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Investigations into the relationship between feedback loops and functional importance of a signal transduction network based on Boolean network modeling.

Kwon YK, Choi SS, Cho KH - BMC Bioinformatics (2007)

Bottom Line: In this respect, we considered a feedback loop which is ubiquitously found in various biological networks.These results led us to infer that such a strong positive correlation between the NuFBL and the importance of a network node might be an intrinsic principle of biological networks in view of network dynamics.This result also suggests the existence of unknown feedback loops around functionally important nodes in biological networks.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Bio and Brain Engineering and KI for the BioCentury, Korea Advanced Institute of Science and Technology, 335 Gwahangno, Yuseong-gu, Daejeon, 305-701, Republic of Korea. kwon@soar.snu.ac.kr

ABSTRACT

Background: A number of studies on biological networks have been carried out to unravel the topological characteristics that can explain the functional importance of network nodes. For instance, connectivity, clustering coefficient, and shortest path length were previously proposed for this purpose. However, there is still a pressing need to investigate another topological measure that can better describe the functional importance of network nodes. In this respect, we considered a feedback loop which is ubiquitously found in various biological networks.

Results: We discovered that the number of feedback loops (NuFBL) is a crucial measure for evaluating the importance of a network node and verified this through a signal transduction network in the hippocampal CA1 neuron of mice as well as through generalized biological network models represented by Boolean networks. In particular, we observed that the proteins with a larger NuFBL are more likely to be essential and to evolve slowly in the hippocampal CA1 neuronal signal transduction network. Then, from extensive simulations based on the Boolean network models, we proved that a network node with the larger NuFBL is likely to be more important as the mutations of the initial state or the update rule of such a node made the network converge to a different attractor. These results led us to infer that such a strong positive correlation between the NuFBL and the importance of a network node might be an intrinsic principle of biological networks in view of network dynamics.

Conclusion: The presented analysis on topological characteristics of biological networks showed that the number of feedback loops is positively correlated with the functional importance of network nodes. This result also suggests the existence of unknown feedback loops around functionally important nodes in biological networks.

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Correlation of connectivity and the NuFBL to the functional importance in Boolean networks. (a) Correlation between connectivity and the functional importance of network nodes with respect to initial state mutations. (b) Correlation between the NuFBL and the functional importance of network nodes with respect to initial state mutations. (c) Correlation between connectivity and the functional importance of network nodes with respect to update rule mutations. (d) Correlation between the NuFBL and the functional importance of network nodes with respect to update rule mutations. In each figure, all nodes were classified into five groups according to their connectivity or NuFBL ranks. All the results represent the average over randomly generated 2000 Boolean networks with /V/ = 14 and /A/ = 19. For each group, the average and the confidence interval for 95% confidence level of the functional importance are shown on the y-axis. Here, the functional importance of a network node is defined by the probability with which the network converges to a different attractor when the value of the node is mutated. For other Boolean networks with different /V/ and /A/, we also obtained similar results (see additional data file 1).
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Figure 2: Correlation of connectivity and the NuFBL to the functional importance in Boolean networks. (a) Correlation between connectivity and the functional importance of network nodes with respect to initial state mutations. (b) Correlation between the NuFBL and the functional importance of network nodes with respect to initial state mutations. (c) Correlation between connectivity and the functional importance of network nodes with respect to update rule mutations. (d) Correlation between the NuFBL and the functional importance of network nodes with respect to update rule mutations. In each figure, all nodes were classified into five groups according to their connectivity or NuFBL ranks. All the results represent the average over randomly generated 2000 Boolean networks with /V/ = 14 and /A/ = 19. For each group, the average and the confidence interval for 95% confidence level of the functional importance are shown on the y-axis. Here, the functional importance of a network node is defined by the probability with which the network converges to a different attractor when the value of the node is mutated. For other Boolean networks with different /V/ and /A/, we also obtained similar results (see additional data file 1).

Mentions: Fig. 2 shows the results of the Boolean networks with /V/ = 14 and /A/ = 19. It turns out that the network nodes with a higher connectivity or NuFBL are more important, which is consistent with the observation in the above neuronal signal transduction network. And, we observed the same result for networks with different sizes (see additional data file 1). Moreover, we found that the NuFBL is a better network measure than the connectivity in evaluating the functional importance of a network node.


