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Volume 20 Supplement 3

Selected articles from the 17th Asia Pacific Bioinformatics Conference (APBC 2019): bioinformatics

Protein complex detection based on flower pollination mechanism in multi-relation reconstructed dynamic protein networks

BMC Bioinformatics volume 20, Article number: 131 (2019) Cite this article

Abstract

Background

Detecting protein complex in protein-protein interaction (PPI) networks plays a significant part in bioinformatics field. It enables us to obtain the better understanding for the structures and characteristics of biological systems.

Methods

In this study, we present a novel algorithm, named Improved Flower Pollination Algorithm (IFPA), to identify protein complexes in multi-relation reconstructed dynamic PPI networks. Specifically, we first introduce a concept called co-essentiality, which considers the protein essentiality to search essential interactions, Then, we devise the multi-relation reconstructed dynamic PPI networks (MRDPNs) and discover the potential cores of protein complexes in MRDPNs. Finally, an IFPA algorithm is put forward based on the flower pollination mechanism to generate protein complexes by simulating the process of pollen find the optimal pollination plants, namely, attach the peripheries to the corresponding cores.

Results

The experimental results on three different datasets (DIP, MIPS and Krogan) show that our IFPA algorithm is more superior to some representative methods in the prediction of protein complexes.

Conclusions

Our proposed IFPA algorithm is powerful in protein complex detection by building multi-relation reconstructed dynamic protein networks and using improved flower pollination algorithm. The experimental results indicate that our IFPA algorithm can obtain better performance than other methods.

Background

Understanding biological processes is an important task in the living organisms. Proteins are vital components in many biological processes, such as metabolism, signaling, transportation and so on. Biological functions are performed by protein complexes composed of proteins interacted with each other, rather than by individual proteins [1, 2]. Detection of protein complexes made great contribution to our knowledge of the molecular mechanisms in cellular life activities. To the best of our knowledge, a large number of works have been done to identify protein complexes from the PPI networks up to now.

As one of the earliest computational methods to predict protein complexes, the Molecular Complex Detection (MCODE) [3] weighted all vertices by using their local neighborhood density and identified the densely connected areas in PPI networks. ClusterONE [4] was utilized to find overlapping protein complexes in the PPI networks. The Clustering-based on Maximal Cliques (CMC) [5] method weighted the interacting protein pairs to identify protein complex. Recent studies TP-WDPIN [6] and NEOComplex [7] were based on the seed-extension idea to mine protein complexes. WG-Cluster [8] considered the edge weights to detect network modules. Markov Clustering (MCL) [9] discovered relatively dense regions based on the random walks. After that, F-MCL [10] used the firefly algorithm into Markov clustering to optimize the parameters and then recognized protein complexes.

It is well known that Gavin et al. [11] introduced the proteins in complexes consist of two types: core and attachment (periphery), namely, core-attachment structure, core represents the proteins that are densely linked and attachment are those proteins that have a few connections to the core. And then, CORE [12] first identified cores and then added proteins that had interactions with the majority of core proteins in the protein complex as attachment proteins. COACH [13] predicted cores in complexes and involved attachments into the cores to obtain protein complexes. Similarly, DCA [14] also used core-attachment feature to identify protein complexes.

In general, the judgment of interactions between two proteins is implemented by using experimental methods. Unfortunately, these methods are not always dependable [1] and it means that this may contain false positive interactions. There are many previous literatures have revealed the fact that the incorporation of additional biological information can improve the accuracy of protein complex prediction to some extent. For example, Zhang et al. [15] proposed CSO method to predict complexes by combining gene ontology (GO) information with PPI networks. InteHC method [16] integrated different types of data sources to predict protein complexes, including PPI data, GO data, gene expression profiles and AP-MS data. Zhao et al. [17] constructed the weighted protein interaction network by using gene expression information for protein complex identification. Zhou et al. [18] utilized GO to measure semantic similarities as the weights.

Since the flower pollination algorithm (FPA) [19] has shown excellent performance in many applications, such as clustering problem [20] and the identification of essential proteins [21], we explore the application of FPA in detecting protein complexes. In this study, we elicit a concept named co-essentiality, whose basic idea is to use the protein essentiality to find essential edges. Then the multi-relation reconstructed dynamic protein networks are built by combining heterogeneous topology and biology information. Next, those closely linked proteins are grouped together as the cores. Finally, based on the core–periphery structure, the modified FPA algorithm is developed to find the optimal pollination plants for pollen, which means that the peripheries attach to the best core to form the predicted protein complex. The experiments between IFPA and several typical algorithms including MCODE, MCL, ClusterONE, CSO, COACH and CORE are performed on three different PPI networks, and the results demonstrate that IFPA algorithm is more robust and powerful than those existing methods in protein complexes recognition.

