Queueing Theory-Based Perspective of the Kinetics of “Channeled” Enzyme Cascade Reactions

Queueing approaches can capture the stochastic dynamics of chemical reactions and provide a more accurate picture of the reaction kinetics than coupled differential equations in situations where the number of molecules is small. A striking example of such a situation is an enzyme cascade with substrate channeling, where reaction intermediates are directly passed from one enzyme to the next via tunnels or surface paths with limited capacity. In order to better understand the contribution of the stochastic dynamics to the observed enhancement in cascade throughput as a result from substrate channeling, we compare the results of a model using differential equations to describe concentration changes with a queueing model. The continuum model and the queueing model yield identical results, except when the maximum rate of reaction of the enzymes are similar. In two enzyme cascades, the queueing model predicts at most a 50% smaller throughput than the continuum model even if the waiting room size (the maximum number of molecules that can fit in the tunnel or surface path between enzymes) is limited to only one molecule and the enzymes are perfectly matched in their kinetic rates. In longer cascades, the discrepancy increases, reaching a 5-fold difference for a 10 enzyme cascade. In line with theoretical results from queueing theory, stochastic effects are found to always reduce cascade throughput, which means they cannot contribute to the experimentally observed enhancement in throughput due to channeling