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Liu Y, Wei X, Chen W, Hu L, He Z. A graph-traversal approach to identify influential nodes in a network. PATTERNS 2021; 2:100321. [PMID: 34553168 PMCID: PMC8441579 DOI: 10.1016/j.patter.2021.100321] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Revised: 05/16/2021] [Accepted: 07/07/2021] [Indexed: 11/19/2022]
Abstract
Influential node identification plays a significant role in understanding network structure and functions. Here we propose a general method for detecting influential nodes in a graph-traversal framework. We evaluate the influence of each node by constructing a breadth-first search (BFS) tree in which the target node is the root node. From the BFS tree, we generate a curve in which the x axis is the level number and the y axis is the cumulative scores of all nodes visited so far. We use the area under the curve value as the final influence score of the target node. Experimental results on various networks across different domains demonstrate that our method can be significantly superior to widely used centrality measures on the task of influential node detection. We propose an influential node detection method, TARank, in a graph-traversal framework We evaluate the influence of each node by constructing a breadth-first search tree TARank is capable of enhancing existing centrality measures TARank can yield new, yet effective, centrality measures as well
The discovery of influential nodes is a fundamental research issue in network science. To quantify the influence of each node in a network, various methods have been presented in the literature. To the best of our knowledge, no previous research efforts address the influential node identification problem from a graph-traversal perspective. To fulfill this void, we propose the TARank method that integrates the information collected from the breadth-first search tree to identify influential nodes. The formulation under the graph-traversal framework opens the door to a fundamentally new type of method of influential node identification. In the future, more effective recognition methods can be expected to be constructed based on this general framework. Since empirical studies have validated the effectiveness of TARank, it would be plausible to employ this method in different applications to reveal new findings.
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Affiliation(s)
- Yan Liu
- School of Software, Dalian University of Technology, Dalian 116024, China
| | - Xiaoqi Wei
- School of Software, Dalian University of Technology, Dalian 116024, China
| | - Wenfang Chen
- School of Software, Dalian University of Technology, Dalian 116024, China
| | - Lianyu Hu
- School of Software, Dalian University of Technology, Dalian 116024, China
| | - Zengyou He
- School of Software, Dalian University of Technology, Dalian 116024, China
- Key Laboratory for Ubiquitous Network and Service Software of Liaoning Province, Dalian 116024, China
- Corresponding author
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2
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Walch P, Selkrig J, Knodler LA, Rettel M, Stein F, Fernandez K, Viéitez C, Potel CM, Scholzen K, Geyer M, Rottner K, Steele-Mortimer O, Savitski MM, Holden DW, Typas A. Global mapping of Salmonella enterica-host protein-protein interactions during infection. Cell Host Microbe 2021; 29:1316-1332.e12. [PMID: 34237247 PMCID: PMC8561747 DOI: 10.1016/j.chom.2021.06.004] [Citation(s) in RCA: 43] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2020] [Revised: 02/24/2021] [Accepted: 05/21/2021] [Indexed: 11/16/2022]
Abstract
Intracellular bacterial pathogens inject effector proteins to hijack host cellular processes and promote their survival and proliferation. To systematically map effector-host protein-protein interactions (PPIs) during infection, we generated a library of 32 Salmonella enterica serovar Typhimurium (STm) strains expressing chromosomally encoded affinity-tagged effectors and quantified PPIs in macrophages and epithelial cells. We identified 446 effector-host PPIs, 25 of which were previously described, and validated 13 by reciprocal co-immunoprecipitation. While effectors converged on the same host cellular processes, most had multiple targets, which often differed between cell types. We demonstrate that SseJ, SseL, and SifA modulate cholesterol accumulation at the Salmonella-containing vacuole (SCV) partially via the cholesterol transporter Niemann-Pick C1 protein. PipB recruits the organelle contact site protein PDZD8 to the SCV, and SteC promotes actin bundling by phosphorylating formin-like proteins. This study provides a method for probing host-pathogen PPIs during infection and a resource for interrogating STm effector mechanisms.
