  Circadian clocks are the central timekeepers of life, allowing cells to
anticipate changes between day and night. Experiments in recent years have
revealed that circadian clocks can be highly stable, raising the question how
reliably they can be read out. Here, we combine mathematical modeling with
information theory to address the question how accurately a cell can infer the
time from an ensemble of protein oscillations, which are driven by a circadian
clock. We show that the precision increases with the number of oscillations and
their amplitude relative to their noise. Our analysis also reveals that their
exists an optimal phase relation that minimizes the error in the estimate of
time, which depends on the relative noise levels of the protein oscillations.
Lastly, our work shows that cross-correlations in the noise of the protein
oscillations can enhance the mutual information, which suggests that
cross-regulatory interactions between the proteins that read out the clock can
be beneficial for temporal information transmission.
