Chapter 5 Quantitative data

5.1.1 Label-free MS2: Spectral counting

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In spectral counting, one simply counts the number of quantified peptides that are assigned to a protein.

Figure 5.1: Spectral counting. Figure from the Pbase package.

5.1.2 Labelled MS2: Isobaric tagging

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Isobaric tagging refers to the labelling using isobaric tags, i.e. chemical tags that have the same mass and hence can’t be distinguished by the spectrometer. The peptides of different samples (4, 6, 10, 11 or 16) are labelled with different tags and combined prior to mass spectrometry acquisition. Given that they are isobaric, all identical peptides, irrespective of the tag and this the sample of origin, are co-analysed, up to fragmentation prior to MS2 analysis. During fragmentation, the isobaric tags fall of, fragment themselves, and result in a set of sample specific peaks. These specific peaks can be used to infer sample-specific quantitation, while the rest of the MS2 spectrum is used for identification.

Figure 5.2: iTRAQ 4-plex isobaric tagging. Tandem Mass Tags (TMT) offer up to 16 tags.

5.1.3 Label-free MS1: extracted ion chromatograms

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In label-free quantitation, the precursor peaks that match an identified peptide are integrated over retention time and the area under that extracted ion chromatogram is used to quantify that peptide in that sample.

Figure 5.3: Label-free quantitation. Figure credit Johannes Rainer.

5.1.4 Labelled MS1: SILAC

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In SILAC quantitation, sample are grown in a medium that contains heavy amino acids (typically arginine and lysine). All proteins grown in this heavy growth medium contain the heavy form of these amino acids. Two samples, one grown in heavy medium, and one grown in normal (light) medium are then combined and analysed together. The heavy peptides precursor peaks are systematically shifted compared to the light ones, and the ratio between the height of a heavy and light peaks can be used to calculate peptide and protein fold-changes.

Figure 5.4: Silac quantitation. Figure credit Wikimedia Commons.

These different quantitation techniques come with their respective benefits and distinct challenges, such as large quantities of raw data processing, data transformation and normalisation, missing values, and different underlying statistical models for the quantitative data (count data for spectral counting, continuous data for the others).

In terms of raw data quantitation in R/Bioconductor, most efforts have been devoted to MS2-level quantitation. Label-free XIC quantitation has been addressed in the frame of metabolomics data processing by the xcms infrastructure.

5.2.1 The QFeatures class

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While mass spectrometers acquire data for spectra/peptides, the biological entity of interest are the protein. As part of the data processing, we are thus required to aggregate low-level quantitative features into higher level data.

Figure 5.6: Conceptual representation of a QFeatures object and the aggregative relation between different assays.

We are going to start to familiarise ourselves with the QFeatures class implemented in the QFeatures package. The class is derived from the Bioconductor MultiAssayExperiment (Ramos et al. ⊕2017Ramos, Marcel, Lucas Schiffer, Angela Re, Rimsha Azhar, Azfar Basunia, Carmen Rodriguez Cabrera, Tiffany Chan, et al. 2017. “Software for the Integration of Multi-Omics Experiments in Bioconductor.” Cancer Research 77(21); e39-42.) (MAE) class. Let’s start by loading the QFeatures package.

library("QFeatures")

Next, we load the feat1 test data, which is composed of single assay of class SummarizedExperiment composed of 10 rows and 2 columns.

data(feat1)
feat1

## An instance of class QFeatures containing 1 assays:
##  [1] psms: SummarizedExperiment with 10 rows and 2 columns

Let’s perform some simple operations to familiarise ourselves with the QFeatures class:

• Extract the sample metadata using the colData() accessor (like you have previously done with SummarizedExperiment objects).

colData(feat1)

## DataFrame with 2 rows and 1 column
##        Group
##    <integer>
## S1         1
## S2         2

We can also further annotate the experiment by adding columns to the colData slot:

colData(feat1)$X <- c("X1", "X2")
feat1$Y <- c("Y1", "Y2")
colData(feat1)

