Contents

The emergence of multi-omics data enabled the development of integration methods.

With netOmics, we go beyond integration by introducing an interpretation tool. netOmics is a package for the creation and exploration of multi-omics networks.

Depending on the provided dataset, it allows to create inference networks from expression data but also interaction networks from knowledge databases. After merging the sub-networks to obtain a global multi-omics network, we propose network exploration methods using propoagation techniques to perform functional prediction or identification of molecular mechanisms.

Furthermore, the package has been developed for longitudinal multi-omics data and can be used in conjunction with our previously published package timeOmics.

Overview

Overview

For more informnation about the method, please check (Bodein et al. 2020)

In this vignette, we introduced a case study which depict the main steps to create and explore multi-omics networks from multi-omics time-course data.

1 Requirements

# install the package via BioConductor
if (!requireNamespace("BiocManager", quietly = TRUE))
    install.packages("BiocManager")

BiocManager::install("netOmics")
# install the package via github
library(devtools)
install_github("abodein/netOmics")
# load the package
library(netOmics)
# usefull packages to build this vignette
library(timeOmics)
library(tidyverse)
library(igraph)

2 Case Study: Human Microbiome Project T2D

The package will be illustrated on longitudinal MO dataset to study the seasonality of MO expression in patients with diabetes (Sailani et al. 2020).

The data used in this vignette is a subset of the data available at: https://github.com/aametwally/ipop_seasonal

We focused on a single individual with 7 timepoints. 6 different omics were sampled (RNA, proteins, cytokines, gut microbiome, metabolites and clinical variables).

# load data
data("hmp_T2D")

3 (optional: timeOmics analysis)

The first step of the analysis is the preprocessing and longitudinal clustering. This step is carried out with timeOmics and should be reserved for longitudinal data.

It ensures that the time profiles are classified into groups of similar profiles so each MO molecule is labbeled with its cluster.

In addition, timeOmics can identify a multi-omics signature of the clusters. These molecules can be, for example, the starting points of the propogation analysis.

For more informations about timeOmics, please check http://www.bioconductor.org/packages/release/bioc/html/timeOmics.html

As illustrated in the R chunk below the timeOmics step includes:

# not evaluated in this vignette

#1 filter fold-change
remove.low.cv <- function(X, cutoff = 0.5){
    # var.coef
    cv <- unlist(lapply(as.data.frame(X), 
                    function(x) abs(sd(x, na.rm = TRUE)/mean(x, na.rm= TRUE))))
    return(X[,cv > cutoff])
}
fc.threshold <- list("RNA"= 1.5, "CLINICAL"=0.2, "GUT"=1.5, "METAB"=1.5,
                     "PROT" = 1.5, "CYTO" = 1)

# --> hmp_T2D$raw
data.filter <- imap(raw, ~{remove.low.cv(.x, cutoff = fc.threshold[[.y]])})

#2 scale
data <- lapply(data.filter, function(x) log(x+1))
# --> hmp_T2D$data


#3 modelling
lmms.func <- function(X){
    time <- rownames(X) %>% str_split("_") %>% 
      map_chr(~.x[[2]]) %>% as.numeric()
    lmms.output <- lmms::lmmSpline(data = X, time = time,
                                   sampleID = rownames(X), deri = FALSE,
                                   basis = "p-spline", numCores = 4, 
                                   keepModels = TRUE)
    return(lmms.output)
}
data.modelled <- lapply(data, function(x) lmms.func(x))

# 4 clustering
block.res <- block.pls(data.modelled, indY = 1, ncomp = 1)
getCluster.res <- getCluster(block.res)
# --> hmp_T2D$getCluster.res


# 5 signature
list.keepX <- list("CLINICAL" = 4, "CYTO" = 3, "GUT" = 10, "METAB" = 3, 
                   "PROT" = 2,"RNA" = 34)
sparse.block.res  <- block.spls(data.modelled, indY = 1, ncomp = 1, scale =TRUE, 
                                keepX =list.keepX)
getCluster.sparse.res <- getCluster(sparse.block.res)
# --> hmp_T2D$getCluster.sparse.res

timeOmics resulted in 2 clusters, labelled 1 and -1

# clustering results
cluster.info <- hmp_T2D$getCluster.res

4 Network building

Each layer of the network is built sequentially and then assembled in a second section.

