proDA

The goal of proDA is to identify differentially abundant proteins in label-free mass spectrometry data. The main challenge of this data are the many missing values. The missing values don’t occur randomly but especially at low intensities. This means that they cannot just be ignored. Existing methods have mostly focused on replacing the missing values with some reasonable number (“imputation”) and then run classical methods. But imputation is problematic because it obscures the amount of available information. Which in turn can lead to over-confident predictions.

proDA on the other hand does not impute missing values, but constructs a probabilistic dropout model. For each sample it fits a sigmoidal dropout curve. This information can then be used to infer means across samples and the associated uncertainty, without the intermediate imputation step. proDA supports full linear models with variance and location moderation.

For full details, please see our preprint:

Constantin Ahlmann-Eltze and Simon Anders: proDA: Probabilistic Dropout Analysis for Identifying Differentially Abundant Proteins in Label-Free Mass Spectrometry. biorXiv 661496 (Jun 2019)

Installation

proDA is implemented as an R package.

You can install it from Bioconductor by typing the following commands into R:

if(!requireNamespace("BiocManager", quietly = TRUE))
    install.packages("BiocManager")
BiocManager::install("proDA")

To get the latest development version from GitHub, you can use the devtools package:

The pkgdown documentation for the package is available on https://const-ae.github.io/proDA/reference.


In the following section, I will give a very brief overview on the main functionality of the proDA package, aimed at experienced R users. New users are advised to skip this “quickstart” and to go directly to section 1.3, where I give a complete walkthrough and explain in detail, what steps are necessary for the analysis of label-free mass spectrometry data.

Quickstart

The three steps that are necessary to analyze the data are

  1. Load the data (see vignette on loading MaxQuant output files)
  2. Fit the probabilistic dropout model (proDA())
  3. Test in which proteins the coefficients of the model differ (test_diff())
# Load the package
library(proDA)
# Generate some dataset with known structure
syn_dataset <- generate_synthetic_data(n_proteins = 100, n_conditions = 2)

# The abundance matrix
syn_dataset$Y[1:5, ]
#>           Condition_1-1 Condition_1-2 Condition_1-3 Condition_2-1 Condition_2-2 Condition_2-3
#> protein_1            NA            NA      18.88592            NA      18.72059      20.06119
#> protein_2      21.37123      20.53557      18.83239      20.41027      21.73266      21.16719
#> protein_3            NA      18.77742      18.98681            NA            NA      19.20291
#> protein_4      25.44209      25.15151      25.38142      25.22754      24.95229      24.97185
#> protein_5      23.46724      23.15808      23.21357      23.29562      23.25999      23.57925

# Assignment of the samples to the two conditions
syn_dataset$groups
#> [1] Condition_1 Condition_1 Condition_1 Condition_2 Condition_2 Condition_2
#> Levels: Condition_1 Condition_2

# Fit the probabilistic dropout model
fit <- proDA(syn_dataset$Y, design = syn_dataset$groups)

# Identify which proteins differ between Condition 1 and 2
test_diff(fit, `Condition_1` - `Condition_2`, sort_by = "pval", n_max = 5)
#>            name         pval     adj_pval      diff t_statistic        se df avg_abundance n_approx
#> 96   protein_96 2.480632e-06 0.0002480632  8.617917    39.39412 0.2187615  4      22.16131 4.022503
#> 95   protein_95 1.025837e-05 0.0005129184 -4.839748   -27.59434 0.1753892  4      21.18996 6.000000
#> 91   protein_91 5.279731e-05 0.0017599104 -4.172440   -18.26958 0.2283818  4      19.09951 4.014839
#> 98   protein_98 2.364378e-04 0.0047851432  4.351147    12.48889 0.3484013  4      21.64483 6.000000
#> 100 protein_100 2.392572e-04 0.0047851432  2.494872    12.45115 0.2003729  4      21.32955 4.954439
#>     n_obs
#> 96      4
#> 95      6
#> 91      4
#> 98      6
#> 100     5

Other helpful functions for quality control are median_normalization() and dist_approx().

proDA Walkthrough

proDA is an R package that implements a powerful probabilistic dropout model to identify differentially abundant proteins. The package was specifically designed for label-free mass spectrometry data and in particular how to handle the many many missing values.

But all this is useless if you cannot load your data and get it into a shape that is useable. In the next section, I will explain how to load the abundance matrix and bring it into a useful form. The steps that I will go through are

  1. Load the proteinGroups.txt MaxQuant output table
  2. Extract the intensity columns and create the abundance matrix
  3. Replace the zeros with NAs and take the log2() of the data
  4. Normalize the data using median_normalization()
  5. Inspect sample structure with a heatmap of the distance matrix (dist_approx())
  6. Fit the probabilistic dropout model with proDA()
  7. Identify differentially abundant proteins with test_diff()

Load Data

I will now demonstrate how to load a MaxQuant output file. For more information about other approaches for loading the data, please take a look at the vignette on loading data.

MaxQuant is one of the most popular tools for handling raw MS data. It produces a number of files. The important file that contains the protein intensities is called proteinGroups.txt. It is a large table with detailed information about the identification and quantification process for each protein group (which I will from now on just call “protein”).

This package comes with an example proteinGroups.txt file, located in the package folder. The file contains the reduced output from an experiment studying the different DHHCs in Drosophila melanogaster.

system.file("extdata/proteinGroups.txt", package = "proDA", mustWork = TRUE)
#> [1] "/Users/ahlmanne/Library/R/3.6/library/proDA/extdata/proteinGroups.txt"

In this example, I will use the base R functions to load the data, because they don’t require any additional dependencies.

# Load the table into memory
maxquant_protein_table <- read.delim(
    system.file("extdata/proteinGroups.txt", package = "proDA", mustWork = TRUE),
    stringsAsFactors = FALSE
)

As I have mentioned, the table contains a lot of information (359 columns!!), but we are first of all interested in the columns which contain the measured intensities.

After extracting the bits from the table we most care about, we will have to modify it.

Firstly, MaxQuant codes missing values as 0. This is misleading, because the actual abundance probably was not zero, but just some value too small to be detected by the mass spectrometer. Accordingly, I will replace all 0 with NA.

Secondly, the raw intensity values have a linear mean-variance relation. This is undesirable, because a change of x units can be a large shift if the mean is small or irrelevant if the mean is large. Luckily, to make the mean and variance independent, we can just log the intensities. Now a change of x units is as significant for highly abundant proteins, as it is for low abundant ones.

Quality Control

Quality control (QC) is essential for a successful bioinformatics analysis, because any dataset shows some unwanted variation or could even contain more serious error like for example a sample swap.

Often we start with normalizing the data to remove potential sample specific effects. But already this step is challenging, because the missing values cannot easily be corrected for. Thus, a first helpful plot is to look how many missing values are in each sample.

We can see that the number of missing values differs substantially between samples (between 30% and 90%) in this dataset. If we take a look at the intensity distribution for each sample, we see that they differ substantially as well.

Note that, the intensity distribution is shifted upwards for samples which also have a large number of missing values (for example the last one). This agrees with our idea that small values are more likely to be missing. On the other hand, this also demonstrates why normalization methods such as quantile normalization, which distort the data until all the distributions are equal, are problematic. I will apply the more “conservative” median normalization, which ignores the missing values and transforms the values so that the median difference between the sample and average across all other samples is zero.

An important tool to identify sample swaps and outliers in the dataset is to look at the sample distance matrix. It shows the distances of samples A to B, A to C, B to C and so on.

The base R dist() function can not handle input data that contains missing values, so we might be tempted to just replace the missing values with some realistic numbers and calculate the distance on the completed dataset. But choosing a good replacement value is challenging and can also be misleading because the samples with many missing values would be considered too close.

