Figure 9.
Bidirectional coupling via mitotic repression of transcription, controlled by CDK1, and BMAL1 induction of Wee1: the synchronization period as a function of the autonomous period of the cell cycle, and birhythmicity. The autonomous period of the circadian clock, TCR, is fixed at 24 h, while the autonomous period of the cell cycle, TCC, increases from 16 to 32 h (by changing the scaling parameter eps from 26.9 to 13.4; see Section 1 in the electronic supplementary material). (a) When KIcdk1 = 0.5 µM and vsw = 0.1 µMh−1, the synchronization period increases gradually from 16 to 32 h, and the synchronization period is close to the period of the cell cycle. (b) When KIcdk1 = 0.5 and vsw = 2, the synchronization period is longer than the autonomous periods of the cell cycle and the circadian clock. Two stable modes of synchronization (birhythmicity) coexist in a range of TCC values extending from 16.8 to 21 h. (c,d) The two coexisting modes of synchronization in the domain of birhythmicity for TCC = 20.5 h, corresponding to the red dots in (b). The bidirectionally coupled system can synchronize at a period of 29.3 h (c) or 23.4 h (d), depending on the initial conditions (listed in Section 9 in the electronic supplementary material). (Online version in colour.)