# Analysing thermal proteome profiling data with the NPARC package

Dorothee Childs and Nils Kurzawa

#### 19 May 2021, 9:22:29 PM

#### Package

NPARC 1.4.0

# Contents

# 1 Introduction

This vignette shows how to reproduce the analysis described by Childs, Bach, Franken et al. (2019): Non-parametric analysis of thermal proteome profiles reveals novel drug-binding proteins using the `NPARC` package.

# 2 Preparation

Load necessary packages.

    library(dplyr)
    library(magrittr)
    library(ggplot2)
    library(broom)
    library(knitr)
    library(NPARC)

# 3 Data import

First, we load data from a staurosporine TPP experiment (Savitski et al. 2014). The necessary ETL (extract, transform, load) steps have already been conducted, including download from the supplements of the respective publication and conversion into tidy format.

    data("stauro_TPP_data_tidy")

Before applying any further transformations and filters we create a copy of the imported data.

    df <- stauro_TPP_data_tidy

Let’s perform a first check of the imported data:

    df %>%
      mutate(compoundConcentration = factor(compoundConcentration),
             replicate = factor(replicate),
             dataset = factor(dataset)) %>%
      summary()

    ##           dataset         uniqueID          relAbundance     temperature
    ##  Staurosporine:307080   Length:307080      Min.   :  0.00   Min.   :40.0
    ##                         Class :character   1st Qu.:  0.17   1st Qu.:46.0
    ##                         Mode  :character   Median :  0.57   Median :53.5
    ##                                            Mean   :  0.58   Mean   :53.5
    ##                                            3rd Qu.:  0.95   3rd Qu.:61.0
    ##                                            Max.   :394.98   Max.   :67.0
    ##                                            NA's   :70990
    ##  compoundConcentration replicate  uniquePeptideMatches
    ##  0 :153540             1:153540   Min.   :  0.00
    ##  20:153540             2:153540   1st Qu.:  2.00
    ##                                   Median :  6.00
    ##                                   Mean   : 10.36
    ##                                   3rd Qu.: 13.00
    ##                                   Max.   :351.00
    ##                                   NA's   :63400

The displayed data contains the following columns:

- `dataset`: The dataset containing the measurements of several TMT-10 experiments. In each experiment, cells were treated with a vehicle or with the compound in one or two concentrations, and measured at ten different temperatures.
- `uniqueID`: The unique identifier for each protein. In the given dataset, it contains the gene symbol concatenated by IPI id. Example: 15 KDA PROTEIN._IPI00879051, 16 KDA PROTEIN._IPI00903282, 17 KDA PROTEIN._IPI00878120, 17 KDA PROTEIN._IPI00736161, 176 KDA PROTEIN._IPI00894060, 18 KDA PROTEIN._IPI00644570 .
- `relAbundance`: The relative signal intensity of the protein in each experiment, scaled to the intensity at the lowest temperature.
- `temperature`: The temperatures corresponding to each of the ten measurements in a TMT experiment.
- `compoundConcentration` The concentration of the administered compound in \(\mu M\).
- `replicate`: The replicate number in each experimental group. Each pair of vehicle and treatment experiments was conducted in two replicates.
- `uniquePeptideMatches`: The number of unique peptides with which a protein was identified.

# 4 Data preprocessing and exploration

The imported data contains 307080 rows with entries for 7677 proteins.

First, we remove all abundances that were not found with at least one unique peptide, or for which a missing value was recorded.

    df %<>% filter(uniquePeptideMatches >= 1)
    df %<>% filter(!is.na(relAbundance))

Next, we ensure that the dataset only contains proteins reproducibly observed with full melting curves in both replicates and treatment groups per dataset. A full melting curve is defined by the presence of measurements at all 10 temperatures for the given experimental group.

    # Count full curves per protein
    df %<>%
      group_by(dataset, uniqueID) %>%
      mutate(n = n()) %>%
      group_by(dataset) %>%
      mutate(max_n = max(n)) %>%
      ungroup

    table(distinct(df, uniqueID, n)$n)

    ##
    ##   10   20   30   40
    ##  992  809  993 4505

We see that the majority of proteins contain 40 measurements. This corresponds to two full replicate curves per experimental group. We will focus on these in the current analysis.