## DataFrame with 2 rows and 3 columns
##        Group           X           Y
##    <integer> <character> <character>
## S1         1          X1          Y1
## S2         2          X2          Y2

• Extract the first (and only) assay composing this QFeatures data using the [[ operator (as you have done to extract elements of a list) by using the assay’s index or name.

feat1[[1]]

## class: SummarizedExperiment 
## dim: 10 2 
## metadata(0):
## assays(1): ''
## rownames(10): PSM1 PSM2 ... PSM9 PSM10
## rowData names(5): Sequence Protein Var location pval
## colnames(2): S1 S2
## colData names(0):

feat1[["psms"]]

## class: SummarizedExperiment 
## dim: 10 2 
## metadata(0):
## assays(1): ''
## rownames(10): PSM1 PSM2 ... PSM9 PSM10
## rowData names(5): Sequence Protein Var location pval
## colnames(2): S1 S2
## colData names(0):

• Extract the psms assay’s row data and quantitative values.

assay(feat1[[1]])

##       S1 S2
## PSM1   1 11
## PSM2   2 12
## PSM3   3 13
## PSM4   4 14
## PSM5   5 15
## PSM6   6 16
## PSM7   7 17
## PSM8   8 18
## PSM9   9 19
## PSM10 10 20

rowData(feat1[[1]])

## DataFrame with 10 rows and 5 columns
##            Sequence     Protein       Var      location      pval
##         <character> <character> <integer>   <character> <numeric>
## PSM1       SYGFNAAR       ProtA         1 Mitochondr...     0.084
## PSM2       SYGFNAAR       ProtA         2 Mitochondr...     0.077
## PSM3       SYGFNAAR       ProtA         3 Mitochondr...     0.063
## PSM4       ELGNDAYK       ProtA         4 Mitochondr...     0.073
## PSM5       ELGNDAYK       ProtA         5 Mitochondr...     0.012
## PSM6       ELGNDAYK       ProtA         6 Mitochondr...     0.011
## PSM7  IAEESNFPFI...       ProtB         7       unknown     0.075
## PSM8  IAEESNFPFI...       ProtB         8       unknown     0.038
## PSM9  IAEESNFPFI...       ProtB         9       unknown     0.028
## PSM10 IAEESNFPFI...       ProtB        10       unknown     0.097

5.2.2 Feature aggregation

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The central functionality of the QFeatures infrastructure is the aggregation of features into higher-level features while retaining the link between the different levels. This can be done with the aggregateFeatures() function.

The call below will

• operate on the psms assay of the feat1 objects;
• aggregate the rows of the assay following the grouping defined in the peptides row data variables;
• perform aggregation using the colMeans() function;
• create a new assay named peptides and add it to the feat1 object.

feat1 <- aggregateFeatures(feat1, i = "psms",
                           fcol = "Sequence",
                           name = "peptides",
                           fun = colMeans)
feat1

## An instance of class QFeatures containing 2 assays:
##  [1] psms: SummarizedExperiment with 10 rows and 2 columns 
##  [2] peptides: SummarizedExperiment with 3 rows and 2 columns

• Let’s convince ourselves that we understand the effect of feature aggregation and repeat the calculations manually and check the content of the new assay’s row data.

## SYGFNAAR
colMeans(assay(feat1[[1]])[1:3, ])

## S1 S2 
##  2 12

assay(feat1[[2]])["SYGFNAAR", ]

## S1 S2 
##  2 12

## ELGNDAYK
colMeans(assay(feat1[[1]])[4:6, ])

## S1 S2 
##  5 15

assay(feat1[[2]])["ELGNDAYK", ]

## S1 S2 
##  5 15

## IAEESNFPFIK
colMeans(assay(feat1[[1]])[7:10, ])

##   S1   S2 
##  8.5 18.5

assay(feat1[[2]])["IAEESNFPFIK", ]

##   S1   S2 
##  8.5 18.5

rowData(feat1[[2]])

## DataFrame with 3 rows and 4 columns
##                  Sequence     Protein      location        .n
##               <character> <character>   <character> <integer>
## ELGNDAYK         ELGNDAYK       ProtA Mitochondr...         3
## IAEESNFPFIK IAEESNFPFI...       ProtB       unknown         4
## SYGFNAAR         SYGFNAAR       ProtA Mitochondr...         3

