Period robustness and entrainability under changing nucleotide concentrations in the post-translational Kai circadian clock

Circadian clocks must be able to entrain to time-varying signals to keep their oscillations in phase with the day-night rhythm. On the other hand, they must also exhibit input compensation: their period must remain about one day in different constant environments. The post-translational oscillator of the Kai system can be entrained by transient or oscillatory changes in the ATP fraction, yet is insensitive to constant changes in this fraction. We study in three different models of this system how these two seemingly conflicting criteria are met: the Van Zon model (Van Zon et al., PNAS, 2007), the Rust model (Phong et al., PNAS, 2013), and our new model (Paijmans et al., arXiv:1612.02715). We find that the new model exhibits the best trade-off between input compensation and entrainability: on the footing of equal phase-response curves, it exhibits the strongest input compensation. Performing stochastic simulations at the level of individual hexamers allows us to identify a new mechanism, which is employed by the new model to achieve input compensation: At lower ATP fraction, the individual hexamers make a shorter cycle in the phosphorylation state space, which compensates for the slower pace at which they traverse the cycle.