Development of surface functionality of casein particles as the controlling parameter of enzymic milk coagulation

Colloids and Surfaces, 44 (1990)

263-279

263

Elsevier Science Publishers B.V., Amsterdam

-

Printed in The Netherlands

Development of Surface Functionality of Casein Particles as the Controlling Parameter of Enzymic Milk Coagulation DONALD Department

J. McMAHON of Nutrition

UT 84322-8700 (Received

and RODNEY

J. BROWN

and Food Science,

Utah State University,

Logan,

(U.S.A.)

15 October 1988; accepted 5 July 1989)

ABSTRACT Changes in a colloidal milk system were monitored by measuring changes in turbidity and the modulus of the resultant milk gel. Turbidity was measured in milk of normal concentration and in milk that had been diluted to eliminate the effects of multiple light scattering. The relationship between true gelation time and observed coagulation time, and how gelation time might affect the theoretical modelling of enzymic milk coagulation are discussed. The turbidity of milk at normal concentration cannot be directly related to particle size but it could be correlated with gel modulus measurements. True gelation time was calculated by fitting gel modulus data to an exponential equation. The result coincided with the inflexion point in the turbidity plots. Surface functionality of casein particles in relation to the collision

area and the extent to which K-casein macropeptide

removed from the particle surface for successful collisions

must be

are discussed.

INTRODUCTION

Enzymic coagulation of milk is the result of a series of chemical and physical changes that occur when chymosin (E.C.3.4.23.4) is added to milk. Each of these reactions is important during the manufacture of milk into cheese and must be considered in the development of new dairy products. These reactions overlap and some are interdependent. They can be categorized as follows: 1. Selective hydrolysis of K-casein at Phe 105-Met106that removes its ability to stabilize casein particles (also called casein micelles). This initiates coagulation. 2. The particle surface become less stable and more reactive. Casein particles aggregate via the Smoluchowski mechanism. 3. Aggregation results in formation of a network of casein particles at the gelation point of the milk coagulation reaction.

0166-6622/90/$03.50

0 1990 Elsevier Science Publishers

B.V.

264

4. After gelation, casein particles continue to be incorporated into the gel network and rearrangements of chains of casein particles can occur. 5. Casein particles fuse and are consolidated into thick strands as excess serum is expelled from the gel. Green et al. (1977) observed that casein particles in milk are more evenly distributed than expected in a simple random distribution. Particles repel each other and their colloidal stability is the result of a combination of thermodynamics forces. Destabilization of this colloidal system by enzyme hydrolysis of Ic-casein can be considered a reduction in its composite stabilization energy. Chymosin (the major enzyme in calf rennet) selectively hydrolyses K-casein, by removing a hydrophilic macropeptide from the surface of the casein particles. This has the following effects on the properties of these particles: 1. Their zeta potential is lowered from - 17 to - 9 mV (Green, 1973 ) , which reduces the electrostatic repulsion between particles. Unlike other hydrophobic colloids, the particle stability of casein particles is only partly due to their surface charge repulsion because such colloids with zeta potentials of less than 20 mV are generally unstable (Darling and Dickson, 1979). Milk, with a zeta potential of - 17 mV, is very stable. 2. Native casein particles approach each other down to atomic distances (Payens, 1977) and so, short range effects predominate. For example, in many biological systems, hydration repulsion is an important short range factor in maintaining integrity. Particles are repulsed when hydration shells of their polar regions on the particle surface overlap. The macropeptide released from the casein particle surface is very hydrophilic and the surface develops a dichotomous character upon its removal. There are regions of positively charged para+-casein and negatively charged x-casein (with intact macropeptide), a,casein, and /I-casein. This not only affects hydration repulsion but also allows ion-pairing between colliding particles. 3. Caseins are among the most hydrophobic of all proteins (Farrell and Thompson, 1974). Removal of the macropeptide domain of K-casein exposes its hydrophobic domain on the particle surface and increases the opportunity for hydrophobic interactions when surface regions collide. These hydrophobic interactions are the driving force for the formation of casein molecules into their characteristic particle structure (McMahon and Brown, 1984a). Therefore, removal of the barrier that limits particle size, i.e. surface macropeptide, means the continuation of these interactions as particles aggregate (McMahon and Brown, 1984b). 4. Steric interactions of surface protein chains also stabilize casein particles. Walstra (1979) showed that the macropeptide domain of K-casein protrudes from the surface of the particles. Removing them would then reduce the stabilizing effects of steric repulsion between particles and allow them to move even closer together. The multiplicity of forces involved in stabilization of casein particles means

