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The reductionist approach of dissecting biological systems into their constituents has been successful in the first stage of the molecular biology to elucidate the chemical basis of several biological processes. This knowledge helped biologists to understand the complexity of the biological systems evidencing that most biological functions do not arise from individual molecules; thus, realizing that the emergent properties of the biological systems cannot be explained or be predicted by investigating individual molecules without taking into consideration their relations. Thanks to the improvement of the current -omics technologies and the increasing understanding of the molecular relationships, even more studies are evaluating the biological systems through approaches based on graph theory. Genomic and proteomic data are often combined with protein-protein interaction (PPI) networks whose structure is routinely analyzed by algorithms and tools to characterize hubs/bottlenecks and topological, functional, and disease modules. On the other hand, co-expression networks represent a complementary procedure that give the opportunity to evaluate at system level including organisms that lack information on PPIs. Based on these premises, we introduce the reader to the PPI and to the co-expression networks, including aspects of reconstruction and analysis. In particular, the new idea to evaluate large-scale proteomic data by means of co-expression networks will be discussed presenting some examples of application. Their use to infer biological knowledge will be shown, and a special attention will be devoted to the topological and module analysis. Keywords: Co-expression network, -Omics data, PPI network, Systems biology, Topological analysis, WGCNA, Pearson’s correlation 1 Introduction The magnitude of -omics data provides the opportunity The development of systems biology approaches based to decode in alternative way the role of biological on graph theory [1–3] is receiving a great boost by the molecules and processes characterizing the emergent improvement of the -omics technologies that allow more phenotypes. In this scenario, a common procedure to and more big amount of accurate qualitative and quanti- evaluate gene expression levels is based on statistics tative measures [4, 5]. New methodologies have also been that measure the dependence between variables, and the developed to increase knowledge about protein-protein resulting co-expression networks are used to identify interactions (PPIs) [6]. As a result, the PPI networks com- genes functionally related or controlled by the same bined with protein and with gene expression levels are transcriptional regulatory program [11–13]. Unlike gene today widespread to investigate biological systems [7–10]. expression levels, the use of proteomic data to infer co-expression networks has been explored through few studies [14–20]. Similar to PPI and gene co-expression *Correspondence: dario.disilvestre@itb.cnr.it networks, these networks have been evaluated at topo- Institute for Biomedical Technologies - National Research Council (ITB-CNR), logical level in terms of edge rearrangement, as well as 93 Fratelli Cervi, Segrate, Milan, Italy of modules associated with common cellular functions. Full list of author information is available at the end of the article © The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Vella et al. EURASIP Journal on Bioinformatics and Systems Biology (2017) 2017:6 Page 2 of 16 Although different aspects including data collection and that make it up; a set of nodes V, stands for the elements network reconstruction need to be improved, the prelim- of the system, while a set of edges E, stands for their rela- inary results are proving this approach promising as alter- tions. Mathematically, we refer to a graph as G = (V , E) native to evaluate large-scale proteomic data. This could (Fig. 1a). have important effects into clinical applications favoring Concerning biological networks, the nodes may be cor- the way toward the use of multiple biomarkers and their related of attributes representing characteristics of inter- relationships [17, 21–24]. Thus, in addition to improve est, such as expression levels or GO terms. In the same basic research, these elements may contribute to develop way, the edges may possess attributes describing the rela- most efficient diagnosis and prognosis methods to a tion between nodes, for example indicating the strength of more preventive, predictive, and personalized medicine the interaction or its reliability; edges may also be directed [25–27]. or undirected, and here we shall mainly deal with undi- Based on these premises, in this review we introduce rected edges. Using the framework described in Fig. 1, a the reader to PPI and co-expression networks. The recent protein interaction network is defined as a complex graph, idea to describe and to evaluate proteomic data by means where the nodes are proteins and the edges represent their of co-expression networks will be discussed presenting relation, generally physical or functional, like proposed by some example of application. Their use will be shown to Vidal et al. [25]. infer biological knowledge, and a special attention will be devoted to the topological and module analysis. 