Two-Parameter Kinetic Model Based on a Time-Dependent Activity Coefficient Accurately Describes Enzymatic Cellulose Digestion

Lignocellulosic biomass is a potential source of renewable, low-carbon-footprint liquid fuels. Biomass recalcitrance and enzyme cost are key challenges associated with the large-scale production of cellulosic fuel. Kinetic modeling of enzymatic cellulose digestion has been complicated by the heterogeneous nature of the substrate and by the fact that a true steady state cannot be attained. We present a two-parameter kinetic model based on the Michaelis-Menten scheme (Michaelis, L., and Menten, M. L. (1913) Biochem. Z., 49, 333-369) with a time-dependent activity coefficient analogous to fractal-like kinetics formulated by Kopelman (Kopelman, R. (1988) Science 241, 1620-1626). We provide a mathematical derivation and experimental support to show that one of the parameters is a total activity coefficient and the other is an intrinsic constant that reflects the ability of the cellulases to overcome substrate recalcitrance. The model is applicable to individual cellulases and their mixtures at low-to-medium enzyme loads. Using biomass degrading enzymes from cellulolytic bacterium Thermobifida fusca, we show that the model can be used for mechanistic studies of enzymatic cellulose digestion. We also demonstrate that it applies to the crude supernatant of the widely studied cellulolytic fungus Trichoderma reesei; thus it can be used to compare cellulases from different organisms. The two parameters may serve a similar role to V-max, K-M, and k(cat) in classical kinetics. A similar approach may be applicable to other enzymes with heterogeneous substrates and where a steady state is not achievable.