The remaining part of this paper is organized as follows. Section 2 (Methods) elucidates our proposed new algorithm called IFPA. Section 3 (Results and Discussion) provides the exhaustive analysis and descriptions for the experiments. Finally, Section 4 (Conclusions) is the summary of this study.

Methods

The PPI network can be represented generally as an undirected graph, and the proteins are treated as nodes and the interactions are considered as edges. Here, the static PPI networks are converted into the multi-relation reconstructed dynamic PPI networks. And then we apply IFPA to add attachments to the appropriate cores based on the core-attachment structure.

Building multi-relation reconstructed dynamic PPI networks

The availability of gene expression data enables researchers to reveal the dynamics of molecular networks and improve the identification of protein complexes [22,23,24]. Hence, based on the study [25], the time course gene expression data is integrated into original static PPI networks to generate dynamic PPI subnetworks so that we can capture the dynamics of protein complexes, that is to say, we split the original static PPI network (OSPN) into twelve dynamic PPI subnetworks (DPSNs), in which all interactions in a DPSN can occur simultaneously, and then perform complex discovery on each DPSN.

First, we use three-sigma method [25] in order to construct dynamic PPI subnetworks with time series gene expression data. The gene expression data involves three metabolic cycles and each cycle contains twelve timestamps. A protein v is considered to be active in DPSN if its gene expression value is not less than the active threshold Active_Th(v):

$$ Active\_ Th(v)=\mu (v)+\kern0.5em 3\sigma (v)\left(1-F(v)\right) $$
(1)
$$ F(v)=\kern0.5em \frac{1}{1+\kern0.5em {\sigma}^2(v)} $$
(2)

where μ(v) is the algorithmic mean of gene expression values of v over times 1 to n and σ(v) is the standard deviation of its gene expression values. For each protein, three-sigma method is used to calculate the active threshold Active_Th(v). A original PPI network can be described as an undirected graph G(V, E), where V denotes node set that are proteins and E presents edge set that are their connections. And the dynamic PPI network can be represented as Gt (Vt, Et) at timestamp t (t = 1,2, …, n). At a certain time point, if two proteins vi and vj are active and interact with each other in the original static PPI network, then there is a connection between protein vi and vj in a DPSN. After that, twelve dynamic PPI subnetworks are constructed from the original static PPI network.

Moreover, integrating heterogeneous data source into a single network can enhance the reliability of networks, which inspires us that assigning the suitable weights to edges can strengthen the confidence of interactions, and the implementation will be discussed in the following. Figure 1 illustrates an example of multi-relation reconstructed dynamic PPI networks construction.

  • Definition 1 (Co-essentiality) Essential proteins are indispensable for the survival of an organism. Then we can believe that the interaction between two essential proteins is also necessary. Hence, a concept based on essential protein is extended to measure the essentiality between two proteins, and the essentiality values are considered as their weights.

Fig. 1
figure1

An example of multi-relation reconstructed dynamic PPI networks construction

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Before giving the concept of co-essentiality, we first elaborate the definition of an essential edge. Given two proteins vi and vj, the edge between them is considered as an essential edge if both of vi and vj are the essential proteins, similarly, the edge between them is considered as an uncertain edge if vi or vj is the essential protein, and the edge between them is considered as a nonessential edge if neither of vi and vj is the essential protein. Only the essential edges are taken into account to reconstruct the networks here. And eeij is the essential edge between vi and vj, the co-essentiality between these two proteins can be represented as follows.

$$ co- essentiality\kern0.5em \left(i,j\right)=\kern0.5em \frac{ESS_{ij}}{sum\kern0.5em \left({ESS}_j\right)} $$
(3)

where ESSij denotes the weight value of essential edge which equals to one and sum(ESSj) denotes the sum of the weight values of a column.

  • Definition 2 (Co-localization) Given two interacting proteins vi and vj, the interaction between them will be more reliable if vi and vj exist in same subcellular location, its co-localization is defined by the following equation.

$$ co- localization\kern0.5em \left(i,j\right)=\kern0.5em \frac{{\left|{SCL}_i\kern0.5em \cap \kern0.5em {SCL}_j\right|}^2}{\mid {SCL}_i\mid \cdot \mid {SCL}_j\mid } $$
(4)

where |SCLi| and |SCLj| are the number of subcellular location of proteins vi and vj, respectively.