2.1 PPI: physical and functional protein links A protein interaction network usually refers to physical 2 Protein interaction networks PPIs [29], but several meanings have been attributed to Graph theory is a powerful abstracting machinery that this term. In fact, a group of proteins working together allows to model several types of system, both natural and to perform a biological function not necessarily are in human-made, ranging from biology to sociology science direct contact, but their relation may be of regulation [28]. A graph, also called network, provides a system rep- or influence, for example, making use of intermediary resentation in terms of relationships among the elements molecules. For this reason, the term PPI has not only been Fig. 1 a Biological networks. Nodes may represent several types of biological elements, while the edges describe the nature of their relationship. If A and B are two nodes connected by an edge, (A, B) ∈ E, B is a neighbor of A or A and B are adjacent. b Protein network classification proposed by Vidal et al. [25] Vella et al. EURASIP Journal on Bioinformatics and Systems Biology (2017) 2017:6 Page 3 of 16 exclusively used to indicate a physical contact between an exhaustive collection of more than 500 databases is proteins, but also proteins connected by functional links. available in the Pathguide website (Fig. 2) [40]. It is important to bear in mind that proteins participate to The development of computational tools to retrieve, physical-chemical connection depending on the biological visualize, and analyze biological networks is a key aspect context where they are [30]. Thus, the interactions com- of the systems biology studies, like the production of accu- posing a given network could not occur in any cell or at rate -omics data and the collection of reliable molecular any time. However, if two interacting proteins are experi- interactions. The most broadly adopted softwares include mentally identified in a given sample, we assume they also Cytoscape and its plugins [41], VisANT [42], atBioNet interact in the system we are studying, thus their rela- [43], PINA [44], and Ingenuity [45] which represents a tion is reported in the reconstructed PPI network to be commercial solution. On the contrary, Cytoscape is a soft- analyzed. ware now developed by an international consortium of open-source developers. Figure 3 shows a possible use of 2.2 PPI: detection, storage, and analysis tools the ReactomeFIViz Cytoscape’s plugin to obtain networks The main approaches to demonstrate physical interac- (both functional and physical) associated with a given tion between proteins are the yeast two-hybrid (Y2H) biological function. ReactomeFIViz is focused to path- method and the tandem affinity purification coupled with ways and patterns related to cancer and other pathologies mass-spectrometry (TAP-MS) [6]. To reduce the identi- [46]. This is of importance in the context of biomedi- fication of false interactions, these experimental data are cal research, and detailed reviews about network models complemented with computational methods of prediction to investigate complex diseases have been published by [31–33]. Other methods are used to identify functional Cho et al. [47] and by Vidal et al. [25]. Both works relationships, and most of them rely on protein expres- show how functional and physical links can be used to sion data [20], analysis of gene co-expression patterns [34], investigate disease mechanisms, and PPI networks emerge and analysis of sequences or phylogenetic properties, as as effective model to evaluate different biomolecules Rosetta Stone or Sequence co-evolution methods [35]. acting in complex biological systems, thus providing an Both physical and functional PPIs are stored in pub- insight on phenomenons involved in a given physio- lic repositories. The most popular include MINT [36], pathological context. IntAct [37], STRING [38], and HPRD [39]. The latter specifically collects interactions related to Homo sapiens, 3 Co-expression networks while other databases like STRING collect different kinds The great amount of data produced by microarray and of interactions (from experiments/biochemistry, anno- RNA-seq technologies has driven the need of methods to tated pathways, gene neighborhood, gene fusion, gene objectively extract meaningful informations, such as genes co-occurrence, gene co-expression, and text-mining) and differentially expressed or sharing a similar expression different organisms. A useful list of repositories presented pattern. A widely adopted approach to evaluate transcript by De Las Rivas et al. [29] provides a classification in cat- levels is based on statistics that measure the dependence egories (primary, meta, and prediction database) accord- between variables [48]. Co-expression represents the first ing to method used to detect interactions. Moreover, step of inference that defines a relation between pairs Fig. 2 Pathguide website [40]. A repository containing information about 547 resources of molecular interactions and pathways Vella et al. EURASIP Journal on Bioinformatics and Systems Biology (2017) 2017:6 Page 4 of 16 Fig. 3 ReactomeFIViz: from disease pathway to PPI network. Main steps to obtain a protein functional and a physical protein network, starting from a specific pathway (oncogene induced senescence). Using ReactomeFIViz, pathways can be visualized in relation with others (a), can be detailed as a diagram showing all intermolecular relationships (b), and as a protein functional interaction network (c) showing just the relation among proteins that cooperate to perform a given molecular function. Finally, starting from a group of protein of interest, it is possible to obtain a network of protein-protein interactions by STRING; in the reported example, the interactions shown are limited to physical type, in particular binding, activation and inhibition (d) of transcripts. It is based on the concept that transcript Gene co-expression networks are topologically ana- profiles of time series, or result of specific perturbations, lyzed to identify hubs/bottlenecks and node communities may be indicative of dynamics and differences between sharing high co-expression score; communities are the transcripts, implying their regulation. Following the pro- starting point to identify topological, functional, and/or cessing of transcript levels, the result is a