Instead proDA provides the dist_approx() function that takes either a fitted model (ie. the output from proDA()) or a simple matrix (for which it internally calls proDA()) and estimates the expected distance without imputing the missing values. In addition, it reports the associated uncertainty with every estimate. The estimates for samples with many missing values will be uncertain, allowing the data analyst to discount them.

da <- dist_approx(normalized_abundance_matrix)

dist_approx() returns two elements the mean of the estimate and the associated sd. In the next step I will plot the heatmap for three different conditions, adding the 95% confidence interval as text to each cell.

Fit the Probabilistic Dropout Model

In the next step, we will fit the actual linear probabilistic dropout model to the normalized data. But before we start, I will create a data.frame that contains some additional information on each sample, in particular to which condition that sample belongs.

Now we can call the proDA() function to actually fit the model. We specify the design using the formula notation, referencing the condition column in the sample_info_df data.frame that we have just created. In addition, I specify that I want to use the S2R condition as the reference because I know that it was the negative control and this way automatically all coefficients measure how much each condition differs from the negative control.

The proDAFit object prints a number of useful information about the convergence of the model, the size of the dataset, the number of missing values, and the inferred hyper parameters.

To make it easy to find available methods on the proDAFit object, the $-operator is overloaded and shows a list of possible functions:

Screenshot from Rstudio suggesting the available functions

Screenshot from Rstudio suggesting the available functions

# Equivalent to feature_parameters(fit)
fit$feature_parameters
#>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      n_approx
#> Q8IP47;Q9VJP8;Q9V435;A0A023GPQ3;Q2PDT6;Q7K540                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        12.00100
#> A0A023GPV6;A8JV04;Q7YU03                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             12.00100
#> A0A023GQA5;P24156                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    19.27983
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#> A0A0B4JCT8;Q9V780                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    12.00100
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#> A0A0B4JCW4;Q9VHJ8;Q95U38                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             28.92211
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#> E1JIU2;Q9VCQ0;A0A0B4JCZ2;A8JR87;A0A0B4KH86                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           12.00100
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#> A0A0B4JD11;Q9NJH0                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    34.50696
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#> A0A0B4JD46;Q8T8R1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    33.97973
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#> A0A0B4JDA0;Q9VF03                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    14.58983
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#> A0A0B4JDG5;Q8IMZ9                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    19.68847
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#> Q9VEZ3;E1JIM4;A0A0B4K664;A0A0B4K700                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  17.49006
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#> A0A0B4K6D2;Q9VH95                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    28.98317
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#> Q9VC62;A0A0B4KGU9;Q7KS16;A0A0B4K6F9                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  12.00100
#> A0A0B4K6G6;Q9VG05                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    36.00000
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#> A0A0B4K6J3;Q8IMW5;A0A0C4DHB7;A0A0B4K7S6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              12.00100
#> A0A0B4K6K7;Q9VI55;Q9VI55-2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           22.56518
#> A0A0B4K6K9;A0A0B4K7Y7;Q9VAW5-1;Q9VAW5;Q9VAW5-2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       27.52419
#> Q9VEF7;A0A0B4KHP1;A0A0B4K6L3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         12.00100
#> A0A0B4K6L4;Q27601                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    12.00100
#> A0A0B4K6N1;Q8MLY8                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    36.00000
#> A0A0B4K6N7;Q9VE34;Q9VE34-2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           34.14228
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#> D0Z768;A0A0B4K6T1;A0A0B4K7U5;E1JH02;A0A0B4KFC5;Q86S05-3;Q86S05-2;Q86S05                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              12.00100
#> A0A0B4K6T7                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           12.00100
#> A0A0B4K6U2;E1JIJ7;Q8INH9                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             12.00100
#> A0A0B4K6U6;Q08473-3;Q08473-2;Q08473;Q08473-4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         17.64724
#> A0A0B4KHW3;A0A0B4K6V1;Q9VA73-3;Q9VA73-2;Q9VA73                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       22.13184
#> A0A0B4K6W1;P08970                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    20.21045
#> A0A0B4K6W2;A0A0B4K7S0;P55824-3;P55824                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                32.25299
#> A0A0B4K6X7;A1Z8J0                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    12.00100
#> Q9VHK3;A0A0B4K6Y7;Q8INQ0;A8JQV7;Q9VHK4;B7Z0U1;Q8MQQ3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 16.28860
#> A0A0B4LHK4;A0A0B4KHZ8;A0A0B4KHR8;A0A0B4K725;Q9VCA8                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   33.14310
#> A0A0B4LF93;A1Z928;A1Z927;A0A0B4LF82;Q5U0Y0;A0A0B4K765                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                12.00100
#> A0A0B4K7A5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           36.00000
#> A0A0B4K7G4;P13469                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    29.01701
#> B7YZQ7;A0A0B4K7G9;O77460                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             12.00100
#> A0A0B4K7H0;Q7KN74                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    12.00100
#> Q9VBU7;A0A0B4K7J2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    33.88476
#> Q95U21;Q7JQ36;A0A0B4K7J3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             17.13504
#> A0A0B4K7K6;Q9VBG6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    12.36380
#> A0A0B4K7L0;Q9W252                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    18.37912
#> A0A0B4K7N2;Q8IN00;D5A7N8;Q9VCX2;Q9VCX1-2;Q9VCX1-4;Q9VCX1-3;Q9VCX1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    19.91169
#> Q9VCH4;A0A0B4K7Q6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    12.00100
#> A0A0B4K7T7;A1ZAN6;A1ZAN7;A0A0B4LFF8                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  18.66593
#> A0A0B4KFL2;A1Z9E0;A1Z9D9;A0A0B4K7Y4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  12.28946
#> A0A0B4K7Z5;Q7KLV9;Q7KLV9-2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           28.86215
#> A0A0B4K812;Q7KNS3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    12.00100
#> A0A0B4KFL0;A0A0B4K851;Q4Z8K6-3;Q4Z8K6-2;Q4Z8K6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       12.00100
#> A1Z945;A0A0B4K859                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    31.86834
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#> A0A0B4K6T7                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            0.0010000
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#> A0A0B4K7A5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           25.6465050
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#> A0A0B4K6T7                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           4.632439e+03
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#> A0A0B4KFE9;A1Z8P9                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    7.146826e+03
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#> A0A0B4KGJ5;Q9NIV1;A0A0B4KG56                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         1.545708e+03
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#> Q9VEV1;A0A0B4KGS4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    9.208772e-02
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#> Q9VEZ3;E1JIM4;A0A0B4K664;A0A0B4K700                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     17
#> Q8INB6;Q86BR9;Q86NK8;Q4AB31;A0A0B4K7C4;A0A0B4K697;A0A0B4KHL4;Q8IHB0                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     32
#> A0A0B4K6B8;A0A0B4K7A6;Q86B87-21;Q86B87-19;Q86B87-20;Q86B87-18;Q86B87-17;Q86B87-16;Q86B87-29;Q86B87-28;Q86B87-15;Q86B87-27;Q86B87-23;Q86B87-14;Q86B87-13;Q86B87-31;Q86B87-12;Q86B87-11;Q86B87-10;Q86B87-24;Q86B87-22;Q86B87-25;Q86B87-9;Q86B87-8;Q86B87-7;Q86B87-30;Q86B87-6;Q86B87-5;Q86B87-4;Q86B87-3;Q86B87-2;Q86B87;Q86B87-26                                                                                                                                                                                                                                                                                                        23
#> A0A0B4K6D2;Q9VH95                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       29
#> A0A0B4K6S1;A0A0B4K6F4;Q8SZN9;E0R905;Q7KSP5;A0A0B4KGA3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1
#> Q9VC62;A0A0B4KGU9;Q7KS16;A0A0B4K6F9                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      4
#> A0A0B4K6G6;Q9VG05                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       36
#> A0A0B4KHY2;A0A0B4K784;A0A0B4K7L2;E1JIZ1;A0A0B4KI37;E1JIZ2;A0A0B4K6M4;A0A0B4K6I1;A0A0B4K7W1;E1JIZ0;Q7KRY7-3;Q7KRY7-5;Q7KRY7-8;Q7KRY7-2;Q7KRY7-9;Q7KRY7;Q7KRY7-7;Q7KRY7-10;A0A0B4KHN3;Q7KRY7-6;Q7KRY7-4                                                                                                                                                                                                                                                                                                                                                                                                                                    2
