6304
Langmuir 1999, 15, 6304-6313
Molecular Mechanism of the Renneting Process of Casein Micelles in Skim Milk, Examined by Viscosity and Light-Scattering Experiments and Simulated by Model SCF Calculations M. Mellema,* F. A. M. Leermakers,† and C. G. de Kruif Product Technology Department, NIZO Food Research, P.O. Box 20, 6710 BA Ede, The Netherlands, and Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6703 HB Wageningen, The Netherlands Received March 1, 1999. In Final Form: May 7, 1999 The properties of the outer hairy layer of casein micelles have been studied using several methods. Viscosity and light-scattering measurements have been performed on rennet-destabilized skim milk at different concentrations of calcium. We have reproduced the known result that calcium promotes destabilization at relatively high κ-casein surface coverages (even at only 50% of the κ-casein molecules cut off). This suggests that calcium bridges contribute to the casein micelle attraction. The effect may be direct by calcium-mediated bridging of β-casein or Rs1-casein (phosphate/carboxylate) or κ-casein (carboxylate) or indirect by altering the interplay between several types of caseins in the micelle. In the analysis of the experiments, we make use of an adhesive hard sphere approximation. The casein hairy layer has further been modeled by a self-consistent field (SCF) theory in which coarse-grained molecular details were included. In these calculations the effect of calcium bridges cannot directly be accounted for. It is shown that a κ-casein layer induces repulsive interactions of mainly steric origin. Cutting the N-terminus part results in reduced (shorter-ranged) repulsive pair potentials, which still dominate over the van der Waals attraction. As a result of the altered interplay between the several types of casein molecules during the renneting process, the Rs1-casein concentration in the outer hairy layer may increase. Again using the SCF model, but now using a less-detailed description of the system, we examine a possible result of this. We confirm that diblock copolymers (simple model for κ-casein) and diblock copolymer with shorter soluble block (simple model for para-κ-casein) give repulsion and triblock copolymers (simple model for Rs1-casein) give attraction by means of bridging (adsorption). The renneting process is simulated by increasing the ratio of model para-κ-casein to κ-casein at a fixed Rs1-casein concentration. As a result, the potential shifts from repulsive to attractive. We show that by reducing the range of repulsive interactions of the diblock copolymers, we can make room available to express the attractive contributions of the model Rs1-casein. This comprises a novel molecular-based mechanism for the renneting process.
Introduction Skim milk is an aqueous dispersion of proteinaceous particles, of which the casein micelles are the most important. A casein micelle is a spheroidal association of several casein proteins containing salt, probably held together by a combination of hydrophobic and electrostatic interactions. The main casein proteins are Rs1-, Rs2-, β-, and κ-casein (originally categorized in terms of their electrophoretic behavior). The protein κ-casein is mainly present in the outer layer of a casein micelle. For recent overviews on casein micelles, see refs 1 and 2. In this study, the properties of the κ-casein “hairy layer” have been studied using light scattering, capillary viscometry, and self-consistent field (SCF) modeling. The casein micelles can be made to aggregate in several ways. In this study we focus on the effect of lowering the κ-casein hairy layer density by enzymatic cutting off or splitting the hairs (using rennet enzymes) and the subsequent interactions between the micelles. The nature of the attractive forces during aggregation of the micelles * To whom correspondence should be addressed. Current address: Food Physics, Department of Food Technology and Nutritional Sciences, Wageningen University, Bomenweg 2, 6703 HD Wageningen, The Netherlands. E-mail: Michel.Mellema@ Phys.FdSci.WAU.NL. † Wageningen University. (1) Walstra, P. J. Dairy Sci. 1990, 73, 1965. (2) Holt, C.; Horne, D. C. Neth. Milk Dairy J. 1996, 50, 85.
is one of the most intriguing mysteries in dairy physics.3 The (possible) involvement of calcium and Rs1-casein is discussed in this paper. Both may contribute to the early stages of bonding between casein micelles before the stage at which mainly the hydrophobic interactions increase the bonding strength. DLVO theory is insufficient in describing the relevant interactions in milk.4 This is partly explained by the high ionic strength (∼0.075 molar) of milk. Therefore, it is believed that the κ-casein layer accounts for a (mainly) steric repulsion between the micelles. A close encounter of two layers is not favorable, because of a local increase of osmotic pressure. Upon destabilization, attraction, at least in the order of kT, becomes operative. The degree of stickiness (which is a product of the whole pair interaction curve) is essential for the type of aggregates and gel structure obtained. Strong long-range attraction or weak short-range attraction (i.e., reversible aggregation) both lead to a situation more similar to phase separation rather than gelation over experimental time scales. In gelling milk, the aggregation is probably very much delayed because of the presence of a long-range repulsive barrier, whereas the aggregation is rather irreversible. Therefore, any details on the properties of the remains of the hairy layer, which may act as a repulsive barrier, are important.5-7 (3) Horne, D. S. Int. Dairy J. 1998, 8, 171. (4) Payens, T. A. J. J. Dairy Res. 1979, 46, 291.
