Table of Contents
Cover
Title Page
Copyright
List of Contributors
Chapter 1: Using the DiffCorr Package to Analyze and Visualize Differential Correlations in Biological Networks
1.1 Introduction
1.2 What is DiffCorr?
1.3 Constructing Co-Expression (Correlation) Networks from Omics Data – Transcriptome Data set
1.4 Differential Correlation Analysis by DiffCorr Package
1.5 Conclusion
Acknowledgments
Conflicts of Interest
References
Chapter 2: Analytical Models and Methods for Anomaly Detection in Dynamic, Attributed Graphs
2.1 Introduction
2.2 Chapter Definitions and Notation
2.3 Anomaly Detection in Graph Data
2.4 Random Graph Models
2.5 Spectral Subgraph Detection in Dynamic, Attributed Graphs
2.6 Implementation in R
2.7 Demonstration in Random Synthetic Backgrounds
2.8 Data Analysis Example
2.9 Summary
Acknowledgments
References
Chapter 3: Bayesian Computational Algorithms for Social Network Analysis
3.1 Introduction
3.2 Social Networks as Random Graphs
3.3 Statistical Modeling Approaches to Social Network Analysis
3.4 Bayesian Inference for Social Network Models
3.5 Data
3.6 Conclusions
References
Chapter 4: Threshold Degradation in R Using iDEMO
4.1 Introduction
4.2 Statistical Overview: Degradation Models
4.3 iDEMO Interface and Functions
4.4 Case Applications
4.5 Concluding Remarks
References
Chapter 5: Optimization of Stratified Sampling with the R Package SamplingStrata: Applications to Network Data
5.1 Networks and Stratified Sampling
5.2 The R Package SamplingStrata
5.3 Application to Networks
5.4 Conclusions
References
Chapter 6: Exploring the Role of Small Molecules in Biological Systems Using Network Approaches
6.1 The Role of Networks in Drug Discovery
6.2 R for Network Analyses
6.3 Linking Small Molecules to Targets, Pathways, and Diseases
6.4 R as a Platform for Network Analyses in Drug Discovery
6.5 Discussion
Acknowledgments
References
Chapter 7: Performing Network Alignments with R
7.1 Introduction
7.2 Problems, Models, and Algorithms
7.3 Algorithms Based on Conditional Random Fields
7.4 Performing Network Alignments with R
7.5 Discussion
References
Chapter 8: ℓ1-Penalized Methods in High-Dimensional Gaussian Markov Random Fields
8.1 Introduction
8.2 Graph Theory: Terminology and Basic Topological Notions
8.3 Probabilistic Graphical Models
8.4 Markov Random Field
8.5 Sparse Inference in High-dimensional GMRFs
8.6 Selecting the Optimal Value of the Tuning Parameter
8.7 Summary and Conclusion
References
Chapter 9: Cluster Analysis of Social Networks Using R
9.1 Introduction
9.2 Cluster Analysis in Social Networks
9.3 Cluster Analysis in Social Networks Using R
9.4 Discussion and Further Readings
References
Chapter 10: Inference and Analysis of Gene Regulatory Networks in R
10.1 Introduction
10.2 Multiple Myeloma
10.3 Installation of Required R Packages from CRAN and Bioconductor
10.4 Data Preprocessing
10.5 Bc3net Gene Regulatory Network Inference
10.6 Retrieving and Generating Gene Sets for a Functional Analysis
10.7 Pathway and Other Gene Set Collections
10.8 Conclusion
References
Chapter 11: Visualization of Biological Networks Using NetBioV
11.1 Introduction
11.2 Network Visualization
11.3 NetBioV
11.4 Example: Visualization of Networks Using NetBioV
11.5 Conclusion
11.6 Appendix
11.7 Spiral View
References
Index
End User License Agreement
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Guide
Cover
Table of Contents
Begin Reading
List of Illustrations
Chapter 1: Using the DiffCorr Package to Analyze and Visualize Differential Correlations in Biological Networks
Figure 1.1 A gene–gene association measure and causal inferences in co-expression analysis. (a) Two kinds of major methods to measure the association between gene expressions. Although the Pearson correlation coefficient (PCC) is widely used in co-expression analysis in plant science, it can only be used to estimate a linear relationship between variables. A gene–gene association is not always a linear correlation. In general, information-theoretic measures can estimate a nonlinear relationship. Note that the Spearman correlation coefficient (SCC) can estimate a nonlinear relationship such as a monotonic function. (b) A concept of differential co-expression networks.
