New and simple post-translational circadian clock models

The first, and presently only known, protein-based circadian oscillator that functions outside cells (in a ``test-tube'') was discovered by Takao Kondo's lab in 2005 (Nakajima et al, Science 2005). There is evidence that other ``post-translational'' oscillators are operative in species other than the cyanobacterial species in which they were discovered (O'Neill and Reddy, Nature 2011; Edgar et al, Nature 2012). This raises the interesting experimental and theoretical question of the potential simplicity and ubiquity of protein-based clocks. I will describe some new and simple general designs (mathematical models) for protein-based post-translational circadian clocks. A protein with two modification sites can serve as a sustained limit cycle oscillator if two conditions are met. One condition is that there is a separation of timescales in the regulatory biochemical kinetics of the two sites (``fast'' vs ``slow'' regulation). The second condition is that one of the four possible protein states sequesters the molecules (cofactors) regulating the dynamics of site occupancy.