Cellulose hydrolysis in evolving substrate morphologies III: time-scale analysis.

We present a time-scale analysis for the enzymatic hydrolysis of solid cellulosic substrates, based on our recently developed kinetic model (Zhou et al., 2009a, Biotechnol Bioeng 104:261-274; Zhou et al., 2009b, Biotechnol Bioeng 104:275-289) which incorporates both enzymatic chain fragmentation and hydrolytic time evolution of the solid substrate morphology. Analytical order-of-magnitude estimates of the relevant single-layer chain depolymerization times are first discussed. These time-scale estimates for pure and mixed enzyme systems can be employed to calculate the degree of synergy between endo- and exo-acting enzymes in a mixed enzyme system. By the way of a quasi-steady-state approximation which allows for a greatly simplified analytical solution of the model, we also explain the origin and give order-of-magnitude estimates of the two characteristic hydrolysis time scales which arise in this model when the solid substrate morphology is taken into account. These analytically derived time-scale relations explain how the embedding of cellulose chains in a solid substrate acts as a crucial rate-limiting factor and results in a substantial slowing down of the hydrolytic conversion process, compared to a hypothetical substrate of immediately enzyme-accessible, isolated chains. The analytical time-scale results are verified by numerical simulations and compared to experimental observations.