    # Filter for full curves per protein:
    df %<>%
      filter(n == max_n) %>%
      dplyr::select(-n, -max_n)

The final data contains 180200 rows with entries for 4505 proteins. This number coincides with the value reported in Table 1 of the corresponding publication (Childs et al. 2019).

# 5 Illustrative example

We first illustrate the principles of nonparametric analysis of response curves (NPARC) on an example protein (STK4) from the staurosporine dataset. The same protein is shown in Figures 1 and 2 of the paper.

## 5.1 Select data

We first select all entries belonging to the desired protein and dataset:

    stk4 <- filter(df, uniqueID == "STK4_IPI00011488")

The table `stk4` has 40 rows with measurements of four experimental groups. They consist of two treatment groups (vehicle: \(0~\mu M\) staurosporine, treatment: \(20~\mu M\) staurosporine) with two replicates each. Let us look at the treatment group of replicate 1 for an example:

    stk4 %>% filter(compoundConcentration == 20, replicate == 1) %>%
      dplyr::select(-dataset) %>% kable(digits = 2)

uniqueID | relAbundance | temperature | compoundConcentration | replicate | uniquePeptideMatches
--- | --- | --- | --- | --- | ---
STK4_IPI00011488 | 1.00 | 40 | 20 | 1 | 8
STK4_IPI00011488 | 1.03 | 43 | 20 | 1 | 8
STK4_IPI00011488 | 1.06 | 46 | 20 | 1 | 8
STK4_IPI00011488 | 1.03 | 49 | 20 | 1 | 8
STK4_IPI00011488 | 0.92 | 52 | 20 | 1 | 8
STK4_IPI00011488 | 0.93 | 55 | 20 | 1 | 8
STK4_IPI00011488 | 0.78 | 58 | 20 | 1 | 8
STK4_IPI00011488 | 0.44 | 61 | 20 | 1 | 8
STK4_IPI00011488 | 0.21 | 64 | 20 | 1 | 8
STK4_IPI00011488 | 0.12 | 67 | 20 | 1 | 8

To obtain a first impression of the measurements in each experimental group, we generate a plot of the measurements:

    stk4_plot_orig <- ggplot(stk4, aes(x = temperature, y = relAbundance)) +
      geom_point(aes(shape = factor(replicate), color = factor(compoundConcentration)), size = 2) +
      theme_bw() +
      ggtitle("STK4") +
      scale_color_manual("staurosporine (mu M)", values = c("#808080", "#da7f2d")) +
      scale_shape_manual("replicate", values = c(19, 17))

    print(stk4_plot_orig)

We will show how to add the fitted curves to this plot in the following steps.

## 5.2 Define function for model fitting

To assess whether there is a significant difference between both treatment groups, we will fit a null model and an alternative models to the data. The null model fits a sigmoid melting curve through all data points irrespective of experimental condition. The alternative model fits separate melting curves per experimental group .

## 5.3 Fit and plot null models

We use the `NPARC` package function `fitSingleSigmoid` to fit the null model:

    nullFit <- NPARC:::fitSingleSigmoid(x = stk4$temperature, y = stk4$relAbundance)

The function returns an object of class `nls`:

    summary(nullFit)

    ##
    ## Formula: y ~ (1 - Pl)/(1 + exp((b - a/x))) + Pl
    ##
    ## Parameters:
    ##    Estimate Std. Error t value Pr(>|t|)
    ## Pl   0.0000     0.1795   0.000  1.00000
    ## a  692.6739   226.9106   3.053  0.00419 **
    ## b   12.5048     4.4989   2.780  0.00851 **
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ##
    ## Residual standard error: 0.1814 on 37 degrees of freedom
    ##
    ## Algorithm "port", convergence message: relative convergence (4)

The function `augment` from the `broom` package provides a convenient way to obtain the predictions and residuals at each temperature in tabular format. By appending the returned predictions and residuals to our measurements, we ensure that relevant data is collected in the same table and can be added to the plot for visualization. The residuals will be needed later for construction of the test statistic:

    nullPredictions <- broom::augment(nullFit)