  • Definition 3 (Co-annotation) Given two interacting proteins vi and vj, they have the similar function if there are some common GO annotations between vi and vj, its co-annotation is calculated as follows.

$$ co- annotation\left(i,j\right)=\frac{{\left|{GO}_i\cap {GO}_j\right|}^2}{\left|{GO}_i\right|\cdot \left|{GO}_j\right|} $$
(5)

where |GOi| and |GOj| are the number of GO annotations of proteins vi and vj, respectively.

  • Definition 4 (Co-cluster) Given two interacting proteins vi and vj, its co-cluster is measured by using the edge clustering coefficient (ECC) [26] as follows.

$$ co- cluster\left(i,j\right)=\frac{Z_{ij}}{\mathit{\min}\left\{\left|{N}_i\right|-1,\left|{N}_j\right|-1\right\}} $$
(6)

where Zij represents the number of triangles built on edge (vi, vj), |Ni| and |Nj| are the degrees of protein vi and vj, respectively.

Multiple relation defined above are used to weight the networks. The multi-relation value between vi and vj is stands for as follows.

$$ multi- relation\left(i,j\right)= co- essentiality\left(i,j\right)+ co- localization\left(i,j\right) $$
$$ + co- annotation\left(i,j\right)+ co- cluster\left(i,j\right) $$
(7)

These multi-relation values are regarded as the weights of edges W(i,j) to upgrade the credibility of interactions. For an edge, its normalized W(i,j) value NW(i,j) is expressed by the following formula.

$$ NW\left(i,j\right)=\frac{multi- relation\left(i,j\right)}{num\left( multi- relation\right)} $$
(8)

where num(multi-relation) is the total number of the network relations, i.e., the four kinds of relations including coessentiality, colocalization, coannotation, cocluster and the networks are reconstructed by mixing them. Eventually, the dynamic PPI subnetworks (DPSNs) are switched into the multi-relation reconstructed dynamic PPI networks (MRDPNs).

Finding cores

As we all know that protein complex core should be a densely connected subgraph in the PPI network. Thus, we pick the seed proteins in the first stage, and extend seed proteins to the cores in the second stage.

  • Definition 5 (Weighted Degree) The proteins with weighted degree greater than average weighted degree are sorted in descending order as the candidate core set CC. The weighted degree of a protein i in the MRDPN is the number of interactions in which this protein is involved, which can be expressed as follows.

$$ Weighted\ Degree(i)=\sum \limits_j interactions\left(i,j\right) $$
(9)

Let first node in the candidate core set CC be a seed protein which plays an irreplaceable role in protein complex. The neighbors of the seed protein are inserted into a core set when the condition that the density of core set is greater than a given threshold DT is satisfied. The threshold DT will be discussed in the next section.

  • Definition 6 (Density) The density of core set CS can measure how close the core is, and its definition is as follows.

$$ Density(CS)=\frac{2\times {\sum}_{\left(i,j\right)} NW\left(i,j\right)}{\left| CS\right|\cdot \left(\left| CS\right|-1\right)} $$
(10)

where |CS| denotes the number of nodes in core set. Initially, core set CS contains one seed protein i. A neighbor of seed protein is added to the core set if adding it can make the Density(CS) greater than the threshold DT. This process is repeated until all neighbors of seed protein are sought and the predicted core is generated. Once a complex core is completed, all nodes in it will be labeled with “1” and cannot be extended into any other complex cores. This process will stop when the CC is empty.

Finding peripheries

Since the core plays a central role, the periphery plays a supporting role. The key idea behind our presented IFPA algorithm is to utilize the pollination mechanism to mimic the process of pollen falling on suitable flowers, which is completely different from other general methods. In this subsection, we first give a brief introduction to the flower pollination algorithm (FPA) [19], and then we find the optimal cores for peripheries by ameliorating it.