#> A0A0B4K6J3;Q8IMW5;A0A0C4DHB7;A0A0B4K7S6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1
#> A0A0B4K6K7;Q9VI55;Q9VI55-2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              23
#> A0A0B4K6K9;A0A0B4K7Y7;Q9VAW5-1;Q9VAW5;Q9VAW5-2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          29
#> Q9VEF7;A0A0B4KHP1;A0A0B4K6L3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             1
#> A0A0B4K6L4;Q27601                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1
#> A0A0B4K6N1;Q8MLY8                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       36
#> A0A0B4K6N7;Q9VE34;Q9VE34-2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              34
#> Q0E9I5;Q0E9K6;Q0E9K0;Q0E9J7;Q0E9J3;Q0E9I7;Q0E9I1;Q0E9H9;A1Z6X3;A0A0C4DHD8;A0A0B4K7I5;A0A0B4K6Z8;Q0E9K7;Q0E9K2;Q0E9J6;Q0E9J1;Q0E9I3;Q0E9I0;Q0E9H7;Q0E9L9;Q0E9L5;Q0E9L4;Q0E9L8;Q0E9I8;A1Z6X1;A0A0B4K7T6;A0A0B4K6Z3;A0A0B4K6R8;Q0E9M3;Q0E9L1;A0A0B4K7H7;A0A0B4K6Y9;Q0E9L0;A1Z6X2;A0A0B4K827;Q0E9M0;Q0E9K3;Q0E9K1;A0A0B4K7H9;Q0E9K4;Q0E9J8;Q0E9J5;Q0E9J4;Q0E9J2;Q0E9I9;Q0E9I4;Q0E9I2;Q0E9H8;Q0E9H5;Q0E9K9;Q0E9K5;Q0E9J9;Q0E9I6;Q0E9H6;A0A0B4K828;A0A0B4K7T5;Q0E9L7;Q0E9L6;Q0E9L3;Q0E9L2;A0A0B4K7T8;Q0E9M4;Q0E9M2;Q0E9M1;Q0E9J0;A0A0B4K824;A0A0B4K7T4;A0A0B4K6R4;A0A0B4K6Q9;A0A0B4K7I3;A0A0B4K6S2;Q0E9K8;A0A0B4K6Z6;A0A0B4K823;A0A0B4KEF4    10
#> D0Z768;A0A0B4K6T1;A0A0B4K7U5;E1JH02;A0A0B4KFC5;Q86S05-3;Q86S05-2;Q86S05                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  2
#> A0A0B4K6T7                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               1
#> A0A0B4K6U2;E1JIJ7;Q8INH9                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 1
#> A0A0B4K6U6;Q08473-3;Q08473-2;Q08473;Q08473-4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            17
#> A0A0B4KHW3;A0A0B4K6V1;Q9VA73-3;Q9VA73-2;Q9VA73                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          22
#> A0A0B4K6W1;P08970                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       20
#> A0A0B4K6W2;A0A0B4K7S0;P55824-3;P55824                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   32
#> A0A0B4K6X7;A1Z8J0                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        0
#> Q9VHK3;A0A0B4K6Y7;Q8INQ0;A8JQV7;Q9VHK4;B7Z0U1;Q8MQQ3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    15
#> A0A0B4LHK4;A0A0B4KHZ8;A0A0B4KHR8;A0A0B4K725;Q9VCA8                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      33
#> A0A0B4LF93;A1Z928;A1Z927;A0A0B4LF82;Q5U0Y0;A0A0B4K765                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1
#> A0A0B4K7A5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              36
#> A0A0B4K7G4;P13469                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       29
#> B7YZQ7;A0A0B4K7G9;O77460                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 7
#> A0A0B4K7H0;Q7KN74                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        6
#> Q9VBU7;A0A0B4K7J2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       34
#> Q95U21;Q7JQ36;A0A0B4K7J3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                17
#> A0A0B4K7K6;Q9VBG6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       12
#> A0A0B4K7L0;Q9W252                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       18
#> A0A0B4K7N2;Q8IN00;D5A7N8;Q9VCX2;Q9VCX1-2;Q9VCX1-4;Q9VCX1-3;Q9VCX1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       21
#> Q9VCH4;A0A0B4K7Q6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        2
#> A0A0B4K7T7;A1ZAN6;A1ZAN7;A0A0B4LFF8                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     18
#> A0A0B4KFL2;A1Z9E0;A1Z9D9;A0A0B4K7Y4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      8
#> A0A0B4K7Z5;Q7KLV9;Q7KLV9-2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              31
#> A0A0B4K812;Q7KNS3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        2
#> A0A0B4KFL0;A0A0B4K851;Q4Z8K6-3;Q4Z8K6-2;Q4Z8K6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           5
#> A1Z945;A0A0B4K859                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       32
#> A0A0B4K882;Q7K2Y9                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1
#> A0A0B4K8A5;Q9W2F2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       29
#> A0A0B4K8A6;Q9W288                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1
#> Q5LJQ4;A0A0B4KEH8;A0A0B4KEC2;Q9W5H8                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      2
#> A0A0B4KED0;Q9W5N2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1
#> A0A0B4KED9;O16844                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       16
#> A0A0B4KEE4;A1Z6Q1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        5
#> E1JGZ7;E1JGZ8;A1Z734;A0A0B4KEE7                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          7
#> A0A0B4KEI5;Q9V9K7                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1
#> Q7JVY0;A0A0B4KEU5;A0A0B4KEJ7                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            10
#> A1Z9L2;A1Z9L0;A0A0B4KFX4;Q8T076;A0A0B4KEP1;A0A0B4LFC1;A0A0B4KFM5;A0A0B4KF25                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             18
#> Q5U156;A0A0B4KER0;Q95RL2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                19
#> A0A0B4KET0;Q1LZ08                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       13
#> A0A0B4KFU3;A0A0B4KG58;B7YZJ2;B7YZJ1;E1JH90;A0A0B4KET5;A0A0B4KFA4;E1JH91;A0A0B4KEY4;A1ZAU8-2;A1ZAU8-3;A1ZAU8;A0A0B4KEY6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  26
#> Q0E901;A0A0B4KFE6;A0A0B4KEW2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             6
#> A0A0B4KFR7;A0A0B4KEW6;Q7KLE5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             1
#> A0A0B4KEX0;A1ZAB5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       35
#> Q0E993;A0A0B4KF06                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       25
#> A0A0B4KF46;Q8T0L3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       28
#> A0A0B4KG14;A0A0B4KF57;Q9VMY8                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            24
#> Q7JQL5;A0A0B4KF86                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        7
#> Q8T0M2;Q0E9C6;A0A0B4KFA3;A8DY97;A8DY98                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   3
#> Q9VHX9;A0A0B4KFA6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       16
#> A0A0B4LGR1;Q9VI14;A0A0B4KFB8;Q6NN86                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      7
#> A1Z7H3;Q8T3L1;A1Z7H2;A0A0B4KFE4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         17
#> A0A0B4KFE5;Q04448-2;Q04448                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               1
#> A0A0B4KFE9;A1Z8P9                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        3
#> A0A0B4KGE6;A0A0B4KFH4;P26270                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             8
#> A0A0B4KFJ7;Q9VHH9                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       14
#> A0A0B4KFN1;A1Z9R6;A0A0B4KFX9;Q9V727                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      1
#> A0A0B4KH36;A0A0B4KFQ0;A0A0B4KGR9;Q9VH01;A0A0B4KG50                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      16
#> A4UZI0;A0A0B4LGK5;A1ZA18;A0A0B4KFR5;A0A0B4KG24                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          26
#> A0A0B4KFX5;A0A0B4KGG9;A4V2S3;A0A0B4KHB2;A0A0B4KFT4;A0A0B4KGZ7;O46036-2;O46036                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           18
#> A0A0B4KFU5;Q9V853                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       11
#> A0A0B4KFW0;Q8T0S6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       25
#> Q9VHC4;A0A0B4KFZ2;Q6AWD5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 5
#> A0A0B4KFZ9;P84040                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       27
#> Q7K0G4;A0A0B4KG11;F0JAK5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 1
#> A0A0B4KG32;A0A0B4KH26;Q9VH20                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            11
#> A0A0B4KG41;Q9VES1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1
#> Q9VF92;A0A0B4KG69                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        2
#> Q9N6D7;A0A0B4KG96                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       23
#> A0A0B4KHS7;A0A0B4KGE1;Q24151;A0A0B4KGI7;Q24151-2;A0A0B4KHS6;A0A0B4KH10;Q24151-4;Q24151-3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                31
#> Q8MQJ5;A0A0B4KGF5;Q9VE69                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                14
#> Q32KD3;Q7KSW1;Q494I1;A0A0B4KGS8;Q9VHW9;A0A0B4KGF6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       25
#> A4V364;A8JR54;Q8IN47;A0A0B4KGK8;Q8IN48;A0A0B4KH21;A0A0B4KH24;A0A0B4KGF9;Q9VDI8;Q7KSA0;A0A0B4KHH8;A0A0B4KHI4;Q95TW4;A0A0B4KGK5;A0A0B4KHT5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 1
#> E1JIR4;A0A0B4KGG8;P13607-7;P13607-6;P13607-2;P13607-4;P13607-5;P13607;P13607-3;A8QI34                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   32
#> A0A0B4KGH0;A0A0B4KHR4;Q9VDW6-2;Q9VDW6-1;Q9VDW6;Q9VDW6-4;Q9VDW6-3;A0A0B4KGB9;Q9VDW3;A0A0B4KHE2;Q7YU29;Q0KI50                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              1
#> A0A0B4KGI6;Q9VN82;A0A0B4KG43;Q8IPP4;Q8IPP3;A0A0B4KF82;A0A0B4KFK9                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        24
#> A0A0B4KGJ5;Q9NIV1;A0A0B4KG56                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             6
#> A0A0B4KGK3;Q95RA8                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        1
#> A0A0B4KGP8;Q24208;Q24208-2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              33
#> Q9VEV1;A0A0B4KGS4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       32
#> A0A0B4KGU4;Q9VHP0;M9PBB5;P09052                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         36
#> A0A0B4KGW0;Q8IMX7-2;A0A0B4J3Z9;Q8IMX7                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1

