Differential gene regulatory networks in development and disease

Abstract

Gene regulatory networks, in which differential expression of regulator genes induce differential expression of their target genes, underlie diverse biological processes such as embryonic development, organ formation and disease pathogenesis. An archetypical systems biology approach to mapping these networks involves the combined application of (1) high-throughput sequencing-based transcriptome profiling (RNA-seq) of biopsies under diverse network perturbations and (2) network inference based on gene–gene expression correlation analysis. The comparative analysis of such correlation networks across cell types or states, differential correlation network analysis, can identify specific molecular signatures and functional modules that underlie the state transition or have context-specific function. Here, we review the basic concepts of network biology and correlation network inference, and the prevailing methods for differential analysis of correlation networks. We discuss applications of gene expression network analysis in the context of embryonic development, cancer, and congenital diseases.

Introduction

One of the most fundamental scientific advancements of the early twenty-first century has been the sequencing of the human genome [1]. Knowledge of the sequence and location of genes in the genome has revolutionized biomedical research and diagnostics. Genetic mutations responsible for congenital diseases can now be physically linked to specific positions in the genome, enabling the systematic mapping of the molecular basis of polygenic diseases and other traits. To fully understand the mechanistic basis of a polygenic trait or biological process, it is necessary to account for interactions such as gene expression correlation or genetic epistasis among the individual trait-associated genes. Gene networks are an intuitive and useful abstraction for representing the totality of such gene–gene interactions for a trait.

The advent of relatively low-cost quantitative transcriptome profiling (first by microarray hybridization and more recently, by high-throughput sequencing or RNA-seq [2, 3]) was key to enabling the systematic mapping of networks of genes whose expression levels are correlated across biological samples, i.e., gene expression correlation networks. Because eukaryotic gene regulation is thought to be hierarchically organized with regulated genes’ protein products in turn regulating the expression of other genes, gene–gene correlation networks provided the first genome-scale view into gene regulation in diverse contexts such as embryogenesis, hematopoiesis, oncogenesis, and inflammation.

Although gene–gene interactions were the earliest biological network type to be analyzed on the whole-organism scale [4], network analysis has since found broad utility in understanding interactions among cellular molecular constituents of all types, with protein-metabolite networks and protein–protein interaction (PPI) networks being particularly widely used. The network abstraction has proved to be applicable across the scale of biological complexity; for example, on the organismal level, where each organ is a separate module that interacts with other organ(s) to form a functional organism, or organelles functioning together within a cell. The discovery that the structure of large-scale molecular interaction networks is functionally related to the networks’ emergent properties such as robustness, which cannot be easily predicted based on knowledge of the functions of the network’s individual components in isolation, led to the development of systems biology, a holistic and quantitative approach to biology. The heart of systems biology is the use—and refinement based on experimental challenge—of quantitative models that are grounded in knowledge of molecular interactions.

Another advantage of grappling with biological complexity from a network perspective includes the condensation of a large amount of data into a simpler, visually intuitive format. For example, in a network, evolutionarily recurrent structural elements such as feedback loops [5], feed-forward loops [6–9], and asymmetric positive feedback loops [10] are evident [11, 12]. On the larger scale, analysis of biological networks has provided insights into critical genes or molecules that are essential for function [13] and evidence for selection for hierarchical modularity [14], and formed the basis for dynamical models of system function [15]. Comparative analysis of biological networks derived from different biological states (such as different environmental conditions, genetic backgrounds, or stages of development), i.e., differential network analysis, has proved particularly useful for uncovering mechanisms in diverse contexts such as cancer biology [16, 17] and organ development [18, 19].

Here, we review differential network analysis, with a particular emphasis on its application to gene expression correlation networks. In this context, differential correlation expression network analysis (DCENA) has been used to identify a three-gene combination able to diagnose glioma [20], and identify gene regulatory networks involved in mouse embryonic fibroblast development [21], among others.

Basic properties of biological networks

It is axiomatic that a complete understanding of a cell biological system requires a complete understanding of the molecular networks within a cell. Such networks can be modeled as a series of points, called nodes (which might be gene-specific types of RNA or protein, or other cellular molecular constituents), connected via edges (representing interactions) to each other. Each edge can be either directed or non-directed, meaning the biological information (or in some network contexts, substrate) flows from one node to the other. Directed networks imply co-dependence between connected nodes, whereas undirected networks assume that only one node is dependent on the other.