Let us look at the values returned by `augment` at two consecutive temperatures. Note that, while the predictions will be the same for each experiment at a given temperature, the residuals will differ because they were computed by comparing the predictions to the actual measurements:

    nullPredictions %>% filter(x %in% c(46, 49)) %>% kable()

x | y | .fitted | .resid
--- | --- | --- | ---
46 | 1.0591140 | 0.9278000 | 0.1313139
49 | 1.0333794 | 0.8363683 | 0.1970111
46 | 0.9449568 | 0.9278000 | 0.0171568
49 | 0.9187253 | 0.8363683 | 0.0823571
46 | 0.8661451 | 0.9278000 | -0.0616550
49 | 0.7139894 | 0.8363683 | -0.1223788
46 | 0.8717407 | 0.9278000 | -0.0560594
49 | 0.7068211 | 0.8363683 | -0.1295471

Now we can append these values to our data frame and show the predicted curve in the plot:

    stk4$nullPrediction <- nullPredictions$.fitted
    stk4$nullResiduals <- nullPredictions$.resid

    stk4_plot <- stk4_plot_orig + geom_line(data = stk4, aes(y = nullPrediction))

    print(stk4_plot)

## 5.4 Fit and plot alternative models

Next we fit the alternative model. Again, we compute the predicted values and the corresponding residuals by the `broom::augment()` function. To take the compound concentration as a factor into account, we iterate over both concentrations and fit separate models to each subset. We implement this by first grouping the data using the function `dplyr::group_by()`, and starting the model fitting by `dplyr::do()`.

    alternativePredictions <- stk4 %>%
    # Fit separate curves per treatment group:
      group_by(compoundConcentration) %>%
      do({
        fit = NPARC:::fitSingleSigmoid(x = .$temperature, y = .$relAbundance, start=c(Pl = 0, a = 550, b = 10))
        broom::augment(fit)
      }) %>%
      ungroup %>%
      # Rename columns for merge to data frame:
      dplyr::rename(alternativePrediction = .fitted,
                    alternativeResiduals = .resid,
                    temperature = x,
                    relAbundance = y)

Add the predicted values and corresponding residuals to our data frame:

    stk4 <- stk4 %>%
      left_join(alternativePredictions,
                by = c("relAbundance", "temperature",
                       "compoundConcentration")) %>%
      distinct()

Add the curves predicted by the alternative model to the plot. Conceptually, it corresponds to the plot shown in Figures 2 (A)/(B) of the paper.

    stk4_plot <- stk4_plot +
      geom_line(data = distinct(stk4, temperature, compoundConcentration, alternativePrediction),
                aes(y = alternativePrediction, color = factor(compoundConcentration)))

    print(stk4_plot)

This plot summarizes Figures 2(A) and 2(B) in the corresponding publication (Childs et al. 2019).

## 5.5 Compute RSS values

In order to quantify the improvement in goodness-of-fit of the alternative model relative to the null model, we compute the sum of squared residuals (RSS):

    rssPerModel <- stk4 %>%
      summarise(rssNull = sum(nullResiduals^2),
                rssAlternative = sum(alternativeResiduals^2))

    kable(rssPerModel, digits = 4)

rssNull | rssAlternative
--- | ---
1.2181 | 0.0831

These values will be used to construct the \(F\)-statistic according to

\[\begin{equation} \label{eq:f_stat} {F} = \frac{{d}_{2}}{{d}_{1}} \cdot \frac{{RSS}^{0} - {RSS}^{1}}{{RSS}^{1}}. \end{equation}\]

To compute this statistic and to derive a p-value, we need the degrees of freedom \({d}_{1}\) and \({d}_{2}\). As described in the paper, they cannot be analytically derived due to the correlated nature of the measurements. The paper describes how to estimate these values from the RSS-values of all proteins in the dataset. In the following Section, we illustrate how to repeat the model fitting for all proteins of a dataset and how to perform hypothesis testing on these models.

# 6 Extend the analysis to all proteins

This section describes the different steps of the NPARC workflow for model fitting and hyothesis testing. Note that the package also provides a function `runNPARC()` that performs all of the following steps with one single function call.

