Introduction
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
- Load the data (see vignette on loading MaxQuant output files)
- Fit the probabilistic dropout model (
proDA()) - 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$Y[1:5, ]
#> Condition_1-1 Condition_1-2 Condition_1-3 Condition_2-1 Condition_2-2 Condition_2-3
#> protein_1 19.17814 NA 18.89003 19.90698 NA 18.83656
#> protein_2 NA NA NA NA NA NA
#> protein_3 23.89169 24.03214 23.73394 23.54467 23.57230 23.92561
#> protein_4 20.94756 21.03668 20.76283 20.51360 21.11377 20.66439
#> protein_5 19.44029 19.74747 19.29078 19.55662 19.28023 19.75506
# Assignment of the samples to the two conditions
syn_dataset$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
#> 99 protein_99 5.179424e-05 0.005179424 -6.7073785 -18.358275 0.3653599 4 22.36647 4.964327
#> 91 protein_91 1.247144e-04 0.006235721 -2.3265851 -14.697286 0.1583003 4 20.36755 6.000000
#> 100 protein_100 1.945516e-03 0.064850542 4.7443894 7.226062 0.6565664 4 20.47024 3.065100
#> 96 protein_96 4.154706e-03 0.103867658 -1.6892848 -5.889937 0.2868086 4 21.94641 6.000000
#> 92 protein_92 6.740103e-03 0.134802067 0.9329294 5.150934 0.1811185 4 20.63209 6.000000
#> n_obs
#> 99 5
#> 91 6
#> 100 3
#> 96 6
#> 92 6Other 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
- Load the
proteinGroups.txtMaxQuant output table - Extract the intensity columns and create the abundance matrix
- Replace the zeros with
NAs and take thelog2()of the data - Normalize the data using
median_normalization() - Inspect sample structure with a heatmap of the distance matrix
(
dist_approx()) - Fit the probabilistic dropout model with
proDA() - 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] "/tmp/RtmplCZc1t/Rinst1ffd1b8b2a47/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.
# I use a regular expression (regex) to select the intensity columns
intensity_colnames <- grep("^LFQ\\.intensity\\.", colnames(maxquant_protein_table), value=TRUE)
head(intensity_colnames)
#> [1] "LFQ.intensity.CG1407.01" "LFQ.intensity.CG1407.02" "LFQ.intensity.CG1407.03"
#> [4] "LFQ.intensity.CG4676.01" "LFQ.intensity.CG4676.02" "LFQ.intensity.CG4676.03"
# Create the intensity matrix
abundance_matrix <- as.matrix(maxquant_protein_table[, intensity_colnames])
# Adapt column and row maxquant_protein_table
colnames(abundance_matrix) <- sub("^LFQ\\.intensity\\.", "", intensity_colnames)
rownames(abundance_matrix) <- maxquant_protein_table$Protein.IDs
# Print some rows of the matrix with short names so they fit on the screen
abundance_matrix[46:48, 1:6]
#> CG1407.01 CG1407.02 CG1407.03 CG4676.01 CG4676.02 CG4676.03
#> A0A0B4K6W1;P08970 713400 845440 0 0 1032600 0
#> A0A0B4K6W2;A0A0B4K7S0;P55824-3;P55824 5018800 4429500 2667200 0 8780200 1395800
#> A0A0B4K6X7;A1Z8J0 0 0 0 0 0 0After 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.
abundance_matrix[abundance_matrix == 0] <- NA
abundance_matrix <- log2(abundance_matrix)
abundance_matrix[46:48, 1:6]
#> CG1407.01 CG1407.02 CG1407.03 CG4676.01 CG4676.02 CG4676.03
#> A0A0B4K6W1;P08970 19.44435 19.68934 NA NA 19.97785 NA
#> A0A0B4K6W2;A0A0B4K7S0;P55824-3;P55824 22.25891 22.07871 21.34689 NA 23.06582 20.41266
#> A0A0B4K6X7;A1Z8J0 NA NA NA NA NA NAQuality 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.
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.
# This chunk only works if pheatmap is installed
# install.packages("pheatmap")
sel <- c(1:3, # CG1407
7:9, # CG59163
22:24)# CG6618
plot_mat <- as.matrix(da$mean)[sel, sel]
# Remove diagonal elements, so that the colorscale is not distorted
plot_mat[diag(9) == 1] <- NA
# 95% conf interval is approx `sd * 1.96`
uncertainty <- matrix(paste0(" ± ",round(as.matrix(da$sd * 1.96)[sel, sel], 1)), nrow=9)
pheatmap::pheatmap(plot_mat,
cluster_rows = FALSE, cluster_cols = FALSE,
display_numbers= uncertainty,
number_color = "black")
Fit the Probabilistic Dropout Model
In the next step, we will fit the actual linear probabilistic dropout model to the normalized data. But before we start, I will create a data.frame that contains some additional information on each sample, in particular to which condition that sample belongs.
# The best way to create this data.frame depends on the column naming scheme
sample_info_df <- data.frame(name = colnames(normalized_abundance_matrix),
stringsAsFactors = FALSE)
sample_info_df$condition <- substr(sample_info_df$name, 1, nchar(sample_info_df$name) - 3)
sample_info_df$replicate <- as.numeric(
substr(sample_info_df$name, nchar(sample_info_df$name) - 1, 20)
)
sample_info_df
#> name condition replicate
#> 1 CG1407.01 CG1407 1
#> 2 CG1407.02 CG1407 2
#> 3 CG1407.03 CG1407 3
#> 4 CG4676.01 CG4676 1
#> 5 CG4676.02 CG4676 2
#> 6 CG4676.03 CG4676 3
#> 7 CG51963.01 CG51963 1
#> 8 CG51963.02 CG51963 2
#> 9 CG51963.03 CG51963 3
#> 10 CG5620A.01 CG5620A 1
#> 11 CG5620A.02 CG5620A 2
#> 12 CG5620A.03 CG5620A 3
#> 13 CG5620B.01 CG5620B 1
#> 14 CG5620B.02 CG5620B 2
#> 15 CG5620B.03 CG5620B 3
#> 16 CG5880.01 CG5880 1
#> 17 CG5880.02 CG5880 2
#> 18 CG5880.03 CG5880 3
#> 19 CG6017.01 CG6017 1
#> 20 CG6017.02 CG6017 2
#> 21 CG6017.03 CG6017 3
#> 22 CG6618.01 CG6618 1
#> 23 CG6618.02 CG6618 2
#> 24 CG6618.03 CG6618 3
#> 25 CG6627.01 CG6627 1
#> 26 CG6627.02 CG6627 2
#> 27 CG6627.03 CG6627 3
#> 28 CG8314.01 CG8314 1
#> 29 CG8314.02 CG8314 2
#> 30 CG8314.03 CG8314 3
#> 31 GsbPI.001 GsbPI. 1
#> 32 GsbPI.002 GsbPI. 2
#> 33 GsbPI.003 GsbPI. 3
#> 34 S2R.01 S2R 1
#> 35 S2R.02 S2R 2
#> 36 S2R.03 S2R 3Now 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.
fit <- proDA(normalized_abundance_matrix, design = ~ condition,
col_data = sample_info_df, reference_level = "S2R")
fit
#> Parameters of the probabilistic dropout model
#>
#> The dataset contains 36 samples and 122 proteins
#> 59.7% of the values are missing
#>
#> Experimental design: y~condition
#> The model has successfully converged.
#>
#> The inferred parameters are:
#> location_prior_mean: 19.5
#> location_prior_scale: 8.37
#> location_prior_df: 3
#> variance_prior_scale: 0.283
#> variance_prior_df: 1.64
#> dropout_curve_position: 19.9, 19, 20.1, 22.8, ...
