Emergent Damped Oscillation Induced by Nutrient-Modulating Growth Feedback

Growth feedback, the inherent coupling between the synthetic gene circuit and the host cell growth, could significantly change the circuit behaviors. Previously, a diverse array of emergent behaviors, such as growth bistability, enhanced ultrasensitivity, and topology-dependent memory loss, were reported to be induced by growth feedback. However, the influence of the growth feedback on the circuit functions remains underexplored. Here, we reported an unexpected damped oscillatory behavior of a self-activation gene circuit induced by nutrient-modulating growth feedback. Specifically, after dilution of the activated self-activation switch into the fresh medium with moderate nutrients, its gene expression first decreases as the cell grows and then shows a significant overshoot before it reaches the steady state, leading to damped oscillation dynamics. Fitting the data with a coarse-grained model suggests a nonmonotonic growth-rate regulation on gene production rate. The underlying mechanism of the oscillation was demonstrated by a molecular mathematical model, which includes the ribosome allocation toward gene production, cell growth, and cell maintenance. Interestingly, the model predicted a counterintuitive dependence of oscillation amplitude on the nutrition level, where the highest peak was found in the medium with moderate nutrients, but was not observed in rich nutrients. We experimentally verified this prediction by tuning the nutrient level in the culture medium. We did not observe significant oscillatory behavior for the toggle switch, suggesting that the emergence of damped oscillatory behavior depends on circuit network topology. Our results demonstrated a new nonlinear emergent behavior mediated by growth feedback, which depends on the ribosome allocation between gene circuit and cell growth.