 Research
 Open Access
iOPTICSGSO for identifying protein complexes from dynamic PPI networks
 Xiujuan Lei^{1}Email author,
 Huan Li^{1},
 Aidong Zhang^{2} and
 FangXiang Wu^{3, 4}Email author
https://doi.org/10.1186/s129200170314x
© The Author(s). 2017
 Published: 28 December 2017
Abstract
Background
Identifying protein complexes plays an important role for understanding cellular organization and functional mechanisms. As plenty of evidences have indicated that dense subnetworks in dynamic proteinprotein interaction network (DPIN) usually correspond to protein complexes, identifying protein complexes is formulated as densitybased clustering.
Methods
In this paper, a new approach named iOPTICSGSO is developed, which is the improved Ordering Points to Identify the Clustering Structure (OPTICS) algorithm with Glowworm swarm optimization algorithm (GSO) to optimize the parameters in OPTICS when finding dense subnetworks. In our iOPTICSGSO, the concept of core node is redefined and the Euclidean distance in OPTICS is replaced with the improved similarity between the nodes in the PPI network according to their interaction strength, and dense subnetworks are considered as protein complexes.
Results
The experiment results have shown that our iOPTICSGSO outperforms of algorithms such as DBSCAN, CFinder, MCODE, CMC, COACH, ClusterOne MCL and OPTICS_PSO in terms of fmeasure and pvalue on four DPINs, which are from the DIP, Krogan, MIPS and Gavin datasets. In addition, our predicted protein complexes have a small pvalue and thus are highly likely to be true protein complexes.
Conclusion
The proposed iOPTICSGSO gains optimal clustering results by adopting GSO algorithm to optimize the parameters in OPTICS, and the result on four datasets shows superior performance. What’s more, the results provided clues for biologists to verify and find new protein complexes.
Keywords
 Ordering points to identify the clustering structure algorithm (OPTICS)
 Glowworm swarm optimization algorithm (GSO)
 Protein complex
 Densitybased clustering
Background
Proteins are the indispensable components in various types of cells and tissues, and the executors of the biological functions. At the same time, each protein in the cell does not exist in isolation, and the occurrence of every life process must involve more than one protein [1]. Protein complexes are not only the basis of normal biological processes, also play important role in the pathological processes [2]. Therefore, identifying protein complexes play an important role in understanding the cellular organizations and functional mechanisms [3]. As a variety of protein interaction database have produced, it is possible to identify protein complexes from proteinprotein interaction (PPI) networks. Living organisms are always changing, so are PPIs in living cells [4]. In addition, the interactions between proteins are changing over time not only with the presence and degradation of protein, but also with the environment. In [5], the authors incorporated the “time” factor for proteins in the form of cellcycle phases into the analysis of complexes and studied the dynamic phenomena of complexes assembly and disassembly across various cell cycles. To express the dynamics, many dynamic data, including gene expression profiles [6], have been used to construct dynamic PPI networks (DPINs).
The discovery of protein complexes is equivalent to find subsets of functionrelated proteins from a data set. Clustering is an effective method, which can find subsets that have some common attributes from the database [7]. Therefore, the development of improved clustering algorithms has received a lot of attention in the last few years. The clustering algorithm based on density is an important type of clustering analysis method and one of its main advantages is able to detect any shape of cluster while being not sensitive to noise [8]. The DensityBased Spatial Clustering of Applications with Noise (DBSCAN) [9], which was proposed by Ester et al., is a clustering algorithm based on density. The DBSCAN algorithm is applicable to any shape and size of the dataset. It is noisetolerant and independent of ordering of data objects. However, it has two initial parameters, the field radius and the minimum point within the field radius. The DBSCAN algorithm requires the user to manually input these two parameters while the clustering results are very sensitive to the values of two parameters. The DBSCAN algorithm also needs initialization parameters. In order to overcome those shortcomings of DBSCAN algorithm, Ankerst et al. [10] proposed a new algorithm called Ordering Points to Identify the Clustering Structure (OPTICS). Its basic idea is similar to DBSCAN when identifying clusters, and both searching for high density regions.
In real life, many optimization problems require not only to calculate the extremum, but also obtain their optimal values. This kind of problem is a serious challenge to the traditional algorithm. In this case, a growing number of swarm intelligence algorithms are successively put forward, such as Genetic Algorithm (GA) [11], Particle Swarm Optimization (PSO) [12]. Glowworm swarm optimization algorithm (GSO) [13], proposed by Krishnan and Ghose in 2005, is a bionic swarm intelligence algorithm. GSO simulates the glowworm group in motion guided by fluorescence to attract other glowworms or foraging around, the greater the value of fluorescein, the bright the glowworm is, and the more attractive it is.
OPTICS algorithm does not produce cluster for a data set explicitly; but instead creates an augmented ordering queue representing its densitybased clustering structure. Then we need to deal with clusterordering and get clustering results. For each network clustering, different parameters settings produce different results. In this study, we put forward the algorithm named iOPTICSGSO which is the improved OPTICS algorithm by using GSO to optimize the parameters in OPTICS. In order to investigate its performance, iOPTICSGSO with other seven computing methods including DBSCAN [9], CFinder [14], MCODE [15], CMC [16], COACH [17], ClusterOne [18], MCL [19] and OPTICS_PSO [20]. At the same time, we also use the pvalue for function enrichment analysis. The experiment results illustrated that iOPTICSGSO achieved better performance compared with other competing algorithms.
The outline of this paper is as follows. In Section 2, after reviewing the GSO algorithm, basic OPTICS and our iOPTICSGSO are presented. In Section 3, experimental results and analysis are described and discussed, and the conclusions are in Section 4.
Methods
GSO algorithm
In the GSO algorithm, glowworms with higher fluorescein are more attractive to other glowworms, and thus a group of glowworms move towards the glowworms with high fluorescein. Each glowworm in its dynamic decision domain radius chooses a glowworm whose fluorescein value is higher than its own fluorescein value to move towards and updates its dynamic decisionmaking domain. Then some glowworms are selected according to probability to update the position from dynamic decisionmaking domain. Finally, the decision domain updated. GSO algorithm has two important phases as follows.
The phase for updating the fluorescein.
The phase of updating the position.
In the GSO, each glowworm is looking for the neighborhood within its field of vision, and then moves to a brighter glowworm. Each time the moving direction depends on the neighborhood selection. In addition, the glowworm decision domain radius size is influenced by the number of glowworms in different neighborhoods, when the number of glowworms is too small, glowworms will increase their decisions radius in order to find more glowworms; On the contrary, they will reduce their own decisionmaking radius. At the end, the GSO makes most of the glowworms gathered in a better position.
Optics
The key idea of densitybased clustering such as OPTICS is that for each object in a cluster the neighborhood within a given radius has to contain at least a minimum number of objects (MinPts), which is the cardinality of the neighborhood. The condition Card(N _{ ε }(q)) ≥ MinPts is called the “core object condition”. If this condition holds for an object p, then we call p a “core object”. Only from core objects, can other objects be directly densityreachable.
In PPI networks, the node degrees obey powerlaw distribution, we select all nodes as core nodes so that the node which degree is small can be considered. As a result, we redefined two definitions as follows.
Definition 1: (Distance_{ core } of node p).
Definition 2: (Distance_{reachability} of node p).
The proposed iOPTICSGSO
 1.
Calculating the distance in a PPI network
 2.
Clustering PPI network.
 3.
iOPTICSGSO Algorithm.
The value of parameters which corresponding to the best result in each subnetwork on DIP
Timestamps  1  2  3  4  5  6  7  8  9  10  11  12 