#> dropout_curve_scale: -0.816, -0.601, -1.02, -1.31, ...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 $-operator is overloaded
and shows a list of possible functions:
Screenshot from Rstudio suggesting the available
functions
# Equivalent to feature_parameters(fit)
fit$feature_parameters
#> n_approx
#> Q8IP47;Q9VJP8;Q9V435;A0A023GPQ3;Q2PDT6;Q7K540 12.00100
#> A0A023GPV6;A8JV04;Q7YU03 12.00100
#> A0A023GQA5;P24156 19.27947
#> Q1RKY1;A0A0B4LG19;A0A0B4J401;B7YZL2;A1ZBH5;B7YZL7;B7YZL6;Q7YTZ4;B7YZL5;B7YZL8;Q0E919;B7YZL1;B7YZL3 12.00100
#> A0A0B4JD00;A8DY69;I0E2I4;A0A0B4JCQ5;Q8SXP0;E5DK16;A0A0B4JD31;A0A0B4JCS1;A0A0B4JD27 17.39251
#> A0A0B4JCT8;Q9V780 12.00100
#> A0A0B4LHQ4;A0A0B4JD62;A0A0B4JDB5;A0A0B4LGQ5;A0A0B4JCW5;A0A0B4JCV6;A0A0B4LGR2;A0A0B4JDA1;Q9VN58 12.00100
#> A0A0B4JCW4;Q9VHJ8;Q95U38 28.92211
#> Q9VDV4;A0A0B4JCY1;Q8IN71;A0A0B4KGH4 12.00100
#> A0A0B4JCY6;Q7KSF4;A0A0B4KHN1;A0A0B4KGT8;Q9VEN1;A0A0B4KGB3;A4V310;B7Z0L2;Q9VEN1-2 12.00100
#> E1JIU2;Q9VCQ0;A0A0B4JCZ2;A8JR87;A0A0B4KH86 12.00100
#> A0A0B4LEY5;A1Z7T2;A0A0B4JD07;A0A0B4K6U3;A0A0B4K727;A0A0B4LF03;A0A0B4LEI8;E1JH15;A0A0B4JD60;A1Z7T1;A1Z7T3;A0A0B4LFX2;A8DY76;A1Z7T0;A1Z7T0-2;A1Z7T4 13.26608
#> A0A0B4JD11;Q9NJH0 34.50686
#> A0A0B4KHW7;Q961V3;A0A0B4KHJ3;A0A0B4KHF5;A0A0B4JD23;Q7KRU0;Q8IMI0;A0A0B4JDE3;Q9VA53 12.00100
#> A0A0B4JD46;Q8T8R1 33.97963
#> A0A0B4JD48;Q95029-2;Q95029 29.09359
#> A0A0B4JD95;Q59E58;A0A0B4JD57;Q59E59;A0A0B4K7Q4;Q99323-2;Q99323-4;Q99323-1;Q99323 21.16544
#> A0A0B4JDA0;Q9VF03 14.59007
#> A0A0B4JDC3;Q9VGU5 12.00100
#> A0A0B4JDG2;Q9I7I8;A0A0B4JDD8;B7Z0M9;Q7KSB3;A0A0B4JCZ0;Q8IN56;Q8IN55 34.87078
#> A0A0B4JDG5;Q8IMZ9 19.68857
#> Q9VNF8;A0A0B4K6T4;A0A0B4K5Z8 14.13381
#> A0A0B4K603;A0A0B4K6V2;A0A0B4KF90;A0A0B4K631;A0A0B4KGC6;B7Z0U7;A0A0B4KFE2;E1JJ78;Q9VI75 12.00100
#> Q7KNC5;Q8MSQ5;Q8IPN9;Q9VNA1;Q0KIB9;A0A0B4K620;B7Z0T3;Q9VNA2;A0A0B4K6S8;A4V2F2;Q4ABH3;A0A0B4K699;A0A0B4KG49;B7Z0T6;Q8IPN8;A0A0B4KF88;Q8IPN6;Q7KTR7;Q7KTR8 13.52804
#> Q9VEZ3;E1JIM4;A0A0B4K664;A0A0B4K700 17.48975
#> Q8INB6;Q86BR9;Q86NK8;Q4AB31;A0A0B4K7C4;A0A0B4K697;A0A0B4KHL4;Q8IHB0 31.78246
#> 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 23.49573
#> A0A0B4K6D2;Q9VH95 28.98290
#> A0A0B4K6S1;A0A0B4K6F4;Q8SZN9;E0R905;Q7KSP5;A0A0B4KGA3 12.00100
#> Q9VC62;A0A0B4KGU9;Q7KS16;A0A0B4K6F9 12.00100
#> A0A0B4K6G6;Q9VG05 36.00000
#> 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 12.00100
#> A0A0B4K6J3;Q8IMW5;A0A0C4DHB7;A0A0B4K7S6 12.00100
#> A0A0B4K6K7;Q9VI55;Q9VI55-2 22.56540
#> A0A0B4K6K9;A0A0B4K7Y7;Q9VAW5-1;Q9VAW5;Q9VAW5-2 27.52470
#> Q9VEF7;A0A0B4KHP1;A0A0B4K6L3 12.00100
#> A0A0B4K6L4;Q27601 12.00100
#> A0A0B4K6N1;Q8MLY8 36.00000
#> A0A0B4K6N7;Q9VE34;Q9VE34-2 34.14210
#> 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 11.40294
#> 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 17.64666
#> A0A0B4KHW3;A0A0B4K6V1;Q9VA73-3;Q9VA73-2;Q9VA73 22.13185
#> A0A0B4K6W1;P08970 20.21044
#> A0A0B4K6W2;A0A0B4K7S0;P55824-3;P55824 32.25275
#> A0A0B4K6X7;A1Z8J0 12.00100
#> Q9VHK3;A0A0B4K6Y7;Q8INQ0;A8JQV7;Q9VHK4;B7Z0U1;Q8MQQ3 16.28831
#> A0A0B4LHK4;A0A0B4KHZ8;A0A0B4KHR8;A0A0B4K725;Q9VCA8 33.14301
#> A0A0B4LF93;A1Z928;A1Z927;A0A0B4LF82;Q5U0Y0;A0A0B4K765 12.00100
#> A0A0B4K7A5 36.00000
#> A0A0B4K7G4;P13469 29.01683
#> B7YZQ7;A0A0B4K7G9;O77460 12.00100
#> A0A0B4K7H0;Q7KN74 12.00100
#> Q9VBU7;A0A0B4K7J2 33.88477
#> Q95U21;Q7JQ36;A0A0B4K7J3 17.13489
#> A0A0B4K7K6;Q9VBG6 12.36403
#> A0A0B4K7L0;Q9W252 18.37926
#> A0A0B4K7N2;Q8IN00;D5A7N8;Q9VCX2;Q9VCX1-2;Q9VCX1-4;Q9VCX1-3;Q9VCX1 19.91114
#> Q9VCH4;A0A0B4K7Q6 12.00100
#> A0A0B4K7T7;A1ZAN6;A1ZAN7;A0A0B4LFF8 18.66579
#> A0A0B4KFL2;A1Z9E0;A1Z9D9;A0A0B4K7Y4 12.28942
#> A0A0B4K7Z5;Q7KLV9;Q7KLV9-2 28.86201
#> A0A0B4K812;Q7KNS3 12.00100
#> A0A0B4KFL0;A0A0B4K851;Q4Z8K6-3;Q4Z8K6-2;Q4Z8K6 12.00100
#> A1Z945;A0A0B4K859 31.86825
#> A0A0B4K882;Q7K2Y9 12.00100
#> A0A0B4K8A5;Q9W2F2 27.59483
#> A0A0B4K8A6;Q9W288 12.00100
#> Q5LJQ4;A0A0B4KEH8;A0A0B4KEC2;Q9W5H8 12.00100
#> A0A0B4KED0;Q9W5N2 12.00100
#> A0A0B4KED9;O16844 14.41989
#> A0A0B4KEE4;A1Z6Q1 12.00100
#> E1JGZ7;E1JGZ8;A1Z734;A0A0B4KEE7 12.00100
#> A0A0B4KEI5;Q9V9K7 12.00100
#> Q7JVY0;A0A0B4KEU5;A0A0B4KEJ7 11.50030
#> A1Z9L2;A1Z9L0;A0A0B4KFX4;Q8T076;A0A0B4KEP1;A0A0B4LFC1;A0A0B4KFM5;A0A0B4KF25 18.49796
