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MetaboFlow - the development of standardised workflows for processing metabolomics data to aid reproducible data sharing and big data initiatives

This pipeline describes the processing and the analysis of Ionomics data. This paper describes a possible application.

Section 0: Import the R package

The workflow is wrapped within the IonFlow R package, and it consists of four sections, respectively

  • Pre-processing
  • Exploratory analysis
  • Clustering which also includes the GO Slim annotation and the GO terms enrichment
  • Network analysis
devtools::install_github("AlinaPeluso/MetaboFlow", subdir="IonFlow")
library(IonFlow)

Section 1: Pre-processing

The pre-processing section is required first as it produces in output the cleaned dataset to be used in the other sections. There is no specific order on how to run the other sections.

The pre-processing section aims to free the data from unreliable samples which will probably lead to wrong outputs. In such way, effective data pre-processing methods are applied to avoid the effects of noisy and unreliable data.

This section requires as input the raw data frame, e.g. ion's concentrations. It is also possible to define a set of ion's standard deviation, as these are possibly computed accounting for some control genes. Note that the latter is an optional input i.e if not provided the standard deviations from the data would be computed to perform the data standardisation (see Section Standardisation).

Inspect the raw data

data(IonData)

We illustrate the Ionomics workflow with ICP-MS data of yeast intracellular ion concentrations measured for 1454 single-gene haploid knockouts (data from Danku, 2009). Ions measured include Ca44, Cd111, Co59, Cu65, Fe56, K39, Mg25, Mn55, Mo95, Na23, Ni60, P31, S34, Zn66. Values of concentration are in ppm and have been adjusted using optical density measurements. Intracellular concentrations are measured for two, four or eight replicas of each mutant depending on the knock-out. Knock-out YDL227C mutant is measured multiple times in every batch as control strain.

Run the pre-processing function

pre_proc <- PreProcessing(data=IonData,stdev=pre_defined_sd)

The concentration values for the raw data ion can be summarised as follow.

pre_proc$stats.raw_data
Ion Min 1st Quartile Median Mean 3rd Quartile Max Variance
1 Ca 0.449 31.73 40.44 45.071 51.015 902.568 829.525
2 Cd 0.174 0.866 0.988 1.002 1.121 2.512 0.051
3 Co 0.007 0.142 0.16 0.162 0.184 0.702 0.001
4 Cu 0.587 1.344 1.586 1.717 1.831 327.79 16.91
5 Fe 0.002 5.527 7.295 9.469 9.332 6624.526 5154.611
6 K 284.273 2060.619 2495.265 2492.765 2879.551 17777.452 534784.375
7 Mg 115.63 546.325 679.275 642.578 753.678 3838.479 31947.598
8 Mn 0.02 0.982 1.206 1.197 1.38 7.339 0.106
9 Mo 0.158 0.656 0.934 1.109 1.327 60.879 1.855
10 Na 0.184 128.831 185.25 196.545 247.747 892.968 9027.944
11 Ni 0.074 0.982 1.258 1.693 1.543 2323.058 565.618
12 P 1194.953 3833.9 4514.476 4289.109 4952.98 21695.748 1151197.05
13 S 20.592 434.61 512.845 529.493 605.436 5484.638 37212.137
14 Zn 7.659 14.785 16.549 17.114 18.334 2221.586 511.804

There is a very high variability of the knockouts across ions and within the batches. There are no missing values in the data.

Outlier detection

We define a lower outer fence: Q1 - 3*IQ and a upper outer fence: Q3 + 3*IQ where Q1 and Q3 are the first and the third quantile of the distribution, respectively. A point beyond the outer fence is considered an extreme outlier.

The outliers are split across ions as follows.

pre_proc$stats.outliers
Ion not_outlier outlier outlier(%)
1 Ca 9694 305 0.22
2 Cd 9950 49 0.04
3 Co 9966 33 0.02
4 Cu 9870 129 0.09
5 Fe 9833 166 0.12
6 K 9980 19 0.01
7 Mg 9991 8 0.01
8 Mn 9984 15 0.01
9 Mo 9909 90 0.06
10 Na 9965 34 0.02
11 Ni 9849 150 0.11
12 P 9991 8 0.01
13 S 9923 76 0.05
14 Zn 9888 111 0.08

Median batch correction

First we take the logarithmm of the concentration value. Then, the data are scaled to the median taken for each ion within each batch.