## 6.1 Start fitting

In order to analyze all datasets as described in the paper, we fit null and alternative models to all proteins using the package function `NPARCfit`:

    BPPARAM <- BiocParallel::SerialParam(progressbar = FALSE)

    fits <- NPARCfit(x = df$temperature,
                     y = df$relAbundance,
                     id = df$uniqueID,
                     groupsNull = NULL,
                     groupsAlt = df$compoundConcentration,
                     BPPARAM = BPPARAM,
                     returnModels = FALSE)

    ## Starting model fitting...

    ## ... complete

    ## Elapsed time: 28.23 secs

    ## Flagging successful model fits...

    ## ... complete.

    ## Evaluating model fits...

    ## Evaluating models ...

    ## ... complete.

    ## Computing model predictions and residuals ...

    ## ... complete.

    ## Starting model fitting...

    ## ... complete

    ## Elapsed time: 1.08 mins

    ## Flagging successful model fits...

    ## ... complete.

    ## Evaluating model fits...

    ## Evaluating models ...

    ## ... complete.

    ## Computing model predictions and residuals ...

    ## ... complete.

    str(fits, 1)

    ## List of 2
    ##  $ predictions: tibble [360,190 x 7] (S3: tbl_df/tbl/data.frame)
    ##  $ metrics    : tibble [13,515 x 15] (S3: tbl_df/tbl/data.frame)

The returned object `fits` contains two tables. The table `metrics` contains the fitted parameters and goodness-of-fit measures for the null and alternative models per protein and group. The table `predictions` contains the corresponding predicted values and residuals per model.

    fits$metrics %>%
      mutate(modelType = factor(modelType), nCoeffs = factor(nCoeffs), nFitted = factor(nFitted), group = factor((group))) %>%
      summary

    ##        modelType         id                  tm                 a
    ##  alternative:9010   Length:13515       Min.   :      44   Min.   :    0.0
    ##  null       :4505   Class :character   1st Qu.:      50   1st Qu.:  837.1
    ##                     Mode  :character   Median :      53   Median : 1103.1
    ##                                        Mean   :    6970   Mean   : 1434.8
    ##                                        3rd Qu.:      56   3rd Qu.: 1489.3
    ##                                        Max.   :88065035   Max.   :15000.0
    ##                                        NA's   :782        NA's   :10
    ##        b                   pl               aumc          resid_sd
    ##  Min.   :  0.00001   Min.   :0.00000   Min.   : 4.87   Min.   :0.007522
    ##  1st Qu.: 16.11868   1st Qu.:0.05277   1st Qu.:11.56   1st Qu.:0.035045
    ##  Median : 21.44813   Median :0.07971   Median :14.46   Median :0.049801
    ##  Mean   : 27.05449   Mean   :0.14063   Mean   :15.03   Mean   :0.064187
    ##  3rd Qu.: 28.40421   3rd Qu.:0.14427   3rd Qu.:18.06   3rd Qu.:0.074676
    ##  Max.   :250.00000   Max.   :1.50000   Max.   :37.42   Max.   :1.896479
    ##  NA's   :10          NA's   :10        NA's   :10      NA's   :10
    ##       rss               loglik           tm_sd           nCoeffs
    ##  Min.   : 0.00113   Min.   :-70.47   Min.   :0.000e+00   3   :13505
    ##  1st Qu.: 0.02923   1st Qu.: 27.31   1st Qu.:0.000e+00   NA's:   10
    ##  Median : 0.06362   Median : 37.21   Median :0.000e+00
    ##  Mean   : 0.19916   Mean   : 39.99   Mean   :5.452e+11
    ##  3rd Qu.: 0.15092   3rd Qu.: 49.52   3rd Qu.:1.000e+00
    ##  Max.   :79.39804   Max.   :123.31   Max.   :2.566e+15
    ##  NA's   :10         NA's   :10       NA's   :784
    ##  nFitted        conv          group
    ##  20  :9001   Mode :logical   0   :4505
    ##  40  :4504   FALSE:10        20  :4505
    ##  NA's:  10   TRUE :13505     NA's:4505
    ##
    ##
    ##
    ##

    fits$predictions %>%
      mutate(modelType = factor(modelType), group = factor((group))) %>%
      summary