Internally the proDAFit object is implemented as a subclass of SummarizedExperiment. This means it can be subsetted, which is for example useful for calculating the distance of a subset of proteins and samples.

Identify Differential Abundance

Lastly, we will use a Wald test to identify in which proteins a coefficient is significantly different from zero. The test_diff() function takes first the fit object produced by proDA() and a contrast argument. This can either be a string or an expression if we want to test more complex combinations. For example conditionCG1407 - (conditionCG6017 + conditionCG5880) / 2 would test for the difference between CG1407 and the average of CG6017 and CG5880.

Alternatively test_diff() also supports likelihood ratio F-tests. In that case instead of the contrast argument specify the reduced_model argument.

# Test which proteins differ between condition CG1407 and S2R
# S2R is the default contrast, because it was specified as the `reference_level`
test_res <- test_diff(fit, "conditionCG1407")
test_res
#>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     name
#> 1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Q8IP47;Q9VJP8;Q9V435;A0A023GPQ3;Q2PDT6;Q7K540
#> 2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               A0A023GPV6;A8JV04;Q7YU03
#> 3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      A0A023GQA5;P24156
#> 4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     Q1RKY1;A0A0B4LG19;A0A0B4J401;B7YZL2;A1ZBH5;B7YZL7;B7YZL6;Q7YTZ4;B7YZL5;B7YZL8;Q0E919;B7YZL1;B7YZL3
#> 5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4JD00;A8DY69;I0E2I4;A0A0B4JCQ5;Q8SXP0;E5DK16;A0A0B4JD31;A0A0B4JCS1;A0A0B4JD27
#> 6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      A0A0B4JCT8;Q9V780
#> 7                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         A0A0B4LHQ4;A0A0B4JD62;A0A0B4JDB5;A0A0B4LGQ5;A0A0B4JCW5;A0A0B4JCV6;A0A0B4LGR2;A0A0B4JDA1;Q9VN58
#> 8                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               A0A0B4JCW4;Q9VHJ8;Q95U38
#> 9                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Q9VDV4;A0A0B4JCY1;Q8IN71;A0A0B4KGH4
#> 10                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      A0A0B4JCY6;Q7KSF4;A0A0B4KHN1;A0A0B4KGT8;Q9VEN1;A0A0B4KGB3;A4V310;B7Z0L2;Q9VEN1-2
#> 11                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            E1JIU2;Q9VCQ0;A0A0B4JCZ2;A8JR87;A0A0B4KH86
#> 12                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4LEY5;A1Z7T2;A0A0B4JD07;A0A0B4K6U3;A0A0B4K727;A0A0B4LF03;A0A0B4LEI8;E1JH15;A0A0B4JD60;A1Z7T1;A1Z7T3;A0A0B4LFX2;A8DY76;A1Z7T0;A1Z7T0-2;A1Z7T4
#> 13                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4JD11;Q9NJH0
#> 14                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    A0A0B4KHW7;Q961V3;A0A0B4KHJ3;A0A0B4KHF5;A0A0B4JD23;Q7KRU0;Q8IMI0;A0A0B4JDE3;Q9VA53
#> 15                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4JD46;Q8T8R1
#> 16                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            A0A0B4JD48;Q95029-2;Q95029
#> 17                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      A0A0B4JD95;Q59E58;A0A0B4JD57;Q59E59;A0A0B4K7Q4;Q99323-2;Q99323-4;Q99323-1;Q99323
#> 18                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4JDA0;Q9VF03
#> 19                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4JDC3;Q9VGU5
#> 20                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   A0A0B4JDG2;Q9I7I8;A0A0B4JDD8;B7Z0M9;Q7KSB3;A0A0B4JCZ0;Q8IN56;Q8IN55
#> 21                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4JDG5;Q8IMZ9
#> 22                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Q9VNF8;A0A0B4K6T4;A0A0B4K5Z8
#> 23                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                A0A0B4K603;A0A0B4K6V2;A0A0B4KF90;A0A0B4K631;A0A0B4KGC6;B7Z0U7;A0A0B4KFE2;E1JJ78;Q9VI75
#> 24                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Q7KNC5;Q8MSQ5;Q8IPN9;Q9VNA1;Q0KIB9;A0A0B4K620;B7Z0T3;Q9VNA2;A0A0B4K6S8;A4V2F2;Q4ABH3;A0A0B4K699;A0A0B4KG49;B7Z0T6;Q8IPN8;A0A0B4KF88;Q8IPN6;Q7KTR7;Q7KTR8
#> 25                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Q9VEZ3;E1JIM4;A0A0B4K664;A0A0B4K700
#> 26                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Q8INB6;Q86BR9;Q86NK8;Q4AB31;A0A0B4K7C4;A0A0B4K697;A0A0B4KHL4;Q8IHB0
#> 27                                                                                                                                                                                                                                                                                                      A0A0B4K6B8;A0A0B4K7A6;Q86B87-21;Q86B87-19;Q86B87-20;Q86B87-18;Q86B87-17;Q86B87-16;Q86B87-29;Q86B87-28;Q86B87-15;Q86B87-27;Q86B87-23;Q86B87-14;Q86B87-13;Q86B87-31;Q86B87-12;Q86B87-11;Q86B87-10;Q86B87-24;Q86B87-22;Q86B87-25;Q86B87-9;Q86B87-8;Q86B87-7;Q86B87-30;Q86B87-6;Q86B87-5;Q86B87-4;Q86B87-3;Q86B87-2;Q86B87;Q86B87-26
#> 28                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4K6D2;Q9VH95
#> 29                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 A0A0B4K6S1;A0A0B4K6F4;Q8SZN9;E0R905;Q7KSP5;A0A0B4KGA3
#> 30                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Q9VC62;A0A0B4KGU9;Q7KS16;A0A0B4K6F9
#> 31                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4K6G6;Q9VG05
#> 32                                                                                                                                                                                                                                                                                                                                                                                                                                 A0A0B4KHY2;A0A0B4K784;A0A0B4K7L2;E1JIZ1;A0A0B4KI37;E1JIZ2;A0A0B4K6M4;A0A0B4K6I1;A0A0B4K7W1;E1JIZ0;Q7KRY7-3;Q7KRY7-5;Q7KRY7-8;Q7KRY7-2;Q7KRY7-9;Q7KRY7;Q7KRY7-7;Q7KRY7-10;A0A0B4KHN3;Q7KRY7-6;Q7KRY7-4
#> 33                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               A0A0B4K6J3;Q8IMW5;A0A0C4DHB7;A0A0B4K7S6
#> 34                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            A0A0B4K6K7;Q9VI55;Q9VI55-2
#> 35                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        A0A0B4K6K9;A0A0B4K7Y7;Q9VAW5-1;Q9VAW5;Q9VAW5-2
#> 36                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Q9VEF7;A0A0B4KHP1;A0A0B4K6L3
#> 37                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4K6L4;Q27601
#> 38                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4K6N1;Q8MLY8
#> 39                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            A0A0B4K6N7;Q9VE34;Q9VE34-2
#> 40  Q0E9I5;Q0E9K6;Q0E9K0;Q0E9J7;Q0E9J3;Q0E9I7;Q0E9I1;Q0E9H9;A1Z6X3;A0A0C4DHD8;A0A0B4K7I5;A0A0B4K6Z8;Q0E9K7;Q0E9K2;Q0E9J6;Q0E9J1;Q0E9I3;Q0E9I0;Q0E9H7;Q0E9L9;Q0E9L5;Q0E9L4;Q0E9L8;Q0E9I8;A1Z6X1;A0A0B4K7T6;A0A0B4K6Z3;A0A0B4K6R8;Q0E9M3;Q0E9L1;A0A0B4K7H7;A0A0B4K6Y9;Q0E9L0;A1Z6X2;A0A0B4K827;Q0E9M0;Q0E9K3;Q0E9K1;A0A0B4K7H9;Q0E9K4;Q0E9J8;Q0E9J5;Q0E9J4;Q0E9J2;Q0E9I9;Q0E9I4;Q0E9I2;Q0E9H8;Q0E9H5;Q0E9K9;Q0E9K5;Q0E9J9;Q0E9I6;Q0E9H6;A0A0B4K828;A0A0B4K7T5;Q0E9L7;Q0E9L6;Q0E9L3;Q0E9L2;A0A0B4K7T8;Q0E9M4;Q0E9M2;Q0E9M1;Q0E9J0;A0A0B4K824;A0A0B4K7T4;A0A0B4K6R4;A0A0B4K6Q9;A0A0B4K7I3;A0A0B4K6S2;Q0E9K8;A0A0B4K6Z6;A0A0B4K823;A0A0B4KEF4
