BioMed Research International

Volume 2014 (2014), Article ID 354539, 8 pages

http://dx.doi.org/10.1155/2014/354539

Research Article

A Novel Algorithm for Detecting Protein Complexes with the Breadth First Search

Xiwei Tang,1,2 Jianxin Wang,¹ Min Li,¹ Yiming He,¹ and Yi Pan1,3

¹School of Information Science and Engineering, Central South University, Changsha 410083, China

²School of Information Science and Engineering, Hunan First Normal University, Changsha 410205, China

³Department of Computer Science, Georgia State University, Atlanta, GA 30302-4110, USA

Received 27 January 2014; Accepted 19 March 2014; Published 10 April 2014

Academic Editor: FangXiang Wu

Copyright © 2014 Xiwei Tang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

Most biological processes are carried out by protein complexes. A substantial number of false positives of the protein-protein interaction (PPI) data can compromise the utility of the datasets for complexes reconstruction. In order to reduce the impact of such discrepancies, a number of data integration and affinity scoring schemes have been devised. The methods encode the reliabilities (confidence) of physical interactions between pairs of proteins. The challenge now is to identify novel and meaningful protein complexes from the weighted PPI network. To address this problem, a novel protein complex mining algorithm ClusterBFS (Cluster with Breadth-First Search) is proposed. Based on the weighted density, ClusterBFS detects protein complexes of the weighted network by the breadth first search algorithm, which originates from a given seed protein used as starting-point. The experimental results show that ClusterBFS performs significantly better than the other computational approaches in terms of the identification of protein complexes.

1. Introduction

Protein complexes are molecular aggregations of proteins assembled by multiple protein-protein interactions. Many proteins are functional only after they are assembled into a protein complex and interact with other proteins in this complex [1–4]. The vast amount of genes and proteins that participate in biological networks imposes the need for determination of protein complexes within the network in order to reduce the complexity, while these complexes will be the first step in deciphering the composite genetic or cellular interactions of the overall network.

High-throughput experimental technologies, along with computational predictions, have produced a large amount of protein interactions [5–11], which make it possible to uncover protein complexes from protein-protein interaction (PPI) networks. Pair-wise protein interactions can be modeled as a graph or network, where vertices represent proteins and edges are protein-protein interactions. Protein complexes are groups of proteins that interact with one another, so they generally correspond to dense subgraphs in PPI networks. Different research groups have developed a wealth of algorithms to identify protein complexes from the PPI networks [12–18]. In these approaches, the protein networks are considered as unweighted graphs. These methods work well on PPI networks and extract successfully protein complexes. Nevertheless, it has been noticed that protein interaction data produced by high-throughput experiments are often associated with high false positive rate and false negative rate due to the limitations of the associated experimental techniques, which may have a negative impact on the complex discovery algorithms [19–23].

In order to address that particular question, a number of data integration and affinity scoring schemes have been devised [10, 23–30]. In the paper of Gavin et al. [11], the weights of the interactions were defined by using the so-called socio-affinity index introduced in [11] that is based on the log-odds of the number of times two proteins were observed together in a purification, relative to the expected frequency of such a cooccurrence based on the number of times the proteins appeared in purifications. Krogan et al. [10] have used MALDI-TOF mass spectrometry and LC-MS/MS to identify protein-protein interactions, based on the observation that either mass spectrometry method often fails to identify a protein, and the usage of two independent methods can increase the coverage and confidence of the obtained interactome. The results of the two methods were combined by supervised machine learning methods with two rounds of learning, using hand-curated protein complexes in the MIPS reference database as a gold standard dataset. Collins et al. [23] have combined the experimentally derived PPI networks of Krogan et al. [10] and Gavin et al. [11] by re-analyzing the raw primary affinity purification data of these experiments using a novel scoring technique called purification enrichment (PE). The PE scores were motivated by the probabilistic socio-affinity scoring framework of Gavin et al. [11] but also take into account negative evidence (i.e., pairs of proteins where one of them fails to appear as a prey when the other one is used as a bait). These affinity scores encode the reliabilities (confidence) of physical interactions between pairs of proteins. Therefore, the challenge now is to mine meaningful and novel complexes from protein interaction networks derived by combining multiple high-throughput datasets and by making use of these affinity scoring schemes. In this direction, some algorithms have also been proposed [25, 31–34].

