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

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 . We find that the Paijmans 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, to the best of our knowledge, a new mechanism, which is employed by the Paijmans 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.

Phase transition in thermodynamically consistent biochemical oscillators

“…There are several models for the oscillations of the phosphorylation level of KaiC proteins (see 47 for a summary). Here, we analyze a modified version of a model introduced in 40 .…”

Bayesian Modeling Reveals Ultrasensitivity Underlying Metabolic Compensation in the Cyanobacterial Circadian Clock

“…This hypothesis-driven approach has been employed extensively in the study of the cyanobacterial clock. These studies have revealed insights into specific aspects of the oscillator function, such as entrainment (Brettschneider et al, 2010; Leypunskiy et al, 2017), synchronization (Yoda et al, 2007; van Zon et al, 2007; Sasai, 2019), irreversibility (Cao et al, 2015), and robustness against variations in temperature (Hatakeyama and Kaneko, 2012; François et al, 2012; Kidd et al, 2015; Murayama et al, 2017), ATP/ADP concentration (Phong et al, 2013; Paijmans et al, 2017a; del Junco and Vaikuntanathan, 2019), protein copy numbers (Brettschneider et al, 2010; Lin et al, 2014; Chew et al, 2018), and environmental noise in general (Pittayakanchit et al, 2018; Monti et al, 2018). This hypothesis-driven approach is pedagogically powerful but gives little indication of the range of the parameter space consistent with a proposed mechanism, which makes it difficult to quantify the uncertainties of model predictions and validate them experimentally.…”

“…We hypothesized that ultrasensitivity in KaiC phosphorylation plays a role in stabilizing the oscillator at low %ATP conditions by suppressing premature phosphorylation during the dephosphorylation stage and thus promoting phase coherence. Currently, the Kai oscillator model most robust against yet tunable by metabolic conditions appears to be that of Paijmans et al (2017a,b). In the Paijmans model, metabolic compensation is achieved both at the hexamer and ensemble level.…”

Robustness of Clocks to Input Noise

“…The chemical rate equation of the PPN is:ẋ p = k f s(t)(x T −x p (t))−k b x p (t), where x p (t) is the concentration of phosphorylated protein, x T is the total concentration, k f s(t) is the phosphorylation rate k f times the input signal s(t), and k b is the dephosphorylation rate. The uncoupled (UHM) and coupled (CHM) hexamer model are based on the Kai system [15][16][17][18][19][20][21][22]. In both models, KaiC switches between an active conformation in which the phosphorylation level tends to rise and an inactive one in which it tends to fall [15,20].…”

“…In both models, KaiC switches between an active conformation in which the phosphorylation level tends to rise and an inactive one in which it tends to fall [15,20]. Experiments indicate that the main Zeitgeber is the ATP/ADP ratio [11,12], meaning the clock predominantly couples to the input s(t) during the phosphorylation phase of the oscillations [11,22]. In both the UHM and the CHM, s(t) therefore modulates the phosphorylation rate of active KaiC.…”