co-expression disease modules related to specific biological phenotypes network defined as an undirected graphs where the nodes [50, 51]. Different studies have shown that genes func- correspond to genes, and the edges indicate significant tionally related, and sharing Gene Ontology (GO) terms, co-expression relationships, but not causality. This aspect usually present higher co-expression score [52]. More- is faced in the context of transcriptional regulatory net- over, variations of the co-expression score are evaluated works [49], where pairs of genes are considered in a sys- to select topological relevant nodes whose number of temic perspective of cooperation, including co-regulation, interactions changes under specific conditions or pertur- activation/suppression, and indirect control through the bations [18] (Fig. 4). action of siRNA, miRNA, proteins, metabolites, and epi- In the last 10 years, the improvement of the liquid chro- genetic mechanisms. This complexity make difficult the matography and the mass spectrometry has given a great inference of transcriptional regulatory networks by using boost to large-scale proteomics analysis, making available exclusively transcriptional profiles. In fact, in addition the expression profiles of thousands of proteins per sam- to co-expression, next levels of inference require more ple [53]. Due to the similarity between gene and protein information and different modeling techniques, includ- matrices, the use of proteomic data to infer protein co- ing Boolean networks, Bayesian networks, or differential expression networks has been recently explored to inves- equations (ODEs), which are revised in more detail in tigate the role of proteins in specific physio-pathological studies addressing reverse engineering approaches [49]. contexts. Although different aspects need to be improved, Vella et al. EURASIP Journal on Bioinformatics and Systems Biology (2017) 2017:6 Page 5 of 16 Fig. 4 The figure shows the ACSL1 protein and its neighbors in two co-expression networks obtained by processing the protein expression profiles of a control group and a group of patients affected by amyloidosis disease. In the considered groups of samples, ACSL1 shows a different degree. It suggests that this protein may have a key role in the emergent phanotypes. Green edges represent a positive correlation between the expression profiles, while black edges indicate negative correlations. The thick edges indicate known interactions present in public repositories as PPI this approach takes into account protein relationships, selection of appropriate experimental samples/conditions and, with respect to conventional methods, it represents to be processed. A condition-independent analysis is used an alternative to gain a deeper insight of the protein char- to find relations of co-expression actual in different bio- acterizing a given system. This issue will be discussed with logical contexts; on the contrary, a condition-dependent greater detail in the paragraph 5. analysis aims to find relations associated with specific phenotypes. 3.1 Aspects of construction The co-expression score computation may be faced by To build a co-expression network, an important aspect using any statistical or computational tool that allows to concerns the computation of a co-expression score, which evaluate the dependence between variables. Some tools weigh the correlation of two genes/proteins in response to have been specifically designed to construct, visualize, the considered conditions (Fig. 5). To address this issue, and analyze co-expression networks. For example, the metrics to measure gene/protein co-expression have to be ExpressionCorrelation Cytoscape’s plugin allows to pro- cess microarray data and provides a similarity matrix considered (Table 1); the most used metrics include Pear- son’s correlation (PC), Spearman’s correlation, Kendall’s computed by PC [58]. In addition to being user-friendly, correlation, and mutual information [48, 54]. Various the main advantage of this tool is that the reconstructed methods have been also proposed to define proper thresh- networks are directly imported in Cytoscape where it may olds to select significant relations. Some of them are based be evaluated by other plugins. on statistical analysis [55] and on network properties [56], WGCNA is one of the most used approaches to build and while other interesting approaches aim to minimize the to analyze gene co-expression networks [59], and it has false positive links [57]. Finally, not less important is the been recently adapted for proteomics use also [14–20]. Fig. 5 Possible cases of correlation between two variables. a Positive correlation. b No correlation. c Negative correlation Vella et al. EURASIP Journal on Bioinformatics and Systems Biology (2017) 2017:6 Page 6 of 16 Table 1 Measures of dependence between two variables Co-expression measures What measures? Input/Output Features Pearson’s correlation (PC) Tendency to respond in oppo- Input: gene expressions value site/same direction across different Output: Sensitivity to outliers samples Bad array of expression level [ 0, 1] both genes increase can determine positive PC [ −1, 0] one increase and other value decrease Measure linear relations Spearman’s correlation (SC) Tendency to respond in oppo- Input: ranking values from expression levels site/same direction across different in samples Robust to outliers samples Output: Detect non-linear associations [ 0, 1] Both genes increase [ −1, 0] One increase and the other decrease Mutual information Reduction of uncertainty of a gene Input: gene expression values given the knowledge about other Output: Measure complex non-linear gene type relations (rarely present 0 there is no interdependence in biological data) >0 there is interdependence More samples are needed than PC, SC Time-consuming computation Kendall