Limits...
Energy landscape reveals that the budding yeast cell cycle is a robust and adaptive multi-stage process.

Lv C, Li X, Li F, Li T - PLoS Comput. Biol. (2015)

Bottom Line: Analysis shows that the cell cycle trajectory is sharply confined by the ambient energy barrier, and the landscape along this trajectory exhibits a generally flat shape.The difference between the landscapes induced by intrinsic and extrinsic noise is also discussed.In our opinion, this meticulous structure of the energy landscape for our simplified model is of general interest to other cell cycle dynamics, and the proposed methods can be applied to study similar biological systems.

View Article: PubMed Central - PubMed

Affiliation: School of Physics, Peking University, Beijing, China.

ABSTRACT
Quantitatively understanding the robustness, adaptivity and efficiency of cell cycle dynamics under the influence of noise is a fundamental but difficult question to answer for most eukaryotic organisms. Using a simplified budding yeast cell cycle model perturbed by intrinsic noise, we systematically explore these issues from an energy landscape point of view by constructing an energy landscape for the considered system based on large deviation theory. Analysis shows that the cell cycle trajectory is sharply confined by the ambient energy barrier, and the landscape along this trajectory exhibits a generally flat shape. We explain the evolution of the system on this flat path by incorporating its non-gradient nature. Furthermore, we illustrate how this global landscape changes in response to external signals, observing a nice transformation of the landscapes as the excitable system approaches a limit cycle system when nutrients are sufficient, as well as the formation of additional energy wells when the DNA replication checkpoint is activated. By taking into account the finite volume effect, we find additional pits along the flat cycle path in the landscape associated with the checkpoint mechanism of the cell cycle. The difference between the landscapes induced by intrinsic and extrinsic noise is also discussed. In our opinion, this meticulous structure of the energy landscape for our simplified model is of general interest to other cell cycle dynamics, and the proposed methods can be applied to study similar biological systems.

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The model of the three-node yeast cell cycle network.(A) The network structure of the yeast cell cycle, where x, y and z represent key regulators of the G1/S, early M and late M modules, respectively. Different modules are connected by activation (lines end with arrow) and inhibition (line end with bar) interactions. (B) and (C) The evolution trajectory of the yeast cell cycle process with parameter values j1 = j2 = j3 = 0.5, k1 = k2 = k3 = 0.2, ki = 5.0, ks = 1.0, and ka1 = ka2 = 0.001. The system starts from P2 and evolves to P1. In (B), the time evolution of the variables x, y and z is shown with the green, red and blue lines, respectively.
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pcbi.1004156.g001: The model of the three-node yeast cell cycle network.(A) The network structure of the yeast cell cycle, where x, y and z represent key regulators of the G1/S, early M and late M modules, respectively. Different modules are connected by activation (lines end with arrow) and inhibition (line end with bar) interactions. (B) and (C) The evolution trajectory of the yeast cell cycle process with parameter values j1 = j2 = j3 = 0.5, k1 = k2 = k3 = 0.2, ki = 5.0, ks = 1.0, and ka1 = ka2 = 0.001. The system starts from P2 and evolves to P1. In (B), the time evolution of the variables x, y and z is shown with the green, red and blue lines, respectively.

Mentions: We first assume that the DNA replication triggers the mitosis as a “domino” mechanism in the budding yeast cell cycle. That is, once the yeast cell passes the Start checkpoint, it will proceed through the whole cell cycle process spontaneously. Based on the key regulatory network [17] and our previous study on budding yeast [22], the cell cycle regulatory network can be simplified and separated into G1/S, early M and late M modules, as shown in Fig. 1A. We ignore the G2 phase for simplification. Each module has a positive feedback, and different modules are connected with activation and repression interactions. The deterministic equations describing this three-module yeast cell cycle network aredxdt=x2j12+x2−k1x−xy+a0,(1a)dydt=y2j22+y2−k2y−yz+ka1x,(1b)dzdt=ksz2j32+z2−k3z−kizx+ka2y,(1c)where x represents the concentrations of key regulators such as cyclins Cln1, 2, Clb5, 6 and transcriptional factors SBF and MBF in the excited G1 and S phases; y represents the concentrations of key regulators such as cyclins Clb1, 2 and transcriptional factor Mcm1/SFF in the early M phase; and z represents the concentrations of key inhibitors such as Cdh1, Cdc20 and Sic1 in the late M/G1 phase.


