Kinetics of enzymatic depolymerization of guar galactomannan

A new mathematical model based on Michaelis Menten (MM) kinetics is developed to predict the changes in molecular weight distribution (MWD) during the enzymatic depolymerization of guar galactomannan. The model accounts for the effect of branching by considering the guar molecule as a substrate having three types of bonds with different MM kinetic parameters. The overall kinetics of the enzymatic reactions then can be represented in terms of composite kinetic parameters that are functions of the MM parameters for the individual bonds. The depolymerization is assumed to follow a random scission mechanism, in which an enzyme randomly attacks the substrate molecule at any one of the three types of bonds, and leaves the substrate on cleavage of the bond. Expressions for the variation in molecular weights during depolymerization are developed by applying moment generating techniques to the kinetic model. The model is evaluated against the complete MWD obtained using gel permeation chromatography. During the initial stages of depolymerization, the enzymatic reaction is in the zero-order regime of MM kinetics and the polydispersity index (PDI) increases with time. Subsequently, the PDI decreases as the depolymerization tends to follow first order kinetics. We also show that for a zero-order, random or nonrandom scission, the variation of PDI with time can exhibit a maximum. These analyses confirm that an increase in PDI during the depolymerization is not necessarily due to nonrandom scission, as previously concluded.