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Affiliation(s)
- Philipp Walch
- European Molecular Biology Laboratory (EMBL), Genome Biology Unit, Heidelberg, Germany; Heidelberg University, Faculty of Biosciences, Heidelberg, Germany
| | - Joel Selkrig
- European Molecular Biology Laboratory (EMBL), Genome Biology Unit, Heidelberg, Germany
| | - Leigh A Knodler
- Paul G. Allen School for Global Health, College of Veterinary Medicine, Washington State University, Pullman, USA; Laboratory of Intracellular Parasites, Rocky Mountain Laboratories, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Hamilton, MT, USA
| | - Mandy Rettel
- EMBL, Proteomics Core Facility, Heidelberg, Germany
| | - Frank Stein
- EMBL, Proteomics Core Facility, Heidelberg, Germany
| | - Keith Fernandez
- European Molecular Biology Laboratory (EMBL), Genome Biology Unit, Heidelberg, Germany
| | - Cristina Viéitez
- European Molecular Biology Laboratory (EMBL), Genome Biology Unit, Heidelberg, Germany; EMBL European Bioinformatics Institute, (EMBL-EBI), Hinxton, UK
| | - Clément M Potel
- European Molecular Biology Laboratory (EMBL), Genome Biology Unit, Heidelberg, Germany
| | - Karoline Scholzen
- European Molecular Biology Laboratory (EMBL), Genome Biology Unit, Heidelberg, Germany
| | - Matthias Geyer
- Institute of Structural Biology, University of Bonn, Bonn, Germany
| | - Klemens Rottner
- Division of Molecular Cell Biology, Zoological Institute, TU Braunschweig, Braunschweig, Germany; Molecular Cell Biology Group, Helmholtz Centre for Infection Research, Braunschweig, Germany
| | - Olivia Steele-Mortimer
- Laboratory of Intracellular Parasites, Rocky Mountain Laboratories, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Hamilton, MT, USA
| | - Mikhail M Savitski
- European Molecular Biology Laboratory (EMBL), Genome Biology Unit, Heidelberg, Germany; EMBL, Proteomics Core Facility, Heidelberg, Germany
| | - David W Holden
- MRC Centre for Molecular Bacteriology and Infection, Imperial College, London, UK
| | - Athanasios Typas
- European Molecular Biology Laboratory (EMBL), Genome Biology Unit, Heidelberg, Germany.
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He Z, Zhao C, Liang H, Xu B, Zou Q. Protein Complexes Identification with Family-Wise Error Rate Control. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2020; 17:2062-2073. [PMID: 31027047 DOI: 10.1109/tcbb.2019.2912602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The detection of protein complexes from protein-protein interaction network is a fundamental issue in bioinformatics and systems biology. To solve this problem, numerous methods have been proposed from different angles in the past decades. However, the study on detecting statistically significant protein complexes still has not received much attention. Although there are a few methods available in the literature for identifying statistically significant protein complexes, none of these methods can provide a more strict control on the error rate of a protein complex in terms of family-wise error rate (FWER). In this paper, we propose a new detection method SSF that is capable of controlling the FWER of each reported protein complex. More precisely, we first present a p-value calculation method based on Fisher's exact test to quantify the association between each protein and a given candidate protein complex. Consequently, we describe the key modules of the SSF algorithm: a seed expansion procedure for significant protein complexes search and a set cover strategy for redundancy elimination. The experimental results on five benchmark data sets show that: (1) our method can achieve the highest precision; (2) it outperforms three competing methods in terms of normalized mutual information (NMI) and F1 score in most cases.
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Wu Z, Liao Q, Liu B. A comprehensive review and evaluation of computational methods for identifying protein complexes from protein–protein interaction networks. Brief Bioinform 2019; 21:1531-1548. [DOI: 10.1093/bib/bbz085] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2019] [Revised: 06/17/2019] [Accepted: 06/17/2019] [Indexed: 02/04/2023] Open
Abstract
Abstract
Protein complexes are the fundamental units for many cellular processes. Identifying protein complexes accurately is critical for understanding the functions and organizations of cells. With the increment of genome-scale protein–protein interaction (PPI) data for different species, various computational methods focus on identifying protein complexes from PPI networks. In this article, we give a comprehensive and updated review on the state-of-the-art computational methods in the field of protein complex identification, especially focusing on the newly developed approaches. The computational methods are organized into three categories, including cluster-quality-based methods, node-affinity-based methods and ensemble clustering methods. Furthermore, the advantages and disadvantages of different methods are discussed, and then, the performance of 17 state-of-the-art methods is evaluated on two widely used benchmark data sets. Finally, the bottleneck problems and their potential solutions in this important field are discussed.