pre_proc$stats.median_batch_corrected_data
Ion Min 1st Quartile Median Mean 3rd Quartile Max Variance
1 Ca -4.311 -0.124 0 0.022 0.148 1.671 0.084
2 Cd -1.749 -0.068 0 0.001 0.068 0.735 0.025
3 Co -2.178 -0.059 0 -0.02 0.054 0.629 0.033
4 Cu -0.681 -0.055 0 0.009 0.06 0.876 0.013
5 Fe -7.332 -0.1 0 0.017 0.115 1.869 0.062
6 K -1.96 -0.124 0 -0.044 0.1 0.938 0.068
7 Mg -1.735 -0.061 0 -0.016 0.059 0.688 0.03
8 Mn -3.71 -0.125 0 -0.023 0.101 0.856 0.052
9 Mo -1.662 -0.163 0 -0.003 0.169 1.623 0.103
10 Na -6.992 -0.26 0 -0.058 0.189 1.403 0.216
11 Ni -2.422 -0.094 0 0.006 0.104 1.443 0.057
12 P -1.059 -0.054 0 -0.009 0.052 0.571 0.017
13 S -2.384 -0.086 0 -0.002 0.091 1.411 0.034
14 Zn -0.416 -0.046 0 0.011 0.054 0.661 0.009

After outlier removal and the median batch correction of the logged concentrations (logConcentration_corr), the data looks as

pre_proc$plot.logConcentration_by_batch 

plot.logConcentration_by_batch

Standardisation

After outlier removal and median batch correction we now standardise the ions' logged concentrations. For each set of knockouts across the ions's type, we normalise the concentrations by dividing for the ions' standard deviation. The ions' standard deviations can be estimated from the data, or a set of pre-defined ions' standard deviations can be used. The latter has been computed on the complete dataset (which includes also some gene controls). At the moment we do not use the pre-defined ion's concenrations to normalise our data.

The concentration values for each ion can be summarised as follow.

pre_proc$stats.standardised_data
Ion Min 1st Quartile Median Mean 3rd Quartile Max Variance
1 Ca -4.135 -1.937 0.057 0.945 3.187 10.698 15.266
2 Cd -2.894 -0.341 0.596 0.558 1.257 4.214 2.111
3 Co -1.863 -0.383 0.167 0.568 1.371 4.942 2.629
4 Cu -1.126 -0.643 -0.363 0.318 0.944 4.662 2.012
5 Fe -1.789 -0.733 -0.48 -0.263 -0.006 2.043 0.724
6 K -2.099 -0.734 0.005 0.285 0.818 5.242 2.307
7 Mg -12.918 -1.082 0.608 0.236 2.425 9.631 12.37
8 Mn -1.85 -0.377 0.93 0.917 2.06 4.133 2.39
9 Mo -5.016 -0.672 1.354 1.522 3.409 11.099 10.04
10 Na -4.029 -1.121 -0.156 -0.242 0.458 3.238 1.791
11 Ni -1.476 -0.414 0.454 0.549 1.009 6.043 1.918
12 P -3.697 -1.269 -0.115 -0.179 0.724 3.667 2.441
13 S -1.345 -0.396 0.283 0.309 0.767 4.961 1.103
14 Zn -1.969 -0.773 -0.476 -0.096 0.44 4.263 1.304

Symbolization

As we are working with the logConcentration_corr_norm we can consider a thresold based on a certain number of sigma (e.g. number-of-sigma thresold=3) to symbolizise the concentrations' profile of the knockouts as follow:

  • Symb=0 if -3<logConcentration_corr_norm<3
  • Symb=1 if logConcentration_corr_norm>=3
  • Symb=-1 otherwise

The choice of the thresold is arbitrary i.e. thresold greater than 3 can be chosen. The highest is the thresold, the highest is the concentration value taken as significant.

Aggregation of the knockout replicates

For each ion measure, we proceed to aggregate the data by taking the median value of the knockout. For each ions we consider around 1,450 genes. And of which we can plot the z-score with the associated sigma as follow.

pre_proc$plot.logConcentration_z_scores

plot.logConcentration_z_scores

Final datasets

Three dataset are obtained as output. The first in the long format (genes as rows and ions as columns), and two in wide format and respectively one with the standardised ion's concentraction, and the other with the symbolised profiles of the knockouts.