10.1021/la9902340 CCC: $18.00 © 1999 American Chemical Society Published on Web 07/02/1999
Molecular Mechanism of the Renneting Process
The hairy layer mainly consists of κ-casein. In a molecular approach, the κ-casein hairs can be seen as amphiphilic block copolymers. Brushes of this type of polymers can be grafted or adsorbed onto the surface of particles to stabilize all kinds of dispersions.8 The comparison to synthetic polymers is justified because caseins, including κ-casein, have very little secondary structure. In addition, in view of the distribution of charges along the protein chain, β- and (to a lesser extent) κ-casein resemble diblock copolymers,9 and Rs1-casein resembles a triblock copolymer (hydrophilic block in the middle, albeit off center).10 The caseins are polyelectrolytes. Under physiological conditions a κ-casein brush behaves, by approximation, like a salted brush.11 This means that the charges along the chain are well screened by salt so that neighboring charges on either the same or different chains only weakly interact. In natural milk the solvent is clearly a good solvent in view of the stability of milk. For poor solvents, chain-chain interactions are preferred over chain-solvent interactions, and a brush will show a tendency to collapse, making the colloidal system aggregate. Acid and ethanol are known for their ability to aggregate the micelles. Ethanol probably decreases the solvent quality for the hairs. The attraction between the hairs would cause a reduction of the layer thickness and also induce attraction between hairs of different particles. Hence ethanol promotes destabilization of the dispersion.2 A different way of destabilization is by cutting off the hairs with rennet enzymes. Rennet, which is added to milk at the beginning of the cheese-making process, is an extract from the stomach of a calf. If the calf is young enough, the main enzyme in this extract is chymosin. This enzyme is able to split κ-casein between residues 105 (Phe) and 106 (Met). The peptides remaining are called paraκ-casein (fairly hydrophobic) and the glycomacropeptide (GMP, hydrophilic). A typical result of the time course of events taking place during the renneting (φb ) 0.02 vol %) of an average sample of skim milk at T ) 30 °C is shown in Figure 1. The curves are based on measurements by strain-controlled Bohlin rheometer (storage modulus G′), Malvern Hi-c dynamic light scattering (DLS; measures an apparent particle radius aapp), Ubbelohde capillary viscometry (dynamic viscosity ηd), and HPLC determination of the concentration of GMP (which is a measure of the percentage of κ-casein cut). From the figure we see an initial decrease of the particle radius and the viscosity. Next, apparent diameter, viscosity, and finally elasticity will increase considerably. Using the adhesive hard spheres (AHS) model,11,12 we can relate changes in surface coverage and the resulting attraction between the particles to an apparent particle diameter or milk viscosity. This paper discusses two main parameters determining the properties of the casein layer and corresponding (5) (a) Mellema, M.; van Opheusden, J. H. J.; van Vliet, T. In Food Emulsions and Foams: Interfaces, Interactions and Stability; Dickinson, E., Rodrı´guez Patino, J. M., Eds.; Royal Society of Chemistry: Cambridge, 1999. (b) Mellema, M.; van Opheusden, J. H. J.; van Vliet, T. J. Chem. Phys., submitted for publication, 1999. (6) van Hooydonk, A. C. M.; Walstra, P. Neth. Milk Dairy J. 1987, 41, 19. (7) Pires, M. S.; Gatti, C. A.; Orellana, G. A.; Pereyra, J. J. Agric. Food Chem. 1997, 45, 4446. (8) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at Interfaces; Chapman & Hall: London, 1993. (9) Mellema, M.; Clark, D. C.; Husband, F. A.; Mackie, A. R. Langmuir 1998, 14, 1753. (10) Dickinson, E.; Horne, D. S.; Pinfield, V. J.; Leermakers, F. A. M. J. Chem. Soc. Faraday Trans. 1997, 93, 425. (11) de Kruif, C. G.; Zhulina, E. B. Colloids Surf. A 1996, 117, 151. (12) de Kruif, C. G. Langmuir 1992, 8, 2932.
Langmuir, Vol. 15, No. 19, 1999 6305
Figure 1. Scheme of events taking place during the renneting (0.02 vol %) of an average sample of skim milk at 30 °C and pH 6.65. Shown are the storage modulus G′, apparent particle radius aapp, dynamic viscosity ηd, and % of κ-casein cut.
colloidal interactions in the system. First we focus on the milk calcium concentration. In natural milk, the main part (∼70%) of the calcium is present as colloidal calcium phosphate (CCP).13,14 Another part is present in ionic form or associated with other milk components. The CCP is believed to play a role in stabilizing the internal structure of casein micelles. Also, a minimum amount of CCP is needed for micelle aggregation. Actually, in dairy practice of cheese-making, use is made of added calcium chloride to control and enhance the renneting process. Moreover, it has recently been shown15 that during renneting, calcium can promote the aggregation of κ-casein-coated latex particles. To study the effect of calcium, we performed light-scattering and viscosity measurements and an AHS analysis on a milk system renneted at different concentrations of added calcium chloride. Next we focus on the molecular properties and composition of the hairy layer. For the purpose of studying the hairy layer consisting purely of κ-casein or para-κcasein (which is a product of κ-casein after renneting, which we assume to stay attached to the micelle), we have performed numerical SCF calculations, with detail up to the level of the amino acid residues. The SCF approach is based on a model originally developed by Scheutjens and Fleer16 and modified by Leermakers et al.17 In the model a mean-field approximation is made, which implies that all interactions within a layer parallel to the interface are averaged. In the paper by Leermakers et al., the SCF model is used to calculate the equilibrium adsorption behavior of β-casein as a function of, for example, ionic strength, pH, and bulk concentration. Our model is identical to the one by Leermakers et al., apart from the fact that we have studied the behavior of κ-casein and not β-casein. An important approximation made in the model is that the (adsorbed) hairy layer consists of linear chains of segments of fixed size, equal to a lattice site. The sequence (13) Walstra, P.; Jenness, R. Dairy Chemistry and Physics; John Wiley & Sons: New York, 1984. (14) Zhang, Z. P.; Aoki, T. Int. Dairy J. 1996, 6, 769. (15) Leaver, J.; Horne, D. S. J. Colloid Interface Sci. 1996, 181, 220. (16) Scheutjens, J. M. H. M.; Fleer, G. J. J. Phys. Chem. 1979, 83, 1619, and 1980, 84, 178. (17) Leermakers, F. A. M.; Atkinson, P. J.; Dickinson, E.; Horne, D. S. J. Colloid Interface Sci. 1996, 178, 681.
6306 Langmuir, Vol. 15, No. 19, 1999
Mellema et al.