ɛ  0.62  0.50  0.52  0.59  0.60  0.58  0.62  0.51  0.55  0.64  0.60  0.60 
MinPts  3  3  3  3  3  3  3  3  3  3  3  3 
precision  0.7500  0.7421  0.8182  0.9000  0.8462  0.8889  0.9048  0.7805  0.6064  0.7419  0.6970  0.9524 
recall  0.5263  0.5122  0.3971  0.4500  0.4400  0.2587  0.3115  0.5565  0.5089  0.5897  0.5349  0.5882 
fmeasure  0.6185  0.6000  0.5347  0.6000  0.5789  0.4324  0.4634  0.6497  0.5534  0.6571  0.6053  0.7273 
It is well known that the GSO algorithm has less parameters, simple operation and good stability, etc. GSO algorithm simulates the characteristic of glowworms glow in nature, by comparing the size of the fluorescein value to achieve the purpose of communication, so as to realize the optimization of the problem. So we introduce the GSO algorithm to optimize the parameters of OPTICS, in order to obtain optimal results. Algorithm2 describes the details of iOPTICSGSO. After several circulations iterative process, a glowworm constantly updates its position and iteratively approaches to the best position. At last, the glowworm finds the best position.
 4.
Time complexity analysis of iOPTICSGSO algorithm

The time complexity of OPTICS algorithm is O (num ^{2}).