We can now aggregate the peptide-level data into a new protein-level assay using the colMedians() aggregation function.

feat1 <- aggregateFeatures(feat1, i = "peptides",
                           fcol = "Protein",
                           name = "proteins",
                           fun = colMedians)
feat1

## An instance of class QFeatures containing 3 assays:
##  [1] psms: SummarizedExperiment with 10 rows and 2 columns 
##  [2] peptides: SummarizedExperiment with 3 rows and 2 columns 
##  [3] proteins: SummarizedExperiment with 2 rows and 2 columns

assay(feat1[["proteins"]])

##        S1   S2
## ProtA 3.5 13.5
## ProtB 8.5 18.5

5.2.3 Subsetting and filtering

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The link between the assays becomes apparent when we now subset the assays for protein A as shown below or using the subsetByFeature() function. This creates a new instance of class QFeatures containing assays with the expression data for protein, its peptides and their PSMs.

feat1["ProtA", , ]

## An instance of class QFeatures containing 3 assays:
##  [1] psms: SummarizedExperiment with 6 rows and 2 columns 
##  [2] peptides: SummarizedExperiment with 2 rows and 2 columns 
##  [3] proteins: SummarizedExperiment with 1 rows and 2 columns

The filterFeatures() function can be used to filter rows the assays composing a QFeatures object using the row data variables. We can for example retain rows that have a pval < 0.05, which would only keep rows in the psms assay because the pval is only relevant for that assay.

filterFeatures(feat1, ~ pval < 0.05)

## 'pval' found in 1 out of 3 assay(s)
## No filter applied to the following assay(s) because one or more filtering variables are missing in the rowData: peptides, proteins.
## You can control whether to remove or keep the features using the 'keep' argument (see '?filterFeature').

## An instance of class QFeatures containing 3 assays:
##  [1] psms: SummarizedExperiment with 4 rows and 2 columns 
##  [2] peptides: SummarizedExperiment with 0 rows and 2 columns 
##  [3] proteins: SummarizedExperiment with 0 rows and 2 columns

filterFeatures(feat1, ~ pval < 0.05, keep = TRUE)

## 'pval' found in 1 out of 3 assay(s)
## No filter applied to the following assay(s) because one or more filtering variables are missing in the rowData: peptides, proteins.
## You can control whether to remove or keep the features using the 'keep' argument (see '?filterFeature').

## An instance of class QFeatures containing 3 assays:
##  [1] psms: SummarizedExperiment with 4 rows and 2 columns 
##  [2] peptides: SummarizedExperiment with 3 rows and 2 columns 
##  [3] proteins: SummarizedExperiment with 2 rows and 2 columns

On the other hand, if we filter assay rows for those that localise to the mitochondrion, we retain the relevant protein, peptides and PSMs.

filterFeatures(feat1, ~ location == "Mitochondrion")

## 'location' found in 3 out of 3 assay(s)

## An instance of class QFeatures containing 3 assays:
##  [1] psms: SummarizedExperiment with 6 rows and 2 columns 
##  [2] peptides: SummarizedExperiment with 2 rows and 2 columns 
##  [3] proteins: SummarizedExperiment with 1 rows and 2 columns

filterFeatures(feat1, ~ location != "Mitochondrion")

## 'location' found in 3 out of 3 assay(s)

## An instance of class QFeatures containing 3 assays:
##  [1] psms: SummarizedExperiment with 4 rows and 2 columns 
##  [2] peptides: SummarizedExperiment with 1 rows and 2 columns 
##  [3] proteins: SummarizedExperiment with 1 rows and 2 columns

You can refer to the Quantitative features for mass spectrometry data vignette and the QFeatures manual page for more details about the class.

5.4.1 Missing values

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Missing values can be highly frequent in proteomics. There are two reasons supporting the existence of missing values, namely biological or technical.