In this study, we propose a novel algorithm to derive yeast complexes from weighted (affinity-scored) PPI network and call it ClusterBFS (Cluster with Breadth First Search). ClusterBFS builds clusters in terms of breadth first search algorithm, starting from local seeds and adding nodes that maintain the weighted density of the clusters. The experimental results show that our ClusterBFS method outperforms existing computational methods, such as MCL [31], ClusterONE [32], HC-PIN [33], SPICi [34], and MCODE [14].

2. Methods

2.1. Preliminaries

Given a weighted network, the goal of our algorithm is to output a set of disjoint dense subgraphs. We model the network as a undirected graph with a confidence score , for every edge . For any two vertices, and without an edge between them, we set . For each set of vertices , we define its weighted density as the sum of the weights of the edges among them divided by the total number of possible edges (i.e., the density of a set is measure of how close the induced subgraph is to clique, and varies from 0 to 1):

2.2. Algorithm Overview

We use a breadth first search approach to build clusters. ClusterBFS builds one cluster at a time, and each cluster is expanded from an original seed protein. The unclustered node is added, if it has the highest edge weight and the density of the cluster remains higher than a user-defined threshold Td; otherwise, the cluster is output. The growth process is repeated from different seeds to form multiple, possibly, overlapping groups. Although some overlaps are likely to have biological importance, groups overlapping to a very high extent in comparison to their sizes should likely be discarded. We quantify the extent of overlap between each pair of groups and discard the smaller group, if the overlap score [14] is above a specified threshold. ClusterBFS thus has two parameters: Td, the weighted density threshold and . For threshold , we set a firm value 0.8 [32]. (See Figure 1 for a simplified example.)

Figure 1: Example to illustrate the clustering process. This example network has 12 vertices, and every edge has confidence. Suppose the weighted density threshold . The vertex 0 is taken as a seed protein and the original cluster 0 is constructed. In the first step of the breadth first search, the vertex 1 has the highest edge weight 0.75 among the neighbors of the vertex 0. We add vertex 1 to the cluster and this cluster now has the weighted density 0.75 that is bigger than the density threshold 0.2. Similarly, the vertices 2, 3, 4, and 5 are added to the cluster in sequence and the cluster now has the weighted density 0.23 which is still more than the threshold 0.2. Next, the neighbors of vertex 4 are considered. Of these, vertex 6 has the highest edge weight 0.52 and is added to the cluster. However, the weighted density of the cluster is 0.19 and less than the threshold 0.2. Thus, the vertex 6 is removed and the neighbor of the vertex 3 is examined. Because the weighted value between the vertex 3 and its neighboring vertex 9 is 0.51 and less than 0.52, the vertex 9 is not added to the cluster. When the neighbors of the vertex 2 are checked, the vertex 10 is added to the cluster. Since the weighted density of the cluster is less than 0.2, the vertex 10 is removed. And, likewise, the vertex 11 is not added to the cluster. We stop extending the cluster and output the final cluster . For simplicity, the elimination of redundant clusters is not shown in this figure.

2.3. Seed Selection

Every vertex in the yeast PPI network is used as the seed and is equally important.

2.4. Cluster Expansion

After obtaining the seed vertex, we use the breadth first search method to grow each cluster in terms of the weighted density. At each step, we have a current vertex set for the cluster, which initially contains one seed protein . We search for the vertex with maximum value of the edge weight amongst all the unclustered vertices that are adjacent to the seed in breadth first. If the weighted density of the cluster is smaller than a threshold, we stop expanding this cluster and output it. If not, we put vertex into and update the density value. If the density value is smaller than our density threshold Td, we do not include in the cluster and output . We repeat this procedure until all vertices in the graph are clustered. Algorithm 1 illustrates the over framework to detect protein complexes. Algorithm 2 is the breadth first search procedure.

