Emergent robust oscillatory dynamics in the interlocked feedback-feedforward loops

One of the challenges that beset modelling complex biological networks is to relate networks to function to dynamics. A further challenge is deciphering the cellular function and dynamics that can change drastically when the network edge is tinkered with by adding or removing it. To illustrate this, the authors took a well-studied three-variable Goodwin oscillatory motif with only a negative feedback loop. To this motif, an edge was added that results in an emergent structure consisting of new feedforward and feedback loops while retaining Goodwin's original negative feedback loop. To relate emergent structure to oscillatory dynamics, the authors took all the combinations of edge signs in the interlocked motif. Bifurcation analysis reveals that all the structural combinations can be grouped into two categories based on their unique dynamics. These two groups also exhibit unique amplitude-frequency (amp-freq) plots. These two categories are attributed to the emergence of interlocked motifs with specific edge signs. To support the ideas, a well-studied plant circadian model of Arabidopsis thaliana was taken to illustrate the importance of interlocked motifs in fine-tuning amplitude and frequency in circadian oscillators. The authors briefly discuss its implications for central oscillators' adaptation to different environmental cues.