Background:The molecular understanding of factors that limit enzymatic hydrolysis of cellulose remains incomplete. Results: Pre-steady-state analysis of cellulolytic activity provides rate constants for basic steps of the overall reaction. Conclusion: Slow dissociation of inactive enzyme-cellulose complexes governs the hydrolytic rate at pseudo-steady state. Significance: Kinetic constants elucidate molecular mechanisms and structure-function relationships for cellulases.

Cellobiohydrolases (exocellulases) hydrolyze cellulose processively, i.e. by sequential cleaving of soluble sugars from one end of a cellulose strand. Their activity generally shows an initial burst, followed by a pronounced slowdown, even when substrate is abundant and product accumulation is negligible. Here, we propose an explicit kinetic model for this behavior, which uses classical burst phase theory as the starting point. The model is tested against calorimetric measurements of the activity of the cellobiohydrolase Cel7A from Trichoderma reesei on amorphous cellulose. A simple version of the model, which can be solved analytically, shows that the burst and slowdown can be explained by the relative rates of the sequential reactions in the hydrolysis process and the occurrence of obstacles for the processive movement along the cellulose strand. More specifically, the maximum enzyme activity reflects a balance between a rapid processive movement, on the one hand, and a slow release of enzyme which is stalled by obstacles, on the other. This model only partially accounts for the experimental data, and we therefore also test a modified version that takes into account random enzyme inactivation. This approach generally accounts well for the initial time course (approximately 1 h) of the hydrolysis. We suggest that the models will be useful in attempts to rationalize the initial kinetics of processive cellulases, and demonstrate their application to some open questions, including the effect of repeated enzyme dosages and the ‘double exponential decay’ in the rate of cellulolysis. Database 
The mathematical model described here has been submitted to the Online Cellular Systems Modelling Database and can be accessed at free of charge.

Processive enzymes perform sequential steps of catalysis without dissociating from their polymeric substrate. This mechanism is considered essential for efficient enzymatic hydrolysis of insoluble cellulose (particularly crystalline cellulose), but a theoretical framework for processive kinetics remains to be fully developed. In this paper, we suggest a deterministic kinetic model that relies on a processive set of enzyme reactions and a quasi steady-state assumption. It is shown that this approach is practicable in the sense that it leads to mathematically simple expressions for the steady-state rate, and only requires data from standard assay techniques as experimental input. Specifically, it is shown that the processive reaction rate at steady state may be expressed by a hyperbolic function related to the conventional MichaelisMenten equation. The main difference is a 'kinetic processivity coefficient', which represents the probability of the enzyme dissociating from the substrate strand before completing n sequential catalytic steps, where n is the mean processivity number measured experimentally. Typical processive cellulases have high substrate affinity, and therefore this probability is low. This has significant kinetic implications, for example the maximal specific rate (V max /E 0 ) for processive cellulases is much lower than the catalytic rate constant (k cat ). We discuss how relationships based on this theory may be used in both comparative and mechanistic analyses of cellulases.