Long format (aggregated knockout replicates):

head(pre_proc$dataR.long)
row_id Knockout Batch_ID id Ion Concentration Outlier logConcentration logConcentration_corr logConcentration_corr_norm Symb
3851 YAL002W 19 3851 Ca 93.4 0 4.54 0.96 6.3 1
3852 YAL002W 19 3852 Ca 98.2 0 4.59 1.01 6.7 1
3853 YAL002W 19 3853 Ca 101.6 0 4.62 1.04 6.9 1
13850 YAL002W 19 3851 Cd 1.5 0 0.42 0.5 8.8 1
13851 YAL002W 19 3852 Cd 1.6 0 0.45 0.53 9.2 1
13852 YAL002W 19 3853 Cd 1.6 0 0.5 0.58 10.1 1

Long format (not aggregated knockout replicates):

head(pre_proc$data.long)
Knockout Ion logConcentration_corr_norm Symb
YAL002W Ca 6.68 1
YAL004W Ca -0.88 0
YAL005C Ca -0.15 0
YAL007C Ca -0.54 0
YAL008W Ca -0.88 0
YAL009W Ca -0.95 0

Wide format, standardised ion's concentraction:

head(pre_proc$data.wide)
Knockout Ca Cd Co Cu Fe K Mg Mn Mo Na Ni P S Zn
YAL002W 6.68 9.64 0.296 0.65 -0.056 -3.56 -1.3357 5.37 -2.7 3.94 -3.73 0.94 -1.24 0.472
YAL004W -0.88 0.9 0.882 -0.59 1.017 0.76 1.5433 -2.45 0.81 -0.13 0.94 0.83 0.52 0.073
YAL005C -0.15 -0.13 0.278 0.94 -0.638 1.3 0.809 -1.33 -0.4 1.79 0.88 0.27 -0.13 -0.081
YAL007C -0.54 -0.2 -0.649 -0.59 0.803 1.41 -0.6495 1.42 3.24 -0.35 -0.68 0.29 -0.58 -0.424
YAL008W -0.88 -0.56 -0.416 -1.3 -0.545 0.32 -0.5299 0.34 1.9 0.13 -0.65 -0.34 -0.83 -0.666
YAL009W -0.95 0.91 -0.016 -0.84 -1.134 0.18 0.0087 1.06 4.91 0.74 -0.84 0.11 0.17 -0.884

Wide format, symbolised profiles:

head(pre_proc$data.wide_Symb)
Knockout Ca Cd Co Cu Fe K Mg Mn Mo Na Ni P S Zn
YAL002W 1 1 0 0 0 -1 0 1 0 1 -1 0 0 0
YAL004W 0 0 0 0 0 0 0 0 0 0 0 0 0 0
YAL005C 0 0 0 0 0 0 0 0 0 0 0 0 0 0
YAL007C 0 0 0 0 0 0 0 0 1 0 0 0 0 0
YAL008W 0 0 0 0 0 0 0 0 0 0 0 0 0 0
YAL009W 0 0 0 0 0 0 0 0 1 0 0 0 0 0

Section 2: Exploratory analysis

This section provide a way to summarize the main characteristics of the data with visual methods. No input needed as this section is built on the output of the previous section.

exp_anal <- ExploratoryAnalysis(data=pre_proc$data.wide)

Pearson correlation

exp_anal$plot.Pearson_correlation 

plot.Pearson_correlation

PCA

The aim of PCA is to reduce the dimensionality of the data while retaining as much information as possible. This is achieved by projecting the data into a new lower-dimensional space defined by the principal components (PC) that combine in a linear way the original (possibly correlated) variables (e.g. ions) in such a way that the variance of the data in the low-dimensional representation is maximized. In practice, it means that each gene is assigned a score on each new PC dimension, and this score is calculated by appling weight to a a linear combination of the original variables. In our case, the data are centred but not further scaled as were normalised in the pre-processing stage thus the variance is homogeneous across variables. The algorithm is able to handle missing values.

exp_anal$plot.PCA_Individual

plot.PCA_Individual

The weights of each of the original variables are stored in the so-called loading vectors associated to each PC.

