Gene coexpression network inference
30 April 2024
Contents
1 Introduction
To date, several packages have been developed to infer gene coexpression networks from expression data, such as WGCNA (Langfelder and Horvath 2008), CEMiTool (Russo et al. 2018) and petal (Petereit et al. 2016). However, network inference and analysis is a non-trivial task that requires solid statistical background, especially for data preprocessing and proper interpretation of results. Because of that, inexperienced researchers often struggle to choose the most suitable algorithms for their projects. Besides, different packages are required for each step of a standard network analysis, and their distinct syntaxes can hinder interoperability between packages, particularly for non-advanced R users. Here, we have developed an all-in-one R package that uses state-of-the-art algorithms to facilitate the workflow of biological network analysis, from data acquisition to analysis and interpretation. This will likely accelerate network analysis pipelines and advance systems biology research.
2 Installation
if(!requireNamespace('BiocManager', quietly = TRUE))
install.packages('BiocManager')
BiocManager::install("BioNERO")# Load package after installation
library(BioNERO)
##
set.seed(123) # for reproducibility3 Data loading and preprocessing
For this tutorial, we will use maize (Zea mays) gene expression data
normalized in TPM. The data were obtained from Shin et al. (2020) and were filtered
for package size issues. For more information on the data set, see ?zma.se.
The data set is stored as a SummarizedExperiment object.1 NOTE: In case you have many tab-separated expression tables in a
directory, BioNERO has a helper function named dfs2one() to load all these
files and combine them into a single data frame.
The input expression data in BioNERO can be both a SummarizedExperiment
object or a gene expression matrix or data frame with genes in rows and samples
in columns. However, we strongly recommend using SummarizedExperiment objects
for easier interoperability with other Bioconductor packages.
data(zma.se)
# Take a quick look at the data
zma.se
## class: SummarizedExperiment
## dim: 10802 28
## metadata(0):
## assays(1): ''
## rownames(10802): ZeamMp030 ZeamMp044 ... Zm00001d054106 Zm00001d054107
## rowData names(0):
## colnames(28): SRX339756 SRX339757 ... SRX2792103 SRX2792104
## colData names(1): Tissue
SummarizedExperiment::colData(zma.se)
## DataFrame with 28 rows and 1 column
## Tissue
## <character>
## SRX339756 endosperm
## SRX339757 endosperm
## SRX339758 endosperm
## SRX339762 endosperm
## SRX339763 endosperm
## ... ...
## SRX2792107 whole_seedling
## SRX2792108 whole_seedling
## SRX2792102 whole_seedling
## SRX2792103 whole_seedling
## SRX2792104 whole_seedling3.1 Step-by-step data preprocessing
This section is suitable for users who want to have more control of their data analysis, as they can inspect the data set after each preprocessing step and analyze how different options to the arguments would affect the expression data. If you want a quick start, you can skip to the next section (Automatic, one-step data preprocessing).
Step 1: Replacing missing values. By default, replace_na() will replace
NAs with 0. Users can also replace NAs with the mean of each row
(generally not advisable, but it can be useful in very specific cases).
exp_filt <- replace_na(zma.se)
sum(is.na(zma.se))
## [1] 0Step 2: Removing non-expressed genes. Here, for faster network
reconstruction, we will remove every gene whose median value is below 10.
The function’s default for min_exp is 1.
For other options, see ?remove_nonexp.
exp_filt <- remove_nonexp(exp_filt, method = "median", min_exp = 10)
dim(exp_filt)
## [1] 8529 28Step 3 (optional): Filtering genes by variance. It is reasonable to remove genes whose expression values do not vary much across samples, since we often want to find genes that are more or less expressed in particular conditions. Here, we will keep only the top 2000 most variable genes. Users can also filter by percentile (e.g., the top 10% most variable genes).
exp_filt <- filter_by_variance(exp_filt, n = 2000)
dim(exp_filt)
## [1] 2000 28Step 4: Removing outlying samples. There are several methods to remove
outliers. We have implemented the Z.K (standardized connectivity)
method (Oldham, Langfelder, and Horvath 2012) in ZKfiltering(), which is a network-based approach to
remove outliers. This method has proven to be more suitable for network
analysis, since it can remove outliers that other methods
(such as hierarchical clustering) cannot identify. By default, BioNERO
considers all samples with ZK < 2 as outliers, but this parameter
is flexible if users want to change it.
exp_filt <- ZKfiltering(exp_filt, cor_method = "pearson")
## Number of removed samples: 1
dim(exp_filt)
## [1] 2000 27Step 5: Adjusting for confounding artifacts. This is an important step to avoid spurious correlations resulting from confounders. The method was described by Parsana et al. (2019), who developed a principal component (PC)-based correction for confounders. After correction, the expression data are quantile normalized, so every gene follows an approximate normal distribution.
exp_filt <- PC_correction(exp_filt)3.2 Automatic, one-step data preprocessing
Alternatively, users can preprocess their data with a single function.