The discovery that biological networks followed a scale-free degree distribution invigorated the field of biological network analysis. A scale-free degree distribution means that the probability that any node in the network, P(k), is attached to k other nodes, decays as a power law P(k) ~ k^−λ [22]. Interestingly, this property is shared by many different types of networks that are the product of organic growth rather than up-front complete design, including paper citations, social networks, and the internet [22]. Following the scale-free property, most nodes have only a few edges while a small number of nodes, called hubs, are highly connected. These hubs are disassortative (i.e., they tend to not share the same neighbors), and are rarely directly connected to each other [22]. These features appear to endow biological networks with a robustness to disruptions of random nodes [23]. On the other hand, they are more susceptible (compared to random networks that are not scale-free) to disruptions that specifically target hubs [23]. The observed scale-free degree distribution of many biological networks appears to be a generic consequence of two assumptions regarding the growth of networks over evolutionary time, random growth with preferential attachment [22].

One of the most powerful network analysis paradigms stems from the guilt by association principle, where nodes that are spatially close to each other often perform similar functions, or are related in some way [24]. A node that is in close network proximity to another node that is directly associated with a disease is likely to be implicated in either the creation or maintenance of the disease state [24]. Spatially proximate nodes also tend to cluster into highly connected clusters, where each cluster performs a specific function [25]. These clusters, termed modules [26], are fundamental units of biological networks (Fig. 1). Modules can identify novel functions and/or pathway associations of known genes and are often conserved between different biological systems [27]. Conserved modules are likely to represent biologically significant processes conserved by evolution and their identification can help answer fundamental questions of biological regulation [27].

Fig. 1.

Basic biological networks. Biological networks are visually represented as a series of nodes (red dots), connected by edges (lines). Typically, a network represents a snapshot in time, for example, a specific cell state. As cells develop, differentiate, or respond to disease, the cellular network changes structure. The two networks shown represent a change in cell state. Edges can be directed or undirected, to represent direction of flow of biological information. Each node (red dot) has a degree k that represents the number of nodes it is connected to. An undirected network has an average degree equal to twice the number of edges divided by the number of nodes. The average degree represents the average length of the shortest path between any two nodes in the network. Nodes that are highly connected are referred to as hubs (blue dot), and in many biological network contexts often correspond to essential or functionally significant nodes [13]. Frequently in biological networks, nodes cluster together topologically into groups known as modules (e.g., blue circle), for example, a group of genes that work together to perform a specific biological function. Nodes that mediate communication between modules are referred to as “bottleneck” nodes (green dot)

Module identification is one of the classic analysis tasks in network biology, in which genes of unknown function can be associated with the function of the module, assuming enough annotated genes are also present. At best, modules can identify novel gene–gene interactions that function as drug targets. As condition-specific global measurements of protein post-translational modifications, gene-level epigenomic profiling, and gene expression have become commonplace, particular emphasis has been placed on the identification of active modules, which are modules with a context-dependent function [27]. Unfortunately, there is no clearly defined optimal method for module identification (although MCODE [28] is one of the most popular, likely due to its ease of use) and instead a variety heuristic approaches are used.

Here, we describe three standard classes of methods used to identify active modules. One such class of method is called significant-area-search [27]. Significant-area-search methods first annotate all edges and nodes with scores that represent their independent activity. Then aggregate scores are computed for different combinations of spatially close and connected nodes and assigned to each subnetwork. The highest scoring subnetworks are then identified as modules. While this method works, it has significant drawbacks. The algorithm is complex, the computations are time intensive, and it requires multiple user-defined thresholds that can complicate reproducibility and are a challenge for non-expert users. A second class of methods is known as diffusion flow [29]. Diffusion flow-based methods are based on the concepts of fluid and heat transfer dynamics. On a basic level diffusion flow methods assume that the flow of biological information within a network diffuses from nodes of interest outwards along the edges of a network and accumulates in other nodes of interest. These methods are less computationally intensive, but are most often used in cancers or diseases where original genes of interest are known. The third type of methods used is biclustering-based methods [30]. Biclustering-based methods simultaneously cluster both interactions in the network and the biological conditions in which the interactions occur, called biclustering. This determines both the strength of network connectivity and the correlation between sample conditions. Biclustering-based methods have the advantage that they can be applied to almost any type of biological data.

Despite the existence of several well-established algorithmic methods, in practice, module detection retains subjective characteristics. This is especially true for clustering-based methods, where some hard value threshold is needed to define module boundaries. Functional classification or analysis of modules is often accomplished using gene ontology (GO) term enrichment techniques. GO term enrichment analysis involves taking a list of genes (often from the identified module) and using publicly available annotated functions to search for enrichment of specific functions in the gene list. The premise of GO term enrichment analysis for module classification is essentially guilt-by-association, i.e., that if a module is enriched in genes from a specific biological function, any unknown genes also in the module are likely to be involved in the same process.

