Volume 12 Supplement 3
Assessing the utility of gene co-expression stability in combination with correlation in the analysis of protein-protein interaction networks
© Patil et al; licensee BioMed Central Ltd. 2011
Published: 30 November 2011
Gene co-expression, in the form of a correlation coefficient, has been valuable in the analysis, classification and prediction of protein-protein interactions. However, it is susceptible to bias from a few samples having a large effect on the correlation coefficient. Gene co-expression stability is a means of quantifying this bias, with high stability indicating robust, unbiased co-expression correlation coefficients. We assess the utility of gene co-expression stability as an additional measure to support the co-expression correlation in the analysis of protein-protein interaction networks.
We studied the patterns of co-expression correlation and stability in interacting proteins with respect to their interaction promiscuity, levels of intrinsic disorder, and essentiality or disease-relatedness. Co-expression stability, along with co-expression correlation, acts as a better classifier of hub proteins in interaction networks, than co-expression correlation alone, enabling the identification of a class of hubs that are functionally distinct from the widely accepted transient (date) and obligate (party) hubs. Proteins with high levels of intrinsic disorder have low co-expression correlation and high stability with their interaction partners suggesting their involvement in transient interactions, except for a small group that have high co-expression correlation and are typically subunits of stable complexes. Similar behavior was seen for disease-related and essential genes. Interacting proteins that are both disordered have higher co-expression stability than ordered protein pairs. Using co-expression correlation and stability, we found that transient interactions are more likely to occur between an ordered and a disordered protein while obligate interactions primarily occur between proteins that are either both ordered, or disordered.
We observe that co-expression stability shows distinct patterns in structurally and functionally different groups of proteins and interactions. We conclude that it is a useful and important measure to be used in concert with gene co-expression correlation for further insights into the characteristics of proteins in the context of their interaction network.
mRNA expression information is often used in combination with protein-protein interaction networks in order to provide a better perspective on proteins and their inter-relationships in the cell. mRNA co-expression of genes across various conditions is quantified in the form of a correlation coefficient of their expression levels across multiple samples. Co-expression correlation has been used in the prediction of protein-protein interactions , though with limited success . Other studies have used the combination of protein-protein interaction information and gene co-expression correlation to identify functional modules of proteins that are active in a particular disease state [3, 4], the rate of evolution of proteins , and the levels of disorder in co-regulated proteins . It has also been used as the primary means of classifying hub proteins in protein-protein interaction (PPI) networks into date hubs and party hubs , or inter-modular and intra-modular hubs , independently and in combination with gene expression stability [9, 10]. In spite of being widely studied, this classification has not been replicated [11, 12] and gene co-expression correlation as a sole means of classifying hubs has been shown to be unreliable , stressing the need for the use of additional information.
Undoubtedly, gene co-expression correlation is an important characteristic when used in the context of protein-protein interaction networks. However, it is often biased due to disproportionately large contributions of a few samples . For instance, genes that are expressed in the same tissue often show a misleadingly high correlation coefficient in spite of the lack of a functional relationship. Gene co-expression stability quantifies the bias in the correlation coefficient by indicating the change in co-expression of a pair of genes on the removal of samples contributing most to the correlation coefficient. It has been shown that genes with high stability are functionally related in spite of low correlation coefficients. On the other hand, those with low stability have fragile co-expression which implies limited, or no functional relation . Thus, the co-expression stability may be viewed as a reliability measure of the co-expression correlation coefficient. The combination of correlation and stability represents the co-expression of genes across multiple samples along with the amount of bias there-in.
In this study, we investigate the usefulness of the gene co-expression stability in concert with co-expression correlation in the analysis of various characteristics of gene pairs in the context of the human protein-protein interaction network. Specifically, we study the relationship of gene co-expression correlation and stability with the interaction promiscuity of proteins, their levels of intrinsic disorder and their tendency towards essentiality and disease-relatedness. We demonstrate that the gene co-expression stability is a useful means of distinguishing different kinds of proteins in the protein-protein interaction network and can be used with the co-expression correlation coefficient for more effective analysis.