The function exp_preprocess() is a wrapper for the functions replace_na(),
remove_nonexp(), filter_by_variance(), ZKfiltering() and PC_correction().
The arguments passed to exp_preprocess() will be used by each of these
functions to generate a filtered expression data frame in a single step.2 NOTE: Here, we are using TPM-normalized data. If you have expression
data as raw read counts, set the argument vstransform = TRUE
in exp_preprocess(). This will apply DESeq2’s variance stabilizing
transformation (Love, Huber, and Anders 2014) to your count data.
final_exp <- exp_preprocess(
zma.se, min_exp = 10, variance_filter = TRUE, n = 2000
)
## Number of removed samples: 1
identical(dim(exp_filt), dim(final_exp))
## [1] TRUE
# Take a look at the final data
final_exp
## class: SummarizedExperiment
## dim: 2000 27
## metadata(0):
## assays(1): ''
## rownames(2000): ZeamMp030 ZeamMp092 ... Zm00001d054093 Zm00001d054107
## rowData names(0):
## colnames(27): SRX339756 SRX339757 ... SRX2792103 SRX2792104
## colData names(1): Tissue4 Exploratory data analysis
BioNERO includes some functions for easy data exploration. These functions
were created to avoid having to type code chunks that, although small, will be
used many times. The idea here is to make the user experience with biological
network analysis as easy and simple as possible.
Plotting heatmaps: the function plot_heatmap() plots heatmaps of
correlations between samples or gene expression in a single line.
Besides the arguments users can pass to parameters in plot_heatmap(),
they can also pass additional arguments to parameters
in ComplexHeatmap::pheatmap() to have additional control additional on
plot aesthetics (e.g., hide/show gene and sample names, activate/deactivate
clustering for rows and/or columns, etc).
# Heatmap of sample correlations
p <- plot_heatmap(final_exp, type = "samplecor", show_rownames = FALSE)
p
# Heatmap of gene expression (here, only the first 50 genes)
p <- plot_heatmap(
final_exp[1:50, ], type = "expr", show_rownames = FALSE, show_colnames = FALSE
)
p
Principal component analysis (PCA): the function plot_PCA() performs a
PCA and plots whatever pair of PCs users choose (PC1 and PC2 by default), as
well the percentage of variance explained by each PC.
plot_PCA(final_exp)
5 Gene coexpression network inference
Now that we have our filtered and normalized expression data, we can
reconstruct a gene coexpression network (GCN) with the
WGCNA algorithm (Langfelder and Horvath 2008). First of all, we need to identify the
most suitable \(\beta\) power that makes the network satisfy the scale-free
topology. We do that with the function SFT_fit(). Correlation values are
raised to a power \(\beta\) to amplify their distances and, hence, to make the
module detection algorithm more powerful. The higher the value of \(\beta\), the
closer to the scale-free topology the network is. However, a very high \(\beta\)
power reduces mean connectivity, which is not desired. To solve this trade-off,
we pick the lowest \(\beta\) power above a certain threshold (by default
in SFT_fit(), 0.8). This makes the network close to the scale-free topology
without dramatically reducing the mean connectivity.
sft <- SFT_fit(final_exp, net_type = "signed hybrid", cor_method = "pearson")
