  Circadian (~24hr) clocks are self-sustained endogenous oscillators with which
organisms keep track of daily and seasonal time. Circadian clocks frequently
rely on interlocked transcriptional- translational feedback loops to generate
rhythms that are robust against intrinsic and extrinsic perturbations. To
investigate the dynamics and mechanisms of the intracellular feedback loops in
circadian clocks, a number of mathematical models have been developed. The
majority of the models use Hill functions to describe transcriptional
repression in a way that is similar to the Goodwin model. Recently, a new class
of models with protein sequestration-based repression has been introduced.
Here, we discuss how this new class of models differs dramatically from those
based on Hill-type repression in several fundamental aspects: conditions for
rhythm generation, robust network designs and the periods of coupled
oscillators. Consistently, these fundamental properties of circadian clocks
also differ among Neurospora, Drosophila, and mammals depending on their key
transcriptional repression mechanisms (Hill-type repression or protein
sequestration). Based on both theoretical and experimental studies, this review
highlights the importance of careful modeling of transcriptional repression
mechanisms in molecular circadian clocks.
