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Funneled landscape leads to robustness of cell networks: yeast cell cycle.

Wang J, Huang B, Xia X, Sun Z - PLoS Comput. Biol. (2006)

Bottom Line: This naturally explains robustness from a physical point of view.The ratio of slope versus roughness of the landscape becomes a quantitative measure of robustness of the network.It provides an optimal criterion for network connections and design.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemistry and Department of Physics, State University of New York at Stony Brook, Stony Brook, New York, United States of America. jin.wang.1@stonybrook.edu

ABSTRACT
We uncovered the underlying energy landscape for a cellular network. We discovered that the energy landscape of the yeast cell-cycle network is funneled towards the global minimum (G0/G1 phase) from the experimentally measured or inferred inherent chemical reaction rates. The funneled landscape is quite robust against random perturbations. This naturally explains robustness from a physical point of view. The ratio of slope versus roughness of the landscape becomes a quantitative measure of robustness of the network. The funneled landscape can be seen as a possible realization of the Darwinian principle of natural selection at the cellular network level. It provides an optimal criterion for network connections and design. Our approach is general and can be applied to other cellular networks.

Show MeSH
Thermodynamic Phase Diagram for the Yeast Cell–Cycle NetworkNative phase with global minimum G0/G1 state or steady state; non-native phase with states less overlapping with global minimum G0/G1 state or steady state; trapping phase with states trapped into the local minimum. The larger of δU/T and smaller of ΔU/T, or the larger δU/ΔU, the more likely the global minimum G1 state is thermodynamically stable and robust.
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pcbi-0020147-g005: Thermodynamic Phase Diagram for the Yeast Cell–Cycle NetworkNative phase with global minimum G0/G1 state or steady state; non-native phase with states less overlapping with global minimum G0/G1 state or steady state; trapping phase with states trapped into the local minimum. The larger of δU/T and smaller of ΔU/T, or the larger δU/ΔU, the more likely the global minimum G1 state is thermodynamically stable and robust.

Mentions: There are at least three possible thermodynamic phases: the global minimum G1 state, the less-overlapping with the global minimum G1 state, and the trapping phase (see Figure 5). The global minimum G1 state in the yeast cell-cycle example corresponds to the final destination at the end of one complete cell cycle. Without further stimulation, the cell will sit at the G1 state and not go into the next stage of development. Clearly, the native transition (to the global minimum G1 state) temperature should be higher than the trapping temperature to guarantee the global thermodynamic stability and avoid nondiscrimination with traps. The ratioTn / Ttrapping should therefore be maximized. From the above expression, this is the equivalent of saying that Λ, or RR, should also be maximized. Therefore, maximizing the ratio of the potential gap (or the slope) versus the roughness of the underlying potential landscape weighted by the entropy of the available states (a measure of the configurational search space) becomes the criterion for the global thermodynamic stability or robustness of the network. Only the cellular network landscape satisfying this criterion will be able to form a thermodynamically stable global steady state, be robust, perform the biological functions, and furthermore survive natural evolution. Similar to the problems of protein folding and binding [30,31], this implies a funneled potential landscape of the cellular network as shown in Figure 2C, which has a directed downhill slope biased towards the global minimum G1 state, dominating the fluctuations or wiggles superimposed on the landscape and the configurational search space. From this picture, at the initial stage of the yeast cell-cycle network process, there are multiple parallel paths leading towards the global minimum G1 state. As the kinetic process progresses, the discrete paths might emerge and give dominant contributions when the roughness of the underlying landscape becomes significant.


Funneled landscape leads to robustness of cell networks: yeast cell cycle.

Wang J, Huang B, Xia X, Sun Z - PLoS Comput. Biol. (2006)

Thermodynamic Phase Diagram for the Yeast Cell–Cycle NetworkNative phase with global minimum G0/G1 state or steady state; non-native phase with states less overlapping with global minimum G0/G1 state or steady state; trapping phase with states trapped into the local minimum. The larger of δU/T and smaller of ΔU/T, or the larger δU/ΔU, the more likely the global minimum G1 state is thermodynamically stable and robust.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC1636676&req=5

pcbi-0020147-g005: Thermodynamic Phase Diagram for the Yeast Cell–Cycle NetworkNative phase with global minimum G0/G1 state or steady state; non-native phase with states less overlapping with global minimum G0/G1 state or steady state; trapping phase with states trapped into the local minimum. The larger of δU/T and smaller of ΔU/T, or the larger δU/ΔU, the more likely the global minimum G1 state is thermodynamically stable and robust.
Mentions: There are at least three possible thermodynamic phases: the global minimum G1 state, the less-overlapping with the global minimum G1 state, and the trapping phase (see Figure 5). The global minimum G1 state in the yeast cell-cycle example corresponds to the final destination at the end of one complete cell cycle. Without further stimulation, the cell will sit at the G1 state and not go into the next stage of development. Clearly, the native transition (to the global minimum G1 state) temperature should be higher than the trapping temperature to guarantee the global thermodynamic stability and avoid nondiscrimination with traps. The ratioTn / Ttrapping should therefore be maximized. From the above expression, this is the equivalent of saying that Λ, or RR, should also be maximized. Therefore, maximizing the ratio of the potential gap (or the slope) versus the roughness of the underlying potential landscape weighted by the entropy of the available states (a measure of the configurational search space) becomes the criterion for the global thermodynamic stability or robustness of the network. Only the cellular network landscape satisfying this criterion will be able to form a thermodynamically stable global steady state, be robust, perform the biological functions, and furthermore survive natural evolution. Similar to the problems of protein folding and binding [30,31], this implies a funneled potential landscape of the cellular network as shown in Figure 2C, which has a directed downhill slope biased towards the global minimum G1 state, dominating the fluctuations or wiggles superimposed on the landscape and the configurational search space. From this picture, at the initial stage of the yeast cell-cycle network process, there are multiple parallel paths leading towards the global minimum G1 state. As the kinetic process progresses, the discrete paths might emerge and give dominant contributions when the roughness of the underlying landscape becomes significant.

Bottom Line: This naturally explains robustness from a physical point of view.The ratio of slope versus roughness of the landscape becomes a quantitative measure of robustness of the network.It provides an optimal criterion for network connections and design.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemistry and Department of Physics, State University of New York at Stony Brook, Stony Brook, New York, United States of America. jin.wang.1@stonybrook.edu

ABSTRACT
We uncovered the underlying energy landscape for a cellular network. We discovered that the energy landscape of the yeast cell-cycle network is funneled towards the global minimum (G0/G1 phase) from the experimentally measured or inferred inherent chemical reaction rates. The funneled landscape is quite robust against random perturbations. This naturally explains robustness from a physical point of view. The ratio of slope versus roughness of the landscape becomes a quantitative measure of robustness of the network. The funneled landscape can be seen as a possible realization of the Darwinian principle of natural selection at the cellular network level. It provides an optimal criterion for network connections and design. Our approach is general and can be applied to other cellular networks.

Show MeSH