Efficient and accurate greedy search methods for mining functional modules in protein interaction networks
- Jieyue He^{1, 2}Email author,
- Chaojun Li^{1},
- Baoliu Ye^{2} and
- Wei Zhong^{3}
https://doi.org/10.1186/1471-2105-13-S10-S19
© He et al; licensee BioMed Central Ltd. 2012
Published: 25 June 2012
Abstract
Background
Most computational algorithms mainly focus on detecting highly connected subgraphs in PPI networks as protein complexes but ignore their inherent organization. Furthermore, many of these algorithms are computationally expensive. However, recent analysis indicates that experimentally detected protein complexes generally contain Core/attachment structures.
Methods
In this paper, a Greedy Search Method based on Core-Attachment structure (GSM-CA) is proposed. The GSM-CA method detects densely connected regions in large protein-protein interaction networks based on the edge weight and two criteria for determining core nodes and attachment nodes. The GSM-CA method improves the prediction accuracy compared to other similar module detection approaches, however it is computationally expensive. Many module detection approaches are based on the traditional hierarchical methods, which is also computationally inefficient because the hierarchical tree structure produced by these approaches cannot provide adequate information to identify whether a network belongs to a module structure or not. In order to speed up the computational process, the Greedy Search Method based on Fast Clustering (GSM-FC) is proposed in this work. The edge weight based GSM-FC method uses a greedy procedure to traverse all edges just once to separate the network into the suitable set of modules.
Results
The proposed methods are applied to the protein interaction network of S. cerevisiae. Experimental results indicate that many significant functional modules are detected, most of which match the known complexes. Results also demonstrate that the GSM-FC algorithm is faster and more accurate as compared to other competing algorithms.
Conclusions
Based on the new edge weight definition, the proposed algorithm takes advantages of the greedy search procedure to separate the network into the suitable set of modules. Experimental analysis shows that the identified modules are statistically significant. The algorithm can reduce the computational time significantly while keeping high prediction accuracy.
Background
With the rapid development of technologies to predict protein interactions, huge data sets portrayed as networks have been available. Most real networks typically contain parts in which the nodes are more highly connected to each other than to the rest of the network. The sets of such nodes are usually called clusters, communities, or modules [1–4]. The presence of biologically relevant functional modules in Protein-Protein Interaction (PPI) graphs has been confirmed by many researchers [4, 5]. Identification of functional modules is crucial to the understanding of the structural and functional properties of networks [6, 7]. There is a major distinction between two biological concepts, namely, protein complexes and functional modules [7]. A protein complex is a physical aggregation of several proteins (and possibly other molecules) via molecular interaction (binding) with each other at the same location and time. A functional module also consists of a number of proteins (and other molecules) that interact with each other to control or perform a particular cellular function. Unlike protein complexes, proteins in a functional module do not necessarily interact at the same time and location. In this paper, we do not distinguish protein complexes from functional modules because the protein interaction data used for detecting protein complex in this work do not provide temporal and spatial information.
Recently, many research works have been conducted to solve the problem of clustering protein interaction networks [8–10]. Some of them are using the graph-based clustering methods for mining functional modules [11, 17–20]. These studies are mainly based on the observation that densely connected regions in the PPI networks often correspond to actual protein functional modules. In short, methods proposed in these studies are used to detect densely connected regions of a graph that are separated by sparse regions. Some graph clustering approaches using PPI networks for mining functional modules are introduced in the following. Bader and Hogue [17] proposed the Molecular COmplex Detection (MCODE) algorithm that utilizes connectivity values in protein interaction graphs to mine for protein complexes. The algorithm first computes the vertex weight value from its neighbour density and then traverses outward from a seed protein with a high weighting value to recursively include neighbouring vertices whose weights are above a given threshold. However, since the highly weighted vertices may not be highly connected to each other, the algorithm does not guarantee that the discovered regions are dense. A simultaneous protein interaction network (SPIN) introduced by Jung et al [12] specifies mutually exclusive interactions (MEIs). Taking advantages of the SPINs, SPIN_MCODE has outperformed the plain MCODE method.
