Origins of activity enhancement in enzyme cascades on scaffolds.

The concept of "metabolic channeling" as a result of rapid transfer of freely diffusing intermediate substrates between two enzymes on nanoscale scaffolds is examined using simulations and mathematical models. The increase in direct substrate transfer due to the proximity of the two enzymes provides an initial but temporary boost to the throughput of the cascade and loses importance as product molecules of enzyme 1 (substrate molecules of enzyme 2) accumulate in the surrounding container. The characteristic time scale at which this boost is significant is given by the ratio of container volume to the product of substrate diffusion constant and interenzyme distance and is on the order of milliseconds to seconds in some experimental systems. However, the attachment of a large number of enzyme pairs to a scaffold provides an increased number of local "targets", extending the characteristic time. If substrate molecules for enzyme 2 are sequestered by an alternative reaction in the container, a scaffold can result in a permanent boost to cascade throughput with a magnitude given by the ratio of the above-defined time scale to the lifetime of the substrate molecule in the container. Finally, a weak attractive interaction between substrate molecules and the scaffold creates a "virtual compartment" and substantially accelerates initial throughput. If intermediate substrates can diffuse freely, placing individual enzyme pairs on scaffolds is only beneficial in large cells, unconfined extracellular spaces or in systems with sequestering reactions.