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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.

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The Averaged Potential U as a Function of Similarity Parameter Q with Respect to the Global Minimum G1 State (or Global Steady State) of Potential U against Perturbations of Chemical Rate Coefficient Parameters with 10% Increase (Decrease), 20% Increase (Decrease)
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pcbi-0020147-g003: The Averaged Potential U as a Function of Similarity Parameter Q with Respect to the Global Minimum G1 State (or Global Steady State) of Potential U against Perturbations of Chemical Rate Coefficient Parameters with 10% Increase (Decrease), 20% Increase (Decrease)

Mentions: Figure 2D shows the 1-D projection of the averaged U, <U>, to the overlapping order parameter Q with respect to the global minimum (Q = ). Q is defined this way so that we can keep track of the degree of “closeness” or overlap between an arbitrary state x and the global minimum state xglobal in the configurational state space of the protein concentrations. Q = 1 represents the global minimum state and Q = 0 represents the states with no overlap (decorrelated) with the global minimum. Here the global minimum is at the same place (in x) as the G0/G1 phase of the cell cycle. We see a downhill slope of the potential < U> in Q towards the global minimum Uglobal. This shows clearly a funnel of < U>along Q towards the global minimum of the potential landscape. When randomly changing the chemical rate coefficients (10%–20%), the slopes of < U> along Q towards the global minimum of the potential landscape do not change very much (as shown in Figure 3). So the landscape is still funneled towards the global minimum under different cellular conditions. Therefore the network is relatively stable and robust. With more drastic changes of the rate parameters (above 50%), the landscape starts to become less stable and loses its robustness.


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

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

The Averaged Potential U as a Function of Similarity Parameter Q with Respect to the Global Minimum G1 State (or Global Steady State) of Potential U against Perturbations of Chemical Rate Coefficient Parameters with 10% Increase (Decrease), 20% Increase (Decrease)
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-0020147-g003: The Averaged Potential U as a Function of Similarity Parameter Q with Respect to the Global Minimum G1 State (or Global Steady State) of Potential U against Perturbations of Chemical Rate Coefficient Parameters with 10% Increase (Decrease), 20% Increase (Decrease)
Mentions: Figure 2D shows the 1-D projection of the averaged U, <U>, to the overlapping order parameter Q with respect to the global minimum (Q = ). Q is defined this way so that we can keep track of the degree of “closeness” or overlap between an arbitrary state x and the global minimum state xglobal in the configurational state space of the protein concentrations. Q = 1 represents the global minimum state and Q = 0 represents the states with no overlap (decorrelated) with the global minimum. Here the global minimum is at the same place (in x) as the G0/G1 phase of the cell cycle. We see a downhill slope of the potential < U> in Q towards the global minimum Uglobal. This shows clearly a funnel of < U>along Q towards the global minimum of the potential landscape. When randomly changing the chemical rate coefficients (10%–20%), the slopes of < U> along Q towards the global minimum of the potential landscape do not change very much (as shown in Figure 3). So the landscape is still funneled towards the global minimum under different cellular conditions. Therefore the network is relatively stable and robust. With more drastic changes of the rate parameters (above 50%), the landscape starts to become less stable and loses its robustness.

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