Amin et al. [18] proposed a cluster periphery tracking algorithm (DPClus) to detect protein complexes by keeping track of the periphery of a detected cluster. DPClus first weighs each edge based on the common neighbours between two proteins and further weighs nodes by their weighted degree. To form a protein complex, DPClus first selects the seed node having the highest weight as the initial cluster and then iteratively augments this cluster by including vertices one by one, which are out of but closely related with the current cluster. Li et al. [13] modified the DPClus algorithm for identifying protein complexes that have a small diameter (or a small average vertex distance) and satisfy a different cluster connectivity-density property. The performance of such algorithms depends heavily on the quality of the seeds and the criterion of extending clusters.
Adamcsek et al. [19] provided a software called CFinder to find functional modules in PPI networks. CFinder detects the k-clique percolation clusters as functional modules using a Clique Percolation Method (CPM)[20]. In particular, a k-clique is a clique with k nodes and two k-cliques are adjacent if they share (k - 1) common nodes. A k-clique percolation cluster is then constructed by linking all the adjacent k-cliques as a bigger subgraph. Li et al. [14] proposed a new clustering algorithm called IPC-MCE to identify protein complexes based on maximal clique, and then extend all the maximal cliques by adding their neighbourhoods iteratively. Liu et al [15] developed an algorithm called Clustering based on Maximal Cliques (CMC) to discover complexes from the weighted PPI network. CMC first finds maximal cliques from PPI networks, and then removes or merges highly overlapped maximal cliques based on their inter-connectivity. However, CMC generates less number of significant functional modules having P-value less than 1E-5 than the DPClus algorithm in the unweighted PPI network [11]. Wang et al. [16] also developed an algorithm called CP-DR based on the new topological model for identifying protein complexes. Wang's algorithm extended the definition of k-clique community of the CPM algorithm and introduced distance restriction.
Above computational studies mainly focus on detecting highly connected subgraphs in PPI networks as protein complexes but ignore their inherent organization. However, recent analysis indicates that experimentally detected protein complexes generally contain Core/attachment structures. Protein complexes often include cores in which proteins are highly co-expressed and share high functional similarity. And core proteins are usually more highly connected to each other and may have higher essential characteristics and lower evolutionary rates than those of peripheral proteins [26]. A protein complex core is often surrounded by some attachments, which assist the core to perform subordinate functions. Gavin et al.'s work [28] also demonstrates the similar architecture and modularity for protein complexes. Therefore, protein complexes have their inherent organization [26, 27, 29] of core-attachment. To provide insights into the inherent organization of protein complexes, some methods [21, 26, 29] are proposed to detect protein complexes in two stages. In the first stage, protein complex cores, as the heart of the protein complexes, are first detected. In the second stage, protein complexes are expanded by incorporating attachments into the protein complex cores. Wu et al. [21] presented a COre-AttaCHment based method (COACH) and Leung et al. also developed an approach called CoreMethod. These approaches are used to detect protein complexes in PPI networks by identifying their cores and attachments separately [29]. To detect cores, COACH performs local search within vertex's neighbourhood graphs while the CoreMethod [29] computes the p-values between all the proteins in the whole PPI networks.
In this paper, a Greedy Search Method based on Core-Attachment structure called GSM-CA is introduced. Comparing with the other methods of core-attachment, the new edge weight calculation method and evaluation criterion for judging a node as a core node or an attachment node are proposed in our GSM-CA method. The GSM-CA method uses a pure greedy procedure to move a node between two different sets. The detected clusters are also core-attachment structures. In particular, GSM-CA firstly defines seed edges of the core from the neighbourhood graphs based on the highest weight and then detects protein-complex cores as the hearts of protein complexes. Finally, GSM-CA includes attachments into these cores to form biologically meaningful structures. The new algorithm is applied to the protein interaction network of S. cerevisiae. The modules identified by the new algorithm are mapped to the MIPS [22] benchmark complexes and validated by GO [23] annotations. The experimental results show that the identified modules are statistically significant. In terms of prediction accuracy, the GSM-CA method outperforms several other competing algorithms. Moreover, most of the previous methods can not detect the overlapping functional modules by generating separate subgraphs. But GSM-CA can not only generate non-overlapping clusters, but also overlapping clusters.
