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Robustness, dissipations and coherence of the oscillation of circadian clock: potential landscape and flux perspectives.

Wang J, Xu L, Wang E - PMC Biophys (2008)

Bottom Line: We also found that the entropy production rate characterizing the dissipation or heat loss decreases as the fluctuations decrease.We also found that the properties from exploring the effects of the inherent chemical rate parameters on the robustness.Our approach is quite general and can be applied to other oscillatory cellular network.PACS Codes: 87.18.-h, 87.18.Vf, 87.18.Yt.

View Article: PubMed Central - HTML - PubMed

Affiliation: State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin, 130022, PR China. jin.wang.1@stonybrook.edu.

ABSTRACT
Finding the global probabilistic nature of a non-equilibrium circadian clock is essential for addressing important issues of robustness and function. We have uncovered the underlying potential energy landscape of a simple cyanobacteria biochemical network, and the corresponding flux which is the driving force for the oscillation. We found that the underlying potential landscape for the oscillation in the presence of small statistical fluctuations is like an explicit ring valley or doughnut shape in the three dimensional protein concentration space. We found that the barrier height separating the oscillation ring and other area is a quantitative measure of the oscillation robustness and decreases when the fluctuations increase. We also found that the entropy production rate characterizing the dissipation or heat loss decreases as the fluctuations decrease. In addition, we found that, as the fluctuations increase, the period and the amplitude of the oscillations is more dispersed, and the phase coherence decreases. We also found that the properties from exploring the effects of the inherent chemical rate parameters on the robustness. Our approach is quite general and can be applied to other oscillatory cellular network.PACS Codes: 87.18.-h, 87.18.Vf, 87.18.Yt.

No MeSH data available.


Related in: MedlinePlus

Coherence. A: The coherence versus the diffusion coefficient D and entropy production rate. B: The coherence versus the Barrier height.
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Figure 8: Coherence. A: The coherence versus the diffusion coefficient D and entropy production rate. B: The coherence versus the Barrier height.

Mentions: where θ(φ) = 1 when φ(t) > 0, and θ(φ) = 0 when φ(t) ≤ 0, and sums are taken over every time step for the simulated trajectory. ξ ≈ 0 means the system moves stochastically and has no coherence. The oscillation is most coherent when ξ is close to 1. The value of ξ becomes larger when the fluctuations are smaller, since the trajectories are more periodic in their evolution. Fig. 8(A) shows ξ decreases as the the diffusion coefficient increases, implying that the coherence of the oscillation can be destroyed by fluctuations. Conversely, less fluctuation yields a more coherent, robust, and stable system. We also see that ξ becomes larger with a lower heat loss or entropy production rate, and conclude that less dissipation leads to more coherence. We further see that ξ increases with barrier height (Fig. 8(B)). This shows that a less dissipated network tends to preserve the coherence of the oscillations.


Robustness, dissipations and coherence of the oscillation of circadian clock: potential landscape and flux perspectives.

Wang J, Xu L, Wang E - PMC Biophys (2008)

Coherence. A: The coherence versus the diffusion coefficient D and entropy production rate. B: The coherence versus the Barrier height.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2667439&req=5

Figure 8: Coherence. A: The coherence versus the diffusion coefficient D and entropy production rate. B: The coherence versus the Barrier height.
Mentions: where θ(φ) = 1 when φ(t) > 0, and θ(φ) = 0 when φ(t) ≤ 0, and sums are taken over every time step for the simulated trajectory. ξ ≈ 0 means the system moves stochastically and has no coherence. The oscillation is most coherent when ξ is close to 1. The value of ξ becomes larger when the fluctuations are smaller, since the trajectories are more periodic in their evolution. Fig. 8(A) shows ξ decreases as the the diffusion coefficient increases, implying that the coherence of the oscillation can be destroyed by fluctuations. Conversely, less fluctuation yields a more coherent, robust, and stable system. We also see that ξ becomes larger with a lower heat loss or entropy production rate, and conclude that less dissipation leads to more coherence. We further see that ξ increases with barrier height (Fig. 8(B)). This shows that a less dissipated network tends to preserve the coherence of the oscillations.

Bottom Line: We also found that the entropy production rate characterizing the dissipation or heat loss decreases as the fluctuations decrease.We also found that the properties from exploring the effects of the inherent chemical rate parameters on the robustness.Our approach is quite general and can be applied to other oscillatory cellular network.PACS Codes: 87.18.-h, 87.18.Vf, 87.18.Yt.

View Article: PubMed Central - HTML - PubMed

Affiliation: State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin, 130022, PR China. jin.wang.1@stonybrook.edu.

ABSTRACT
Finding the global probabilistic nature of a non-equilibrium circadian clock is essential for addressing important issues of robustness and function. We have uncovered the underlying potential energy landscape of a simple cyanobacteria biochemical network, and the corresponding flux which is the driving force for the oscillation. We found that the underlying potential landscape for the oscillation in the presence of small statistical fluctuations is like an explicit ring valley or doughnut shape in the three dimensional protein concentration space. We found that the barrier height separating the oscillation ring and other area is a quantitative measure of the oscillation robustness and decreases when the fluctuations increase. We also found that the entropy production rate characterizing the dissipation or heat loss decreases as the fluctuations decrease. In addition, we found that, as the fluctuations increase, the period and the amplitude of the oscillations is more dispersed, and the phase coherence decreases. We also found that the properties from exploring the effects of the inherent chemical rate parameters on the robustness. Our approach is quite general and can be applied to other oscillatory cellular network.PACS Codes: 87.18.-h, 87.18.Vf, 87.18.Yt.

No MeSH data available.


Related in: MedlinePlus