#> 41                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               D0Z768;A0A0B4K6T1;A0A0B4K7U5;E1JH02;A0A0B4KFC5;Q86S05-3;Q86S05-2;Q86S05
#> 42                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            A0A0B4K6T7
#> 43                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              A0A0B4K6U2;E1JIJ7;Q8INH9
#> 44                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          A0A0B4K6U6;Q08473-3;Q08473-2;Q08473;Q08473-4
#> 45                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        A0A0B4KHW3;A0A0B4K6V1;Q9VA73-3;Q9VA73-2;Q9VA73
#> 46                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4K6W1;P08970
#> 47                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 A0A0B4K6W2;A0A0B4K7S0;P55824-3;P55824
#> 48                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4K6X7;A1Z8J0
#> 49                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Q9VHK3;A0A0B4K6Y7;Q8INQ0;A8JQV7;Q9VHK4;B7Z0U1;Q8MQQ3
#> 50                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    A0A0B4LHK4;A0A0B4KHZ8;A0A0B4KHR8;A0A0B4K725;Q9VCA8
#> 51                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 A0A0B4LF93;A1Z928;A1Z927;A0A0B4LF82;Q5U0Y0;A0A0B4K765
#> 52                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            A0A0B4K7A5
#> 53                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4K7G4;P13469
#> 54                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              B7YZQ7;A0A0B4K7G9;O77460
#> 55                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4K7H0;Q7KN74
#> 56                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     Q9VBU7;A0A0B4K7J2
#> 57                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Q95U21;Q7JQ36;A0A0B4K7J3
#> 58                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4K7K6;Q9VBG6
#> 59                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4K7L0;Q9W252
#> 60                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4K7N2;Q8IN00;D5A7N8;Q9VCX2;Q9VCX1-2;Q9VCX1-4;Q9VCX1-3;Q9VCX1
#> 61                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     Q9VCH4;A0A0B4K7Q6
#> 62                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   A0A0B4K7T7;A1ZAN6;A1ZAN7;A0A0B4LFF8
#> 63                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   A0A0B4KFL2;A1Z9E0;A1Z9D9;A0A0B4K7Y4
#> 64                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            A0A0B4K7Z5;Q7KLV9;Q7KLV9-2
#> 65                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4K812;Q7KNS3
#> 66                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        A0A0B4KFL0;A0A0B4K851;Q4Z8K6-3;Q4Z8K6-2;Q4Z8K6
#> 67                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A1Z945;A0A0B4K859
#> 68                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4K882;Q7K2Y9
#> 69                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4K8A5;Q9W2F2
#> 70                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4K8A6;Q9W288
#> 71                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Q5LJQ4;A0A0B4KEH8;A0A0B4KEC2;Q9W5H8
#> 72                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4KED0;Q9W5N2
#> 73                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4KED9;O16844
#> 74                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4KEE4;A1Z6Q1
#> 75                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       E1JGZ7;E1JGZ8;A1Z734;A0A0B4KEE7
#> 76                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4KEI5;Q9V9K7
#> 77                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Q7JVY0;A0A0B4KEU5;A0A0B4KEJ7
#> 78                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           A1Z9L2;A1Z9L0;A0A0B4KFX4;Q8T076;A0A0B4KEP1;A0A0B4LFC1;A0A0B4KFM5;A0A0B4KF25
#> 79                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Q5U156;A0A0B4KER0;Q95RL2
#> 80                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4KET0;Q1LZ08
#> 81                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                A0A0B4KFU3;A0A0B4KG58;B7YZJ2;B7YZJ1;E1JH90;A0A0B4KET5;A0A0B4KFA4;E1JH91;A0A0B4KEY4;A1ZAU8-2;A1ZAU8-3;A1ZAU8;A0A0B4KEY6
#> 82                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Q0E901;A0A0B4KFE6;A0A0B4KEW2
#> 83                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          A0A0B4KFR7;A0A0B4KEW6;Q7KLE5
#> 84                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4KEX0;A1ZAB5
#> 85                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     Q0E993;A0A0B4KF06
#> 86                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4KF46;Q8T0L3
#> 87                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          A0A0B4KG14;A0A0B4KF57;Q9VMY8
#> 88                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     Q7JQL5;A0A0B4KF86
#> 89                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Q8T0M2;Q0E9C6;A0A0B4KFA3;A8DY97;A8DY98
#> 90                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     Q9VHX9;A0A0B4KFA6
#> 91                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   A0A0B4LGR1;Q9VI14;A0A0B4KFB8;Q6NN86
#> 92                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       A1Z7H3;Q8T3L1;A1Z7H2;A0A0B4KFE4
#> 93                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            A0A0B4KFE5;Q04448-2;Q04448
#> 94                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4KFE9;A1Z8P9
#> 95                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          A0A0B4KGE6;A0A0B4KFH4;P26270
#> 96                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4KFJ7;Q9VHH9
#> 97                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   A0A0B4KFN1;A1Z9R6;A0A0B4KFX9;Q9V727
#> 98                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    A0A0B4KH36;A0A0B4KFQ0;A0A0B4KGR9;Q9VH01;A0A0B4KG50
#> 99                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        A4UZI0;A0A0B4LGK5;A1ZA18;A0A0B4KFR5;A0A0B4KG24
#> 100                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        A0A0B4KFX5;A0A0B4KGG9;A4V2S3;A0A0B4KHB2;A0A0B4KFT4;A0A0B4KGZ7;O46036-2;O46036
#> 101                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    A0A0B4KFU5;Q9V853
#> 102                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    A0A0B4KFW0;Q8T0S6
#> 103                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             Q9VHC4;A0A0B4KFZ2;Q6AWD5
#> 104                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    A0A0B4KFZ9;P84040
#> 105                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             Q7K0G4;A0A0B4KG11;F0JAK5