Correspondence/compatibility Input: gene expression value among two rankings Output: Similar to SC Robust to outliers 1 perfect correspondence Assumes fewer values than -1 rankings exactly inverted SC in the range [ −1, 1] It provides a weighted network model by converting a of outliers. In this case, the biweight midcorrelation is co-expression measure to a connection weight. The net- recommended because it is more robust to outliers. The work is fully specified by an adjacency matrix, where the package allows to compute both the correlation and the component a defines the strength of connection between Student p value for multiple correlations in case of missing ij nodes i and j. The value of a is computed through the co- data (see function corAndPvalue and bicorAndPvalue), ij expression similarity s (1), defined as the absolute value while the function qvalue computes the q value to mea- ij of correlation among the profiles of nodes i and j. It can sure the significance of each feature in terms of false be definedintwo ways:toobtainanunweightednet- discovery rate rather than false positive rate [61]. The work, the s is filtered by a threshold τ such that a takes unweighted network displays sensitivity to the choice of ij ij on value [0,1] (hard-thresholding) (2), while to obtain a the correlation values cut-off, thus, it is important to use weighted network a is defined by a power adjacency a proper criterion to select the edges to include in the ij function (soft-thresholding) (3): network. It is important to take into account the corre- lations are computed among each pairs of genes/proteins s =|cor(i, j)| (1) ij leading to a high rate of false positive values. Thus, to build an unweighted network and to reduce the inclu- 1 s ≥ τ ij sion of not significant correlations, it is recommended a = (2) ij 0 s <τ ij to set a cut-off also for p and q values. Concerning the weighted networks, the choice of the β parameter is based a = s (3) ij ij on the scale-free topology criterion [62]. This method rep- The R WGCNA package provides the possibility to use resents an improvement over unweighted networks based on dichotomizing the correlation matrix; the continuous different types of metrics, including Spearman’, Pearson’, nature of the gene co-expression information is preserved, Kendall’s correlation (see function cor), and the biweight and the results of weighted network analyses are highly midcorrelation (see function bicor) [60]. Spearman’s cor- robust with respect to the choice of the parameter β (soft- relation is a non-parametric measure of correlation. Pear- thresholding power). However, this thresholding method son’s correlation can be used when data are normally is based on the assumption that the network follows a distributed, but it is quite susceptible to the presence Vella et al. EURASIP Journal on Bioinformatics and Systems Biology (2017) 2017:6 Page 7 of 16 scale-free topology, a hypothesis weak in some cases, as tissue) under a given condition. Starting from this point, discussed in Section 4.1. many studies aim to face biological questions by investi- gating the network models in terms of topology [67] and 3.2 WGCNA and proteomic issues modular properties [68]. As for theoretical mathemati- When the WGCNA is applied to proteomic or to cal models proposed to describe the biological networks, metabolomic data, the choice of the optimal cutting the most claimed are Erdös–Rényi random graphs [69] and scale-free [70] (see Fig. 6). Other models, such as parameters should be evaluated in relation to the nature of the data analyzed. In fact, due to the low coverage of the the geometric random graph (GEO) [71] and the small- current analytical technologies, the produced dataset are world [72], have recently been proposed. In the context often incomplete, and the methods need to be properly of biology, the random graph, proposed in 1950, has been modified [63]. A major concern is the high rate of missing overtaken by the scale-free model; in fact, the degree dis- values that introduce loss of information and significant tribution of the scale-free model is a power-law curve that bias. To address this issue, several approaches including fits better than Poisson curve (typical of random graphs) K nearest neighbor, least square methods, or local least the degree distribution of the experimental networks [70] square methods have been proposed for proteomic and (Fig. 7). Based on power law distribution, most nodes metabolomic datasets too [64]. In other cases, a very sim- have a degree value far from the mean; specifically, most ple approach has been adopted, such as the removal of nodes have a low number of interactions while few nodes all species with a number of missing data bigger than a have a high number of interactions. These features lead given threshold [65]. However, to implement a more accu- a network structure less vulnerable and make the related rate analysis, it is recommended to process data by using system biologically robust [73]. Of note, the degree dis- an imputation method taking into account the nature of tribution may reflect the different role of proteins/genes, missing data. Three types of missing value have been iden- and those with a highest number of connections, so-called tified: MCAR (missing completely at random), i.e., due hubs, have a higher probability to be more biologically to stochastic fluctuations in a proteomic dataset, MAR relevant than others. In other words, removal or modifica- (missing at a random), i.e., due to multiple minor errors, tion of hubs may induce stronger alteration of the system and MNAR (missing not at a random), i.e., due to lim- equilibrium rather than removal or modification of nodes its of abundance of peptides/proteins that instruments are with low degree [74]. able to detect. In general, methods work fine when a low Although some topological