    ##        modelType           id                  x              y
    ##  alternative:180029   Length:360190      Min.   :40.0   Min.   :0.0000
    ##  null       :180161   Class :character   1st Qu.:46.0   1st Qu.:0.1563
    ##                       Mode  :character   Median :53.5   Median :0.5785
    ##                                          Mean   :53.5   Mean   :0.5644
    ##                                          3rd Qu.:61.0   3rd Qu.:0.9571
    ##                                          Max.   :67.0   Max.   :8.2379
    ##                                          NA's   :10     NA's   :10
    ##     .fitted            .resid           group
    ##  Min.   :0.01099   Min.   :-1.156805   0   : 90024
    ##  1st Qu.:0.15963   1st Qu.:-0.025283   20  : 90005
    ##  Median :0.58459   Median : 0.000311   NA's:180161
    ##  Mean   :0.56007   Mean   : 0.004377
    ##  3rd Qu.:0.96271   3rd Qu.: 0.028124
    ##  Max.   :1.50000   Max.   : 7.240276
    ##  NA's   :10        NA's   :10

## 6.2 Check example

The results of the STK4 example from earlier can be selected from this object as follows.

First, we check the RSS values of the null and alterantive models:

    stk4Metrics <- filter(fits$metrics, id == "STK4_IPI00011488")

    rssNull <- filter(stk4Metrics, modelType == "null")$rss
    rssAlt <- sum(filter(stk4Metrics, modelType == "alternative")$rss) # Summarize over both experimental groups

    rssNull

    ## [1] 1.218132

    rssAlt

    ## [1] 0.08314745

Next, we plot the predicted curves per model and experimental group:

    stk4Predictions <- filter(fits$predictions, modelType == "alternative", id == "STK4_IPI00011488")

    stk4_plot_orig +
      geom_line(data = filter(stk4Predictions, modelType == "alternative"),
                aes(x = x, y = .fitted, color = factor(group))) +
        geom_line(data = filter(stk4Predictions, modelType == "null"),
                aes(x = x, y = .fitted))

# 7 Compute test statistics

## 7.1 Why we need to estimate the degrees of freedom

In order to compute \(F\)-statistics per protein and dataset according to Equation (), we need to know the degrees of freedom of the corresponding null distribution. If we could assume independent and identically distributed (iid) residuals, we could compute them from the number of fitted values and model parameters. In the following, we will show why this simple equation is not appropriate for the curve data we are working with.

First, we compute the test statistics and p-values with theoretical degrees of freedom. These would be true for the case of iid residuals:

    modelMetrics <- fits$metrics
    fStats <- NPARCtest(modelMetrics, dfType = "theoretical")

Let us take a look at the computed degrees of freedom:

    fStats %>%
      filter(!is.na(pAdj)) %>%
      distinct(nFittedNull, nFittedAlt, nCoeffsNull, nCoeffsAlt, df1, df2) %>%
      kable()

df1 | df2 | nFittedNull | nFittedAlt | nCoeffsNull | nCoeffsAlt
--- | --- | --- | --- | --- | ---
3 | 34 | 40 | 40 | 3 | 6

We plot the \(F\)-statistics against the theoretical \(F\)-distribution to check how well the null distribution is approximated now:

    ggplot(filter(fStats, !is.na(pAdj))) +
      geom_density(aes(x = fStat), fill = "steelblue", alpha = 0.5) +
      geom_line(aes(x = fStat, y = df(fStat, df1 = df1, df2 = df2)), color = "darkred", size = 1.5) +
      theme_bw() +
      # Zoom in to small values to increase resolution for the proteins under H0:
      xlim(c(0, 10))

    ## Warning: Removed 176 rows containing non-finite values (stat_density).

    ## Warning: Removed 176 row(s) containing missing values (geom_path).

The densities of the theoretical \(F\)-distribution (red) do not fit the observed values (blue) very well. While the theoretical distribution tends to overestimate the number of proteins with test statistics smaller than 2.5, it appears to underestimate the amount of proteins with larger values. This would imply that even for highly specific drugs, we observe many more significant differences than we would expect by chance. This hints at an anti-conservative behaviour of our test with the calculated degree of freedom parameters. This is reflected in the p-value distributions. If the distribution assumptions were met, we would expect the null cases to follow a uniform distribution, with a peak on the left for the non-null cases. Instead, we observe a tendency to obtain fewer values than expected in the middle range (around 0.5), but distinct peaks to the left.