Figure 1.2 An overview of analysis steps and main functions in DiffCorr. An outline of the DiffCorr approach with the three main processes. HCA, hierarchical cluster analysis.
Figure 1.3 Heatmaps of the correlation matrices. Heatmaps of the gene expression correlation matrices. Horizontal and vertical show the probe set identifiers in each experiment. Pink = positive correlation, blue = negative correlation between the two probe sets.
Figure 1.4 Correlation network visualization with the igraph package and Cytoscape. (a) Correlation networks with the igraph package. Nodes are the probe sets, and the edges mean that there are correlation coefficients over 0.95 between the connected nodes. We colored the nodes that are in the degree over 20 (magenta) and those that are not (green). (b) Correlation networks with Cytoscape [65]. Cytoscape has functionality to change the layout of the network interactively. Here, we applied yFiles [66] “Organic” layout to the network.
Figure 1.5 Workflow for constructing a co-expression network from microarray data and for evaluating detected network modules by Gene Ontology (GO) term enrichment analysis.
Figure 1.6 HTML report of Gene Ontology (GO) enrichment analysis. Results of network Module 1 by GO enrichment analysis (filename: res_mod1.html). GO biological process ontology terms are listed in order of predominance in the cluster module.
Figure 1.7 Module network visualization with the DiffCorr package and Cytoscape. (a) Differentially co-expressed module networks with the DiffCorr package. Nodes are the probe set modules; the edges mean that there is a significant difference in co-expression between two nodes. (b) Differentially co-expressed module networks with Cytoscape. To explore panel (a) interactively, we imported panel (a) to Cytoscape and applied yFiles “Hierarchic” layout to the network.
Figure 1.8 An example of gene expression patterns between two conditions.
Figure 1.9 A typical result of pairwise differential correlations from the DiffCorr package.
Figure 1.10 Interconnections in the pathways of central metabolism and aromatic amino acids for WT (a) and tt4 plants (b). The metabolites whose levels changed less than 10% (p < 0.05) in tt4 /WT are indicated with orange characters in (b); the metabolites with black characters in (b) exhibited no significant changes; the metabolites with gray characters were undetectable. The gray arrows indicate the metabolic pathways. The curved lines show correlations between metabolite pairs. The thickness of the edges between the metabolites represents the significance of correlations (r Met > 0.88). Although the sinapoylmalate level in tt4 did not increase, correlations of malate with aromatic compounds were intensified in the tt4 mutant, indicating a possible adaptive response to UV stress by the flavonoid-deficient tt4 mutant by reconfiguration of the networks in tt4 . Inset photo images show that tt4 plants exhibit yellow seed color due to the nonaccumulation of proanthocyanidins in the seed coat. Abbreviations: CHS, chalcone synthase; p -coumarate, 4-hydroxycinnamic acid; Phe, phenylalanine; and Tyr, tyrosine.
Chapter 2: Analytical Models and Methods for Anomaly Detection in Dynamic, Attributed Graphs
Figure 2.1 A graph with a normative pattern. A five-vertex substructure is repeated three times, with additional edges connecting the substructures. One form of graph anomaly detection is to detect substructures that deviate from such a typical pattern.