## Power SFT.R.sq slope truncated.R.sq mean.k. median.k. max.k.
## 1 3 0.220 -0.218 0.178 278.0 303.00 598.0
## 2 4 0.416 -0.382 0.272 196.0 199.00 472.0
## 3 5 0.573 -0.468 0.462 145.0 136.00 381.0
## 4 6 0.675 -0.536 0.584 110.0 95.70 312.0
## 5 7 0.748 -0.584 0.676 86.3 70.00 259.0
## 6 8 0.791 -0.653 0.735 68.8 51.90 221.0
## 7 9 0.803 -0.717 0.761 55.8 38.60 191.0
## 8 10 0.815 -0.775 0.790 45.8 29.90 167.0
## 9 11 0.821 -0.828 0.815 38.1 22.90 147.0
## 10 12 0.838 -0.874 0.850 32.0 17.90 130.0
## 11 13 0.847 -0.913 0.876 27.2 14.30 116.0
## 12 14 0.856 -0.943 0.893 23.2 11.80 104.0
## 13 15 0.875 -0.973 0.913 20.0 9.79 93.0
## 14 16 0.892 -0.997 0.937 17.3 8.00 83.9
## 15 17 0.897 -1.020 0.941 15.1 6.75 76.0
## 16 18 0.891 -1.070 0.948 13.3 5.79 69.7
## 17 19 0.888 -1.100 0.950 11.7 4.96 64.2
## 18 20 0.888 -1.130 0.957 10.4 4.27 59.4
sft$power
## [1] 9
power <- sft$powerAs we can see, the optimal power is 9. However,
we strongly recommend a visual inspection of the simulation of
different \(\beta\) powers, as WGCNA can fail to return the most
appropriate \(\beta\) power in some cases.3 PRO TIP: If your \(\beta\) power is too low (say below 6), look at the plot as a sanity check. The function SFT_fit()
automatically saves a ggplot object in the second element of the resulting
list. To visualize it, you simply have to access the plot.
sft$plot
Now, we can use the power calculated by SFT_fit() to infer the GCN.
The function exp2gcn() infers a GCN and outputs a list of 7 elements, each of
which will be used by other functions in the analysis pipeline.
net <- exp2gcn(
final_exp, net_type = "signed hybrid", SFTpower = power,
cor_method = "pearson"
)
## ..connectivity..
## ..matrix multiplication (system BLAS)..
## ..normalization..
## ..done.
names(net)
## [1] "adjacency_matrix" "MEs" "genes_and_modules"
## [4] "kIN" "correlation_matrix" "params"
## [7] "dendro_plot_objects"The function exp2gcn() saves objects in the last element of the resulting
list that can be subsequently used to plot common figures in GCN papers.
The figures are publication-ready and display i. a dendrogram of genes and
modules; ii. heatmap of pairwise correlations between module eigengenes.
# Dendro and colors
plot_dendro_and_colors(net)
# Eigengene networks
plot_eigengene_network(net)
Let’s see the number of genes per module.
plot_ngenes_per_module(net)
6 Gene coexpression network analysis
Now that we have our coexpression network, we can start exploring some of its properties.
6.1 Assessing module stability
The function module_stability() allows users to check if the identified
coexpression modules are stable (i.e., if they can resist removal of a
particular sample). This function will resample the data set and rerun the
module detection algorithm n times (default: 30) and return a PDF figure
displaying a gene dendrogram and colors representing modules identified in
each run. By looking at the figure, you can detect if a particular module is
only found in a very small fraction of the runs, which suggests instability.
Here, we will perform only 5 resampling runs for demonstration purposes.4 NOTE: The calculations performed by this function may take a
long time depending on the your network size. Use it only if you have
some reason to suspect that the modules are highly dependent on a particular
set of samples.
module_stability(final_exp, net, nRuns = 5)
## ...working on run 1 ..
## ...working on run 2 ..
## ...working on run 3 ..
## ...working on run 4 ..
## ...working on run 5 ..
## ...working on run 6 ..
6.2 Module-trait associations
The function module_trait_cor() can be used to calculate module-trait
correlations. This analysis is useful to identify modules that are positively
or negatively correlated with particular traits, which means that their gene
expression levels go up or down in these conditions. Here, tissues will be
considered traits, so we want to identify groups of genes whose expression
levels are inhibited or induced in particular tissues. Alternatively, one can
use continuous variables (e.g., metabolite content, protein concentration,
height) or discrete variables (e.g., disease index) as traits.5 NOTE: The function gene_significance() works just
like module_trait_cor(), but it correlates individual genes (not the
whole module) to traits. This function is very useful if you have a set of
candidate genes and you want to find which of them are more associated with
the trait of interest. See ?gene_significance() for more details.