All the functions in the package can be used on one element or a list of elements. In the longitudinal context of the data, kinetic cluster sub-networks are built plus a global network (1, -1 and All).

4.1 Inference Network

Multi-omics network building starts with a first layer of gene. Currently, the ARACNe algorithm handles the inference but we will include more algorithms in the future.

The function get_grn return a Gene Regulatory Network from gene expression data. Optionally, the user can provide a timeOmics clustering result (?getCluster) to get cluster specific sub-networks. In this case study, this will automatically build the networks (1, -1 and All), as indicated previously.

The get_graph_stats function provides basic graph statistics such as the number of vertices and edges. If the vertices have different attributes, it also includes a summary of these.

cluster.info.RNA <- timeOmics::getCluster(cluster.info, user.block = "RNA")
graph.rna <- get_grn(X = hmp_T2D$data$RNA, cluster = cluster.info.RNA)

# to get info about the network
get_graph_stats(graph.rna)
##     node.c node.i  edge edge.density type:gene mode:core cluster:-1 cluster:1
## All    759     16 70539    0.2351888       775       775        610       165
## 1      155     10  2922    0.2159645       165       165         NA       165
## -1     595     15 61000    0.3284072       610       610        610        NA

4.2 Interaction from databases

As for the genes, the second layer is a protein layer (Protein-Protein Interaction). This time, no inference is performed. Instead, known interactions are extracted from a database of interaction (BIOGRID).

The function get_interaction_from_database will fetch the interactions from a database provided as a data.frame (with columns from and to) or a graph (igraph object). In addition to the interactions between the indicated molecules, the first degree neighbors can also be collected (option user.ego = TRUE)

# Utility function to get the molecules by cluster
get_list_mol_cluster <- function(cluster.info, user.block){
  require(timeOmics)
    tmp <- timeOmics::getCluster(cluster.info, user.block) 
    res <- tmp %>% split(.$cluster) %>% 
        lapply(function(x) x$molecule)
    res[["All"]] <- tmp$molecule
    return(res)
}

cluster.info.prot <- get_list_mol_cluster(cluster.info, user.block = 'PROT')
graph.prot <-  get_interaction_from_database(X = cluster.info.prot, 
                                             db = hmp_T2D$interaction.biogrid, 
                                             type = "PROT", user.ego = TRUE)
# get_graph_stats(graph.prot)

In this example, only a subset of the Biogrid database is used (matching elements).

4.3 Other inference methods

Another way to compute networks from expression data is to use other inference methods. In the following chunk, we intend to illustrate the use of the SparCC algorithm (Friedman and Alm 2012) on the gut data and how it can be integrate into the pipeline. (sparcc is not included in this package)

# not evaluated in this vignette
library(SpiecEasi)

get_sparcc_graph <- function(X, threshold = 0.3){
    res.sparcc <- sparcc(data = X)
    sparcc.graph <- abs(res.sparcc$Cor) >= threshold
    colnames(sparcc.graph) <-  colnames(X)
    rownames(sparcc.graph) <-  colnames(X)
    res.graph <- graph_from_adjacency_matrix(sparcc.graph, 
                                             mode = "undirected") %>% simplify
    return(res.graph)
}

gut_list <- get_list_mol_cluster(cluster.info, user.block = 'GUT')

graph.gut <- list()
graph.gut[["All"]] <- get_sparcc_graph(hmp_T2D$raw$GUT, threshold = 0.3)
graph.gut[["1"]] <- get_sparcc_graph(hmp_T2D$raw$GUT %>% 
                                       dplyr::select(gut_list[["1"]]), 
                                     threshold = 0.3)
graph.gut[["-1"]] <- get_sparcc_graph(hmp_T2D$raw$GUT %>% 
                                        dplyr::select(gut_list[["-1"]]), 
                                      threshold = 0.3)
class(graph.gut) <- "list.igraph"
graph.gut <- hmp_T2D$graph.gut
# get_graph_stats(graph.gut)

4.4 Other examples

For this case study, we complete this first step of network building with the missing layers.

