Molecular Implementations of Positive and Negative FeedbackInform Robustness in Biological Oscillator Motifs

Biological oscillators like the cell cycle, the circadian sleep-wake cycle, etc. are vital to an organism's survival. Biochemical oscillator circuits are typically classified based on the net logic of the regulatory connections between interacting molecules. However, we show that the robustness response of biochemical oscillator motifs vary substantially based on the regulatory implementation of the logic of interactions encoded in the circuit topology. Nullcline analyses and linear stability arguments predict the robustness response of different mechanisms of a topology. Robust regulatory implementations not only enhance the probability of obtaining stable limit cycles over larger ranges of parameter variations, but also exhibit an increased resilience of oscillations to stochasticity. We further show that there are preferred regulatory implementations for particular biological functions, and that the most robust regulatory implementations of a topology are realized in naturally occurring oscillator systems where high phase coherence is desired.