Figure 2. Primary structure of the κ-casein molecule κ-casein, as used in SCF modeling.
of the segments, defined at the level of the amino acids, is shown in Figure 2 (for a more detailed discussion of Figure 2, including the NANA-group, we refer to the section Parameters for SCF Calculations). Note that the model molecules are highly simplified; they cannot form secondary structures or calcium bridges. By taking into account all possible conformations of the molecules on the lattice, each weighted with its Boltzmann probability factor, the segment density profile of a polymer-solvent system at the interface can be calculated. The hairy layer on casein micelles may also contain other caseins such as β-casein (at low temperature or prolonged rennet activity) or Rs1-casein. It was shown in SCF computer modeling18 and by experiments on emulsions19 that Rs1-casein can act as a bridging agent between surfaces. Possibly, this is due to the triblock copolymerlike character of the primary structure of Rs1-casein. To test this hypothesis, we investigated the effect of incorporation of a model triblock in a diblock hairy layer, making use of SCF calculations with less detail than shown in Figure 2. In this (second) type of SCF calculations, we will assume the κ-casein, para-κ-casein, and Rs1-casein to be simple forms of block copolymers consisting of two or three large hydrophobic and hydrophilic blocks. Theory and Models Renneting. The main premises of the AHS model have already been well-documented by de Kruif et al.12,20,21 and Cichoki and Felderhof.22 We will only give the most relevant equations in this section (and the next two). The cutting off or renneting of κ-casein follows firstorder reaction kinetics.6,11 During this reaction, κ-casein is split into para-κ-casein and GMP, of which the latter goes into bulk solution. We can write:
(
)
σ(0) [GMP] [E] 1) exp - k t = [GMP]∞ [E]0 σ(t)
(1)
where [GMP]/[GMP]∞ is the fraction of κ-casein cut by the enzyme, [E]/[E]0 is the relative concentration of chymosin ([E]0 is a reference concentration, chosen to be 0.01 vol % calf rennet), t (s) is the time, k(s-1) is a reaction constant, and σ(0) and σ(t) are κ-casein chain densities at time t ) 0 and t ) t after rennet addition. On cutting of the hairs, the effective hydrodynamic radius of the micelles will decrease. For our discussion it (18) Dickinson, E.; Pinfield, V. J.; Horne, D. S.; Leermakers, F. A. M. J. Chem. Soc. Faraday Trans. 1997, 93, 1785. (19) Dickinson, E.; Semenova, M. G.; Antipova, A. S. Food Hydrocolloids 1998, 12, 227. (20) de Kruif, C. G.; Jeurnink, T. J. M.; Zoon, P. Neth. Milk Dairy J. 1992, 46, 123. (21) de Kuif, C. G.; Hoffmann, M. A. M.; van Marle, M. E.; van Mil, P. J. J. M.; Roefs, S. P. F. M.; Verheul, M.; Zoon, N. Faraday Discuss. 1995, 101, 185. (22) Cichocki, B.; Felderhof, B. U. J. Chem. Phys. 1990, 93, 442.
may suffice to assume that the hydrodynamic thickness reduces linearly with [GMP]/[GMP]∞ (of course, more refined models could be developed). Among the fitting parameters are the initial particle radius (which can be derived using DLS at t ) 0), the characteristic thickness of the κ-casein layer (which can be derived using DLS and SCF modeling), and the initial bulk volume fraction. The values chosen are presented in the Results and Discussion section on Surface Coverage and Particle Interactions. The κ-casein hairs provide a highly effective short-range repulsion. Cutting the hairs or collapsing the layer allows attractive forces to become operative. For short-range potentials the precise shape of the potential interaction curve is of little importance in predicting the events in the very early stages of aggregation.5,23 The attraction that results from cutting off the hairs was modeled as a square well with width ∆ and depth . A second virial coefficient B2 can be introduced: this parameter is actually a measure of the integral over the interaction potential curve:12
B2 ) 4 + 12
∆ (1 - e/kT) σHS
(2)
where σHS is the radius (which can be derived using DLS; see later) of the hard sphere. The reference state is given by ) 0 for hard spheres, which would mean that B2 ) 4 in that case. On cutting of the hairs, increases (∆ is considered constant). Therefore B2 decreases and eventually becomes negative. This will lead to an effective attraction. The relation between the Baxter parameter τ and B2 is given by:
B2 ) 4 - 1/τ
(3)
The Baxter parameter τ is a function of particle stickiness or adhesiveness.24,25 See also eqs 6 and 7. Viscosity. In skim milk, the solvent of the casein micelles is the milk serum, which is in its composition nearly equal to that of the whey liquid remaining after the cheese-making. From the kinematic viscosity ηk (m2 s-1) a dynamic viscosity ηd (Pa s) can be calculated using the serum density σd (kg m-3), and the relative viscosity ηr (-) can be calculated using the serum viscosity ηd,0.
ηd ) ηkσd
(4)
ηd ηd,0
(5)
ηr )
The viscosity of a dilute dispersion of AHS is given by:22
(
ηr ) 1 + 2.5φb + 5.913 +
1.899 φb2 τ
)
(6)
where φb is the particle volume fraction. The behavior of noninteracting hard spheres is given for τ f ∞. The equation above is applicable to skim milk (φb ∼ 0.1). The AHS model would permit the quantitative prediction of the viscosity or apparent particle radius (see next section) as a function of time after rennet addition. It combines enzyme kinetics and the rheology of AHS to predict the inital fall and subsequent rise of these parameters. As a consequence, it could be used to model (23) Regnaut, C.; Ravey, J. C. J. Chem. Phys. 1989, 91, 1211. (24) Baxter, R. J. J. Chem. Phys. 1968, 49, 2770. (25) Russel, W. B. J. Chem. Soc. Faraday Trans. 1984, 2, 31.
