Optimizing intermittent reaction paths

Various examples of biochemical reactions in cells, such as DNA/protein interactions, reveal that in extremely diluted regimes reaction paths are not always simple brownian trajectories. They can rather be qualified as intermittent, since they combine slow diffusion phases on one hand and a second mode of faster transport on the other hand, which can be either a faster diffusion mode, as in the case of DNA-binding proteins, or a ballistic mode powered by molecular motors in the case of intracellular transport. In this article, we introduce simple theoretical models which permit to calculate explicitly the reaction rates for reactions limited by intermittent transport. This approach shows quantitatively that intermittent reaction pathways are actually very efficient, since they permit to significantly increase the reaction rates, which could explain why they are observed so often. Moreover, we give theoretical arguments which suggest that intermittent transport could also be useful for in vitro chemistry. Indeed, we show that intermittent transport naturally pops up in the context of reaction at interfaces, where reactants combine surface diffusion phases and bulk excursions, and could permit to enhance reactivity. In this case, adjusting chemically the affinity of reactants with the interface makes possible to optimize the reaction rate.