    ggplot(filter(fStats, !is.na(pAdj))) +
      geom_histogram(aes(x = pVal, y = ..density..), fill = "steelblue", alpha = 0.5, boundary = 0, bins = 30) +
      geom_line(aes(x = pVal, y = dunif(pVal)), color = "darkred", size = 1.5) +
      theme_bw()

## 7.2 How to estimate the degrees of freedom

In the paper, we describe an alternative way to estimate the degrees of freedom by fitting \(\chi^2\) distributions to the numerator and denominator across all proteins in a dataset. To enable fitting of the distributions, we first need to re-scale the variables by a scaling factor. Because the scaling factors are characteristic for each dataset (it depends on the variances of the residuals in the respective dataset), we estimate them from the data according to:

\[\begin{align} \label{eq:scale-param} \sigma_0^2 &= \frac{1}{2} \frac{V}{M}, \end{align}\]

where \(V\) is the variance of the distribution, and \(M\) is the mean of the distribution.

The following functin estimates \(V\) and \(M\) from the empirical distributions of the RSS differences \(({RSS}^1 - {RSS}^0)\). To increase robustness, it estimate \(M\) and \(V\) by their D-estimates Marazzi (2002) (median and median absolute deviation). It then scales the numerator and denominator of the \(F\)-statistic by these scaling factors and estimate the degree of freedom parameters by fitting unscaled \(\chi^2\) distributions. Finally, it fits the degrees of freedom parameters numerically, computes the test statistics according to Equation () and derives p-values.

    modelMetrics <- fits$metrics
    fStats <- NPARCtest(modelMetrics, dfType = "empirical")

We plot the \(F\)-statistics against the theoretical \(F\)-distribution to check how well the null distribution is approximated now:

    ggplot(filter(fStats, !is.na(pAdj))) +
      geom_density(aes(x = fStat), fill = "steelblue", alpha = 0.5) +
      geom_line(aes(x = fStat, y = df(fStat, df1 = df1, df2 = df2)), color = "darkred", size = 1.5) +
      theme_bw() +
      # Zoom in to small values to increase resolution for the proteins under H0:
      xlim(c(0, 10))

    ## Warning: Removed 110 rows containing non-finite values (stat_density).

    ## Warning: Removed 110 row(s) containing missing values (geom_path).

Also check the p-value histograms. We expect the null cases to follow a uniform distribution, with a peak on the left for the non-null cases:

    ggplot(filter(fStats, !is.na(pAdj))) +
      geom_histogram(aes(x = pVal, y = ..density..), fill = "steelblue", alpha = 0.5, boundary = 0, bins = 30) +
      geom_line(aes(x = pVal, y = dunif(pVal)), color = "darkred", size = 1.5) +
      theme_bw()

The \(F\)-statistics and p-values approximate the expected distributions substantially closer when based on the estimated degrees of freedom than when based on the theoretical degrees of freedom.

# 8 Detect significantly shifted proteins

Finally, we can select proteins that are significantly shifted by putting a threshold on the Benjamini-Hochberg corrected p-values.

    topHits <- fStats %>%
      filter(pAdj <= 0.01) %>%
      dplyr::select(id, fStat, pVal, pAdj) %>%
      arrange(-fStat)

The table `topHits` contains 80 proteins with Benjamini-Hochberg corrected p-values \(\leq 0.01\).