The GSM-CA method achieves high accuracy. However, it is computationally expensive. Many module detection approaches are based on the traditional hierarchical methods, which is also computationally inefficient because the hierarchical tree structure generated by the repeated computational process cannot provide adequate information to identify whether a network belongs to a module structure or not. To further improve the computational process of these module detection approaches, the Greedy Search Method based on Fast Clustering (GSM-FC) is proposed in this paper. The edge weight based GSM-FC method uses the greedy procedure to traverse all edges just once to separate the network into the suitable sets of modules. The experimental results demonstrate that the newly proposed algorithm can reduce the computational time noticeably while maintaining high prediction accuracy compared to GSM-CA.
Briefly then, the outline of this paper is as follows. In Section 2 the implementation of our two methods are described in details. In Section 3, our algorithm is applied to the protein interaction network of S. cerevisiae yeast and the results are analyzed. In Section 4, the conclusions are given.
Methods
Definitions
Protein interaction networks can be represented as an undirected graph G = (V , E), where V is the set of vertices and E = {(u,v)| u,v ∈ V} is the set of edges between the vertices. For a node v ∈ V , the set of v's direct neighbours is denoted as N_{ v }. N_{ v } is defined as N_{ v } = {u| u ∈ V,(u,v) ∈ E}. Before introducing details of the algorithm, some terminologies used in this paper are defined.
Here, NC_{ n } is the set of n's direct neighbours in cluster c, and NC_{ k } is the set of k's direct neighbours in cluster c.
The DPClus algorithm defines the weight w_{ uv } of an edge (u,v) ∈ E as the number of the common neighbours of the nodes u and v. It is likely that two nodes that belong to the same cluster have more common neighbours than two nodes that do not. For two edges having the same number of common neighbours, the one that has more interactions between the common neighbours is more likely to belong to the same cluster.
Here N_{ uv } = N_{ u } ∩ N_{ v }, E_{ uv } = {(v_{ j }, v_{ k })| (v_{ j }, v_{ k }) ∈ E, v_{ j }, v_{ k } ∈ N_{ uv }} and α is the interaction factor to indicate how important the interactions are. α's default value is set as 1.
The number of common neighbours between any two nodes is actually equal to the number of paths of length 2 between them. This definition of weight is used to cluster the graphs that have densely connected regions separated by sparse regions. In relatively sparse graphs, the nodes on the path of edges with length 3 or length 4 can be considered.
The highest edge weight of a node n is defined as hw_{ n } = max (w_{ nu }) for all u such that (n, u) ∈ E. The highest weight edge (n, v) of node n is the edge satisfying the condition that w_{ nv } = hw_{ n }.
Greedy Search Method based on Core Attachment structure (GSM-CA)
Because core and peripheral proteins may have different roles and properties due to their different topological characteristics, a Greedy Search Method based on Core Attachment structure called GSM-CA is proposed based on the definition of the edge weight and two evaluation criterion for judging a node as a core node or an attachment node. GSM-CA uses a greedy procedure to get the suitable set of clusters. It first generates the core of a cluster, and then selects reliable attachments cooperating with the core to form the final cluster. The algorithm is divided into six steps: 1) Input & initialization; 2) Termination check; 3) Seed selection; 4) Core formation; 5) Attachments selection; 6) Output & update. The functional modules are determined by final clusters. The whole description of the GSM-CA algorithm is shown in the following.