Despite its promise for elucidating biological mechanisms, large-scale biological network analysis has several inherent limitations. The most obvious is that it necessarily entails a dramatic simplification of biological systems, for example, ignoring constraints, kinetic rate constants, and context-dependent subcellular localization [25, 27, 31]. Another key limitation is presented by the dynamic nature of living systems; accounting for dynamics in network modeling is more complex and can involve generating multiple static networks of the same biological system over different conditions. These considerations have led to the use of differential network techniques, as described below.

Differential networks

Differential network analysis is a powerful technique for identifying pathways or modules with a context- or condition-specific activity or function, for example, in diseased vs. healthy tissue, different time points in embryonic development, or in tissues with and without a specific molecular or genetic perturbation (e.g., a gene knockout). Differential networks are generated by comparing static networks from the same biological system over different conditions and are used to determine the parts of a network that are context specific [27, 31] (Fig. 2). Differential networks encode the changes in connections among nodes between the conditions or states. Nodes that change their connection between different network states are considered to be rewired, and are of significant biological interest [24]. Under the principle that nodes that are functionally involved in the change of state rewire more frequently than uninvolved nodes, “guilt by rewiring” can be used to identify nodes or modules responsible for creating and/or maintaining different states [24].

Fig. 2.

Basic differential network. Differential networks are generated by “subtracting” two static networks from each other, for example, a “baseline” tissue (or cell) state from a “disease” tissue state. a An example network from a control state. Nodes are shown as circles, and edges are lines, with weights representing how strong correlation between nodes is. b An example network from a disease state. Nodes gain and lose edges, creating a substantially different network topology. c Network B subtracted from network A. Red edges represent loss in correlation between two nodes, and green edges represent a gain in correlation. Differential networks allow simple visualization of correlation changes between nodes. Nodes that are “rewired” (i.e., that are connected in the differential network) are likely to be involved in the maintenance or creation of the change in cell state, a principle known as “guilt by rewiring”

For both gene co-expression networks and condition-specific PPI networks, differential network analysis serves as a powerful complement to other forms of quantitative expression analysis, specifically differential expression analysis [31]. Differential expression analysis detects nodes that change between conditions, but does not reveal interactions between the nodes. Therefore, nodes with interaction but not expression changes will only be revealed in a differential network analysis [31]. Similarly, node interactions that are present in both conditions can be assumed to be unaffected by the perturbation, even if the node is differentially expressed between conditions [31]. Thus, differential expression analysis has the potential to be more sensitive and specific than standard node-based differential expression analysis for detecting context-specific molecular interactions (Fig. 3).

Fig. 3.

Differential correlation between samples. Correlation between genes is determined by plotting normalized expression values of one gene vs. another across all biopsies within a biopsy group. Each dot represents a single biopsy and several biopsies represent a biopsy group. Correlation is determined by how well a line fits the plotted data, not by the slope of the line. SCC and P values (based on the Spearman test for independence based on 10,000 resamplings) for each correlation are shown on the plot. a Genes G1 and G2 show a strong negative correlation in healthy biopsies, but in the disease state G1 and G2 correlation becomes positive. RPKM, reads (for this gene) per kilobase per million mapped reads, represents normalized gene expression data. b Genes G1 and G3 show no correlation in healthy biopsies, and their correlation switches to strongly positive in the disease biopsies. c Genes G2 and G3 show positive correlation in healthy biopsies, and additionally stronger positive correlation in disease biopsies. Genes that change in correlation between the cell states are likely to be involved in creating or maintaining the difference in cell states, making them candidates for therapeutics and diagnostics. Blue lines represent best-fit linear regressions and indicate positive or negative correlations

Rewiring has different biological meanings depending on the components of the network. In PPI networks, rewiring represents the gain and loss of direct physical interactions between the proteins, which could occur due to changes in the protein post-translational modification state or subcellular localization. In transcriptional networks, rewiring between nodes represents functional consequences of the change in cell or tissue state between conditions [31]. These functional consequences could be changes in the co-expression patterns of genes caused by disruption of the regulator that mediates the genes’ co-expression. Due to the ubiquity and archetypical role of transcriptome profiling as a systems approach, for the remainder of this review, we will discuss differential analysis of transcriptional co-expression networks.