Molecular Mechanism of the Renneting Process
Langmuir, Vol. 15, No. 19, 1999 6307
the initial stages of renneting and allows the prediction of an effective stickiness through calculation of the Baxter parameter τ. Light Scattering. The diffusivity or mobility of casein micelles can be probed using DLS. Because of Brownian motion of the particles, the scattered light intensity autocorrelation function shows an exponential decay in time. This leads to an expression for the intensity autocorrelation function g2(t) and a prediction of the diffusion coefficient D. Next, the diffusion coefficient D can be related to the well-known Stokes-Einstein equation, which states that D is inversely proportional to the particle diameter dapp and the liquid viscosity ηk,0. In the setup used for this study, a backscatter experiment is performed. The measuring angle θ is 180°, which means that we are probing light fluctuations in the limit Ka f ∞ (Ka ∼ 2.2 if a ) 100 nm, n ) 1.33, and λ ) 780). Therefore, we are mostly probing short-time self diffusion.12 The apparent diameter increases when the micelles attract each other. The attraction can be expressed in the Baxter parameter τ. For short-time self diffusion the diffusion coefficient equals12,22
D 0.295 ) 1 - 1.8315 + φb D0 τ
(
)
(7)
where D0 is the diffusion coefficient at φ f 0. Parameters for SCF Calculations. The molecular modeling approach in this study is similar to the one previously described by Leermakers et al.17 on β-casein. For most details, we refer to this study. Instead of β-casein, the statistical behavior of grafted κ-casein and para-κcasein look-alikes is considered in this study. By mixing κ-casein and para-κ-casein look-alikes at various ratios with increasing amount of para-κ-casein, the cutting of the hairs is simulated. In lattice-based SCF calculations one has to decide on the typical length scale, or size of the lattice site, δ. In this study we chose δ ) 0.3 nm, which is the characteristic size of a water molecule. As a consequence, the length scale of the polymer units (amino acids) is not realistic as to the space-filling aspects. However, for short ranges along the chain, the correlations are modeled in an extremely primitive way (nonoverlap of two consecutive segments). As a consequence, the size of the amino acid residue should be interpreted as an effective one that incorporates the various short-range (repulsive and attractive) interactions. If attractive interactions dominate (e.g., local hydrogen bonds), the effective size is smaller than the real size. More realistic SCF models should include local stiffness and other effects, at the cost of an order of magnitude more CPU time. In a first series of detailed calculations we have represented each κ-casein or para-κ-casein molecule as a flexible linear excluded-volume copolymer made up of just three types of segments: apolar, polar (i.e., charged), and ionic (i.e., charged depending on pH-pK). The sequence of segments is taken to represent the known primary structure of κ-casein (See Introduction, Figure 2). Paraκ-casein was modeled essentially the same as κ-casein, minus residues 107-169. Note that a side group lookalike is included in the κ-casein representation. A wellaccepted name for this sugar group, which is often present in native κ-casein (sometimes even twice per κ-casein molecule), is NANA-group, originating from N-acetyl neuraminic acid.6 We have simply modeled it as a collection of two water and two acid groups.
Nearest-neighbor interactions between polymer segments and solvent molecules are taken into account by a Flory-Huggins parameter χ. We also assign an adsorption energy χs to the apolar segments upon contact with the interface. Note that the (hydrophobic) interface is assumed to be flat and solid. In addition, each segment has its own pKa and relative dielectric constant. The values of these parameters are give in Table 1 of ref 17. The remaining amino acid residues Pro, Ile, Phe, Ala, Tyr, Val, Leu, Gly, Trp, and Met are modeled as type A (hydrophobic). Gln, Asn, Cys, Ser, and Thr are modeled as type B (hydrophilic). Note that we have defined the hydrophobicity of the segments in terms of the hydrophobicity of the side groups of the protein chain. The ionic strength and the pH were fixed at 0.055 and 6.7, respectively. It is very important to note that trial calculations showed that the results are rather insensitive to the ionic strength chosen (in the range 0.001 to 0.1) because the brush is already oversaturated with salt. We found that the effect was even less than for layers of β-casein.17 For β-casein, it was found that the presence of a typical dilute tail in the segment density profile is independent of the ionic strength, pH, and bulk concentration. In contrast, dephosphorylation9,17 has a significant effect. Other parameters that we frequently use are the surface coverage Θ and the dimensionless segment density concentration φ. The local segment density φ (z) expresses the fraction of sites occupied by segments in layer z. The summation over the excess density profile is the coverage Θ ) ∑z(φ(z) - φb). In addition, we performed less-detailed calculations with model diblock and triblock copolymers, where details on the primary structure have been reduced to a minimum. We performed these calculations because from detailed SCF calculations, an attraction can be observed between layers consisting of model Rs1-casein.18 Only repulsion is observed between layers of β-casein17,19 and, as we will see later, layers of κ- and para-κ-casein. In this paper, we put forward a possible mechanism of destabilization of casein micelles on the basis of the block copolymer-like molecular character of the caseins involved. The model molecules used have a generalized form of AB: A25-B25; AB*: A25-B5; and ABA: A25-B40-A25. They are, respectively, very simplified models for κ-casein, para-κ-casein, and Rs1-casein. Note that the model polymers are not charged. We clearly have to distinguish model calculations using these simple block copolymers from the more detailed calculations with the heteropolymers, as described in the previous paragraph. Free Energy of Interaction from SCF Calculations. From a solution of the SCF equations the partition function, of the system can be analyzed. Subsequently, from the partition function, various thermodynamic quantities such as the excess free energy per unit area, Aσ, proportional to the surface tension, γ, can be computed. The surface tension γ of an interface decreases as molecules such as caseins adsorb at that interface. When two interfaces, both covered with a casein brush, approach each other, the surface tension and thus the excess free energy per unit area becomes a function of the distance, H ) Mδ, between the surfaces (M is the layer separation in number of lattice sites). Exactly how this quantity changes can tell us much about the interaction forces in the system. The dimensionless free energy of interaction at full equilibrium of the casein layers, Aint(H), is given by the difference between the excess free energy at separation H and that of infinite separation divided by kT:
6308 Langmuir, Vol. 15, No. 19, 1999
Aint(H) )
Aσ(H) - Aσ(∞) kT
Mellema et al.