#> Q5U156;A0A0B4KER0;Q95RL2 19.45310
#> A0A0B4KET0;Q1LZ08 12.99128
#> A0A0B4KFU3;A0A0B4KG58;B7YZJ2;B7YZJ1;E1JH90;A0A0B4KET5;A0A0B4KFA4;E1JH91;A0A0B4KEY4;A1ZAU8-2;A1ZAU8-3;A1ZAU8;A0A0B4KEY6 24.48288
#> Q0E901;A0A0B4KFE6;A0A0B4KEW2 12.00100
#> A0A0B4KFR7;A0A0B4KEW6;Q7KLE5 12.00100
#> A0A0B4KEX0;A1ZAB5 34.95651
#> Q0E993;A0A0B4KF06 25.94287
#> A0A0B4KF46;Q8T0L3 28.61873
#> A0A0B4KG14;A0A0B4KF57;Q9VMY8 23.37394
#> Q7JQL5;A0A0B4KF86 12.00100
#> Q8T0M2;Q0E9C6;A0A0B4KFA3;A8DY97;A8DY98 12.00100
#> Q9VHX9;A0A0B4KFA6 16.73868
#> A0A0B4LGR1;Q9VI14;A0A0B4KFB8;Q6NN86 12.00100
#> A1Z7H3;Q8T3L1;A1Z7H2;A0A0B4KFE4 17.03606
#> A0A0B4KFE5;Q04448-2;Q04448 12.00100
#> A0A0B4KFE9;A1Z8P9 12.00100
#> A0A0B4KGE6;A0A0B4KFH4;P26270 12.00100
#> A0A0B4KFJ7;Q9VHH9 14.25233
#> A0A0B4KFN1;A1Z9R6;A0A0B4KFX9;Q9V727 12.00100
#> A0A0B4KH36;A0A0B4KFQ0;A0A0B4KGR9;Q9VH01;A0A0B4KG50 15.88330
#> A4UZI0;A0A0B4LGK5;A1ZA18;A0A0B4KFR5;A0A0B4KG24 25.95769
#> A0A0B4KFX5;A0A0B4KGG9;A4V2S3;A0A0B4KHB2;A0A0B4KFT4;A0A0B4KGZ7;O46036-2;O46036 18.97894
#> A0A0B4KFU5;Q9V853 10.50357
#> A0A0B4KFW0;Q8T0S6 25.39207
#> Q9VHC4;A0A0B4KFZ2;Q6AWD5 12.00100
#> A0A0B4KFZ9;P84040 27.96637
#> Q7K0G4;A0A0B4KG11;F0JAK5 12.00100
#> A0A0B4KG32;A0A0B4KH26;Q9VH20 11.49537
#> A0A0B4KG41;Q9VES1 12.00100
#> Q9VF92;A0A0B4KG69 12.00100
#> Q9N6D7;A0A0B4KG96 23.14041
#> A0A0B4KHS7;A0A0B4KGE1;Q24151;A0A0B4KGI7;Q24151-2;A0A0B4KHS6;A0A0B4KH10;Q24151-4;Q24151-3 31.04213
#> Q8MQJ5;A0A0B4KGF5;Q9VE69 14.40945
#> Q32KD3;Q7KSW1;Q494I1;A0A0B4KGS8;Q9VHW9;A0A0B4KGF6 25.49767
#> A4V364;A8JR54;Q8IN47;A0A0B4KGK8;Q8IN48;A0A0B4KH21;A0A0B4KH24;A0A0B4KGF9;Q9VDI8;Q7KSA0;A0A0B4KHH8;A0A0B4KHI4;Q95TW4;A0A0B4KGK5;A0A0B4KHT5 12.00100
#> E1JIR4;A0A0B4KGG8;P13607-7;P13607-6;P13607-2;P13607-4;P13607-5;P13607;P13607-3;A8QI34 32.35331
#> A0A0B4KGH0;A0A0B4KHR4;Q9VDW6-2;Q9VDW6-1;Q9VDW6;Q9VDW6-4;Q9VDW6-3;A0A0B4KGB9;Q9VDW3;A0A0B4KHE2;Q7YU29;Q0KI50 12.00100
#> A0A0B4KGI6;Q9VN82;A0A0B4KG43;Q8IPP4;Q8IPP3;A0A0B4KF82;A0A0B4KFK9 26.15977
#> A0A0B4KGJ5;Q9NIV1;A0A0B4KG56 12.00100
#> A0A0B4KGK3;Q95RA8 12.00100
#> A0A0B4KGP8;Q24208;Q24208-2 31.57354
#> Q9VEV1;A0A0B4KGS4 31.92691
#> A0A0B4KGU4;Q9VHP0;M9PBB5;P09052 36.00000
#> A0A0B4KGW0;Q8IMX7-2;A0A0B4J3Z9;Q8IMX7 12.00100
#> df
#> Q8IP47;Q9VJP8;Q9V435;A0A023GPQ3;Q2PDT6;Q7K540 0.0010000
#> A0A023GPV6;A8JV04;Q7YU03 0.0010000
#> A0A023GQA5;P24156 8.9259450
#> Q1RKY1;A0A0B4LG19;A0A0B4J401;B7YZL2;A1ZBH5;B7YZL7;B7YZL6;Q7YTZ4;B7YZL5;B7YZL8;Q0E919;B7YZL1;B7YZL3 0.0010000
#> A0A0B4JD00;A8DY69;I0E2I4;A0A0B4JCQ5;Q8SXP0;E5DK16;A0A0B4JD31;A0A0B4JCS1;A0A0B4JD27 7.0389850
#> A0A0B4JCT8;Q9V780 0.0010000
#> A0A0B4LHQ4;A0A0B4JD62;A0A0B4JDB5;A0A0B4LGQ5;A0A0B4JCW5;A0A0B4JCV6;A0A0B4LGR2;A0A0B4JDA1;Q9VN58 0.0010000
#> A0A0B4JCW4;Q9VHJ8;Q95U38 18.5685826
#> Q9VDV4;A0A0B4JCY1;Q8IN71;A0A0B4KGH4 0.0010000
#> A0A0B4JCY6;Q7KSF4;A0A0B4KHN1;A0A0B4KGT8;Q9VEN1;A0A0B4KGB3;A4V310;B7Z0L2;Q9VEN1-2 0.0010000
#> E1JIU2;Q9VCQ0;A0A0B4JCZ2;A8JR87;A0A0B4KH86 0.0010000
#> A0A0B4LEY5;A1Z7T2;A0A0B4JD07;A0A0B4K6U3;A0A0B4K727;A0A0B4LF03;A0A0B4LEI8;E1JH15;A0A0B4JD60;A1Z7T1;A1Z7T3;A0A0B4LFX2;A8DY76;A1Z7T0;A1Z7T0-2;A1Z7T4 2.9125568
#> A0A0B4JD11;Q9NJH0 24.1533321
#> A0A0B4KHW7;Q961V3;A0A0B4KHJ3;A0A0B4KHF5;A0A0B4JD23;Q7KRU0;Q8IMI0;A0A0B4JDE3;Q9VA53 0.0010000
#> A0A0B4JD46;Q8T8R1 23.6261073
#> A0A0B4JD48;Q95029-2;Q95029 18.7400618
#> A0A0B4JD95;Q59E58;A0A0B4JD57;Q59E59;A0A0B4K7Q4;Q99323-2;Q99323-4;Q99323-1;Q99323 10.8119177
#> A0A0B4JDA0;Q9VF03 4.2365420
#> A0A0B4JDC3;Q9VGU5 0.0010000
#> A0A0B4JDG2;Q9I7I8;A0A0B4JDD8;B7Z0M9;Q7KSB3;A0A0B4JCZ0;Q8IN56;Q8IN55 24.5172515
#> A0A0B4JDG5;Q8IMZ9 9.3350410
#> Q9VNF8;A0A0B4K6T4;A0A0B4K5Z8 3.7802832
#> A0A0B4K603;A0A0B4K6V2;A0A0B4KF90;A0A0B4K631;A0A0B4KGC6;B7Z0U7;A0A0B4KFE2;E1JJ78;Q9VI75 0.0010000
#> Q7KNC5;Q8MSQ5;Q8IPN9;Q9VNA1;Q0KIB9;A0A0B4K620;B7Z0T3;Q9VNA2;A0A0B4K6S8;A4V2F2;Q4ABH3;A0A0B4K699;A0A0B4KG49;B7Z0T6;Q8IPN8;A0A0B4KF88;Q8IPN6;Q7KTR7;Q7KTR8 3.1745156
#> Q9VEZ3;E1JIM4;A0A0B4K664;A0A0B4K700 7.1362219
#> Q8INB6;Q86BR9;Q86NK8;Q4AB31;A0A0B4K7C4;A0A0B4K697;A0A0B4KHL4;Q8IHB0 21.4289300
#> 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 13.1422033
#> A0A0B4K6D2;Q9VH95 18.6293685
#> A0A0B4K6S1;A0A0B4K6F4;Q8SZN9;E0R905;Q7KSP5;A0A0B4KGA3 0.0010000
#> Q9VC62;A0A0B4KGU9;Q7KS16;A0A0B4K6F9 0.0010000
#> A0A0B4K6G6;Q9VG05 25.6464732
