  It is possible that there are post-translational circadian oscillators that
continue functioning in the absence of negative feedback transcriptional
repression in many cell types from diverse organisms. Apart from the KaiABC
system from cyanobacteria, the molecular components and interactions required
to create in-vitro ("test-tube") circadian oscillations in different cell types
are currently unknown. Inspired by the KaiABC system, I provide
"proof-of-principle" mathematical models that a protein with 2 (or more)
modification sites which selectively sequesters an effector/cofactor molecule
can function as a circadian time-keeper. The 2-site mechanism can be
implemented using two relatively simple coupled non-linear ODEs in terms of
site occupancy; the models do not require overly special fine-tuning of
parameters for generating stable limit cycle oscillations.
