Entrainment of the cell cycle through the Cdk inhibitor p21 induced by the circadian clock protein REV-ERBα.
(A) Domains of entrainment of the cell cycle by the circadian clock at 24 h and 48 h. As in Fig. 4, periods of the cell cycle smaller or larger than 24 h can be entrained at 24 h by the circadian clock, although the domain enlarges for periods less than 24 h. The two domains are close to each other when the autonomous period is in the range 30 h–40 h. (B) Time series showing the switch from entrainment of the cell cycle by the circadian clock at 48 h (t<240 h) to entrainment at 24 h (t>240 h) resulting from an increase of about 6.5% in coupling strength, when the autonomous period is equal to 34 h. The light-dark (LD) cycle is represented by a dashed line; the high and low portions of the square wave correspond to the L (16 h) and D (8 h) phases, respectively. In the presence of entrainment at 24 h, cyclin B/Cdk1 peaks at the end of the L phase, in agreement with experimental observations . Parameter values in eqs.  and  (see Methods) are: Kip21 = 0.05 nM, nmp21 = 1, Vdmp21 = 0.5 µM h−1, Kdmp21 = 0.5 µM, and vs1p21 = 50 h−1. Moreover, in (B), at t = 240 h parameter vsmp21 measuring coupling strength increases from 0.46 µM h−1 to 0.49 µM h−1. As in Fig. 2, the values of the parameters in the model for the circadian clock are those corresponding to Fig. 8 of the Supporting Information in Ref.  with Kib = 1 nM. While the shift in entrainment pattern in (B) follows from a permanent change in parameter value (here the coupling strength), a similar switch between the two modes of entrainment could also result from a transient perturbation, because in the region where the two domains of entrainment are close to each other in (A), numerical simulations indicate that the two stable modes of entrainment to 24 h and 48 h may sometimes coexist in the same conditions. This coexistence phenomenon corresponds to birhythmicity , .