FPA is a nature-inspired optimization algorithm that comprises two main patterns, that is global pollination and local pollination. The global pollination can be represented as:

$$ {x}_i^{t+1}={x}_i^t+L\left({x}_i^t-G\right)\ (11) $$

where \( {x}_i^t \) is the pollen i at iteration t, and G is the current best solution. The parameter L is the strength of the pollination, namely a step size, we use a Lévy flight to represent that insects move over a long distance with various distance steps. That is, L is greater than 0 and obeys the Lévy distribution:

$$ L\sim \frac{\lambda \varGamma \left(\lambda \right)\sin \left(\pi \lambda /2\right)}{\pi}\frac{1}{s^{1+\lambda }},\left(s\gg {s}_0>0\right)\ (12) $$

where Γ(λ) is the standard gamma function. The local pollination can be defined as:

$$ {x}_i^{t+1}={x}_i^t+\varPsi \left({x}_j^t-{x}_k^t\right)\ (13) $$

where \( {x}_j^t \) and \( {x}_k^t \) are pollen from the different flowers of the same plant species. This substantially simulates the flower constancy in a limited neighborhood. Mathematically, if \( {x}_j^t \) and \( {x}_k^t \) come from the same plant species or select from the same population, this can be seen as a local random walk if Ψ obeys the uniform distribution of 0 to 1.

Then, we use IFPA which is an advanced version of FPA algorithm to find the closest cores for peripheries, which is equivalent to finding the most satisfactory flowering plants for pollen. The workflow of IFPA algorithm is shown in Fig. 2. Those proteins not included in the core set are considered as the candidate pollen. In IFPA algorithm, the pollen corresponds to attachments and the pollination plants correspond to cores. The pollen position equals the core sequence numbers. The update of pollen position is expressed as follows.

$$ {S}_{i,j}^{t+1}=\left\{\begin{array}{c}\ {S}_{i,j}^t, if\ {Pollination\ Priority}_{i,j}> Thr\ \\ {}\ randperm\left( Num,d\right), otherwise\end{array}\right.\ (14) $$

where Thr denotes a threshold and it is set as 0.2 here. The function of randperm is to return an integer from one to Num which means to find new core sequence number, and Num is the number of cores and the value of d is one.

Fig. 2
figure2

The overall framework of our presented IFPA algorithm

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Definition 7 (Pollination Priority) As a part of an entire protein complex, the attachments maintain relatively close relationship with the core, we call this relationship as pollination priority. The “pollination priority” of a pollen to its core set CS is represented as follows.

$$ Pollination\ Priority\left( pollen, CS\right)=\sum \limits_{u\in CS} co- cluster\left( pollen,u\right)\ (15) $$

where u is the protein in core set CS. The pollination priority depends on the affinity between the pollen and the flowers. The closer the relationship between pollen and a flower, the higher priority it pollinates on this flower. In the update procedure, if the pollen can find a flower that makes the value of pollination priority better, then the pollen falls on this flower, otherwise, the pollen finds a new flower to pollinate.

Finally, we further merge all the candidate protein complexes mined in twelve subnetworks and filter highly overlapping complexes, as our final predicted protein complexes. Algorithm 1 outlines the implementation process of our IFPA method.

Results and discussion

Datasets

Three popular datasets, i.e., DIP [27], MIPS [28] and Krogan [29], are used to verify our proposed IFPA algorithm. The DIP dataset contains 5028 proteins and 22,302 interactions, the MIPS dataset composes of 4546 proteins and 12,319 interactions, and the Krogan dataset includes 2674 proteins and 7075 interactions. The gene expression data is obtained from GEO [30] and the dataset contains 9336 genes in three cell life cycles, each cycle having twelve time points. The dynamic PPI networks are built by combining original static PPI networks with gene expression data and the details of dynamic PPI networks on three datasets are presented in Table 1.

Table 1 The number of proteins and interactions in dynamic PPI networks on three datasets
Full size table

The protein subcellular localization dataset is downloaded from the COMPARTMENTS database [31]. There are eleven subcellular localizations as follows: Cytoskeleton, Golgi apparatus, Peroxisome, Nucleus, Extracellular space, Vacuole, Cytosol, Endosome, Mitochondrion, Plasma membrane, Endoplasmic reticulum. After preprocessing, it still includes 6892 subcellular localization records. The GO information was gained from the SGD database [32]. There are 1285 essential proteins are collected from the following databases: MIPS [33], SGD [32], DEG [34], and SGDP (http://sequence.stanford.edu/group/yeast_deletion_project). CYC2008 [35] is used as the benchmark dataset which contains 408 protein complexes.

Evaluation metrics

The most commonly used evaluation metrics are used in our experiments and their specific definitions are described below.