Differential co-expression networks (DCEN)

Differential co-expression networks are correlation networks based on gene expression data such that each node represents a gene, and each edge represents co-expression or interactions between the genes, such as activation or repression [32]. The premise of differential co-expression network analysis is that differentially expressed genes (DEGs) represent functional changes in the biology of the system, and functionally work together at some level to alter the system [32]. DCENs have been shown to have (1) a scale-free degree distribution, (2) low clustering coefficients, and (3) an unexpectedly high average all-pairs-shortest-paths path length [33].

The power of the DCEN analysis approach is its ability to highlight genes that drive molecular mechanisms behind specific biological processes [32]. Additionally, DCENs have been used to identify the potential mechanisms involved in biological pathways, the pathways that are functionally involved in the system being studied, and the key regulators of identified pathways or modules [32]. These mechanisms and regulators are often identified as new biomarkers for specific processes or diseases, leading to more accurate diagnosis. Most software that is mentioned in this review is freely available and can be found online (Table 1).

Table 1.

Software used for DCENA

Program	Method	Software	Comments	References
CoXpress	PCC	R, https://sourceforge.net/projects/coxpress/	Arbitrary cutoff for module ID	[43]
DiffCorr	PCC	R, https://cran.r-project.org/web/packages/DiffCorr/index.html	Used for gene expression profiling, metabolomics, etc.	[44]
MCODE	CC	http://baderlab.org/Software/MCODE	Includes data visualization	[28]
R/Ebcoexpress	CC	R, http://bioconductor.org/packages/release/bioc/html/EBcoexpress.html	Has built in data visualization	[46]
DGCA	CC	R, https://github.com/andymckenzie/DGCA	Requires gene list as input (targeted)	[52]
DiNA	CC	http://dina.tigem.it/	Requires gene list as input (targeted)	[56]
WGCNA	CC	R, https://labs.genetics.ucla.edu/horvath/CoexpressionNetwork/Rpackages/WGCNA/	Has built in data visualization, compatible with other R packages	[58]
iMDM	CC	Contact authors	Meant for multiple conditions	[57]
DiffCoEx	WGCNA	R, based of WGCNA, see additional file 1 in publication	Requires and uses WGCNA	[55]
MINDy	CMI	http://wiki.c2b2.columbia.edu/workbench/index.php/Home		[65]
CINDy	CMI	http://califano.c2b2.columbia.edu/mindy2-cindy	Based on MINDy	[67]
CMI2NI	CMI	http://comp-sysbio.org/cmi2ni/index.html		[68]
DMI	CMI	http://dmi.tigem.it/	Requires gene list as input (targeted)	[70]
MAGIC	CMI	MATLAB, https://github.com/chiuyc/MAGIC		[33]
DIGGIT	CMI	R, https://www.bioconductor.org/packages/release/bioc/html/diggit.html		[66]

An early example of differential correlation expression analysis was an applied form of hierarchical clustering analysis of time-course gene expression data from yeast Saccharomyces cerevisiae under a variety of culture perturbations and from serum-stimulated human fibroblasts [34]. This type of analysis clusters genes based on similar coexpression between the samples in an unsupervised manner. A weakness of this type of analysis is the poorly defined module that it generates. Although clear patterns emerge, there is no hard threshold, and the identification of modules between the samples is highly sensitive to and based on the user-specified cutoff. A more significant weakness of this algorithm is that it assigns each gene to one and only one module. This singular assignment is a poor representation of biological systems wherein genes frequently participate in multiple processes or occasionally act alone. This method is still prevalent with heat maps but is now more often combined with other methods when used for module identification.

The current, predominantly used methods for co-expression network inference fall into two broad categories, correlation-based and mutual information-based methods. The correlation-based methods for co-expression network inference involve the filtering of all-pairs Pearson correlation coefficients (PCC), nonparametric Spearman (SCC) correlation coefficients, or partial correlation coefficients to obtain the network adjacency matrix. The PCC and SCC are direct statistical measures of interdependence of two variables, whereas partial correlation coefficients are measures of interdependence of two variables’ residual measurements after conditioning on one or more other explanatory variables [32, 35, 36]. The related method of weighted gene co-expression network analysis (WGCNA) is based on correlation coefficients, but includes an additional rescaling before the filtering step [37]. Mutual information (MI)-based methods depend on higher order moments of the joint pairwise distribution of gene expression measurements (rather than just the covariance), through the use of an information-theoretic measure of how informative one gene’s expression level is for predicting the expression level of another gene [38, 39]. MI-based methods have the benefit of being sensitive to potentially non-monotonic relationships between the expression level of a regulator gene and a target gene, but the disadvantage of being computationally expensive to estimate in comparison to purely correlation-based methods.