#> 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 0.0010000
#> A0A0B4K6J3;Q8IMW5;A0A0C4DHB7;A0A0B4K7S6 0.0010000
#> A0A0B4K6K7;Q9VI55;Q9VI55-2 12.2118748
#> A0A0B4K6K9;A0A0B4K7Y7;Q9VAW5-1;Q9VAW5;Q9VAW5-2 17.1711765
#> Q9VEF7;A0A0B4KHP1;A0A0B4K6L3 0.0010000
#> A0A0B4K6L4;Q27601 0.0010000
#> A0A0B4K6N1;Q8MLY8 25.6464731
#> A0A0B4K6N7;Q9VE34;Q9VE34-2 23.7885696
#> 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 1.0494088
#> D0Z768;A0A0B4K6T1;A0A0B4K7U5;E1JH02;A0A0B4KFC5;Q86S05-3;Q86S05-2;Q86S05 0.0010000
#> A0A0B4K6T7 0.0010000
#> A0A0B4K6U2;E1JIJ7;Q8INH9 0.0010000
#> A0A0B4K6U6;Q08473-3;Q08473-2;Q08473;Q08473-4 7.2931375
#> A0A0B4KHW3;A0A0B4K6V1;Q9VA73-3;Q9VA73-2;Q9VA73 11.7783244
#> A0A0B4K6W1;P08970 9.8569163
#> A0A0B4K6W2;A0A0B4K7S0;P55824-3;P55824 21.8992215
#> A0A0B4K6X7;A1Z8J0 0.0010000
#> Q9VHK3;A0A0B4K6Y7;Q8INQ0;A8JQV7;Q9VHK4;B7Z0U1;Q8MQQ3 5.9347806
#> A0A0B4LHK4;A0A0B4KHZ8;A0A0B4KHR8;A0A0B4K725;Q9VCA8 22.7894833
#> A0A0B4LF93;A1Z928;A1Z927;A0A0B4LF82;Q5U0Y0;A0A0B4K765 0.0010000
#> A0A0B4K7A5 25.6464731
#> A0A0B4K7G4;P13469 18.6633062
#> B7YZQ7;A0A0B4K7G9;O77460 0.0010000
#> A0A0B4K7H0;Q7KN74 0.0010000
#> Q9VBU7;A0A0B4K7J2 23.5312472
#> Q95U21;Q7JQ36;A0A0B4K7J3 6.7813653
#> A0A0B4K7K6;Q9VBG6 2.0105056
#> A0A0B4K7L0;Q9W252 8.0257366
#> A0A0B4K7N2;Q8IN00;D5A7N8;Q9VCX2;Q9VCX1-2;Q9VCX1-4;Q9VCX1-3;Q9VCX1 9.5576121
#> Q9VCH4;A0A0B4K7Q6 0.0010000
#> A0A0B4K7T7;A1ZAN6;A1ZAN7;A0A0B4LFF8 8.3122608
#> A0A0B4KFL2;A1Z9E0;A1Z9D9;A0A0B4K7Y4 1.9358958
#> A0A0B4K7Z5;Q7KLV9;Q7KLV9-2 18.5084879
#> A0A0B4K812;Q7KNS3 0.0010000
#> A0A0B4KFL0;A0A0B4K851;Q4Z8K6-3;Q4Z8K6-2;Q4Z8K6 0.0010000
#> A1Z945;A0A0B4K859 21.5147189
#> A0A0B4K882;Q7K2Y9 0.0010000
#> A0A0B4K8A5;Q9W2F2 17.2413061
#> A0A0B4K8A6;Q9W288 0.0010000
#> Q5LJQ4;A0A0B4KEH8;A0A0B4KEC2;Q9W5H8 0.0010000
#> A0A0B4KED0;Q9W5N2 0.0010000
#> A0A0B4KED9;O16844 4.0663615
#> A0A0B4KEE4;A1Z6Q1 0.0010000
#> E1JGZ7;E1JGZ8;A1Z734;A0A0B4KEE7 0.0010000
#> A0A0B4KEI5;Q9V9K7 0.0010000
#> Q7JVY0;A0A0B4KEU5;A0A0B4KEJ7 1.1467780
#> A1Z9L2;A1Z9L0;A0A0B4KFX4;Q8T076;A0A0B4KEP1;A0A0B4LFC1;A0A0B4KFM5;A0A0B4KF25 8.1444363
#> Q5U156;A0A0B4KER0;Q95RL2 9.0995742
#> A0A0B4KET0;Q1LZ08 2.6377520
#> A0A0B4KFU3;A0A0B4KG58;B7YZJ2;B7YZJ1;E1JH90;A0A0B4KET5;A0A0B4KFA4;E1JH91;A0A0B4KEY4;A1ZAU8-2;A1ZAU8-3;A1ZAU8;A0A0B4KEY6 14.1293507
#> Q0E901;A0A0B4KFE6;A0A0B4KEW2 0.0010000
#> A0A0B4KFR7;A0A0B4KEW6;Q7KLE5 0.0010000
#> A0A0B4KEX0;A1ZAB5 24.6029793
#> Q0E993;A0A0B4KF06 15.5893473
#> A0A0B4KF46;Q8T0L3 18.2652057
#> A0A0B4KG14;A0A0B4KF57;Q9VMY8 13.0204121
#> Q7JQL5;A0A0B4KF86 0.0010000
#> Q8T0M2;Q0E9C6;A0A0B4KFA3;A8DY97;A8DY98 0.0010000
#> Q9VHX9;A0A0B4KFA6 6.3851562
#> A0A0B4LGR1;Q9VI14;A0A0B4KFB8;Q6NN86 0.0010000
#> A1Z7H3;Q8T3L1;A1Z7H2;A0A0B4KFE4 6.6825328
#> A0A0B4KFE5;Q04448-2;Q04448 0.0010000
#> A0A0B4KFE9;A1Z8P9 0.0010000
#> A0A0B4KGE6;A0A0B4KFH4;P26270 0.0010000
#> A0A0B4KFJ7;Q9VHH9 3.8988004
#> A0A0B4KFN1;A1Z9R6;A0A0B4KFX9;Q9V727 0.0010000
#> A0A0B4KH36;A0A0B4KFQ0;A0A0B4KGR9;Q9VH01;A0A0B4KG50 5.5297716
#> A4UZI0;A0A0B4LGK5;A1ZA18;A0A0B4KFR5;A0A0B4KG24 15.6041618
#> A0A0B4KFX5;A0A0B4KGG9;A4V2S3;A0A0B4KHB2;A0A0B4KFT4;A0A0B4KGZ7;O46036-2;O46036 8.6254142
#> A0A0B4KFU5;Q9V853 0.1500442
#> A0A0B4KFW0;Q8T0S6 15.0385439
#> Q9VHC4;A0A0B4KFZ2;Q6AWD5 0.0010000
#> A0A0B4KFZ9;P84040 17.6128479
#> Q7K0G4;A0A0B4KG11;F0JAK5 0.0010000
#> A0A0B4KG32;A0A0B4KH26;Q9VH20 1.1418454
#> A0A0B4KG41;Q9VES1 0.0010000
#> Q9VF92;A0A0B4KG69 0.0010000
#> Q9N6D7;A0A0B4KG96 12.7868801
#> A0A0B4KHS7;A0A0B4KGE1;Q24151;A0A0B4KGI7;Q24151-2;A0A0B4KHS6;A0A0B4KH10;Q24151-4;Q24151-3 20.6886007
#> Q8MQJ5;A0A0B4KGF5;Q9VE69 4.0559271
#> Q32KD3;Q7KSW1;Q494I1;A0A0B4KGS8;Q9VHW9;A0A0B4KGF6 15.1441388
#> A4V364;A8JR54;Q8IN47;A0A0B4KGK8;Q8IN48;A0A0B4KH21;A0A0B4KH24;A0A0B4KGF9;Q9VDI8;Q7KSA0;A0A0B4KHH8;A0A0B4KHI4;Q95TW4;A0A0B4KGK5;A0A0B4KHT5 0.0010000
#> E1JIR4;A0A0B4KGG8;P13607-7;P13607-6;P13607-2;P13607-4;P13607-5;P13607;P13607-3;A8QI34 21.9997835
#> A0A0B4KGH0;A0A0B4KHR4;Q9VDW6-2;Q9VDW6-1;Q9VDW6;Q9VDW6-4;Q9VDW6-3;A0A0B4KGB9;Q9VDW3;A0A0B4KHE2;Q7YU29;Q0KI50 0.0010000
#> A0A0B4KGI6;Q9VN82;A0A0B4KG43;Q8IPP4;Q8IPP3;A0A0B4KF82;A0A0B4KFK9 15.8062443
#> A0A0B4KGJ5;Q9NIV1;A0A0B4KG56 0.0010000
#> A0A0B4KGK3;Q95RA8 0.0010000
#> A0A0B4KGP8;Q24208;Q24208-2 21.2200100