The time complexity of computing the fitness of glowworms is O (PopSize * O (num ^{2}).

The time complexity of glowworms moving process is O (PopSize ^{2}).

The time complexity for updating the position O is (PopSize).
Results and discussion
Experimental datasets
In this study, we used four static PPI networks for yeast, including DIP [24], Krogan [25], MIPS [26] and Gavin [27] to evaluate our proposed iOPTICSGSO. The DIP data consists of 4995 proteins and 21,554 interactions, Krogan data consists of 2674 proteins and 7075 interactions, MIPS data consists of 4546 proteins and 12,319 interactions and Gavin data consists of 1430 proteins and 6531 interactions. For verifying protein complexes identified by our proposed method, the set of protein complexes derived from CYC2008 [28] is selected as the gold standard dataset in this study, which includes 408 protein complexes and covers 1492 proteins,
The number of proteins and interactions in each subnetwork of the four datasets contain
DIP data  Timestamps  1  2  3  4  5  6  7  8  9  10  11  12 

Proteins  797  941  796  623  610  530  493  944  1090  591  661  461  
Interactions  981  1444  1188  745  750  646  573  1705  2185  856  974  526  
Krogan data  Timestamps  1  2  3  4  5  6  7  8  9  10  11  12 
Proteins  336  379  320  256  206  189  202  580  626  304  330  250  
Interactions  334  464  331  234  210  184  213  1025  1081  314  373  258  
MIPS data  Timestamps  1  2  3  4  5  6  7  8  9  10  11  12 
Proteins  737  897  781  583  570  531  470  839  1,014  523  616  402  
Interactions  1097  1443  1183  754  684  642  504  1238  1637  878  1207  700  
Gavin data  Timestamps  1  2  3  4  5  6  7  8  9  10  11  12 
Proteins  177  228  215  135  112  102  96  379  419  174  190  146  
Interactions  242  334  317  150  135  118  135  1019  1043  230  264  184 
Performance evaluation
The effect of parameter
In Fig. 4, the effect of different values of MinPts on fmeasure is not very big, and this also confirms that the reachabilityplot is rather insensitive to the input parameter of the method. We observe that the value of fmeasure increases initially as the value of MinPts increases and decreases after reaching the maximum. Then we chose the value of MinPts at which the fmeasure reaches the maximum in iOPTICSGSO. As a result, we find that the optimal values of MinPts are 3, 2, 2 and 4 for DIP, Krogan, MIPS and Gavin, respectively.
Clustering comparisons
Description of clusters predicted by several clustering algorithms
Algorithms  Category  Cluster  Average Size  

DIP  Krogan  MIPS  Gavin  DIP  Krogan  MIPS  Gavin  
CMC [16]  Density  1263  907  168  486  4.39  4.56  –  5.55 
COACH [17]  Core  903  547  448  361  3.89  8.97  –  8.26 
MCL [19]  Flow  623  932  –  425  6.57  3.62  –  3.93 
MCODE [15]  Density  63  85  85  150  19.00  5.88  –  6.63 
ClusterOne [18]  Graph  372  373  256  312  4.90  4.29  –  6.35 
CFinder [14]  Density  609  88  –  137  6.18  12.73  –  9.6 
DBSCAN [19]  Density  492  96  130  24  6.26  34.43  14.3  12.7 
OPTICS  Density  107  278  439  108  5.90  4.17  9  13.5 
OPTICS_PSO [20]  Density  76  119  98  84  5.59  8.05  33  8.45 
iOPTICSGSO  Density  99  143  86  101  5.76  5.62  26.5  8.14 
From Table 3, we can see that the numbers of clusters obtained by the proposed algorithm on four datasets are smaller than those compared methods. The reason of this result is that the number of interactions in most subnetworks is sparse, so the distance of these nodes calculated by Eq. (7) would be up to 1, and these nodes were regarded as a class, respectively. In the final phase, we filtered the results from each sunnetwork clustering, and deleted some clustering modules whose density was smaller or had only one node.
Comparison of the functional enrichment of protein complexes with other algorithms on four datasets
Dataset  Algorithm  <E15  [E15, E10]  [E10, E5]  [E5, 0.01]  <0.01 significant  ≥0.01 insignificant 