(8)
Note that Aint is an energy per lattice site, which means that the actual interaction energy can be calculated if the contact area is known. An important characteristic of a charged brush is that the charge inside the brush can be compensated by mobile counterions. These ions can do this by entering the brush. The amount of charge compensation is a function of the Debye length κ-1 of the system. If the Debye length is of the same order or longer than the thickness of the brush, that is, at low ionic strength, a significant part of the counterions do not enter the brush and a classical electric Gouy-Chapman (or Debye-Hu¨ckel) layer8 develops outside the brush. Then the interaction curve shows a linear regime in a ln[Aint(H)] versus H plot in the region where the GouyChapman layers overlap. More precisely, the theory predicts this interaction to be
Aint ∝ 2π(ψd)2 e-κH
(9)
where ψd is the electrostatic potential at the periphery of the brush. If the ionic strength is high, so that the brush is locally neutral, the Gouy-Chapman repulsion is very small, and typically one will find that the interaction curve only reflects contributions from steric interaction (brush deformation). Experimental Section Skim Milk. Reconstituted skim milk was used for lightscattering and Ubbelohde experiments. It was prepared by dispersing 10 g of low-heat skim milk powder (NIZO, Ede, The Netherlands) in 100 g of demineralized water at T ) 40 °C (( 2 °C). It was stirred for 30 min, then quickly heated to 50 °C, cooled to 30.6 °C, and kept at this temperature for 45 min (before measurements or rennet addition). Ultrafiltration permeate (milk serum) was made from the same skim milk, using a hollow-fiber cartridge Amicon Himpo I-43 (cutoff 0.1 µm). In some experiments various amounts of a 1 M solution in water of CaCl2 (Merck, pro analysi) were added. A calciumselective electrode (F2112Ca, ion83 ionmeter, Radiometer; Copenhagen, Denmark) was used to determine the Ca2+ activity in water and skim milk with various amounts of added CaCl2. A Metrohm 691 pH meter was used in the pH correction of the milk to a constant value of 6.65 in all experiments. To correct the pH of milk after adding CaCl2, 0.46 (( 0.3) mol NaOH (Merck, pro analysi) was added per mole calcium (rule applicable in the range of added amount of calcium; [Ca] ) 0 to 0.6 M). The amounts added did not change the ionic strength of the milk significantly. Rennet. Commercial calf rennet (10 800 SU) from CSK (Leeuwarden, The Netherlands) was used; about 80% of its activity originates from chymosin. The rennet was diluted 50fold prior to addition. Then usually 10 mL of this preparation per 100 mL of milk were added. HPLC. The hydrolysis of κ-casein was followed by measuring the concentration of caseinomacropeptide or GMP in a 8% trichloroacetic acid (TCA) filtrate, using an HPLC column as described by van Hooydonk and Olieman.26 At t ) 0 a fixed concentration of chymosin was added to skim milk with different concentrations of calcium. From these solutions samples were taken at different time intervals. To a sample just taken, the TCA was added to stop the chymosin action instantly. One milliliter of concentrated TCA solution was added to 3 mL of milk. Each sample was filtered and subsequently analyzed by HPLC to determine the concentration of GMP in the milk. (26) van Hooydonk, A. C. M.; Olieman, C. Neth. Milk Dairy J. 1982, 36, 153.
Viscosity. Viscosity measurements were made using an Ubbelohde capillary viscometer (Schott Gera¨te, type 531 10/I; capillary diameter 0.63 mm). Before filling the Ubbelohde, one drop of 1-octanol (Merck) was added to 50 mL of the solution to prevent foaming. The filled Ubbelohde was placed in an LKB precision water bath (T ) 30.6 °C ( 0.03 °C). Measurements were made after 5 min of equilibration. In most cases this means that at this point (t ) 0) rennet was added. The flow time of the sample was automatically determined at time intervals (0.5-2 min) with an accuracy of (0.5%, using an AVS 350 viscometer (Schott Gera¨te). Flow times were about 80-140 s. The flow times were corrected by a small Hagenbach factor (c2), and the kinematic viscosity ηk was calculated by multiplying the flow time with c1 (both c1 and c2 as given by Schott Gera¨te). The Ubbelohde was cleaned with nitric acid (70%, BDH Analar) and rinsed with demineralized water and acetone. Before measurements the capillary was allowed to dry. A Mettler/Paar DMA (Landre Intertechmij) fluid density measuring apparatus was used for measuring the density of the milk and the permeate. Light Scattering. For the light-scattering measurements we used the Malvern Hi-C (high-concentration) particle sizer, which exploits the fact that from highly turbid systems, data can be obtained from the diffuse backscattering of light. In this setup the value of Ka ≈ 2.2 (wavelength λ0 ) 780 nm). Although this value of Ka is not beyond the oscillations in the structure factor of a casein micelle dispersion (i.e., some collective diffusion is measured), we compare the diffusivity data as obtained from the initial decay of the correlation function with the short-time selfdiffusion coefficient. The results of Philipse and Vrij27 show that this is qualitatively correct. Note that we ignore the fact that we are dealing with not perfectly spherical but somewhat randomly irregularly shaped particles, which might cause extra relaxation times. However, the signal is already a sum of a large number of relaxation times because the dispersion is very polydisperse, which is why we fitted a single exponent. We do not expect that the particles are ellipsoidal with aspect ratios so large that significant contributions of extra relaxation times are measured. Taking into account random particle surface irregularities, polydispersity, and the fact that we are not dealing with infinite dilution, we are only claiming to measure an apparent particle diameter.12 Refractive indices were measured with a Zeiss 79472. The refractive index is, like the bulk viscosity, needed to calculate the correct diffusion coefficient from DLS measurements. We also monitored the diffusivity when increasing concentrations of neuramidase enzyme [lot no. 253007 A, from Vibrio comma, Behringwerke AG, Marburg, Germany] up to 1 g/L. The neuramidase, as the name suggests, cuts off all neuramic (or NANA)groups on the casein molecules.
Results and Discussion Calcium Concentration. Addition of calcium chloride solution appeared not to change the milk’s density σd (1.036 kg dm-3) or refractive index n (1.3456) in the range of [Ca] (added) (0 to 0.5 M). With a calcium electrode the activity of calcium was measured in the skim milk and in water (pH ) 6.65). We found that in pure water the signal (mV) increases linearly with log([Ca] added). In the skim milk, we see that some calcium activity is already present. As we add more calcium the activity increases less than proportionally. This indicates that a percentage of this extra calcium will be bound or inactivated. At added amounts larger than log([Ca] ) -2), the relation is again linear with the same slope as in water. In general, the procedure confirms that significant amounts of calcium can be bound in milk.1 Renneting. To study the effect of adding calcium chloride to skim milk on the activity of chymosin, the production of GMP as a function of time was analyzed by HPLC. The results of the HPLC measurements are shown (27) Philipse, A. P.; Vrij, A. J. Chem. Phys. 1988, 88, 6459.
Molecular Mechanism of the Renneting Process
Figure 3. Concentration of GMP as a function of time as analyzed by HPLC. Plotted like this, the slope of these charts equals the reaction constant k × [E]/[E0]. [Ca] is the concentration of CaCl2 added.