#> 106                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         A0A0B4KG32;A0A0B4KH26;Q9VH20
#> 107                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    A0A0B4KG41;Q9VES1
#> 108                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Q9VF92;A0A0B4KG69
#> 109                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Q9N6D7;A0A0B4KG96
#> 110                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             A0A0B4KHS7;A0A0B4KGE1;Q24151;A0A0B4KGI7;Q24151-2;A0A0B4KHS6;A0A0B4KH10;Q24151-4;Q24151-3
#> 111                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             Q8MQJ5;A0A0B4KGF5;Q9VE69
#> 112                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Q32KD3;Q7KSW1;Q494I1;A0A0B4KGS8;Q9VHW9;A0A0B4KGF6
#> 113                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             A4V364;A8JR54;Q8IN47;A0A0B4KGK8;Q8IN48;A0A0B4KH21;A0A0B4KH24;A0A0B4KGF9;Q9VDI8;Q7KSA0;A0A0B4KHH8;A0A0B4KHI4;Q95TW4;A0A0B4KGK5;A0A0B4KHT5
#> 114                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                E1JIR4;A0A0B4KGG8;P13607-7;P13607-6;P13607-2;P13607-4;P13607-5;P13607;P13607-3;A8QI34
#> 115                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          A0A0B4KGH0;A0A0B4KHR4;Q9VDW6-2;Q9VDW6-1;Q9VDW6;Q9VDW6-4;Q9VDW6-3;A0A0B4KGB9;Q9VDW3;A0A0B4KHE2;Q7YU29;Q0KI50
#> 116                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     A0A0B4KGI6;Q9VN82;A0A0B4KG43;Q8IPP4;Q8IPP3;A0A0B4KF82;A0A0B4KFK9
#> 117                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         A0A0B4KGJ5;Q9NIV1;A0A0B4KG56
#> 118                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    A0A0B4KGK3;Q95RA8
#> 119                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           A0A0B4KGP8;Q24208;Q24208-2
#> 120                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Q9VEV1;A0A0B4KGS4
#> 121                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      A0A0B4KGU4;Q9VHP0;M9PBB5;P09052
#> 122                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                A0A0B4KGW0;Q8IMX7-2;A0A0B4J3Z9;Q8IMX7
#>             pval     adj_pval        diff t_statistic        se df avg_abundance n_approx n_obs
#> 1   9.041054e-01 9.643171e-01 -0.13197309 -0.12175674 1.0839078 24      18.93537 12.00100     5
#> 2   9.228458e-01 9.643171e-01 -0.09926167 -0.09787319 1.0141865 24      18.44216 12.00100     1
#> 3   3.561254e-02 2.647212e-01 -2.91628269 -2.22664829 1.3097186 24      19.25697 19.27983    14
#> 4   6.674303e-01 9.643171e-01  0.63210212  0.43502624 1.4530207 24      18.71535 12.00100     6
#> 5   9.189871e-01 9.643171e-01  0.06891434  0.10278570 0.6704662 24      19.99188 17.39307    17
#> 6   9.226888e-01 9.643171e-01 -0.09951655 -0.09807306 1.0147186 24      18.50970 12.00100     1
#> 7   9.229678e-01 9.643171e-01 -0.09906384 -0.09771790 1.0137737 24      18.42516 12.00100     1
#> 8   6.434555e-01 9.643171e-01 -0.19662994 -0.46878223 0.4194484 24      21.87309 28.92211    29
#> 9   2.948952e-01 8.608983e-01  1.94720060  1.07083423 1.8183959 24      18.72725 12.00100     4
#> 10  5.977712e-01 9.643171e-01 -0.78261866 -0.53470805 1.4636373 24      18.96533 12.00100     4
#> 11  4.180174e-01 9.643171e-01  1.06811244  0.82406468 1.2961512 24      18.69294 12.00100     7
#> 12  5.444283e-01 9.643171e-01  0.65459176  0.61486774 1.0646058 24      18.72351 13.26599    13
#> 13  2.131380e-01 7.247578e-01 -1.92931574 -1.27896523 1.5084974 24      21.94096 34.50696    34
#> 14  9.225138e-01 9.643171e-01 -0.09980085 -0.09829572 1.0153122 24      18.49506 12.00100     1
#> 15  5.677737e-01 9.643171e-01 -0.30681826 -0.57931712 0.5296206 24      23.11365 33.97973    34
#> 16  4.364242e-01 9.643171e-01  0.63853127  0.79146721 0.8067691 24      21.83207 29.09390    29
#> 17  5.513705e-01 9.643171e-01 -0.92548437 -0.60421453 1.5317149 24      18.76627 21.16573    17
#> 18  1.265250e-01 5.322777e-01 -1.44866342 -1.58294091 0.9151721 24      18.76068 14.58983    13
#> 19  9.232499e-01 9.643171e-01 -0.09860718 -0.09735891 1.0128213 24      18.43896 12.00100     1
#> 20  8.456488e-01 9.643171e-01  0.13751343  0.19679002 0.6987825 24      24.96475 34.87011    35
#> 21  3.890306e-01 9.593122e-01 -0.49601587 -0.87728286 0.5654002 24      19.62093 19.68847    19
#> 22  5.796524e-03 6.833745e-02 -3.03236583 -3.02866863 1.0012207 24      19.39205 14.13399    12
#> 23  7.940276e-01 9.643171e-01  0.53549900  0.26400794 2.0283443 24      19.52978 12.00100     9
#> 24  7.822569e-01 9.643171e-01 -0.29071971 -0.27949849 1.0401477 24      19.93328 13.52792    13
#> 25  5.813170e-03 6.833745e-02 -2.36743316 -3.02746517 0.7819853 24      19.70369 17.49006    17
#> 26  7.660945e-04 2.710675e-02  1.31591990  3.85155010 0.3416598 24      22.63306 31.78235    32
#> 27  5.272829e-01 9.643171e-01 -0.39004152 -0.64149148 0.6080229 24      20.49255 23.49625    23
#> 28  2.138630e-01 7.247578e-01 -1.08737737 -1.27687450 0.8515930 24      21.40463 28.98317    29
#> 29  7.362019e-01 9.643171e-01 -0.34931409 -0.34082366 1.0249115 24      18.44341 12.00100     1
#> 30  2.927058e-01 8.608983e-01  1.36822590  1.07581648 1.2718023 24      18.76668 12.00100     4
#> 31  3.864093e-01 9.593122e-01  0.61668223  0.88221913 0.6990125 24      24.31247 36.00000    36
#> 32  8.433075e-01 9.643171e-01  0.28664737  0.19981653 1.4345529 24      18.54707 12.00100     2
#> 33  9.228504e-01 9.643171e-01 -0.09925422 -0.09786734 1.0141710 24      18.48510 12.00100     1
#> 34  2.977740e-01 8.608983e-01 -0.38453818 -1.06432295 0.3612984 24      21.23648 22.56518    23
#> 35  6.009883e-01 9.643171e-01  0.22887460  0.52998994 0.4318471 24      21.24522 27.52419    29
#> 36  9.181121e-01 9.643171e-01 -0.10707848 -0.10390000 1.0305917 24      18.56855 12.00100     1
#> 37  1.492533e-01 6.069632e-01 -1.68691214 -1.48998782 1.1321651 24      18.55429 12.00100     1
#> 38  4.587328e-02 2.647212e-01  1.14516920  2.10574906 0.5438298 24      28.10487 36.00000    36
#> 39  3.163508e-03 6.432467e-02  1.94489788  3.27986039 0.5929819 24      23.81095 34.14228    34
#> 40  2.233232e-02 1.816362e-01  3.30063096  2.44234451 1.3514191 24      19.57507 11.40295    10
#> 41  6.159690e-01 9.643171e-01  0.68682472  0.50817629 1.3515481 24      18.49667 12.00100     2
#> 42  9.081067e-01 9.643171e-01 -0.12457335 -0.11665170 1.0679086 24      18.56211 12.00100     1
#> 43  4.409985e-01 9.643171e-01  1.20409501  0.78349841 1.5368187 24      18.31312 12.00100     1
#> 44  9.151516e-03 9.304041e-02 -2.30696320 -2.83503908 0.8137324 24      20.17084 17.64724    17
#> 45  7.886930e-01 9.643171e-01  0.06831714  0.27102003 0.2520741 24      20.00811 22.13184    22
#> 46  4.954627e-01 9.643171e-01 -0.18675522 -0.69218740 0.2698044 24      19.82606 20.21045    20
#> 47  5.476326e-01 9.643171e-01 -0.44500254 -0.60994169 0.7295821 24      22.27409 32.25299    32
#> 48  9.186813e-01 9.643171e-01 -0.10612366 -0.10317509 1.0285783 24      18.41575 12.00100     0
#> 49  8.845945e-02 4.150789e-01  1.52566425  1.77573561 0.8591731 24      19.81764 16.28860    15