Input:

     weighted PPI network ;

     weighted density threshold ;

     overlap score threshold ;

Output:

     set of protein complexes SC discovered from ;

Description:

(1) ; initialization

(2) for each vertex   do

(3)     construct the complex, ;

(4)     ;

(5)     Redundancy-filtering ();

Algorithm 1: ClusterBFS algorithm.

(1)

(2) create a queue

(3)

(4) while   is not empty:

(5) begin

(6)  

(7)  

(8)   if  :

(9)         

(10)   else

(11)          

(12) end

(13) return results

Algorithm 2: Breadth First Search: .

Since all vertices in the graph have been selected as seeds, the clusters produced have large overlaps, which will result in high redundancy. Hence, a Redundancy-filtering procedure is designed to process candidate clusters and finally generate protein complexes by eliminating such kind of redundancy. Algorithm 3 shows details of the redundancy process. Suppose that SC is the set of all currently detected complexes and is a newly identified complex. We will first selected an element in SC, which has the highest similarity (OS, overlap score) [14] with . In Algorithm 3, the procedure Redundancy-filtering () is used to check and decide whether to discard or preserve the newly selected Complex . If and are not quite similar (with ), will be inserted into in lines 2-3; otherwise, we prefer to preserve the complexes that have larger size in lines 4–8. For instance, suppose Complex of Figure 2 is one complex belonging to the complex set and is the most similar to the new complex, that is, Complex . After computing the of the two complexes, we obtain a score 0.11 which is less than the threshold . So Complex will be inserted into the complex set SC.

(1) ;

is 's most similar subgraph in SC

(2) if    do

(3)  insert into SC (Inserting);

(4) else

(5)   if    do

(6)      insert into in place of (Substituting);

(7)   else

(8)    discard (Discarding)

Algorithm 3: Redundancy-filtering ().

Figure 2: Example to illustrate the Redundancy-filtering. Complex and Complex contain 14 and 10 proteins, respectively. They share 4 proteins A, B, C, and D.

3. Results

We test the performance of our ClusterBFS method with other five competing algorithms, Markov cluster (MCL) [31], clustering with overlapping neighborhood expansion (ClusterONE) [32], hierarchical clustering on protein interaction network (HC-PIN) [33], speed and performance in clustering (SPICi) [34], and molecular complex detection (MCODE) [14] using the weighted Collins [23] and Krogan datasets [10]. For each algorithm, the final results are obtained after having optimized the algorithm parameters to yield the best possible results. We compare predicted complexes to the reference complex set CYC2008 [35]. We assess the quality of the predicted complexes by two scores: the fraction of protein complexes matched by at least one predicted complex and the maximum matching ratio (MMR) [32]. Our benchmarks show that ClusterBFS outperforms the other approaches on weighted networks, matching more complexes with a higher -measure and providing a better one-to-one mapping with reference complexes in three datasets. To examine the biological relevant of detected complexes we calculate the colocalization and coannotation scores of the entire identified complex set [24]. Comparison of colocalization and coannotation scores of ClusterBFS complexes and other algorithms reveals that ClusterBFS has higher scores on three datasets.

3.1. Data Sources

Yeast has long been known as a highly effective model organism for mammalian biological functions and diseases. We evaluate the effectiveness of ClusterBFS using three different yeast PPI weighted networks. The first dataset is prepared by Collins et al. [23]. For the weighted interaction map of Collins et al., we use the top 9074 interactions as suggested by the authors. These interactions among 1622 proteins have very high confidence scores. The second dataset is the Krogan core dataset [10]. It consists of 7123 reliable interactions involving 2708 proteins. We also use Krogan’s extended dataset [10] containing 3672 nodes and 14317 edges to test ClusterBFS. For evaluating our identified complexes, the set of real complexes from [35] is selected as benchmark.