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Affiliation(s)
- Zhourun Wu
- School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen, Guangdong, China
| | - Qing Liao
- School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen, Guangdong, China
| | - Bin Liu
- School of Computer Science and Technology, Beijing Institute of Technology, Beijing, China
- Advanced Research Institute of Multidisciplinary Science, Beijing Institute of Technology, Beijing, China
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Tian B, Duan Q, Zhao C, Teng B, He Z. Reinforce: An Ensemble Approach for Inferring PPI Network from AP-MS Data. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2019; 16:365-376. [PMID: 28534782 DOI: 10.1109/tcbb.2017.2705060] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Affinity Purification-Mass Spectrometry (AP-MS) is one of the most important technologies for constructing protein-protein interaction (PPI) networks. In this paper, we propose an ensemble method, Reinforce, for inferring PPI network from AP-MS data set. The new algorithm named Reinforce is based on rank aggregation and false discovery rate control. Under the null hypothesis that the interaction scores from different scoring methods are randomly generated, Reinforce follows three steps to integrate multiple ranking results from different algorithms or different data sets. The experimental results show that Reinforce can get more stable and accurate inference results than existing algorithms. The source codes of Reinforce and data sets used in the experiments are available at: https://sourceforge.net/projects/reinforce/.
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Su Y, Zhao C, Chen Z, Tian B, He Z. On the statistical significance of protein complex. QUANTITATIVE BIOLOGY 2018. [DOI: 10.1007/s40484-018-0153-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Alvarez-Ponce D. Recording negative results of protein-protein interaction assays: an easy way to deal with the biases and errors of interactomic data sets. Brief Bioinform 2018; 18:1017-1020. [PMID: 27542401 DOI: 10.1093/bib/bbw075] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2016] [Indexed: 11/13/2022] Open
Abstract
In recent years, it has become increasingly common to use assays that can test whether two proteins interact, such as yeast two-hybrid and tandem affinity purification followed by mass spectrometry. Such techniques, particularly when applied at a large scale, suffer from high rates of false positives and false negatives. In addition, interactomic data sets are subjected to a number of biases, which limits considerably their usefulness to address biological questions. Interactomic databases only keep track of the positive results of protein interaction assays (those indicating that the tested proteins interact). Despite their importance, negative results (those indicating that the tested proteins do not interact) are not recorded in interactomic databases. Indeed, current interactomic databases do not support negative results. Here, I argue that systematically recording not only positive but also negative results of protein interaction assays would help scientists identify errors and deal with biases, thus enormously increasing the value of interactomic data sets. The challenges of implementing this change, along with potential solutions, are discussed.
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Tian B, Zhao C, Gu F, He Z. A two-step framework for inferring direct protein-protein interaction network from AP-MS data. BMC SYSTEMS BIOLOGY 2017; 11:82. [PMID: 28950876 PMCID: PMC5615237 DOI: 10.1186/s12918-017-0452-y] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Abstract
Background Affinity purification-mass spectrometry (AP-MS) has been widely used for generating bait-prey data sets so as to identify underlying protein-protein interactions and protein complexes. However, the AP-MS data sets in terms of bait-prey pairs are highly noisy, where candidate pairs contain many false positives. Recently, numerous computational methods have been developed to identify genuine interactions from AP-MS data sets. However, most of these methods aim at removing false positives that contain contaminants, ignoring the distinction between direct interactions and indirect interactions. Results In this paper, we present an initialization-and-refinement framework for inferring direct PPI networks from AP-MS data, in which an initial network is first generated with existing scoring methods and then a refined network is constructed by the application of indirect association removal methods. Experimental results on several real AP-MS data sets show that our method is capable of identifying more direct interactions than traditional scoring methods. Conclusions The proposed framework is sufficiently general to incorporate any feasible methods in each step so as to have potential for handling different types of AP-MS data in the future applications. Electronic supplementary material The online version of this article (doi:10.1186/s12918-017-0452-y) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Bo Tian
- School of Software, Dalian University of Technology, Tuqiang Road, Dalian, China
| | - Can Zhao
- School of Software, Dalian University of Technology, Tuqiang Road, Dalian, China
| | - Feiyang Gu
- School of Software, Dalian University of Technology, Tuqiang Road, Dalian, China
| | - Zengyou He
- School of Software, Dalian University of Technology, Tuqiang Road, Dalian, China. .,Key Laboratory for Ubiquitous Network and Service Software of Liaoning, Tuqiang Road 321, Dalian, 116600, China.
