A kinetic model for the burst phase of processive cellulases

Abstract

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.

Origin of Initial Burst in Activity for Trichoderma reesei endo-Glucanases Hydrolyzing Insoluble Cellulose

“…This is much lower that reported product inhibition constants for the investigated enzymes (13,70,71), and it, therefore, seems unlikely that the slowdown depends on product inhibition. This reasoning is supported in both Figs.…”

“…The number-averaged degree of polymerization (DP N ) was calculated from the ratio of reducing ends measured by BCA (see below) and total sugars. The crystallinity index of RAC was determined using solid state 13 C cross-polarization/magic angle spinning nuclear magnetic resonance (NMR) with settings adapted from Matulova et al (49) and described in Murphy et al (46). Cello-oligosaccharides (COS) were prepared according to Zhang and Lynd (50), and purity was determined using high performance anion exchange chromatography with pulsed amperometric detection (46).…”

“…2. A more likely interpretation is a reversible inactivation model where rapid hydrolysis prevails until the enzyme encounters some structure in the substrate (an "obstacle" or "trap"), which dictates a protracted (but finite) inactive period (13,14). In this case the activity is high over some initial period, but it will decrease as more and more enzyme gets stalled by obstacles.…”

Kinetics of Cellobiohydrolase (Cel7A) Variants with Lowered Substrate Affinity

“…One corollary of a dissociation-controlled rate is that not all adsorbed enzyme can be catalytically active at the same time (20,23), and this is congruent with suggestions of a bound but inactive population of processive cellulases. This may rely on irregularities in the cellulose structure, which obstruct processive movement (20,30,65) or "traffic jams" in which enzymes collide and stall (60). In any case, slow release will be associated with an adsorbed but catalytically inactive population of enzyme.…”

“…We have previously suggested (23,30) that experimental data for processive enzymes may be analyzed by a reaction scheme (Scheme 1), according to which the free enzyme, E, combines with a cellulose strand, C m , to form an activated complex, EC m . The enzyme subsequently moves along the strand, which is sequentially shortened by one cellobiose, moiety C, for each step (so the strand is converted to C m-1 , C m-2 , etc.).…”