3.2. Evaluation Measures

One evaluation method we use is to match the generated complexes with known complex set [35] and calculate sensitivity, positive predictive value (PPV), -measure, and MMR, respectively. In information retrieval, positive predictive value is called precision, and sensitivity is called recall. We derive 408 typical complexes including two or more proteins from the CYC2008 [35] as the benchmark complex set and use the same scoring scheme used by [14] to determine how effectively a predicted complex matches a reference complex. If two complexes overlap each other, they must share one or more proteins. The overlap score (OS) of a predicted complex versus a benchmark complex is then a measure of biological significance of the prediction, assuming that the benchmark set of complexes is biologically relevant. The overlap score between a predicted and a real complex is calculated using

where refers to the number of proteins shared by a predicted complex and a benchmark complex, is the number of proteins in the predicted complex, and is the number of proteins in the benchmark complex. If OS is 1, it means that a complex has the same proteins as a benchmark complex. On the contrary, when OS is more than 0, there is not a shared protein between the predicted complex and the benchmark complex [14].

The number of true positives (TP) is defined as the number of predicted complexes with OS over a threshold value and the number of false positives (FP) is the total number of predicted complexes minus TP. The number of false negatives (FN) equals the number of known complexes not matched by predicted complexes. and are defined as TP(TP + FN) and TP/(TP + FP), respectively [14]. -measure, or the harmonic mean of and , can then be used to evaluate the overall performance of the clustering algorithms:

MMR score is proposed by Nepusz et al. [32] based on a maximal one-to-one mapping between detected and reference complexes. Figure 3 illustrates the maximum matching ratio.

Figure 3: Example to illustrate the maximum matching ratio. R1 and R2 are real complexes, while P1, P2, and P3 are three predictions. An edge connects a reference complex and a predicted complex, if their overlap score is larger than zero. The maximum matching is shown by the thick edges. Note that P2 was not matched to R1 since P1 provides a better match with R1. The maximum matching ratio in this example is (0.8 + 0.75)/2 = 0.775.

Owing to the fact that gold standard protein complex sets are incomplete [36], a predicted complex that does not match any of the reference complexes may belong to a valid but previously uncharacterized complex as well. To this end, the matching measures should be complemented with scores that assess the biological relevance of predicted complexes based on the colocalization and coannotation of the constituent proteins instead of relying on a predefined gold standard. Since protein complexes are formed to perform a specific cellular function, proteins within the same complex tend to share common functions and be colocalized [37]. Generally, higher coannotation and colocalization scores [24] show that proteins within the same protein complexes tend to share higher functional similarity. We employ the software suite ProCope (http://www.bio.ifi.lmu.de/Complexes/ProCope/) to compute the colocalization and coannotation scores in our experiment.

3.3. Comparison with the Real Complexes on the Collins Dataset

Table 1 shows the number of detected complexes that match at least one real complex over a range of OS thresholds from threshold of 0 to 1.0 (in 0.1 increments). From Table 1, it can be found that the ClusterBFS algorithm detects the most complexes which match at least one known complex over every interval of OS. The second line in Table 1 shows the number of all complexes discovered by each approach. For instance, ClusterBFS predicts altogether 1229 complexes from the Collins dataset, whereas MCL, ClusterONE, HC-PIN, SPICi, and MCODE find 300, 203, 281, 156, and 111 complexes, respectively. The third line displays that when OS is more than 0.1, ClusterBFS curates 829 complexes matched at least one real complex but MCL, ClusterONE, HC-PIN, SPICi, and MCODE merely mine 199, 148, 187, 123, and 98 complexes like that, respectively. Table 2 gives the number of real complexes which match at least a predicted one. Table 2 shows that the number of real complexes matched by predicted ones from ClusterBFS is also the largest. The experimental results demonstrate that although ClusterBFS obtains the largest number of complexes, the matched complexes from ClusterBFS are much more than those from the other techniques. That is, ClusterBFS identifies a vast amount of high-quality complexes from the weighted Collins network.

Table 1: Comparison of the number of predictions matching at least one known complex.