properties are well percentage of missing value (≤10%) is present, but this described by a theoretical model, it may not be enough to affirm that the model represents well the real-world threshold could be different in relation to the missingness mechanisms and imputation approach used [63, 64]. network considered [75]. For example, a study on PPI In addition to missing value, another important step network of Drosophila Melanogaster and Saccharomyces of proteomic data preprocessing concerns their normal- Cerevisiae showed that the degree distribution was in ization [66]. Batch effects may occur in datasets run agreement with scale-free model, but diameter, clus- in different days or by different technicians. This phe- ter coefficient, and graphlet frequency were closer to nomenon may increase by using isotope reagents which GEO [76]. Of note, based on graphlet frequency, the allow the quantitation of a limited number of sam- comparison among scale-free, random graph, and GEO ples, thus, preventing a simultaneous analysis of multiple models has shown a higher agreement of GEO with PPI samples which could reduce data heterogeneity. For network from eukaryotic organism [77, 78]. A possible these reasons, an appropriate data transformation is a reason of these findings is that the scale-free model fits prerequisite to capture true correlations. Also in the networks that emerged from a stochastic growth, not case of protein co-expression, valid correlations have to subjected to an optimization process; while, PPI networks be selected by applying proper thresholds. To date, the emerge from stochastic processes, and their structure is most applications of WGCNA method on proteomic influenced by the evolutionary optimization that living datasets used a the soft-thresholding, which defines the systems have gone through [76]. β value according the scale-free criterion [15, 16, 65]. Another model used to describe the PPI networks is However, since the application of WGCNA to proteomic the small-world. Like the random graph model, it is char- dataset is a recent issue, and literature reports, few acterized by a Poisson curve. In a study focused on the examples, the future evaluation of hard-thresholding investigation of proteins regulating the fat storage, the cor- approach might be useful. responding PPI network had a degree-distribution close to a Poisson curve rather than a power-law [79]. More- over, the network showed a low average path length 4 Network topological analysis and a high clustering coefficient typical of small-world The structure of biological networks is closely related to the biological functions performed by a system (cell or model. These parameters indicate a network organized Vella et al. EURASIP Journal on Bioinformatics and Systems Biology (2017) 2017:6 Page 8 of 16 Fig. 6 Shape and degree distribution of random, small-world, and scale-free model with respect to a biological network. Models were calculated by ELIXIR web tool [131] Fig. 7 Functions used to describe the degree distribution of biological networks. Poisson curve a and power-law b shown for different parameters. c Example of graphlet of three nodes with frequency equal to 5 Vella et al. EURASIP Journal on Bioinformatics and Systems Biology (2017) 2017:6 Page 9 of 16 into communities, like observed in PPI networks [80]. The Generally called centralities, metrics can be subdivided small-world model preserves a modularity structure, and into measures related to nodes, edges, or whole network. it is not characterized by hub nodes making the small- Table 2 lists the main basic centralities used in the network world networks more robust in the case of removal or topological analysis [83]. modification of any node [73]. In the context of network organization, these centrali- The topological evaluation of gene co-expression net- ties facilitate the answer to question about which proteins works has shown that they are characterized by small- are most important and why. To give an idea of such anal- world and by scale-free properties, similar to many other ysis, we say that a vertex (i.e., a protein) is important real-world networks [81]. A study showed that the co- (or central) if it is close to many other vertexes. There expression networks generated from large datasets are are many number of different centrality measures that scale-free, but with an average clustering coefficient of have been proposed in literature but probably the most several orders of magnitude higher than expected for applied, and simple, is called vertex degree. The degree similarly sized scale-free networks [82]. These opposite d(v) of a vertex v,inanetwork G = (V , E),counts findings could be explained by the evidence that the topo- the number of edges in E incident upon v.Given G, logical properties of the co-expression networks may be define f (d) to be the fraction of vertexes v ∈ V with influenced by different parameters, including the expres- degree d(v) = d. For different d , d , ... , d , the collection 1 2 n sion data or the similarity measures to evaluate the depen- {f (d ), f (d ), ... , f (d )} is called the degree distribution 1 2 n dency between variables. of G. A useful generalization of degree is the notion of ver- 4.1 Topological analysis tex strength, which is obtained simply by summing up the A key point of topological studies is the definition of weights of edges incident to a given vertex. The distribu- mathematical models and metrics to describe the net- tion of strength is sometimes called the weighted degree work’s properties and to select the most relevant nodes distributions defined in analogy to the ordinary degree and substructures that may be of biological significance. distribution. Table 2 Centralities calculated by the CentiScaPe Cytoscape’s plugin Centrality Description Biological meaning Diameter Defines the longest shortest