Fig. 5: A mathematical model of nuclear PER2 and CRY1 dynamics in mammalian circadian clock cells reproduces experimental findings.

a Model of the PER2:CRY1 loop together with the predictions regarding half-lives and association/dissociation events that arise from our simulations (see main text). Dashed black lines represent degradation events; thicker arrows represent reactions that are predicted to occur at a higher rate. The red solid arrow depicts the inhibition of clock gene expression, exerted solely by the PER2:CRY1 nuclear complex. For a full reasoning of the model design and parameter choice, see Supplementary Note 2 and Supplementary Fig. 9. b The model exhibits sustained 24.7 h oscillations with nuclear PER2 preceding CRY1 rhythms, and with PER2 oscillating with a higher amplitude and lower magnitude than CRY1, thus reproducing experimental results. The parameter set is given in Supplementary Tab. 7. c The amplitude of PER2 rhythms increases with period in knock-in cells with significantly rhythmic oscillations (n = 87 cells, left). Exemplary raw time series and corresponding cosine fits (right) illustrate that long-period rhythms typically display larger amplitudes. The size of the circles depict the number of cells that fall in each bin. Error bars represent SEM. d Our mathematical model reproduces the positive correlation of PER2 amplitude and period. We simulated n = 100 “artificial” cells by randomly varying all transcription, translation, degradation, nuclear import and export rates. Parameter values were drawn from a uniform distribution on the interval given by the default parameter value ± 10% (see Supplementary Note 2 for simulation details). The size of the circles depict the number of cells that fall in each bin. Error bars represent SEM. rAMP relative amplitude.