# CYTO -> from database (biogrid)
cyto_list = get_list_mol_cluster(cluster.info = cluster.info, 
                                 user.block = "CYTO")
graph.cyto <-  get_interaction_from_database(X = cyto_list,
                                             db = hmp_T2D$interaction.biogrid, 
                                             type = "CYTO", user.ego = TRUE)
# get_graph_stats(graph.cyto)

# METAB -> inference
cluster.info.metab <-  timeOmics::getCluster(X = cluster.info, 
                                             user.block = "METAB")
graph.metab <-  get_grn(X = hmp_T2D$data$METAB, 
                        cluster = cluster.info.metab)
# get_graph_stats(graph.metab)

# CLINICAL -> inference
cluster.info.clinical <- timeOmics::getCluster(X = cluster.info, 
                                               user.block = 'CLINICAL')
graph.clinical <- get_grn(X = hmp_T2D$data$CLINICAL,
                          cluster = cluster.info.clinical)
# get_graph_stats(graph.clinical)

5 Layer merging

We included 2 types of layer merging:

5.1 Merging with interactions

The function combine_layers enables the fusion of different network layers. It combines the network (or list of network) in graph1 with the network (or list of network) in graph2, based on the shared vertices between the networks.

Additionally, the user can provide an interaction table interaction.df (in the form of a data.frame or igraph object).

In the following chunk, we sequentially merge RNA, PROT and CYTO layers and uses the TFome information (TF protein -> Target Gene) to connect these layers.

full.graph <- combine_layers(graph1 = graph.rna, graph2 = graph.prot)
full.graph <- combine_layers(graph1 = full.graph, graph2 = graph.cyto)

full.graph <- combine_layers(graph1 = full.graph,
                             graph2 = hmp_T2D$interaction.TF)
# get_graph_stats(full.graph)

5.2 Merging with correlations

To connect omics layers for which no interaction information is available, we propose to use a threshold on the correlation between the expression profiles of two or more omics data.

The strategy is as follows: we isolate the omics from the data and calculate the correlations between this omics and the other data.

all_data <- reduce(hmp_T2D$data, cbind)

# omic = gut
gut_list <- get_list_mol_cluster(cluster.info, user.block = "GUT")
omic_data <- lapply(gut_list, function(x)dplyr::select(hmp_T2D$data$GUT, x))
## Note: Using an external vector in selections is ambiguous.
## ℹ Use `all_of(x)` instead of `x` to silence this message.
## ℹ See <https://tidyselect.r-lib.org/reference/faq-external-vector.html>.
## This message is displayed once per session.
# other data = "RNA", "PROT", "CYTO"
other_data_list <- get_list_mol_cluster(cluster.info,
                                        user.block = c("RNA", "PROT", "CYTO"))
other_data <- lapply(other_data_list, function(x)dplyr::select(all_data, x))

# get interaction between gut data and other data
interaction_df_gut <- get_interaction_from_correlation(X = omic_data,
                                                       Y = other_data,
                                                       threshold = 0.99)

# and merge with full graph
full.graph <- combine_layers(graph1 = full.graph,
                             graph2 = graph.gut,
                             interaction.df = interaction_df_gut$All)
# omic =  Clinical
clinical_list <- get_list_mol_cluster(cluster.info, user.block = "CLINICAL")
omic_data <- lapply(clinical_list, 
                    function(x)dplyr::select(hmp_T2D$data$CLINICAL, x))

# other data = "RNA", "PROT", "CYTO", "GUT"
other_data_list <- get_list_mol_cluster(cluster.info,
                                        user.block = c("RNA", "PROT", 
                                                       "CYTO", "GUT"))
other_data <- lapply(other_data_list, function(x)dplyr::select(all_data, x))


# get interaction between gut data and other data
interaction_df_clinical <- get_interaction_from_correlation(X = omic_data
                                                            , Y = other_data,
                                                            threshold = 0.99)