Loadings (first 10) for PC1:

head(exp_anal$stat.loadings_PC1,10)
Knockout value.var
YAL019W 0.27
YAL026C 0.27
YAL031C 0.27
YAL034C 0.26
YAL037W 0.24
YAL040C 0.23
YAL042W 0.21
YAL045C 0.19
YAL046C 0.15
YAL048C 0.13

Loadings (first 10) for PC2:

head(exp_anal$stat.loadings_PC2,10)
Knockout value.var
YAL002W -0.21
YAL004W -0.18
YAL005C -0.16
YAL007C -0.15
YAL008W -0.15
YAL009W -0.13
YAL010C -0.12
YAL013W 0.12
YAL014C -0.12
YAL015C -0.12

Heatmap

We employ an heatmap as a graphical representation of data where the knockout values contained are represented as colors. A dendrogram is also added to the left side (clustering of genes knockout) and to the top (clustering of ions).

exp_anal$plot.heatmap 

plot.heatmap

Pairwise correlation map

We employ a correlation map to visualise the paiwise correlation coefficients across ions.

exp_anal$plot.pairwise_correlation_map 

plot.pairwise_correlation_map

Regularized partial correlation network

We now inspect the (statistical) relationships between ions in the form of graphical models. The graph is made of n nodes (ions) connected by m edges (knockout) and the relationships between ions is visualised as weighted edges.

We compute a network of partial correlation coefficients. Such networks can also be termed concentration graphs (Cox & Wermuth, 1994) or Gaussian graphical models (Lauritzen, 1996). Each link in the network represents a partial correlation coefficient between two variables after conditioning on all other variables in the dataset. These coefficients range from -1 to 1 and encode the remaining association between two nodes after controlling for all other information possible, also known as conditional independence associations.

The connections are visualized using red lines indicating negative partial correlations, green lines indicating positive partial correlations, and wider and more saturated connections indicate partial correlations that are far from zero.

Whenever the partial correlation is exactly zero, no connection is drawn between two nodes, indicating that two variables are independent after controlling for all other variables in the network. This is of particular interest since such a missing connection indicates one of the two variables could not have caused the other. As such, whenever there is a connection present, it highlights a potential causal pathway between two variables.

exp_anal$plot.regularized_partial_correlation_network 

plot.regularized_partial_correlation_network

Section 3: Clustering

# Inspect data for GO Slim annotation 
data(data_GOslim)
head(data_GOslim)

# Inspect data for GO Terms for enrichment
data(ORF2KEGG)
head(ORF2KEGG)
gene_clust <- GeneClustering(data=pre_proc$data.wide, data_Symb=pre_proc$data.wide_Symb)

Clustering

We compute the manhattan distances between the knockouts' symbolised profile to cluster genes having relative distances equal to 0. We proceed to investigate the clusters which have at least 10 genes.

gene_clust$stats.clusters
cluster_id nGenes
2 747
3 30
7 28
15 29
16 37
18 46
25 19
30 27
39 13
55 20
90 20

We then compute a profile plot for each cluster.

gene_clust$plot.profiles 

plot.profiles

Go Slim annotation

We now highlight the the biological process, the cellular component, and the molecular function of the genes within each cluster. We retain the annotations that map at least 5% of the genes in the cluster. We do not include in the results the first cluster (Cluster 1) as this the "null" cluster which contains a mix of knockouts having no impact on the ions. The first five entries of each cluster can be access as follows.