ClusterBFS
MCL
ClusterONE
HC-PIN
SPICi
MCODE

OS ≥ 0.0
1229
300
203
281
156
111

OS ≥ 0.1
829
199
148
187
123
98

OS ≥ 0.2
697
182
131
170
114
91

OS ≥ 0.3
571
169
123
159
111
88

OS ≥ 0.4
496
161
116
150
107
81

OS ≥ 0.5
398
146
98
139
95
74

OS ≥ 0.6
287
135
87
129
83
64

OS ≥ 0.7
177
106
69
97
65
52

OS ≥ 0.8
128
93
51
86
51
42

OS ≥ 0.9
102
77
38
75
39
34

OS = 1.0
102
74
33
70
33
30

Table 2: Comparison of the number of real complexes matching at least one detected complex.

ClusterBFS
MCL
ClusterONE
HC-PIN
SPICi
MCODE

OS ≥ 0.0
408
408
408
408
408
408

OS ≥ 0.1
298
256
195
244
176
142

OS ≥ 0.2
269
227
164
209
142
113

OS ≥ 0.3
239
196
149
185
129
103

OS ≥ 0.4
224
181
137
171
117
92

OS ≥ 0.5
206
159
111
150
104
82

OS ≥ 0.6
181
145
96
136
88
70

OS ≥ 0.7
133
109
73
100
68
54

OS ≥ 0.8
115
94
52
87
53
42

OS ≥ 0.9
102
77
38
75
39
34

OS = 1.0
102
74
33
70
33
30

In addition, as shown in Tables 1 and 2, when OS is 1, ClusterBFS identifies 102 real complexes. In other words, 102 predicted complexes from ClusterBFS also belong to the known complex set [35] and are much more than ones from one of the other approaches including MCL, ClusterONE, HC-PIN, SPICi, and MCODE, respectively. More importantly, we observe that the reference set includes 408 real complexes, of which 259 complexes are the small size complex only containing 2 or 3 proteins. Actually, our statistical results (not presented in the tables of the paper) show that, in the 102 real complexes predicted by ClusterBFS, there are 78 small size complexes like that. However, MCL, HC-PIN, SPICi, and MCODE only find 74, 70, 33, and 30 real complexes, respectively. At the same time, MCL, HC-PIN, SPICi, and MCODE just detect 54, 49, 15, and 9 small size real complexes. Since ClusterONE discards the complex candidates that contain less than three proteins, we do not compare it with ClusterBFS. The experimental results show that ClusterBFS has the significant performance advantage over the other algorithms in terms of the identification of small size complexes.

Next, we calculate the -measure and MMR scores of the complex sets detected by various techniques. When the -measure is computed, the OS between a predicted complex and a real complex in the benchmark is set as 0.2 [14]. Figure 4 displays the overall comparison according to -measure and MMR. On Collins dataset, the -measure of ClusterBFS is 0.68, which is 23.6%, 51.1%, 30.8%, 58.1%, and 83.8% higher than MCL, ClusterONE, HC-PIN, SPICi, and MCODE, respectively. ClusterBFS can achieve the highest -measure, which shows that our method can predict protein complexes very accurately. From Figure 4, it also can be found that our ClusterBFS method obtains the highest MMR of 0.64, which is 21.8%, 33.3%, 21.8%, 25.5%, and 36.2% higher than MCL, ClusterONE, HC-PIN, SPICi, and MCODE, respectively. That is, ClusterBFS provides a better one-to-one mapping with real complexes in the Collins dataset.

Figure 4: The -measure and MMR of various algorithms on Collins dataset.

3.4. Biological Coherence of Predicted Complexes on Collins Dataset

Figure 5 shows the colocalization and coannotation scores of complexes detected by various methods. From Figure 5, it can be observed that ClusterBFS has the second highest colocalization score in the five methods after SPICi. However, SPICi cannot handle overlaps. Proteins may have multiple functions, and therefore the corresponding nodes may belong to more than one cluster; for example, 207 of 1,628 proteins in the CYC2008 hand-curated yeast complex dataset [35] participate in more than one complex. So it is important to detect the overlapping complexes. In addition, it can be seen that the coannotation score of ClusterBFS is lower than that of MCODE. It means that the complexes mined by MCODE have the highest biological significance. However, the disadvantage of MCODE is that it only discovers 111 complexes. In other words, the high-quality complexes identified by MCODE are not too many. In terms of the coannotation and colocalization, the complexes predicted by our ClusterBFS method are observed to have comparable quality with those predicted by SPICi and MCODE but much better than those predicted by MCL, ClusterONE, and HC-PIN.