Langmuir, Vol. 15, No. 19, 1999 6309
Figure 5. Apparent diameter dapp of skim milk as a function of time after rennet addition at various concentrations of added CaCl2 ([Ca]). Table 1. Viscosity (a) and Light-Scattering (b) Data (a) tsc (s)
σ(0)/σ(t) (no dim)
Baxter parameter τ
well depth /kT
0 8.0 × 10-4 4.0 × 10-3 2.2 × 10-2
3420 2880 2190 990
0.06 0.10 0.17 0.45
0.15 0.16 0.18 0.32
3.66 3.60 3.48 2.95
0 2.0 × 10-3 4.0 × 10-3 1.0 × 10-2 2.0 × 10-2
2730 2340 1920 1200 870
0.11 0.15 0.22 0.38 0.50
3.26 3.45 3.77 4.91 6.09
1.00 0.97 0.92 0.77 0.66
[Ca] (M, added)
(b)
Figure 4. The dynamic viscosity ηd of skim milk as a function of time after rennet addition at various concentrations of added CaCl2 ([Ca]).
in Figure 3. The results are plotted in a special way (see eq 1). The slope of these charts equals the reaction constant k [E]/[E0]. With a reference concentration [E0] of 10 mL of calf rennet (CSK) per 100 mL of milk, it was found that k ) 0.8 × 10-3 (( 0.2 × 10-3) s-1 for [E]/[E]0 ) 1 for the milk without extra calcium chloride. A value of k ) 1.6 × 10-3 s-1 was found by de Kruif and May28 using the same chymosin sample and [E]/[E]0 ) 2. From the figures we can confirm that adding calcium chloride has no significant influence on the activity of chymosin. From the values of k we can calculate the presumed relative chain density σ(0)/σ(t) of hairs at the micelle’s surface, using eq 1 (see section on surface coverage and particle interactions). Viscosity. In Figure 4 the dynamic viscosity of skim milk is plotted against time (0.01 vol % rennet is added at t ) 0), applying various calcium chloride additions. We (28) de Kruif, C. G.; May, R. P. Eur. J. Biochem. 1991, 200, 431.
clearly see that the initial stages of renneting have basically two effects on the viscosity. First, cutting the hairs of κ-casein decreases the volume fraction and thus lowers the viscosity. Next, with the loss of the stabilization layer the micelles show a concomitant mutual attraction (eq 6). The attraction increases viscosity significantly even before any aggregation is visible and is more pronounced at higher concentrations of added CaCl2. As gelation is reached, the viscosity can no longer be measured. The shape of the curves can be approximated using the AHS model. We can derive values for τ and at the gel-time tsc. See Table 1a. Light Scattering. We checked whether adding neuramidase made the milk more sensitive to flocculation or change of the apparent micellar radius. This was not the case. Assuming that the NANA groups are indeed cut off by the neuramidase, we could not confirm the supposition that NANA residues are a large factor involved in the formation of an extended κ-casein brush. In the Figure 5 the apparent diameter dapp of skim milk is plotted against time after rennet addition at different calcium concentrations. A similar behavior of the curves is found as in Figure 4. Again, the curves are approximated using the AHS model. For τ and values at tsc see Table 1b. Surface Coverage and Particle Interactions. We can calculate the relative chain density σ(0)/σ(t) from the chymosin activity parameter k (eq 1) at any time t. We define a time tsc at which the viscosity or apparent diameter during renneting reaches the same value as at t ) 0. This
6310 Langmuir, Vol. 15, No. 19, 1999
time tsc we assume to be an approximate measure of (or at least proportional to) the milk clotting time.29 In Table 1a and b, σ(0)/σ(t) is given corresponding to every tsc derived from Figures 4 and 5. In addition, we give the values of τ and /kT at the given tsc, calculated from the data using the AHS model,12,20,21 of which the main equations are given by eqs 1-3, 6, and 7. Data are presented calculated from viscosity (Table 1a) and DLS (Table 1b) measurements. The fitting parameters were the characteristic thickness of the hairy layer (which can be extracted from SCF modeling and DLS), ∆ ) 1.2 nm (arbitrary value), σHS ) 82 nm, the initial particle radius ) 89 nm (both from DLS, of which the latter was separately measured on a nonrenneting system), and k ) 8 × 10-4 s-1 (from HPLC analysis). An initial volume fraction of 0.1 was found to give approximately ηr (t ) 0) ) 1.34 using eq 6 and assuming τ ) ∞. This is the same as ηr calculated from the following parameters measured by a capillary viscometer: ηd ) 1.18 mPa s, ηd,0 ) 0.86 mPa s, and σd ) 1.036 kg m-3, using eqs 4 and 5. As we see from Table 1a and b, the attractive energy as given by /kT at tsc is much lower for DLS. The values of the data from the viscosity measurements correlate well with other data,20 and the attractive energies at tsc from viscosity measurements are more close to values sufficient for actual aggregation to take place (i.e., higher than kT). This proves that these data are probably more reliable. The discrepancy is not a trivial problem and we are not sure of what is causing it. Maybe the light-scattering technique deals with polydispersity, particle anisotropy, or time scales in a different way. However, we feel this is unlikely to affect the results given in Table 1b significantly (note that we also found only small changes in or τ assuming long-time diffusion or collective diffusion12). In part, the discrepancy can be caused by the (rather arbitrary) definition of tsc, or the value chosen for the hardsphere radius, initial radius, or initial volume fraction. We have chosen all fitting parameters equal in the calculation of Table 1a and b. We can conclude that there are indications that we need more information to obtain the correct fitting parameters for the DLS data. This should be a goal in future research. From Table 1a and 1b we see that τ increases with the coverage σ(0)/σ(t). This gives us a relation between stickiness and κ-casein surface coverage. The procedure confirms that at high [Ca], the relative surface coverage at tsc can be quite high1,6 (it should be noted that a great deal of references on quantitative data on this subject is given by Dalgleish30). The observation suggests a role of long-range attractive forces in the aggregation, possibly due to calcium bridging of κ or (more likely because of higher content of phosphate groups) one of the other caseins, such as β-casein. Carboxylate bridging can also occur, because Ca2+ can interact with negative charges on two separate chains. However, Ca2+ has a higher affinity for the phosphate groups. Despite the high storage modulus of casein gels, the attractive interactions, as shown in Table 1a and b and given in the literature,5-7 are relatively small. This can be explained by assuming a change in interactions with (29) de Kruif, C. G. In Food Colloids and Polymers; Stability and Mechanical Properties; Dickinson, E., Walstra, P., Eds.; Royal Society of Chemistry: Cambridge, 1993. (30) Dalgleish, D. G. In Advanced Dairy Chemistry, Volume 1: Proteins; Fox, P. F., Ed.; Elsevier Applied Science: London and New York, 1992.