265

that coagulation can be induced in a variety of ways: by enzyme action, by heat, and by acidification. This complicates the study and understanding of milk coagulation because the colloidal casein particles can aggregate whenever the net stabilizing energy is reduced below a critical level. Geometric model of milk coagulation The aggregation of casein particles can be considered as addition of clusters of particles. Computer simulations by Sutherland (1970)) Sutherland and Goodarz-nia (1971) and Goodarz-nia (1978) have shown that chain formation is much more extensive from the addition of such clusters of particles rather than the aggregation of individual particles. This is basically Smoluchowski’s simple coagulation theory (Overbeek, 1952) in which the process involves clusters containing varying numbers of primary particles. Chains of particles are formed as a direct consequence of the random geometry of the coagulation process. As the aggregation reaction proceeds, aggregates build up and the number of potential interaction sites increases, and the size of casein aggregates increases rapidly. In milk of normal concentration an extended space network of casein particles is eventually formed. This network is formed abruptly after a critical cluster size is attained (Darling and Van Hooydonk, 1981); after this, any further diffusion results in immediate collision with other particles (McMahon et al., 1984a). Gelation occurs at this point and the physical state of milk changes from a colloidal fluid to a two-phase system containing a gel and entrapped serum. It is analogous to the gel point in nonlinear condensation polymerization reactions. At the point of gelation, the modulus of the gel is too small to be recorded on any of the instruments now used to monitor gel development during milk coagulation. For example, use of the Formagraph instrument (McMahon and Brown, 1982) requires that the gel be rigid enough to restrict movement of milk through an immersed wire loop. In measuring the gel point, the accuracy of the various methods used to monitor milk coagulation (McMahon and Brown, 1983) depends on the ability to detect very small changes in gel modulus. This problem might be solved by fitting experimental data to mathematical equations that describe milk coagulation. The measurements of gel modulus could then be used to calculate the true gelation time (McMahon et al., 1984b ). Measurement of gel&ion time Most researchers who compare enzymic coagulation time of milk to enzyme activity think that the relationship conforms to the following type of equation:

E(t,-x)

(1)

=k

This equation is a modification by Holter (1932) of the original Starch and Segelcke (1874) equation describing milk coagulation. In this equation, E is enzyme activity, t, is the observed coagulation time, x is a lag time required for the aggregation of enzymically converted casein, and lzis a constant. There have been many reports of this inverse relationship between coagulation time and enzyme activity (McMahon and Brown, 1983). The lag time in the above equation implies that individual casein particles have to have a certain proportion of their K-casein removed before they will aggregate. Dalgleish (1979) calculated that this proportion was about 90%. However, these theories are based on observed coagulation time, which may differ greatly from the true gelation time. To solve this discrepancy, we tried to find a method to experimentally determine true gelation time in order to derive mathematical models to describe the enzymic milk coagulation process. METHODS

Materials

Milk substrate was prepared by dispersing 12 g of nonfat dry milk powder in 100 g of water or aqueous CaCl, solution of various concentrations. This was then stored at 4°C overnight to allow for hydration of milk constituents. Before each analysis, the milk substrate was warmed to 30 or 35 ‘C and maintained at that temperature for 30 min. An ion exchange purified chymosin solution (New Zealand Cooperative Rennet Co. Ltd, Eltham, New Zealand) of clotting activity 188 rennet units (RU) ml-’ (Emstrom, 1956) was diluted with distilled water to the required activity levels. Formagraph

coagulation measurement

The Formagraph method of McMahon and Brown (1982) was used to record changes in gel modulus following chymosin addition. The chart recorder was started when enzyme was added to the milk. After mixing of the enzyme-milk solution the sample is brought into contact with an immersed wire loop pendulum and is subjected to a linear oscillation. Uncoagulated milk passes freely through the wire loop and there is insufficient force to tilt the pendulum. Following gelation, the resultant increase in modulus pulls the pendulum; this movement is recorded on photosensitive paper. The observed coagulation time (RCT ) was determined by measuring the distance from the origin to the point where the baseline diverges (Fig. 1).

