Volume 11 Supplement 3

## Selected articles from the 2009 IEEE International Conference on Bioinformatics and Biomedicine

# Identification of functional hubs and modules by converting interactome networks into hierarchical ordering of proteins

- Young-Rae Cho
^{1}Email author and - Aidong Zhang
^{2}

**11(Suppl 3)**:S3

**DOI: **10.1186/1471-2105-11-S3-S3

© Cho et al; licensee BioMed Central Ltd. 2010

**Published: **29 April 2010

## Abstract

### Background

Protein-protein interactions play a key role in biological processes of proteins within a cell. Recent high-throughput techniques have generated protein-protein interaction data in a genome-scale. A wide range of computational approaches have been applied to interactome network analysis for uncovering functional organizations and pathways. However, they have been challenged because ofcomplex connectivity. It has been investigated that protein interaction networks are typically characterized by intrinsic topological features: high modularity and hub-oriented structure. Elucidating the structural roles of modules and hubs is a critical step in complex interactome network analysis.

### Results

We propose a novel approach to convert the complex structure of an interactome network into hierarchical ordering of proteins. This algorithm measures functional similarity between proteins based on the path strength model, and reveals a hub-oriented tree structure hidden in the complex network. We score hub confidence and identify functional modules in the tree structure of proteins, retrieved by our algorithm. Our experimental results in the yeast protein interactome network demonstrate that the selected hubs are essential proteins for performing functions. In network topology, they have a role in bridging different functional modules. Furthermore, our approach has high accuracy in identifying functional modules hierarchically distributed.

### Conclusions

Decomposing, converting, and synthesizing complex interaction networks are fundamental tasks for modeling their structural behaviors. In this study, we systematically analyzed complex interactome network structures for retrievingfunctional information. Unlike previous hierarchical clustering methods, this approach dynamically explores the hierarchical structure of proteins in a global view. It is well-applicable to the interactome networks in high-level organisms because of its efficiency and scalability.

## Background

Recent high-throughput experimental techniques, such as yeast two-hybrid system [1] and mass spectrometry [2], have made remarkable advances in identifying protein-protein interactions on a genome-wide scale. Since the evidence of protein-protein interactions provides insights into the underlying mechanisms of biological processes within a cell, the availability of a large amount interaction data has introduced a new paradigm towards functional characterization of proteins on a system level.

A protein interactome network is structured by the set of genome-wide protein-protein interactions determined in each organism. A wide range of computational approaches [3–6] have attempted to analyze the interaction networks effectively for the purpose of predicting protein function or detecting functional modules. However, unraveling the complex connectivity has been a critical challenge. The false positive interactions, which typically appear in high-throughput experimental data, and functionally inconsistent interacting pairs [7] have reinforced the complexity. Thus, refining the noisy data and restructuring the complex network into a well-organized data format should be crucial pre-processes to enhance the network analysis.

In recent years, it has been investigated that protein interaction networks are characterized by intrinsic features [8], such as high modularity and hub-oriented structure. A network comprises a collection of functional modules that are interpreted as sets of proteins participating in the same function [9]. In general, a module is considered as a sub-graph whose nodes are densely connected with each other and sparsely connected with the others. Density-based clustering methods have been proposed to seek densely connected sub-graphs using various density functions [10–13]. However, they are not able to capture the global patterns of functional organizations from protein interaction networks. Functional modules are typically organized in a recursive manner such that a module includes one or more sub-modules having more specific functions. Hierarchical clustering methods have thus been applied to the networks for finding functional organizations[14–17]. The bottom-up approaches iteratively merge nodes or sub-networks, whereas the top-down approaches recursively divide the network into sub-networks. However, as a critical drawback, they are typically sensitive to complex connectivity and noisy data.

Hubs in a scale-free network [8] play a central role in characterizing its structure. Intramodule hubs ('party' hubs) have high connectivity to the members in a module, and intermodule hubs ('date' hubs) bridge different modules [18]. Previous studies have observed that such hubs in protein interaction networks are essential in terms of functionality [19–22] and, in particular, intramodule hubs have low evolutionary rates [23, 24]. The concepts of modules and hubs, extending from specific (local) to general (global), suggest the potential structure of a hierarchy that might be hidden in complex interaction networks. How can we then effectively extract the hierarchical structure of proteins from the complex network to reveal the global picture of functional organizations?

