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This article is part of the supplement: Selected articles from The 5th IEEE International Conference on Systems Biology (ISB 2011)

Open Access Research

Synchronization ability of coupled cell-cycle oscillators in changing environments

Wei Zhang and Xiufen Zou*

Author Affiliations

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

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BMC Systems Biology 2012, 6(Suppl 1):S13  doi:10.1186/1752-0509-6-S1-S13

Published: 16 July 2012

Additional files

Additional file 1:

The synchronization behavior of the coupled oscillators. The coupled system achieved synchronization when the parameters were set as in Table 1. N is the number of cells. The character C refers to CDK1, P refers to PLK1, A refers to APC and R refers to the complex protein.

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Additional file 2:

The sensitivity of the coupled system to the perturbation of parameters. (A) Sensitivity of CDK1 to the perturbation of parameters. (B) Sensitivity of PLK1 to the perturbation of parameters. (C) Sensitivity of APC to the perturbation of parameters. (D) Sensitivity of R to the perturbation of parameters.

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Additional file 3:

The bifurcation diagrams for K1, K2, α1 and α3. (A) The bifurcation diagrams of the activation coefficients K1 in the Hill function. (B) The bifurcation diagrams of the activation coefficients K2 in the Hill function. (C) The bifurcation diagrams of the activation constants α1. (D) The bifurcation diagrams of the activation constants α3.

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Additional file 4:

The bifurcation diagrams for the degradation rates. (A) The bifurcation diagrams of degradation rates β2. (B) The bifurcation diagrams of degradation rates β3. (C) The bifurcation diagrams of the degradation rate of complex protein R. (D) The coupled system achieved an asymptotically steady state when km = 1.25.

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Additional file 5:

The bifurcation diagrams for the coupling parameters. (A) The bifurcation diagrams for the activation coefficients KL in the Hill function. (B) The bifurcation diagrams for the activation coefficients Ka in the Hill function. (C) The bifurcation diagrams for the coupling strength k. (D) The bifurcation diagram for the activation constant k0.

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Additional file 6:

The effects of K1 and K3 on the period and amplitude. The above two diagrams show the effects of K1 on the period and amplitude of the coupled system when synchronization is achieved. The two diagrams below show the effects of K3 on the period and amplitude of the coupled system when synchronization is achieved.

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Additional file 7:

The effects of K2 on the period and amplitude. The above two diagrams show the effects of K2 on the period and amplitude of the coupled system when synchronization is achieved at the first synchronization interval. The two diagrams below show the effects of K2 on the period and amplitude of the coupled system when synchronization is achieved at the second synchronization interval.

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Additional file 8:

The effects of α1 and α3 on the period and amplitude when synchronization is achieved. The left two diagrams show the effects of α1 on the period and amplitude of the coupled system when synchronization is achieved at the first synchronization interval. The two diagrams on the right show the effects of α3 on the period and amplitude of the coupled system when synchronization is achieved at the second synchronization interval.

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Additional file 9:

The effects of parameters KL, Ka, k and k0 on the period when synchronization is achieved. With an increase in these parameters in their synchronization intervals, the oscillation periods for parameters KL, Ka and k increase, but the oscillation period for parameter k0 decreases.

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Additional file 10:

The effects of parameters KL, Ka, k and k0 on the amplitude when achieved synchronization. With an increase in these parameters in their synchronization intervals, the oscillation amplitudes for parameters KL and Ka increase, but the oscillation amplitudes for parameters k and k0 decreases.

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