DEPENDENCE OF GELATION TIME UPON ENZYME CONCENTRATION FOR ISOTROPIC AND ANISOTROPIC CASEIN MICELLES

We have carried out Monte Carlo simulations of two lattice models of e nzyme-activated gelation of casein micelles in order to discover how t he gelation time, t(g), depends upon the enzyme concentration, [E]. En zymes and micelles occupy the sites of a cubic lattice with periodic b oundary conditions and we define probabilities for enzymes to Split ka ppa-casein molecules and for micelles to irreversibly aggregate. The m odel allows for micelles to exhibit anisotropy in their stability agai nst aggregation. No approximations are made in solving for quantities of interest so that any disagreement with experiments are known, a pri ori, to be defects of the model only. For isotropic micelles, we concl ude that as [E] --> 0, t(g) is-proportional-to [E]-1 for nearly all ca ses studied, and that, as [E] becomes very large and the probability, per Monte Carlo step, for irreversible aggregation approaches unity, t (g) --> t(g)infinity, which is very much smaller than tg obtained for small values of [E]. These results are in agreement with experimental data. Our results show that as the micelles become very anisotropic, f or fixed [E] --> 0, t(g) is-proportional-to [E]-sigma where sigma almo st-equal-to 0.9. However we present an argument that this is because w e have not achieved a sufficiently small value of [E] so as to observe asymptotic behavior, so that we expect sigma = 1.0 for anisotropic mi celles. It is possible that the use of insufficiently small values of [E] is the reason why early measurements yield a range of sigma < 1. W e discuss how the model can be modified to include changes in pH or io n concentration and other phenomena.