On enzymic clotting processes V: Rate equations for the case of arbitrary rate of production of the clotting species

The rate theory for enzyme-triggered coagulation reactions, such as the clotting of fibrin or casein, is extended to the case of an arbitrary rate of production of the clotting species. It is shown that the general expression for the growth of the weight-average molecular weight of the clotting product, -M_w, is given by -M_w = M₁{1 + k_s {∫₀^tP(t)² dt}/P(t)}, where M₁ is the “monomer” molecular weight, k_s the smoluchowskian flocculation rate constant and P(t) the total number of monomers produced by the enzyme in t. In the purely smoluchowskian case P(t) stands for the total number of monomers at the beginning of the clotting process. Numerical examples in which the rate of enzymic production is governed by complete Michaelis-Menten kinetics, are compared to cases in which this rate equals V_max- It is shown that after exhaustion of the substrate the system continues to coagulate in a purely smoluchowskian way. Turbidimetric experiments on the clotting of micelles of whole and κ-casein are presented which suggest inactivation of the enzyme by non-productive binding in the flocs formed.