Input & initialization
The input to the algorithm is an undirected simple graph and hence the associated matrix of the graph is read first. The user need decide the minimum value for closeness in cluster formation. The minimum value will be referred to as cn_{ in }. Each edge's weight is computed based on formula (2). It is computed just once and will not be recalculated in the following steps.
Termination check
Once a cluster is generated, it is removed from the graph. The next cluster is then formed in the remaining graph and the process goes on until no seed edge whose weight is above one (i.e. w_{ uv } > 1) can be found in the remaining graph.
Seed selection
Each cluster starts at a deterministic edge called the seed edge. The highest weight edge (n, v) of node n satisfying the condition that w_{ nv } =hw_{ n } is considered as the seed edge in the remaining graph.
Core formation
A protein complex core is a small group of proteins which show a high co-expression patterns and share high degree of functional similarity. It is the key functional unit of the complex and largely determines the cellular role and essentiality of the complex [21, 26–28]. For example, a protein in a core often has many interacting partners and protein complex cores often correspond to small, dense and reliable subgraphs in PPI networks [28].
The core starts from a single edge and then grows gradually by adding nodes one by one from the neighbours. The neighbours of a core are the nodes connected to any node of the core but not part of the core. The core is referred to as C. For a neighbour u of C, if u's neighbour v linked by u's highest weight edge (u, v) is in C, u is considered to be included into the core. Before including u to C, the condition, cn_{ uv } >= cn_{ in } , is checked and the neighbour whose highest edge weight is largest is included. This process goes on until no such neighbour can be found, and then the core of one cluster is generated.
Attachments selection
After the core of one cluster has been detected, the peripheral information of each core is extracted and reliable attachments cooperating with it are selected to form the final cluster. For each neighbour u of the core C, if u's neighbour v linked by u's highest weight edge (u, v) is in C, $\frac{\left|{V}_{uv}\right|}{\left|{N}_{uv}\right|}$ is computed. V_{ uv } is the common neighbours of u and v in the core C. N_{ uv } is the common neighbours of u and v in graph G.
If $\frac{\left|{V}_{uv}\right|}{\left|{N}_{uv}\right|}>0.5$, u will be selected as an attachment. After all neighbours of the core are checked, the final cluster is generated.
Output & update
Table 1
Algorithm GSM-CA |
---|
Input: a graph G = (V , E), parameters cn_{ in } ; Output: identified modules; (1) Compute the edge weight For each edge e(u,v) ∈E do compute w_{ uv }; End For (2) Form core Select the edge e(u,v) with highest weight in G; If w_{ uv } < 1 then exit; End If Initial core C ={u,v}; While neighbour i whose neighbor j linked by i's highest weight edge is in C and cn_{ ij } ≥ cn_{ in } do C. add (i); End While (3) Select attachments for core For each neighbor u of the core C do If u's neighbor v linked by u's highest weight edge is in C and $\frac{\left|{V}_{uv}\right|}{\left|{N}_{uv}\right|}>0.5$then u is selected as attachment of C End If End For each (4) Output results and update the highest edge weight Output C and delete C from G, update each vertex's highest edge weight in the remaining G (5) Repeat from step 2 to step 4, until reaching the termination condition of step 2. |
Generation of overlapping clusters
In the above algorithm, once a cluster is generated it is marked as clustered and not considered in the following, and the next cluster is generated in the remaining graph. Therefore, non-overlapping clusters are generated. In order to generate overlapping clusters, the existing non-overlapping clusters are extended by adding nodes to them from their neighbours in the original graph (considering the marked nodes and edges). Then in the original graph excluding the edges between the nodes that have been marked as clustered, each node's highest edge weight is updated.