In order to evaluate the utility of gene co-expression stability in combination with co-expression correlation coefficient, we used a high confidence human protein-protein interaction network from the database, HitPredict . Gene co-expression correlation coefficients were calculated for interacting protein pairs over 18800 samples from the Gene Expression Omnibus  and normalized using the MAS5 algorithm. Stability was calculated as shown in Kinoshita and Obayashi  and briefly described in the Methods (Equation 1). Genes pairs with co-expression correlation coefficient less than 0.2 were ignored since the stability measure was not found to be sufficiently informative below this threshold. This gave a dataset of 8182 interactions among 3715 proteins. We looked at various properties of the proteins and the interactions in relation to their gene co-expression correlation and stability.
Co-expression correlation and stability in the protein-protein interaction network
The average co-expression correlation coefficient and stability for each protein were calculated as shown in Equations 2 and 3, respectively (See Methods). Proteins show a distribution that is similar to interactions in the correlation coefficient and stability landscape (Figure 1b). Co-expression correlation and stability show no correlation (Spearman's rank correlation=0.013, p=0.22). There are, however, a few outliers with larger values of correlation and stability. Average co-expression correlation coefficients for proteins with low stability must be used with caution due to the large amount of bias.
Hubs and hub types in the protein-protein interaction network
Network characteristics of hub proteins in 3 categories.
Average clustering coefficient
Average betweenness centrality (10-4)
Category 1 (41 hubs)
Category 2 (264 hubs)
Category 3 (315 hubs)
Hubs in Category 1 have a high clustering coefficient and low betweenness centrality (Table 1, See also Figure S2 in Additional File 1). These hubs have a high co-expression correlation and a high stability with their interaction partners. Taken together, this implies that hubs in Category 1 correspond to obligate hubs or intra-modular hubs that are parts of complexes and constitutively expressed with their interaction partners. A Gene Ontology (GO) term enrichment analysis confirms this result with significantly enriched terms like DNA replication initiation, DNA replication checkpoint, proteasome core complex, MCM complex, etc (Tables S2-S4 in Additional File 1). Examples of category 1 hubs include proteasome complex subunits and ORC subunits among others.
On the other hand, Category 2 hubs, which have a low co-expression correlation and high stability, have low a clustering coefficient and high betweenness centrality indicating their inter-modular nature. The low co-expression correlation of these hubs denotes the ability to participate in transient interactions. The high stability values show low levels of bias in the correlation coefficients. These hubs are significantly enriched for GO terms like Ras protein signal transduction, ATP binding and transcription factor complex among others (Tables S2-S4 in Additional file 1), signifying roles in signal transduction and transcription regulation. BRCA2, p53 and NF kappa B are some of the hubs in category 2. Categories 1 and 2 correspond to the party and date hubs respectively, as proposed by Han et al. . This distinction is further supported by the fact that hubs in both these categories show high co-expression stability indicating that their co-expression correlation coefficients are not fragile.
Hubs in category 3 have low co-expression correlation and low stability with their interaction partners. The low co-expression correlation and stability indicates high variation in co-expression and fragile correlation coefficients. These hubs have network characteristics that are intermediate to those of category 1 and 2 hubs, with low clustering coefficient but also low betweenness centrality. This indicates that the hubs in category 3 are neither inter-modular, nor intra-modular, but belong to an entirely different class. GO term analysis confirms this result by showing significantly enriched terms like nuclear mRNA splicing via spliceosome, mRNA transport and RNA binding, spliceosome (Tables S2-S4 in Additional file 1). This class includes several small nuclear ribonucleoproteins. In spite of their inherent functional differences, the hubs in categories 2 and 3 are often combined into a single class of transient (date, inter-modular) hubs in classification systems using average co-expression correlation coefficient alone. The use of stability helps separate these hubs further into two functionally distinct groups.
This result demonstrates the ability of the stability measure as an information source that is independent of the co-expression correlation coefficient. More importantly, this analysis shows that the currently accepted classification of hubs into just two types -transient and obligate - using co-expression correlation coefficient alone, is insufficient to separate the many functionally distinct groups that exist in the PPI network. Using different measures along with the co-expression correlation coefficient will improve the identification of these groups.
