Analysis and quantification of a mixed exo-acting and endo-acting polysaccharide depolymerization system.
A new mathematical model has been proposed based on a model presented by Suga, van Dedem, and Moo-Young. The model requires a separate differential equation for each polymeric species (differentiated by degree of polymerization) in the reaction mixture. The main contribution of this model is the incorporation of experimental molecular weight distributions as the initial conditions. These molecular weight distributional as the initial conditions were obtained using modern analytical equipment previouly unknown for this application. The equipment, SEC/LALLS, measures relative concentrations of specific molecular weight species along with the corresponding molecular weights, thus yielding (through some mathematical manipulation) the absolute concentration of each molecular weight species. The concentration at each molecular weight can then be incorporated as the initial condition for that equation. Theoretically, the system of differential equations can be solved to give a more realistic time course of reaction.Synergism between endo-acting and exo-acting enzymes was examined theoretically using the mathematical model. Through model predictions, it was found that synergy is based on two fundamental parameters: (1) each enzyme's activity relative to the sum of enzyme activities and, (2) overall substrate concentration relative to the exo-acting enzyme's Michaeiis kinetic constant K(m). Theoretically, synergism increases as a function of reaction time. Intermediate endo fractions (ratio of endo-acting enzyme activity to the sum of endo-acting and exo-acting enzyme activity) from 0.3 to 0.7 exhibit the most synergism. Values of kappa [log(K(m, exo)/S(0))] above about zero also exhibits the most synergism.An examination of experimental data obtained both by SEC/LALLS and by reducing sugar measurements shows that the model is inadequate for successfully predicting quantities associated with the substrate during reaction. This is especially true for synergism predictions. At short reaction times, the model predicts the data fairly well, but at longer times the predictions are inconsistent with experimental data. These inconsistencies may be due to complicating phenomena such as enzyme inhibitions.
Dean
S W
SW
American Cyanamid Co., Princeton, New Jersey, USA.
Rollings
J E
JE