Application of the direct quadrature method of moments for the modelling of the enzymatic hydrolysis of cellulosic substrates

Models based on extension/modification of Michaelis-Menten type kinetics are widely used for the description of the biomass hydrolysis reaction. However, in-depth statistical analysis shows that the identifiability of the model parameters by the regression of typical saccharification data is defective since (i) the number of the parameters is high compared to the optimization reference data (ii) the structure of the model is not adapted to take into account the particulate nature of the substrate (Sin et al., 2010).

Here, we propose a population balance approach to describe the elementary mechanisms of the enzyme attacks and the particle size distribution evolution during the hydrolysis reaction. In the case of cellulosic substrates, Endoglucanases break randomly the polymer chains whereas Cellobiohydrolyses proceed with chain-end scission and release cellobiose. Previous works described the particulate substrate as a collection of cellulose chains (Lebaz et al., 2014). This makes the numerical resolution challenging. We propose to solve the population balance equation by using the Direct Quadrature Method of Moments (DQMOM) (Marchisio et al., 2005). The model variable is the substrate particles size allowing the substrate specific surface estimate for a better modelling of the enzyme adsorption. The two main cellulase activities are taken into account: the Endoglucanase cleaves randomly the chains and affect the particles cohesion whereas the Cellobiohydrolases activity is assimilated to an erosion process. Adsorption and enzymes inhibition by the end-products are incorporated and a time-dependent probability for the breakage of the particles is formulated. The results are discussed in comparison with experimental measurements.