Period Robustness and Entrainability of the Kai System to Changing Nucleotide Concentrations

TL;DR

This study compares three models of the Kai circadian system to evaluate their robustness and ability to entrain to changing nucleotide levels, revealing that a new model offers the best balance between stability and responsiveness.

Contribution

The paper introduces a new model of the Kai system that outperforms previous models in balancing input compensation and entrainability.

Findings

The new model shows the strongest input compensation among the three models.

Hexamer-level simulations reveal a mechanism where shorter cycles at lower ATP levels compensate for slower traversal.

The new model achieves a superior trade-off between robustness and entrainability.

Abstract

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.