Composite functional module inference: detecting cooperation between transcriptional regulation and protein interaction by mantel test
- Chao Wu†1,
- Fan Zhang†1,
- Xia Li1Email author,
- Shihua Zhang1,
- Jiang Li1,
- Fei Su1,
- Kongning Li1 and
- Yuqing Yan2
© Wu et al; licensee BioMed Central Ltd. 2010
Received: 9 December 2009
Accepted: 10 June 2010
Published: 10 June 2010
Functional modules are basic units of cell function, and exploring them is important for understanding the organization, regulation and execution of cell processes. Functional modules in single biological networks (e.g., the protein-protein interaction network), have been the focus of recent studies. Functional modules in the integrated network are composite functional modules, which imply the complex relationships involving multiple biological interaction types, and detect them will help us understand the complexity of cell processes.
We aimed to detect composite functional modules containing co-transcriptional regulation interaction, and protein-protein interaction, in our pre-constructed integrated network of Saccharomyces cerevisiae. We computationally extracted 15 composite functional modules, and found structural consistency between co-transcriptional regulation interaction sub-network and protein-protein interaction sub-network that was well correlated with their functional hierarchy. This type of composite functional modules was compact in structure, and was found to participate in essential cell processes such as oxidative phosphorylation and RNA splicing.
The structure of composite functional modules containing co-transcriptional regulation interaction, and protein-protein interaction reflected the cooperation of transcriptional regulation and protein function implementation, and was indicative of their important roles in essential cell functions. In addition, their structural and functional characteristics were closely related, and suggesting the complexity of the cell regulatory system.
Functional modules are basic units of cells that consist of molecules that work together to perform a desired biological function. The investigation of functional modules facilitates the understanding of the organization, regulation and execution of cell processes. Currently, several functional modules have been computationally extracted from the structural characteristics of biological networks, such as the transcriptional regulation networks, protein-protein interaction networks and metabolic networks [1–10]. However, these studies have mainly been performed on single networks, and cooperation between different types of networks is seldom considered.
The global cell network integrates single networks , such as the one governing transcriptional regulation, that appear to interact, rather than operate independently [12–16]. Recently, substantial cooperative structures called composite motifs have been discovered within integrated networks [13–15], and show functionally relatedness [13, 15]. These composite motifs include two nodes, three nodes and four nodes motifs, such as composite pairs of co-transcriptional regulation and protein-protein interaction (CT-PPI). Three reports [13, 15, 17] showed that composite pairs of CT-PPI (C-pairs of CT-PPI) played important roles in cell function, especially in protein complexes which were also one kind of functional modules. But not all protein complexes are with high consistency between co-transcriptional regulation interactions (CTs) and protein-protein interactions (PPIs). Using yeast as model, Nicolas Simonis et al and Kai Tan et al discovered that protein complexes in the cell were not significant co-regulated.
Thus, we wished to investigate cooperation among different networks in a higher network structure hierarchy. In this work, we investigated the composite functional module of co-transcriptional regulation and protein-protein interaction (CT-PPI modules), and explored its structural and functional characteristics. Co-transcriptional regulation interactions (CTs) and protein-protein interactions (PPIs) are basic regulatory structures of transcriptional regulation and protein function. Our results showed that CTs and PPIs were highly consistent within the CT-PPI modules, indicating the important role of CT-PPI modules in cooperation between transcriptional regulation and implementation of protein function. We detected 15 CT-PPI modules that participated in essential cell processes including the oxidative phosphorylation pathway, RNA splicing, and DNA-dependent positive transcription regulation.
Results and Discussion
Structural significance and functional coherence of composite CT-PPI pairs
However, they also behaved as functionally coherent units. A C-pair was considered to be functionally coherent if both genes were annotated under the same GO term. Using a background of general (GO terms in our integrated network) or narrow (leaf terms) annotations, and considering only CC and BP branches, we compared the functional coherence fraction of 168 C-pairs to 38,351 CT pairs, and 1434 PPI pairs. A higher fraction of the C-pairs were functionally coherent, than the CT and PPI pairs (Figure 2B).
This result demonstrated that the cooperation between CTs and PPIs had important network structure and cell function effects. We searched for additional CT-PPI modules and investigated their characteristics.
Detecting CT-PPI modules
Functional modules in single networks are usually detected from "structure to function", meaning that modules are searched first by network, then by functional annotation analysis [1–9]. We chose a "function to structure" method to detect CT-PPI modules by first defining the functional module, and then conducting topological analysis for consistency between CT and PPI sub-networks. The detail is shown in Figure 1. First, we constructed an integrated network of CTs and PPIs in Saccharomyces cerevisiae. Proteins were grouped into different functional modules according to their gene ontology (GO) annotations . Finally, we used a network structure comparison Mantel test  to detect CT-PPI modules by their structural consistency between CT and PPI sub-networks in a given functional module.