1. Values that are missing due to the absence (or extremely low concentration) of a protein are observed for biological reasons, and their pattern aren’t random (MNAR). A protein missing due to the suppression of its expression will not be missing at random: it will be missing in the condition in which it was suppressed, and be present in the condition where it is expressed.

2. Due to its data-dependent acquisition, mass spectrometry isn’t capable of assaying all peptides in a sample. Peptides that are less abundant than some of their co-eluting ions, peptides that do not ionise well or peptides that do not get identified might be sporadically missing in the final quantitation table, despite their presence in the biological samples. Their absence patterns are (completely) random (MAR or MCAR) in such cases.

Often, third party software that produce quantitative data use zeros instead of properly reporting missing values. We can use the zeroIsNA() function to replace the 0 by NA values in our cptac_se object and then explore the missing data patterns across columns and rows.

cptac_se <- zeroIsNA(cptac_se)
nNA(cptac_se)

## $nNA
## DataFrame with 1 row and 2 columns
##         nNA       pNA
##   <integer> <numeric>
## 1     31130  0.452497
## 
## $nNArows
## DataFrame with 11466 rows and 3 columns
##                name       nNA       pNA
##         <character> <integer> <numeric>
## 1     AAAAGAGGAG...         4  0.666667
## 2         AAAALAGGK         0  0.000000
## 3        AAAALAGGKK         0  0.000000
## 4     AAADALSDLE...         0  0.000000
## 5     AAADALSDLE...         0  0.000000
## ...             ...       ...       ...
## 11462 YYSIYDLGNN...         6  1.000000
## 11463 YYTFNGPNYN...         3  0.500000
## 11464    YYTITEVATR         4  0.666667
## 11465 YYTVFDRDNN...         6  1.000000
## 11466 YYTVFDRDNN...         6  1.000000
## 
## $nNAcols
## DataFrame with 6 rows and 3 columns
##          name       nNA       pNA
##   <character> <integer> <numeric>
## 1        6A_7      4743  0.413658
## 2        6A_8      5483  0.478196
## 3        6A_9      5320  0.463980
## 4        6B_7      4721  0.411739
## 5        6B_8      5563  0.485174
## 6        6B_9      5300  0.462236

Figure 5.8: Distribution of missing value (white). Peptides row with more missing values are moved towards the top of the figure.

Let’s now explore these missing values:

• Explore the number or proportion of missing values across peptides and samples of the cptac_se data.

barplot(nNA(cptac_se)$nNAcols$pNA)

table(nNA(cptac_se)$nNArows$nNA)

## 
##    0    1    2    3    4    5    6 
## 4059  990  884  717  934  807 3075

• Remove rows that have too many missing values. You can do this by hand or using the filterNA() function.

## remove rows that have 4 or more NAs out of 6
cptac_se <- filterNA(cptac_se, pNA = 4/6)

5.4.2 Imputation

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Imputation is the technique of replacing missing data with probable values. This can be done with impute() method. As we have discussed above, there are however two types of missing values in mass spectrometry-based proteomics, namely data missing at random (MAR), and data missing not at random (MNAR). These two types of missing data, those missing at random, and those missing not at random, need to be imputed with different types of imputation methods (Lazar et al. ⊕2016Lazar, C, L Gatto, M Ferro, C Bruley, and T Burger. 2016. “Accounting for the Multiple Natures of Missing Values in Label-Free Quantitative Proteomics Data Sets to Compare Imputation Strategies.” J Proteome Res 15 (4): 1116–25. https://doi.org/10.1021/acs.jproteome.5b00981.).

Figure 5.9: Mixed imputation method. Black cells represent presence of quantitation values and light grey corresponds to missing data. The two groups of interest are depicted in green and blue along the heatmap columns. Two classes of proteins are annotated on the left: yellow are proteins with randomly occurring missing values (if any) while proteins in brown are candidates for non-random missing value imputation.

Figure 5.10: Effect of the nature of missing values on their imputation. Root-mean-square error (RMSE) observations standard deviation ratio (RSR), KNN and MinDet imputation. Lower (blue) is better.