In this study, we present a novel method for restructuring a complex interactome network into a hierarchical data format in order to reveal functional hubs and organizations. Our algorithm uses a weighted interaction network as an input. Because the network includes a significant number of false positive connections, the reliability or intensity of interactions should be assessed and assigned into the edges as weights. For network restructuring, we design a path strength model which proposes the quantification of functional similarity between two proteins. The interactome network having complex connectivity is then dynamically converted into a hub-oriented tree structure by the definition of path-strength-based centrality. From the hierarchical structure, we score hub confidence for each node, and generate hierarchically organized clusters of proteins. Unlike degree as a local significance measure, the hub confidence estimates the global significance of nodes. It is thus capable of selecting hubs that are located in critical positions of the network. The experimental results demonstrate that the hubs with high confidence are essential for performing functions. In network topology, they mostly bridge different functional modules. Furthermore, our approach has higher accuracy in identifying functional modules than other hierarchical clustering methods.

## Methods

### Path strength model

*S*of a path

*p*is defined as the product of the weighted probabilities that each node on

*p*chooses its succeeding node. The weighted probability from a node

*v*

_{ i }to

*v*

_{ j }is the ratio of the weight between

*v*

_{ i }and

*v*

_{ j }to the sum of the weights between

*v*

_{ i }and its directly connected neighbors.

*p*= 〈

*v*

_{0},

*v*

_{1}…,

*v*

_{n}〉

*w*

_{i(i+1)}denotes the weight of the edge between

*v*

_{ i }and

*v*

_{(i+1)}, which is normalized into the range between 0 and 1.

*d*

^{ wt }(

*v*

_{ i }) represents the shape parameter that indicates the weighted degree of the node

*v*

_{ i }. The weighted degree of

*v*

_{ i }is the sum of the edge weights between

*v*

_{ i }and its neighbors.

*λ*is the scale parameter which depends on the specific type, structure and properties of the input network. To make the problem simple, the scale parameter will be set by 1. Based on the assumption that the shape parameter does not force the starting and ending nodes of

*p*, Formula 1 then becomes:

The path strength of a path *p* thus has a positive relationship with the weights of the edges on *p*, and a negative relationship with the weighted degrees of the nodes on *p.* Formula 2 also implies that the path strength has an inverse relationship with the length of *p* because the weighted probability, *w*_{i(i=1)} / *d*^{
wt
}(*v*_{
i
}), is in the range between 0 and 1, inclusive. As the length of *p* increases, the product of the weighted probability decreases monotonically. In the same manner, as the average degree of the nodes on *p* increases, the path strength of *p* is likely to decrease.

*ℱ*between two proteins

*a*and

*b*in an interactome network is described as the maximum path strength between them.

Since any node pair selected in a small world network [25] are directly or indirectly connected with a relatively small path length, the maximum path length between them is typically limited. However, Formula 3 still has a computational problem when it enumerates all possible paths between *a* and *b.* To solve the computational complexity, we restrict the maximal boundary of path length.

*k*-length path strength

*S*

_{ k }as the maximum strength of all distinct paths with length

*k*between

*a*and

*b.*

*θ*to set the maximal boundary of

*k*, the functional similarity

*ℱ*between

*a*and

*b*is calculated by the maximum

*k*-length path strength.

where *l ≤ k ≤ l* + *θ* and *l* is the shortest path length between *a* and *b*. Based on the assumption that edge weights represent the likelihood of functional linkage of interacting protein pairs, Formula 5 measures the potential of functional association between two proteins, directly or indirectly connected in a protein interactome network.

### Network restructuring

*C*of a node

*a*in a network

*G*(

*V, E*) is defined as the sum of the functional similarity scores between

*a*and the other nodes in

*V*.

*T*of a node

*a*as the nodes whose centrality is greater than the centrality of

*a.*

*T*(

*a*), the node that are functionally the most similar with

*a*becomes the parent node

*p*(

*a*) of

*a*.

Selecting a parent node for each node by Formula 8 then efficiently constructs a hierarchical tree structure. The node having the highest centrality among all the nodes in the network has no parent and becomes the root node. This hierarchical structure is dynamically converted on network growth, depending on the distribution of the path-strength-based centrality of nodes.

