A steady-state theory for processive cellulases.

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 Michaelis-Menten 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)/E0) 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.

Pre-steady-state kinetics for hydrolysis of insoluble cellulose by cellobiohydrolase Cel7A.

The transient kinetic behavior of enzyme reactions prior to the establishment of steady state is a major source of mechanistic information, yet this approach has not been utilized for cellulases acting on their natural substrate, insoluble cellulose. Here, we elucidate the pre-steady-state regime for the exo-acting cellulase Cel7A using amperometric biosensors and an explicit model for processive hydrolysis of cellulose. This analysis allows the identification of a pseudo-steady-state period and quantification of a processivity number as well as rate constants for the formation of a threaded enzyme complex, processive hydrolysis, and dissociation, respectively. These kinetic parameters elucidate limiting factors in the cellulolytic process. We concluded, for example, that Cel7A cleaves about four glycosidic bonds/s during processive hydrolysis. However, the results suggest that stalling the processive movement and low off-rates result in a specific activity at pseudo-steady state that is 10-25-fold lower. It follows that the dissociation of the enzyme-substrate complex (half-time of ~30 s) is rate-limiting for the investigated system. We suggest that this approach can be useful in attempts to unveil fundamental reasons for the distinctive variability in hydrolytic activity found in different cellulase-substrate systems.

A kinetic model for the burst phase of processive 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.