A review is presented of the various inter molecular forces important in stabilizing protein structure and association. Emphasis is put on entropic as well as enthalpic contributions to the free energy. The factors affecting size and size distribution in protein aggregates are discussed. A theory is presented for the size distribution of casein micelles, taking into account the spherical nature of the micelles and the importance of surface repulsive forces in limiting size.

In reconstituted casein systems, complete sub-micelles were previously observed only under extreme conditions of ionic strength, namely a NaCl concentration of 2 M or greater. However, studies with the analytical ultracentrifuge on phosphate-containing casein systems revealed that under certain conditions, a stable sub-micelle-micelle equilibrium was established. Conditions which were standard throughout were 7.5 mg/ml protein, 0.04 M-NaCl, pH 6.6 and 37 °C. The concentrations of added CaCl2 (Ca2+) and inorganic phosphate (P1) were variable. With no P1 present, Ca-sensitive caseins precipitated or formed micelles when k-casein was present, between 6 and 7 mM-Ca2+. With 10–20 mM-P1 precipitation or micelle formation began at about 4 mM-Ca2+ and was complete at about 5 mM-Ca2+. Over this interval, during micelle formation, a sub-micelle peak with s20, w of about 13 S was observed in equilibrium with the broad micelle peak. In a system containing a 2:2:1 weight ratio of ±sI-:²-:k-casein, this sub-micelle was isolated at 4 mM-Ca2+ and 2.5 mM-P1. The mol. wt was 760000 and it thus contained approximately 33 monomer caseins. The reconstituted micelle system formed in the absence of P1 was quite temperature sensitive, forming at 37 °C but disappearing upon cooling. In the presence of P1 the micelles formed at 37 °C but were stable to cooling as are natural micelles. Evidently, a combination of hydrophobic and electrostatic interactions are involved in natural micelle formation, probably with the production of salt bridges of Ca and phosphate ions between sub-micelles.

A model for the coagulation of Ca2+ αsl-caseinate is described wherein the casein molecules are considered to aggregate as polyfunctional units. The functionalities on the protein molecules are produced as a consequence of the binding of Ca2+, and the multiple equilibria which are established during this binding produce a distribution in which not all casein molecules have the same functionality. The theory is compared with experimental data of the precipitation reaction, and is shown to provide an adequate quantitative description of the precipitation.

The aggregation of αs1-casein by Ca is viewed as resulting from a reduction in the net negative charge by the binding of positively charged Ca2+. This reduction in charge leads to the equivalent of isoelectric precipitation. A quantitative relationship between the rate of aggregation of the casein and the monomer net charge is predicted in this isoelectric precipitation model. Precipitation results are presented for αs1-casein labelled with dansyl chloride. Providing the changes in charge brought about by the modification are taken into account, the precipitation behaviour of these caseins can be reconciled with that of native αs1-casein. This emphasises the role of electrostatic repulsion in this process and lends further support to the isoelectric precipitation model.

The self-association of SH-κ-casein at pH 7·0 in 0·01 m-EDTA, 0·001 m-dithiothreitol buffer, containing 0·1, 0·2, 0·5 or 1·0 m-NaCl is of a monomer–polymer type. The polymer is a spherical particle, diam. 23 nm and mol. wt 570000 (30 monomers). These parameters are not greatly influenced by variations in ionic strength above 0·1. The critical micelle concentration, which is a property of a monomer–polymer equilibrium, decreases with increasing ionic strength. The standard free energy of association is about – 36 kJ/mol. monomer at 20 °C.

The size and number average molecular weight have been determined for β-casein monomers and polymers from electron micrographs using the freeze-etching procedure with spray-frozen specimens. For the spherical β-casein monomers we found a mol. wt of 22600 and a diam. about 10 nm, which compared quite well with data obtained from ultracentrifugation, light scattering and viscosity measurements. Polymer sizes were in agreement with molecular weight determinations from ultracentrifugation and light scattering, assuming that the volume and weight of the particles are proportional.

The temperature and concentration dependent association of β-casein was studied by means of viscometry, gel filtration chromatography, electron microscopy, analytical ultracentrifugation and UV difference spectrophotometry. Degrees of polymerization of 12, 22 and 49 and free energies of association of –21, –23 and – 25 kJ/mole monomer were found at temperatures of 10, 15 and 20 °C respectively in 0·2 M Na phosphate buffer pH 6·7.