### Identifying hubs and clustering proteins

*a,*we obtain the set of child nodes

*D*(

*a*) of

*a.*

*a*and combine every child node set to produce a set of all descendant nodes

*L*

_{ a }of

*a*

*H*of a node

*a*is calculated by the sum of the functional similarity scores between

*a*and the members of

*L*

_{ a }

*,*divided by the functional similarity score between

*a*and its parent node. If

*a*is the root node, we use the sum of the functional similarity scores between

*a*and all the other nodes as its hub confidence.

The hub confidence in Formula 11 quantifies how likely the node is to be a structural hub. Since an edge weight represents the functional consistency between two ending nodes, the structural hubs have a significant role in not only maintaining topology but also functionality.

We finally generate clusters as functional modules from the tree structure. We iteratively select a structural hub *a* with the highest hub confidence score and output *L*_{
a
} as a cluster until the hub confidence of the selected node *a* reaches a user-specified threshold. The clusters are hierarchically arranged based on the positions of their hubs in the tree structure.

*k*cluster is

*k*. For example, in Figure 1 (b) and 1 (d), {

*D, F*} is a depth-1 cluster, and {

*E, D, F, G, H*} is a depth-2 cluster. In typical, the functional module with a smaller depth is conceptually more specific and topologically denser in the network.

## Results and discussion

### Data sources

Currently, genome-wide protein-protein interaction data of several model organisms are publicly available in a number ofopen databases, for example, BioGRID [26], MIPS [27], DIP [28], MINT [29] and IntAct [30]. They have been mostly generated by high-throughput methods. However, because of unreliability of the high-throughput experimental data, we tested our algorithm using the core protein-protein interaction data of Saccharomyces cerevisiae from DIP, which were curated by other biological information such as protein sequences and expression profiles. They include total 2526 distinct proteins and 5725 interactions between them.

*N*(

*v*

_{ i }) and

*N*(

*v*

_{ j }) are the sets of directly connected neighboring nodes of

*v*

_{ i }and

*v*

_{ j }. To estimate the weight

*w*

_{ i,j }of the interaction between

*v*

_{ i }and

*v*

_{ j }, we used

*p*—value from the hypergeometric distribution.

*|N*(

*v*

_{ i }) ∩

*N*(

*v*

_{ j })| proteins in

*|N*(

*v*

_{ j })| are included in

*|N*(

*v*

_{ i })| by random chance. In other words, it means the probability that two nodes

*v*

_{ i }and

*v*

_{ j }have alternative indirect paths with length-1. The weight

*w*

_{ i, }

_{ j }of the interaction between

*v*

_{ i }and

*v*

_{ j }can be then computed by

Next, we applied gene co-expression profiles for interacting proteins. The gene expression data were obtained from SMD [31], and the coherence of expressions was calculated by the Pearson coefficient. Finally, we adopted annotations in the GO [32] database. The semantic similarity measure [5] was used to compute the functional similarity of each pair of interacting proteins.

### Evaluation of path strength model

*ℱ*(

*a,*

*b*), we have to enumerate all

*k*-length paths

*S*

_{ k }(

*a, b*) between two proteins

*a*and

*b*for all possible

*k*. However, the impact of

*S*

_{ k }(

*a, b*) on

*S*(

*a, b*) in Formula 5 significantly decreases with the increment of

*k*. In the experiment with randomly selected 10,000 protein pairs, the functional similarity rapidly decreases by the increment of path length, and is close to 0 with the path length of greater than 3, as shown in Figure 3. For efficient computation of functional similarity between

*a*and

*b,*we thus selected the maximum path strength by limiting the maximal k to (

*l*+ 2) where

*l*is the shortest path length between them. In other words, we considered the paths between two nodes with length-

*l*, (

*l*+ 1) and (

*l*+ 2).

### Topological significance of structural hubs

We implemented the conversion of the weighted interaction network to a hierarchical tree structure by Formula 8. We then identified the structural hub proteins based on their hub confidence scores in Formula 11. To make topological assessment of the structural hubs, we tested network vulnerability on random and hub attacks. It has been known that typical scale-free networks are robust on random attacks, but vulnerable on targeted attacks to the hubs. For this experiment, we observed the fractions of the largest component when we repeatedly disrupted a randomly selected node, a hub with the highest degree and a structural hub with the highest hub confidence score, respectively.

