Evolution of the repression mechanisms in circadian clocks

Abstract

Background: Circadian (daily) timekeeping is essential to the survival of many organisms. An integral part of all circadian timekeeping systems is negative feedback between an activator and repressor. However, the role of this feedback varies widely between lower and higher organisms.

Results: Here, we study repression mechanisms in the cyanobacterial and eukaryotic clocks through mathematical modeling and systems analysis. We find a common mathematical model that describes the mechanism by which organisms generate rhythms; however, transcription's role in this has diverged. In cyanobacteria, protein sequestration and phosphorylation generate and regulate rhythms while transcription regulation keeps proteins in proper stoichiometric balance. Based on recent experimental work, we propose a repressor phospholock mechanism that models the negative feedback through transcription in clocks of higher organisms. Interestingly, this model, when coupled with activator phosphorylation, allows for oscillations over a wide range of protein stoichiometries, thereby reconciling the negative feedback mechanism in Neurospora with that in mammals and cyanobacteria.

Conclusions: Taken together, these results paint a picture of how circadian timekeeping may have evolved.

Keywords: Circadian clocks; Evolution; Phosphorylation; Protein sequestration; Transcription.

Fig. 1

Reaction diagrams for the cyanobacterial clock models. Reaction diagrams for the detailed model (A), core model (B), TTFL model (C), and the PTR model (D). A Squares are proteins in various states; small circles indicate the phosphatase groups on the corresponding sites (red corresponds to the T432 site and yellow to the S431 site). Arrows indicate reactions among proteins, the width of which shows the relative strength. B The schematic of the core mechanism where KaiA enhances only the phosphorylation from U to T. C Extension of the core mechanism: the TTFL as an inhibition scheme where KaiC-S acts like an inhibitor of the kaiBC gene. D Schematic of the post-translational regulation (PTR) model with a constitutive source of transcription

Fig. 2

Simulations of the detailed model recapitulate experimental results. A, B Comparison with experimental data from Rust et al. [10]. In both results, τ₁=9.5 h is the phosphorylation phase duration and τ₂=18.5 h is the dephosphorylation phase duration. C–F Comparison with circadian data from Phong et al. [12], our model shows a robust period around 24 h under many ATP/ADP ratios. G, H Comparison with Phong et al. [12], where we confirmed the importance of the CI domain in sustaining oscillations. We simulate the model with weak KaiB-KaiC binding representing the KaiC muted in the CI domain (CI cat-) and the oscillation is abolished

Fig. 3

Simulations of core cyanobacterial models reveal keys to robust circadian oscillations. A Profile of the KaiA amount ([A]) with respect to the KaiC-S amount ([S]). As the curves move from blue to red, the binding affinity increases (i.e., K_d decreases from 10⁻² to 10⁻⁴. Here, A_T=8. B The sensitivity of the KaiA amount (A) with respect to the KaiC-S amount ([S]). Again, blue curves indicate weaker binding affinity while red curves reflect tighter binding. C The core model generates oscillations for a lower fraction of parameter sets as K_d increases from 10⁻⁴ to 10⁻¹. The parameter sets are plotted as sample points (indicated by “*”) with a fitted curve on a log plot. D Any parameter set that generates oscillations is located above the line C_T=1/3A_T, verifying the balanced molar ratio condition. E, F Simulation of the TTFL model and the PTR oscillator model. Each oscillation is plotted as a point with a scaled color representing the period length. See Table S1 (Additional file 1: Supplementary Information) for a detailed description of the parameters

Fig. 4

Novel “phospholock” model of the eukaryotic circadian clock. A Schematic of the “phospholock” model of the eukaryotic circadian clock. The activator complex, A, promotes transcription of the repressor gene, which is then translated to the repressor protein r. Next, the repressor protein(s) form complexes with other proteins, specifically kinases. Then, the repressor complex binds to the activator complex. Over time, the repressor proteins become gradually more phosphorylated until it dissociates, leaving the activator complex free, and thus completing the cycle. B The repression function f(R) (top) from System (E) and the sensitivity (bottom) for a specific parameter set (see the “Methods” section) with K_d=1. The ratio of phosphorylation to dephosphorylation is increased from 1 (blue) to 10000 (red). As the ratio increases, the cusp of the repression function sharpens, reflected in the increase in the magnitude of the peak sensitivity (bottom). C The percent of parameter sets that exhibit oscillations increases with increasing phosphorylation strength and varying K_d values (0.0001, 0.001, 0.01, 0.1, and 1). When the K_d values are small (≤ 0.01), the system is more likely to generate oscillations when dephosphorylation is stronger than phosphorylation. However, at more likely K_d levels, i.e., K_d≥0.1, the system is more likely to generate oscillations when phosphorylation is stronger than dephosphorylation. D Schematic of the phospholock mechanism with the additional phosphorylation of the activator (as in the Neurospora system). E The distribution of stoichiometric ratios (R:A) calculated from parameter sets that generate oscillations for increasing k₃ values. Adding phosphorylation of the activator increases the range of stoichiometric ratios from parameter sets that exhibit oscillations as the k₃ parameter increases