  The cyanobacterium Synechococcus elongatus uses both a protein
phosphorylation cycle and a transcription-translation cycle to generate
circadian rhythms that are highly robust against biochemical noise. We use
stochastic simulations to analyze how these cycles interact to generate stable
rhythms in growing, dividing cells. We find that a protein phosphorylation
cycle by itself is robust when protein turnover is low. For high decay or
dilution rates (and co mpensating synthesis rate), however, the
phosphorylation-based oscillator loses its integrity. Circadian rhythms thus
cannot be generated with a phosphorylation cycle alone when the growth rate,
and consequently the rate of protein dilution, is high enough; in practice, a
purely post-translational clock ceases to function well when the cell doubling
time drops below the 24 hour clock period. At higher growth rates, a
transcription-translation cycle becomes essential for generating robust
circadian rhythms. Interestingly, while a transcription-translation cycle is
necessary to sustain a phosphorylation cycle at high growth rates, a
phosphorylation cycle can dramatically enhance the robustness of a
transcription-translation cycle at lower protein decay or dilution rates. Our
analysis thus predicts that both cycles are required to generate robust
circadian rhythms over the full range of growth conditions.