Figure 2.2 Spectral characteristics of matrices derived from simulated graphs. The eigenvalue spectrum (a, c, e) and the two principal eigenvectors (b, d, f) are shown for the adjacency matrix (a, b), the traditional modularity matrix (c, d), and the residuals matrix that accounts for categorical vertex pair attributes (e, f). The eigenvalue spectrum's density is shown in red, and its support is shown at the bottom in black. The first, second, and third vertex categories are denoted in the scatter plots by red dots, green triangles, and blue squares, respectively.
Figure 2.3 Detection performance in simulated graphs. Simulations were run in which the detection algorithm either includes (b, d) or does not include (a, c) dynamics, and includes (c, d) or does not include (a, b) vertex pair attributes. Densities listed are the greatest density of the signal subgraph over an eight-sample window. Detection performance improves as the subgraph gets denser, and as more features of the graph are considered.
Figure 2.4 Data from the Web of Science citation graph. Singular values of the integrated residuals matrices grow over time, with a large spike in values in 1976 (a). The singular vectors in 1976 (b) show six outliers corresponding to chemistry papers with high cross-subject citation, in addition to some outliers based on degree alone. Without accounting for attributes (c), while the highdegree vertices still stand out in the principal residuals space, those with significant crosssubject citation do not.
Chapter 3: Bayesian Computational Algorithms for Social Network Analysis
Figure 3.1 Dolphin undirected network graph.
Figure 3.2 MCMC diagnostics for the overall chain. The three plot columns are estimated marginal posterior densities (left), traces (center), and autocorrelation plots (right).
Figure 3.3 Latent positions obtained by using the latentnet package.
Figure 3.5 Latent positions obtained by using the lvm4net package.
Figure 3.6 Estimated latent positions from LPCM with two clusters obtained by using the latentnet package.
Figure 3.7 Estimated latent positions from LPCM with two clusters obtained by using the VBLPCM package.
Figure 3.8 GoF diagnostics for ERGM (Bergm package). The red line displays the goodness-of-fit statistics for the observed data together with box plots of GoF network statistics based on 100 simulated networks from the posterior distribution.
Figure 3.9 GoF diagnostics for LSM (latentnet package). The solid black line displays the goodness-of-fit statistics for the observed data together with box plots of GoF network statistics based on 100 simulated networks from the posterior distribution.
Figure 3.11 GoF diagnostics for LSM (lvm4net package): The red line displays the goodness-of-fit statistics for the observed data together with box plots of GoF network statistics based on 100 simulated networks from the posterior distribution.
Figure 3.12 GoF diagnostics for LPCM with two clusters (latentnet package). The solid black line displays the goodness-of-fit statistics for the observed data together with box plots of GoF network statistics based on 100 simulated networks from the posterior distribution.
Figure 3.13 GoF diagnostics for LPCM with two clusters (VBLPCM package). The solid black line displays the goodness-of-fit statistics for the observed data together with box plots of GoF network statistics based on 100 simulated networks from the posterior distribution.
Chapter 4: Threshold Degradation in R Using iDEMO
Figure 4.1 The initial iDEMO window.
Figure 4.2 Open file window.
Figure 4.4 Data list window.
Figure 4.3 Data list window.
Figure 4.5 Degradation model selection window.
Figure 4.6 The tabbed notebook widgets of single degradation model analysis. (a) The parameter estimation tab. (b) The lifetime information tab.
Figure 4.7 The tabbed notebook widgets of stochastic process. (a) Gamma degradation-based process tab. (b) IG degradation-based process tab.
Figure 4.8 Figure options window for the lifetime information.
Figure 4.9 Laser data. (a) The plot of the degradation paths. (b) The box plot of the degradation paths for each measurement.
Figure 4.10 Lifetime information for laser data. The plot of (a) PDF and (b) CDF estimation.
Figure 4.11 Graphical representation of goodness-of-fit for laser data. (a) PP plot. (b) QQ plot.
Figure 4.12 Fatigue data. (a) The plot of the degradation paths. (b) The missing values in the degradation paths.
Figure 4.13 The box plot of the degradation paths for each measurement.
