Consistent dissection of the protein interaction network by combining global and local metrics
© Wang et al.; licensee BioMed Central Ltd. 2008
Received: 22 June 2007
Accepted: 21 December 2007
Published: 21 December 2007
We propose a new network decomposition method to systematically identify protein interaction modules in the protein interaction network. Our method incorporates both a global metric and a local metric for balance and consistency. We have compared the performance of our method with several earlier approaches on both simulated and real datasets using different criteria, and show that our method is more robust to network alterations and more effective at discovering functional protein modules.
Protein complexes are building blocks of cellular components and pathways. A comprehensive understanding of a biological system requires knowledge about how protein complexes are assembled, regulated, and organized to form cellular components and perform cellular functions. The emergence of a variety of genomic and proteomic techniques to systematically obtain such information has generated an enormous amount of data [1–11]. However, interpretation and analysis of such data in terms of biological function has not kept pace with data acquisition, mainly due to the complexity of the problem and the limitation of current techniques to handle the data.
In this paper, we address the issue of constructing protein interaction modules from the protein interaction data. Highly connected protein modules are mostly found to be protein complexes performing a specific biological function. The concept of protein interaction modules as fundamental functional units was first outlined by Hartwell et al. . Protein interaction modules are composed of a variable number of proteins, with discrete functions arising from their individual constituents and their synergistic interactions. A multi-protein complex, such as the ribosome, is one common form of interaction module; other examples of protein functional modules include proteins working collectively in a pathway, such as signal transduction, that do not necessarily form a tightly associated, stable protein complex.
To detect protein interaction modules from protein interaction data, we use a graph theory approach. Protein interaction networks are routinely represented as graphs, with proteins as nodes and interactions as edges. In a graphical representation of a protein interaction network, a functional unit, or a group of functionally related proteins, is tightly connected as a community, while proteins from different functional units are more loosely connected. In the past few years, new algorithms have been developed to extract communities from a generic network. Girvan and Newman  proposed a decomposition algorithm (GN algorithm) to analyze community structure in networks. Their algorithm iteratively removes edges based on betweenness values, the number of shortest paths between all pairs of nodes in the network running through an edge, in contrast to the traditional hierarchical clustering algorithm where closely connected nodes are iteratively joined together into larger and larger communities. In a different approach, Radicchi et al.  replaced the edge betweenness metric with an edge clustering coefficient - the number of triangles to which a given edge belongs, divided by the number of triangles that might potentially include it, given the degrees of the adjacent nodes. The edge clustering coefficient is a local topology-based metric and a candidate edge with the lowest clustering coefficient is removed one at a time in the algorithm of Radicchi et al. (the 'edge clustering coefficient' algorithm, ECC algorithm for short).
When applied to a large network, these two algorithms give substantially different results. The reason is that an individual edge with larger betweenness does not necessarily have a lower clustering coefficient, although on average it will. Ultimately, the global metric in the GN algorithm behaves differently from the local metric in the ECC algorithm. In this paper, we propose to resolve this conflict by combining the global and local metrics to form a consistent and robust algorithm. We make three additional significant contributions: a new metric (commonality) that takes into account the effects of random edge distributions; a new definition of a protein interaction module; and a novel filtering procedure to remove false-positive interactions based on a random graph model analysis. We demonstrate that our new algorithm is more effective and robust in terms of discovering protein interaction modules in protein interaction networks than either the global or local algorithm by application to the large yeast protein interaction network.
Results and discussion
The principal result of this paper is the development of a new algorithm for extracting protein interaction modules from a protein interaction network. We first present the new methodology developments and then compare the performance of different algorithms, including the MCL algorithm , on simulated networks where protein complexes were known. The MCL algorithm is a fast and scalable unsupervised cluster algorithm for graphs based on simulation of stochastic flow in graphs  and was found to be overall the best performing one by the Brohee and van Helden study . Note that our proposed new algorithm, the GN algorithm, and the ECC algorithm are divisive partitioning-type algorithms, while the MCL algorithm is a non-partitioning algorithm. Both the modularity  measure and productive cuts in the following sections are not applicable to the MCL algorithm. Second, we compare the results of different algorithms on a small protein interaction network where protein complexes are largely known. Lastly, we apply our new algorithm, the GN algorithm, the ECC algorithm, and the MCL algorithm, whenever applicable, to two large yeast protein interaction networks and evaluate the performance of each algorithm based on the value of modularity , overlap with Munich Information Center for Protein Sequences (MIPS) complexes  and Gene Ontology (GO) term enrichment of each cluster.