#> Q9VEV1;A0A0B4KGS4 21.5733881
#> A0A0B4KGU4;Q9VHP0;M9PBB5;P09052 25.6464732
#> A0A0B4KGW0;Q8IMX7-2;A0A0B4J3Z9;Q8IMX7 0.0010000
#> s2
#> Q8IP47;Q9VJP8;Q9V435;A0A023GPQ3;Q2PDT6;Q7K540 3.807766e+03
#> A0A023GPV6;A8JV04;Q7YU03 2.439146e+03
#> A0A023GQA5;P24156 4.073854e+00
#> Q1RKY1;A0A0B4LG19;A0A0B4J401;B7YZL2;A1ZBH5;B7YZL7;B7YZL6;Q7YTZ4;B7YZL5;B7YZL8;Q0E919;B7YZL1;B7YZL3 8.497823e+02
#> A0A0B4JD00;A8DY69;I0E2I4;A0A0B4JCQ5;Q8SXP0;E5DK16;A0A0B4JD31;A0A0B4JCS1;A0A0B4JD27 4.702317e-01
#> A0A0B4JCT8;Q9V780 2.472292e+03
#> A0A0B4LHQ4;A0A0B4JD62;A0A0B4JDB5;A0A0B4LGQ5;A0A0B4JCW5;A0A0B4JCV6;A0A0B4LGR2;A0A0B4JDA1;Q9VN58 2.410135e+03
#> A0A0B4JCW4;Q9VHJ8;Q95U38 2.170357e-01
#> Q9VDV4;A0A0B4JCY1;Q8IN71;A0A0B4KGH4 1.797596e+03
#> A0A0B4JCY6;Q7KSF4;A0A0B4KHN1;A0A0B4KGT8;Q9VEN1;A0A0B4KGB3;A4V310;B7Z0L2;Q9VEN1-2 1.881432e+03
#> E1JIU2;Q9VCQ0;A0A0B4JCZ2;A8JR87;A0A0B4KH86 9.632541e+02
#> A0A0B4LEY5;A1Z7T2;A0A0B4JD07;A0A0B4K6U3;A0A0B4K727;A0A0B4LF03;A0A0B4LEI8;E1JH15;A0A0B4JD60;A1Z7T1;A1Z7T3;A0A0B4LFX2;A8DY76;A1Z7T0;A1Z7T0-2;A1Z7T4 1.942910e-01
#> A0A0B4JD11;Q9NJH0 3.789067e+00
#> A0A0B4KHW7;Q961V3;A0A0B4KHJ3;A0A0B4KHF5;A0A0B4JD23;Q7KRU0;Q8IMI0;A0A0B4JDE3;Q9VA53 2.480900e+03
#> A0A0B4JD46;Q8T8R1 3.536554e-01
#> A0A0B4JD48;Q95029-2;Q95029 8.611482e-01
#> A0A0B4JD95;Q59E58;A0A0B4JD57;Q59E59;A0A0B4K7Q4;Q99323-2;Q99323-4;Q99323-1;Q99323 6.828734e+00
#> A0A0B4JDA0;Q9VF03 1.110449e+00
#> A0A0B4JDC3;Q9VGU5 2.356914e+03
#> A0A0B4JDG2;Q9I7I8;A0A0B4JDD8;B7Z0M9;Q7KSB3;A0A0B4JCZ0;Q8IN56;Q8IN55 6.475658e-01
#> A0A0B4JDG5;Q8IMZ9 2.620282e-01
#> Q9VNF8;A0A0B4K6T4;A0A0B4K5Z8 1.937352e+00
#> A0A0B4K603;A0A0B4K6V2;A0A0B4KF90;A0A0B4K631;A0A0B4KGC6;B7Z0U7;A0A0B4KFE2;E1JJ78;Q9VI75 1.174323e+03
#> Q7KNC5;Q8MSQ5;Q8IPN9;Q9VNA1;Q0KIB9;A0A0B4K620;B7Z0T3;Q9VNA2;A0A0B4K6S8;A4V2F2;Q4ABH3;A0A0B4K699;A0A0B4KG49;B7Z0T6;Q8IPN8;A0A0B4KF88;Q8IPN6;Q7KTR7;Q7KTR8 1.251952e+00
#> Q9VEZ3;E1JIM4;A0A0B4K664;A0A0B4K700 6.147079e-01
#> Q8INB6;Q86BR9;Q86NK8;Q4AB31;A0A0B4K7C4;A0A0B4K697;A0A0B4KHL4;Q8IHB0 1.421839e-01
#> 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 4.241726e-01
#> A0A0B4K6D2;Q9VH95 1.002541e+00
#> A0A0B4K6S1;A0A0B4K6F4;Q8SZN9;E0R905;Q7KSP5;A0A0B4KGA3 2.405006e+03
#> Q9VC62;A0A0B4KGU9;Q7KS16;A0A0B4K6F9 1.218269e+03
#> A0A0B4K6G6;Q9VG05 7.309951e-01
#> 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 1.846585e+03
#> A0A0B4K6J3;Q8IMW5;A0A0C4DHB7;A0A0B4K7S6 2.434476e+03
#> A0A0B4K6K7;Q9VI55;Q9VI55-2 9.974344e-02
#> A0A0B4K6K9;A0A0B4K7Y7;Q9VAW5-1;Q9VAW5;Q9VAW5-2 2.030310e-01
#> Q9VEF7;A0A0B4KHP1;A0A0B4K6L3 3.130949e+03
#> A0A0B4K6L4;Q27601 2.460680e+03
#> A0A0B4K6N1;Q8MLY8 4.398148e-01
#> A0A0B4K6N7;Q9VE34;Q9VE34-2 4.486041e-01
#> 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 2.689342e+00
#> D0Z768;A0A0B4K6T1;A0A0B4K7U5;E1JH02;A0A0B4KFC5;Q86S05-3;Q86S05-2;Q86S05 1.913818e+03
#> A0A0B4K6T7 4.633338e+03
#> A0A0B4K6U2;E1JIJ7;Q8INH9 2.473004e+03
#> A0A0B4K6U6;Q08473-3;Q08473-2;Q08473;Q08473-4 5.212385e-01
#> A0A0B4KHW3;A0A0B4K6V1;Q9VA73-3;Q9VA73-2;Q9VA73 6.512060e-02
#> A0A0B4K6W1;P08970 7.476826e-02
#> A0A0B4K6W2;A0A0B4K7S0;P55824-3;P55824 6.971225e-01
#> A0A0B4K6X7;A1Z8J0 3.227568e+03
#> Q9VHK3;A0A0B4K6Y7;Q8INQ0;A8JQV7;Q9VHK4;B7Z0U1;Q8MQQ3 9.108018e-01
#> A0A0B4LHK4;A0A0B4KHZ8;A0A0B4KHR8;A0A0B4K725;Q9VCA8 2.468253e-01
#> A0A0B4LF93;A1Z928;A1Z927;A0A0B4LF82;Q5U0Y0;A0A0B4K765 2.432647e+03
#> A0A0B4K7A5 4.282069e-01
#> A0A0B4K7G4;P13469 1.045587e+00
#> B7YZQ7;A0A0B4K7G9;O77460 7.558386e+02
#> A0A0B4K7H0;Q7KN74 1.396696e+03
#> Q9VBU7;A0A0B4K7J2 5.182516e-01
#> Q95U21;Q7JQ36;A0A0B4K7J3 1.280906e-01
#> A0A0B4K7K6;Q9VBG6 2.923486e-01
#> A0A0B4K7L0;Q9W252 1.306916e-01
#> A0A0B4K7N2;Q8IN00;D5A7N8;Q9VCX2;Q9VCX1-2;Q9VCX1-4;Q9VCX1-3;Q9VCX1 2.304374e-01
#> Q9VCH4;A0A0B4K7Q6 9.881891e+04
#> A0A0B4K7T7;A1ZAN6;A1ZAN7;A0A0B4LFF8 3.082105e-01
#> A0A0B4KFL2;A1Z9E0;A1Z9D9;A0A0B4K7Y4 2.336057e+01
#> A0A0B4K7Z5;Q7KLV9;Q7KLV9-2 3.950359e-01
#> A0A0B4K812;Q7KNS3 2.758784e+03
#> A0A0B4KFL0;A0A0B4K851;Q4Z8K6-3;Q4Z8K6-2;Q4Z8K6 3.226574e+03
#> A1Z945;A0A0B4K859 4.515632e-01
#> A0A0B4K882;Q7K2Y9 2.426330e+03
#> A0A0B4K8A5;Q9W2F2 1.120027e-01
#> A0A0B4K8A6;Q9W288 2.443921e+03
#> Q5LJQ4;A0A0B4KEH8;A0A0B4KEC2;Q9W5H8 2.228324e+03
#> A0A0B4KED0;Q9W5N2 2.706176e+03
#> A0A0B4KED9;O16844 7.111088e-01
