a . T h e p r o c e d u r e s d e s c r i b e d in this p a p e r f o r p r e p a r i n g t h e s u b s t r a t e a n d m e a s u r i n g coa g u l a t i o n t i m e allow e n z y m e a c t i v i t y t o b e m e a s u r e d a c c u r a t e l y in c o m p a r i s i o n t o a s t a n d a r d curve, w i t h o u t h a v i n g t o d i l u t e t h e u n k n o w n t o t h e same c o n c e n t r a t i o n as t h e reference. T h e s t a n d a r d curve c a n c o v e r a range t h a t e x t e n d s a t least f r o m .0011 R U / m l t o .16 R U / m l . By m o d i f y i n g t h e p r o c e d u r e t o allow a d d i t i o n o f a larger a m o u n t o f e n z y m e , this m e t h o d can m e a s u r e m i l k - c l o t t i n g e n z y m e a c t i v i t y w i t h i n t h e range o f t h e gel d i f f u s s i o n test o f H o l m e s e t al. (8). REFERENCES
1 Berridge, N. J. 1952. Some observations on the determination of the activity of rennet. Analyst 77:57. 2 Darling, D. F., and A.C.M. Van Hooydonk. 1981. Derivation of a mathematical model for the mechanism of casein micelle coagulation by rennet. J. Dairy Res. 48:189. 3 Ernstrom, C. A. 1956. Studies on rennet and rennin. Ph.D. thesis, Univ. Wisconsin, Madison. 4 Ernstrom, C. A. 1958. Heterogeneity of crystalline rennin. J. Dairy Sci. 41:1663. 5 Ernstrom, C. A. 1974. Milk-clotting enzymes and cheese chemistry, Part 1. Milk-clotting enzymes and their action. Page 691 in Fundamentals of dairy chemistry. B. H. Webb, A. H. Johnson, and J. A. Alford, ed. 2nd ed. Avi Publ. Co., Westport, CT. 6 Foltmann, B. 1959. On the enzymatic and the coagulation stages of the rennetting process. Proc. XV Int. Dairy Congr. 2:655. 7 Foltmann, B. 1962. Studies on rennin. VI. The heterogeneity of prorennin and its transformation
Journal of Dairy Science Vol. 66, No. 2, 1983
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