Greedy Search Method based on Fast Clustering (GSM-FC)
Many module detection approaches including GSM-CA is computationally expensive. The traditional hierarchical tree structure generated by these approaches can't provide adequate information to identify which subtree belongs to a module structure. As a result, the module structure need be evaluated repeatedly based on the module definition. During the computational process, the edge weight of neighbouring nodes need be recomputed after one edge is deleted. The edge weight calculation is based on the shortest path between vertices. Since the shortest path problem has high time complexity, these approaches are even not scalable for the networks with the medium size.
The GSM-FC can avoid repeated module structure evaluation because the module structure can be identified based on inherent network organization and the greedy algorithm. The GSM-FC traverses all edges once then generates the clusters. Moreover, the GSM-FC utilizes properties of subnetworks, which can reflect the network topology more effectively. As a result, the computational efficiency of the GSM-FC method can be improved noticeably.
The GSM-FC algorithm is divided into three steps: 1) Input & initialization; 2) Cluster formation; 3) Output.
Input & initialization
The input to the algorithm is an undirected simple graph and hence the associated matrix of the graph is read first. Each edge's weight is computed based on formula (2). All vertices in the graph G are initialized as singleton clusters at first step.
Cluster formation
During this step, all edges are traversed gradually and a greedy procedure is used to assemble the nodes into clusters. For one edge (u, v), if u and v are not in the same cluster, they are considered to be merged. If the edge weight w_{ uv } is u's highest edge weight, and then an edge from u to v is added in order to merge the cluster including u into the cluster including v. Similarly, if the edge weight w_{ uv } is v's highest edge weight, and then an edge between v and u is added in order to merge the cluster including v with the cluster including u. If the edge weight w_{ uv } is neither u's highest edge weight nor v's highest edge weight, the edge (u, v) is ignored and the next edge is evaluated.
Output
Table 2
Algorithm GSM-FC |
---|
Input: a graph G = (V , E); Output: identified modules; (1)For each edge e(u,v) ∈E do compute w_{ uv }; add e(u,v) to queue S_{ q } End for (2)While Sq ≠ ∅ do; e(u, v) ← S_{ q }; If L(u) ≠ L(v) then //L is cluster label i = L(u); j =L (v); If w_{ uv } ==hw_{ u } || w_{ uv } == hw_{ v } then V (C_{ i }) = V (C_{ i }) ∪ V(C_{ j }); //C represents the cluster End if End if End while |
Efficiency analysis
Compared to the other algorithms, the advantage of the GSM-FC algorithm are computationally efficient. The GSM-FC algorithm just needs to visit all edges once without any parameter input. The time complexity of the clustering process is linear. The edge weight calculation is the most time-consuming step for the clustering process. Let n and m denote the number of vertices and edges in a protein interaction network respectively; k be the average number of neighbours of all the vertices, i.e. $k=\frac{1}{n}{\sum}_{v\in V}\left|{N}_{v}\right|$; Then, the complexity of calculating all the edge clustering coefficients is O(k^{2}m). Since the time complexity of the hierarchical merging process is O(m), the total time complexity of the GSM-FC algorithm is O(k^{2}m). In general, k is much smaller than the number of vertices n and can be considered as a constant because it is well known that the protein interaction network is scale-free, in which most proteins only participate in a small number of interactions [31].
Experimental setup and result analysis
Data set and the criterion of performance evaluation
In order to evaluate effectiveness of the new system, our algorithm is applied to the full DIP (the Database of Interacting Proteins) [24] yeast dataset, which consists of 17201 interactions among 4930 proteins [21]. It is more complex and difficult to identify the modules using the full dataset than using the core dataset. The performance of our method is compared with several competing algorithms including MCODE, CFinder, DPClus, and COACH. The parameter selection for these algorithms is based on authors' recommendation. Several metrics including f-measures and p-value are used for rigorous performance evaluation.
The experimental results are based on a reference dataset of known yeast protein complexes retrieved from the MIPS [22]. While it is probably one of the most comprehensive public datasets of yeast complexes available up to date, it is by no means a complete dataset--there are still many yeast complexes that need to be discovered. After filtering the predicted protein complexes and complexes composed of a single protein from the dataset, a final set of 214 yeast complexes are used as our evaluation benchmark.
