The Robust Ticking of a Circadian Clock

Abstract

Many organisms use circadian clocks to anticipate changes between day and night. It had long been believed that these clocks are driven primarily by transcription translation cycles (TTCs) built on negative feedback on gene expression. However, while circadian clocks can maintain robust rhythms for years in the absence of any daily cue, recent experiments have vividly demonstrated that gene expression is often highly stochastic. This raises the question of how these clocks can be so robust against biochemical noise. In multicellular organisms, the robustness might be explained by intercellular interactions, but it is now known that even unicellular organisms can have very stable circadian rhythms. The clock of the cyanobacterium S. elongatus, for example, has a correlation time of several months, even though the clocks of the different cells in a population hardly interact with one another. How circadian clocks can be so stable even at the single cell level is not understood. Interestingly, it has recently been discovered that the S. elongatus clock also includes a protein phosphorylation cycle (PPC) that can run independently of the transcription-translation cycle (TTC). Here, we use mathematical modeling to study how these two clocks interact in growing, dividing cells. We find that a clock built on a PPC alone is highly stable when protein turnover is low. For high protein turnover rates, however, a PPC becomes unstable; indeed, at high growth rates, when protein turnover is necessarily high, a TTC becomes indispensable for the PPC to function. On the other hand, a clock based on a TTC alone functions only when the protein turnover rate is large; it fails dramatically at low growth rates in the absence of active protein degradation. The power of coupling a PPC to a TTC is that the clock becomes robust over the full range of growth conditions. Importantly, the TTC and the PPC in S. elongatus are much more tightly intertwined than conventional coupled phase oscillators; as a result, particularly for intermediate growth rates, the combination of the two far outperforms not just each of its two components individually, but also a hypothetical system in which the two parts are coupled in normal textbook fashion.