Overall, a protein interaction network is more vulnerable on structural hub attacks than random attacks. It is noticeable that the hub confidence measure is effective at selecting topologically significant hub proteins in complex networks. In general, hub confidence has a positive relationship with node degree. However, some low-degree structural hubs with high hub confidence can be detected by our algorithm. Whereas degree is a factor for local significance of nodes in network topology, the hub confidence formula measures the global significance of nodes to select hubs in the hierarchical structure.

### Biological essentiality of hub proteins

### Modularity of clusters

We implemented clustering of proteins using the tree structure converted from a protein interaction network, and inspected whether the output clusters are likely to be functional modules. Modularity of a sub-network has been commonly estimated by the ratio of the number of edges within the sub-network to the number of all edges starting from the nodes in the sub-network. However, in this estimation, the modularity depends on the number of nodes in the sub-network. For example, suppose a network *G* has 500 nodes. Sub-networks *G′* and *G″* of *G* consist of 10 and 100 nodes, respectively. A node in *G″* has a higher probability having links to the nodes within the same sub-network (intraconnections) and a lower probability having links to the nodes outside of the sub-network (interconnections), comparing to a node in *G′.* We thus normalized the formula of modularity by the probability of a node in the sub-network being linked to the members in the same sub-network.

*Y*in a module

*X*has denser intraconnections than

*X*. The experimental result is shown in Figure 8. As the cluster depth decreases, the modularity has a monotonic increase. In particular, it rapidly increases when the depth is less than 6. This result satisfies our expectation of the modularity pattern in a hierarchy. It strongly implies that the hierarchy structured by our approach corresponds to the functional organizations in a protein interaction network. To evaluate clustering accuracy, we used the

*f*-measure, which is the harmonic mean of precision and recall. Suppose an output cluster

*X*is mapped to an actual functional modules

*F*

_{ i }

*.*Recall, which is also called a true positive rate or sensitivity, is the proportion of common members between

*X*and

*F*

_{ i }to the size of

*F*

_{ i }

*.*Precision, which is also called a positive predictive value, is the proportion of common members between

*X*and

*F*

_{ i }to the size of

*X*

*f*-measure is an appropriate evaluation method since it gives a higher chance to score high when the functional module has the similar size with a cluster. As actual functional modules, we used the annotations on the 2nd-level, 3rd-level and 4th-level functions in a hierarchy from MIPS. Starting from the most general functions on the 1st-level, functions become more specific as the level increases. Then, for each function, we selected a cluster with the best match by

*f*-measure. We finally calculated the average

*f*-measure across the functions on each level. Table 1 shows the clustering accuracy of our network-conversion approach. For more specific functions, i.e., higher-level functions, we achieved higher accuracy. It indicates that our approach more accurately generated the small-sized clusters for specific functions. Comparing the accuracy of two competing methods of hierarchical clustering: Edge-Betweenness algorithm [16] and ProDistIn [15], our network-conversion approach outperforms the other methods across all levels of functions as shown in Table 1. We additionally evaluated the output clusters comparing to protein complexes from MIPS. The gap of clustering accuracy between our approach and the competing methods becomes even larger.

Clustering performance comparison by *f* — measure

Network-conversion | Edge-betweenness | ProDistIn | |
---|---|---|---|

2nd-level functions | 0.326 | 0.248 | 0.211 |

3rd-level functions | 0.383 | 0.247 | 0.215 |

4th-level functions | 0.438 | 0.226 | 0.235 |

protein complexes | 0.425 | 0.135 | 0.184 |

## Conclusions

Decomposing, converting and synthesizing complex systems are fundamental tasks for modeling their structural behavior. Recently, such approaches in protein interaction networks has been widely attempted to understand biological processes and functional organizations within a cell. We have studied the methodology for converting a protein interactome network into an effective structure for the purpose of functional knowledge discovery. For this task, we designed the path strength model and exploited the novel concept of centrality. The generated hierarchical tree structure can be applied to selecting functionally essential hub proteins and identifying functional modules. Unlike other hierarchical clustering methods, our approach dynamically explores the entire hierarchical structure of proteins in a global view. All the individual parent-child relationships between proteins in the hierarchy are meaningful and comparable. The performance of our approach can be more improved by developing the advanced methods, which efficiently integrate a massive amount of current heterogeneous biological data and accurately analyze the reliability of functional associations between interacting proteins.

