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Neutral space analysis for a Boolean network model of the fission yeast cell cycle network.

Ruz GA, Timmermann T, Barrera J, Goles E - Biol. Res. (2014)

Bottom Line: Through simulations it was found that in the generated neutral graph, the functional networks that are not in the wildtype connected component have in general a Hamming distance more than 3 with the wildtype, and more than 10 between the other disconnected functional networks.Significant differences were found between the functional networks in the connected component of the wildtype network and the rest of the network, not only at a topological level, but also at the state space level, where significant differences in the distribution of the basin of attraction for the G1 fixed point was found for deterministic updating schemes.The proposed method to construct a neutral graph is general and can be used to explore the neutral space of other biologically interesting networks, and also formulate new biological hypotheses studying the functional networks in the wildtype network connected component.

View Article: PubMed Central - PubMed

Affiliation: Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal las Torres 2640, Peñalolén, Santiago, Chile. gonzalo.ruz@uai.cl.

ABSTRACT

Background: Interactions between genes and their products give rise to complex circuits known as gene regulatory networks (GRN) that enable cells to process information and respond to external stimuli. Several important processes for life, depend of an accurate and context-specific regulation of gene expression, such as the cell cycle, which can be analyzed through its GRN, where deregulation can lead to cancer in animals or a directed regulation could be applied for biotechnological processes using yeast. An approach to study the robustness of GRN is through the neutral space. In this paper, we explore the neutral space of a Schizosaccharomyces pombe (fission yeast) cell cycle network through an evolution strategy to generate a neutral graph, composed of Boolean regulatory networks that share the same state sequences of the fission yeast cell cycle.

Results: Through simulations it was found that in the generated neutral graph, the functional networks that are not in the wildtype connected component have in general a Hamming distance more than 3 with the wildtype, and more than 10 between the other disconnected functional networks. Significant differences were found between the functional networks in the connected component of the wildtype network and the rest of the network, not only at a topological level, but also at the state space level, where significant differences in the distribution of the basin of attraction for the G1 fixed point was found for deterministic updating schemes.

Conclusions: In general, functional networks in the wildtype network connected component, can mutate up to no more than 3 times, then they reach a point of no return where the networks leave the connected component of the wildtype. The proposed method to construct a neutral graph is general and can be used to explore the neutral space of other biologically interesting networks, and also formulate new biological hypotheses studying the functional networks in the wildtype network connected component.

No MeSH data available.


Related in: MedlinePlus

Sate transition graph of the wildtype network using a sequential updating scheme. State transition graph using the following updating scheme (Start)(SK)(Cdc2/Cdc13)(Ste9)(Rum1)(Slp1)(Cdc2/Cd13 ∗)(Wee1/Mik1)(Cdc25)(PP). (Color online) the fix point states are represented by red circles.
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Fig7: Sate transition graph of the wildtype network using a sequential updating scheme. State transition graph using the following updating scheme (Start)(SK)(Cdc2/Cdc13)(Ste9)(Rum1)(Slp1)(Cdc2/Cd13 ∗)(Wee1/Mik1)(Cdc25)(PP). (Color online) the fix point states are represented by red circles.

Mentions: The density of the basin of attraction of the G1 fixed point of the functional networks in the wildtype connected component (blue/dashed line) and the rest of the networks (green/solid line) appears in Figure 4A for the parallel update, B for a block sequential update, C for a sequential update, and D for the fully asynchronous update. We can appreciate that both densities are quite different, regardless of the updating scheme, except for the fully asynchronous. For the deterministic updating schemes, we notice that while the functional networks in the connected component have a basin of attraction mostly concentrated between 700 ∼900 (the wildtype has a basin of attraction of size 762 using the parallel update), nevertheless, the rest of the networks show a density that stretches out more. For the asynchronous update, we notice that the size of the basin of attraction of the G1 fixed point does not concentrate in a specific range of values as do the deterministic updating schemes. It seems that each initial state converges to one of the different attractors with equal probability without having a particular preference for the G1 fixed point as in the other deterministic cases. Finally, Figure 5 shows the state transition graph for the wildtype network using the parallel updating scheme, Figure 6 shows the state transition graph for the wildtype network using a block sequential updating scheme, and Figure 7 shows the state transition graph for the wildtype network using a sequential updating scheme. From these state transition graphs, one can appreciate the large basin of attraction for the G1 fixed point.Figure 4


Neutral space analysis for a Boolean network model of the fission yeast cell cycle network.