Generally, it is recommended to use hot deck methods (nearest neighbour (left), maximum likelihood, …) when data are missing at random.Conversely, MNAR features should ideally be imputed with a left-censor (minimum value (right), but not zero, …) method.

There are various methods to perform data imputation, as described in ?impute. The imp4p package contains additional functionality, including some to estimate the randomness of missing data.

The general syntax for imputation is shown below, using the se_na2 object as an example:

data(se_na2)
## impute missing values using knn imputation
impute(se_na2, method = "knn")

## Imputing along margin 1 (features/rows).

## Warning in knnimp(x, k, maxmiss = rowmax, maxp = maxp): 12 rows with more than 50 % entries missing;
##  mean imputation used for these rows

## class: SummarizedExperiment 
## dim: 689 16 
## metadata(3): MSnbaseFiles MSnbaseProcessing MSnbaseVersion
## assays(1): ''
## rownames(689): AT1G09210 AT1G21750 ... AT4G11150 AT4G39080
## rowData names(2): nNA randna
## colnames(16): M1F1A M1F4A ... M2F8B M2F11B
## colData names(1): nNA

impute(se_na2, "mixed",
       randna = rowData(se_na2)$randna,
       mar = "knn", mnar = "zero")

## class: SummarizedExperiment 
## dim: 689 16 
## metadata(3): MSnbaseFiles MSnbaseProcessing MSnbaseVersion
## assays(1): ''
## rownames(689): AT1G09210 AT1G21750 ... AT4G11150 AT4G39080
## rowData names(2): nNA randna
## colnames(16): M1F1A M1F4A ... M2F8B M2F11B
## colData names(1): nNA

imp1 <- impute(se_na2, method = "knn")

## Imputing along margin 1 (features/rows).

## Warning in knnimp(x, k, maxmiss = rowmax, maxp = maxp): 12 rows with more than 50 % entries missing;
##  mean imputation used for these rows

imp2 <- impute(se_na2, method = "bpca")

## Imputing along margin 1 (features/rows).

summary(abs(assay(imp1)[is.na(assay(se_na2))] - assay(imp2)[is.na(assay(se_na2))]))

##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## 5.332e-05 6.594e-03 1.535e-02 2.315e-02 2.855e-02 2.579e-01

summary(as.numeric(na.omit(assay(se_na2))))

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.0170  0.1865  0.2440  0.2500  0.3080  0.6587

► Question

When assessing the impact of missing value imputation on real data, one can’t use the strategy above. Another useful approach is to assess the impact of the imputation method on the distribution of the quantitative data. For instance, here is the intensity distribution of the se_na2 data. Verify the effect of applying knn, zero, MinDet and bpca on this distribution.

plot(density(na.omit(assay(se_na2))))

Figure 5.11: Intensity disctribution of the naset data.

cls <- c("black", "red", "blue", "steelblue", "orange")
plot(density(na.omit(assay(se_na2))), col = cls[1])
lines(density(assay(impute(se_na2, method = "knn"))), col = cls[2])

## Imputing along margin 1 (features/rows).

## Warning in knnimp(x, k, maxmiss = rowmax, maxp = maxp): 12 rows with more than 50 % entries missing;
##  mean imputation used for these rows

lines(density(assay(impute(se_na2, method = "zero"))), col = cls[3])
lines(density(assay(impute(se_na2, method = "MinDet"))), col = cls[4])

## Imputing along margin 2 (samples/columns).

lines(density(assay(impute(se_na2, method = "bpca"))), col = cls[5])

## Imputing along margin 1 (features/rows).

legend("topright", legend = c("orig", "knn", "zero", "MinDet", "bpca"),
       col = cls, lwd = 2, bty = "n")

Tip: When downstream analyses permit, it might be safer not to impute data and deal explicitly with missing values. Indeed missing data imputation is not straightforward, and is likely to dramatically fail when a high proportion of data is missing (10s of %). It is possible to keep NAs when performing hypothesis tests77 Still, it is recommended to explore missingness as part of the exploratory data analysis., but (generally) not to perform a principal component analysis.