267 0

10 -

': z

RUlllll

A: 1.00 20 -

B: 0.47

5. F g

c: 0.31 D: 0.23

30-

E: 0.185

40 -

50-

Fig. 1. Measurement at various chymosin

of coagulation and gel modulus, using the Formagraph, as a function of time activities. (Reprinted from McMahon and Brown, 1982.)

Gel modulus curve fitting A computer program was written to digitize data from the Formagraph record of changes in gel modulus (McMahon et al., 198413). The photographic paper from the Formagraph was placed on a Tektronix 4662 interactive digital plotter and a cross-hair eyepiece was used to trace the curve and record data points on magnetic tape on a Tektronix 4052 computer. A Gauss-Newton nonlinear least squares regression iteration program was used to estimate parameters for a prediction equation. Changes in gel modulus by enzymic action on milk were described by ScottBlair and Burnett (1963) by the exponential equation: G=G_,exp-‘lt

(2)

where G is the pseudo modulus of rigidity, G, is the theoretical maximum modulus at infinite time, ,I is the time required after gelation for the modulus to equal GJexp and t is time after coagulation. Fitting experimental data to this equation is tedious (Garnot and Olson, 1982) because the true gelation time is unknown (it occurs sometime before any increase in gel modulus is visually observed). Changes in gel modulus are therefore normally expressed as time from enzyme addition. A modified form of Eqn (2) was used so that it could be solved by least squares regression techniques (McMahon et al., 1984b). The modified equation was defined as: G=O

for t-c7

G= Gaexp-dk(t-T)

for t> z

(3)

where t is time subsequent to enzyme addition, 7 is the true gelation time, and k is the relative rate of initial increase in gel modulus.

268

Light scattering measurements Changes in light scattering, at 600 nm, in milk due to chymosin action were monitored using a Beckman DU-8B UV/Vis spectrophotometer with a temperature controlled cuvette holder and light scattering accessory. Most researchers who have studied milk coagulation using light scattering (Dalgleish, 1979, 1980; Surkov et al., 1982) used milk samples diluted by a factor of l/60 to l/100. However, dilution changes the coagulation properties of milk because it reduces casein particle concentration. Dilution has been necessary because multiple light scattering becomes increasingly predominant at higher milk concentrations. At its normal concentration, skim milk has a turbidity in a 1 cm pathlength cuvette > 3 absorbance units, which exceeds the capabilities of most spectrophotometers. The effect of dilution was studied by diluting milk substrate with 0.01 M CaCl,. The Beckman DU-8B spectrophotometer is a single beam instrument with a working range of up to 4 absorbance units. Light passing through the sample cuvette can be collected in any of three modes. Normal specular measurements use a 0 to 7” light collection mirror. The light scattering accessory has a 0 to 30” mirror, which can be utilized to collect light in the total 30” cone or in a scattering mode in which the 30” cone minus the 7” specular cone is used. Three milliliters of milk substrate were pipetted into a disposable cuvette (1 cm pathlength) and maintained in the cell compartment at the desired temperature during the analysis. The spectrophotometer was then set to read zero with milk substrate in the lightpath. An appropriate aliquot (10 or 20 ~1) of a dilute chymosin solution was added and mixed rapidly ( N 5 s ). The average of two measurements was recorded every 4 s and the data was transmitted via an RS232 connection to a Tektronix 4052 computer and stored on magnetic tape. The light scattering curves were then time-averaged and plotted on a Tektronix 4662 interactive digital plotter. RESULTS