## Authors contributions

YRC designed and implemented the method, analyzed the results, and drafted the manuscript. AZ coordinated the project, analyzed the results, and revised the final manuscript.

## Declarations

### Acknowledgements

This article has been published as part of *BMC Bioinformatics* Volume 11 Supplement 3, 2010: Selected articles from the 2009 IEEE International Conference on Bioinformatics and Biomedicine. The full contents of the supplement are available online at http://www.biomedcentral.com/1471-2105/11?issue=S3.

## Authors’ Affiliations

## References

- Parrish JR, Gulyas KD, Finley RL:
**Yeast two-hybrid contributions to interactome mapping.***Current Opinion in Biotechnology*2006,**17:**387–393. 10.1016/j.copbio.2006.06.006View ArticlePubMed - Aebersold R, Mann M:
**Mass spectrometry-based proteomics.***Nature*2003,**422:**198–207. 10.1038/nature01511View ArticlePubMed - Sharan R, Ulitsky I, Shamir R:
**Network-based prediction of protein function.***Molecular Systems Biology*2007,**3:**88. 10.1038/msb4100129PubMed CentralView ArticlePubMed - Li W, Liu Y, Huang H-C, Peng Y, Lin Y, Ng W-K, Ong K-L:
**Dynamic systems for discovering protein complexes and functional modules from biological networks.***IEEE/ACM Transactions on Computational Biology and Bioinformatics*2007,**4**(2):233–250. 10.1109/TCBB.2007.070210View ArticlePubMed - Cho Y-R, Hwang W, Ramanathan M, Zhang A:
**Semantic integration to identify overlapping functional modules in protein interaction networks.***BMC Bioinformatics*2007,**8:**265. 10.1186/1471-2105-8-265PubMed CentralView ArticlePubMed - Banks E, Nabieva E, Peterson R, Singh M:
**NetGrep: fast network schema searches in interactomes.***Genome Biology*2008,**9:**R138. 10.1186/gb-2008-9-9-r138PubMed CentralView ArticlePubMed - Cho Y-R, Shi L, Ramanathan M, Zhang A:
**A probabilistic framework to predict protein function from interaction data integrated with semantic knowledge.***BMC Bioinformatics*2008,**9:**382. 10.1186/1471-2105-9-382PubMed CentralView ArticlePubMed - Barabasi A-L, Oltvai ZN:
**Network biology: understanding the cell's functional organization.***Nature Reviews: Genetics*2004,**5:**101–113. 10.1038/nrg1272View ArticlePubMed - Wang Z, Zhang J:
**In search of the biological significance of modular structures in protein networks.***PLoS Computational Biology*2007.,**3**(6): - Spirin V, Mirny LA:
**Protein complexes and functional modules in molecular networks.***Proc. Natl. Acad. Sci. USA*2003,**100**(21):12123–12128. 10.1073/pnas.2032324100PubMed CentralView ArticlePubMed - Bader GD, Hogue CW:
**An automated method for finding molecular complexes in large protein interaction networks.***BMC Bioinformatics*2003,**4:**2. 10.1186/1471-2105-4-2PubMed CentralView ArticlePubMed - Altaf-Ul-Amin M, Shinbo Y, Mihara K, Kurokawa K, Kanaya S:
**Development and implementation of an algorithm for detection of protein complexes in large interaction networks.***BMC Bioinformatics*2006,**7:**207. 10.1186/1471-2105-7-207PubMed CentralView ArticlePubMed - Palla G, Derenyi I, Farkas I, Vicsek T:
**Uncovering the overlapping community structure of complex networks in nature and society.***Nature*2005,**435:**814–818. 10.1038/nature03607View ArticlePubMed - Rives AW, Galitski T:
**Modular organization of cellular networks.***Proc. Natl. Acad. Sci. USA*2003,**100**(3):1128–1133. 10.1073/pnas.0237338100PubMed CentralView ArticlePubMed - Brun C, Herrmann C, Guenoche A:
**Clustering proteins from interaction networks for the prediction of cellular functions.***BMC Bioinformatics*2004,**5:**95. 