5.4.3 Identification quality control

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As discussed in the previous chapter, PSMs are deemed relevant after comparison against hits from a decoy database. The origin of these hits is recorded with + in the Reverse variable:

table(rowData(cptac_se)$Reverse)

## 
##         + 
## 7572   12

Similarly, a proteomics experiment is also searched against a database of contaminants:

table(rowData(cptac_se)$Potential.contaminant)

## 
##         + 
## 7558   26

Let’s visualise some of the cptac’s metadata using standard ggplot2 code:

rowData(cptac_se) %>%
    as_tibble() %>%
    ggplot(aes(x = Score, colour = Reverse)) +
    geom_density()

rowData(cptac_se) %>%
    as_tibble() %>%
    ggplot(aes(x = PEP, colour = Reverse)) +
    geom_density()

Note: it is also possible to compute and visualise protein groups as connected components starting from a quantitative dataset such as a SummarizedExperiment. See the Using quantitative data section in the Understanding protein groups with adjacency matrices vignette.

5.4.4 Creating the QFeatures data

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We can now create our QFeatures object using the SummarizedExperiment as shown below.

cptac <- QFeatures(list(peptides = cptac_se))
cptac

## An instance of class QFeatures containing 1 assays:
##  [1] peptides: SummarizedExperiment with 7584 rows and 6 columns

We should also assign the QFeatures column data with the SummarizedExperiment slot.

colData(cptac) <- colData(cptac_se)

Note that it is also possible to directly create a QFeatures object with the readQFeatures() function and the same arguments as the readSummarizedExperiment() used above. In addition, most functions used above and below work on single SummarizedExperiment objects or assays within a QFeatures object.

5.4.5 Filtering out contaminants and reverse hits

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cptac <-
    cptac %>%
    filterFeatures(~ Reverse != "+") %>%
    filterFeatures(~ Potential.contaminant != "+") %>%
    filterFeatures(~ PEP < 0.05)

## 'Reverse' found in 1 out of 1 assay(s)

## 'Potential.contaminant' found in 1 out of 1 assay(s)

## 'PEP' found in 1 out of 1 assay(s)

5.4.6 Log-transformation and normalisation

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The two code chunks below log-transform and normalise using the assay i as input and adding a new one names as defined by name.

cptac <- logTransform(cptac, i = "peptides",
                      name = "log_peptides")

cptac <- normalize(cptac, i = "log_peptides",
                   name = "lognorm_peptides",
                   method = "center.median")

► Solution

par(mfrow = c(1, 3))
limma::plotDensities(assay(cptac[["peptides"]]))
limma::plotDensities(assay(cptac[["log_peptides"]]))
limma::plotDensities(assay(cptac[["lognorm_peptides"]]))

Figure 5.12: Three peptide level assays: raw data, log transformed and normalised.

5.4.7 Aggregation

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cptac <-
    aggregateFeatures(cptac,
                      "lognorm_peptides",
                      name = "proteins_med",
                      fcol = "Leading.razor.protein",
                      fun = colMedians,
                      na.rm = TRUE)

Looking at the .n row variable computed during the aggregation, we see that most proteins result from the aggregation of 5 peptides or less, while very few proteins are accounted for by tens of peptides.

table(rowData(cptac[["proteins_med"]])$.n)

## 
##   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20 
## 327 234 167 132  84  73  62  49  49  29  29  24  20  13  15  12   4   6  11   5 
##  21  22  23  24  25  26  28  29  30  31  32  34  37  38  39  42  51  52  62 
##   7   4   7   2   2   3   1   3   1   2   2   1   1   1   1   2   1   1   1

5.4.8 Principal component analysis

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library("factoextra")

pca_pep <-
    cptac[["lognorm_peptides"]] %>%
    filterNA() %>%
    assay() %>%
    t() %>%
    prcomp(scale = TRUE, center = TRUE) %>%
    fviz_pca_ind(habillage = cptac$condition, title = "Peptides")

pca_prot <-
    cptac[["proteins_med"]] %>%
    filterNA() %>%
    assay() %>%
    t() %>%
    prcomp() %>%
    fviz_pca_ind(habillage = cptac$condition,
                 title = "Proteins (median aggregation)")

library("patchwork")
pca_pep + pca_prot

Figure 5.13: Peptide and protein level PCA analyses.