lapply(gene_clust$stats.Kegg_Goslim_annotation, function(x) head(x,5))
Term Ontology Count Percent
## Cluster 2 (747 genes)
cellular bud Cellular component 39 5.2
cytoplasm Cellular component 474 63.5
DNA binding Molecular function 40 5.4
endomembrane system Cellular component 102 13.7
endoplasmic reticulum Cellular component 67 9
## Cluster 3 (30 genes)
carbohydrate metabolic process Biological process 3 10
chromatin organization Biological process 4 13.3
cofactor metabolic process Biological process 2 6.7
cytoplasm Cellular component 21 70
cytoplasmic vesicle Cellular component 3 10
## Cluster 7 (28 genes)
ATPase activity Molecular function 2 7.1
cell wall organization or biogenesis Biological process 2 7.1
cellular amino acid metabolic process Biological process 2 7.1
cellular bud Cellular component 2 7.1
cellular response to DNA damage stimulus Biological process 3 10.7
## Cluster 15 (29 genes)
cellular respiration Biological process 5 17.2
cofactor metabolic process Biological process 2 6.9
cytoplasm Cellular component 26 89.7
generation of precursor metabolites and energy Biological process 5 17.2
hydrolase activity Molecular function 5 17.2
## Cluster 16 (37 genes)
carbohydrate metabolic process Biological process 2 5.4
cell cortex Cellular component 2 5.4
cellular response to DNA damage stimulus Biological process 5 13.5
chromatin organization Biological process 2 5.4
chromosome Cellular component 4 10.8
## Cluster 18 (46 genes)
cell cortex Cellular component 4 8.7
cellular amino acid metabolic process Biological process 4 8.7
cellular bud Cellular component 4 8.7
cytoplasm Cellular component 36 78.3
endomembrane system Cellular component 9 19.6
## Cluster 25 (19 genes)
carbohydrate metabolic process Biological process 2 10.5
carbohydrate transport Biological process 1 5.3
cell budding Biological process 1 5.3
cell cortex Cellular component 1 5.3
cell wall Cellular component 1 5.3
## Cluster 30 (27 genes)
chromosome Cellular component 3 11.1
cytoplasm Cellular component 14 51.9
DNA binding Molecular function 2 7.4
endomembrane system Cellular component 3 11.1
endoplasmic reticulum Cellular component 2 7.4
## Cluster 39 (13 genes)
cellular amino acid metabolic process Biological process 1 7.7
cytoplasm Cellular component 9 69.2
endomembrane system Cellular component 2 15.4
endoplasmic reticulum Cellular component 1 7.7
Golgi apparatus Cellular component 1 7.7
## Cluster 55 (20 genes)
cellular amino acid metabolic process Biological process 3 15
cellular response to DNA damage stimulus Biological process 2 10
chromosome Cellular component 2 10
cytoplasm Cellular component 17 85
DNA recombination Biological process 2 10
## Cluster 90 (20 genes)
cytoplasm Cellular component 16 80
endomembrane system Cellular component 3 15
Golgi apparatus Cellular component 2 10
hydrolase activity Molecular function 2 10
ion transport Biological process 2 10

Go terms enrichment

We perform the enrichment of the genes in the clusters by employing the all GO terms annotation in the SGD online database. The first five entries of each cluster can be access as follows.

lapply(gene_clust$stats.Goterms_enrichment, function(x) head(x,5))
GO_ID Description Pvalue Count CountUniverse
## Cluster 2 (747 genes)
GO:0030427 site of polarized growth 0.0066 49 75
GO:0005886 plasma membrane 0.0177 84 141
GO:0009277 fungal-type cell wall 0.021 23 33
GO:0030312 external encapsulating structure 0.0245 24 35
GO:0005933 cellular bud 0.0287 41 65
## Cluster 3 (30 genes)
GO:1903293 phosphatase complex 0.0084 2 7
GO:0031984 organelle subcompartment 0.0084 7 117
GO:0005789 endoplasmic reticulum membrane 0.0176 5 75
GO:0031965 nuclear membrane 0.027 2 13
GO:0005798 Golgi-associated vesicle 0.0378 2 15
## Cluster 15 (29 genes)
GO:0031975 envelope 3.6E-15 20 140
GO:0005740 mitochondrial envelope 2.25E-14 16 94
GO:0005743 mitochondrial inner membrane 8.44E-14 14 66
GO:0005739 mitochondrion 1.287E-13 24 294
GO:0031090 organelle membrane 1.595E-08 19 268
## Cluster 16 (37 genes)
GO:0031083 BLOC-1 complex 0.000066 3 4
GO:0005657 replication fork 0.009434 2 6
GO:0044445 cytosolic part 0.046995 4 53
## Cluster 18 (46 genes)
GO:0005789 endoplasmic reticulum membrane 0.0097 7 75
GO:0005934 cellular bud tip 0.0135 4 29
GO:0031984 organelle subcompartment 0.0335 8 117
## Cluster 30 (27 genes)
GO:0005887 integral component of plasma membrane 0.011 3 25
GO:0044459 plasma membrane part 0.041 3 40
## Cluster 39 (13 genes)
GO:0098588 bounding membrane of organelle 0.033 4 177
GO:0044446 intracellular organelle part 0.035 8 623
## Cluster 55 (20 genes)
GO:0005759 mitochondrial matrix 3E-10 10 53
GO:0005739 mitochondrion 5.4E-10 17 294
GO:0000313 organellar ribosome 4.1057E-07 6 24
GO:0043233 organelle lumen 2.64737E-05 11 209
GO:0005763 mitochondrial small ribosomal subunit 0.000196584 3 9
## Cluster 90 (20 genes)
GO:0019005 SCF ubiquitin ligase complex 0.0025 2 6
GO:0000151 ubiquitin ligase complex 0.0208 2 17
GO:0005739 mitochondrion 0.028 8 294
GO:0031967 organelle envelope 0.043 4 113
GO:0031966 mitochondrial membrane 0.0473 4 105