Intrinsic disorder in interacting proteins
Finally, when combined with the previously described categories in hubs, this result shows that not all hubs have high levels of intrinsic disorder. Specifically, hubs in categories 1 and 2 show high levels of intrinsic disorder. On the other hand, hubs in category 3, which have fragile co-expression correlation, show low levels of disorder. It is possible that the fragile patterns of co-expression are not conducive to the presence of large disordered regions in these proteins. Thus, with the help of co-expression stability and correlation information, we can conclude that the amount of intrinsic disorder affects the expression patterns of hubs, and proteins, in general.
Interactions between ordered and disordered proteins
Given the differences in the levels of co-expression patterns of proteins with high levels of intrinsic disorder, we examined these patterns for interactions between proteins with high or low levels of disorder. We specifically looked at distributions of co-expression correlation and stability for interactions where both interacting proteins have high levels of intrinsic disorder (intrinsic disorder >= 30%), one protein has high levels of intrinsic disorder, and both proteins are ordered (intrinsic disorder < 30%).
These results show that interacting protein pairs with varying levels of intrinsic disorder show distinct patterns of not only co-expression correlation, but also stability, being either constitutively or transiently expressed with their partner proteins.
Essential and disease genes
Thus, co-expression stability provides additional information about genes and their functions when used with gene co-expression correlation.
Gene co-expression stability has been used to identify the functional relationship between pairs of co-expressed genes in Arabidopsis thaliana. However, functional relation is a foregone conclusion in the context of two interacting proteins. Hence, we tried to assess the utility of co-expression stability of interacting proteins in order to elucidate the relationships between proteins and the nature of their interactions. This is an important aspect of the study of PPI networks, since the current static data of protein interactions does not necessarily reflect the spatial and temporal relationships between the interacting proteins under physiological conditions. Our primary goal throughout this study has been to look for specific patterns of stability in distinct groups of proteins and interactions, which are separate from their patterns of co-expression correlation. We were able to find such differences in several groups of proteins and interactions, allowing us to conclude that stability is an informative measure, which when used in combination with co-expression correlation, provides information that is otherwise inaccessible.
A case in point is the identification of a class of hubs having characteristics that are distinct from the currently accepted transient and obligate hubs. Not only does this result highlight the usefulness of the stability measure, but it also shows the insufficiency of using the co-expression correlation alone as a means of classifying hubs. Different measures like stability are needed to broaden this classification. Gene expression stability has been proposed as one such measure , as is simple GO term based classification .
The distinct patterns of co-expression correlation and stability for proteins with different levels of intrinsic disorder, and different disease annotations, further confirm the utility of using the combination of correlation and stability. This also leads to new insights about the proteins and their properties. For instance, we find that proteins with low co-expression stability have low levels of intrinsic disorder. In another example it is observed that non-essential disease genes primarily participate in obligate interactions as indicated by their high correlation and stability. Such inter-relationships are easily elucidated through the combined usage of correlation coefficients and stability.
Other measures that have been similarly used in combination with the co-expression correlation include the gene expression variability and the rank of co-expression correlation. The gene expression variability, in the form of standard deviation, has been successfully used to classify hubs  and identify selective gene expression patterns . Rank of co-expression correlation between genes has also been used to address the issue of bias in co-expression correlation. The absolute values of correlation often change with the samples used for calculation making it difficult to introduce a single threshold value to determine significantly correlated gene pairs. The rank of correlation provides a solution for this problematic bias. It works as a better indicator of functionally related genes than the correlation coefficient . Since rank of correlation is a general approach, multidimensional correlation – that have been used to calculate the stability - can be converted into multidimensional rank by considering the rank of correlation in each dimension. We have not checked the efficiency of the multidimensional rank, but it will be interesting to compare the results obtained using the stability measure with rank measures as well.
It is also conceivable to use the stability measure as a parameter in prediction studies along with the co-expression correlation, either in the prediction of different classes of proteins, like disordered or ordered, or those that are active in different diseases or functional modules. The gene co-expression stability is an extensible and easily accessible measure. Values for gene co-expression stability can be obtained for several species, including human, from COXPRESdb , and for Arabidopsis thaliana from ATTEDII . In this study, we have limited ourselves to assessing the utility of this measure. However, each of the findings needs to be explored independently in greater detail.