Figure 5: Co-localization and co-annotation scores of complexes identified by various methods on Collins dataset.

3.5. Results Using Krogan Dataset

To support the credibility of our method, we perform our ClusterBFS on Krogan’s core dataset [10]. The -measure and MMR of each method using this data are shown in Figure 6. The -measure of our ClusterBFS is 0.50, which is 25.0%, 19.0%, 28.2%, 19.0%, and 127.3% higher than MCL, ClusterONE, HC-PIN, SPICi, and MCODE, respectively. From the perspective of MMR, ClusterBFS obtains the score 0.53, which is 39.5%, 23.2%, 26.2%, 17.8%, and 82.76%higher than MCL, ClusterONE, HC-PIN, SPICi, and MCODE, respectively. Additionally, we also test the biological coherence on Krogan’s core data and gain the results which are similar to ones from Collins data. For simplicity, the results are not shown in the paper. In order to evaluate whether ClusterBFS can apply to the larger scale dataset, we test it on Krogan’s extended dataset. The results are shown in Figure 7. From Figure 7, it can be found that ClusterBFS still obtains the highest scores of -measure and MMR. The experimental results demonstrate that ClusterBFS is not dependent to a particular kind of dataset and can run well on the larger dataset. Besides, it takes around 1 second on an IBM PC with 3.19 GHz processor and 2 GB RAM to generate clusters from Krogan’s extended dataset.

Figure 6: -measure and MMR of various methods for Krogan’s core dataset.

Figure 7: -measure and MMR of various methods for Krogan’s extended dataset.

3.6. Effect of the Parameter Td

In this experiment, we study the effect of the thresholds Td and on the performance of ClusterBFS. Nepusz et al. have merged pairs of complexes with an overlap score OS larger 0.8 [32]. So we also set the parameter 0.8 in order to investigate the performance of ClusterBFS under different Td values. Figure 8 shows the -measure of ClusterBFS under different values of Td based Collins dataset. As shown in Figure 8, when 0.01 ≤ Td ≤ 0.22, the -measure score of ClusterBFS is more than 0.6 and much higher than those of the other algorithms (See Figure 4). Besides, Figure 8 also shows that when , ClusterBFS gets the highest -measure score. In this interval, the -measure score remains unchanged. Therefore, the parameter Td is set as 0.1 in our experiment.

Figure 8: The effect of parameter Td. Figure 8 shows how the variation of parameter Td affects the -measure of ClusterBFS.

4. Conclusion

Protein complexes are important for understanding principles of cellular organization and function. Therefore, much work has been concerned with the prediction of protein complexes from the PPI networks. However, the PPI datasets from high-throughput techniques are flooded with false interactions. In response, some research groups propose a number of data integration and affinity scoring schemes and construct various weighted networks.

In this research, we devise a novel algorithm called ClusterBFS to identify protein complexes from the weighted PPI networks. ClusterBFS derives from the breadth first search method and constitutes protein complexes that originate from a protein seed based on the weighted density. In order to characterize these clusters as protein complexes, we check their biological relevance. This is achieved through some criteria such as -measure, MMR, colocalization, and coannotation measures. The evaluation of our predictions demonstrates the following advantages of ClusterBFS over the compared approaches. First, ClusterBFS has achieved significantly higher -measure and MMR than the existing methods. Thus, our predicted complexes match very well with benchmark complexes. Second, ClusterBFS also performs very well in terms of other measures such as coannotation and colocalization, indicating that ClusterBFS can predict protein complexes very accurately. Last but not least, as mentioned above, the real complex set CYC2008 contains a lot of small complexes and so it is necessary to mine them. In comparison with the other approaches, ClusterBFS discovers much more small size complexes. Our identified complexes, therefore, could be probably the true complexes to help the biologists to get novel biological insights.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of the paper.

