title: Synchronization ability of coupled cell-cycle oscillators in changing environments.
abstract: BACKGROUND
  The biochemical oscillator that controls periodic events during the Xenopus embryonic cell cycle is centered on the activity of CDKs, and the cell cycle is driven by a protein circuit that is centered on the cyclin-dependent protein kinase CDK1 and the anaphase-promoting complex (APC). Many studies have been conducted to confirm that the interactions in the cell cycle can produce oscillations and predict behaviors such as synchronization, but much less is known about how the various elaborations and collective behavior of the basic oscillators can affect the robustness of the system. Therefore, in this study, we investigate and model a multi-cell system of the Xenopus embryonic cell cycle oscillators that are coupled through a common complex protein, and then analyze their synchronization ability under four different external stimuli, including a constant input signal, a square-wave periodic signal, a sinusoidal signal and a noise signal.
  
  
  RESULTS
  Through bifurcation analysis and numerical simulations, we obtain 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 the synchronization period and amplitude, and find interesting phenomena, e.g., there are two synchronization intervals with activation coefficient in the Hill function of the activated CDK1 that activates the Plk1, and different synchronization intervals have distinct influences on the synchronization period and amplitude. To quantify the speediness and robustness of the synchronization, we use two quantities, the synchronization time and the robustness index, to evaluate the synchronization ability. More interestingly, we find that the coupled system has an optimal signal strength that maximizes the synchronization index under different external stimuli. Simulation results also show that the ability and robustness of the synchronization for the square-wave periodic signal of cyclin synthesis is strongest in comparison to the other three different signals.
  
  
  CONCLUSIONS
  These results suggest that the reaction process in which the activated cyclin-CDK1 activates the Plk1 has a very important influence on the synchronization ability of the coupled system, and the square-wave periodic signal of cyclin synthesis is more conducive to the synchronization and robustness of the coupled cell-cycle oscillators. Our study provides insight into the internal mechanisms of the cell cycle system and helps to generate hypotheses for further research.
authors.affiliation: School of Mathematics and Statistics, Wuhan University, Wuhan, China.
authors.forename: Wei
authors.initials: W
authors.lastname: Zhang
authors.forename: Xiufen
authors.initials: X
authors.lastname: Zou
mesh_terms: D064173:Anaphase-Promoting Complex-Cyclosome; D000818:Animals; D016203:CDC2 Protein Kinase / Q000378:metabolism; D002453:Cell Cycle; D018797:Cell Cycle Proteins / Q000378:metabolism; D004625:Embryo, Nonmammalian / Q000166:cytology* / Q000378:metabolism; D004789:Enzyme Activation; D008954:Models, Biological; D017346:Protein Serine-Threonine Kinases / Q000378:metabolism; D011518:Proto-Oncogene Proteins / Q000378:metabolism; D013997:Time Factors; D043743:Ubiquitin-Protein Ligase Complexes / Q000378:metabolism; D014981:Xenopus / Q000196:embryology*; D000097869:Polo-Like Kinase 1
chemical_list: D064173:Anaphase-Promoting Complex-Cyclosome; D016203:CDC2 Protein Kinase; D018797:Cell Cycle Proteins; D017346:Protein Serine-Threonine Kinases; D011518:Proto-Oncogene Proteins; D043743:Ubiquitin-Protein Ligase Complexes; D000097869:Polo-Like Kinase 1