We obtained 47 functional modules with a significant r value. We investigated the structural consistency of these functional modules to detect CT-PPI modules.
Association between structural consistency and functional hierarchy of CT-PPI modules
coenzyme biosynthetic process
proton-transporting two-sector ATPase complex
group transfer coenzyme metabolic process
ribonucleoside triphosphate biosynthetic process
purine ribonucleotide biosynthetic process
mitochondrial membrane part
mitochondrial inner membrane
small nuclear ribonucleoprotein complex
condensed nuclear chromosome
positive regulation of transcription, DNA-dependent
Global structural consistency of CT-PPI modules
Significance and corresponding rank of CT-PPI modules in enrichment analysis method
Considering only local consistency generated many functional modules enriched with C-pairs. Of 198 functional modules containing C-pairs in the integrated network, 140 were enriched with C-pairs (p < 0.01). This relatively large number changed little as p decreased, so that even at p < 1 × 10-10, 41 functional modules were still found to be enriched with C-pairs (see Additional file 2), although this level of cooperation between CTs and PPIs associated with cell functions is implausible (Additional file 3). In addition, no clear relationship between p (representing the degree of enrichment of C-pairs in functional modules), and the functional hierarchy of such functional modules was found (Additional file 4).
Structure compactness of CT-PPI modules
In single networks, links between genes in a module are more compact than links to genes in other modules . If the inner link density C in , was greater than the outer link density C out, we considered the module compact (see Materials and Methods for detailed definitions of C in and C out ). Compactness analysis of the functional modules separated the integrated network into CT and PPI networks, then examined the compactness of these sub-networks of functional modules. If both sub-networks were compact, we considered the integrated sub-network compact.
CT-PPI modules involved in essential functions
Functions of CT-PPI modules
TFs regulated C-pairs of CT-PPI
positive regulation of
condensed nuclear chromosome
We investigated the transcriptional factors (TFs) regulating the C-pairs in the nine compact CT-PPI modules. Although many TFs regulated more than one gene in the nine CT-PPI modules, only HAP4 regulated C-pairs (Table 3). This suggested that HAP4 plays an important role in the regulation of the oxidative phosphorylation pathway, especially complexes III, IV and V, consistent with a previous report .
CT-PPI modules GO:0005684 and GO:0030532 appeared to affect RNA splicing, and shared TF genes STE12 and DIG1 with the CT-PPI modules GO:0045893 (Table 3). However, the term description of GO:0045893 in GO shows it plays roles in "the positive regulation of transcription, DNA-dependent". Transcription and RNA splicing are time-sequential, so shared TFs ensures the coordination of these two processes. We conclude that these CT-PPI modules participate in transcription, which, if interrupted, prevents successful production of mRNA and protein.
CT-PPI modules GO:0007131 and GO:0000794 both appeared to have roles in DNA structure changes in meiosis. CT-PPI modules GO:0000790 annotated as "nuclear chromatin", which is also involved in the chromosome formation. These three CT-PPI modules seemed to be involved in the maintenance and transmission of genetic material.
The above analysis shows that CT-PPI modules are involved in essential eukaryote cellular functions. Their network structure, evaluated as consistency of CT and PPI, reflects the cooperation of transcriptional regulation and implementing protein function, with this type of structure ensuring stable regulation. The network characteristic of CT-PPI modules ensures the stable regulation of their functions.
Our results indicated that cooperation between CT and PPI is important to cell regulation. CT-PPI modules, which reflect the cooperation between CT and PPI in a module, were involved in essential cell functions. In addition, C-pairs, which reflected cooperation between CT and PPI motifs, were functionally coherent.
Our results also suggest that the structure and function of CT-PPI modules are closely related. Their network structure appeared to be conserved, as it coordinated two basic regulatory structures (CT and PPI). This type of structure could help ensure the stability of essential functions. Structural consistency and functional hierarchy in CT-PPI modules were associated, with their both functional and structural modularity. These findings reflect a close relationship between the structure and function of CT-PPI modules and show the complexity of cell regulation.
Many studies have investigated the relationship between the structure and function of special structures within networks, but findings have differed and the relationships have been ambiguous [13–15, 25–31]. In eukaryotes, cell networks have undergone evolutionary pressure for billions of years, generating special structures. Molecular evolution hypothesizes that most evolutionary events behave non-directionally, so special structures that occur in the network do not always carry out corresponding functions. Therefore, we propose that investigating the biological meaning implied in the structures before exploring their functions is the most logical method of studying network structures.