path in the network Average distance Defines the mean length of all the shortest paths in the net- work Degree Describes the number of neighbors a node has Highlights the number of nodes that regulated/regulate the node v Eccentricity Describes the longest shortest paths a node develop, giving us Highlights the easiness of a protein to reach/to be reached by a proximity information all the other proteins in the network Closeness Describes, for the node v, the minimal sum of all the distances Highlights the probability of a protein to be functionally rele- in the network vant for several proteins, but irrelevant for a few others Radiality Describes the integration of a node into the network Highlights the ability of a protein to be functionally relevant for several proteins, but irrelevant for a few others Centroid Describes the neighborhood of nodes by highlighting nodes Highlights a protein that tends to be functionally capable of that have the highest number of neighbors separated by the organizing discrete protein clusters or modules minimal shortest path Stress Describes the number of shortest paths that pass through a Highlights the relevance of a protein as functionally capable of node holding together communicating nodes Betweenness Describes, for each couple of nodes, the number of shortest Highlights the relevance of a protein as functionally capable of paths that pass through a specific node holding together communicating nodes Bridging Describes the neighborhood of nodes by highlighting nodes Highlights a protein possibly bringing in communication sets with a high number of high-degree neighbors of regulatory protein Eigenvector Describes a sort of weighted degree, where not only the num- Highlights a protein interacting with several important pro- ber of the neighbors is important but also the Eigenvector of teins, suggesting a central super-regulatory role or a critical the neighbors itself target of a regulatory pathways Edge betweenness Describes, for each couple of nodes, the shortest paths that Highlights the relevance of the interaction as capable of orga- pass through a specific edge nizing regulatory process a b c For each centrality, it is described the topological and biological meaning. The indicates network’s properties. The indicatesnode’sproperties. The indicates edge’s property Vella et al. EURASIP Journal on Bioinformatics and Systems Biology (2017) 2017:6 Page 10 of 16 Another centrality measure widely used is known as new plugins implementing recent developed topological betweenness [84]. It can be defined as follows: this mea- centralities are CytoNCA [92] and CytoHubba [90]. sure summarizes the extent to which a vertex is located “between” other pairs of vertexes. In this case, central- 4.2 Module analysis ity is based upon the perspective that importance relates Regardless of the approaches used to obtain a network, to where a vertex is located with respect to the paths in the detection of protein/gene modules is of great interest the network graph. In other terms, betweenness central- becausetheyrepresent thefunctionalunits at thebaseof ity is based on communication flow. Nodes with a high the mechanisms responsible of the cellular life. In biolog- betweenness centrality are interesting because they lie on ical networks, the term module has acquired three mean- communication paths and control information flow. Also ings: topological, functional, and pathological/disease. called hubs/bottlenecks [85], they can represent impor- The analysis of the network structure allows to detect tant proteins in signaling pathways and can form targets the topological modules defined as group of nodes highly for drug discovery. For example, by combining this data interconnected [68]. These nodes are often related to well- with interference analysis, targeted attacks on protein- defined molecular functions, thus, their detection PPI protein interaction networks have been simulated to pre- networks can help to identify functional modules [93], dict which proteins were better drug candidates [86]. defined as a group of functionally related proteins/genes Formally, betweenness can be defined as highly connected by genetic/physical interactions, co- expression, as well as membership of the same molecu- σ(s, t|v) lar complex or biological pathway [94]. The comparison Cl(v) = (4) σ(s, t) between pathological and physiological conditions has s=t=v∈V finally led to the definition of disease modules, such where σ(s, t|v) is the total number of shortest paths as a set of nodes with a putative key role concerning between s and t that pass through v,and σ(s, t) is the total mechanisms impaired due to disease [26, 51]. Topological, number of shortest paths between s and t (regardless of functional, and disease modules are generally not fully whether or not they pass through v). overlapped and often a single topological module can Other centralities used to globally evaluate the structure be linked to different functional or disease modules or of a network include: vice-versa (Fig. 8). Due to the complex connectivity of the biological net- Degree distribution: a function describing the works, the identification of modules is a challenging proportion of nodes related to each observed degree task. Various methods have been proposed, and most Modularity: evaluates the presence of modules, such of them are exclusively based on network topology. as a group of nodes characterized by the tendency to Some representative examples include the betweenness- form more connections within the group than based method [95], the modularity optimization method outside [87] [96], the spectral partitioning method [97], the core- Cluster coefficient: the ratio of the number of edges attachment based method [98], and the graph-theoretic among a node and its neighbors and the maximum approach relying on cliques [99] and other