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. 2011 Dec;7(12):e1002309.
doi: 10.1371/journal.pcbi.1002309. Epub 2011 Dec 15.

Tuning the Mammalian Circadian Clock: Robust Synergy of Two Loops

Free PMC article

Tuning the Mammalian Circadian Clock: Robust Synergy of Two Loops

Angela Relógio et al. PLoS Comput Biol. .
Free PMC article


The circadian clock is accountable for the regulation of internal rhythms in most living organisms. It allows the anticipation of environmental changes during the day and a better adaptation of physiological processes. In mammals the main clock is located in the suprachiasmatic nucleus (SCN) and synchronizes secondary clocks throughout the body. Its molecular constituents form an intracellular network which dictates circadian time and regulates clock-controlled genes. These clock-controlled genes are involved in crucial biological processes including metabolism and cell cycle regulation. Its malfunction can lead to disruption of biological rhythms and cause severe damage to the organism. The detailed mechanisms that govern the circadian system are not yet completely understood. Mathematical models can be of great help to exploit the mechanism of the circadian circuitry. We built a mathematical model for the core clock system using available data on phases and amplitudes of clock components obtained from an extensive literature search. This model was used to answer complex questions for example: how does the degradation rate of Per affect the period of the system and what is the role of the ROR/Bmal/REV-ERB (RBR) loop? Our findings indicate that an increase in the RNA degradation rate of the clock gene Period (Per) can contribute to increase or decrease of the period--a consequence of a non-monotonic effect of Per transcript stability on the circadian period identified by our model. Furthermore, we provide theoretical evidence for a potential role of the RBR loop as an independent oscillator. We carried out overexpression experiments on members of the RBR loop which lead to loss of oscillations consistent with our predictions. These findings challenge the role of the RBR loop as a merely auxiliary loop and might change our view of the clock molecular circuitry and of the function of the nuclear receptors (REV-ERB and ROR) as a putative driving force of molecular oscillations.

Conflict of interest statement

The authors have declared that no competing interests exist.


