Mean field kinetics of the enzyme-triggered gelation of casein micelles

Abstract

The kinetics of the milk-clotting process is treated with the Flory—Stockmayer (or “mean field”) approximation. It is shown that the gelation of milk is preceded by a small, but distinct, decrease in the weight-average degree of aggregation, which can be used to measure the proteolytic activity of the clotting enzyme. The gelpoint itself occurs at t g = (π/2) ( k 0 · <υ>) − 1 2 , where k 0 is the flocculation rate constant of a pair of single micelles of paracasein and <υ> the time-averaged rate of ϰ-casein proteolysis. A simple expression is given for the so-called proteolysis-to-clotting ratio of the clotting rennet and examples are given showing the influence of the degree of concentration of the milk at its gelpoint. With undiluted milk, light scattering techniques to monitor the clotting are not very feasible due to the opacity of the sample and multiple scattering and interference effects. Viscosity methods, on the other hand, suffer from the drawback that the relationship between the weight-average degree of aggregation and the viscosity increment is not clear. The existence of a lag phase in the clotting and the small initial decrease in the average degree of aggregation were confirmed in experiments with a very low-stress, parallel plate viscometer.