We assessed the utility of the gene co-expression stability as a measure for further understanding the properties of proteins and their inter-relationships within the human protein-protein interaction network, in combination with gene co-expression correlation. We demonstrate that different types of proteins and interactions not only show distinct patterns of co-expression correlation but also of co-expression stability. We show the inadequacy of co-expression correlation as a means of classifying hubs and find that stability improves its performance. Specifically, we identify transient and obligate hubs along with a previously unknown type that is functionally distinct. Other patterns that we elucidated include low co-expression correlation and high stability of protein with high levels of intrinsic disorder. This combination of parameters also gives distinct co-expression patterns for pairs of interacting proteins that are highly ordered or disordered. We also show that disease and essential genes have very high co-expression stability and thus stable co-expression patterns with their interaction partners, independent of their co-expression correlation. Finally, we show that genes in different classes of diseases have distinct co-expression stability providing a possible means of distinguishing them based on co-expression and interaction patterns. Thus, we show that gene co-expression stability is a useful measure to be used in concert with co-expression correlation and provides additional information leading to a better understanding of proteins in PPI networks. Future prospects include studying each of the results obtained here in greater detail, comparing our results with other measures of gene co-expression stability, as well as implementing a predictor using this combination in the prediction of membership of proteins to distinct classes.
High confidence human protein-protein interactions were taken from the HitPredict  database. Hubs within the entire network were denoted as proteins with 5 or more interactions. This definition of hubs has previously been shown to be robust . Hubs in each category based on gene expression correlation and stability, were denoted as proteins having 5 or more interacting partners with whom they show specific levels of co-expression correlation and stability as required by the category cutoffs.
where cor i is the correlation without the first i PCs, cor max is the maximum value from cor 0 to cor 10 , i = 0..N, and N = 10.
Pairs of genes with cor 0 less than 0.2 were ignored since the stability measure for these was not found to be sufficiently informative. Using protein pairs in the interaction network with co-expression correlation and stability values, resulted in 8182 interactions among 3715 proteins.
where n = number of interactions of the protein,
r ai = co-expression correlation coefficient in PC space (cor0 in equation (1)) for genes of protein a and it’s i th interaction partner
where n = number of interactions of the protein,
S ai = co-expression stability for genes of protein a and it’s i th interaction partner as calculated by equation (1)
where N = number of hubs in category i,
CC j = clustering coefficient of hub j in category i
where N = number of hubs in category i,
BC j = clustering coefficient of hub j in category i
Significantly enriched Gene Ontology (GO) terms  for Biological Process, Molecular Function and Cellular Component in each category of hubs were determined separately using the hypergeometric distribution at a significance level of p < 0.01.
Intrinsic disorder was predicted in all proteins using the program metaPrDOS  at a false positive rate of 5%. Regions with 30 consecutive residues predicted as disordered were considered as disordered regions. Interaction types were assigned based on the intrinsic disorder content in the interacting proteins. Table S5 in Additional File 1 gives the number of interactions in each type.
Disease and essential genes were obtained as in Goh et al.  Disease annotations for proteins in the PPI network were obtained from the Online Mendelian Inheritance in Man (OMIM) . Essential genes were identified as orthologs of mouse genes whose disruption was lethal in the embryonic or postnatal stages, as obtained from Mouse Genome Informatics (MGI) . Disease classes, as given by Goh et al. , were assigned to disease genes. The number of disease and essential genes found in the dataset are shown in Table S6 in Additional File 1.
List of abbreviations
Principal component analysis
Pearson’s correlation coefficient.
Acknowledgements and funding
We would like to thank Dr. Takashi Ishida for help with predicting the disordered regions in proteins using metaPrDOS. Computation time was provided by the Super Computer System, Human Genome Center, Institute of Medical Science, University of Tokyo. This work was supported by the Annual Research Budget provided to KK by the Graduate School of Information Science, Tohoku University and Japan Society for the Promotion of Science (JSPS) through its Funding Program for World-Leading Innovative R&D in Science and Technology (FIRST Program).
This article has been published as part of BMC Genomics Volume 12 Supplement 3, 2011: Tenth International Conference on Bioinformatics – First ISCB Asia Joint Conference 2011 (InCoB/ISCB-Asia 2011): Computational Biology. The full contents of the supplement are available online at http://www.biomedcentral.com/1471-2164/12?issue=S3.
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