The Interplay of cis-Regulatory Elements Rules Circadian Rhythms in Mouse Liver

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.

with the values of 1.
The second step was the addition of Per2 inhibition. The term c ck+[P er2] (t−τ P er2 ) n was added to the three new mRNAs (n represents the number of E-boxes of specic gene). Parameter values were adjusted to get optimal phases and amplitudes.
The next step in the model building was the incorporation of Rev -erbα inhibition of Cry1 and Rorγ by adding the term a ak+[Rev−erba] (t−τ Rev−erba ) n , and Dbp activation of Rev -erbα, Per2, and Cry1 by adding (t−τ Dbp ) to the production term. The terms were added step by step and parameters were tted according to their eects noted in the table below.
For the six genes, regulation through combined eect of Per2 and Bmal1 on E-boxes could reproduce correct phases, since the interplay of inhibition and activation can create a phase between peak of activation via Bmal1 and anti-inhibition via Per2 (Supplementary Information S3.1).
Experimentally determined ranges for explicit delays τ were taken from the time dierence between peak of mRNA and protein expression from the same experimental setup (Preitner et al , 2002;Lee et al , 2001;Hamilton and Kay, 2008 Hamilton and Kay (2008); 1.5 h was chosen to get the best t. Increasing τ Dbp has almost no eect on period length and increases amplitudes of all genes. It has an eect on phase of Per2 , but also on phases of Cry1 , Dbp, and Rorg , which could also be a network eect through changes in Per2 .  (2009)). The value outside this range was determined to enable the correct phase. This decision is supported by RRE discovery in Rev-erba regulatory region (Yamamoto et al (2004)), which could explain larger degradation rate (auto-inhibition of Rev-erba could cause increase in the eective degradation rate). Increasing  (2011)). A value outside this range was chosen to enable the correct phase. As with Rev-erba, RREs were discovered in Dbp regulatory region (Yamamoto et al (2004) represents basal transcription rate of Rev-erba through E/E'-boxes. Increasing c2 and ck2 simultaneously without changing their ratio makes Rev-erba less sensitive through regulation via Per2 . That causes longer period length, larger amplitudes (except for Cry1 and Rorg), and earlier phases of all genes relative to Bmal1 . Increasing c2 to the value of 1.3 increases the period length and amplitudes of all genes except Per2 , Cry1 , and Rorg. It has the strongest eect on phases of Dbp and Rev-erba (relative to Bmal1 ). Beyond the value of 1.3, the period length jumps to about 16 h and phase distribution of all genes is dierent. ck2 0.9 Increasing ck2 decreases the period length and amplitudes of Dbp, Rev-erba, and Bmal1 the most. The largest inuence on the phases is on the ones of Per2 , Dbp, and Rev-erba. Decreasing ck2 below 0.3 changes the behaviour of the system (large decrease in period length, changes in amplitudes and phases of all genes).
1.1 c3 ck3 * b3 bk3 represents basal transcription rate of Per2 through E/E'-boxes. Increasing c3 and ck3 simultaneously without changing their ratio makes Per2 less sensitive to its auto-inhibition. This shortens the period, but the amplitudes are smaller and phases of all genes relative to Bmal1 are delayed. When c3 and ck3 are larger than 1.4, period length shortens to 16 h and the overall behaviour of the system changes, although oscillations still persist.
c3 has a strong inuence on the whole system. Eect on the period length is variable, at values smaller than 1 the system changes considerably regarding the period and phases of all genes, but oscillations still persist. represents basal transcription rate of Dbp through E/E'-boxes. Increasing c6 and ck6 simultaneously without changing their ratio makes Dbp less sensitive to inhibition via Per2 , which has almost no eect on periods length and phases. If c6 and ck6 are both decreased below 0.6, the system changes considerably (period length of 16 h, dierent phases of most genes). Increasing c6 leads to longer period lengths. Decreasing it to below 0.6 causes large changes in the system regarding amplitudes, phase shifts between components, and period length. ck6 0.75 Increasing ck6 to the value of 1.2 slightly increases period length and decreases the amplitudes of all genes. It mostly inuences the phase of Dbp. Beyond the value of 1.2, the period length decreases rapidly and there are large changes in amplitudes and phases of all genes. b2 1 c2 ck2 * b2 bk2 represents basal transcription rate of Rev-erba through E/E'-boxes. Increasing b2 and bk2 in tandem without changing their ratio decreases period length and slightly decreases amplitudes of most genes. If they are both multiplied with factors smaller than 0.5, the system behaviour changes considerably (period length of about 18 h, smaller Per2 amplitude, dierent phases of most genes). Increasing b2 increases the period length and has an eect on all amplitudes (decrease in Per2 , Cry1 , and Rorg amplitudes, increase in others). Increasing it beyond 1.3 has complex eects on the whole system (decrease of all amplitudes, changes of phases of all genes). bk2 1.5 Increasing bk2 decreases period length and increases phase dierences of all genes relative to Bmal1 . At values smaller than 0.6, Cry1 and Rorg peaks are delayed. b3 0.06 c3 ck3 * b3 bk3 represents basal transcription rate of Per2 through E/E'-boxes. Increasing b3 and bk3 in tandem without changing their ratio increases the period length and amplitudes of all genes. Multiplying both by a factor lower than 0.6 results in decreased amplitudes and changes in phases of Per2 , Cry1 , and Rorg. Increasing b3 increases the period length and all amplitudes. Decreasing it below 0.04 has complex eects on the whole system, which results in lower amplitudes and dierent phases of all genes.  Rev-erba Increasing f v2 increases the period and has variable small eects on amplitudes of most genes. It also inuences phases of all genes; compared to Bmal1 , Per2 , Dbp, and Rev-erba are advanced and Cry1 and Rorg delayed.
f 3 1 f 3 f k3 represents the basal transcription rate of Per2 through D-boxes. Increasing f 3 and f k3 in tandem without changing their ratio decreases period length, amplitudes of all genes, decreases phase dierences between  and Rorg-Bmal1 , and increases the others. Increasing f 3 decreases the period length and amplitudes of all genes. It has the largest eect on phase dierences between Cry1-Bmal1 , Rorg-Bmal1 , and Per2-Bmal1 . Above the value of 1.4, the system changes considerably regarding period length, amplitudes, and phases.
f k3 0.1 Increasing f k3 slightly increases the period length and amplitudes of all genes. It has the strongest eect on phase dierence between Cry1 and Bmal1 , but the eect is relatively small compared to some other parameters. f 4 1 f 4 f k4 represents the basal transcription rate of Cry1 through D-boxes. Increasing f 4 and f k4 in tandem without changing their ratio decreases Cry1 amplitude and slightly phase dierence between Cry1 and Bmal1 . Increasing f 4 decreases Cry1 amplitude and increases phase dierence between Cry1 and Bmal1 . Increasing f v4 slightly increases the Cry1 amplitude and decreases phase dierence between Cry1 and Bmal1 . Decreasing it below 1 increases Cry1 amplitude and causes delayed phase with respect to Bmal1 .