Acknowledgments

This work is supported in part by the National Natural Science Foundation of China under Grant nos. 61232001, 61370024, and 61379108, the Program for New Century Excellent Talents in University (NCET-12-0547), the Hunan Provincial Natural Science Foundation of China nos. 13JJ6086 and 12JJ6056, and the Hunan Provincial Soft Science Major Program of China no. 2013ZK2014.

References

R. Sharan, I. Ulitsky, and R. Shamir, “Network-based prediction of protein function,” Molecular Systems Biology, vol. 3, pp. 1–13, 2007.

A. D. King, N. Pržulj, and I. Jurisica, “Protein complex prediction via cost-based clustering,” Bioinformatics, vol. 20, no. 17, pp. 3013–3020, 2004.

C. von Mering, R. Krause, B. Snel et al., “Comparative assessment of large-scale data sets of protein-protein interactions,” Nature, vol. 417, no. 6887, pp. 399–403, 2002.

J. Wang, X. Peng, M. Li, and Y. Pan, “Construction and application of dynamic protein interaction network based on time course gene expression data,” Proteomics, vol. 13, no. 2, pp. 301–312, 2013.

T. Ito, T. Chiba, R. Ozawa, M. Yoshida, M. Hattori, and Y. Sakaki, “A comprehensive two-hybrid analysis to explore the yeast protein interactome,” Proceedings of the National Academy of Sciences of the United States of America, vol. 98, no. 8, pp. 4569–4574, 2001.

O. Puig, F. Caspary, G. Rigaut et al., “The tandem affinity purification (TAP) method: a general procedure of protein complex purification,” Methods, vol. 24, no. 3, pp. 218–229, 2001.

Y. Ho, A. Gruhler, A. Heilbut et al., “Systematic identification of protein complexes in Saccharomyces cerevisiae by mass spectrometry,” Nature, vol. 415, no. 6868, pp. 180–183, 2002.

M. Schena, D. Shalon, R. W. Davis, and P. O. Brown, “Quantitative monitoring of gene expression patterns with a complementary DNA microarray,” Science, vol. 270, no. 5235, pp. 467–470, 1995.

G. Ramsay, “DNA chips: state-of-the art,” Nature Biotechnology, vol. 16, no. 1, pp. 40–44, 1998.

N. J. Krogan, G. Cagney, H. Yu et al., “Global landscape of protein complexes in the yeast Saccharomyces cerevisiae,” Nature, vol. 440, no. 7084, pp. 637–643, 2006.

A.-C. Gavin, P. Aloy, P. Grandi et al., “Proteome survey reveals modularity of the yeast cell machinery,” Nature, vol. 440, no. 7084, pp. 631–636, 2006.

V. Spirin and L. A. Mirny, “Protein complexes and functional modules in molecular networks,” Proceedings of the National Academy of Sciences of the United States of America, vol. 100, no. 21, pp. 12123–12128, 2003.

G. Palla, I. Derényi, I. Farkas, and T. Vicsek, “Uncovering the overlapping community structure of complex networks in nature and society,” Nature, vol. 435, no. 7043, pp. 814–818, 2005.

G. D. Bader and C. W. V. Hogue, “An automated method for finding molecular complexes in large protein interaction networks,” BMC Bioinformatics, vol. 4, no. 1, p. 2, 2003.

J. Wang, P. Tan, J. Yao, Q. Feng, and J. Chen, “On the minimum link-length rectilinear spanning path problem: complexity and algorithms,” IEEE Transactions on Computers, 2014.

M. Wu, X. Li, C.-K. Kwoh, and S.-K. Ng, “A core-attachment based method to detect protein complexes in PPI networks,” BMC Bioinformatics, vol. 10, no. 1, article 169, 2009.

X. Ding, W. Wang, X. Peng, and J. Wang, “Mining protein complexes from PPI networks using the minimum vertex cut,” Tsinghua Science and Technology, vol. 17, no. 6, pp. 674–681, 2012.