Definition 8 (Overlapping Score) Given a predicted protein complex P and a known protein complex K, the Overlapping Score (OS) between P and K is defined as follows.

$$ OverlappingScore\left(P,K\right)=\frac{{\left|{V}_P\cap {V}_K\right|}^2}{\mid {V}_P\mid \cdot \mid {V}_K\mid }(16) $$

where |VP ∩ VK| is the number of common proteins in the predicted protein complex P and the known protein complex K, |VP| is the size of the predicted complex and |VK| is the size of the known complex. If OS ≥ 0.2, we consider that the predicted complex matches with the real one.

Definition 9 (Sensitivity, Specificity and F-measure) Sensitivity (Sn), Specificity (Sp) and F-measure are represented as follows.

$$ Sn=\frac{TP}{TP+ FN}\ (17) $$
$$ Sp=\frac{TP}{TP+ FP}\ (18) $$
$$ F- measure=\frac{2\cdot Sn\cdot Sp}{Sn+ Sp}(19) $$

where TP is the number of the predicted complexes which are matched with the known complexes, FN is the number of known complexes which are not matched with any predicted complexes, and FP is the number of the predicted complexes which are not matched with any known complexes. F-measure is a comprehensive metric combined sensitivity and specificity.

Definition 10 (p-value) In order to estimate the statistical significance of detected protein complexes, the researchers annotate their biological functions by using p-value. Given a predicted protein complex, the p-value [36] is the probability that a protein complex is enriched by a given functional group by chance. Let k is the number of proteins of the functional group in the complex, N is the size of the whole PPI network, C is the size of a protein complex and F is the size of a functional group in the network. And the p-value is defined as follows.

$$ p- value=1-\sum \limits_{i=0}^{k-1}\frac{\left(\genfrac{}{}{0pt}{}{F}{i}\right)\left(\genfrac{}{}{0pt}{}{N-F}{C-i}\right)}{\left(\genfrac{}{}{0pt}{}{N}{C}\right)}\ (20) $$

The p-value is used to evaluate the biological relevance of the predicted protein complexes. Generally, the protein complex is considered to be meaningless if its p-value is greater than 0.01. And for a complex, the smaller its p-value is, the more biological significance it has.

Parameter analysis

The density threshold DT decides whether a protein could be merged into the current core. How to choose a relatively suitable DT should be carefully considered to achieve better performance of our IFPA algorithm. Thus, varying DT from 0.1 to 0.9 with the interval 0.05, we calculate F-measure to observe the effect of the variation of DT on the performance of our IFPA algorithm, so as to choose the relatively appropriate DT, as shown in Fig. 3. Obviously, all three datasets show similar trends in most cases from Fig. 3. Especially, the major evaluation metrics F-measure obtains the better value when DT is set as 0.25 based on the both DIP and MIPS datasets and when DT is set as 0.15 based on the Krogan dataset, which means that IFPA is more effective. For this reason, the density threshold DT is set as 0.25 in DIP and MIPS datasets and 0.15 in Krogan dataset.

Fig. 3
figure3

The impact of DT on the performance of IFPA in terms of F-measure

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Performance comparison

To prove the validity of our proposed algorithm, we compare IFPA algorithm with MCODE, MCL, ClusterONE, CSO, COACH and CORE on three different PPI networks. Figures 4, 5, 6 show the overall comparison in terms of Sn, Sp and F-measure based on DIP, MIPS and Krogan datasets, respectively. Apparently, IFPA algorithm yields the best F-measure in comparison with other existing methods in all datasets, which means that our IFPA method remarkably outperforms other methods. Besides, in Table 2, PC denotes the total number of detected protein complexes, MPC is the number of detected protein complexes which were matched, MKC represents the number of matched known protein complexes, Perfect denotes OS = 1 which means that the predicted protein complexes are perfectly matched with the known protein complexes. As shown in Table 2, the protein complexes detected by our IFPA method dominates other methods in the aspects of Perfect both in DIP and MIPS datasets.