5.4.9 Visualisation

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Below, we use the longFormat() function to extract the quantitative and row data in a long format, that can be directly reused by the tidyverse tools.

longFormat(cptac["P02787ups|TRFE_HUMAN_UPS", ,
                 c("lognorm_peptides", "proteins_med")]) %>%
    as_tibble() %>%
    mutate(condition = ifelse(grepl("A", colname), "A", "B")) %>%
    ggplot(aes(x = colname, y = value, colour = rowname, shape = condition)) +
    geom_point(size = 3) +
    geom_line(aes(group = rowname)) +
    facet_grid(~ assay) +
    ggtitle("P02787ups|TRFE_HUMAN_UPS")

Figure 5.14: Peptide and protein expression profile.

We can also visualise the assays withing a QFeatures object and their relation.

plot(cptac)

normalize(cptac, "log_peptides",
          name = "logquantiles_peptides",
          method = "quantiles.robust") |>
    aggregateFeatures(
        "logquantiles_peptides",
        name = "proteins_med2",
        fcol = "Leading.razor.protein",
        fun = colMedians,
        na.rm = TRUE) |>
    plot()

5.4.10 Statistical analysis

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R in general and Bioconductor in particular are well suited for the statistical analysis of quantitative proteomics data. Several packages provide dedicated resources for proteomics data:

• MSstats and MSstatsTMT: A set of tools for statistical relative protein significance analysis in Data dependent (DDA), SRM, Data independent acquisition (DIA) and TMT experiments.

• msmsTests: Statistical tests for label-free LC-MS/MS data by spectral counts, to discover differentially expressed proteins between two biological conditions. Three tests are available: Poisson GLM regression, quasi-likelihood GLM regression, and the negative binomial of the edgeR package. All can be readily applied on MSnSet instances produced, for example by MSnID.

• DEP provides an integrated analysis workflow for the analysis of mass spectrometry proteomics data for differential protein expression or differential enrichment.

• MSqRob: The MSqRob package allows a user to do quantitative protein-level statistical inference on LC-MS proteomics data. More specifically, our package makes use of peptide-level input data, thus correcting for unbalancedness and peptide-specific biases. As previously shown (Goeminne et al. (2015)), this approach is both more sensitive and specific than summarizing peptide-level input to protein-level values. Model estimates are stabilized by ridge regression, empirical Bayes variance estimation and downweighing of outliers. The new version makes use of the QFeatures infrastructure. Label-free proteomics data are supported. msqrob2, and TMT workflows with msqrob2tmt.

• proDA accounts for missing values in label-free mass spectrometry data without imputation. The package implements a probabilistic dropout model that ensures that the information from observed and missing values are properly combined. It adds empirical Bayesian priors to increase power to detect differentially abundant proteins.

Others, while not specfic to proteomics, are also recommended, such as the limma package. When analysing spectral counting data, methods for high throughput sequencing data are applicable. Below, we illustrate how to apply a typical edgeR test to count data using the msms.edgeR function from the msmsTests package.

Below, we are going to perform our statistical analysis on the protein data using limma.

prots <- getWithColData(cptac, "proteins_med")

## Warning: 'experiments' dropped; see 'drops()'

## Warning: Ignoring redundant column names in 'colData(x)':

The limma package is the precursor package that enables the consistent application of linear models to normalliy distributed omics data in general, and microarrays in particular.

The limma package implements an empirical Bayes method that borrows information across features to estimate the standard error and calculate (so called moderated) t statistics. This approach is demonstrably more powerful that a standard t-tests when the number of samples is low.

