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Fig. 4 | Theoretical Biology and Medical Modelling

Fig. 4

From: A mathematical model of circadian rhythms and dopamine

Fig. 4

Panels a and b: REV-ERB and ROR expression levels. a Data from Ikeda et al. [12] of REV-ERB and ROR expression levels relative to their peak values in the mouse ventral striatum. Both REV-ERB and ROR peak at around 14 hours Zeitgeber time (ZT14). For REV-ERB, RMSE=0.1260. For ROR, RMSE=0.1206. b Model predictions of REV and ROR relative to their peak values. We use the same parameter values (Table 2) and set the phase of the model to pertain to the mouse ventral striatum [12], since circadian protein peak times vary across different locations in the body. As in Fig. 4a, REV and ROR peak at ZT14, with ROR dropping to around 40% of its peak value, and REV declining to almost zero. REV and ROR compete to bind to the ROR-response elements (ROREs) in Bmal1, Th, and DRD3 gene promoters. The inhibition by REV is thought to be stronger than the activation by ROR [12, 44], and in our model, the competition between REV and ROR creates a net effect of inhibition near the peaks at ZT14 and a net effect of activation away from the peaks. Panels c and d: Phase-shifting impact of a REV-ERB agonist. The blue curves show the variation of PN relative to its peak value in the normal model. The dashed orange curves show levels of PN in the model after injecting Ag. c Mouse experiments by Solt et al. [11] demonstrate the potential for a REV-ERB agonist that bolsters the effects of inhibition by REV-ERB to aid in the treatments of metabolic and sleep disorders. At a molecular level, injection of a REV-ERB agonist alters the phase of core clock genes. Consistent with Figure 2e of [11], our simulation of a REV-ERB agonist (Ag) injection at ZT0 shifts the clock’s phase 1–3 hours to the right for at least 48 hours, even though the agonist has left the system within 24 hours. While Solt et al. [11] measured core clock gene expression levels for 48 hours after injection of a REV-ERB agonist, we ran our model for 120 hours and observed that the clock returns to its light-entrained phase within 2–6 days depending on the amount of agonist. d In Figure 2e of [11], only the effects of an injection at ZT0 are considered, as opposed to other injection times. A REV-ERB agonist injection at ZT9 results in a larger initial phase shift in our model, with disrupted circadian rhythms in the long run. This suggests that for certain individuals, circadian rhythms may be sensitive to injection time

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