MEtrait <- module_trait_cor(exp = final_exp, MEs = net$MEs)
head(MEtrait)
## ME trait cor pvalue group
## 1 MEblack endosperm -0.166480994 0.4065715 Tissue
## 2 MEblack pollen 0.213691004 0.2845053 Tissue
## 3 MEblack whole_seedling -0.020227505 0.9202318 Tissue
## 4 MEbrown endosperm 0.003843583 0.9848197 Tissue
## 5 MEbrown pollen -0.020729547 0.9182584 Tissue
## 6 MEbrown whole_seedling 0.012815311 0.9494147 TissueNext, you can use the function plot_module_trait_cor() to visualize the output
of module_trait_cor() as follows:
plot_module_trait_cor(MEtrait)
6.3 Visualizing module expression profile
The heatmap above shows that genes in the yellow module are negatively
correlated with endosperm samples. We can visually explore it
with plot_expression_profile().
plot_expression_profile(
exp = final_exp,
net = net,
plot_module = TRUE,
modulename = "yellow"
)
6.4 Enrichment analysis
After identifying modules that are inhibited or enhanced in particular tissues, users would likely want to find to which biological processes (e.g., GO biological process) or pathways (e.g., Reactome, KEGG, MapMan) these genes are related. This can be done with enrichment analyses, which can uncover terms that are found more than expected by chance in a module.
The easiest way to accomplish this is to use the
function module_enrichment(), which performs enrichment analysis for
all modules at once. To illustrate it, we will scan coexpression modules
for enriched protein domains using all genes in the network as background.
The Interpro annotation was downloaded from
the PLAZA 4.0 Monocots database (Van Bel et al. 2018).
# Enrichment analysis for conserved protein domains (Interpro)
data(zma.interpro)
interpro_enrichment <- module_enrichment(
net = net,
background_genes = rownames(final_exp),
annotation = zma.interpro
)
## Enrichment analysis for module black...
## Enrichment analysis for module brown...
## Enrichment analysis for module darkgreen...
## Enrichment analysis for module darkolivegreen...
## Enrichment analysis for module greenyellow...
## Enrichment analysis for module lightyellow...
## Enrichment analysis for module midnightblue...
## Enrichment analysis for module paleturquoise...
## Enrichment analysis for module violet...
## Enrichment analysis for module yellow...
# Print results without geneIDs for better visualization
interpro_enrichment[, -6]
## term genes all pval padj
## 184 Histone H2A/H2B/H3 43 44 2.155952e-09 4.840112e-07
## 185 Histone H2B 14 14 6.217795e-04 3.489738e-02
## 186 Histone H3/CENP-A 15 15 3.659921e-04 2.347578e-02
## 187 Histone H4 15 15 3.659921e-04 2.347578e-02
## 188 Histone-fold 58 60 1.083394e-11 4.864438e-09
## 326 Ribosomal protein L2 domain 2 18 18 7.448332e-05 6.688602e-03
## 395 Translation protein SH3-like domain 22 22 8.872064e-06 1.327852e-03
## 396 Translation protein, beta-barrel domain 26 27 1.235834e-05 1.387224e-03
## 299 Protein kinase domain 5 18 1.202246e-04 2.699043e-02
## 448 Zinc finger, RING/FYVE/PHD-type 5 18 1.202246e-04 2.699043e-02
## 46 Aquaporin transporter 3 5 9.644015e-05 4.330163e-02
## module
## 184 black
## 185 black
## 186 black
## 187 black
## 188 black
## 326 black
## 395 black
## 396 black
## 299 lightyellow
## 448 lightyellow
## 46 midnightblueAs we can see, two modules are enriched in genes with particular protein
domains. We could get the same result with the
function enrichment_analysis(), which performs enrichment analysis for
a user-defined gene set instead of all modules.6 NOTE: The functions module_enrichment()
and enrichment_analysis() can be parallelized with BiocParallel to
increase speed. The default parallel back-end is SerialParam(), but this can
be modified in the argument bp_param.
6.5 Hub gene identification
Hub genes are often identified using two different
metrics: module membership (MM) (i.e., correlation of a gene to its
module eigengene) and degree (i.e., sum of connection weights of a
gene to all other genes in the module). Some researchers consider the
top 10% genes with the highest degree as hubs, while others consider those
with MM > 0.8. To avoid false positives, BioNERO’s algorithm combines
both metrics and defines hub genes as the top 10% genes with highest degree
that have MM > 0.8. Hubs can be identified with the function get_hubs_gcn().
