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

Speed. A: the deterministic oscillation for the three variables M, Pc and PN over a period. B: the forces of M, Pc and PN over the period. C: the speed along the cycle with time. The 'star' time parameters are as follows:t1 = 3.8, t2 = 8.5, t3 = 15.5, t4 = 21.2. D:The speed along a limit cycle: the 'star' time parameters are the same as Fig. 4C.
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Figure 4: Speed. A: the deterministic oscillation for the three variables M, Pc and PN over a period. B: the forces of M, Pc and PN over the period. C: the speed along the cycle with time. The 'star' time parameters are as follows:t1 = 3.8, t2 = 8.5, t3 = 15.5, t4 = 21.2. D:The speed along a limit cycle: the 'star' time parameters are the same as Fig. 4C.

Mentions: We can clearly see the probability distribution is not distributed evenly along the limit cycle. In order to know the nature of attractive nature of the limit cycle, we have to observe the dynamics of the network. The deterministic oscillation for the three variables M, Pc, and PN over a period are shown in Fig. 4(A). The forces on M, Pc, and PN over the period are shown in Fig. 4(B). The speed along the cycle is shown in Fig. 4(C). Fig. 4(D) shows the corresponding limit cycle with the time marks. The sign 'star' on the limit cycle shows where the values of the force and the speed have been denoted at given times. The speed along the limit cycle has two maxima, at which the amount of time spent will be smaller than at other part of the phase space. Thus, the steady probability distribution is larger at the slower speed[1].


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

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

Speed. A: the deterministic oscillation for the three variables M, Pc and PN over a period. B: the forces of M, Pc and PN over the period. C: the speed along the cycle with time. The 'star' time parameters are as follows:t1 = 3.8, t2 = 8.5, t3 = 15.5, t4 = 21.2. D:The speed along a limit cycle: the 'star' time parameters are the same as Fig. 4C.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: Speed. A: the deterministic oscillation for the three variables M, Pc and PN over a period. B: the forces of M, Pc and PN over the period. C: the speed along the cycle with time. The 'star' time parameters are as follows:t1 = 3.8, t2 = 8.5, t3 = 15.5, t4 = 21.2. D:The speed along a limit cycle: the 'star' time parameters are the same as Fig. 4C.
Mentions: We can clearly see the probability distribution is not distributed evenly along the limit cycle. In order to know the nature of attractive nature of the limit cycle, we have to observe the dynamics of the network. The deterministic oscillation for the three variables M, Pc, and PN over a period are shown in Fig. 4(A). The forces on M, Pc, and PN over the period are shown in Fig. 4(B). The speed along the cycle is shown in Fig. 4(C). Fig. 4(D) shows the corresponding limit cycle with the time marks. The sign 'star' on the limit cycle shows where the values of the force and the speed have been denoted at given times. The speed along the limit cycle has two maxima, at which the amount of time spent will be smaller than at other part of the phase space. Thus, the steady probability distribution is larger at the slower speed[1].

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