Single-cell zeroth-order protein degradation enhances the robustness of synthetic oscillator

In Escherichia coli, protein degradation in synthetic circuits is commonly achieved by the ssrA-tagged degradation system. In this work, we show that the degradation kinetics for the green fluorescent protein fused with the native ssrA tag in each cell exhibits the zeroth-order limit of the Michaelis-Menten kinetics, rather than the commonly assumed first-order. When measured in a population, the wide distribution of protein levels in the cells distorts the true kinetics and results in a first-order protein degradation kinetics as a population average. Using the synthetic gene-metabolic oscillator constructed previously, we demonstrated theoretically that the zeroth-order kinetics significantly enlarges the parameter space for oscillation and thus enhances the robustness of the design under parametric uncertainty.