Correlation coefficient methods

Correlation coefficient (CC)-based methods involve the use of one of several statistical correlation measures to determine the dependence of one variable on another. The PCC and SCC are both pairwise correlation coefficients, but they differ in that the PCC is most sensitive to a linear relationship between variables while the SCC allows for a non-linear relationship. This difference stems from the fact that the SCC is computed using the ranked values for each variable, rather than the gene expression measurement values themselves. Relevant to DCENs, the correlation coefficient represents a proxy for the extent of co-regulation between two variables, or genes.

Because CC-based methods involve the calculation of correlation coefficients for all pairs of genes, naïve application of such methods to all 20,000 genes in the human genome would require the calculation 2 × 10⁸ correlation coefficients, which is both time and memory intensive. In practice, pairwise correlations are calculated for a subset of genes that are selected for probable relevance to the biological process being studied, such as selecting for differentially expressed genes, or known genes of interest. This reduces computational time and memory but at least for the “known genes” approach, it can also miss unexpected correlations. Due to their simplicity, CC-based methods have been a popular tool to analyze DCENs. One significant advantage of CC-based methods is that they can be used with small sample sizes (n = 16), although increasing n adds more statistical power and will uncover weaker correlations with higher confidence.

Frequently, CC-based methods are used to identify new putative biomarkers for different types of diseases. Recently, PCC-based methods were used to identify differentially correlated gene pairs in the prefrontal cortex between healthy patients and patients with Huntington’s disease [40]. Focusing on the gene ENT1 from a previous study, targeted analysis revealed that ENT1 gains over 60 correlations in samples from patients with Huntington’s disease, identifying ENT1 as a potential biomarker and drug target for neurodegeneration in the early stages of Huntington’s disease. Similarly, PCC-based methods were used to compare differentially correlated miRNA pairs from the plasma of healthy subjects and patients suffering from mild cognitive impairment [41]. The network of differentially correlated miRNA pairs was analyzed for known transcriptional regulatory interactions (based on the Ingenuity Pathways Analysis commercial database of gene regulatory interactions), suggesting that TP53 (p53) directly regulates all 11 correlated miRNAs in healthy patients. Additionally, in patients with mild cognitive impairment, gene expression changes of insulin-related genes (identified using ingenuity pathway analysis) were associated with a loss in miRNA correlations, and could also serve as a new biomarker in early Huntington’s disease.

CC-based methods have also been used in conjunction with gene ontology (GO)-based functional enrichment analysis. Southworth et al. used SCC-based methods to compare blood from old and young mice to examine the effect of aging on co-regulation of genes [42]. They found an overall decrease in gene co-expression in older mice, consistent with previous reports of transcriptional instability in older mice. When GO term enrichment was observed in differentially correlated modules, a stronger correlation existed among NFκβ direct target genes in young mice relative to old. It was concluded that old age may affect the stability of NFκβ expression and, therefore, affect its downstream targets. Similarly, proximal clustering on chromosomes of enriched genes in the differentially correlated modules was observed, implying that chromosomal degradation could be a contributing factor to gene expression variance.

In the last decade, several CC-based methods (including methods for downstream analysis and module detection) have been implemented as documented software packages for use in the R statistical computing environment [43], whose free-software open-source approach has spurred methods development and resource sharing in bioinformatics. One of the first of such software packages is CoXpress [44] combines PCC-based methods along with hierarchical clustering to identify differentially correlated modules between samples or conditions. Because CoXpress uses hierarchical clustering, it identifies modules rather than differentially correlated genes. A second limitation of CoXpress is that each gene is only assigned to one module and it requires a hard-arbitrary cutoff for the clustering analysis, which in turn decreases reproducibility.

More recently, the DiffCorr [45] R package has been developed and released for DCEN analysis. It combines PCC-based methods with the Fisher Z-transformation to identify genes that are differentially correlated between conditions. DiffCorr is able to detect changes in sign or magnitude of the correlation coefficient for a gene pair between different conditions, and it can be applied to any form of normalized data, including metabolomics and lipidomics.

DiffCorr has been used to identify differentially correlated genes and modules between healthy and pathogen-infected Arabidopsis samples [46]. DiffCorr analysis uncovered (1) the gene AT3G03440, which previously had no known role in pathogen response, as a hub in the correlation network from pathogen-infected samples; and (2) 36 pathways whose gene–gene correlations were differentially rewired. Additionally, no significant correlation was detected between differentially expressed genes and differentially correlated genes, and only 40% of sequence-specific transcription factors that were differentially correlated were differentially expressed. These findings support the viewpoint that DCEN analysis supplements—rather than replaces—traditional one-gene-at-a-time differential expression analysis.