Section 4: Network analysis

gene_net <- GeneNetwork(data=pre_proc$data.wide, data_Symb=pre_proc$data.wide_Symb)

The aim of the following network analysis is to group genes with same symbolic profile.

First we compute the Manhattan distance between al gene pairs. This measure is then used in the linkage algorithm (method=single) and then the unique partition is found by cutting the hierarchical tree at zero-distances.

For this analysis we filter the clusters as we do not consider the largest cluster as it contains genes with no phenotype as well as few smaller clusters of less than 10 genes.

We compute the empirical correlation matrix between genes (method = "pearson", use = "pairwise.complete.obs"), then we subset the correlation matrix based on the cluster filtering. Moreover, as we are interested only in positive correlations among genes we filter the correlation matrix based on an arbitrary correlation's thresold of 0.6 such that the clustering can be interpreted in terms of posivite correlation between gene profiles.

Network plot

We then generate the network from the described correlation matrix. And finally we can visualise the corresponding network plot.

gene_net$plot.pnet

plot.pnet

Impact and betweeness scores

We are now interested to highlight the most central genes. To do so we can consider two metrics i.e. the impact and the betweeness. From the empirical correlation matrix between genes we can compute the betweenness measure as the fraction of shortest paths that pass through each gene (node). Next a measure of impact can be computed as the L2 norm (Euclidean distance) of each gene. These two centrality measures can be then used togheter to cluster the genes as follow.

gene_net$plot.impact_betweenees

plot.impact_betweenees

We can also access to the impact and betweeness value as follow (only first 10 value shown).

head(gene_net$stats.impact_betweeness,10)
Knockout Impact Betweenness Position Cluster
YAL007C 4.2 67 Low impact, low betweenness Cluster 3 (30 genes): Mo(+)
YAL009W 5.6 575 Low impact, high betweenness Cluster 3 (30 genes): Mo(+)
YAL015C 4.1 1263 Low impact, high betweenness Cluster 3 (30 genes): Mo(+)
YAL017W 4.3 108 Low impact, low betweenness Cluster 3 (30 genes): Mo(+)
YAL020C 9 326 Low impact, low betweenness Cluster 7 (28 genes): Na(-)
YAL039C 12.7 789 High impact, high betweenness Cluster 15 (29 genes): K(-), Mn(-), Mo(-)
YAL042W 5.3 88 Low impact, low betweenness Cluster 16 (37 genes): Cd(+)
YAL044C 7.3 253 Low impact, low betweenness Cluster 18 (46 genes): Na(+)
YAL048C 13.3 76 High impact, low betweenness Cluster 15 (29 genes): K(-), Mn(-), Mo(-)
YAL062W 3.6 378 Low impact, low betweenness Cluster 18 (46 genes): Na(+)

We can also associate each cluster to low or high values of impact and betwenees based on the highest number of genes in that cathegory.

gene_net$stats.impact_betweeness_by_cluster
Cluster Position nGenes
Cluster 15 (29 genes): K(-), Mn(-), Mo(-) High impact, low betweenness 18
Cluster 16 (37 genes): Cd(+) Low impact, low betweenness 29
Cluster 18 (46 genes): Na(+) Low impact, low betweenness 34
Cluster 25 (19 genes): Cd(+), Na(-) Low impact, low betweenness 15
Cluster 3 (30 genes): Mo(+) Low impact, high betweenness 18
Cluster 30 (27 genes): Mn(+), Ni(+), Na(-) High impact, low betweenness 20
Cluster 39 (13 genes): S(-) Low impact, low betweenness 10
Cluster 55 (20 genes): K(-), Mn(-) High impact, low betweenness 15
Cluster 7 (28 genes): Na(-) Low impact, low betweenness 26
Cluster 90 (20 genes): Mo(-) Low impact, high betweenness 10

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R pipeline for the processing and analysis of Ionomics data

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