Monomeric β-casein was not a completely random coil but became more compact with increasing temperature, due to hydrophobic interactions.

Multiple regression analysis was applied to sedimentation equilibrium data for determination of the molecular weight distribution (MWD) of model systems consisting of up to 3 components. Negative weight fractions which were frequently encountered during multiple regression analysis were forced to zero by sequentially eliminating from the regression matrix the corresponding molecular weights in order of the magnitude of negative t-values. The simplex optimization of Morgan & Deming (1974), modified by incorporating a prohibit–range– trespassing routine, was used to search for the best fit values for weight average molecular weights and relative concentrations of the components. This method almost quantitatively reproduced the molecular weights and concentrations of the original model systems. This quantitative information supplemented the multiple regression matrix to improve the resolution of MWD.

A direct comparison using model systems revealed that the multiple regression method in conjunction with the simplex optimization routine was more quantitative than the linear programming method of Scholte (1969). When applied to mixtures of standard proteins (ribonuclease A; ovalbumin; γ-globulin and ovalbumin; γ-globulin; apoferritin), the simplex optimization routine yielded values for average molecular weights and relative concentrations of the component proteins which were in good agreement with the known values in the original mixtures.

The MWD of αs1-k-casein mixtures at an ionic strength of 0.1 suggested that k-casein was readily dissociated to the monomer (or the dimer) and interacted with the monomer (or the dimer) of αs1-casein forming a complex of approximately 400000.

The colloidal properties of micellar casein are reviewed. It is shown that the behaviour of intact micelles is much at variance with the predictions from the Schulze–Hardy rule, and that therefore their stability cannot be explained by the principles of the DLVO theory. Towards electrolyte, micelles behave as a protein rather than a lyophobic colloid.

Casein is a strong protective colloid. In the micelle, however, it does not completely cover the inorganic constituent which remains sensitive to changes in the ionic environment.

The rate theory of the enzyme-induced clotting of casein micelles is summarized. It is shown that the lag phase in the clotting is due to the second order of the coagulation reaction. Flocculation rate constants of micelles have been deduced from clotting times. Their relatively low values can be attributed to an orientational constraint. Practical consequences of the theory with respect to clot structure, gelation of sterilized products and cheese manufacture are discussed.

Skim-milk was fractionated by permeation chromatography on CPG-10 (300 nm) at 20 °C with synthetic milk serum. The elution profile, which was highly reproducible, showed 3 partly resolved peaks. On treatment with 0.1% glutaralde-hyde before chromatography, a similar profile was obtained indicating no appreciable micellar dissociation during chromatography of the milk. The casein composition of the eluent fractions, determined by quantitative chromatography on hydroxyapatite, showed that 12.1% of total casein was associated with the low molecular weight peak. The micelle content of ²- and κ-casein increased with increasing elution volume, and the ±s/κ ratio showed a progressive diminution from 4·3 to 2·3. Large differences were found in the colloidal phosphate contents and the weight average diameters of the micelle fractions which clearly show that CPG-10 fractionates on the basis of molecular size.

Casein micelles fractionated on controlled pore glass (CPG-10/3000) were shown to be stable by recycling experiments. Only minor effects on the size distribution of the casein micelles were found after heating skim-milk to 100 °C for 10 min, or freeze-drying skim-milk at – 70 °C followed by resuspension in the synthetic milk serum of Jenness & Koops (1962). The heating caused some whey proteins (β-lactoglobulin) to enter the micelle fractions while the freeze-drying caused some of the largest micelles to disrupt. In colloidal calcium phosphate-free skim-milk prepared according to Pyne & McGann (1960) all the micelles appeared to dissociate into monomeric caseins.

A comparison of literature results on the voluminosity of casein micelles yields large differences, largely related to the method of determination. After applying some corrections, methods based on hydrodynamic radius yield a value of roughly 3·9ml/g dry casein, other methods (microscopy, sediment volume) about 2·2. Roughly half of the discrepancy can be explained by the micelles being not perfectly spherical. To explain the remaining difference, it is assumed that the micelles are hairy, i.e. they have molecular chains protruding into the milk serum. The hairyness would increase with decreasing temperature and be largely removed by the action of rennet. It would cause some entropic repulsion between micelles at close approach.