Ruz GA, Timmermann T, Barrera J, Goles E - Biol. Res. (2014)

Sate transition graph of the wildtype network using a sequential updating scheme. State transition graph using the following updating scheme (Start)(SK)(Cdc2/Cdc13)(Ste9)(Rum1)(Slp1)(Cdc2/Cd13 ∗)(Wee1/Mik1)(Cdc25)(PP). (Color online) the fix point states are represented by red circles.
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4335775&req=5

Fig7: Sate transition graph of the wildtype network using a sequential updating scheme. State transition graph using the following updating scheme (Start)(SK)(Cdc2/Cdc13)(Ste9)(Rum1)(Slp1)(Cdc2/Cd13 ∗)(Wee1/Mik1)(Cdc25)(PP). (Color online) the fix point states are represented by red circles.
Mentions: The density of the basin of attraction of the G1 fixed point of the functional networks in the wildtype connected component (blue/dashed line) and the rest of the networks (green/solid line) appears in Figure 4A for the parallel update, B for a block sequential update, C for a sequential update, and D for the fully asynchronous update. We can appreciate that both densities are quite different, regardless of the updating scheme, except for the fully asynchronous. For the deterministic updating schemes, we notice that while the functional networks in the connected component have a basin of attraction mostly concentrated between 700 ∼900 (the wildtype has a basin of attraction of size 762 using the parallel update), nevertheless, the rest of the networks show a density that stretches out more. For the asynchronous update, we notice that the size of the basin of attraction of the G1 fixed point does not concentrate in a specific range of values as do the deterministic updating schemes. It seems that each initial state converges to one of the different attractors with equal probability without having a particular preference for the G1 fixed point as in the other deterministic cases. Finally, Figure 5 shows the state transition graph for the wildtype network using the parallel updating scheme, Figure 6 shows the state transition graph for the wildtype network using a block sequential updating scheme, and Figure 7 shows the state transition graph for the wildtype network using a sequential updating scheme. From these state transition graphs, one can appreciate the large basin of attraction for the G1 fixed point.Figure 4

Bottom Line: Through simulations it was found that in the generated neutral graph, the functional networks that are not in the wildtype connected component have in general a Hamming distance more than 3 with the wildtype, and more than 10 between the other disconnected functional networks.Significant differences were found between the functional networks in the connected component of the wildtype network and the rest of the network, not only at a topological level, but also at the state space level, where significant differences in the distribution of the basin of attraction for the G1 fixed point was found for deterministic updating schemes.The proposed method to construct a neutral graph is general and can be used to explore the neutral space of other biologically interesting networks, and also formulate new biological hypotheses studying the functional networks in the wildtype network connected component.

View Article: PubMed Central - PubMed

Affiliation: Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal las Torres 2640, Peñalolén, Santiago, Chile. gonzalo.ruz@uai.cl.

ABSTRACT

Background: Interactions between genes and their products give rise to complex circuits known as gene regulatory networks (GRN) that enable cells to process information and respond to external stimuli. Several important processes for life, depend of an accurate and context-specific regulation of gene expression, such as the cell cycle, which can be analyzed through its GRN, where deregulation can lead to cancer in animals or a directed regulation could be applied for biotechnological processes using yeast. An approach to study the robustness of GRN is through the neutral space. In this paper, we explore the neutral space of a Schizosaccharomyces pombe (fission yeast) cell cycle network through an evolution strategy to generate a neutral graph, composed of Boolean regulatory networks that share the same state sequences of the fission yeast cell cycle.

Results: Through simulations it was found that in the generated neutral graph, the functional networks that are not in the wildtype connected component have in general a Hamming distance more than 3 with the wildtype, and more than 10 between the other disconnected functional networks. Significant differences were found between the functional networks in the connected component of the wildtype network and the rest of the network, not only at a topological level, but also at the state space level, where significant differences in the distribution of the basin of attraction for the G1 fixed point was found for deterministic updating schemes.

Conclusions: In general, functional networks in the wildtype network connected component, can mutate up to no more than 3 times, then they reach a point of no return where the networks leave the connected component of the wildtype. The proposed method to construct a neutral graph is general and can be used to explore the neutral space of other biologically interesting networks, and also formulate new biological hypotheses studying the functional networks in the wildtype network connected component.

No MeSH data available.


Related in: MedlinePlus