Bidirectional coupling of the circadian clock and the cell cycle, through BMAL1 induction of Wee1 and REV-ERBα phosphorylation by CDK1. Before coupling, the cell cycle and the circadian clock oscillate independently with an autonomous period of 20 h and 24 h, respectively (a). Upon bidirectional coupling at t = 1110 h (vertical arrows), depending on the strengths of coupling, the cell cycle and the circadian clock can synchronize at a period shorter than 20 h (b), between 20 and 24 h (c), or longer than 24 h (d). In (b) where the synchronization period is 18.48 h, the coupling strength of the cell cycle to the circadian clock (vsw, in μMh−1) is 0.0794 and the reverse coupling strength (VCdk1, in nMh−1) is 501.2. In (c) where the synchronization period is 21.8 h, vsw = 0.0158 and VCdk1 = 19.95. In (d) the synchronization period is 25.47 h, vsw = 2.512 and VCdk1 = 100. Curves in black, blue and red represent the time evolution of nuclear BMAL1, nuclear REV-ERBα and Cyclin B/CDK1, respectively. The transients in (b)–(d) last for one or two cycles. The data in (b), (c) and (d) correspond, respectively, to the points marked 1, 2 and 3 in figure 5a. (Online version in colour.)