#> A0A0B4KEE4;A1Z6Q1 1.657456e+03
#> E1JGZ7;E1JGZ8;A1Z734;A0A0B4KEE7 8.154825e+02
#> A0A0B4KEI5;Q9V9K7 2.427034e+03
#> Q7JVY0;A0A0B4KEU5;A0A0B4KEJ7 4.505301e+00
#> A1Z9L2;A1Z9L0;A0A0B4KFX4;Q8T076;A0A0B4KEP1;A0A0B4LFC1;A0A0B4KFM5;A0A0B4KF25 1.962839e-01
#> Q5U156;A0A0B4KER0;Q95RL2 3.755972e-01
#> A0A0B4KET0;Q1LZ08 2.571277e-01
#> A0A0B4KFU3;A0A0B4KG58;B7YZJ2;B7YZJ1;E1JH90;A0A0B4KET5;A0A0B4KFA4;E1JH91;A0A0B4KEY4;A1ZAU8-2;A1ZAU8-3;A1ZAU8;A0A0B4KEY6 4.156280e-01
#> Q0E901;A0A0B4KFE6;A0A0B4KEW2 1.565232e+03
#> A0A0B4KFR7;A0A0B4KEW6;Q7KLE5 2.546300e+03
#> A0A0B4KEX0;A1ZAB5 1.494648e-01
#> Q0E993;A0A0B4KF06 1.813517e+00
#> A0A0B4KF46;Q8T0L3 1.650985e+00
#> A0A0B4KG14;A0A0B4KF57;Q9VMY8 1.994748e-01
#> Q7JQL5;A0A0B4KF86 1.071743e+03
#> Q8T0M2;Q0E9C6;A0A0B4KFA3;A8DY97;A8DY98 2.814596e+03
#> Q9VHX9;A0A0B4KFA6 1.076857e+00
#> A0A0B4LGR1;Q9VI14;A0A0B4KFB8;Q6NN86 1.413083e+03
#> A1Z7H3;Q8T3L1;A1Z7H2;A0A0B4KFE4 2.088224e-01
#> A0A0B4KFE5;Q04448-2;Q04448 2.491382e+03
#> A0A0B4KFE9;A1Z8P9 7.149919e+03
#> A0A0B4KGE6;A0A0B4KFH4;P26270 6.236227e+02
#> A0A0B4KFJ7;Q9VHH9 1.230594e-01
#> A0A0B4KFN1;A1Z9R6;A0A0B4KFX9;Q9V727 2.451446e+03
#> A0A0B4KH36;A0A0B4KFQ0;A0A0B4KGR9;Q9VH01;A0A0B4KG50 2.540545e-01
#> A4UZI0;A0A0B4LGK5;A1ZA18;A0A0B4KFR5;A0A0B4KG24 2.191322e-01
#> A0A0B4KFX5;A0A0B4KGG9;A4V2S3;A0A0B4KHB2;A0A0B4KFT4;A0A0B4KGZ7;O46036-2;O46036 4.198537e-01
#> A0A0B4KFU5;Q9V853 1.412908e+01
#> A0A0B4KFW0;Q8T0S6 1.291399e-01
#> Q9VHC4;A0A0B4KFZ2;Q6AWD5 2.669622e+03
#> A0A0B4KFZ9;P84040 1.683215e+00
#> Q7K0G4;A0A0B4KG11;F0JAK5 2.455465e+03
#> A0A0B4KG32;A0A0B4KH26;Q9VH20 8.044606e-01
#> A0A0B4KG41;Q9VES1 2.416966e+03
#> Q9VF92;A0A0B4KG69 1.901122e+03
#> Q9N6D7;A0A0B4KG96 6.471157e-02
#> A0A0B4KHS7;A0A0B4KGE1;Q24151;A0A0B4KGI7;Q24151-2;A0A0B4KHS6;A0A0B4KH10;Q24151-4;Q24151-3 1.938739e-01
#> Q8MQJ5;A0A0B4KGF5;Q9VE69 1.797635e-01
#> Q32KD3;Q7KSW1;Q494I1;A0A0B4KGS8;Q9VHW9;A0A0B4KGF6 1.610470e-01
#> A4V364;A8JR54;Q8IN47;A0A0B4KGK8;Q8IN48;A0A0B4KH21;A0A0B4KH24;A0A0B4KGF9;Q9VDI8;Q7KSA0;A0A0B4KHH8;A0A0B4KHI4;Q95TW4;A0A0B4KGK5;A0A0B4KHT5 2.451835e+03
#> E1JIR4;A0A0B4KGG8;P13607-7;P13607-6;P13607-2;P13607-4;P13607-5;P13607;P13607-3;A8QI34 5.822208e-01
#> A0A0B4KGH0;A0A0B4KHR4;Q9VDW6-2;Q9VDW6-1;Q9VDW6;Q9VDW6-4;Q9VDW6-3;A0A0B4KGB9;Q9VDW3;A0A0B4KHE2;Q7YU29;Q0KI50 7.202892e+03
#> A0A0B4KGI6;Q9VN82;A0A0B4KG43;Q8IPP4;Q8IPP3;A0A0B4KF82;A0A0B4KFK9 2.162127e+00
#> A0A0B4KGJ5;Q9NIV1;A0A0B4KG56 1.545995e+03
#> A0A0B4KGK3;Q95RA8 2.428345e+03
#> A0A0B4KGP8;Q24208;Q24208-2 6.938111e-01
#> Q9VEV1;A0A0B4KGS4 9.208987e-02
#> A0A0B4KGU4;Q9VHP0;M9PBB5;P09052 6.360815e-01
#> A0A0B4KGW0;Q8IMX7-2;A0A0B4J3Z9;Q8IMX7 2.465582e+03
#> n_obs
#> Q8IP47;Q9VJP8;Q9V435;A0A023GPQ3;Q2PDT6;Q7K540 5
#> A0A023GPV6;A8JV04;Q7YU03 1
#> A0A023GQA5;P24156 14
#> Q1RKY1;A0A0B4LG19;A0A0B4J401;B7YZL2;A1ZBH5;B7YZL7;B7YZL6;Q7YTZ4;B7YZL5;B7YZL8;Q0E919;B7YZL1;B7YZL3 6
#> A0A0B4JD00;A8DY69;I0E2I4;A0A0B4JCQ5;Q8SXP0;E5DK16;A0A0B4JD31;A0A0B4JCS1;A0A0B4JD27 17
#> A0A0B4JCT8;Q9V780 1
#> A0A0B4LHQ4;A0A0B4JD62;A0A0B4JDB5;A0A0B4LGQ5;A0A0B4JCW5;A0A0B4JCV6;A0A0B4LGR2;A0A0B4JDA1;Q9VN58 1
#> A0A0B4JCW4;Q9VHJ8;Q95U38 29
#> Q9VDV4;A0A0B4JCY1;Q8IN71;A0A0B4KGH4 4
#> A0A0B4JCY6;Q7KSF4;A0A0B4KHN1;A0A0B4KGT8;Q9VEN1;A0A0B4KGB3;A4V310;B7Z0L2;Q9VEN1-2 4
#> E1JIU2;Q9VCQ0;A0A0B4JCZ2;A8JR87;A0A0B4KH86 7
#> A0A0B4LEY5;A1Z7T2;A0A0B4JD07;A0A0B4K6U3;A0A0B4K727;A0A0B4LF03;A0A0B4LEI8;E1JH15;A0A0B4JD60;A1Z7T1;A1Z7T3;A0A0B4LFX2;A8DY76;A1Z7T0;A1Z7T0-2;A1Z7T4 13
#> A0A0B4JD11;Q9NJH0 34
#> A0A0B4KHW7;Q961V3;A0A0B4KHJ3;A0A0B4KHF5;A0A0B4JD23;Q7KRU0;Q8IMI0;A0A0B4JDE3;Q9VA53 1
#> A0A0B4JD46;Q8T8R1 34
#> A0A0B4JD48;Q95029-2;Q95029 29
#> A0A0B4JD95;Q59E58;A0A0B4JD57;Q59E59;A0A0B4K7Q4;Q99323-2;Q99323-4;Q99323-1;Q99323 17
#> A0A0B4JDA0;Q9VF03 13
#> A0A0B4JDC3;Q9VGU5 1
#> A0A0B4JDG2;Q9I7I8;A0A0B4JDD8;B7Z0M9;Q7KSB3;A0A0B4JCZ0;Q8IN56;Q8IN55 35
#> A0A0B4JDG5;Q8IMZ9 19
#> Q9VNF8;A0A0B4K6T4;A0A0B4K5Z8 12
#> A0A0B4K603;A0A0B4K6V2;A0A0B4KF90;A0A0B4K631;A0A0B4KGC6;B7Z0U7;A0A0B4KFE2;E1JJ78;Q9VI75 9
#> Q7KNC5;Q8MSQ5;Q8IPN9;Q9VNA1;Q0KIB9;A0A0B4K620;B7Z0T3;Q9VNA2;A0A0B4K6S8;A4V2F2;Q4ABH3;A0A0B4K699;A0A0B4KG49;B7Z0T6;Q8IPN8;A0A0B4KF88;Q8IPN6;Q7KTR7;Q7KTR8 13
#> 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 1Internally 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.