Mellema et al.
Figure 6. Density profiles of grafted and adsorbed κ-casein (at Θ ) 4), and of an adsorbed κ-casein 4-mer.
bonding time due to changing molecular equilibria. It can even be envisaged that the pair interactions show a hysteresis caused by formation of more calcium bridges in time or by increasing hydrophobic interactions due to molecular rearrangements at the contact area of the micelles. No quantitative studies are available on this subject so far. Density Profiles from SCF Calculations. We performed SCF calculations based on the Scheutjens-Fleer lattice model. Generally, the segment density profiles φ(z) that we calculated were monotonically decreasing functions of the distance z (given in nanometers; the size of one lattice site is 0.3 nm) away from the flat, solid, hydrophobic surface. The density profiles approach the bulk value φb far away from the surface. The density profiles near the maximum monolayer coverage are of most interest, because in this regime brush-like behavior is most likely to be found. In Figure 6, we plotted segment density profiles of anchored/grafted (Θ ) 5, grafted at residue number as indicated) and adsorbed (φb ) 0.001, which gives Θ ) 4 for monomeric κ-casein and Θ ) 4.7 for the 4-mer). The grafted situation at residue number 1 would lead to the formation of a more extended monolayer, with parts of the hairs penetrating considerably into the bulk phase (i.e., formation of a hump in the density profile). This suggests that in skim milk the κ-casein on the casein micelles is more likely to be anchored than (weakly) adsorbed. Grafting at residue number 100 would lead to a more compact layer. This is to be expected, because the N-terminus half of the chain is more hydrophobic than the other half. The molecule κ-casein is known to polymerize in milk (by way of intermolecular S-S bridging). For this reason, we calculated a density profile of an adsorbed κ-casein multimer, which we plotted in Figure 6. The numbers denote the residues at which the monomers are connected to each other. In the case of the 4-mer, this means that two κ-casein molecules are connected to each other at residue 1 and both molecules are branched by connecting an extra κ-casein at residue 80. We see that multimer or (in the adsorbed state) tuft formation may contribute to a higher level of colloidal stability, albeit to a small extent, because of the formation of a more extended brush layer. Most of the increase in stability may be attributed to the higher surface affinity of the multimer. The density profile
Molecular Mechanism of the Renneting Process
Langmuir, Vol. 15, No. 19, 1999 6311
Figure 8. Free energy of interaction (calculated from eq 8) between two penetrating monolayers of κ-casein or of para-κcasein, as a function of plate separation.
Figure 7. (a) Density profiles of adsorbed mixtures of κ-casein and para-κ-casein; (b) log scale of (a).
of an anchored κ-casein look-alike without the sugar (NANA) group added could not be distinguished from the one with the sugar group (not shown in Figure 6). The hypothesis that NANA residues constitute a major factor involved in the formation of an extended κ-casein brush thus cannot be confirmed. In Figure 7a the calculated density profiles of adsorbed mixtures of κ-casein and para-κ-casein are shown. The parameter Θ was fixed for the situation of 0% of the hairs cut, namely Θ0 ) 4. We calculated density profiles for adsorbed mixtures in which the Θtot [) Θ(κ-casein) + Θ(para-κ-casein)] decreased according to a decrease in Θ(κ-casein), proportional increase in Θ(para-κ-casein), and the subsequent decrease in average chain length. In this way we simulated the cutting of the hairs. The ratio Θ(κ-casein):Θ(para-κ-casein) was varied according to the values given in the legend. With 60-80% of the hairs cut, there is mainly a decrease in monolayer density 1-2 nm from the surface. This may be the critical event for destabilization. Interestingly, this dense inner layer is also the region that is most influenced by grafting and tuft formation. In Figure 7b the data from Figure 7a are replotted on a log scale for the ordinate axis. This graph allows inspection of the outer part of the casein layer models.
We, quite arbitrarily, define a layer thickness as the coordinate where φ ) 0.003 from Figure 7b. Upon renneting from 0% to 100%, the decrease of this thickness is by approximation 8 nm. This result corresponds well with, for example, photon correlation studies of κ-caseincoated latex particles by Leaver and Horne (Figure 3 in ref 15) and is in accordance with the relative decrease in volume fraction obtained from light-scattering and Ubbelohde techniques, as presented in this study. Interaction Curves from SCF Calculations. In Figure 8 we plotted the interaction energy curve Aint(H) (see eq 8) between two penetrating monolayers of κ-casein or para-κ-casein. The most striking result is that all net interactions are repulsive and much larger than the van der Waals attraction alone. So the van der Waals attractive energy is unlikely to be sufficient to induce aggregation of the casein micelles. Note that the van der Waals contribution plotted in this figure was not the result of the computer modeling, but was calculated assuming a Hamaker constant of 1 × 10-20 J (which is probably too high for casein micelles). Next, we can conclude from the figure that there would be a significant decrease in the repulsion from 0% to 100% cutting of the chains. The fact that some repulsion remains after 100% cutting supports the view that remains of the hairy layer might contribute to an activation energy for aggregation of casein micelles.5-7 Also we see that the repulsion would already start at a layer distance H corresponding to a double layer spacing of 18 nm. This means that the most extended tails at 9 nm from the surface contribute to the colloidal stability. We also determined the logarithm of the interaction free energy ln(Aint) as a function of the plate separation (not shown). No linear part could be detected in such a graph (see eq 9). This confirms that the interaction energy is not given by the classical DLVO theory. The linear part should have been present at plate distances corresponding to the interpenetration of the most extended regions of the layer. We may conclude that casein micelles are predominantly sterically stabilized, that is, repulsion resulting from brush overlap. This may be due to the fact that the layer is salted.11 Interaction Curves from SCF Calculations with Block Copolymers. In Figure 9, we show interaction free energy curves of pure AB diblock copolymers and
6312 Langmuir, Vol. 15, No. 19, 1999
Figure 9. Interaction curves of penetrating monolayers of AB diblock copolymer and ABA triblock copolymer. Parameters chosen φb,AB ) 1 × 10-3, ΘAB (at H f ∞) ) 1.6, φb,ABA ) 2 × 10-3, ΘAB (at H f ∞) ) 2.4.
