Synchronization feature of coupled cell-cycle oscillators

Based on the model of the Xenopus embryonic cell cycle proposed in literature [1], which can exhibit sustained limit cycle oscillations, we first build a multi-cell system of these oscillators that are coupled through a common complex protein that plays an important role in the core regulation of cell-cycle oscillators, and then show synchronization features in this coupled multi-cell system. Through bifurcation analysis and numerical simulations, we give synchronization intervals of the sensitive parameters in the individual oscillator and the coupling parameters in the coupled oscillators. Then, we analyze the effects of these parameters on synchronization time, period and amplitude, and find interesting phenomena, e.g., there are two synchronization intervals of activation coefficient in the Hill function of the activated CDK1 that activates the Plk1, and different synchronization intervals have distinct influences on synchronization time, period and amplitude. More interestingly, we find that the coupled system can switch between a stable state and a stable periodic orbit. These results suggest that the reaction process that the activated cyclin-CDK1 activates the Plk1 has very important influence on the synchronization ability of the coupled system. Our work not only can be viewed as an important step toward the comprehensive understanding for mechanisms of Xenopus embryonic cell cycle and but also can provide the guide for further biological experiments.