Model of Processive Catalysis with Site Clustering and Blocking and Its Application to Cellulose Hydrolysis

Interactions between particles moving on a linear track and their possible blocking by obstacles can lead to crowding, impeding the particles' transport kinetics. When the particles are enzymes processively catalyzing a reaction along a linear polymeric substrate, these crowding and blocking effects may substantially reduce the overall catalytic rate. Cellulose hydrolysis by exocellulases processively moving along cellulose chains assembled into insoluble cellulose particles is an example of such a catalytic transport process. The details of the kinetics of cellulose hydrolysis and the causes of the often observed reduction of hydrolysis rate over time are not yet fully understood. Crowding and blocking of enzyme particles are thought to be one of the important factors affecting the cellulose hydrolysis, but its exact role and mechanism are not clear. Here, we introduce a simple model based on an elementary transport process that incorporates the crowding and blocking effects in a straightforward way. This is achieved by making a distinction between binding and non-binding sites on the chain. The model reproduces a range of experimental results, mainly related to the early phase of cellulose hydrolysis. Our results indicate that the combined effects of clustering of binding sites together with the occupancy pattern of these sites by the enzyme molecules play a decisive role in the overall kinetics of cellulose hydrolysis. It is suggested that periodic desorption and rebinding of enzyme molecules could be a basis of a strategy to partially counter the clustering of and blocking by the binding sites and so enhance the rate of cellulose hydrolysis. The general nature of the model means that it could be applicable also to other transport processes that make a distinction between binding and non-binding sites, where crowding and blocking are expected to be relevant.