topological possible number of edges among all of them [72] properties [100]. To improve the accuracy of module Motif/graphlet frequency: evaluates the presence of detection, the integration of functional information is small subgraphs with a specific pattern that appear in more and more used [101–104]. These methods exploit a real-world network more frequently than in the the GO terms which in some cases are used to compute a relative random network [88] similarity score that measures the edge weight and drives Edge clustering coefficient: the ratio between the the module detection [105, 106]. number of triangles (three nodes connected by three The GO term enrichment analysis is routinely used edges) including an edge, and the maximum number also after the module detection to assess their bio- of possible triangles may include the edge [89] logical relevance [107, 108]. Making use of statistical Maximal Clique centrality: a property of a node taking tests, these approaches evaluate if genes/proteins of a into account the cliques (i.e, a subgraph in which each module are enriched in common functional properties pair of nodes is connected) including the node [90] (Fig. 9). During this process, standard methods treat each The simplest way to perform a network topologi- gene/protein as an isolated objects. However, in the last cal analysis by evaluating these centralities is through few years some network-based enrichment approaches Cytoscape’s plugins, such as CentiScaPe [83] and Net- have emerged taking into consideration also the interac- workAnalyzer [91], that provide the main basic methods tions among molecules [109–111]. The commonly used methods for module detection to compute the topological properties of nodes, edges, have been extended to co-expression networks to evaluate and networks, both directed and undirected. Moreover, Vella et al. EURASIP Journal on Bioinformatics and Systems Biology (2017) 2017:6 Page 11 of 16 Fig. 8 Example of topological, functional and disease modules not fully overlapped. The green nodes indicate a topological module, the blue nodes indicate a functional module, while the yellow nodes indicate a disease module the conditional patterns of co-expression and to provide Cluster Algorithm (MCL) [115] or CFinder [99]. For a insight into the cellular processes underlying the emer- detailed view of these tools, the review by J.Ji et al. [116] is gent phenotypes. Since genes could be co-regulated only recommended. across a subset of phenotypes, a biologically-motivated clustering method should be able to detect these patterns. 5 Studies related to the use of protein This issue is faced by biclustering algorithms which clus- co-expression networks terize both genes and experimental conditions. They are The investigation of proteomic data by co-expression- widely studied, and many different approaches have been based approaches has been first addressed by Gibbs et al. published and applied to identify genes regulated in a to infer the protein abundance and to overcome issues state-specific manner [112]. linked to peptide-protein mapping [14]. Starting from In the context of module detection, the WGCNA pack- experimental datasets obtained by LC-MS, and by using age also provides a procedure consisting of a hierarchical a method derived from WGCNA, the authors proposed clustering algorithm based on a distance matrix calcu- a protein co-expression network approach (ProCoNa) lated by similarity measure between gene/protein pairs where the nodes are peptides and the edges are calcu- [59]. After assigning nodes to modules, an aggregate mod- lated by processing their intensity. The modules computed ule signature, called eigenvector, is computed; it can be by co-expression analysis were strictly correlated with the considered as an object representing the expression pro- investigated phenotypes and showed a significant enrich- files of the molecules belonging to the module, thus, it ment of some GO terms. Following these findings, the simplifies the comparison of different modules [113]. A authors explored the relationship between co-expression wide range of tools to perform module analysis are avail- networks reconstructed from transcriptomic and pro- able. They include several Cytoscape’s plugins, such as teomic data [15]. In this study, concerning SARS-CoV ClusterOne [114] and MCODE [100] and the Markov infection, they used a bipartite graph analysis to evaluate Fig. 9 Procedure used to identify/predict modules in biological networks. The network structure is used to identify groups of highly connected nodes by graph clustering algorithm, while the GO annotations are used to improve the accuracy of the cluster prediction. The final result are clusters of nodes highly connected and related to functions/processes significantly enriched, thus acting at the basis of the emergent phenotypes Vella et al. EURASIP Journal on Bioinformatics and Systems Biology (2017) 2017:6 Page 12 of 16 phenotype associations, overlaps, and module correla- and their use to infer biological knowledge by topolog- tion, thus, providing a foundation of a true multi-omics ical and module analysis. Although literature is yet too signatures. weak, protein co-expression networks represent a valid The idea to use the WGCNA method on proteomic approach to obtain a novel overview of proteomic data data was followed also by MacDonald et al. [18] to clar- and to provide new hypotheses about key molecules act- ify the role of the glutamate signaling in schizophrenia ing in pathophysiological states. Of course, its real value (SCZ). The topological evaluation of the co-expression has to be assessed by further studies, but preliminary networks from SCZ affected subjects and healthy con- findings make it promising. The main limitation to per- trols led to observe in SCZ affected group a lower average form the construction