B. Zhao, J. Wang, M. Li, F. Wu, and Y. Pan, “Detecting protein complex based on uncertain graph model,” IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2013.

E. Sprinzak, S. Sattath, and H. Margalit, “How reliable are experimental protein-protein interaction data?” Journal of Molecular Biology, vol. 327, no. 5, pp. 919–923, 2003.

J. Chen and B. Yuan, “Detecting functional modules in the yeast protein-protein interaction network,” Bioinformatics, vol. 22, no. 18, pp. 2283–2290, 2006.

G. D. Bader and C. W. V. Hogue, “Analyzing yeast protein-protein interaction data obtained from different sources,” Nature Biotechnology, vol. 20, no. 10, pp. 991–997, 2002.

N. N. Batada, L. D. Hurst, and M. Tyers, “Evolutionary and physiological importance of hub proteins,” PLoS Computational Biology, vol. 2, article e88, 2006.

S. R. Collins, P. Kemmeren, X.-C. Zhao et al., “Toward a comprehensive atlas of the physical interactome of Saccharomyces cerevisiae,” Molecular and Cellular Proteomics, vol. 6, no. 3, pp. 439–450, 2007.

C. C. Friedel, J. Krumsiek, and R. Zimmer, “Bootstrapping the interactome: unsupervised identification of protein complexes in yeast,” Journal of Computational Biology, vol. 16, no. 8, pp. 971–987, 2009.

X. Tang, Q. Feng, J. Wang, Y. He, and Y. Pan, “Clustering based on multiple biological information: approach for predicting protein complexes,” IET Systems Biology, vol. 7, no. 5, pp. 223–230, 2013.

M. Wu, Z. Xie, X. Li, C. K. Kwoh, and J. Zheng, “Identifying protein complexes from heterogeneous biological data,” Proteins: Structure, Function, and Bioinformatics, vol. 81, no. 11, pp. 2023–2033, 2013.

X. Tang, J. Wang, J. Zhong, and Y. Pan, “Predicting essential proteins based on weighted degree centrality,” IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2014.

M. Li, R. Zheng, H. Zhang, J. Wang, and Y. Pan, “Effective identification of essential proteins based on priori knowledge, network topology and gene expressions,” Methods, 2014.

W. Kim, “Prediction of essential proteins using topological properties in GO-pruned PPI network based on machine learning methods,” Tsinghua Science and Technology, vol. 17, no. 6, pp. 645–658, 2012.

G. Liu, L. Wong, and H. N. Chua, “Complex discovery from weighted PPI networks,” Bioinformatics, vol. 25, no. 15, pp. 1891–1897, 2009.

A. J. Enright, S. van Dongen, and C. A. Ouzounis, “An efficient algorithm for large-scale detection of protein families,” Nucleic Acids Research, vol. 30, no. 7, pp. 1575–1584, 2002.

T. Nepusz, H. Yu, and A. Paccanaro, “Detecting overlapping protein complexes in protein-protein interaction networks,” Nature Methods, vol. 9, no. 5, pp. 471–472, 2012.

J. Wang, M. Li, J. Chen, and Y. Pan, “A fast hierarchical clustering algorithm for functional modules discovery in protein interaction networks,” IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. 3, pp. 607–620, 2011.

P. Jiang and M. Singh, “SPICi: a fast clustering algorithm for large biological networks,” Bioinformatics, vol. 26, no. 8, pp. 1105–1111, 2010.

S. Pu, J. Wong, B. Turner, E. Cho, and S. J. Wodak, “Up-to-date catalogues of yeast protein complexes,” Nucleic Acids Research, vol. 37, no. 3, pp. 825–831, 2009.

R. Jansen and M. Gerstein, “Analyzing protein function on a genomic scale: the importance of gold-standard positives and negatives for network prediction,” Current Opinion in Microbiology, vol. 7, no. 5, pp. 535–545, 2004.

R. Jansen, H. Yu, D. Greenbaum et al., “A bayesian networks approach for predicting protein-protein interactions from genomic data,” Science, vol. 302, no. 5644, pp. 449–453, 2003.