The enzyme-triggered coagulation of casein micelles

Rennet coagulation of milk in the presence of sucrose

The aim of this work was to test the diffusion-controlled hypothesis of milk coagulation kinetics by reducing the diffusion coefficient of casein micelles. This has been achieved by increasing the solvent viscosity of milk through sucrose addition. Milk was reconstituted from skim milk powder and sucrose added at 100–300 g kg–1. Hydrolysis and coagulation were followed by chromatographic determination of caseinomacropeptide content and optical, thermal and viscoelastic measurements. Soluble and ionic calcium were determined by atomic absorption spectrophotometry and ionometry and micelle size was measured by dynamic light scattering. Addition of sucrose resulted in a substantial retardation of both enzymic and aggregation steps, a re-equilibration of calcium because of water reduction, and a micelle size increase. The enzymic rate constant was inversely proportional to the viscosity, according to a diffusion-controlled model, and the lag or characteristic times for the aggregation reaction were inversely proportional to the viscosity. These results are consistent with the involvement of diffusion-controlled steps in the sequence of reactions.

Enzyme-induced coagulation of casein micelles: a number of different kinetic models

Several mathematical models are presented in an attempt to describe the kinetics of the enzyme-induced coagulation of casein micelles. In each model the primary phase of the clotting reaction is assumed to follow first order kinetics. The only differences amongst the various models centre on the definition of the flocculation rate constant, which is defined in seven different ways. The rate constants are defined and discussed in terms of activation energy and functionality theory. The first model is such that the number of functional sites is two. The second is such that the number is much larger. The third and fourth are such that there is an exponential energy barrier, one which has a magnitude proportional to the extent of proteolysis caused by the clotting enzyme. These two definitions differ only in the pre-exponent. In one case the pre-exponent is a constant, whereas in the other it is dependent on the size of clotting particles. The fifth and sixth definitions are also energy barrier rate constants, but the energy barrier changes in an arbitrary fashion with respect to time during proteolysis. The seventh definition assumes a large number of functional sites, but such that the number increases with extent of proteolysis. In the Payens nomenclature (Payens, 1989), all models could be considered to be ‘source’ models, and all are derived using the Drake moment equation (Drake, 1972). Only the first model has a truly constant flocculation rate parameter, and only this model has a relatively simple analytical solution. All other models yield analytical solutions only by way of infinite series expansions. Thus, all models are presented in terms of power series expansions, and only through the first five time-dependent coefficients. This confines all models to the early stages of coagulation. In all cases the first three coefficients are virtually the same. The first two coefficients involve only proteolysis, and the third includes initial flocculation information. Time-dependent changes in the flocculation rate constant begin to take effect in the fourth coefficient. When the fourth coefficients of the third and seventh models are compared, a simple relationship is suggested between free energy barrier removal and functional site generation, but only assuming that the number of functionalities is large.

Characterization of Enzymatically Induced Aggregation of Casein Micelles in Natural Concentration by in Situ Static Light Scattering and Ultra Low Shear Viscosimetry

The aggregation of casein micelles in undiluted skim milk after the addition of chymosin was studied by static light scattering and ultra low shear viscometry. The static light scattering measurements were made with two different sample thicknesses, 72 and 16 µm. The scattering data were analyzed by indirect Fourier transformation and by the polydispersity inversion technique which led to pair distance distribution functions and size distribution function, respectively. The minimum scattering angle was 1 degrees, which allows for the determination of particle sizes up to a maximum diameter of 12 µm. The fractal dimension determined from double logarithmic plots of intensity versus scattering vector resulted in values between 1.9 and 2.0. The influence of multiple scattering was determined by comparison of the measurements with the different sample thicknesses. The measurements show no significant influence of multiple scattering when the transmission is above 0.85. Due to the very complex and porous structure of the casein aggregates the Rayleigh-Debye-Gans scattering theory has been used in the data analysis. Measurements with a new instrument using ultra low shear showed good agreement with theory. Copyright 1999 Academic Press.

A Novel Approach to Turbidimetry of Dense Systems: An Investigation of the Enzymatic Gelation of Casein Micelles

A novel approach to turbidimetry enabling the extraction of structural information about highly turbid systems has been developed. Turbidimetric spectra have been obtained in the wavelength region 500-1100 nm using an acceptance angle of 1 degrees for detecting the transmitted light. It is demonstrated that the influence of multiple scattering can be eliminated by measurement of turbidimetric spectra at several sample thicknesses and subsequent extrapolation to zero thickness. The validity of this method is demonstrated by Monte Carlo simulations of multiple scattering of light using simple Rayleigh-Debye-Gans theory. The simulations demonstrate that turbidimetric spectra are very insensitive to multiple scattering measured with an acceptance angle of 1 degrees when the particles are smaller than about 1 µm. It was further shown that no shape information can be derived from turbidimetric spectra under our condition for objects having diameters up to 6 µm. The turbidimetric spectra of casein aggregation/gelation have been fitted by modeling the aggregates either as homogeneous spheres or as fractals. The turbidimetric averaged mean radii found using the sphere model are at all stages of the process consistently smaller than radii found by either static or dynamic light scattering. This is found to be a consequence of the angular integration involved in turbidimetry which weights larger radii less than in the case of light scattering. Copyright 1998 Academic Press.