Observed coagulation time Observed coagulation times (RCT) measured from Formagraph records were linear over a wide range of enzyme activity (Fig. 2 ) . The linear regression equation, however, contained a relatively large y intercept. This would seem to confirm the existence of a lag time between the primary phase of enzyme hydrolysis and the secondary phase of particle aggregation. However, comparison of RCTs with enzyme activity involves an arbitrary point in the coagulation process. For the Formagraph, this is when the gel modulus is rigid enough to inhibit movement of a wire pendulum through milk. Enzymically induced coagulation of milk is a continuous process and there-

269

y = 0.47 + 3.82X R&2 I 0.997

30-

0

4

2

l/Enzyme

6

8

10

Activity (mL/RU)

Fig. 2. Linear regression of Formagraph observed coagulation time on inverse chymosin over the activity range of 0.0022-0.078 RU ml-‘. Triplicate samples at each activity.

activity

100

0

13

14

15

16

17

18

TIME (MIN.)

Fig. 3. Viscosity versus time after chymosin addition (2% of 0.40 RU ml-‘) of reconstituted nonfat dry milk (12 g+ 100 g 0.01 A4 CaCl,) showing measurement of coagulation by three methods: Formagraph (F); rolling bottles (R); and viscosity (V). (Reprinted from McMahon and Brown, 1983.)

fore RCT is not really an integral part of the coagulation system. Determination of RCT by turbidity or rheological methods results in an endpoint that simply corresponds to attainment of a particular degree of aggregation. In a previous paper (McMahon and Brown, 1982) we showed that results differ when different methods are used to determine coagulation time (Fig. 3 ) . The RCT for the Sommer and Matsen (1935) rolling bottle method, which is defined as the breaking of a milk film on the inner surface of the bottle, occurs prior to the RCT for the Formagraph. The RCT for the Kopelman and Cogan

270

(1976) viscosity procedure, which is defined as the extrapolated intersection of the two straight line portions of the viscosity versus time plot, is between the RCTs as measured by the other two methods. Because light scattering or turbidity measurements of milk usually involves diluted milk, it is difficult to correlate these results with those from other methods of measuring RCT. In this study, we monitored changes in light scattering in undiluted milk to determine whether observations involving dilute solutions were similar to those involving normal milk. It also allowed us to correlate such measurements with changes in gel modulus. We were using a “non-ideal” light scattering system, but this was necessary to duplicate situations faced by dairy processors. Milk has a high particle concentration, a broad particle size distribution (which is close to the wavelength size of the incident light), a protein type and concentration which varies from cow to cow (and from season to season), and a salt system of calcium phosphate which is in equilibrium between its colloidal insoluble form, soluble complexes of calcium phosphate, calcium complexed with proteins, and free calcium ions. Dilution studies Diluting skim milk to eliminate multiple light scattering (l/60) makes it possible to obtain similar information from both the specular and scatter modes of light collection (Figs 4 and 5). The turbidity increase in the specular mode is recorded as a decrease in the scatter mode. However, much information is lost when milk is diluted. Aggregation rate

0

3

6 TIME

9

12

15

hid

Fig. 4. Turbidity (600 nm) by specular mode of light collection versus time after chymosin addition (0.66% of 2 RU ml-‘) of reconstituted nonfat dry milk (12 g+ 100 g 0.01 M CaCl,) diluted l/60 with 0.01 A4 CaCl,.

271

a. IS

0

6

3

9 TIME

12

IS

Cmld

Fig. 5. Turbidity (600 nm) by scatter mode of light collection versus time after chymosin addition (0.66% of 2 RU ml-r) of reconstituted nonfat dry milk (12 g+ 100 g 0.01 M CaCI,) diluted l/60 with 0.01 A4 CaCl,.

