Cluster Channeling in Cascade Reactions

Enzymatic cascade reactions, where a substrate is converted into a product in several steps, play a critical role in many biological systems. The enzymes in such reactions are often clustered inside intracellular compartments. To understand the effect of localization, we develop a theory for cascade reactions converting substrates into intermediates and then into products when the enzymes are localized in clusters. The theory shows that the kinetic scheme that describes the reaction with dispersed enzymes changes as a result of clustering. A new reaction channel, in which the substrate is directly converted into product, appears with a diffusion-influenced rate that is expressed in terms of enzyme catalytic efficiencies, diffusion coefficient, and cluster size. This rate is proportional to the cluster channeling probability, which is the probability that an intermediate is converted into product within the cluster in which the intermediate was formed. Simple analytic formulas allow one to quantify how enzyme clustering can affect product formation and regulate the direction of metabolic reaction flux in biological and synthetic systems. The rate of the substrate conversion decreases whereas the cluster channeling probability increases as the number of enzyme molecules in a cluster increases. The interplay between these factors leads to an optimal number of enzyme molecules that maximizes the clustering efficiency.