A theoretical equation describing the time evolution of the concentration of a selected range of substrate molecular weights in depolymerization processes mediated by single-attack mechanismendo -enzymes

Abstract

Monitoring the time evolution of the concentration of a selected range of molecular weights of substrate, referred to as "detectable" substrate, has been used to determine endo-enzymic activities in polysaccharide depolymerizing processes. In the methodologies based on the use of dye-labeled substrates, the "detectable" substrate extends from a given molecular weight threshold downward. On the contrary, in the fluorescent probe-flow injection analysis methodology, initially developed to determine (1 --> 3)-(1 --> 4)-beta-D-glucanase activities, the "detectable" substrate extends from a given molecular weight threshold upward. Assuming that the time evolution of the molecular weight distribution of the substrate follows the most probable distribution (the enzymic attack is random and its mechanism is single attack), a theoretical equation describing the time evolution of the concentration of "detectable" substrate (from a given molecular weight threshold upward or downward) has been deduced. This equation, Wd = Wo. (1 + alphat). e-alphat, where Wd is the concentration of "detectable" substrate, Wo is the initial concentration of the substrate, t is the depolymerization time, and alpha is a parameter correlated through a hyperbola with the initial concentrations of enzyme and substrate and the Michaelis-Menten constant, Km, has been tested against different (1 --> 3)-(1 --> 4)-beta-D-glucan/(1 --> 3)-(1 --> 4)-beta-D-glucanase systems using the fluorescent probe-flow injection analysis methodology and Calcofluor as the fluorescent probe. The most important predictions of the theoretical equation, which allow accurate determination of both endo-enzymic activities and kinetic constants, have been experimentally confirmed.