RedeR: R/Bioconductor package for representing modular structures, nested networks and multiple levels of hierarchical associations

Abstract

Visualization and analysis of molecular networks are both central to systems biology. However, there still exists a large technological gap between them, especially when assessing multiple network levels or hierarchies. Here we present RedeR, an R/Bioconductor package combined with a Java core engine for representing modular networks. The functionality of RedeR is demonstrated in two different scenarios: hierarchical and modular organization in gene co-expression networks and nested structures in time-course gene expression subnetworks. Our results demonstrate RedeR as a new framework to deal with the multiple network levels that are inherent to complex biological systems. RedeR is available from http://bioconductor.org/packages/release/bioc/html/RedeR.html.

Figure 1

Schematic representation of the RedeR callback engine. In the low-level interface, the Apache xmlrpc webserver [9] is used to link R and Java.

Figure 2

Schematic representation of RedeR data packing and storing. (a) Data structure. The software emulates a mixed graph with two layers and multiple levels in order to organize and manage the hierarchical associations. (b) Data abstraction. For the end-user, the data abstraction corresponds to the network layout that represents the data structure. A flat network is shown to contrast an ordinary representation (left) with RedeR hierarchical topology (right). (c) Data encapsulation: end-users and R developers have access to the outer level of the application through the methods handled by the interface.

Figure 3

Hierarchical and modular organization in co-expressed gene networks. R script describing step-by-step all intermediate R objects required to obtain the results presented in the first case study. TSS, transcriptional start site.

Figure 4

Hierarchical networks. (a) Dendrogram derived from complete-linkage clustering analysis using Euclidean distance on the gene expression matrix of all genes differently expressed at 3 h (related to 0 h) in estrogen-treated MCF-7 cells (Carroll et al. [6] dataset). (b) Hierarchical network obtained by superimposing the dendrogram onto the corresponding co-expression gene network. The co-expression associations were computed for the same set of genes (for additional details on the pre-processed data please see Additional file 1 and Figure 3). Node coloring depicts differential expression as log2 fold-change (logFC) and node size indicates the kilobase distance of the transcription start site to the nearest ER binding site. Out-edge width represents the sum of all edges between modules divided by the total possible edges.

Figure 5

Nested structures in time-course gene expression subnetworks. R script describing step-by-step all intermediate R objects required to obtain the results presented in the second case study. logFC, log2 fold-change.

Figure 6

Nested subnetworks. Genes differentially expressed in estrogen-treated MCF-7 cells at 3, 6 or 12 h (relative to 0 h; Carroll et al. [6] dataset) were mapped to the human interactome (HPRD database [17]) and for each time point the largest subnetwork was selected in order to demonstrate how RedeR represents nested structures (additional details in Figure 5). Node coloring depicts differential expression as log2 fold-change (logFC). The insets correspond to the overlap between consecutive time points.

Figure 7

Performance of six graph tools loading scale free networks of increasing size. Each point in the plot corresponds to the average elapsed time (in seconds) required to load one of these networks. The inset shows the first 10 s of the same tests (± standard deviation, n = 10). The networks were obtained by the function 'barabasi.game' available in the R package igraph [19]. Briefly, each network has ϖ vertices and ε edges generated by a step-model where the first step generates a single vertex and no edge; the subsequent steps generate one vertex linked to an old vertex according to a probability distribution proportional to the degree of the nodes; therefore, in the end there are ϖ-1 edges. The networks were obtained and set prior to the performance tests, and only with minimum information in order to guarantee equal conditions among the software (that is, without any graph attribute, such as color, size, and so on). Versions tested: R version 2.14.1, RedeR_1.0.3, igraph_0.5.5-4, RCytoscape_1.4.3, Cytoscape 2.8.1, CytoscapeRPC 1.7, Rgraphviz_1.32.0. Platform: x86_64-apple-darwin9.8.0/x86_64 (64-bit). Hardware: MacPro4.1 2 × Quad-core Intel Xeon 2.26 GHz, 6 GB RAM. The source code used to run the complete analysis is available in Additional files 2 and 3.