A new commonality metric
Our goal is to discover protein interaction modules. Intuitively, when two protein functional modules are sparsely connected, edges between them should have higher edge-betweenness values and lower commonality, whereas edges within a module should have high commonality and low edge-betweeness. Thus, for sparsely connected functional modules, edge-betweenness highly correlates with edge-commonality. When protein functional modules overlap, the correlation between the global metric and local metric becomes less clear. For this reason, we combine these two metrics to build a more consistent and robust metric. The new BCD (Betweenness-Commonality Decomposition) algorithm is summarized as follows: step 1, calculate the edge commonality (C) for each edge in the network; step 2, calculate the edge-betweenness (B) for each edge in the current subnetwork; step 3, remove the edge with the maximal ratio B/C; and step 4, repeat steps 2 and 3 until no edges remain.
Like the edge clustering coefficient in the ECC algorithm, the edge commonality is a static property of an edge in the context of the entire network, telling how strong the affinity is between two nodes it connects. The edge commonality is calculated only once at the beginning of a decomposition process, while the edge-betweenness is updated each time an edge is removed to achieve best results . This algorithm runs with O(M2N) computational complexity, where M is the number of edges and N is the number of nodes in a network. As a practical matter, we calculate the betweenness using the fast algorithm of Brandes  where the edge-betweenness value can be obtained by summing pair-dependencies over all traversals , so that we can easily parallelize the computationally costly betweenness calculation.
A new definition of protein interaction module
Intuitively, a protein interaction module is a subnetwork in the protein interaction network with more internal interactions than external interactions. A precise definition of the interaction module is not trivial. A number of definitions of community (or protein interaction module in terms of the protein interaction network) have been proposed with different criteria [14, 17, 22]. No clear consensus of module definition exists.
Filtering false-positive interactions
Most yeast protein interaction data were obtained from large-scale, high-throughput experiments, which generally contain false positives . To minimize the number of false positive interactions, we apply a statistical test to measure the reliability of an interaction (edge). We rigorously calculate the statistical significance of each interaction between two proteins as the random probability (P value) that the number of common interacting partners occurs at or above the observed number. Previous work has shown that the statistical significance based on the number of common interacting partners highly correlates with the functional association of two proteins [24, 25].
where k0 is the observed number of common partners shared by two interacting proteins. An interaction with P value greater than 0.01 is considered to be a 'false positive' and is discarded. We remove the edge with the highest P value and recalculate the P value for affected edges. The process is repeated until no edge has a P value > 0.01. We found in analysis of yeast data, this filtering always improves the quality of discovered protein interaction modules.
Application to simulated yeast protein interaction networks
To compare the performance of our BCD algorithm, the GN algorithm, the ECC algorithm with the original edge clustering coefficient definition (ECC1), and the ECC algorithm with our commonality metric (ECC2), and the MCL algorithm , in which the inflation parameter was set to the optimal value 1.8 according to the study , we built a test graph on the basis of 198 complexes manually annotated in the MIPS database  in a way similar to that used in Brohee and van Helden's study . Briefly, for each manually annotated MIPS complex, an edge was created between each pair of proteins within that complex. The resulting graph (referred to as test graph) contains 1,078 proteins and 9,919 interactions. To evaluate the robustness to false positives and false negatives, we derived 16 altered networks by randomly removing edges from or adding edges to the test graph in various proportions. We then assessed the quality of clustering results on each derived network by different algorithms with each annotated complex. As done in Brohee and van Helden's study , we computed a geometric accuracy value and a separation value to estimate the overall correspondence between a clustering result (a set of clusters) and the collection of annotated complexes, where both a high geometric accuracy value and a high separation value indicate good clustering (please see  for more details).
