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 P(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. Biotechnol. Bioeng. 2009;104: 261-274. (C) 2009 Wiley Periodicals, Inc.