# This chunk only works if pheatmap is installed
# install.packages("pheatmap")
pheatmap::pheatmap(dist_approx(fit[1:20, 1:3], by_sample = FALSE)$mean)
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 9.041638e-01 9.643243e-01 -0.13188573 -0.12168220 1.0838539 24 18.93510 12.00100 5
#> 2 9.228967e-01 9.643243e-01 -0.09918871 -0.09780845 1.0141118 24 18.44182 12.00100 1
#> 3 3.560604e-02 2.647376e-01 -2.91655531 -2.22673435 1.3097904 24 19.25682 19.27947 14
#> 4 6.672440e-01 9.643243e-01 0.63245871 0.43528652 1.4529710 24 18.71512 12.00100 6
#> 5 9.187959e-01 9.643243e-01 0.06907997 0.10302911 0.6704898 24 19.99179 17.39251 17
#> 6 9.227391e-01 9.643243e-01 -0.09944452 -0.09800907 1.0146462 24 18.50939 12.00100 1
#> 7 9.230188e-01 9.643243e-01 -0.09899063 -0.09765296 1.0136982 24 18.42480 12.00100 1
#> 8 6.434646e-01 9.643243e-01 -0.19662577 -0.46876935 0.4194510 24 21.87309 28.92211 29
#> 9 2.948261e-01 8.604143e-01 1.94756665 1.07099113 1.8184713 24 18.72697 12.00100 4
#> 10 5.977812e-01 9.643243e-01 -0.78258708 -0.53469337 1.4636184 24 18.96502 12.00100 4
#> 11 4.178567e-01 9.643243e-01 1.06847195 0.82435318 1.2961337 24 18.69267 12.00100 7
#> 12 5.441868e-01 9.643243e-01 0.65494811 0.61523966 1.0645414 24 18.72339 13.26608 13
#> 13 2.131241e-01 7.247683e-01 -1.92937145 -1.27900519 1.5084938 24 21.94101 34.50686 34
#> 14 9.225645e-01 9.643243e-01 -0.09972813 -0.09823120 1.0152388 24 18.49471 12.00100 1
#> 15 5.677647e-01 9.643243e-01 -0.30683429 -0.57933063 0.5296359 24 23.11366 33.97963 34
#> 16 4.364241e-01 9.643243e-01 0.63854291 0.79146742 0.8067836 24 21.83207 29.09359 29
#> 17 5.513747e-01 9.643243e-01 -0.92551871 -0.60420811 1.5317880 24 18.76609 21.16544 17
#> 18 1.264958e-01 5.321548e-01 -1.44873790 -1.58306894 0.9151452 24 18.76053 14.59007 13
#> 19 9.233008e-01 9.643243e-01 -0.09853410 -0.09729406 1.0127453 24 18.43859 12.00100 1
#> 20 8.460135e-01 9.643243e-01 0.13719200 0.19631877 0.6988227 24 24.96480 34.87078 35
#> 21 3.890401e-01 9.589291e-01 -0.49601939 -0.87726502 0.5654157 24 19.62089 19.68857 19
#> 22 5.793576e-03 6.835079e-02 -3.03264877 -3.02888214 1.0012436 24 19.39186 14.13381 12
#> 23 7.940260e-01 9.643243e-01 0.53553354 0.26401005 2.0284589 24 19.52960 12.00100 9
#> 24 7.823159e-01 9.643243e-01 -0.29065025 -0.27942071 1.0401887 24 19.93314 13.52804 13
#> 25 5.808166e-03 6.835079e-02 -2.36772393 -3.02782662 0.7819880 24 19.70360 17.48975 17
#> 26 7.661357e-04 2.706278e-02 1.31592467 3.85152871 0.3416630 24 22.63306 31.78246 32
#> 27 5.273318e-01 9.643243e-01 -0.39001682 -0.64141503 0.6080569 24 20.49251 23.49573 23
#> 28 2.138661e-01 7.247683e-01 -1.08738773 -1.27686559 0.8516070 24 21.40463 28.98290 29
#> 29 7.359838e-01 9.643243e-01 -0.34957127 -0.34111707 1.0247839 24 18.44307 12.00100 1
#> 30 2.925751e-01 8.604143e-01 1.36858458 1.07611484 1.2717830 24 18.76639 12.00100 4
#> 31 3.864079e-01 9.589291e-01 0.61668179 0.88222189 0.6990098 24 24.31248 36.00000 36
#> 32 8.431146e-01 9.643243e-01 0.28700452 0.20006596 1.4345495 24 18.54677 12.00100 2
#> 33 9.229012e-01 9.643243e-01 -0.09918138 -0.09780270 1.0140965 24 18.48476 12.00100 1
#> 34 2.978004e-01 8.604143e-01 -0.38452742 -1.06426347 0.3613085 24 21.23648 22.56540 23
#> 35 6.009911e-01 9.643243e-01 0.22887180 0.52998576 0.4318452 24 21.24523 27.52470 29
#> 36 9.181624e-01 9.643243e-01 -0.10700595 -0.10383586 1.0305298 24 18.56819 12.00100 1
#> 37 1.491777e-01 6.066562e-01 -1.68717458 -1.49027688 1.1321216 24 18.55395 12.00100 1
#> 38 4.587378e-02 2.647376e-01 1.14516830 2.10574378 0.5438308 24 28.10487 36.00000 36
#> 39 3.165797e-03 6.437121e-02 1.94482319 3.27956356 0.5930128 24 23.81097 34.14210 34
#> 40 2.231816e-02 1.815211e-01 3.30100741 2.44263208 1.3514141 24 19.57488 11.40294 10
#> 41 6.157843e-01 9.643243e-01 0.68718234 0.50844371 1.3515406 24 18.49639 12.00100 2
#> 42 9.081562e-01 9.643243e-01 -0.12450249 -0.11658866 1.0678782 24 18.56173 12.00100 1
#> 43 4.410637e-01 9.643243e-01 1.20381211 0.78338519 1.5366797 24 18.31278 12.00100 1
#> 44 9.158652e-03 9.311296e-02 -2.30687017 -2.83470493 0.8137955 24 20.17078 17.64666 17
#> 45 7.886891e-01 9.643243e-01 0.06832203 0.27102516 0.2520874 24 20.00811 22.13185 22
#> 46 4.954961e-01 9.643243e-01 -0.18675176 -0.69213329 0.2698205 24 19.82604 20.21044 20
#> 47 5.476340e-01 9.643243e-01 -0.44501136 -0.60993967 0.7295990 24 22.27411 32.25275 32
#> 48 9.187336e-01 9.643243e-01 -0.10604799 -0.10310855 1.0285082 24 18.41538 12.00100 0
#> 49 8.842528e-02 4.149186e-01 1.52584952 1.77593809 0.8591795 24 19.81745 16.28831 15
#> 50 7.816869e-01 9.643243e-01 -0.12516067 -0.28025044 0.4466029 24 22.00212 33.14301 33
#> 51 9.791853e-01 9.791853e-01 -0.03248589 -0.02636363 1.2322237 24 18.41638 12.00100 1
#> 52 2.214135e-08 2.701244e-06 4.37565645 8.16097938 0.5361681 24 27.33515 36.00000 36
#> 53 3.643800e-01 9.589291e-01 -0.80749559 -0.92459576 0.8733499 24 22.35190 29.01683 29
#> 54 3.877427e-02 2.647376e-01 -3.39264291 -2.18636617 1.5517268 24 19.17241 12.00100 7
#> 55 3.755705e-01 9.589291e-01 1.16713156 0.90286503 1.2926977 24 18.93403 12.00100 6
#> 56 6.408318e-02 3.257561e-01 -1.22489060 -1.94105764 0.6310429 24 23.05052 33.88477 34
#> 57 1.589511e-01 6.255495e-01 1.53064611 1.45381288 1.0528495 24 19.66369 17.13489 17
#> 58 1.130134e-01 5.106534e-01 -1.15471919 -1.64496341 0.7019726 24 18.99589 12.36403 12
#> 59 8.171997e-01 9.643243e-01 -0.09960770 -0.23370022 0.4262200 24 19.61493 18.37926 18
#> 60 1.067029e-02 1.001366e-01 1.19360624 2.76894680 0.4310687 24 21.05397 19.91114 21
#> 61 5.466171e-01 9.643243e-01 1.17443187 0.61150130 1.9205713 24 18.70051 12.00100 2
#> 62 7.919784e-01 9.643243e-01 0.13105532 0.26669993 0.4913962 24 19.78737 18.66579 18
#> 63 5.057267e-01 9.643243e-01 1.14363382 0.67564180 1.6926629 24 19.26065 12.28942 8
#> 64 3.145202e-01 8.720788e-01 -0.56938008 -1.02730452 0.5542466 24 23.37251 28.86201 31
#> 65 9.198396e-01 9.643243e-01 -0.10420449 -0.10170009 1.0246254 24 18.53520 12.00100 2
#> 66 9.084611e-01 9.643243e-01 0.13442691 0.11619980 1.1568600 24 18.41083 12.00100 5
#> 67 9.671284e-01 9.751212e-01 -0.02482167 -0.04164223 0.5960698 24 22.46841 31.86825 32
#> 68 6.859511e-01 9.643243e-01 -0.48270127 -0.40929767 1.1793404 24 18.45400 12.00100 1
#> 69 5.907936e-01 9.643243e-01 -0.16494569 -0.54498381 0.3026616 24 22.89393 27.59483 29
#> 70 5.767968e-01 9.643243e-01 0.71895023 0.56577804 1.2707284 24 18.35351 12.00100 1
