The interplay of cis-regulatory elements rules circadian rhythms in mouse liver

Abstract

The mammalian circadian clock is driven by cell-autonomous transcriptional feedback loops that involve E-boxes, D-boxes, and ROR-elements. In peripheral organs, circadian rhythms are additionally affected by systemic factors. We show that intrinsic combinatorial gene regulation governs the liver clock. With a temporal resolution of 2 h, we measured the expression of 21 clock genes in mouse liver under constant darkness and equinoctial light-dark cycles. Based on these data and known transcription factor binding sites, we develop a six-variable gene regulatory network. The transcriptional feedback loops are represented by equations with time-delayed variables, which substantially simplifies modelling of intermediate protein dynamics. Our model accurately reproduces measured phases, amplitudes, and waveforms of clock genes. Analysis of the network reveals properties of the clock: overcritical delays generate oscillations; synergy of inhibition and activation enhances amplitudes; and combinatorial modulation of transcription controls the phases. The agreement of measurements and simulations suggests that the intrinsic gene regulatory network primarily determines the circadian clock in liver, whereas systemic cues such as light-dark cycles serve to fine-tune the rhythms.

Figure 1. Gene expression of six core clock genes in mouse liver in constant darkness (DD) and 12 h∶12 h light-dark cycles (LD).

Data were normalised by three reference genes and fitted by a function with 24 h and 12 h trigonometric terms (Equation (S1) in Supplementary Information S1 - Fitting of trigonometric functions to gene expression data).

Figure 2. One-variable model - Per2 self-inhibition.

(A) Scheme of the one-variable model of self-inhibition of the clock gene Per2 with explicit delay and two E-boxes (2E). (B) Observed delays and non-linearities provided by these two E-boxes (as described by Equation (1)) lead to 24 h oscillations. (C) Bifurcation analysis reveals oscillation onset at about 5.3 h. For larger explicit delays , we plot maxima and minima of the oscillation. (D) Control of the period length for different parameters shows that the explicit delay has the strongest effect on the period. Parameter values for simulations: h-1; ; ; h. Gene expression in panels B and C is represented as normalised values divided by the mean of Per2 expression.

Figure 3. Two-variable model - nuclear receptor loop.

(A) Scheme of the two-variable model of the Bmal1 - Rev-erba loop showing the number of relevant CCEs of each gene (2R - two RREs; 3E - three E-boxes). (B) Simulations show that 24 h oscillations with a correct phase difference can be generated by using experimentally observed explicit delays and non-linearities arising from the number of CCEs. (C) The phase difference between the two genes is effected by model parameters with different strength. (D) The waveform is controlled by the explicit delays; greater delays lead to sharper peaks. Parameter values for simulations: h-1; h-1; ; ; ; ; ; h; h. Gene expression in panels B and C is represented as normalised values divided by the mean of the expression of the corresponding gene.

Figure 4. Six-variable model of core clock.

(A) Model network containing six clock genes. The numbers of the CCEs are shown next to the arrowheads for each gene (E, E-box; D, D-box; R, RRE) and the explicit delays are noted at the arrows. (B) Regulatory regions containing the CCEs are shown for the six genes included in the model. Experimental evidence for the CCEs is given in Supplementary Information S4 - Clock-controlled elements.

Figure 5. Comparison of experimental data and the six-variable model.

(A) Fitted experimental gene expression data of the six core clock genes in mouse liver for the DD regime. (B) Our model (Equations (4) to (9)) reproduces the experimental data for the period length, phases, amplitudes and waveforms of these core clock genes. In both panels, gene expression is normalised by dividing by the mean expression of the respective gene.

Figure 6. Regulation of phase variability.

Thick lines in panels A, B, C refer to the corresponding mRNA and black lines mark the production terms; coloured lines in B and C represent “modulation factors”, see text. Long half-lives lead to later peaks of mRNAs (thick lines) compared to production terms (black lines). (A) Delayed Rev-erba inhibits Bmal1 expression. (B) Per2 and Bmal1 modulators determine Dbp production. (C) RRE modulator (green) and E-box modulator (red) govern Cry1 production. (D) Reducing the amounts of regulators Bmal1, Per2, Dbp, and Rev-erba mimics RNAi experiments and knock-outs. The resulting phase shifts agree with experimental data (see text).

Figure 7. Experimental data and model in DD and LD regimes.

(A) Normalised gene expression of Bmal1, Per2, and Cry1 under DD and LD regimes. (B) Adding a 12 h∶12 h step function that modulates Per2 transcription increases the Per2 amplitude (not shown) and causes phase advance of all genes except Rorg and Cry1. (C) Starting from the endpoint in panel B, increasing the explicit delay of Bmal1 leads to correct Rorg and Cry1 amplitudes and phases without substantially changing the dynamics of the other genes.

Figure 8. Phases of clock and clock output genes in DD.

The outer circle represents the regions of the predicted expression phase of the clock genes that are regulated by the three CCEs included in our model. The phases of the genes from our model are depicted with black arrows, to serve as guidelines for other genes. Some clock genes that we measured in our experimental setup are also included with gray arrows. The phases of additional genes have been extracted from and are shown with orange arrows.