Limits...
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

Barrier. The barrier height Barrier1 = Ufix - Umin and Barrier2 = Ufix - Umax versus diffusion coefficient D.
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Figure 5: Barrier. The barrier height Barrier1 = Ufix - Umin and Barrier2 = Ufix - Umax versus diffusion coefficient D.

Mentions: We can explore the global stability and robustness of the circadian clock when we obtain the potential landscape. The barrier height represents the system escaping from the oscillation attractor. Fig. 5 shows the barrier height versus the diffusion coefficient D. Barrier1 is equivalent to Ufix minus Umax, and Barrier2 is equivalent to Ufix minus Umin, where Ufix is the potential local maximum inside the limit cycle; Umax is the potential maximum along the limit cycle; and Umin is the potential minimum along the limit cycle. We can see the barrier height becomes larger when the fluctuations decrease. It is harder for the system to go from the doughnut of attraction to outside when fluctuations are small. This means the doughnut shape of the landscape is robust, and a stable oscillation is essentially guaranteed for small fluctuations. It also implies that the barrier height can be used as a quantitative measure of the stability and robustness of the network 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)

Barrier. The barrier height Barrier1 = Ufix - Umin and Barrier2 = Ufix - Umax versus diffusion coefficient D.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 5: Barrier. The barrier height Barrier1 = Ufix - Umin and Barrier2 = Ufix - Umax versus diffusion coefficient D.
Mentions: We can explore the global stability and robustness of the circadian clock when we obtain the potential landscape. The barrier height represents the system escaping from the oscillation attractor. Fig. 5 shows the barrier height versus the diffusion coefficient D. Barrier1 is equivalent to Ufix minus Umax, and Barrier2 is equivalent to Ufix minus Umin, where Ufix is the potential local maximum inside the limit cycle; Umax is the potential maximum along the limit cycle; and Umin is the potential minimum along the limit cycle. We can see the barrier height becomes larger when the fluctuations decrease. It is harder for the system to go from the doughnut of attraction to outside when fluctuations are small. This means the doughnut shape of the landscape is robust, and a stable oscillation is essentially guaranteed for small fluctuations. It also implies that the barrier height can be used as a quantitative measure of the stability and robustness of the network 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