Application to the yeast protein interaction network
We used the yeast protein interaction network from the BioGrid database (version 2.0.24) , from which we extracted 36,238 unique interactions among 5,273 yeast proteins. We applied the filtering process to the data and the resulting dataset retained 3,030 yeast proteins and 17,242 high-confidence interactions, which we call the filtered dataset. On both the original and filtered datasets, we tested five algorithms: our BCD algorithm, the GN algorithm, the ECC1 algorithm with its original edge clustering coefficient, the ECC2 algorithm with our commonality metric and the MCL algorithm whenever applicable.
Results on a small yeast protein interaction network
Before diving into the entire complex network, we first decomposed a small yeast transcription network with 225 proteins and 1,792 interactions, where known protein interaction modules can be inferred from the annotations of well-studied proteins (Figure 2a). Figure 2b displays a hierarchical decomposition tree by the BCD algorithm (decomposition trees constructed by the other three algorithms are provided in Additional data file 1). Note that there is no decomposition tree for the MCL algorithm.
The proposed definition of protein interaction module works well for both the GN and BCD algorithms because almost all proteins within the same computed protein module do indeed belong to the same known protein complex. Decomposition trees obtained using the ECC1 algorithm and the ECC2 algorithm with our commonality metric are shown in Additional data file 1. They produce irregularly large modules and an excess number of singletons. This suggests that the purely local metric used in the ECC algorithm is not effective. Additional data file 1 also shows good results for both the GN and BCD algorithms that combine global and local metrics. They clearly produce more consistent and robust results.
The BCD algorithm revealed 21 functional modules (Figure 2); all proteins within known protein complexes are also located within the same module, suggesting that the BCD algorithm is superior at unveiling fine structure buried in complex protein interaction networks. The MCL algorithm predicts only 11 clusters from this small yeast transcription network. Several functional modules are grouped together: the three RNA dependent RNA polymerases (A, B, C) and the RNA polymerase II mediator complex are merged into one cluster; the NuA4 histone acetyltransferase complex, the SWR1 complex, and the INO80 chromatin remodeling complex are grouped into one cluster; the TFIIA complex, the Elongator complex, the SAGA histone acetyltransferase complex, and the TFIID complex are grouped into one cluster; and the COMPASS complex and the mRNA cleavage and polyadenylation specificity complex (CPF) are grouped into one cluster. Apparently, the MCL algorithm is inefficient in discovering boundaries between functionally related protein complexes and tends to group them together. The quality of modules obtained using the GN algorithm is not as good; members of four functional modules, transcription factor IIA (TFIIA) [TOA1, TOA2], TFIID [TAF2, TAF3, TAF4, TAF7, TAF8, TAF11, TAF13], nuclear pore-associated [SAC3, CDC31, THP1], and a new one [ABD1, SPT6] predicted by the BCD algorithm, are misplaced. The ECC algorithm has the same tendency to separate peripheral members of the same known protein complex into incorrect protein modules. For instance, in the transcription network, the ECC algorithm disjoins peripheral proteins such as FOB1, RPC10, RRP8 and RPL6B in a very early phase of the decomposition process, causing those derived singletons to be separated from most functional modules. Singletons do not provide useful information for inferring the function of any module. Therefore, the number of singletons generated by an algorithm is an additional indicator of that algorithm's performance: an excess number of singletons indicates poor performance of a particular algorithm. On this small network, the ECC algorithm produces 13 singletons, while the BCD and GN algorithms produce 9 and 3 singletons, respectively. While the difference between the ECC algorithm and the BCD algorithm is only four singletons, those ECC singletons lose their connections with other modules as they are isolated at a much earlier stage of the decomposition process. Although the GN algorithm produces the least number of singletons in the example network, it is at the expense of generating mosaic modules. Similar trends are seen in following experiments of large networks.