#> 50  7.816759e-01 9.643171e-01 -0.12516567 -0.28026492 0.4465977 24      22.00212 33.14310    33
#> 51  9.793620e-01 9.793620e-01 -0.03221180 -0.02613976 1.2322914 24      18.41672 12.00100     1
#> 52  2.214043e-08 2.701132e-06  4.37565997  8.16099836 0.5361672 24      27.33514 36.00000    36
#> 53  3.644474e-01 9.593122e-01 -0.80732733 -0.92446356 0.8732928 24      22.35185 29.01701    29
#> 54  3.876274e-02 2.647212e-01 -3.39268355 -2.18650755 1.5516450 24      19.17257 12.00100     7
#> 55  3.757219e-01 9.593122e-01  1.16676903  0.90257401 1.2927129 24      18.93425 12.00100     6
#> 56  6.408596e-02 3.257703e-01 -1.22481842 -1.94103583 0.6310128 24      23.05049 33.88476    34
#> 57  1.590711e-01 6.260217e-01  1.53028107  1.45337664 1.0529143 24      19.66376 17.13504    17
#> 58  1.131192e-01 5.111311e-01 -1.15443889 -1.64445458 0.7020193 24      18.99606 12.36380    12
#> 59  8.171631e-01 9.643171e-01 -0.09962472 -0.23374783 0.4262060 24      19.61498 18.37912    18
#> 60  1.066650e-02 1.001010e-01  1.19360307  2.76910017 0.4310437 24      21.05399 19.91169    21
#> 61  5.466287e-01 9.643171e-01  1.17432662  0.61148338 1.9204555 24      18.70086 12.00100     2
#> 62  7.919738e-01 9.643171e-01  0.13105252  0.26670600 0.4913745 24      19.78741 18.66593    18
#> 63  5.057939e-01 9.643171e-01  1.14337132  0.67553404 1.6925444 24      19.26095 12.28946     8
#> 64  3.145789e-01 8.722416e-01 -0.56927461 -1.02717720 0.5542127 24      23.37249 28.86215    31
#> 65  9.197907e-01 9.643171e-01 -0.10427451 -0.10176237 1.0246863 24      18.53550 12.00100     2
#> 66  9.083037e-01 9.643171e-01  0.13467183  0.11640049 1.1569697 24      18.41111 12.00100     5
#> 67  9.671411e-01 9.751340e-01 -0.02481156 -0.04162617 0.5960568 24      22.46840 31.86834    32
#> 68  6.861313e-01 9.643171e-01 -0.48243024 -0.40904871 1.1793956 24      18.45434 12.00100     1
#> 69  5.908034e-01 9.643171e-01 -0.16493733 -0.54496937 0.3026543 24      22.89392 27.59466    29
#> 70  5.766823e-01 9.643171e-01  0.71923197  0.56594920 1.2708419 24      18.35385 12.00100     1
#> 71  9.227639e-01 9.643171e-01 -0.09939453 -0.09797740 1.0144638 24      18.53772 12.00100     2
#> 72  9.206463e-01 9.643171e-01 -0.10285901 -0.10067301 1.0217138 24      18.47949 12.00100     1
#> 73  9.406044e-01 9.643171e-01 -0.05427922 -0.07529465 0.7208909 24      19.99532 14.41933    16
#> 74  7.009700e-01 9.643171e-01 -0.45739794 -0.38863842 1.1769241 24      18.69750 12.00100     5
#> 75  6.332662e-01 9.643171e-01  0.68952793  0.48329505 1.4267225 24      18.86672 12.00100     7
#> 76  5.034613e-01 9.643171e-01 -0.78512326 -0.67927729 1.1558214 24      18.47957 12.00100     1
#> 77  4.086408e-02 2.647212e-01 -2.43952580 -2.16134050 1.1287096 24      19.52318 11.50015    10
#> 78  9.553710e-01 9.712939e-01 -0.02783767 -0.05655103 0.4922575 24      19.40221 18.49791    18
#> 79  2.643095e-01 8.485727e-01 -0.82707846 -1.14300801 0.7235981 24      20.34291 19.45324    19
#> 80  3.034314e-01 8.608983e-01  1.16286378  1.05165640 1.1057450 24      19.37861 12.99106    13
#> 81  6.460869e-01 9.643171e-01  0.29912727  0.46505093 0.6432140 24      20.93932 24.48471    26
#> 82  9.246688e-01 9.643171e-01 -0.09632425 -0.09555318 1.0080696 24      18.49860 12.00100     6
#> 83  9.219635e-01 9.643171e-01 -0.10069764 -0.09899623 1.0171865 24      18.51485 12.00100     1
#> 84  3.931608e-01 9.593122e-01 -0.30146312 -0.86954862 0.3466892 24      24.03786 34.95610    35
#> 85  8.909985e-01 9.643171e-01 -0.15418119 -0.13850296 1.1131978 24      21.03032 25.94325    25
#> 86  6.161573e-03 6.833745e-02 -3.12259785 -3.00300548 1.0398242 24      21.28131 28.61920    28
#> 87  5.662968e-01 9.643171e-01  0.24855823  0.58154351 0.4274112 24      20.65478 23.37489    24
#> 88  2.860154e-01 8.608983e-01  1.38672126  1.09120856 1.2708123 24      19.09672 12.00100     7
#> 89  2.012315e-01 7.247578e-01  2.52039510  1.31410981 1.9179486 24      18.63057 12.00100     3
#> 90  2.369339e-01 7.812416e-01  1.21140104  1.21300108 0.9986809 24      20.50976 16.73872    16
#> 91  9.256282e-01 9.643171e-01 -0.09479415 -0.09433248 1.0048941 24      18.55994 12.00100     7
#> 92  8.887460e-04 2.710675e-02 -2.48594417 -3.79244092 0.6554998 24      19.83720 17.03640    17
#> 93  9.224449e-01 9.643171e-01 -0.09991298 -0.09838347 1.0155464 24      18.33192 12.00100     1
#> 94  4.582331e-02 2.647212e-01 -2.68606602 -2.10627611 1.2752678 24      18.86580 12.00100     3
#> 95  2.230302e-03 5.441937e-02 -3.91939652 -3.42256483 1.1451636 24      19.05694 12.00100     8
#> 96  4.878551e-01 9.643171e-01  0.29259449  0.70457684 0.4152769 24      19.05484 14.25221    14
#> 97  9.227330e-01 9.643171e-01 -0.09944476 -0.09801679 1.0145687 24      18.38561 12.00100     1
#> 98  1.782027e-02 1.552909e-01 -1.79833541 -2.54385073 0.7069343 24      20.02498 15.88401    16
#> 99  5.901771e-02 3.130505e-01  0.83306672  1.98221179 0.4202713 24      21.13012 25.95821    26
#> 100 4.550496e-03 6.833745e-02 -1.84444394 -3.12973639 0.5893288 24      19.56241 18.97891    18
#> 101 9.357241e-01 9.643171e-01 -0.13285593 -0.08149505 1.6302333 24      19.71583 10.50293    11
#> 102 3.463236e-01 9.389217e-01  0.31169419  0.96061703 0.3244729 24      20.53835 25.39201    25
#> 103 1.262833e-01 5.322777e-01  2.28575527  1.58400097 1.4430264 24      19.16008 12.00100     5
#> 104 6.925939e-01 9.643171e-01  0.42254441  0.40013843 1.0559956 24      20.63359 27.96731    27
#> 105 9.226612e-01 9.643171e-01 -0.09956140 -0.09810820 1.0148122 24      18.36957 12.00100     1
#> 106 8.580194e-01 9.643171e-01 -0.15295408 -0.18083004 0.8458444 24      18.97029 11.49544    11
#> 107 9.229830e-01 9.643171e-01 -0.09903924 -0.09769858 1.0137224 24      18.45665 12.00100     1
#> 108 6.273476e-01 9.643171e-01  0.66626468  0.49177315 1.3548212 24      18.56544 12.00100     2
#> 109 7.995168e-02 3.901642e-01 -0.45962634 -1.82836344 0.2513867 24      20.59743 23.14033    23
#> 110 4.773661e-02 2.647212e-01 -0.82728014 -2.08645261 0.3965008 24      22.16902 31.04219    31
#> 111 4.555582e-02 2.647212e-01 -1.34306297 -2.10910636 0.6367924 24      19.23886 14.40934    14
#> 112 2.137807e-01 7.247578e-01  0.46126776  1.27711141 0.3611805 24      20.58297 25.49768    25
#> 113 1.849850e-01 7.052554e-01 -1.54457675 -1.36477003 1.1317487 24      18.54254 12.00100     1
#> 114 5.582864e-01 9.643171e-01 -0.39746200 -0.59367135 0.6694984 24      22.07904 32.35369    32
#> 115 8.928653e-01 9.643171e-01 -0.15414526 -0.13611550 1.1324592 24      18.62768 12.00100     1
#> 116 2.088060e-04 1.273716e-02  6.30315637  4.36497128 1.4440316 24      20.30641 26.15976    24
#> 117 9.263544e-01 9.643171e-01 -0.09364303 -0.09340857 1.0025100 24      18.90580 12.00100     6
#> 118 4.478138e-01 9.643171e-01 -0.88731768 -0.77171825 1.1497949 24      18.48807 12.00100     1
#> 119 5.279699e-01 9.643171e-01 -0.46123120 -0.64041589 0.7202057 24      23.83053 31.57225    33
#> 120 5.993421e-03 6.833745e-02  0.83088692  3.01464062 0.2756172 24      22.26676 31.92679    32
#> 121 6.925957e-01 9.643171e-01 -0.26042810 -0.40013601 0.6508489 24      24.23721 36.00000    36
#> 122 9.227127e-01 9.643171e-01 -0.09947767 -0.09804258 1.0146374 24      18.55530 12.00100     1