0

5

I0 TIME

I5

20

25

crn~d

Fig. 6. Turbidity (600 nm) by specular and scatter modes of light collection versus time after chymosin addition (0.33% of 2 RU ml-‘) of reconstituted nonfat dry milk (12 g+ 100 g 0.01 A4 CaCl,) diluted l/2 with 0.01 M CaCl,. The same shape curve is obtained with undiluted milk substrate.

kinetics can be calculated for the dilute system but we are primarily interested in the formation of the milk gel and the consequences associated with its formation. Skim milk at its normal concentration or diluted l/2 gave the same results in both the specular and scatter modes (Fig. 6). Multiple scattering occurred but the complete coagulation process could be followed. Note the ap-

272

pearance of a “shoulder” just before coagulation is visible. It did not appear when the milk had been diluted greater than l/10. Gel formation, however, is a continuous process and there are no sudden changes in type or extent of aggregation. Therefore, the shoulder in the turbidity plot is a function of the scattering of the incident light as particle size increases. This has also been observed by Hardy et al. (1981) and Yuan (1989, unpublished data) when diffuse reflection photometry is used to follow milk coagulation. There is a change in the manner in which light interacts with particles as the size of the particles approaches the wavelength of the incident light. When a shorter wavelength is used the shoulder appears earlier. Even though multiple light scattering means this method cannot be directly related to particle size it is a valuable tool for monitoring the coagulation process. Full strength milk must be used if measurements of curd firming are to be related to turbidity changes. This is a necessity in studying milk coagulation because instruments that measure gel firmness only provide data after the coagulation time is passed. They give no information on particle aggregation that occurs prior to development of the space network of interconnected casein micelles. In comparison, monitoring light scattering enables detection of changes in the milk system from the time the enzyme is added through the _. .-

0.06

+0.006

0

5

15

10

TIME

20

25

30

(min)

Fig. 7. Turbidity (600 nm) versus time after chymosin addition of reconstituted nonfat dry milk (12 gt 100 g 0.005 M CaCl,). Arrows represent Formagraph observed coagulation time (F) and gelation time (7) estimated by Eqn (3). The lower curve is the derivative of the upper curve and the occurrence of 7 at the derivative maximum is shown by an arrow.

273

40 y.

0

-.04+3.43x

2

l/Enzyme

4

R"2 -0.998

6

8

1

Activity (mUFiLl)

Fig. 8. Linear regression of true gelation time on inverse chymosin activity over the activity range of 0.0022-0.078 RU ml-‘. True gelation time was determined by fitting Formagraph data to Eqn (3

). Duplicate samples at each activity.

gelation point. So the two methods compliment each other even though interpretation of changes in light scattering of full strength milk is difficult. When changes in gel modulus in coagulating milk were also measured, the RCT measured on the Formagraph occurred after the shoulder (Fig. 7). However, the true gelation time determined by fitting Formagraph data to Eqn (3 ) coincided with the inflexion point of the light scattering curve. This is the maximum in the first derivative of the light scattering plot. Thus, if a model of enzymic milk coagulation is based upon measurements of RCTs it would be in error by as much as 20-25%. All models of enzymic milk coagulation should be based upon true gelation times, which can now be measured only by light scattering in milk at its normal concentration or by calculation true gelation time from the gel modulus. The effect of using true gelation time was apparent when it was plotted against the inverse of enzyme activity (Fig. 8) and compared to the regression equation when RCT measurements were used (Fig. 2). The intercept with true gelation time was within the experimental error of zero, as predicted by Starch and Segelcke in 1874 and reported by Brown and Collinge in 1986. A critical criterion to consider when comparing different methods of measuring milk coagulation time is the nearness of the intercept to zero. Differences between RCT and true gelatin time are artifacts of the measurement procedure.

274

Aggregation

of casein particles

We had previously observed that there were considerable changes in the colloidal milk system within a few seconds of adding chymosin (McMahon et al., 1984a). Initially, scattering decreased as macropeptide was cleaved from the surface of casein particles. Scattering soon increased as particles begin to aggregate. This occurred within the first minute after the addition of enzyme even though RCT was not observed for a further six minutes. Significant aggregation had begun within 20% of the true gelation time. Thus, aggregation had started well before the completion of enzymic hydrolysis of K-casein. Time required for coagulation simply reflects differences in orders of reaction of the enzyme hydrolysis and particle aggregation. The aggregation reaction has the potential to occur at any time as casein particles diffuse and collide. When stabilization energy at the collision zone between any two particles has been sufficiently reduced a successful collision occurs resulting in aggregation of the two particles. This process of particle collisions is occurring continuously and particle clusters are only built up as the enzyme hydrolyzes more Ic-casein. DISCUSSION