of protein co-expression networks node degree. This result was probably due to the loss of may be attributed to the difficulty in measuring a pro- coordination of the biological functions, as well as disease teome with enough coverage. A major consequence is the heterogeneity. However, in SCZ network, it was found high rate of missing values that introduce loss of infor- the exclusive presence of a module enriched in GO terms mation and significant bias. In addition, batch effects may related to glutamate signaling and whose proteins had a occur in datasets run in different days or by different tech- significant increased degree. nicians. Thus, data normalization is another key point The application of the WGCNA on protein expression in the context of proteomic data preprocessing. These profiles was also faced by Chang Guo et al. to characterize aspects will be surely improved by future advances of the role of different protein isoforms in E. Coli resistance the proteomic technologies which in recent years have to serum killing [13]. Like in other cases, the authors received a big boost from genome sequencing and from evaluated the topological variations of the co-expression the combination of liquid chromatography and mass spec- networks between control- and serum-treated groups. By trometry [117]. In any case, the availability of large-scale considering the connectivity of modules identified in both proteomic data already offers a new range of opportunities networks, a protein, IleS, was found with a differential to improve the existing network models, and in partic- number of connections in control and treated groups. ular PPI, in understanding the mechanisms behind the Of note, its involvement in the response to serum killing emergent phenotypes [8, 10, 108, 118, 119]. was confirmed by independent functional test based on a The results shown through the reviewed studies have gene-deletion mutant, thus, confirming the utility to use evidenced a good relation between the topology of protein co-expression networks also to identify putative protein co-expression network and the emergent phe- drug targets. notypes. Like PPI networks, the characterization of To find phenotype-related biomarkers in the context hubs/bottlenecks and functional, topological and disease of renal dysfunction, D. Wu et al. followed an approach modules has proved to select the most important based on the combination of differentially expressed pro- molecules. Despite these findings, statistical methods teins and PPI networks. For each pair of connected nodes to construct co-expression networks by processing they calculated the PC score, and the topological anal- large-scale proteomic data still need to be improved ysis of the reconstructed co-expression networks led to [63, 64, 66]. To date, the available applications are mainly identify twelve proteins involved in the pathology [44]. based on WGCNA framework, and studies evaluating Likewise, Yu et al. investigated the molecular mechanisms other approaches are expected. Gaussian graphical mod- underlying the glioblastoma multiforme (GBM)[20]. They els [120], partial correlation [121], or Bayesian networks analyzed samples of macaque rhesus brain by both iTRAQ [122] are more sophisticated approaches that are gain- and RNA-seq approaches. The proteins identified were ing favor over simple correlations due to their ability to combined with STRING database and, for each experi- separate direct from indirect variable associations. These mentally validated PPI, the PC score was calculated using methods need to use prior knowledge to estimate proba- both protein and transcript levels. Since the PC score from bilistic interactions, and their implementation on typical proteomic data resulted significantly higher than score -omics data may be computationally challenging due to calculated using transcript levels, the authors focused on the curse of dimensionality. However, they are widely WGCNA to identify protein modules involved in the dis- adopted to integrate different -omics data [123, 124] and ease. Finally, a more detailed evaluation of these modules to infer transcriptional regulatory networks in the context allowed the selection of eight genes of interest, and two of of reverse-engineering processing techniques [48, 49]. them were already known drug targets of GBM. Collection and integration of different -omics data rep- resent essential points to perform a global evaluation 6Conclusions of the biological systems and to improve the effective- ness of the current systems biology approaches. For these The aim of this review was to provide an overview on PPI and co-expression networks. In particular, present- purposes, genomic and proteomic data are often used ing the recent idea of the protein co-expression networks in combination with PPI networks. Since many studies Vella et al. EURASIP Journal on Bioinformatics and Systems Biology (2017) 2017:6 Page 13 of 16 are reporting a low direct correlation between mRNA Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in and protein abundance [125, 126], their integration with published maps and institutional affiliations. molecules acting in the post-transcriptional regulation [127, 128] and metabolomic data [10] is necessary. In this Author details scenario, PPIs and co-expression networks provide the Institute for Biomedical Technologies - National Research Council (ITB-CNR), 93 Fratelli Cervi, Segrate, Milan, Italy. Department of Computer Science, possibility to apply a multi-omic strategy [15] that should Systems and Communication DiSCo, University of Milano-Bicocca, 336 Viale improve level of significance in understanding biological Sarca, Milan, Italy. mechanisms, including those related to diseases. 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Published: Mar 20, 2017
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