# and merge with full graph
full.graph <- combine_layers(graph1 = full.graph,
                             graph2 = graph.clinical, 
                             interaction.df = interaction_df_clinical$All)
# omic =  Metab
metab_list <- get_list_mol_cluster(cluster.info, user.block = "METAB")
omic_data <- lapply(metab_list, function(x)dplyr::select(hmp_T2D$data$METAB, x))

# other data = "RNA", "PROT", "CYTO", "GUT", "CLINICAL"
other_data_list <- get_list_mol_cluster(cluster.info,
                                        user.block = c("RNA", "PROT", "CYTO", 
                                                       "GUT", "CLINICAL"))
other_data <- lapply(other_data_list, function(x)dplyr::select(all_data, x))

# get interaction between gut data and other data
interaction_df_metab <- get_interaction_from_correlation(X = omic_data,
                                                         Y = other_data, 
                                                         threshold = 0.99)

# and merge with full graph
full.graph <- combine_layers(graph1 = full.graph, 
                             graph2 = graph.metab, 
                             interaction.df = interaction_df_metab$All)

6 Addition of supplemental layers

For the interpretation of the MO integration results, the use of additional information layers or molecules can be useful to enrich the network.

6.1 Over Representation Analysis

ORA is a common step to include knowledge. The function get_interaction_from_ORA perform the ORA analysis from the desired molecules and return an interaction graph with the enriched terms and the corresponding molecules.

Then, the interaction graph with the new vertices can be linked to the network as illustrated in the previous step.

Here, ORA was performed with RNA, PROT, and CYTO against the Gene Ontology.

# ORA by cluster/All
mol_ora <- get_list_mol_cluster(cluster.info, 
                                user.block = c("RNA", "PROT", "CYTO"))

# get ORA interaction graph by cluster
graph.go <- get_interaction_from_ORA(query = mol_ora,
                                     sources = "GO",
                                     organism = "hsapiens",
                                     signif.value = TRUE)

# merge
full.graph <- combine_layers(graph1 = full.graph, graph2 = graph.go)

6.2 External knowledge

Additionally, knowledge from external sources can be included in the network.

In the following chunk, we performed disease-related gene enrichment analysis from medlineRanker (http://cbdm-01.zdv.uni-mainz.de/~jfontain/cms/?page_id=4). We converted the results into a data.frame (with the columns from and to) and this acted as an interaction database.

# medlineRanker -> database
medlineranker.res.df <- hmp_T2D$medlineranker.res.df %>% 
  dplyr::select(Disease, symbol) %>% 
  set_names(c("from", "to"))
  
mol_list <-  get_list_mol_cluster(cluster.info = cluster.info,
                                  user.block = c("RNA", "PROT", "CYTO"))
graph.medlineranker <-  get_interaction_from_database(X = mol_list,
                                                      db = medlineranker.res.df, 
                                                      type = "Disease",
                                                      user.ego = TRUE)
# get_graph_stats(graph.medlineranker)

# merging
full.graph <- combine_layers(graph1 = full.graph, graph2 = graph.medlineranker)

We complete the MO network preparation with attribute cleaning and addition of several attributes such as:

  • mode = “core” if the vertex was originally present in the data; “extended” otherwise
  • sparse = TRUE if the vertex was present in kinetic cluster signature; FALSE otherwise
  • type = type of omics (“RNA”,“PROT”,“CLINICAL”,“CYTO”,“GUT”,“METAB”,“GO”, “Disease”)
  • cluster = ‘1’, ‘-1’ or ‘NA’ (for vertices not originally present in the original data)
# graph cleaning
graph_cleaning <- function(X, cluster.info){
    # no reusability
    X <- igraph::simplify(X)
    va <- vertex_attr(X)
    viewed_mol <- c()
    for(omic in unique(cluster.info$block)){
        mol <- intersect(cluster.info %>% dplyr::filter(.$block == omic) %>%
                           pull(molecule), V(X)$name)
        viewed_mol <- c(viewed_mol, mol)
        X <- set_vertex_attr(graph = X, 
                             name = "type", 
                             index = mol, 
                             value = omic)
        X <- set_vertex_attr(graph = X, 
                             name = "mode",
                             index = mol,
                             value = "core")
    }
    # add medline ranker and go
    mol <- intersect(map(graph.go, ~ as_data_frame(.x)$to) %>%
                       unlist %>% unique(), V(X)$name) # only GO terms
    viewed_mol <- c(viewed_mol, mol)
    X <- set_vertex_attr(graph = X, name = "type", index = mol, value = "GO")
    X <- set_vertex_attr(graph = X, name = "mode", 
                         index = mol, value = "extended")
    