Payens (1976,1978) developed equations to describe changes in the number of casein particles during aggregation. According to his hypothesis, the only requirement for a successful collision was that the interaction zone between two colliding particles be stripped of macropeptide regardless of the nature of the remaining particle surface. Thus, a micelle may have considerable rc-casein hydrolyzed (Fig. 9) but still not aggregate on collision with another micelle. Its rotational orientation must also be considered. When the interaction zone of both micelles consists of para-lc-casein, a successful collision takes place and the particles aggregate. Early work by Dalgleish (1979) suggested that more than 90% of the macropeptide must be removed before an individual particle can participate in aggregation. Current thinking, however, is that enzymic milk coagulation must be considered as a one step process rather than as two separate steps of enzymic hydrolysis followed by subsequent aggregation. That is, the enzymic and aggregation phases (both of which are time dependent) occur concurrently. According to either nonlinear polymerization or cluster growth theory there is a buildup of reactive sites on the surface of the aggregating particles. This is necessary for the sudden transformation of milk from a fluid to a gel. Gel formation will only occur when the aggregating casein particle develop a surface functionality greater than two.

275

.

COLLlSlON

pare-k-carein

UNSUCCESSFUL

NO RGGREGRTION

COLLISION

SUCCESSFUL L

RGGREGIITIoN

Fig. 9. Schematic

0CCIJAS

diagram of successful and unsuccessful

collisions

between casein particles.

Caseinparticle functionality There are two factors that affect this increase in functionality of the particle surface from an initial value of zero (native casein micelles) to a maximum, which occurs when all the rc-casein macropeptide has been completely removed from the particle surface: 1. Size of the collision area between two particles necessary to create a reactive site. 2. How much macropeptide must be removed in the collision area so that the energy barrier is reduced enough to enable two particles to stick together. In other words, the energy barrier surrounding casein particles varies depending on the amount of macropeptide removed from the surface. The required size of a reactive area also varies because of variations in the size of casein particles in milk; if casein particles are small, fewer K-casein molecules must be hydrolyzed to collide successfully with another particle (Fig. 10). Therefore, the outcome of a collision between two particles depends only on

276

Fig. 10. Schematic

diagram of successful collisions between casein particles of different

sizes.

the reduction in the energy barrier at the collision area between the two particles. It is still not known whether there is some relationship between the size of collision area and extent of macropeptide removal required to create a reactive site. We know that individual K-casein molecules should not be identified as reactive sites but we do not known whether, for example, a large area in which 80% of the macropeptide has been removed is just as reactive as a small area in which all the macropeptide has been removed. Immediately after enzyme is added, two particles are unlikely to have reactive sites in their collision zone. Assuming the movement of the attacking enzyme is controlled by Brownian motion, hydrolysis will occur randomly over the particle surface without bias to hydrolyze part of the surface while leaving other portions intact. Consequently, the aggregation rate will initially be very low and coagulation will not occur until a large portion of the Ic-casein has been hydrolyzed. As macropeptide is released, the aggregation rate will increase. A considerable region of the particle surface must be free of macropeptide before enough reactive sites are produced to increase the surface functionality above two. If the energy barrier between colliding particles could be reduced in some other way, it should be possible to shorten the coagulation time. The slow increase in the functionality of the casein particles and cluster addition growth provide valuable insights concerning the influence of milk composition on coagulation. This influence of surface functionality on coagulation can be observed when milk substrate is prepared with various calcium concentrations.