Experimentally identified interactions between TFs and their target genes in S. cerevisiae were extracted from chip-chip experiments , with data treated as Liao et al.  (p < 0.001). We obtained 4433 TIs for 113 TFs and 2400 target genes. If target genes shared TF (or TFs), we considered them co-regulated. In total, 167,708 CTs were found among 2376 genes.
Experimentally identified PPIs were extracted from the Database of Interacting Proteins (downloaded on September 2007) , yielding 17491 PPIs among 4392 genes, excluding homomultimeric proteins.
By overlapping the two data sets, we found 1856 genes with both types of links. For these genes, we selected GO items (layer > 5, annotated genes > 9 in BP and CC branches), and performed GO annotation analysis (downloaded on September 2007). Gene sets with ascendant and descendant GO terms were filtered for the descendant. We obtained 1107 genes annotated with 300 items (100 BP, 200 CC), with 38,351 CTs and 1434 PPIs. We defined a functional module as a gene group annotated in the same GO term in the integrated network.
Structure significance analysis of C-pairs
We defined the number of C-pairs in the integrated network as N real , randomized the integrated network, and defined the number of C-pairs as N rand . The integrated network was randomized according to Yeger-Lotem et al. . The integrated network was separated into CT and PPI networks. The two were randomized while keeping the degrees of nodes in each network unchanged, then integrated, for a total of 1000 randomizations. To our work, N real = 168, N rand = 109.8 ± 9.66 and the corresponding Z score = 6.03.
Functional coherence analysis of C-pairs
When comparing C-pairs with CT pairs,
x was the number of functionally coherent C-pairs in the integrated network,
M was the number of CT pairs,
K was the number of functionally coherent CT pairs, and
N was the number of C-pairs.
C-pairs were compared to PPI pairs in the same way.
Replacing the 300 GO terms with leaf GO terms and repeating the processing gave results under the narrow annotation system.
Detecting CT-PPI modules
To detect CT-PPI modules, we used Mantel test, which accounts for distance correlations, to measure the consistency between the CT and PPI sub-networks of a functional module. The simple Mantel test was used to calculate the similarity of two symmetric matrices. Parameter r was a measure of similarity between matrices, and was the Pearson correlation coefficient of the corresponding elements in the lower or upper triangular parts of the two matrices. Parameter p, which measures the significance of the Pearson correlation coefficient r, was calculated as the probability that the number of r in the randomized networks would be equal to or greater than that in the real network.
Where A was the adjacency matrix representing the PPIs among 1107 genes. A ij was the Boolean value representing the interaction between protein i and j. When A ij = 1, PPI existed between i and j, and if A ij = 0 it did not. B was the adjacency matrix representing the CTs among 1107 genes. B ij was the boolean value representing co-regulation between proteins i and j. If B ij = 1, CT existed between genes i and j, and if B ij = 0 it did not.
In this study, r represented the consistency between the CT and PPI sub-networks of a functional module, and p represented the significance of the consistency.
We used zt software , designed for Mantel tests, to calculate the consistency between CT and PPI sub-networks of the 300 functional modules. To test the significance of consistency, 10,000 randomizations were performed. We used p < 0.01 (FDR q value < 0.05) as the threshold.
Enrichment analysis of C-pairs
When analyzing the enrichment of C-pairs in a functional module m;
a was the number of C-pairs in the functional module m,
X was equal to , was the total number of genes in the integrated network,
Y was the number of C-pairs in the integrated network,
Z was equal to , and was the number of genes in the functional module m.
Structure compactness analysis of CT-PPI modules
All the genes in a functional module were designated inner genes, and those outside a functional module were designated outer genes. For a functional module, the inner link density was defined as C in = L in /G in and the outer link density as C out = L out /G out .
L in was the number of links between inner genes,
G in was the number of inner genes with links to other inner genes,
L out was the number of links between G in inner genes and outer genes.
G out was the number of outer genes with links to G in inner genes,
If C in was greater than C out , we recognized the functional module as compact.
This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 30871394, 30370798 and 30571034), the National High Tech Development Project of China, the 863 Program (Grant Nos. 2007AA02Z329), the National Basic Research Program of China, the 973 Program (Grant Nos. 2008CB517302) and the National Science Foundation of Heilongjiang Province (Grant Nos. ZJG0501, 1055HG009, GB03C602-4, JC200711 and BMFH060044).
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