Fig 1.
(A) Network graph of the circadian oscillator model. Activating and inhibiting influences between genes are colored in blue and red, respectively. (B) Simulation of gene expression of all 5 genes. (C) Each variable in the model represents a group of genes with similar functional characteristics.
Fig 2.
Effect of parameter alterations on the period (fraction of default value on logarithmic x-scale).
(A) Change of Per2 delay. (B) Change of Cry1 mRNA degradation rate. (C) Change of Cry1 inhibition strength on Per2. (D) Change of Bmal1 activation strength on Rev-erb-α. The default parameter values, corresponding to 1 on the x-axis, are: Per2 delay τ3 = 3.82, Cry1 degradation d4 = 0.2, Rev-erb-α activation by Bmal1 actn1,2 = 3.26 and Per2 inhibition by Cry1 inh4,3 = 0.37. Blue symbols refer to increasing parameters, whereas orange symbols refer to the reverse parameter variation (see S2 Appendix for details).
Fig 3.
Cry1, Per2 and Rev-erb-α oscillations are most critical for circadian rhythm generation.
All possible combinations of gene-subsets were analyzed for oscillating solutions by clamping the remaining genes to their respective oscillation mean values (A: one gene clamped; B: three genes clamped). Blue bars indicate the percentage of parameter sets around the default values that result in oscillating solutions. Red bars depict the median period among these solutions. Only 3 of 10 combinations of 2 genes oscillate at all, which are shown in (B). Error bars give the upper and lower quartiles for the period.
Fig 4.
(A) Simulation of gene expression of Rev-erb-α and Bmal1 with other genes (Cry1, Per2 and Dbp) clamped to their constant mean value. Upon doubling the strength of Bmal1 to Rev-erb-α activation, oscillations are rescued with a period of 24h. (B) Simulation of gene expression of Rev-erb-α, Per2 and Cry1, with other genes (Dbp and Bmal1) clamped to their constant mean value. The period lengthens, but oscillations are retained without parameter adjustments being necessary.
Fig 5.
The repressilator comprising RevErba, Per2 and Cry1.
The relative abundancy of processes in oscillating sub-networks is mapped to the edge width. All edges of the repressilator are highly prominent among all oscillating networks, which reflects its role as the dominant source of oscillations in the model.