Cellulose hydrolysis in evolving substrate morphologies I: A general modeling formalism.

We develop a general framework for a realistic rate equation modeling of cellulose hydrolysis using non-complexed cellulase. Our proposed formalism, for the first time, takes into account explicitly the time evolution of the random substrate morphology resulting from the hydrolytic cellulose chain fragmentation and solubilization. This is achieved by integrating novel geometrical concepts to quantitatively capture the time-dependent random morphology, together with the enzymatic chain fragmentation, into a coupled morphology-plus-kinetics rate equation approach. In addition, an innovative site number representation, based on tracking available numbers of beta(1,4) glucosidic bonds, of different "site" types, exposed to attacks by different enzyme types, is presented. This site number representation results in an ordinary differential equation (ODE) system, with a substantially reduced ODE system size, compared to earlier chain fragmentation kinetics approaches. This formalism enables us to quantitatively simulate both the hydrolytically evolving random substrate morphology and the profound, and heretofore neglected, morphology effects on the hydrolysis kinetics. By incorporating the evolving morphology on an equal footing with the hydrolytic chain fragmentation, our formalism provides a framework for the realistic modeling of the entire solubilization process, beyond the short-time limit and through near-complete hydrolytic conversion. As part I of two companion papers, the present paper focuses on the development of the general modelling formalism. Results and testable experimental predictions from detailed numerical simulations are presented in part II.

Cellulose hydrolysis in evolving substrate morphologies II: Numerical results and analysis.

Numerical simulation results are presented for a cellulose hydrolysis model which incorporates both the enzymatic glucan chain fragmentation kinetics and the hydrolytic substrate morphology evolution within the general framework of our companion article I. To test the local Poisson (LP) approximation employed in the site number formalism of I, we numerically compare it to the corresponding exact chain number formalism of I. The LP results agree to very high accuracy with the exact chain number kinetics, assuming realistic parameters. From simulations of different types of random and non-random model morphologies, we then show that the details of the random substrate morphology distribution, and its hydrolytic time evolution, profoundly affect the hydrolysis kinetics. Essential, likely very general, experimentally testable features of such morphology-based hydrolysis models are (i) the existence of two distinct time scales, associated with the hydrolysis of the outermost surface-exposed cellulose chains and, respectively, of the entire substrate; (ii) a strongly morphology-dependent hydrolysis slow-down effect, which has also been observed in previous experimental work. Our results also suggest that previously proposed non-morphologic chain fragmentation models can only be applied to describe the hydrolytic short-time behavior in the low enzyme limit. Further experiments to test our modeling framework and its potential applications to the optimization of the hydrolytic conversion process are discussed.