277

Effect of calcium on milk coagulation As previous researchers have shown (Qvist, 1979 ), calcium content of milk has a large effect on coagulation and gel formation. We applied curve fitting techniques to Formagraph data from a previous study (McMahon et al., 1984c) and calculated true gelation times and other parameters describing gelation (Table 1) . Addition of calcium reduced milk gelation time and increased gel modulus. At added calcium levels of 1 to 10 m&I, the true gelation time was calculated as occurring at 85 5 1% of the measured Formagraph coagulation time. At 20 miI4 added calcium the gel firming rate (k) is at its lowest value and z= 77% RCT. This suggests that initial aggregation proceeds more rapidly but the network rearrangements that serve to strengthen the gel are inhibited. At high calcium levels, RCT is retarded and this is assumed to be because of effects of high ionic strength. A further increase in calcium content beyond a critical value reduces the maximum gel modulus. The effect of calcium on coagulation can be better understood if we consider its effects on the formation of reactive sites on the particle surface. Calcium binds to the phosphoserine groups on the casein molecules (particularly /3casein) and it can also form ion pairs with aspartic and glutamic acid residues. This binding is dependent on the calcium ion concentration of milk. As calcium binds to the proteins, it neutralizes the net negative charge of the casein particles and increases the hydrophobicity of adjacent regions on the particle surface (Green and Marshall, 1977). This not only reduces the electrostatic repulsion between particles but increases their hydrophobicity. The reduction in overall energy barrier between particles implies that either the required size of a reactive site has become smaller or that less macropeptide TABLE

1

Coagulation parameters of nonfat dry milk reconstituted (12 g+ 100 g) in distilled water and various calcium solutions. Observed coagulation time (RCT) was measured from Formagraph records. True gelation times (T), initial rate parameter (h), and theoretical maximum gel modulus (G,)

were calculated by fitting Formagraph

Calcium concentration

(mM)

RCT (min)

data to Eqn (3) 5 (min)

z/RCT

k

GW (mm)

(%)

0

30.9

26.7

86

1.31

40.4

1 4 8

27.3 21.6 16.7

24.0 18.8 14.5

88 87 87

1.49 1.31 1.23

40.0 43.3 44.3

10 20 40 80

14.9 11.9 11.4 16.2

12.6 9.2 9.9 15.8

85 77 87 98

1.12 0.79 1.36 2.58

45.7 47.1 30.3 21.1

278

must be removed from the region for two particles to coalesce. So, reactive sites would be produced more quickly and a critical functionality reached sooner, thus reducing gelation time. We reported in a previous paper (McMahon et al., 1984c) that the addition of calcium to milk not only shortens coagulation time but also decreased the light scattering following coagulation. When the amount of enzyme was adjusted to equalize RCTs, addition of extra calcium reduced the maximum change in light scattering. This apparently reflects the effect of calcium on the rate at which surface functionality increases. More rapid development of functionality would increase the openness of the gel network and decrease the amount of casein forming the initial gel network. Slower development would produce denser aggregates. Any casein particles free at the gelation point would form secondary cross-links and strengthen the existing particle linkages. CONCLUSIONS

The methods we used to measure true gelation time of milk provided data useful in developing models of this process. Aggregation of enzyme-treated casein particles commences at an early stage in the coagulation reaction. It reaches significant proportions by at least 50% of its RCT. True gelation time can be calculated by fitting measurements of gel modulus to an appropriate equation, such as a modified Scott-Blair and Burnett (1963) equation. Also, true gelation time corresponded to the inflexion point of turbidity plots made by coagulation milk at its normal concentration. Growth kinetics that favor cluster addition accentuate chain formation and lead to the formation of an open network of casein particles. Once gelation has occurred, internal rearrangements of the chains and the addition of more particles to the network permits the transfer of stresses placed on the network structure. The controlling parameter during the coagulation process is the rate at which surface functionality is increased as reactive sites are formed on the particle surface. The type of gel structure depends on whether functionality increases rapidly or slowly. There is still much to learn about the processes governing the coagulation of milk. Further insights into milk coagulation under various conditions will provide the basis for controlling coagulation in the manufacture of new dairy products. ACKNOWLEDGEMENTS

This research was supported by a grant from the USDA Agricultural Research Service and by the Utah Agricultural Experiment Station, Journal Article No 3708. The Formagraph was supplied by Foss Food Technology Corporation, Eden Praire, MN.

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