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A copula method for modeling directional dependence of genes.

Kim JM, Jung YS, Sungur EA, Han KH, Park C, Sohn I - BMC Bioinformatics (2008)

Bottom Line: We have compared our results with those from other methods in the literature.Although microarray results show a transcriptional co-regulation pattern and do not imply that the gene products are physically interactive, this tight genetic connection may suggest that each gene product has either direct or indirect connections between the other gene products.Moreover, our copula approach can be extended to investigate the effects of local environments on protein-protein interactions.

View Article: PubMed Central - HTML - PubMed

Affiliation: Division of Science and Mathematics, University of Minnesota, Morris, MN, 56267, USA. jongmink@morris.umn.edu

ABSTRACT

Background: Genes interact with each other as basic building blocks of life, forming a complicated network. The relationship between groups of genes with different functions can be represented as gene networks. With the deposition of huge microarray data sets in public domains, study on gene networking is now possible. In recent years, there has been an increasing interest in the reconstruction of gene networks from gene expression data. Recent work includes linear models, Boolean network models, and Bayesian networks. Among them, Bayesian networks seem to be the most effective in constructing gene networks. A major problem with the Bayesian network approach is the excessive computational time. This problem is due to the interactive feature of the method that requires large search space. Since fitting a model by using the copulas does not require iterations, elicitation of the priors, and complicated calculations of posterior distributions, the need for reference to extensive search spaces can be eliminated leading to manageable computational affords. Bayesian network approach produces a discretely expression of conditional probabilities. Discreteness of the characteristics is not required in the copula approach which involves use of uniform representation of the continuous random variables. Our method is able to overcome the limitation of Bayesian network method for gene-gene interaction, i.e. information loss due to binary transformation.

Results: We analyzed the gene interactions for two gene data sets (one group is eight histone genes and the other group is 19 genes which include DNA polymerases, DNA helicase, type B cyclin genes, DNA primases, radiation sensitive genes, repaire related genes, replication protein A encoding gene, DNA replication initiation factor, securin gene, nucleosome assembly factor, and a subunit of the cohesin complex) by adopting a measure of directional dependence based on a copula function. We have compared our results with those from other methods in the literature. Although microarray results show a transcriptional co-regulation pattern and do not imply that the gene products are physically interactive, this tight genetic connection may suggest that each gene product has either direct or indirect connections between the other gene products. Indeed, recent comprehensive analysis of a protein interaction map revealed that those histone genes are physically connected with each other, supporting the results obtained by our method.

Conclusion: The results illustrate that our method can be an alternative to Bayesian networks in modeling gene interactions. One advantage of our approach is that dependence between genes is not assumed to be linear. Another advantage is that our approach can detect directional dependence. We expect that our study may help to design artificial drug candidates, which can block or activate biologically meaningful pathways. Moreover, our copula approach can be extended to investigate the effects of local environments on protein-protein interactions. The copula mutual information approach will help to propose the new variant of ARACNE (Algorithm for the Reconstruction of Accurate Cellular Networks): an algorithm for the reconstruction of gene regulatory networks.

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3D and contour plots for selected pairs of histone genes.
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Figure 4: 3D and contour plots for selected pairs of histone genes.

Mentions: Because of the small number of gene data sets, the estimates of FGM parameters and proportions for directional dependence in Table 1 do not strongly support our claim that each pair of these 8 histone genes are dependent on each other in both directions. Figure 4 shows 3-dimensional and contour plots for HTA1 vs HTB2, HTA2 vs HTB1, HTA2 vs HTB2, and HTB1 vs HTB2. Irregularly shaped contours indicate the existence of directional dependence, i.e., the asymmetry of dependence. From the plots, we see that the asymmetry of dependence is not clear for each pair of genes. Contour plots for other pairs of histone genes show similar patterns. Figure 4 together with Table 1 tells us that the 3D and contour plots are relatively symmetric which means a weak directional dependence in this gene data set.


A copula method for modeling directional dependence of genes.