DIP  COACH  33(6.96%)  44(9.28%)  205(43.25%)  126(26.58%)  408(86.08%)  66(13.92%) 
MCL  19(1.80%)  47(4.46%)  183(17.38%)  362(34.38%)  611(58.02%)  442(41.98%)  
MCODE  12(7.27%)  17(10.30%)  80(48.48%)  38(23.03%)  147(89.09%)  18(10.91%)  
ClusterOne  21(3.66%)  52(9.06%)  177(30.84%)  184(32.06%)  434(75.61%)  140(24.39%)  
OPTICS  7(7.87%)  13(14.61%)  40(44.94%)  21(23.6%)  81(91.01%)  8(8.99%)  
OPTICS_PSO  5(6.85%)  10(13.70%)  27(36.99%)  23(31.51%)  65(89.04%)  8(10.96%)  
iOPTICSGSO  6(8.70%)  15(21.74%)  29(42.03%)  13(18.84%)  63(91.30%)  6(8.70%)  
Krogan  COACH  23(10.41%)  37(16.74%)  91(41.18%)  54(24.43%)  205(92.76%)  16(7.24%) 
MCL  16(3.97%)  43(10.67%)  103(25.56%)  119(29.53%)  281(69.73%)  122(30.27%)  
MCODE  8(5.00%)  28(17.50%)  68(42.50%)  46(28.75%)  150(93.75%)  10(6.25%)  
ClusterOne  13(3.26%)  43(10.78%)  98(24.56%)  120(30.08%)  274(68.67%)  125(31.33%)  
OPTICS  13(8.44%)  26(16.88%)  56(36.36%)  31(20.13%)  126(81.82%)  28(18.18%)  
OPTICS_PSO  9(9.47%)  19(20.0%)  41(43.16%)  21(22.11%)  90(94.74%)  5(5.26%)  
iOPTICSGSO  11(12.22%)  23(25.56%)  37(41.11%)  19(21.11%)  90(100%)  0(0%)  
MIPS  COACH  16(4.04%)  46(11.62%)  145(36.62%)  149(37.63%)  356(89.9%)  40(10.10%) 
MCL  5(0.83%)  13(2.15%)  94(15.51%)  220(36.30%)  332(54.79%)  274(45.21%)  
MCODE  5(3.70%)  10(7.41%)  70(51.58%)  39(28.89%)  124(91.85%)  11(8.15%)  
ClusterOne  7(1.88%)  16(4.30%)  117(31.45%)  126(33.87%)  266(71.51%)  106(28.49%)  
OPTICS  16(5.63%)  6(2.11%)  26(9.15%)  74(26.06%)  122(42.96%)  162(57.04%)  
OPTICS_PSO  10(11.76%)  3(3.53%)  28(32.94%)  30(35.29%)  71(83.53%)  14(16.47%)  
iOPTICSGSO  7(11.67%)  5(8.33%)  12(20%)  25(41.67%)  49(81.67%)  11(18.33%)  
Gavin  COACH  35(14.96%)  39(16.67%)  100(42.72%)  55(23.50%)  229(97.86%)  5(2.14%) 
MCL  22(9.69%)  34(14.98%)  88(38.77%)  66(29.07%)  110(92.51%)  17(7.49%)  
MCODE  12(7.74%)  20(12.90%)  80(51.61%)  39(25.16%)  151(97.42%)  4(2.58%)  
ClusterOne  31(10.62%)  34(11.64%)  118(40.41%)  82(28.08%)  292(90.75%)  27(9.25%)  
OPTICS  20(18.52%)  13(12.04%)  53(49.07%)  19(17.59%)  105(97.22%)  3(2.78%)  
OPTICS_PSO  15(18.07%)  13(15.66%)  38(45.78%)  16(19.28%)  82(98.80%)  1(1.20%)  
iOPTICSGSO  21(26.25%)  11(13.75%)  31(38.75%)  16(20%)  79(98.75%)  1(1.25%) 
Some examples of the predicted complexes with small pvalue on Gavin data
No.  Predicted protein complex  pvalue  Gene Ontology term  OS 