    mol <- intersect(as.character(medlineranker.res.df$from), V(X)$name)
    viewed_mol <- c(viewed_mol, mol)
    X <- set_vertex_attr(graph = X, name = "type",
                         index = mol, value = "Disease")
    X <- set_vertex_attr(graph = X, name = "mode",
                         index = mol, value = "extended")
    
    other_mol <- setdiff(V(X), viewed_mol)
    if(!is_empty(other_mol)){
        X <- set_vertex_attr(graph = X, name = "mode",
                             index = other_mol, value = "extended")
    }
    X <- set_vertex_attr(graph = X, name = "mode", 
                         index = intersect(cluster.info$molecule, V(X)$name), 
                         value = "core")
    
    # signature
    mol <-  intersect(V(X)$name, hmp_T2D$getCluster.sparse.res$molecule)
    X <- set_vertex_attr(graph = X, name = "sparse", index = mol, value = TRUE)
    mol <-  setdiff(V(X)$name, hmp_T2D$getCluster.sparse.res$molecule)
    X <- set_vertex_attr(graph = X, name = "sparse", index = mol, value = FALSE)
    
    return(X)
}
FULL <- lapply(full.graph, function(x) graph_cleaning(x, cluster.info))
get_graph_stats(FULL)
##     node.c node.i  edge edge.density cluster:-1 cluster:1 type:CLINICAL
## All   2115    123 89483   0.03574740        681       238            39
## 1      492     76  5569   0.03458405         NA       238            18
## -1    1725     69 62454   0.03883180        681        NA            22
##     type:CYTO type:Disease type:GO type:GUT type:METAB type:PROT type:RNA
## All        37          178     174       58        105       872      775
## 1          15          110      17       33         56       150      169
## -1         24          174     121       25         49       758      621
##     mode:core mode:extended sparse:FALSE sparse:TRUE
## All      1009          1229         2134         104
## 1         292           276          523          45
## -1        738          1056         1734          60

7 Network exploration

7.1 Basics network exploration

We can use basic graph statistics to explore the network such as degree distribution, modularity, and short path.

# degree analysis
d <- degree(FULL$All)
hist(d)
d[max(d)]

# modularity # Warnings: can take several minutes
res.mod <- walktrap.community(FULL$All)
# ...

# modularity
sp <- shortest.paths(FULL$All)

7.2 Random walk with restart

RWR is a powerful tool to explore the MO networks which simulates a particle that randomly walk on the network. From a starting point (seed) it ranks the other vertices based on their proximity with the seed and the network structure.

We use RWR for function prediction and molecular mechanism identification.

In the example below, the seeds were the GO terms vertices.

# seeds = all vertices -> takes 5 minutes to run on regular computer
# seeds <- V(FULL$All)$name
# rwr_res <- random_walk_restart(FULL, seeds)

# seed = some GO terms
seeds <- head(V(FULL$All)$name[V(FULL$All)$type == "GO"])
rwr_res <- random_walk_restart(FULL, seeds)

7.2.1 Find vertices with specific attributes

After the RWR analysis, we implemented several functions to extract valuable information.

To identify MO molecular functions, the seed can be a GO term and we are interested to identify vertices with different omics type within the closest nodes.

The function rwr_find_seeds_between_attributes can identify which seeds were able to reach vertices with different attributes (ex: type) within the closest k (ex: 15) vertices.

The function summary_plot_rwr_attributes displays the number of different values for a seed attribute as a bar graph.

rwr_type_k15 <- rwr_find_seeds_between_attributes(X = rwr_res, 
                                                  attribute = "type", k = 15)

# a summary plot function
summary_plot_rwr_attributes(rwr_type_k15)

summary_plot_rwr_attributes(rwr_type_k15$All)