Figure 4.14 Lifetime information for fatigue data. (a) The plot of PDF estimation. (b) The plot of CDF estimation.
Figure 4.15 Graphical representation of goodness-of-fit for fatigue data. (a) PP plot. (b) QQ plot.
Figure 4.16 T25 data. (a) The plot of the degradation paths. (b) The box plot of the degradation paths for each measurement.
Figure 4.17 T105 data. (a) The plot of the degradation paths. (b) The box plot of the degradation paths for each measurement.
Figure 4.19 Lifetime information for T25 data. The plot of (a) PDF and (b) CDF estimation.
Figure 4.21 Lifetime information for T105 data. The plot of (a) PDF and (b) CDF estimation.
Figure 4.22 Graphical representation of goodness-of-fit for T25 data. (a) PP plot. (b) QQ plot.
Figure 4.24 Graphical representation of goodness-of-fit for T105 data. (a) PP plot. (b) QQ plot.
Chapter 5: Optimization of Stratified Sampling with the R Package SamplingStrata: Applications to Network Data
Figure 5.1 Generation of solutions.
Figure 5.2 RMSEs of
Figure 5.3 Correspondence between sample sizes and centrality measures correlation with target variables.
Chapter 6: Exploring the Role of Small Molecules in Biological Systems Using Network Approaches
Figure 6.1 A SALI network constructed from set of 62 dihydroquinoline derivatives that were designed to inhibit the glucocorticoid receptor. See Ref. [72] for further details.
Figure 6.2 An example of a scaffold. In this case, this scaffold is common to many tricyclic antidepressants.
Figure 6.3 An example of a scaffold tree displayed as a radial network, generated from a set of pyruvate kinase inhibitors.
Figure 6.4 An example of the scaffolds generated using the Scaffold Tree and Scaffold Network algorithms, starting from Alosetron. Blue scaffolds are generated by both methods and green scaffolds are generated only by the Scaffold Network method. Modified from Figure 1 in Varin et al. [88].
Figure 6.5 An example of a scaffold-document network, limited to three iterations. Squares represent fragments and circles represent documents. Document nodes are colored based on their major topic MeSH heading. The seed document is shown with a red border (top left).
Figure 6.6 An example of a similarity network, where nodes are molecules and are connected if they exhibit a Tanimoto similarity greater than 0.6. Nodes are colored based on the PANTHER [99] class of their primary target.
Chapter 7: Performing Network Alignments with R
Figure 7.1 The parallel comparison of the sequence and network alignment methods, and the general milestones on a timeline. General milestones for both fields are shown in the middle (gray box) [[5]].
Figure 7.2 A flow chart of the pairwise network alignment [[5]].
Figure 7.3 A small example of PNA. The dash lines are the corresponding mappings. The edge
Figure 7.4 An illustration of gaps [[18]]. A network alignment model needs to deal with node mutations (e.g., insertion, deletion, duplication, mismatch, and also functional change) and the edge mutations (e.g., detachment, attachment).
Figure 7.5 Examples of network schemas from NetGrep [[30]]. Unlabeled schema proteins are considered to be “wildcards” and can match any protein in the interaction network. (a) A signaling pathway schema. (b) A MAP kinase schema. (c) A feed-forward loop network motif schema. (d) A “kinate” feedback loop network motif schema. (e) An SH3 domain interaction schema. (f) A specific protein schema.
Figure 7.6 A small example of MNA [[32]]. Græmlin 2.0 [[32]] used the equivalence class to present conserved homology proteins in different networks. A network alignment is an equivalence relation. In this example, four protein interaction networks are inputted to multiple alignment. A network alignment partitions proteins into equivalence classes (indicated by boxes).
