Mixed positive and negative feedback loops drive diverse single-cell gene expression dynamics

Genetic circuits with only a few components can generate complex gene regulatory dynamics. Here, we combine stochastic modelling and single-cell time-lapse microscopy to map how a common circuit motif, the mixed positive/negative feedback loop, gives rise to diverse single-cell behaviours. Our minimal stochastic model of this motif reveals ten distinct classes of dynamic output, including stochastic pulsing, oscillations, and bistability. We systematically map how the circuit's core parameters can be tuned to generate each of the behaviours. Experimental validation in two different mixed feedback circuits in the bacterium Bacillus subtilis, σ^B and σ^V, confirms our model's predictive power. Guided by our simulations, we are able to transition between selected dynamic behaviours by modulating in vivo parameters. Together, these results establish a quantitative framework for how mixed feedback loops generate diverse single-cell dynamics, improving our understanding of this common biological network motif and informing our efforts to engineer them for synthetic biology applications.