Application of the Direct Quadrature Method of Moments for the modelling of the enzymatic hydrolysis of cellulose: I. Case of soluble substrate

The modelling of the enzymatic hydrolysis of cellulosic polymers is investigated through a population balance approach. Both Endoglucanase (EG) and Exoglucanase (CBH) activities are taken into account. EG achieves random attacks along cellulosic chains and cleaves the β-glycosidic bonds whereas CBH produces cellobiose molecules by chain-end scission mechanism. The EG activity is modelled as a pure breakage while the CBH activity is assimilated to an erosion process with a specific product (cellobiose). In the two cases, the inhibition of the cellulases activity by the end-product is incorporated. The population balance equation (PBE) accounting for breakage processes is solved using the Direct Quadrature Method of Moments (DQMOM) coupled to a distribution reconstruction technique based on the Maximum Entropy (ME) principle in order to track the time evolution of the chain length distribution (CLD) during the hydrolysis reaction. The β-glucosidase activity transforming the produced cellobiose into glucose is modelled as a Michaelis-Menten type kinetic with a competitive inhibition effect and solved simultaneously with the PBE. The numerical results show the time-evolution of the CLD during the hydrolysis reaction as well as the rate of conversion of the substrate into simple sugars. These results are in concordance with those predicted analytically. The synergistic action of the EG and CBH is highlighted and discussed and the inhibition effect is investigated. The approach is promising by its accuracy and fastness for the analysis of dynamic experimental data of the enzymatic hydrolysis reaction.