1  YKL144C YNR003C YPR110C YPR190C YDL150W YKR025W YNL151C YBR154C YJL011C YNL113W YDR045C YNL248C YJR063W YOR340C YIL021W YML010W  1.22E35  0.44  
2  YJL069C YLR409C YLR222C YLR129W YDR449C YCR057C YGL171W YDR365C YKR060W YDR299W YGR145W YDL213C YNL075W YHR148W YLR186W YLL011W YJR002W YPL217C YGR128C YNL132W YMR093W YCL059C YPR144C YER082C YPR137W YBR247C YPL126W YDR324C YHR196W YOR078W YDL148C YJL109C YMR128W YOL010W YNL308C YHR169W YPR112C YDL166C YLR003C YGR081C YOR056C YGR054W YKL143W YNL207W YPL204W YCL011C YJL033W YKL059C YLR115W YAL043C YLR277C YNL317W YKL018W YJR093C  5.46E32  0.11  
3  YML114C YCR042C YPL011C YDR167W YMR236W YBR198C YGL112C YMR005W YML015C YDR145W YMR227C YBR081C YLR055C YDR448W YGR252W YDR392W YPL254W  2.37E26  0.47  
4  YCR042C YML114C YMR005W YML015C YPL011C YMR236W YGR274C YBR198C YGL112C YLR055C YCL010C YDR448W YPL254W  1.67E21  0.41  
5  YLR129W YLR409C YDR449C YCR057C YPL266W YPR112C YDR299W YGR128C YPL126W YJR002W YDR324C YNL132W YPL217C YBL004W YDL148C YER082C YHR196W YGR090W YCL059C YLR003C YCL011C YCL031C YDL213C  2.91E17  0.12  
6  YLR418C YGL244W YOL145C YBR279W YOR123C YGL019W YOR039W YMR309C YPL181W  6.89E14  RNA polymerase II Cterminal domain phosphoserine binding (GO:1990269)  0.36 
7  YHL025W YBR289W YPL016W YPR034W YJL176C YFL049W YHR023W YPL082C YNL059C YNL272C YML114C YPL011C YDR176W YBR198C YDR392W YGL066W YOL148C YDR145W YER164W YKR001C YDR073W YML069W YKL088W YMR172W  4.3E11  0.17  
8  YHR156C YHR165C YER172C YPR082C YDL087C YGR013W YDR283C YJL203W YDR416 YGL128C YLR117C YAL032C YPR178W YBL104C YGL100W YIL061C  2.45E07  second spliceosomal transesterification activity (GO:0000386)  0.07 
Conclusions
Protein complexes are not only the basis of normal biological processes, but also play an important role in the pathological process. Therefore, identifying protein complexes play an important role in understanding the cellular organizations and functional mechanisms. In this study, we have put forward the algorithm named iOPTICSGSO, which is the improved OPTICS algorithm by using GSO to optimize the parameter in OPTICS, and we changed the concept of core node and redefine the similarity which makes more accord with the actual situation of PPI network. As different parameter setting have different results on each subnetwork of DPIN, we have used GSO algorithm to optimize these parameters, and finally checked the quality of every cluster and gained the optimal cluster results. The experiment results have shown that our iOPTICSGSO outperforms competing algorithms in terms of fmeasure and pvalue. It means the results from iOPTICSGSO are more biologically meaningful than others for identifying significant proteins complexes. However we also found that the number of clustering modules is relatively small and the recall of clustering results is lower than other algorithms in iOPTICSGSO results. The reason may be that each protein only can belong to one cluster in iOPTICSGSO, which causes that other clustering modules are small. Therefore, it would be our focus to discover the effective strategy to improve the result and detect more protein complexes in the future.
Declarations
Acknowledgements
We are grateful to the help of National Natural Science Foundation of China. We appreciate the experimental conditions provided by our college. Especially, we thank our laboratory members for useful discussion and comments.
Funding
This paper is supported by the National Natural Science Foundation of China (61,672,334, 61,502,290, and 61,401,263).
Availability of data and materials
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
About this supplement
This article has been published as part of BMC Medical Genomics Volume 10 Supplement 5, 2017: Selected articles from the IEEE BIBM International Conference on Bioinformatics & Biomedicine (BIBM) 2016: medical genomics. The full contents of the supplement are available online at https://bmcmedgenomics.biomedcentral.com/articles/supplements/volume10supplement5.
Authors’ contributions
X.L. conceive the study, guided the design of the method and the algorithm. H.L. designed and performed the experiment and analyzed the data. X.L. and H.L. drafted the manuscript. A.ZH. and F.X.W revised the manuscript and polished the English expression. All the authors read and approved the manuscript.
Ethics approval and consent to participate
Not applicable
Consent for publication
Not applicable
Competing interests
The authors declare that they have no competing interests.
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Authors’ Affiliations
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