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Ou-Yang L, Zhang XF, Dai DQ, Wu MY, Zhu Y, Liu Z, Yan H. Protein complex detection based on partially shared multi-view clustering. BMC Bioinformatics 2016; 17:371. [PMID: 27623844 PMCID: PMC5022186 DOI: 10.1186/s12859-016-1164-9] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2015] [Accepted: 07/23/2016] [Indexed: 01/05/2023] Open
Abstract
Background Protein complexes are the key molecular entities to perform many essential biological functions. In recent years, high-throughput experimental techniques have generated a large amount of protein interaction data. As a consequence, computational analysis of such data for protein complex detection has received increased attention in the literature. However, most existing works focus on predicting protein complexes from a single type of data, either physical interaction data or co-complex interaction data. These two types of data provide compatible and complementary information, so it is necessary to integrate them to discover the underlying structures and obtain better performance in complex detection. Results In this study, we propose a novel multi-view clustering algorithm, called the Partially Shared Multi-View Clustering model (PSMVC), to carry out such an integrated analysis. Unlike traditional multi-view learning algorithms that focus on mining either consistent or complementary information embedded in the multi-view data, PSMVC can jointly explore the shared and specific information inherent in different views. In our experiments, we compare the complexes detected by PSMVC from single data source with those detected from multiple data sources. We observe that jointly analyzing multi-view data benefits the detection of protein complexes. Furthermore, extensive experiment results demonstrate that PSMVC performs much better than 16 state-of-the-art complex detection techniques, including ensemble clustering and data integration techniques. Conclusions In this work, we demonstrate that when integrating multiple data sources, using partially shared multi-view clustering model can help to identify protein complexes which are not readily identifiable by conventional single-view-based methods and other integrative analysis methods. All the results and source codes are available on https://github.com/Oyl-CityU/PSMVC. Electronic supplementary material The online version of this article (doi:10.1186/s12859-016-1164-9) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Le Ou-Yang
- College of Information Engineering, Shenzhen University, Nanhai Ave 3688, Shenzhen, 518060, China.,Department of Electronic and Engineering, City University of Hong Kong, Tat Chee Avenue, Hong Kong, China
| | - Xiao-Fei Zhang
- School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, China
| | - Dao-Qing Dai
- Intelligent Data Center and Department of Mathematics, Sun Yat-Sen University, Xin Gang Road West, Guangzhou, 510275, China.
| | - Meng-Yun Wu
- School of Statistics and Management, Shanghai University of Finance and Economics, Guoding Road, Shanghai, 200433, China
| | - Yuan Zhu
- School of Automation, China University of Geosciences, Wuhan, China
| | - Zhiyong Liu
- Shenzhen Polytechnic, Shenzhen, 518055, China
| | - Hong Yan
- Department of Electronic and Engineering, City University of Hong Kong, Tat Chee Avenue, Hong Kong, China
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PIPINO: A Software Package to Facilitate the Identification of Protein-Protein Interactions from Affinity Purification Mass Spectrometry Data. BIOMED RESEARCH INTERNATIONAL 2016; 2016:2891918. [PMID: 26966684 PMCID: PMC4761381 DOI: 10.1155/2016/2891918] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/30/2015] [Revised: 11/28/2015] [Accepted: 11/29/2015] [Indexed: 11/17/2022]
Abstract
The functionality of most proteins is regulated by protein-protein interactions. Hence, the comprehensive characterization of the interactome is the next milestone on the path to understand the biochemistry of the cell. A powerful method to detect protein-protein interactions is a combination of coimmunoprecipitation or affinity purification with quantitative mass spectrometry. Nevertheless, both methods tend to precipitate a high number of background proteins due to nonspecific interactions. To address this challenge the software Protein-Protein-Interaction-Optimizer (PIPINO) was developed to perform an automated data analysis, to facilitate the selection of bona fide binding partners, and to compare the dynamic of interaction networks. In this study we investigated the STAT1 interaction network and its activation dependent dynamics. Stable isotope labeling by amino acids in cell culture (SILAC) was applied to analyze the STAT1 interactome after streptavidin pull-down of biotagged STAT1 from human embryonic kidney 293T cells with and without activation. Starting from more than 2,000 captured proteins 30 potential STAT1 interaction partners were extracted. Interestingly, more than 50% of these were already reported or predicted to bind STAT1. Furthermore, 16 proteins were found to affect the binding behavior depending on STAT1 phosphorylation such as STAT3 or the importin subunits alpha 1 and alpha 6.