Kim JM, Jung YS, Sungur EA, Han KH, Park C, Sohn I - BMC Bioinformatics (2008)

3D and contour plots for selected pairs of histone genes.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2386493&req=5

Figure 4: 3D and contour plots for selected pairs of histone genes.
Mentions: Because of the small number of gene data sets, the estimates of FGM parameters and proportions for directional dependence in Table 1 do not strongly support our claim that each pair of these 8 histone genes are dependent on each other in both directions. Figure 4 shows 3-dimensional and contour plots for HTA1 vs HTB2, HTA2 vs HTB1, HTA2 vs HTB2, and HTB1 vs HTB2. Irregularly shaped contours indicate the existence of directional dependence, i.e., the asymmetry of dependence. From the plots, we see that the asymmetry of dependence is not clear for each pair of genes. Contour plots for other pairs of histone genes show similar patterns. Figure 4 together with Table 1 tells us that the 3D and contour plots are relatively symmetric which means a weak directional dependence in this gene data set.

Bottom Line: We have compared our results with those from other methods in the literature.Although microarray results show a transcriptional co-regulation pattern and do not imply that the gene products are physically interactive, this tight genetic connection may suggest that each gene product has either direct or indirect connections between the other gene products.Moreover, our copula approach can be extended to investigate the effects of local environments on protein-protein interactions.

View Article: PubMed Central - HTML - PubMed

Affiliation: Division of Science and Mathematics, University of Minnesota, Morris, MN, 56267, USA. jongmink@morris.umn.edu

ABSTRACT

Background: Genes interact with each other as basic building blocks of life, forming a complicated network. The relationship between groups of genes with different functions can be represented as gene networks. With the deposition of huge microarray data sets in public domains, study on gene networking is now possible. In recent years, there has been an increasing interest in the reconstruction of gene networks from gene expression data. Recent work includes linear models, Boolean network models, and Bayesian networks. Among them, Bayesian networks seem to be the most effective in constructing gene networks. A major problem with the Bayesian network approach is the excessive computational time. This problem is due to the interactive feature of the method that requires large search space. Since fitting a model by using the copulas does not require iterations, elicitation of the priors, and complicated calculations of posterior distributions, the need for reference to extensive search spaces can be eliminated leading to manageable computational affords. Bayesian network approach produces a discretely expression of conditional probabilities. Discreteness of the characteristics is not required in the copula approach which involves use of uniform representation of the continuous random variables. Our method is able to overcome the limitation of Bayesian network method for gene-gene interaction, i.e. information loss due to binary transformation.

Results: We analyzed the gene interactions for two gene data sets (one group is eight histone genes and the other group is 19 genes which include DNA polymerases, DNA helicase, type B cyclin genes, DNA primases, radiation sensitive genes, repaire related genes, replication protein A encoding gene, DNA replication initiation factor, securin gene, nucleosome assembly factor, and a subunit of the cohesin complex) by adopting a measure of directional dependence based on a copula function. We have compared our results with those from other methods in the literature. Although microarray results show a transcriptional co-regulation pattern and do not imply that the gene products are physically interactive, this tight genetic connection may suggest that each gene product has either direct or indirect connections between the other gene products. Indeed, recent comprehensive analysis of a protein interaction map revealed that those histone genes are physically connected with each other, supporting the results obtained by our method.

Conclusion: The results illustrate that our method can be an alternative to Bayesian networks in modeling gene interactions. One advantage of our approach is that dependence between genes is not assumed to be linear. Another advantage is that our approach can detect directional dependence. We expect that our study may help to design artificial drug candidates, which can block or activate biologically meaningful pathways. Moreover, our copula approach can be extended to investigate the effects of local environments on protein-protein interactions. The copula mutual information approach will help to propose the new variant of ARACNE (Algorithm for the Reconstruction of Accurate Cellular Networks): an algorithm for the reconstruction of gene regulatory networks.

Show MeSH
Related in: MedlinePlus