Modeling the Kinetics of the Pectin Methylesterase Catalyzed De-esterfication of Pectin in Frozen Systems

The applicability of the William, Landel, and Ferry (WLF) equation with a modification to take into account the effect of melt-dilution and an empirical log-logistic equation were evaluated to model the kinetics of diffusion-controlled reactions in frozen systems. Kinetic data for the pectin methylesterase catalyzed hydrolysis of pectin in four model systems with different glass transition temperatures: sucrose, maltodextrin (DE = 16.5-19.5), carboxymethylcellulose (CMC) and fructose in a temperature range of -24 to 0° C were used. The modified WLF equation was evaluated with a concentration-dependent glass transition temperature (Tg) as well as the glass transition temperature of the maximally freeze-concentrated matrix (Tgʹ) as reference temperatures. The equation with temperaturedependent Tg described the reaction kinetics reasonably well in all the model systems studied. However the kinetics was better described by a linear relationship between log(V0/V0ref) and (T - Tref) in all cases except CMC. The log-logistic equation also described the kinetics reasonably well. The effect of melt-dilution on reactant concentration was found to be minimal in all cases.