Figure 7.7 An illustration of network querying process. Given the query network (left) and target network (middle), the feature functions are constructed based on the node similarity and the topology similarity between two networks. Then, the CRF model is applied to find the best matching subnetwork (right) in the target network. (b) An example of transforming the network querying problem to labeling problem. The left is the query network
Figure 7.8 Real examples of network querying [[23]]. (a) S. cerevisiae protein metabolism cluster [[48]] is queried in D. melanogaster PPI network. (b) A super pantothenate coenzymeA biosynth pathway in E. coli and the best matching pantothenate coenzymeA biosynth pathway in S. cerevisiae with one mismatch. The solid edges are the matching interactions and the dashed edge is the mismatching edge. (c) A tree-like pathway containing part of the T. thermophilus and its best match in E. coli .
Figure 7.9 Compared CNetA with IsoRank on one simulated data set measured by the edge accuracy with different evolution times [[57]].
Figure 7.10 A conserved alignment including proteins involved in cell division in all aligned species [[46]].
Figure 7.11 (a) A small example of multiple network alignment. (b) The workflow of proposed network-structure update strategy.
Figure 7.12 (a) Running time for CNetMA with different network size. (b) Running time for CNetMA with different number of networks.
Chapter 8: ℓ1-Penalized Methods in High-Dimensional Gaussian Markov Random Fields
Figure 8.1 Genetic network estimated by neighborhood selection and edge set estimated by AND rule.
Figure 8.2 Gradient and coefficient path. Black curves are referred to the edges that are included in the true edge set, while gray curves are referred to the other edges. Vertical dashed lines correspond to the first inclusion transition values.
Figure 8.3 Sequence of undirected graphs estimated using the glasso estimator. Black edges are referred to the true edges, while the gray edges are referred to the false edges.
Figure 8.4 Sequence of Bayesian information criterion values for different values of the tuning parameter. Panel (a) is referred to the patients with lung cancer while panel (b) to the normal patients. Vertical dashed lines identify the optimal
Figure 8.5 Genetic network of the differentially expressed genes. The sparse structure is estimated applying the glasso estimator to the gene expression measures obtained using the patients with lung cancer. Gray undirected edges are specific for condition of the patients while shared edges are drawn by black lines.
Figure 8.6 (a) Surface of the Bayesian information criterion computed for different values of the two tuning parameters. (b) Profile BIC criterion as a function of the second tuning parameter.
Figure 8.7 Sequence of the leave-one-out cross-validate Kullback–Leibler divergence for different values of the tuning parameter. Vertical dashed line identifies the optimal
Figure 8.8 Sequence of the first four networks estimated by fglasso(). Directed dashed edges are referred to the nonzero elements of the submatrices at lag one.
Chapter 9: Cluster Analysis of Social Networks Using R
Figure 9.1 Studentnets network.
Figure 9.2 Social subgraph.
Figure 9.3 Task subgraph.
Figure 9.4 Studentnets dendrogram obtained with hclust().
Figure 9.5 Studentnets dendrogram.
Figure 9.6 Clusters obtained with Silhouette index.
Figure 9.7 Dendrogram for Edge betweenness community structure.
Figure 9.8 Edge betweenness clusters.
Figure 9.9 Dendrogram for fast greedy community structure.
Figure 9.10 Clusters obtained with fastgreedy algorithm.
Figure 9.11 Dendrogram for walktrap community structure.
Figure 9.12 Communities identified by Walktrap algorithm.
Figure 9.13 Communities without the shaded regions.
Chapter 10: Inference and Analysis of Gene Regulatory Networks in R
Figure 10.1 Global visualization of the myeloma gene regulatory network with ECR
Figure 10.2 Multiple myeloma cell cycle subnetwork with bc3net ECR
Chapter 11: Visualization of Biological Networks Using NetBioV
Figure 11.1 Visualization of the same network using a random layout (a) and using Kamada–Kawai algorithm (b).
Figure 11.2 Visualization of the PPI interactions of Arabidopsis thaliana using different layout algorithms. (a) Fruchterman–Reingold; (b) Hive plot; (c) Sugiyama; (d) NetBioV (modular plot).