We also note that the original ECC1 algorithm performs more poorly than the ECC2 algorithm with our commonality index (Additional data file 1). From now on, we will not discuss the original ECC1 algorithm. When we refer to the ECC algorithm, we mean the ECC algorithm using our commonality index.
Results on the global yeast network
In this section, we discuss the results of BCD decomposition of a specific network (yeast), the quality of computed modules, and comparison to MIPS hand-curated protein complex data.
Number of predicted complexes and singletons
Comparison of modularity coefficients for network decomposition on three networks of varying sizes
Filtered global data
Unfiltered global data
Overlap with MIPS complexes
Comparison of predicted protein complexes with known MIPS complexes
Therefore, to estimate the overall correspondence between a resulting cluster by one approach and the collection of annotated complexes, we computed the geometric accuracy and separation as done in the described study . The results are shown in Table 3. Clearly, the BCD algorithm achieves better accuracy than the other three algorithms on both unfiltered and filtered datasets. In terms of separation, it is the MCL algorithm that performs best among the four algorithms on both datasets (Table 3).
GO term enrichment
Predicted protein complexes of size ≥3 enriched in GO terms
e-15 to e-10
e-10 to e-5
e-5 to 1
e-15 to e-10
e-10 to e-5
e-5 to 1
Prediction of possible novel protein complexes
Predicted protein modules where either GO terms are greatly enriched (P < 1e-15) or all members of a best-matching MIPS complex are found (overlap = 100%)
The effects of filtering false-positive interactions
In all experiments, the results on the filtered data are consistently better than the results on the original data. For example, in Table 3, the non-overlap between computed protein modules by the BCD algorithm and known protein complexes was reduced from 601 for the original data to 209 on the filtered data. In Table 4, the percentage of GO terms with probability <e-10 is always higher in the filtered data than in the original data.
Protein interaction networks are examples of complex systems that are difficult to understand from raw experimental data alone. Methods to organize, filter, extract significant features and display these data are critical to understanding these systems. A number of network partition algorithms have been proposed to find modular structures in protein interaction networks [22, 34–39]. Our work is a further development along the network decomposition approach [13, 14]. Our main contribution is to combine the global metric with a local metric in the decomposition procedure. We also resolved several critical technical issues. We propose a new commonality metric based on random graph analysis, a clear definition of protein modules utilizing the decomposition tree structure, and a noise filtering algorithm based on random graph analysis. These advances in methodology result in an effective, consistent, and robust algorithm, as demonstrated on both simulated datasets and the experimental yeast interaction data. The protein modules obtained have clear biological functions, as shown in Table 5. Our approach to recover protein interaction modules is fully self-contained, that is, it does not need other input or parameters to identify protein module boundaries. Our test experiments on yeast show that this method can effectively predict protein interaction modules from a complex interaction network. We plan to further automate this algorithm to compute protein interaction modules for a large number of organisms.
Materials and methods
Computing geometric accuracy and separation
We computed the geometric accuracy and separation by following the approach described in the study by Brohee and van Helden . Briefly, each clustering result was compared with the annotated complexes by building a contingency table T, where row i corresponds to the ith annotated complex and column j to the jth cluster and the value of a cell Tij indicates the number of proteins found in common between complex i and cluster j. The contingency table has n rows (complexes) and m columns (clusters).
Additional data files
The following additional data are available with the online version of this paper. Additional data file 1 shows hierarchical decomposition trees of a yeast transcriptional sub-network by different algorithms. Additional data file 2 lists predicted protein interaction modules by the BCD algorithm on the unfiltered dataset. Additional data file 3 lists predicted protein interaction modules by the BCD algorithm on the filtered dataset.
edge clustering coefficient
Girvan and Newman
Munich Information Center for Protein Sequences.
This research is supported by the program Molecular Assemblies, Genes, and Genomics Integrated Efficiently (MAGGIE) funded by the Office of Science, Office of Biological and Environmental Research, US Department of Energy, under contract number DE-AC02-05CH11231. We gratefully acknowledge Dr Elizabeth Holbrook for editing this manuscript.
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