Investigations into the relationship between feedback loops and functional importance of a signal transduction network based on Boolean network modeling.

Kwon YK, Choi SS, Cho KH - BMC Bioinformatics (2007)

Correlation of connectivity and the NuFBL to the functional importance in Boolean networks. (a) Correlation between connectivity and the functional importance of network nodes with respect to initial state mutations. (b) Correlation between the NuFBL and the functional importance of network nodes with respect to initial state mutations. (c) Correlation between connectivity and the functional importance of network nodes with respect to update rule mutations. (d) Correlation between the NuFBL and the functional importance of network nodes with respect to update rule mutations. In each figure, all nodes were classified into five groups according to their connectivity or NuFBL ranks. All the results represent the average over randomly generated 2000 Boolean networks with /V/ = 14 and /A/ = 19. For each group, the average and the confidence interval for 95% confidence level of the functional importance are shown on the y-axis. Here, the functional importance of a network node is defined by the probability with which the network converges to a different attractor when the value of the node is mutated. For other Boolean networks with different /V/ and /A/, we also obtained similar results (see additional data file 1).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
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getmorefigures.php?uid=PMC2100072&req=5

Figure 2: Correlation of connectivity and the NuFBL to the functional importance in Boolean networks. (a) Correlation between connectivity and the functional importance of network nodes with respect to initial state mutations. (b) Correlation between the NuFBL and the functional importance of network nodes with respect to initial state mutations. (c) Correlation between connectivity and the functional importance of network nodes with respect to update rule mutations. (d) Correlation between the NuFBL and the functional importance of network nodes with respect to update rule mutations. In each figure, all nodes were classified into five groups according to their connectivity or NuFBL ranks. All the results represent the average over randomly generated 2000 Boolean networks with /V/ = 14 and /A/ = 19. For each group, the average and the confidence interval for 95% confidence level of the functional importance are shown on the y-axis. Here, the functional importance of a network node is defined by the probability with which the network converges to a different attractor when the value of the node is mutated. For other Boolean networks with different /V/ and /A/, we also obtained similar results (see additional data file 1).
Mentions: Fig. 2 shows the results of the Boolean networks with /V/ = 14 and /A/ = 19. It turns out that the network nodes with a higher connectivity or NuFBL are more important, which is consistent with the observation in the above neuronal signal transduction network. And, we observed the same result for networks with different sizes (see additional data file 1). Moreover, we found that the NuFBL is a better network measure than the connectivity in evaluating the functional importance of a network node.

Bottom Line: In this respect, we considered a feedback loop which is ubiquitously found in various biological networks.These results led us to infer that such a strong positive correlation between the NuFBL and the importance of a network node might be an intrinsic principle of biological networks in view of network dynamics.This result also suggests the existence of unknown feedback loops around functionally important nodes in biological networks.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Bio and Brain Engineering and KI for the BioCentury, Korea Advanced Institute of Science and Technology, 335 Gwahangno, Yuseong-gu, Daejeon, 305-701, Republic of Korea. kwon@soar.snu.ac.kr

ABSTRACT

Background: A number of studies on biological networks have been carried out to unravel the topological characteristics that can explain the functional importance of network nodes. For instance, connectivity, clustering coefficient, and shortest path length were previously proposed for this purpose. However, there is still a pressing need to investigate another topological measure that can better describe the functional importance of network nodes. In this respect, we considered a feedback loop which is ubiquitously found in various biological networks.

Results: We discovered that the number of feedback loops (NuFBL) is a crucial measure for evaluating the importance of a network node and verified this through a signal transduction network in the hippocampal CA1 neuron of mice as well as through generalized biological network models represented by Boolean networks. In particular, we observed that the proteins with a larger NuFBL are more likely to be essential and to evolve slowly in the hippocampal CA1 neuronal signal transduction network. Then, from extensive simulations based on the Boolean network models, we proved that a network node with the larger NuFBL is likely to be more important as the mutations of the initial state or the update rule of such a node made the network converge to a different attractor. These results led us to infer that such a strong positive correlation between the NuFBL and the importance of a network node might be an intrinsic principle of biological networks in view of network dynamics.

Conclusion: The presented analysis on topological characteristics of biological networks showed that the number of feedback loops is positively correlated with the functional importance of network nodes. This result also suggests the existence of unknown feedback loops around functionally important nodes in biological networks.

Show MeSH