Figure 10. Interaction curves of mixed monolayers of AB and AB* diblock copolymers in the presence of an ABA triblock copolymer. Cutting of the hairs follows the sequence of curves 1f2f3. Exact parameters, curve 1: φb,AB ) 9 × 10-4, φb,AB* ) 0.6 × 10-4, φb,ABA ) 0.01 × 10-4; curve 2: φb,AB ) 5 × 10-4, φb,AB* ) 3 × 10-4, φb,ABA ) 1 × 10-4; and curve 3: φb,AB ) 0, φb,AB* ) 6 × 10-4, φb,ABA ) 1 × 10-4. These bulk concentrations correspond to a coverage (at H f ∞) of: curve 1: ΘAB ) 0.9, ΘAB* ) 0.56, ΘABA ) 0.19; curve 2: ΘAB ) 0.13, ΘAB* ) 0.78, ΘABA ) 1.1; and curve 3: ΘAB ) 0, ΘAB* ) 1.1, ΘABA ) 0.83.
pure ABA triblock copolymer monolayers as a function of the layer spacing in lattice sites M. Note the resemblance of these curves with those in Figure 8 (κ-casein) and ref 18 (Rs1-casein). The length scales are similar, that is, the regime at or around the attractive well (in nanometers) is made available on cutting of the hairs (see Figure 7b). The diblock induces a monotonic repulsive interaction curve. The triblock clearly shows an attractive well at a distance of about M ) 3. This effect may well be due to a bridging effect: the second hydrophobic sideblock resides on the interface opposite to the first one. To imitate the effect of cutting of the hairs, we plotted in Figure 10 the results of two calculations at different bulk concentrations of model para-κ-casein (AB* diblock copolymer with shorter soluble block). From this we see
Mellema et al.
the appearance of an attractive well at large layer separation at higher cutting levels (i.e., higher AB* content). The concentrations corresponding to the curves are given in the legend. Note that the surface coverage (Θ) changes also with different ratios of bulk concentrations (φb). Particularly, the affinity of the ABA triblock copolymer, coming from bulk solution, for the surface is large. Note the difference of the interaction curves derived using SCF theory, and the interaction well assumed in the AHS model. The AHS square well model is of course too simplistic, but can still be very useful as a first approximation, considering the complexity of the milk system. The observations presented above would support a hypothesis of Rs1-casein being involved in the early-stage aggregation of casein micelles. That is, we have shown that the proposed mechanism (which involves diblock and triblock copolymers) might work if the concentrations are chosen correctly. Inside the casein micelles there are at least three mechanisms for keeping the casein molecules together in the micelle: (a) casein bridges between hydrophobic domains, (b) casein bridges between domains with a high degree of calcium phosphate clusters (CCP crystals), and (c) CaPh bridges between caseins (κ-casein not contributing). So several types of heterocoagulates are formed. Note that there is a relative abundance of Rs1- and β-caseins over the other types of caseins in the micelle. We can now speculate why Rs1-casein can surface at high cutting degrees even though its concentration in the bulk is very low: it is very hard for Rs1-casein to take part in mechanisms mentioned above at the same time, because it is likely to be in a loop conformation and there is only a small distance between the phosphate groups and the hydrophilic blocks along the chain. We therefore expect it to participate in mechanism (a). If we now add calcium, this may reduce the necessity of the Rs1-casein taking part in mechanism (a). Consequently, the amount of Rs1-casein in the hairy layer may increase. Note that if β-casein would surface (there are indications that this also happens at low T), this only leads to a restabilization. In general in the renneting process, the cutting of the κ-casein hairs not only reduces the steric repulsion, but also changes the molecular equilibria. This latter effect is, along with the formation of calcium bridges between carboxylate or phosphate groups, essential for attractive interactions to become operative. An important assumption in the model is that the mobility of the caseins is high enough at the relevant time scales. Conclusions The traditional view that the colloidal stability of the milk is due to the stabilizing properties of an extended, almost brush-like κ-casein protein layer on the casein micelles is valid. An AHS approximation can be used to link the surface coverage to relevant casein micelle interactions at different calcium concentrations. Using sensitive methodology, we can confirm a considerable effect of calcium, especially on the gel time. In addition, we reproduce the known result that calcium is able to promote destabilization of milk at surprisingly high κ-casein surface coverages (∼0.5) and low attractive energies (∼1 kT), possibly because of ion bridging between the outer, most extended parts of two encountering hairy layers. However, the effect may also be indirect by induced changes in molecular equilibria. It is important to note that the values of the gel-time tsc are systematically lower for DLS, suggesting that this
Molecular Mechanism of the Renneting Process
method is somehow more sensitive to the interactions in the system. This causes part of the discrepancy between the values of, for example, the Baxter parameter τ derived from viscosity and DLS results. We do not promptly consider the discrepancy a failure of the AHS theory. Probably the fitting data for AHS analysis of the DLS data should differ from those used in the analysis of the viscosity data (e.g., hard-sphere radius, initial volume fraction, etc.). SCF calculations show that the repulsion between model κ-casein monolayers is of mainly steric origin and that the layer is not a true brush. Tuft formation and especially anchoring contribute to a higher level of penetration of the hairs into the bulk phase. In the model, the van der Waals interaction is not sufficient to induce instability. On the basis of less detailed SCF calculations, where we modeled κ-, para-κ-, and Rs1-casein as block copolymers,
Langmuir, Vol. 15, No. 19, 1999 6313
we have shown a possible involvement of Rs1-casein in the aggregation of casein micelles. In this approach, pure Rs1casein layers lead to attraction and κ- and para-κ-casein layers lead to repulsion. More importantly, we can make the interaction potential shift from repulsive to attractive by reducing the range of repulsive interactions of the diblock copolymers (by increasing the ratio of model κ- to para-κ-casein). The cutting of the hairs reduces the steric layer thickness, which makes room available to express the attractive contributions of the model Rs1-casein. Acknowledgment. We thank Pieter Walstra (Wageningen) for helpful comments on early versions of the manuscript. LA9902340