Energy landscape reveals that the budding yeast cell cycle is a robust and adaptive multi-stage process.

Lv C, Li X, Li F, Li T - PLoS Comput. Biol. (2015)

The model of the three-node yeast cell cycle network.(A) The network structure of the yeast cell cycle, where x, y and z represent key regulators of the G1/S, early M and late M modules, respectively. Different modules are connected by activation (lines end with arrow) and inhibition (line end with bar) interactions. (B) and (C) The evolution trajectory of the yeast cell cycle process with parameter values j1 = j2 = j3 = 0.5, k1 = k2 = k3 = 0.2, ki = 5.0, ks = 1.0, and ka1 = ka2 = 0.001. The system starts from P2 and evolves to P1. In (B), the time evolution of the variables x, y and z is shown with the green, red and blue lines, respectively.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4368831&req=5

pcbi.1004156.g001: The model of the three-node yeast cell cycle network.(A) The network structure of the yeast cell cycle, where x, y and z represent key regulators of the G1/S, early M and late M modules, respectively. Different modules are connected by activation (lines end with arrow) and inhibition (line end with bar) interactions. (B) and (C) The evolution trajectory of the yeast cell cycle process with parameter values j1 = j2 = j3 = 0.5, k1 = k2 = k3 = 0.2, ki = 5.0, ks = 1.0, and ka1 = ka2 = 0.001. The system starts from P2 and evolves to P1. In (B), the time evolution of the variables x, y and z is shown with the green, red and blue lines, respectively.
Mentions: We first assume that the DNA replication triggers the mitosis as a “domino” mechanism in the budding yeast cell cycle. That is, once the yeast cell passes the Start checkpoint, it will proceed through the whole cell cycle process spontaneously. Based on the key regulatory network [17] and our previous study on budding yeast [22], the cell cycle regulatory network can be simplified and separated into G1/S, early M and late M modules, as shown in Fig. 1A. We ignore the G2 phase for simplification. Each module has a positive feedback, and different modules are connected with activation and repression interactions. The deterministic equations describing this three-module yeast cell cycle network aredxdt=x2j12+x2−k1x−xy+a0,(1a)dydt=y2j22+y2−k2y−yz+ka1x,(1b)dzdt=ksz2j32+z2−k3z−kizx+ka2y,(1c)where x represents the concentrations of key regulators such as cyclins Cln1, 2, Clb5, 6 and transcriptional factors SBF and MBF in the excited G1 and S phases; y represents the concentrations of key regulators such as cyclins Clb1, 2 and transcriptional factor Mcm1/SFF in the early M phase; and z represents the concentrations of key inhibitors such as Cdh1, Cdc20 and Sic1 in the late M/G1 phase.

Bottom Line: Analysis shows that the cell cycle trajectory is sharply confined by the ambient energy barrier, and the landscape along this trajectory exhibits a generally flat shape.The difference between the landscapes induced by intrinsic and extrinsic noise is also discussed.In our opinion, this meticulous structure of the energy landscape for our simplified model is of general interest to other cell cycle dynamics, and the proposed methods can be applied to study similar biological systems.

View Article: PubMed Central - PubMed

Affiliation: School of Physics, Peking University, Beijing, China.

ABSTRACT
Quantitatively understanding the robustness, adaptivity and efficiency of cell cycle dynamics under the influence of noise is a fundamental but difficult question to answer for most eukaryotic organisms. Using a simplified budding yeast cell cycle model perturbed by intrinsic noise, we systematically explore these issues from an energy landscape point of view by constructing an energy landscape for the considered system based on large deviation theory. Analysis shows that the cell cycle trajectory is sharply confined by the ambient energy barrier, and the landscape along this trajectory exhibits a generally flat shape. We explain the evolution of the system on this flat path by incorporating its non-gradient nature. Furthermore, we illustrate how this global landscape changes in response to external signals, observing a nice transformation of the landscapes as the excitable system approaches a limit cycle system when nutrients are sufficient, as well as the formation of additional energy wells when the DNA replication checkpoint is activated. By taking into account the finite volume effect, we find additional pits along the flat cycle path in the landscape associated with the checkpoint mechanism of the cell cycle. The difference between the landscapes induced by intrinsic and extrinsic noise is also discussed. In our opinion, this meticulous structure of the energy landscape for our simplified model is of general interest to other cell cycle dynamics, and the proposed methods can be applied to study similar biological systems.

Show MeSH
Related in: MedlinePlus