Figure 1
Figure 1. A model for the mammalian circadian clock.
The model comprises two major compartments, the nucleus (light grey) and the cytoplasm. There are 20 species including 5 genes (highlighted in blue boxes), their corresponding cytoplasmic proteins and cytoplasmic protein complexes (indexed “C” and highlighted in violet boxes) and nuclear proteins and nuclear protein complexes (indexed “N” and highlighted in yellow boxes). Dead-end orange lines represent transcription inhibition reactions brown lines represent complex formation/dissociation reactions and green arrows show other reactions (transcription, translation, import/export, phosphorylation/dephosphoryplation). The dashed horizontal line visually divides the model into two large subunits: the RBR loop and the PC loop.
Figure 2
Figure 2. In silico expression data fits known experimental data.
The circular graphic shows expression data for 6 variables present in the model: 5 RNAs (Ror-blue; Rev-Erb-red; Bmal-green; Per-violet; Cry-turquoise) and the PER/CRY nuclear pool (orange). Each variable is represented by one ring. The dark colour tone marks the published time interval corresponding to the highest expression level of the given variable. The full yellow circle indicates the peak of expression in our in silico experiments. Correspondent circadian times (CT) in hours are given.
Figure 3
Figure 3. The mammalian circadian clock can be represented by a merged two-loop system.
A) In silico expression profiles show robust oscillations with a period of 23.5 hours can be obtained with the model. In silico expression data for phases and amplitudes fit known published experimental data. Elements of the RBR loop (Rev-Erb, Ror, Bmal) and from the PC loop (Per, Cry, PER/CRYpool) are represented. B) In silico expression profiles for the RBR loop. The RBR loop is a low amplitude oscillator given a constitutive PC loop. This loop is able to oscillate with smaller amplitude and larger period then the full clock model. The oscillatory effect of the PER/CRY pool is replaced by its mean value (PC = 1.71). The behaviour of the system for different mean values of PC is shown in Supplementary Figure S2. C) The PC loop is a damped oscillator (for our default parameters) given a constitutive RBR loop. The connection to the RBR loop is replaced by a constitutive CLOCK/BMAL and a constitutive REV-ERB nuclear (each variable is replaced by its mean value, x1 = 1.7 and x5 = 2.4).
Figure 4
Figure 4. Bmal is regulated by the antagonistic action of REV-ERB and ROR.
Represented are in silico expression profiles for the nuclear protein REV-ERBN and RORN, and for Bmal RNA. The nuclear proteins RORN (red) and REV-ERBN (blue) recognize and compete for the cis-regulatory elements in the Bmal (green) promoter region to act, respectively, as positive and negative drivers of Bmal expression.
Figure 5
Figure 5. Degradation control can increase and decrease the period.
A non-monotonic behaviour can be seen for Per RNA when a gradient of the degradation rate is applied to the system. The graphic represents the period as a function of the degradation rate. We marked 2 points (B, C) in the decreasing period region of the graphic and 2 points (D, E) in the increasing period region. (B, C) The period decreases with increasing degradation rate of Per RNA (dy1). (D, F) The period increases with increasing degradation rate of Per RNA (dy1). The wild type scenario is shown in Figure 3 A.
Figure 6
Figure 6. Increase in transcription in elements of both RBR and PC loops can destroy the circadian oscillator.
(A–D) After a transient period of about 20 days we plotted the expression patterns for each of the four genes indicated. Skipping the transient region allows an enhancement of the effects on the system: damped oscillations give rise to flat expression profiles and small phase differences became better visible. Expression profiles for the indicated RNA are shown given different values of the respective RNA transcription rate. Transcription rates vary from 0 to approximately 3 times the value used in the model producing a total of 10 profiles. The profile curves are produced using Xppaut. We constrained the simulations to a fixed number of 9 steps. Each step corresponds to a specific value Vmax, equally distributed, within the range in which the parameter is allowed to vary. This procedure leads to a total of 10 expression profiles which together with the wild type profile generate the 11 profiles represented in each panel of the figure. The light pink line corresponds to a transcription rate value of 0 followed, in a step wise manner, by darker pink tones, orange, yellow, light and dark green, turquoise, blue and violet as a result of the highest value simulated for the transcription rate. The thick red line shows the expression profile corresponding to the transcription rate used in the wild type (WT) model.
Figure 7
Figure 7. Experimental data for Rora and Rev-Erbα overexpression verify model predictions.
The graphics show Bmal expression levels upon constitutive in silico and in vitro overexpression of Ror and Rev-Erb. (A) In silico overexpression of Ror. A constitutive exogenous Ror RNA is added to the system in increasing amounts. The ratio between exogenous constitutive Ror RNA and the mean value of the endogenous one is given. The wild type is shown in red. A gradient in fold change between exogenous RNA and the endogenous WT is shown from 3 to a maximum of 12 as indicated in the figure. (B, D) Human U-2 OS cells harbouring a Bmal1-luciferase reporter were lentivirally transduced with GFP control (red), or Rora (orange to blue) (B), or 250, 500 and 1000 µl lentiviral supernatant of Rev-Erbα overexpression plasmid. Cells were synchronized by a single pulse of dexamethasone and luciferase activity was monitored for several days. Depicted are de-trended data of biological replicas ((B) n = 6) and technical replicates ((D) n = 4) for each condition according to the fold difference in luciferase signal intensity of the reporter in Rora or Rev-Erbα overexpressing cells relative to GFP controls from the raw data. (C) In silico overexpression of Rev-Erb. A constitutive exogenous Rev-Erb is added to the system, the amount of endogenous RNA is given as a percentage of the endogenous wild type. The wild type is show in red and the increasing amount of constitutive exogenous RNA is show from 20 to 60% increase to the WT, as indicated in the figure. Overexpression data on Rev-Erb was previously reported as repressing Bmal1 as well .

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