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Ou-Yang L, Wu M, Zhang XF, Dai DQ, Li XL, Yan H. A two-layer integration framework for protein complex detection. BMC Bioinformatics 2016; 17:100. [PMID: 26911324 PMCID: PMC4765032 DOI: 10.1186/s12859-016-0939-3] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2015] [Accepted: 01/27/2016] [Indexed: 01/05/2023] Open
Abstract
Background Protein complexes carry out nearly all signaling and functional processes within cells. The study of protein complexes is an effective strategy to analyze cellular functions and biological processes. With the increasing availability of proteomics data, various computational methods have recently been developed to predict protein complexes. However, different computational methods are based on their own assumptions and designed to work on different data sources, and various biological screening methods have their unique experiment conditions, and are often different in scale and noise level. Therefore, a single computational method on a specific data source is generally not able to generate comprehensive and reliable prediction results. Results In this paper, we develop a novel Two-layer INtegrative Complex Detection (TINCD) model to detect protein complexes, leveraging the information from both clustering results and raw data sources. In particular, we first integrate various clustering results to construct consensus matrices for proteins to measure their overall co-complex propensity. Second, we combine these consensus matrices with the co-complex score matrix derived from Tandem Affinity Purification/Mass Spectrometry (TAP) data and obtain an integrated co-complex similarity network via an unsupervised metric fusion method. Finally, a novel graph regularized doubly stochastic matrix decomposition model is proposed to detect overlapping protein complexes from the integrated similarity network. Conclusions Extensive experimental results demonstrate that TINCD performs much better than 21 state-of-the-art complex detection techniques, including ensemble clustering and data integration techniques. Electronic supplementary material The online version of this article (doi:10.1186/s12859-016-0939-3) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Le Ou-Yang
- College of Information Engineering, Shenzhen University, Shenzhen, 518060, China. .,Intelligent Data Center and Department of Mathematics, Sun Yat-Sen University, Guangzhou, 510275, China. .,Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China.
| | - Min Wu
- Institute for Infocomm Research (I2R), A*STAR, 1 Fusionopolis Way, Singapore, Singapore.
| | - Xiao-Fei Zhang
- School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, China.
| | - Dao-Qing Dai
- Intelligent Data Center and Department of Mathematics, Sun Yat-Sen University, Guangzhou, 510275, China.
| | - Xiao-Li Li
- Institute for Infocomm Research (I2R), A*STAR, 1 Fusionopolis Way, Singapore, Singapore.
| | - Hong Yan
- Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China.
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Zhang XF, Ou-Yang L, Hu X, Dai DQ. Identifying binary protein-protein interactions from affinity purification mass spectrometry data. BMC Genomics 2015; 16:745. [PMID: 26438428 PMCID: PMC4595009 DOI: 10.1186/s12864-015-1944-z] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2014] [Accepted: 09/22/2015] [Indexed: 02/04/2023] Open
Abstract
Background The identification of protein-protein interactions contributes greatly to the understanding of functional organization within cells. With the development of affinity purification-mass spectrometry (AP-MS) techniques, several computational scoring methods have been proposed to detect protein interactions from AP-MS data. However, most of the current methods focus on the detection of co-complex interactions and do not discriminate between direct physical interactions and indirect interactions. Consequently, less is known about the precise physical wiring diagram within cells. Results In this paper, we develop a Binary Interaction Network Model (BINM) to computationally identify direct physical interactions from co-complex interactions which can be inferred from purification data using previous scoring methods. This model provides a mathematical framework for capturing topological relationships between direct physical interactions and observed co-complex interactions. It reassigns a confidence score to each observed interaction to indicate its propensity to be a direct physical interaction. Then observed interactions with high confidence scores are predicted as direct physical interactions. We run our model on two yeast co-complex interaction networks which are constructed by two different scoring methods on a same combined AP-MS data. The direct physical interactions identified by various methods are comprehensively benchmarked against different reference sets that provide both direct and indirect evidence for physical contacts. Experiment results show that our model has a competitive performance over the state-of-the-art methods. Conclusions According to the results obtained in this study, BINM is a powerful scoring method that can solely use network topology to predict direct physical interactions from AP-MS data. This study provides us an alternative approach to explore the information inherent in AP-MS data. The software can be downloaded from https://github.com/Zhangxf-ccnu/BINM. Electronic supplementary material The online version of this article (doi:10.1186/s12864-015-1944-z) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Xiao-Fei Zhang
- School of Mathematics and Statistics, Central China Normal University, Luoyu Road, Wuhan, 430079, China.
| | - Le Ou-Yang
- Intelligent Data Center and Department of Mathematics, Sun Yat-Sen University, Xingang West Road, Guangzhou, 510275, China.
| | - Xiaohua Hu
- School of Computer, Central China Normal University, 774 Luoyu Road, Wuhan, 430079, China. .,College of Information Science and Technology, Drexel University, Chestnut Street, Philadelphia, 19104, USA.
| | - Dao-Qing Dai
- Intelligent Data Center and Department of Mathematics, Sun Yat-Sen University, Xingang West Road, Guangzhou, 510275, China.
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