10.1186/1471-2105-5-95PubMed CentralView ArticlePubMed - Dunn R, Dudbridge F, Sanderson CM:
**The use of edge-betweenness clustering to investigate biological function in protein interaction networks.***BMC Bioinformatics*2005.,**6:** - Luo F, Yang Y, Chen C-F, Chang R, Zhou J, Scheuermann RH:
**Modular organization of protein interaction networks.***Bioinformatics*2007,**23**(2):207–214. 10.1093/bioinformatics/btl562View ArticlePubMed - Han J-DJ, Bertin N, Hao T, Goldberg DS, Berriz GF, Zhang LV, Dupuy D, Walhout AJM, Cusick ME, Roth FP, Vidal M:
**Evidence for dynamically organized modularity in the yeast protein-protein interaction network.***Nature*2004,**430:**88–93. 10.1038/nature02555View ArticlePubMed - Jeong H, Mason SP, Barabasi A-L, Oltvai ZN:
**Lethality and centrality in protein networks.***Nature*2001,**411:**41–42. 10.1038/35075138View ArticlePubMed - Chen Y, Xu D:
**Understanding protein dispensability through machine-learning analysis of high-throughput data.***Bioinformatics*2005,**21**(5):575–581. 10.1093/bioinformatics/bti058View ArticlePubMed - He X, Zhang J:
**Why do hubs tend to be essential in protein networks?***PLoS Genetics*2006,**2**(6):e88. 10.1371/journal.pgen.0020088PubMed CentralView ArticlePubMed - Batada NN, Reguly T, Breitkreutz A, Boucher L, Breitkreutz B-J, Hurst LD, Tyers M:
**Stratus not altocumulus: a new view of the yeast protein interaction network.***PLoS Biology*2006,**4**(10):e317. 10.1371/journal.pbio.0040317PubMed CentralView ArticlePubMed - Fraser HB:
**Modularity and evolutionary constraint on proteins.***Nature Genetics*2005,**37**(4):351–352. 10.1038/ng1530View ArticlePubMed - Saeed R, Deane CM:
**Protein-protein interactions, evolutionary rate, abundance and age.***BMC Bioinformatics*2006,**7:**128. 10.1186/1471-2105-7-128PubMed CentralView ArticlePubMed - Watts DJ, Strogatz SH:
**Collective dynamics of 'small-world' networks.***Nature*1998,**393:**440–442. 10.1038/30918View ArticlePubMed - Breitkreutz B-J, Stark C, Reguly T, Boucher L, Breitkreutz A, Livstone M, Oughtred R, Lackner DH, Bahler J, Wood V, Dolinski K, Tyers M:
**The BioGRID interaction database: 2008 update.***Nucleic Acids Research*2008,**36:**D637-D640. 10.1093/nar/gkm1001PubMed CentralView ArticlePubMed - Mewes HW, Dietmann S, Frishman D, Gregory R, Mannhaupt G, Mayer KFX, Munsterkotter M, Ruepp A, Spannagl M, Stumptflen V, Rattei T:
**MIPS: analysis and annotation of genome information in 2007.***Nucleic Acid Research*2008,**36:**D196-D201. 10.1093/nar/gkm980View Article - Salwinski L, Miller CS, Smith AJ, Pettit FK, Bowie JU, Eisenberg D:
**The database of interacting proteins: 2004 update.***Nucleic Acid Research*2004,**32:**D449-D451. 10.1093/nar/gkh086View Article - Chatr-aryamontri A, Ceol A, Montecchi-Palazzi L, Nardelli G, Schneider MV, Castagnoli L, Cesareni G:
**MINT: the Molecular INTeraction database.***Nucleic Acids Research*2007,**35:**D572-D574. 10.1093/nar/gkl950PubMed CentralView ArticlePubMed - Kerrien S,
*et al*.:**IntAct - open source resource for molecular interaction data.***Nucleic Acids Research*2007,**35:**D561-D565. 10.1093/nar/gkl958PubMed CentralView ArticlePubMed - Demeter J,
*et al*.:**The Stanford Microarray Database: implementation of new analysis tools and open source release of software.***Nucleic Acid Research*2007,**35:**D766-D770. 10.1093/nar/gkl1019View Article - The Gene Ontology Consortium:
**The Gene Ontology project in 2008.***Nucleic Acids Research*2008,**36:**D440-D444. 10.1093/nar/gkm883PubMed CentralView Article

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