Entrainment of the Mammalian Cell Cycle by the Circadian Clock: Modeling Two Coupled Cellular Rhythms
Figure 6
Complex oscillatory behavior of the cell cycle induced by coupling to the circadian clock.
As in Figs. 2–5 and 7, coupling is achieved through the kinase Wee1. Shown is the time evolution of cyclin E/Cdk2 (blue) and cyclin B/Cdk1 (red) in the absence (t<120 h) or presence (t>120 h) of coupling to the circadian clock. Conditions A–D correspond, respectively, to the points D–G surrounding the domain of entrainment to 24 h in Fig. 4A. (A) Complex periodic oscillations. The autonomous period of the cell cycle is equal to 4 h and the coupling strength, measured by the rate constant for the synthesis of Wee1 mRNA, vsw, is equal to 0.05 µM h−1; the period of the cell cycle is too short to be well entrained by the circadian clock, and two peaks of cyclin B/Cdk1 appear every 24 h, together with a small and a large peak in cyclin E/Cdk2. (B) The autonomous period of the cell cycle is equal to 30 h and vsw is still equal to 0.05 µM h−1. In this case, two peaks of cyclin E/Cdk2 appear for each peak of cyclin B/Cdk1. Such complex periodic oscillations would correspond to tetraploidy. (C) The autonomous period of the cell cycle is equal to 16 h and vsw is equal to 0.01 µM h−1. Coupling is not strong enough to allow correct entrainment of the cell cycle by the circadian clock, resulting in irregular, chaotic oscillatory behavior (cyclin E/Cdk2 is not shown, for the sake of clarity). The chaotic nature of the oscillations was characterized by means of Poincaré sections, as described in Fig. 9 of [25]. (D) The autonomous period of the cell cycle is equal to 16 h and vsw is equal to 0.3 µM h−1. Here, the coupling is so strong that it induces a high level of Wee1, which continuously inhibits the kinase Cdk1 while oscillations of Cdk2 persist. This simple periodic behavior would correspond to endoreplication. Other parameter values are as in Fig. 4A.