P-values are used to evaluate the biological significance of our predicted complexes. P-values represent the probability of co-occurrence of proteins with common functions. Low p-value of a predicted complex generally indicates that the collective occurrence of these proteins in the module does not happen merely by chance and thus the module has high statistical significance. In our experiments, the p-values of complexes are calculated by the tool called SGD's Go::TermFinder [23]. SDG's Go: TermFinder uses all the three types of ontology including Biological Process (BP), Molecular Function (MF) and Cellular Component (CC). The cutoff of the p-value is set as 0.01. The average -log(p-value) of all modules is calculated by mapping each module to the annotation with the lowest p-value.
Where F_{ i }is a functional category mapped to module M. The proteins in functional category F_{ i } are considered as true predictions, the proteins in module M are considered as positive predictions, and the common proteins of F_{ i } and M are considered as true positive predictions. Recall is the fraction of the true-positive predictions out of all the true predictions, and precision is the fraction of the true positive predictions out of all the positive predictions [25]. The average f-measure value of all modules is calculated by mapping each module to the function with the highest f-measure value.
Experimental results for GSM-CA method
Results of various algorithms compared with MIPS complexes using DIP data
Algorithms | MCODE | CFinder | DPClus | COACH | GSM-CA |
---|---|---|---|---|---|
#predicted | 59 | 245 | 1143 | 745 | 353 |
complexes | |||||
|TP| | 18 | 52 | 133 | 155 | 105 |
|TB| | 19 | 61 | 144 | 106 | 119 |
s-measure | 0.132 | 0.231 | 0.198 | 0.307 | 0.380 |
Comparison of the results before and after adding attachments
Average Size | f-measure of BP | -log(p-value) | |
---|---|---|---|
Before | 5.29 | 0.356 | 7.2 |
After | 7.37 | 0.362 | 8.6 |
Statistical significance of functional modules predicted by various methods
Algorithms | No. of Modules size>=3 | No. of Significant Modules | Average Size | Maximum | f-measure of BP | -log(p-value) | Parameters |
---|---|---|---|---|---|---|---|
MCODE | 59 | 54 | 83.8 | 549 | 0.296 | 10.87 | fluff = 0.1; VWP = 0.2 |
CFinder | 245 | 157 | 10.2 | 1409 | 0.246 | 4.49 | K = 3 |
DPClus | 217 | 187 | 5.23 | 25 | 0.335 | 6.78 | Density = 0.7;CP_{in}=0.5 |
COACH | 746 | 608 | 8.54 | 44 | 0.272 | 6.96 | Null |
GSM-CA | 187 | 168 | 7.37 | 79 | 0.362 | 8.6 | CN _{ in } =0.5 |
GSM-FC | 113 | 106 | 9.65 | 118 | 0.359 | 10.46 | Null |
List of top ten scoring modules identified by GSM-CA and their most enriched GO terms for Biological Process
ID | Size of module | Number of proteins enriched the same GO Term | Size of GO Term | Name of GO Term | p-value |
---|---|---|---|---|---|
1 | 35 | 33 | 221 | rRNA processing | 1.70e-41 |
2 | 42 | 38 | 323 | ribosome biogenesis | 1.61e-39 |
3 | 13 | 13 | 15 | tRNA transcription | 1.92e-35 |
4 | 19 | 14 | 19 | mRNA polyadenylation | 1.96e-31 |
5 | 11 | 11 | 12 | cyclin catabolic process | 8.92e-31 |
6 | 14 | 12 | 14 | polyadenylation-dependent snoRNA 3'-end processing | 1.91e-30 |
7 | 19 | 18 | 93 | mitochondrial translation | 8.08e-30 |
8 | 16 | 14 | 29 | energy coupled proton transport, down electrochemical gradient | 1.33e-29 |
9 | 22 | 14 | 20 | RNA polymerase II transcriptional preinitiation complex assembly | 2.70e-29 |
10 | 19 | 18 | 101 | nuclear mRNA splicing, via spliceosome | 8.91e-29 |
Experimental results for the GSM-FC method
Comparison of the running time of the GSM-FC algorithm and other algorithms
Algorithms | The running time |
---|---|
MCODE | 71.5 s |
COACH | 6.8 s |
CFinder | 24.4 s |
DPClus | 926.0 s |
GSM-AC | 82.6 s |
GSM-FC | 3.4 s |
Table 5 compares the biological significance of modules predicted by several algorithms. The improved average f-measure and -log(p-value) demonstrate that the modules identified by the GSM-FC method have higher statistical significance than other methods. The GSM-FC method generates fewer numbers of clusters with the bigger average cluster size compared to the GSM-CA method. Both Table 5 and Table 7 show that the GSM-FC method can reduce the computational time noticeably while keeping high prediction accuracy compared to GSM-CA. Furthermore, the GSM-FC method which doesn't require any input parameters can be applied to even larger protein interaction networks.