The code chunk below illustrates how to set up the model, fit it, and apply the empirical Bayes moderation.

library("limma")
design <- model.matrix(~ prots$condition)
fit <- lmFit(assay(prots), design)

## Warning: Partial NA coefficients for 25 probe(s)

fit <- eBayes(fit)

Finally, the topTable() function is used the extract the results for the coefficient of interest.

res <-
    topTable(fit, coef = "prots$condition6B", number = Inf) %>%
    rownames_to_column("protein") %>%
    as_tibble() %>%
    mutate(TP = grepl("ups", protein))

Note the warning about partial NA coefficients for 23 probes:

na_coefs <-
    filter(res, is.na(t)) %>%
    pull(protein)
assay(prots[na_coefs, ])

##                                6A_7      6A_8       6A_9       6B_7       6B_8
## P00167ups|CYB5_HUMAN_UPS        NaN       NaN        NaN -0.7840558 -2.0282987
## P01112ups|RASH_HUMAN_UPS        NaN       NaN        NaN -1.5564896        NaN
## P05413ups|FABPH_HUMAN_UPS       NaN       NaN        NaN -3.3419480        NaN
## P08758ups|ANXA5_HUMAN_UPS       NaN       NaN        NaN -2.7973872 -2.0137585
## sp|P06704|CDC31_YEAST           NaN       NaN        NaN -1.2032046 -2.1252371
## sp|P25574|EMC1_YEAST      -1.506177 -1.983737 -0.7795009        NaN        NaN
## sp|P32608|RTG2_YEAST            NaN       NaN        NaN        NaN -4.4424189
## sp|P32769|HBS1_YEAST            NaN -1.384031 -0.7285780        NaN        NaN
## sp|P34217|PIN4_YEAST            NaN       NaN        NaN -0.8378614 -0.1316397
## sp|P34237|CASP_YEAST            NaN       NaN        NaN -1.5645172 -1.6600291
## sp|P38166|SFT2_YEAST      -1.585685 -1.076707        NaN        NaN        NaN
## sp|P40056|GET2_YEAST            NaN -1.091696 -1.4014211        NaN        NaN
## sp|P40533|TED1_YEAST            NaN       NaN        NaN -2.0491876        NaN
## sp|P43582|WWM1_YEAST            NaN       NaN        NaN -0.5538711 -0.7360990
## sp|P46965|SPC1_YEAST            NaN -3.428771 -3.6321984        NaN        NaN
## sp|P48363|PFD3_YEAST            NaN       NaN        NaN -0.1904905        NaN
##                                 6B_9
## P00167ups|CYB5_HUMAN_UPS  -1.1230809
## P01112ups|RASH_HUMAN_UPS  -1.5618192
## P05413ups|FABPH_HUMAN_UPS -3.8907081
## P08758ups|ANXA5_HUMAN_UPS -2.0894752
## sp|P06704|CDC31_YEAST     -1.5844104
## sp|P25574|EMC1_YEAST             NaN
## sp|P32608|RTG2_YEAST      -2.7873186
## sp|P32769|HBS1_YEAST             NaN
## sp|P34217|PIN4_YEAST      -0.1989392
## sp|P34237|CASP_YEAST      -1.6877463
## sp|P38166|SFT2_YEAST             NaN
## sp|P40056|GET2_YEAST             NaN
## sp|P40533|TED1_YEAST      -1.7474812
## sp|P43582|WWM1_YEAST      -0.7207043
## sp|P46965|SPC1_YEAST             NaN
## sp|P48363|PFD3_YEAST      -0.5087747
##  [ reached getOption("max.print") -- omitted 9 rows ]

We can now visualise the results using a volcano plot:

res %>%
    ggplot(aes(x = logFC, y = -log10(adj.P.Val))) +
    geom_point(aes(colour = TP)) +
    geom_vline(xintercept = c(-1, 1)) +
    geom_hline(yintercept = -log10(0.05)) +
    scale_color_manual(values = c("black","red"))

## Warning: Removed 25 rows containing missing values or values outside the scale
## range (`geom_point()`).

Figure 5.15: Volcano plot highlighing spiked-in proteins in red.

Using the pipeline described above, we would identify a single differentially expressed protein at an 5 percent FDR but miss out the other 36 expected spike-in proteins.

We can assess our results in terms of true/false postitves/negatives:

• True positives: 1
• False positives: 0
• True negatives: 1330
• False negatives: 32