Fig. 4
figure4

Comparative performance of IFPA and other methods on DIP dataset

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Fig. 5
figure5

Comparative performance of IFPA and other methods on MIPS dataset

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Fig. 6
figure6

Comparative performance of IFPA and other methods on Krogan dataset

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Table 2 Comparative performance of IFPA and other methods on three datasets
Full size table

Many of our detected protein complexes have a good match with the known protein complexes. We consider a detected complex to be biologically significant if its p-value is less than 0.01. In order to confirm the biological significance of detected protein complexes, the p-value is calculated by using the tool GO::TermFinder (https://www.yeastgenome.org/cgi-bin/GO/goTermFinder.pl). We randomly select some predicted protein complexes to calculate their p-value concerning Biological Process ontologies based on Krogan dataset, as shown in Table 3. From Table 3, all of these detected protein complexes obtain smaller p-value and it demonstrates that the protein complexes predicted by our IFPA method have strong biological significance. The predicted complexes with strong biological significance can provide help for biology researches to some extent.

Table 3 Function enrichment analysis of predicted protein complexes detected on Krogan dataset
Full size table

Figure 7 visualizes an example of predicted protein complex named golgi transport complex in Krogan dataset so as to display the detection result more obviously. Figure 7 (A) displays a benchmark protein complex, Fig. 7 (B), (C), (D), (E) and (F) illustrate the identified protein complexes by MCODE, MCL, CORE, ClusterONE and IFPA, respectively. The purple nodes are the correctly identified proteins, the blue nodes are proteins that are not recognized, and the pink nodes are the wrongly identified proteins. From Fig. 7, we can see that MCODE and CORE correctly identifies four and two proteins, respectively. And MCL identifies a total of four proteins including one that is misidentified. Albeit ClusterONE recognizes more proteins, it also has misidentifications. IFPA successfully detects the most proteins and all of them are correct, indicating that our predicted complex match very well with benchmark complex and our IFPA method is more accurate than other comparative methods.

Fig. 7
figure7

The golgi transport complex detected by different methods

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Conclusions

Identification of protein complexes from PPI networks is distinctly important in proteomics. In this study, a flower pollination mechanism-based method is proposed to detect protein complexes in multi-relation reconstructed dynamic protein networks. To begin with, we build multi-relation reconstructed dynamic protein networks. Then, according to the core–periphery structure, we group the closely connected proteins as the cores and apply IFPA algorithm to attach peripheries to the optimal cores to form the predicted protein complexes. IFPA algorithm has been carried out on three different multi-relation reconstructed dynamic PPI networks and the experimental results demonstrate that our IFPA algorithm can obtain better clustering performance compared with other methods in most cases. The protein complexes we detected are likely to help the biologists gain some useful biological insights.

Abbreviations

ECC:

Edge clustering coefficient

FPA:

Flower pollination algorithm

GO:

Gene ontology

OS:

Overlapping Score

PPI:

Protein-protein interaction

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Acknowledgements

This paper is supported by the National Natural Science Foundation of China (61672334, 61502290, 61401263) and the Fundamental Research Funds for the Central Universities (No. GK201901010).

Funding

Publication of this article was funded by the National Natural Science Foundation of China (61672334).

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 Bioinformatics Volume 20 Supplement 3, 2019: Selected articles from the 17th Asia Pacific Bioinformatics Conference (APBC 2019): bioinformatics. The full contents of the supplement are available online at https://bmcbioinformatics.biomedcentral.com/articles/supplements/volume-20-supplement-3.

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Affiliations

  1. School of Computer Science, Shaanxi Normal University, 710119, Xi’an, China

    Xiujuan Lei & Ming Fang

  2. College of Life Sciences, Shaanxi Normal University, 710119, Xi’an, China

    Ling Guo

  3. Department of Mechanical Engineering and Division of Biomedical Engineering, University of Saskatchewan, Saskatoon, SK, S7N 5A9, Canada

    Fang-Xiang Wu

Authors
  1. Xiujuan Lei
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  2. Ming Fang
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  3. Ling Guo
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  4. Fang-Xiang Wu
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Contributions

XL conceptualized the algorithm, designed the method and drafted the manuscript, MF designed the method and drafted the manuscript, MF and LG analyzed the data and carried out the experiments, FXW modified the manuscript and polished the English expression. All of the authors have read and approved the final manuscript.

Corresponding author

Correspondence to Xiujuan Lei.

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Lei, X., Fang, M., Guo, L. et al. Protein complex detection based on flower pollination mechanism in multi-relation reconstructed dynamic protein networks. BMC Bioinformatics 20, 131 (2019). https://doi.org/10.1186/s12859-019-2649-0

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Keywords

  • Protein complex
  • Dynamic protein-protein interaction (PPI) network
  • Essential protein
  • Flower pollination algorithm

BMC Bioinformatics

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