hubs <- get_hubs_gcn(final_exp, net)
head(hubs)
## Gene Module kWithin
## 1 Zm00001d033147 black 188.3864
## 2 Zm00001d049790 black 181.4522
## 3 Zm00001d005649 black 180.7062
## 4 Zm00001d045448 black 180.6744
## 5 Zm00001d008203 black 178.7147
## 6 Zm00001d023340 black 177.75536.6 Extracting subgraphs
Subgraph extraction can be particularly useful to visualize specific
modules, and it can be done with the function get_edge_list(). The
function returns the subgraph as an edge list. Users can also extract an
edge list for a particular gene set instead of a module.
edges <- get_edge_list(net, module="midnightblue")
head(edges)
## Gene1 Gene2 Weight
## 45 Zm00001d001857 Zm00001d002384 0.9401886
## 89 Zm00001d001857 Zm00001d002690 0.9675345
## 90 Zm00001d002384 Zm00001d002690 0.9185426
## 133 Zm00001d001857 Zm00001d003962 0.7178340
## 134 Zm00001d002384 Zm00001d003962 0.6534956
## 135 Zm00001d002690 Zm00001d003962 0.6840004The function get_edge_list() returns a fully connected subgraph for
the specified module or gene set. However, filtering weak correlations is
desirable and can be accomplished by setting the argument filter = TRUE,
which will remove edges based on one of optimal scale-free topology
fit (default), p-value, Z-score, or an arbitrary minimum correlation
coefficient.7 PRO TIP: Generally, we advise you to filter by optimal scale-free
topology fit (default). However, if you want to specify your own correlation
filter for some reason (e.g., visualization), we strongly recommend using
the function check_SFT() to check if your resulting graph satisfies the
scale-free topology. If it does not, then your graph does not resemble real
biological networks and, hence, one cannot trust it for
biological interpretations. For more details details, check ?get_edge_list().
# Remove edges based on optimal scale-free topology fit
edges_filtered <- get_edge_list(net, module = "midnightblue", filter = TRUE)
## The correlation threshold that best fits the scale-free topology is 0.7
dim(edges_filtered)
## [1] 588 3
# Remove edges based on p-value
edges_filtered <- get_edge_list(
net, module = "midnightblue",
filter = TRUE, method = "pvalue",
nSamples = ncol(final_exp)
)
dim(edges_filtered)
## [1] 921 3
# Remove edges based on minimum correlation
edges_filtered <- get_edge_list(
net, module = "midnightblue",
filter = TRUE, method = "min_cor", rcutoff = 0.7
)
dim(edges_filtered)
## [1] 588 36.7 Network visualization
As we now have an edge list for a module, let’s visualize it with the
function plot_gcn(). By default, this function only labels the top 5 hubs
(or less if there are less than 5 hubs). However, this can be customized
according to the user’s preference (see ?plot_gcn for more information).
plot_gcn(
edgelist_gcn = edges_filtered,
net = net,
color_by = "module",
hubs = hubs
)
Networks can also be visualized interactively by
setting interactive = TRUE in plot_gcn.
plot_gcn(
edgelist_gcn = edges_filtered,
net = net,
color_by = "module",
hubs = hubs,
interactive = TRUE,
dim_interactive = c(500, 500)
)6.8 Network statistics
Finally, the function net_stats() can be used to calculate the main
network statistics (or properties, or indices), namely: connectivity,
scaled connectivity, clustering coefficient, maximum adjacency ratio,
density, centralization, heterogeneity, diameter,
betweenness (optional), and closeness (optional).
Depending on your system capacities and network size, this may take a very long time. Hence, if you are willing to calculate network statistics for your data set, grab a cup of coffee, because the waiting may be long.
Session information
This vignette was created under the following conditions:
sessionInfo()
## R version 4.4.0 beta (2024-04-15 r86425)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 22.04.4 LTS
##
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## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.10.0
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## [121] codetools_0.2-20 tibble_3.2.1
## [123] BiocManager_1.30.22 cli_3.6.2
## [125] rpart_4.1.23 xtable_1.8-4
## [127] munsell_0.5.1 jquerylib_0.1.4
## [129] network_1.18.2 Rcpp_1.0.12
## [131] GenomeInfoDb_1.40.0 coda_0.19-4.1
## [133] png_0.1-8 XML_3.99-0.16.1
## [135] fastcluster_1.2.6 parallel_4.4.0
## [137] ggplot2_3.5.1 blob_1.2.4
## [139] scales_1.3.0 crayon_1.5.2
## [141] GetoptLong_1.0.5 rlang_1.1.3
## [143] KEGGREST_1.44.0References
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