A similar R package, R/Ebcoexpress, combines a CC-based approach with posterior probability calculations and a false discovery rate (FDR) cutoff [47]. R/Ebcoexpress has been used to detect differentially correlated genes and modules between human rectal adenocarcinoma and healthy tissue [48], with the network analysis platform Cytoscape [49] used for module detection. The network was constructed using nodes and edges from only differentially expressed genes calculated by edgeR [50] and only edges with a CC of at least 0.6 were retained. Six hub genes (defined by 8 or more edges) were identified in the network with most unsurprisingly involved in cell adhesion. MCODE identified three modules in the network enriched in cell adhesion-related GO terms. When the network was combined with drug-to-transcriptome-response data from the Connectivity Map database [51], several small molecules including the histone deacetylase inhibitor scriptaid and antiallergenic drug spaglumic acid were predicted to interact with the network. Thus, the analysis identified potential biomarkers and new therapeutic approaches for rectal adenocarcinoma.

Another differential correlation analysis R package, the Discordant method, uses PCC combined with binning to identify differentially correlated genes and modules [52]. Using simulated data sets, the Discordant method outperformed R/Ebcoexpress in computational time and accuracy. When the Discordant method was applied to publicly available glioblastoma data sets, the hsa-mir-545 was identified as a candidate functional regulator in glioblastoma. The Discordant method assumes independence of the bivariate expression levels of gene pairs, which is biologically implausible but reduced the computational time required.

One of the more comprehensive R packages released recently, differential gene correlation analysis (DGCA), uses CCs transformed into normalized Z-scores to identify differentially correlated genes and modules while performing downstream analysis, including data visualization, GO enrichment, and network construction tools [53]. This method is similar to Discordant and DiffCorr while also including an FDR cutoff to control the type I error rate. Module identification is performed using the network alignment algorithm MAGNA [54]. DGCA was found to outperform two other methods (DICER [55] and DiffCoEx [56]) in speed and accuracy on simulated data sets. Furthermore, for larger numbers of samples (n > 50), DGCA outperformed R/Ebcoexpress and Discordant.

A primary limitation of the DCEN analysis approach is the computational time and statistical power that it requires to apply to all genes in a higher eukaryote (~ 25,000 protein-coding genes). This limitation can be mitigated by performing DCEN on a collection of subsets of genes selected based on prior biological knowledge. These gene sets are essentially user-defined modules, and thus, the reduced computation time comes at the cost of introducing bias. One example of a tool using such an approach is DIfferential Network Analysis (DINA), which identifies differentially correlated gene sets between conditions [57]. Publicly available data consisting of sequence-specific transcription factor (SSTF)-pathway associations were combined with datasets comprising thousands of microarrays from different tissue types to identify coregulated pathways between tissue types in both mouse and human. The DINA analysis identified 22 pathways that were coregulated between the tissue types, including pathways that were not differentially expressed between tissues. DINA identified the pathways as being regulated by nuclear receptor family transcription factors and agrees with the literature. Interestingly, YEATS2, a little-studied protein, was predicted to be a negative regulator of metabolic pathways in hepatocytes, and subsequently validated through targeted experiments.

Another challenge of DCEN analysis is identifying modules whose gene members have differential coexpression across more than two conditions. Some packages, such as DINA, are able to identify correlated modules, but require a gene list as input. A recent algorithm called Inference of Multiple Differential Modules (iMDM) was specifically created to work with more than two conditions [58]. iMDM uses PCC-based methods to identify both unique and differentially correlated modules between multiple conditions. The algorithm was validated using RNA-seq transcriptome profiling data from mouse hearts in four different stages of hypertrophy, and identified multiple modules that are both unique and differentially correlated between conditions.

Weighted gene co-expression network analysis (WGCNA)

WGCNA, introduced above, is one of the most popular methods for CC-based DCEN analysis, owing in part to its availability as a point-and-click software application and an R software package [37]. A key benefit of WGCNA is that it identifies modules based on topological overlap and hierarchical clustering, and as such, does not require a hard threshold on the adjacency matrix for module detection [37]. While interpretation of the results of hierarchical clustering can be subjective, identified modules can be tested with GO term enrichment to verify whether the genes share a common function. WGCNA identifies differentially correlated genes and modules and performs subsequent downstream analysis including data visualization and GO term enrichment via other packages available in R.

