Combining a Toggle Switch and a Repressilator within the AC-DC Circuit Generates Distinct Dynamical Behaviors

Summary Although the structure of a genetically encoded regulatory circuit is an important determinant of its function, the relationship between circuit topology and the dynamical behaviors it can exhibit is not well understood. Here, we explore the range of behaviors available to the AC-DC circuit. This circuit consists of three genes connected as a combination of a toggle switch and a repressilator. Using dynamical systems theory, we show that the AC-DC circuit exhibits both oscillations and bistability within the same region of parameter space; this generates emergent behaviors not available to either the toggle switch or the repressilator alone. The AC-DC circuit can switch on oscillations via two distinct mechanisms, one of which induces coherence into ensembles of oscillators. In addition, we show that in the presence of noise, the AC-DC circuit can behave as an excitable system capable of spatial signal propagation or coherence resonance. Together, these results demonstrate how combinations of simple motifs can exhibit multiple complex behaviors.
Graphical Abstract
Highlights • The AC-DC circuit shows robust coexistence between oscillatory and steady expression • The circuit allows control over the coherence of oscillations in a cell population • The circuit shows excitable properties, allowing the spatial propagation of signals • These suggest its prominence in development and its potential in synthetic biology
The AC-DC circuit, formed by the combination of a repressilator and a toggle switch, is explored in detail using dynamical systems theory and stochastic simulations. These analyses reveal that the coexistence of oscillatory and stable gene expression gives rise to novel dynamical behaviors such as control of oscillation coherence and spatial signal propagation.