#> 71 9.228150e-01 9.643243e-01 -0.09932118 -0.09791237 1.0143885 24 18.53738 12.00100 2
#> 72 9.206975e-01 9.643243e-01 -0.10278538 -0.10060791 1.0216431 24 18.47912 12.00100 1
#> 73 9.406114e-01 9.643243e-01 -0.05427536 -0.07528570 0.7209253 24 19.99521 14.41989 16
#> 74 7.007871e-01 9.643243e-01 -0.45767005 -0.38888899 1.1768655 24 18.69725 12.00100 5
#> 75 6.332506e-01 9.643243e-01 0.68955793 0.48331727 1.4267190 24 18.86651 12.00100 7
#> 76 5.032984e-01 9.643243e-01 -0.78539227 -0.67953901 1.1557722 24 18.47923 12.00100 1
#> 77 4.084725e-02 2.647376e-01 -2.43971275 -2.16153740 1.1286933 24 19.52296 11.50030 10
#> 78 9.553744e-01 9.712973e-01 -0.02783650 -0.05654678 0.4922739 24 19.40220 18.49796 18
#> 79 2.643541e-01 8.487156e-01 -0.82702245 -1.14289864 0.7236184 24 20.34289 19.45310 19
#> 80 3.032608e-01 8.604143e-01 1.16322170 1.05203591 1.1056863 24 19.37852 12.99128 13
#> 81 6.458739e-01 9.643243e-01 0.29933696 0.46535280 0.6432474 24 20.93926 24.48288 26
#> 82 9.247196e-01 9.643243e-01 -0.09625171 -0.09548862 1.0079914 24 18.49839 12.00100 6
#> 83 9.220123e-01 9.643243e-01 -0.10062788 -0.09893406 1.0171207 24 18.51451 12.00100 1
#> 84 3.930037e-01 9.589291e-01 -0.30157840 -0.86984173 0.3467049 24 24.03787 34.95651 35
#> 85 8.909958e-01 9.643243e-01 -0.15419724 -0.13850641 1.1132860 24 21.03027 25.94287 25
#> 86 6.162776e-03 6.835079e-02 -3.12274466 -3.00292331 1.0399016 24 21.28132 28.61873 28
#> 87 5.663474e-01 9.643243e-01 0.24854613 0.58146718 0.4274465 24 20.65474 23.37394 24
#> 88 2.858877e-01 8.604143e-01 1.38707750 1.09150488 1.2707937 24 19.09649 12.00100 7
#> 89 2.011896e-01 7.247683e-01 2.52076917 1.31423635 1.9180486 24 18.63022 12.00100 3
#> 90 2.369017e-01 7.811354e-01 1.21150963 1.21308687 0.9986998 24 20.50964 16.73868 16
#> 91 9.256791e-01 9.643243e-01 -0.09472152 -0.09426777 1.0048135 24 18.55965 12.00100 7
#> 92 8.873042e-04 2.706278e-02 -2.48623580 -3.79308792 0.6554649 24 19.83715 17.03606 17
#> 93 9.224960e-01 9.643243e-01 -0.09983964 -0.09831847 1.0154719 24 18.33157 12.00100 1
#> 94 4.582412e-02 2.647376e-01 -2.68607172 -2.10626757 1.2752756 24 18.86539 12.00100 3
#> 95 2.227404e-03 5.434865e-02 -3.91965332 -3.42309309 1.1450619 24 19.05677 12.00100 8
#> 96 4.878794e-01 9.643243e-01 0.29259735 0.70453700 0.4153044 24 19.05477 14.25233 14
#> 97 9.227841e-01 9.643243e-01 -0.09937135 -0.09795170 1.0144933 24 18.38527 12.00100 1
#> 98 1.780186e-02 1.551305e-01 -1.79860486 -2.54431175 0.7069121 24 20.02491 15.88330 16
#> 99 5.902625e-02 3.130958e-01 0.83307014 1.98213982 0.4202883 24 21.13011 25.95769 26
#> 100 4.549239e-03 6.835079e-02 -1.84449934 -3.12985123 0.5893249 24 19.56236 18.97894 18
#> 101 9.357136e-01 9.643243e-01 -0.13283344 -0.08150843 1.6296895 24 19.71566 10.50357 11
#> 102 3.463325e-01 9.389460e-01 0.31169553 0.96059889 0.3244804 24 20.53834 25.39207 25
#> 103 1.262672e-01 5.321548e-01 2.28602625 1.58407173 1.4431330 24 19.15972 12.00100 5
#> 104 6.925948e-01 9.643243e-01 0.42256602 0.40013720 1.0560528 24 20.63351 27.96637 27
#> 105 9.227121e-01 9.643243e-01 -0.09948829 -0.09804337 1.0147376 24 18.36925 12.00100 1
#> 106 8.579832e-01 9.643243e-01 -0.15298521 -0.18087664 0.8457986 24 18.97010 11.49537 11
#> 107 9.230339e-01 9.643243e-01 -0.09896621 -0.09763378 1.0136472 24 18.45629 12.00100 1
#> 108 6.271619e-01 9.643243e-01 0.66662219 0.49203969 1.3548139 24 18.56516 12.00100 2
#> 109 7.996825e-02 3.902451e-01 -0.45962145 -1.82825635 0.2513988 24 20.59743 23.14041 23
#> 110 4.773956e-02 2.647376e-01 -0.82727822 -2.08642260 0.3965056 24 22.16902 31.04213 31
#> 111 4.549897e-02 2.647376e-01 -1.34335248 -2.10970976 0.6367475 24 19.23875 14.40945 14
#> 112 2.137881e-01 7.247683e-01 0.46126979 1.27709009 0.3611881 24 20.58297 25.49767 25
#> 113 1.848967e-01 7.049186e-01 -1.54484034 -1.36505484 1.1317057 24 18.54220 12.00100 1
#> 114 5.582565e-01 9.643243e-01 -0.39751111 -0.59371676 0.6695299 24 22.07906 32.35331 32
#> 115 8.929166e-01 9.643243e-01 -0.15407310 -0.13604984 1.1324754 24 18.62727 12.00100 1
#> 116 2.086324e-04 1.272657e-02 6.30361394 4.36529844 1.4440282 24 20.30633 26.15977 24
#> 117 9.264026e-01 9.643243e-01 -0.09357470 -0.09334724 1.0024367 24 18.90552 12.00100 6
#> 118 4.476596e-01 9.643243e-01 -0.88758599 -0.77198366 1.1497471 24 18.48773 12.00100 1
#> 119 5.276726e-01 9.643243e-01 -0.46157706 -0.64088124 0.7202224 24 23.83062 31.57354 33
#> 120 5.993750e-03 6.835079e-02 0.83089014 3.01461755 0.2756204 24 22.26677 31.92691 32
#> 121 6.925950e-01 9.643243e-01 -0.26042807 -0.40013693 0.6508474 24 24.23722 36.00000 36
#> 122 9.227629e-01 9.643243e-01 -0.09940573 -0.09797866 1.0145651 24 18.55499 12.00100 1This 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 4.4.1 (2024-06-14)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 24.04.1 LTS
#>
#> Matrix products: default
#> BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0
#>
#> locale:
#> [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C LC_TIME=en_US.UTF-8
#> [4] LC_COLLATE=C LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
#> [7] LC_PAPER=en_US.UTF-8 LC_NAME=C LC_ADDRESS=C
#> [10] LC_TELEPHONE=C LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
#>
#> time zone: Etc/UTC
#> tzcode source: system (glibc)
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] proDA_1.19.0 BiocStyle_2.33.1
#>
#> loaded via a namespace (and not attached):
#> [1] sass_0.4.9 SparseArray_1.5.35 lattice_0.22-6
#> [4] digest_0.6.37 evaluate_0.24.0 grid_4.4.1
#> [7] RColorBrewer_1.1-3 fastmap_1.2.0 jsonlite_1.8.8
#> [10] Matrix_1.7-0 GenomeInfoDb_1.41.1 BiocManager_1.30.25
#> [13] httr_1.4.7 extraDistr_1.10.0 UCSC.utils_1.1.0
#> [16] scales_1.3.0 jquerylib_0.1.4 abind_1.4-8
#> [19] cli_3.6.3 rlang_1.1.4 crayon_1.5.3
#> [22] XVector_0.45.0 Biobase_2.65.1 munsell_0.5.1
#> [25] cachem_1.1.0 DelayedArray_0.31.11 yaml_2.3.10
#> [28] S4Arrays_1.5.7 tools_4.4.1 colorspace_2.1-1
#> [31] GenomeInfoDbData_1.2.12 SummarizedExperiment_1.35.1 BiocGenerics_0.51.1
#> [34] buildtools_1.0.0 R6_2.5.1 matrixStats_1.4.1
#> [37] stats4_4.4.1 lifecycle_1.0.4 zlibbioc_1.51.1
#> [40] S4Vectors_0.43.2 IRanges_2.39.2 bslib_0.8.0
#> [43] gtable_0.3.5 glue_1.7.0 Rcpp_1.0.13
#> [46] xfun_0.47 GenomicRanges_1.57.1 highr_0.11
#> [49] sys_3.4.2 MatrixGenerics_1.17.0 knitr_1.48
#> [52] htmltools_0.5.8.1 rmarkdown_2.28 maketools_1.3.0
#> [55] pheatmap_1.0.12 compiler_4.4.1