Use of WGCNA has led to the implication of a variety of genes and modules in specific biological contexts. For example, WGCNA analysis of T cells implicated the genes GABARAP and MPEG1 in asthma [59]. Combined with upstream regulator analysis, the cytokine genes IL2 and IL4 were identified as drivers of the asthma response. WGCNA was also used to investigate gene regulation during the various stages of coral development [18]. Early developmental stage-specific modules were detected that are highly enriched in long non-coding RNA (lncRNA), suggesting a lncRNA regulatory role in coral gastrulation. When WGCNA was applied to human brain development, significant rewiring of regulatory modules was detected between pre- and postnatal brain development [60], consistent with a model that brain development is organized into multiple stage-specific regulatory networks with little interstage overlap. Gene promoter sequence analysis identified specific SSTF binding sites uniquely enriched in each module, suggesting module-specific regulation. Finally, WGCNA analysis of skin transcriptomes from patients in a psoriasis study that were healthy or treated with a TNF-α inhibitor implicated a lncRNA-rich module via the guilt-by-rewiring principle [61].

WGCNA has also been used to analyze transcriptome datasets spanning multiple tissue types, for example in a study of Huntington’s disease [62] in which both human and mouse datasets were used. The analysis yielded multiple insights including the identification of an astrocyte-specific module and the identification of the transcription FOXO3 as a candidate regulator of the module.

Modified weighted gene correlation network analysis (mWGCNA)

Several network analysis algorithms in use are variants of WGCNA, of which the most popular and best known is DiffCoEx [56]. DiffCoEx follows the WGCNA method initially, but obtains the adjacency matrix as the difference of correlation matrices between the conditions. By design, DiffCoEx detects differentially correlated modules, not gene pairs. DiffCoEx’s popularity is likely due in part to its inclusion of GO enrichment analysis functionality and the small number of tunable parameters required for its operation.

Klein et al. [63] combined WGCNA with a topological overlap matrix (TOM) by constructing the TOM of the matrix of gene–gene correlation coefficients and then testing for differences in the TOM between sample groups. This approach has high sensitivity for identifying differentially correlated gene pairs and modules, but requires user-defined parameters, some of which the authors report must be experimentally determined. In their application of the method to a transcriptome study of ovarian, lung, breast, and skin cancer samples with different TP53 (p53) mutations, Klein et al. detected differential correlation of KIR3DL2, identifying a novel gene in the p53 pathway in cancer.

In their differential correlation regulatory analysis (DGCA) approach, Zuo et al. [48] combined WGCNA with genome location data (SSTF → target gene) to detect differential activity of transcriptional regulatory mechanisms. DGCA application to glioma transcriptomes identified three SSTFs, ZNF423, AHR, and NFIL3, with differential regulatory signal across tumor grades, providing three potential new prognostic indicators.

Mutual information (MI)-based methods

A third form of DCEN analysis, used mainly to infer transcriptional regulatory relationships, utilizes mutual information (MI)-based methods. MI is a measure of dependence between two random variables, and like the correlation coefficient, is generally applicable to any type of multivariate biological measurement. As with correlation-based networks, MI is sensitive to indirect regulatory relationships, introducing spurious edges into the regulatory network. Similar to the method of partial correlation coefficients, the use of conditional mutual information (CMI) [64] mitigates this problem using the mutual information between two variables conditioned on the value of a third variable, while also being able to detect direct or indirect relationships.

Among the widely used CMI-based methods is Modulator Inference by Network Dynamics (MINDy) [65], which uses gene expression data from different conditions to identify SSTF-target interactions that change based on the expression of a third gene, the modulator. Wang et al. [65] applied MINDy to transcriptome data from B cell lymphoma, identifying new modulators of the MYC protein. Like all MI-based methods, MINDy has the advantage of being sensitive to non-monotonic regulatory relationships. However, MINDy also has some limitations, including that it requires data from a large number of samples and is unable to detect if a SSTF switches from an activator to a repressor (or vice versa). The R software package Driver-gene Inference by Genetic-Genomic Information Theory (DIGGIT) applies the MINDy algorithm to discover master regulator genes responsible for cell states or phenotypes [66]. Since DIGGIT factors copy number variation in its calculations, it is best suited for cancer-related datasets. Another CMI-based algorithm is Conditional Inference of Network Dynamics (CINDy) [67]. Similar to MINDy, CINDy calculates the CMI between SSTFs and their targets based on the expression of a signaling protein. In a side-by-side comparison with MINDy using microarray data, RNA-seq data, and a validated PPI network, CINDy outperformed MINDy in terms of both recall and precision and it required half the memory (but double the computational time) that MINDy required. Application of CINDy to B cell lymphoma transcriptomes revealed a CDK2–HMG1 regulatory interaction. The same CMI-intrinsic limitations, described above for MINDy, also apply to CINDy. Another method, CMI2NI [68] makes use of a path consistency algorithm which gradually removes redundant edges in a network based on conditional dependences. By design, CMI2NI infers an undirected network of probable regulatory interactions, in contrast to MINDy and CINDy, which infer directed regulatory networks.

