Including Rebinding Reactions in Well-Mixed Models of Distributive Biochemical Reactions

The behavior of biochemical reactions requiring repeated enzymatic substrate modification depends critically on whether the enzymes act processively or distributively. Whereas processive enzymes bind only once to a substrate before carrying out a sequence of modifications, distributive enzymes release the substrate after each modification and thus require repeated bindings. Recent experimental and computational studies have revealed that distributive enzymes can act processively due to rapid rebindings (so-called quasi-processivity). In this study, we derive an analytical estimate of the probability of rapid rebinding and show that well-mixed ordinary differential equation models can use this probability to quantitatively replicate the behavior of spatial models. Importantly, rebinding requires that connections be added to the well-mixed reaction network; merely modifying rate constants is insufficient. We then use these well-mixed models to suggest experiments to 1) detect quasi-processivity and 2) test the theory. Finally, we show that rapid rebindings drastically alter the reaction's Michaelis-Menten rate equations.