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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.


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Definition of phase coherence.
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Figure 7: Definition of phase coherence.

Mentions: The robustness of the oscillation with respect to the diffusion coefficient D can be quantified further by the phase coherence ξ, which measures the degree of periodicity of the time evolution of a given variable[39]. The phase coherence ξ quantitatively measures the degree of persistence of the oscillatory phase, and is defined as follows: First, the vector N(t) = n1(t)e1 + n2(t)e2 + n3(t)e3 is shown in Fig. 7. The unit vectors are e1 = (0, 1), e2 = (-/2, -1/2) and e3 = (-/2, 1/2), where n1(t), n2(t), and n3(t) are the concentrations of the three kinds of protein molecules at time t. φ(t) is the phase angle between N(t) and N(t + τ), where τ should be smaller than the deterministic period and larger than the fast fluctuations. We choose τ = 0.2 k-1. The oscillation goes in the positive orientation (counterclockwise), so φ(t) > 0. The formula for ξ is then:


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

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

Definition of phase coherence.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 7: Definition of phase coherence.
Mentions: The robustness of the oscillation with respect to the diffusion coefficient D can be quantified further by the phase coherence ξ, which measures the degree of periodicity of the time evolution of a given variable[39]. The phase coherence ξ quantitatively measures the degree of persistence of the oscillatory phase, and is defined as follows: First, the vector N(t) = n1(t)e1 + n2(t)e2 + n3(t)e3 is shown in Fig. 7. The unit vectors are e1 = (0, 1), e2 = (-/2, -1/2) and e3 = (-/2, 1/2), where n1(t), n2(t), and n3(t) are the concentrations of the three kinds of protein molecules at time t. φ(t) is the phase angle between N(t) and N(t + τ), where τ should be smaller than the deterministic period and larger than the fast fluctuations. We choose τ = 0.2 k-1. The oscillation goes in the positive orientation (counterclockwise), so φ(t) > 0. The formula for ξ is then:

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