A kinetic model of the clotting of casein by rennet

A method for the inline measurement of milk gel firmness using an optical sensor

At present, selection of cutting time during cheesemaking is made based on subjective methods, which has effects on product homogeneity and has prevented complete automation of cheesemaking. In this work, a new method for inline monitoring of curd firmness is presented. The method consisted of developing a model that correlates the backscatter ratio of near infrared light during milk coagulation with the rheological storage modulus. The model was developed through a factorial design with 2 factors: protein concentration (3.4 and 5.1%) and coagulation temperature (30 and 40°C). Each treatment was replicated 3 times; the model was calibrated with the first replicate and validated using the remaining 2 replicates. The coagulation process was simultaneously monitored using an optical sensor and small-amplitude oscillatory rheology. The model was calibrated and successfully validated at the different protein concentrations and coagulation temperatures studied, predicting the evolution of storage modulus during milk coagulation with coefficient of determination values >0.998 and standard error of prediction values <3.4 Pa. The results demonstrated that the proposed method allows inline monitoring of curd firming in cheesemaking and cutting the curd at a proper firmness to each type of cheese.

Application of polymer cross-linking theory to rennet-induced milk gels

A general theory of gel formation by cross-linking of polymer molecules, orginally developed for the study of rubber vulcanization, is proposed as a model for milk gel formation. The model divides gel formation and development into 4 stages, an enzymic and a non-enzymic stage preceding gelation, then a stage of material transition from the sol to the gelled state and a stage of increase in gel strength due to internal cross-link formations. The 2 post-gelation stages overlap to a variable degree depending upon particular circumstances. Gel formation and properties are interpreted in terms of the number of initial units which combine to form the gel and the number of cross-links eventually formed by each unit. When combined with a kinetic expression for the rate of cross-link formation the time course of gel shear modulus development or of the incorporation of material into the gel may be predicted. The classical asymmetric sigmoid shape of gel shear modulus development curves results from the third stage of material transition into the gel, which in turn depends upon the number of cross-links eventually formed by each initial unit. The modulus of mature gels is found to depend upon the square of material concentration, and gel breaking strength is found to be proportional to the modulus, in agreement with the predictions of the theory.

Derivation of a mathematical model for the mechanism of casein micelle coagulation by rennet

The action of rennet on the stability of casein micelles has been described theoretically by combining Michaelis–Menten enzyme kinetics with von Smoluchow-ski's theory for slow coagulation. The casein micelle is considered to be stabilized by stcric interactions arising from a highly hydrated surface protein layer. The stability factor, in von Smoluchowski's theory, is then considered as a variable and determined by the concentration of unhydrolysed κ-casein.

The theoretical approach describes semi-quantitatively experimental observations on clotting time (CT) as a function of temperature, rennet concentration, and total protein concentration. The model also predicts that, under certain circumstances, the CT is inversely proportional to the enzyme concentration. Furthermore, the model agrees with other workers' experimental observations on the effect of κ-cascin concentration, the presence of a lag phase, and that the lag phase is commonly about 60% of the CT.

A mathematical model for the description of chymosin action on casein micelles

A mathematical model for chymosin action on casein micelles is presented in a two-stage equation which results in a single curve demonstrating the lag time from enzyme addition to the end of coagulum firming. The model uses the Michaelis–Menten enzyme kinetics equation for the first reaction followed by an nth order reaction for the casein micelles agglomeration stage. The computer output using these equations shows that lag time is elongated as enzyme concentration is lowered. Regression analysis of time of gelation against l/E0 shows good correlation. Viscosity of the milk drops at the beginning of the κ-casein hydrolysis and increases thereafter, when the coagulum is being formed.

Action of rennin on casein. III. Effect of alpha s- and beta-casein on the secondary phase

The action of rennin on kappa-casein was studied as a function of time, employing turbidity measurements at 610 nm and the release of nonprotein nitrogen. kappa-Casein was converted to para-kappa-casein by the action of rennin. The para-kappa-casein aggregated to increase turbidity and then precipitated. Turbidity development was enhanced initially and then retarded severely by increasing concentrations of added alpha s- and beta-casein. The addition of selected amino acids and salts had variable effects on increase of turbidity.