Conclusions
Identification of functional modules is crucial to the understanding of the structural and functional properties of protein interaction networks. The increasing amount of protein interaction data has enabled us to detect protein functional modules. In this paper, a Greedy Search Method based on Core-Attachment structure called GSM-CA is proposed to mine functional modules from the protein interaction networks. Because core and peripheral proteins may have different roles and properties due to their different topological characteristics, the GSM-CA method defines edge weight and two criterion for determining core nodes and attachment nodes. It first generates the core of a module, and then forms the module by including attachments into the core. The GSM-CA method is applied to the typical PPI networks of S. cerevisiae. The MIPS benchmark and the GO annotation are used to validate the identified modules and compare the performances of our algorithm with several other algorithms including MCODE, CFinder, DPClus, and COACH. The evaluation and analysis show that most of the functional modules predicted by our algorithm have high functional similarity and match well with the benchmark. The quantitative comparisons reveal that our algorithm outperforms the other competing algorithms. Many module detection approaches utilize the traditional hierarchical clustering methods, which are computationally costly because the tree structure produced by the hierarchical clustering methods can not provide adequate information to identify whether a network belongs to a module structure or not. To overcome these problems, the Greedy Search Method based on Fast Clustering (GSM-FC) is proposed. The GSM-FC method takes advantages of the greedy search procedure to separate the network into the suitable set of modules. The experimental results show that the GSM-FC method can reduce the computational time significantly while keeping high prediction accuracy compared to GSM-CA. For the future work, the algorithm need be applied to the weighted graph. How to incorporate diverse biological information into the explorative analysis of protein complexes in PPI networks is another interesting question for further research.
Declarations
Acknowledgements
This article has been published as part of BMC Bioinformatics Volume 13 Supplement 10, 2012: "Selected articles from the 7th International Symposium on Bioinformatics Research and Applications (ISBRA'11)". The full contents of the supplement are available online at http://www.biomedcentral.com/bmcbioinformatics/supplements/13/S10.
The authors would like to thank Bader G. and Hogue C. for their sharing the tool of MCODE, to Adamcsek B., Palla G., Farkas I., Derenyi I., and Vicsek T. for their publicity of CFinder. The authors are also thankful to Altaf-UI-Amin Md, Shinbo Y., Mihara K., Kurokawa K., and Kanaya S. for their kindly sharing the tool of DPClus, to Wu M., Li X., Kwoh C.-K. and Ng S.-K. for their sharing the source code of COACH. The authors also thank the anonymous reviewers for their helpful and constructive suggestions.
This research work is supported by State Key Laboratory for Novel Software Technology of Nanjing University (KFKT2010B03) and Open Research Foundation of Key Laboratory for Computer Network and Information Integration, Southeast University (K93-9-2010-19).
Authors’ Affiliations
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