This walkthrough ends with the identification which proteins are differentially abundant. But for a real dataset, now the actual analysis only just begins. A list of significant proteins is hardly ever a publishable result, one often needs to make sense what the relevant underlying biological mechanisms are. But for this problem other tools are necessary, which depend on the precise question associated with the biological problem at hand.

Session Info

sessionInfo()
#> R version 3.6.1 (2019-07-05)
#> Platform: x86_64-apple-darwin15.6.0 (64-bit)
#> Running under: macOS Mojave 10.14.6
#> 
#> Matrix products: default
#> BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
#> LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
#> 
#> locale:
#> [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#> [1] proDA_0.99.10    BiocStyle_2.12.0
#> 
#> loaded via a namespace (and not attached):
#>  [1] SummarizedExperiment_1.14.0 xfun_0.8                    lattice_0.20-38            
#>  [4] colorspace_1.4-1            htmltools_0.3.6             stats4_3.6.1               
#>  [7] yaml_2.2.0                  rlang_0.4.0                 pkgdown_1.3.0              
#> [10] pillar_1.4.2                BiocParallel_1.18.0         BiocGenerics_0.30.0        
#> [13] RColorBrewer_1.1-2          matrixStats_0.54.0          GenomeInfoDbData_1.2.1     
#> [16] stringr_1.4.0               zlibbioc_1.30.0             munsell_0.5.0              
#> [19] commonmark_1.7              gtable_0.3.0                memoise_1.1.0              
#> [22] evaluate_0.14               Biobase_2.44.0              knitr_1.24                 
#> [25] IRanges_2.18.1              GenomeInfoDb_1.20.0         parallel_3.6.1             
#> [28] Rcpp_1.0.2                  backports_1.1.4             scales_1.0.0               
#> [31] BiocManager_1.30.4          DelayedArray_0.10.0         S4Vectors_0.22.0           
#> [34] desc_1.2.0                  XVector_0.24.0              fs_1.3.1                   
#> [37] digest_0.6.20               stringi_1.4.3               bookdown_0.12              
#> [40] GenomicRanges_1.36.0        rprojroot_1.3-2             grid_3.6.1                 
#> [43] tools_3.6.1                 bitops_1.0-6                magrittr_1.5               
#> [46] RCurl_1.95-4.12             tibble_2.1.3                crayon_1.3.4               
#> [49] pkgconfig_2.0.2             MASS_7.3-51.4               pheatmap_1.0.12            
#> [52] Matrix_1.2-17               xml2_1.2.0                  assertthat_0.2.1           
#> [55] rmarkdown_1.13              roxygen2_6.1.1              extraDistr_1.8.11          
#> [58] rstudioapi_0.10             R6_2.4.0                    compiler_3.6.1