Figure 11.3 Visualization of the PPI interactions of Arabidopsis thaliana using (a) Eigenvectors of the Laplacian matrix of the network and (b) BioFabric plot.
Figure 11.4 Global layouts using different options available in NetBioV: (a) Global layout style of artificial network 1. The positions of the nodes in the MST are determined by Fruchterman–Reingold algorithm. Edges found by the MST are white, while other edges are shades of red to yellow. (b) Global network layout of A. thaliana . (c) Coloring vertices of B-cell lymphoma network based on the external information such as expression value (red to blue—smaller to higher expression value). (d) Coloring nodes are in red, MST edges in “green,” and other edges are in “blue.”
Figure 11.5 Modular layouts using different options available in NetBioV: (a) Modular layout style of artificial network 1. The colors for the modules are chosen randomly from a compiled list of bright colors. (b) Abstract modular view of A. thaliana ; each module is labeled with the most significant enriched GO-pathway. Edge width is proportional to the number of connections between modules. (c) Information flow view in A. thaliana network by highlighting shortest paths between nodes of modules 1, 5, and 17, 21. (d) Highlighting the edges of the modules of B-cell network by choosing a random set of colors.
Figure 11.6 Layered layouts using different options available in NetBioV: (a) Layered layout style of artificial network 1 with a compact view. Root nodes are selected randomly. (b) Layered layout view of A. thaliana with a spread view, the six nodes A. thaliana network.
Figure 11.7 Spiral layouts using different options available in NetBioV. Setting different tuning parameters and standard layout algorithms as an input for the placement of nodes.
List of Tables
Chapter 3: Bayesian Computational Algorithms for Social Network Analysis
Table 3.1 Comparison of the main features of the packages for latent space modeling
Table 3.2 Timings in seconds to fit LSMs (no clustering, G = 1)
Table 3.3 Timings in seconds to fit LPCM with two clusters (G = 2)
Chapter 5: Optimization of Stratified Sampling with the R Package SamplingStrata: Applications to Network Data
Table 5.1 Results of the application of the methods implemented in R package stratification and of the genetic algorithm implemented in R package SamplingStrata to the four data sets
Table 5.2 Correlation matrix between centrality measures and target variables
Table 5.3 Centrality measures: average correlation with target estimates and obtained sample size after optimization
Chapter 7: Performing Network Alignments with R
Table 7.1 The characteristics of different categories of biological network alignment
Chapter 8: ℓ1-Penalized Methods in High-Dimensional Gaussian Markov Random Fields
Table 8.1 Some equality constraints on the elements of the submatrices
Chapter 10: Inference and Analysis of Gene Regulatory Networks in R
Table 10.1 A selection of sources for gene sets that can be integrated for the analysis of gene regulatory networks
Chapter 11: Visualization of Biological Networks Using NetBioV
Table 11.1 A list of public databases provide information about biological networks
Table 11.2 A list of algorithms used for visualizing biological networks
Table 11.3 Comparison between NetBioV and some popular network visualization packages
Table 11.4 A list of R functions available in NetBioV
Quantitative and Network Biology
Series editors M. Dehmer and F. Emmert-Streib
Volume 7
Computational Network Analysis with R
Applications in Biology, Medicine, and Chemistry
Edited by
Matthias Dehmer, Yongtang Shi, and Frank Emmert-Streib
The Editors
Prof. Matthias Dehmer
UMIT – The Health and Life Sciences University
Eduard Wallnoefer Zentrum 1
6060 Hall
Austria
and
Nankai University
College of Computer and Control Engineering
300071 Tianjin
P.R. China
Prof. Yongtang Shi
Nankai University
Center for Combinatorics
No. 94 Weijin Road
300071 Tianjin
China
Prof. Frank Emmert-Streib
Tampere University of Technology
Predictive Medicine and Analytics Lab
Department of Signal Processing
Tampere
Finland
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Andrey Prokhorov/iStock (Background Picture)
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