One weakness of SSTF-gene CMI-based approaches (e.g., MINDy and CINDy) is that they require SSTFs and their target genes to be co-expressed across the full set of gene expression profiles, an assumption that does not hold for many SSTFs in many tissues and in various model species [69]. The algorithm differential multi-information (DMI) somewhat relaxes this biologically implausible requirement by assuming that the target genes of a TF are co-expressed if and only if the SSTF is expressed [70]. DMI is computationally more efficient than MINDy, but also requires more input information. As such, DMI is a complementary tool to MINDy rather than a replacement.

One of the most powerful CMI-based algorithms to be developed recently infers correlated gene pairs based on the expression of a modulator, similar to CINDy and MINDy. ModulAted Gene/gene set InteraCtion (MAGIC) measures the difference in MI between sample groups to identify SSTF–target pairs that have sample group-dependent interactions [33]. MAGIC can optionally make use of user-supplied gene lists, and thus it can be operated in either a targeted or untargeted mode. When applied to gene expression data from estrogen receptor (ER) ± breast cancer cell lines, MAGIC revealed a novel ER-mediated FGFR1–FOXP3 interaction. From an algorithmic standpoint, MAGIC, which is implemented in MATLAB, is most similar to DIGGIT, but requires less computational time. MAGIC can be applied to and integrate multiple different types of data such as expression, DNA methylation, and gene sets.

Network analysis in single-cell RNA-seq

One of the newest applications of DCENA is analysis of single-cell RNA-seq data. For example, DCENA was applied to single-cell gene expression profiles from mouse hippocampal cells from three different developmental states [19]. The network was limited to cellular adhesion, exocytosis, RhoGAP and RhoGEF-related genes, and constructed from pairwise PCCs. Interestingly, the analysis revealed two distinct subnetworks with minimal overlap, with the first subnetwork corresponding to early developmental expression, and the second subgraph corresponding to later-stage expression. Both subnetworks and their independence were highly conserved across all cell types, implying that a conserved network is responsible for different stages of hippocampal-cell development. In another case, DCENA was applied to single cells from different stages of mouse-embryonic fibroblast-derived neuronal cells [21]. When filtered to only transcription factors, the analysis revealed three different subnetworks, each with high intraconnectivity, and each composed of genes specific to a certain stage. In the network, expression of the gene Ascl1 was highly correlated with transcription factors that were specific to the initiation and maturation subnetworks while strongly negatively correlated with those specific to the MEFs. This supports a previous discovery that Ascl1 maintains a chromatin state that enables induced-neuronal cell maturation. Due to the significant increase in sample size (in this case, the number of individual cells profiled) for correlation estimation that is made possible by single-cell RNA-seq, the technique promises to significantly advance the field of regulatory network inference and enable the development of new network reconstruction approaches [71, 72]).

Conclusions and future directions

For all its strengths, DCN as an analytical approach has several challenges that will need to be overcome for the full potential of the approach to be realized. The most pressing of these involves the statistical methods used, both for correlations and module identification [31]. While there exists an agreed upon set of statistics (FDR, PCC, SCC) that most algorithms use, the set will need to be expanded as networks become more complex. This is especially true in the context of network inference using multi-omics datasets (e.g., gene expression, PPI, metabolomic, protein–DNA, expression quantitative trait locus, or DNA methylation data). A second challenge is delineating the “noise” contributions of (1) inherent stochasticity of molecular abundances (e.g., cell-to-cell variation in transcript or protein abundance due to “gene expression noise” [73]), (2) biological variation between conditions or genotypes, and (3) variation due to measurement error. Distinguishing these different sources of variation will require advances in methods for “ground-truth” measurement, methods for normalization of datasets to account for batch effects, and more mechanistically based statistical models.

The abundant new insights derived from the studies summarized in this review underscore that the analysis of biological networks, and especially differential correlation networks, has significant potential to generate new biological knowledge. While an inferred network by itself is a useful abstraction whose qualitative analysis can lead to insights, complex biological networks are most useful in the context of quantitative analysis to identify key regulators, modules, and functions. Most importantly, the amount of biological data we are able to generate continually increases. As sequencing costs decline and the amount of starting material required for sequencing is decreasing, the field of biological network profiling may approach a point where the limiting step in DCN analysis is the implementation and validation of the network analysis algorithms rather than the experimental assays [74].