Let us look at the targets detected in each dataset. The same proteins are shown in Fig. S3, S4, S6, and S7 of the paper.

    knitr::kable(topHits)

id | fStat | pVal | pAdj
--- | --- | --- | ---
CDK5_IPI00023530 | 369.91001 | 0.0000000 | 0.0000000
MAP2K2_IPI00003783 | 148.56418 | 0.0000000 | 0.0000000
CSK_IPI00013212 | 138.73894 | 0.0000000 | 0.0000000
PMPCA_IPI00166749 | 137.23184 | 0.0000000 | 0.0000000
AURKA_IPI00298940 | 131.22883 | 0.0000000 | 0.0000000
FECH_IPI00554589 | 128.72024 | 0.0000000 | 0.0000000
IRAK4_IPI00007641 | 122.32095 | 0.0000000 | 0.0000000
CAMKK2_IPI00290239 | 116.74940 | 0.0000000 | 0.0000000
PAK4_IPI00014068 | 113.40654 | 0.0000000 | 0.0000000
STK4_IPI00011488 | 102.44996 | 0.0000000 | 0.0000000
STK38_IPI00027251 | 99.74864 | 0.0000000 | 0.0000000
PDPK1_IPI00002538 | 96.96762 | 0.0000000 | 0.0000000
GSK3B_IPI00216190 | 93.08706 | 0.0000000 | 0.0000001
ADRBK1_IPI00012497 | 82.47454 | 0.0000000 | 0.0000001
BMP2K_IPI00337426 | 74.68966 | 0.0000000 | 0.0000003
FER_IPI00029263 | 70.44067 | 0.0000000 | 0.0000005
MAP2K1_IPI00219604 | 62.28640 | 0.0000000 | 0.0000011
MAP2K7_IPI00302112 | 59.79821 | 0.0000000 | 0.0000015
MAP4K2_IPI00149094 | 57.41734 | 0.0000000 | 0.0000019
MAPK12_IPI00296283 | 55.79760 | 0.0000000 | 0.0000023
PRKCE_IPI00024539 | 54.58750 | 0.0000000 | 0.0000025
ADK_IPI00290279 | 54.52631 | 0.0000000 | 0.0000025
STK3_IPI00411984 | 53.33665 | 0.0000000 | 0.0000028
MAPK8_IPI00220306 | 50.15869 | 0.0000000 | 0.0000041
MAPKAPK5_IPI00160672 | 50.13862 | 0.0000000 | 0.0000041
PKN1_IPI00412672 | 50.03979 | 0.0000000 | 0.0000041
PTK2_IPI00413961 | 49.36147 | 0.0000000 | 0.0000042
AAK1_IPI00916402 | 49.35151 | 0.0000000 | 0.0000042
CHEK2_IPI00423156 | 46.56284 | 0.0000000 | 0.0000063
CDK2_IPI00031681 | 45.30593 | 0.0000001 | 0.0000075
MAP2K4_IPI00024674 | 44.30181 | 0.0000001 | 0.0000084
CPOX_IPI00093057 | 44.25784 | 0.0000001 | 0.0000084
PHKG2_IPI00012891 | 43.03757 | 0.0000001 | 0.0000101
TNIK_IPI00514275 | 42.46317 | 0.0000001 | 0.0000108
VRK1_IPI00019640 | 41.38569 | 0.0000001 | 0.0000127
MAPKAPK2_IPI00026054 | 38.02183 | 0.0000002 | 0.0000232
MARK2_IPI00555838 | 37.80725 | 0.0000002 | 0.0000236
CAMK2G_IPI00908444 | 36.19262 | 0.0000003 | 0.0000316
GSK3A_IPI00292228 | 36.05387 | 0.0000003 | 0.0000316
PRKAR2B_IPI00554752 | 35.81922 | 0.0000003 | 0.0000324
RIOK2_IPI00306406 | 35.29313 | 0.0000003 | 0.0000352
PRKACA_IPI00396630 | 33.90313 | 0.0000004 | 0.0000452
RPS6KA3_IPI00020898 | 33.86492 | 0.0000004 | 0.0000452
MAPK3_IPI00018195 | 33.29311 | 0.0000005 | 0.0000499
STK24_IPI00872754 | 32.22266 | 0.0000006 | 0.0000617
MARK3_IPI00183118 | 30.06396 | 0.0000010 | 0.0000988
TTK_IPI00151170 | 29.47828 | 0.0000012 | 0.0001110
MKNK1_IPI00304048 | 26.03457 | 0.0000027 | 0.0002571
PDCD10_IPI00298558 | 25.81602 | 0.0000029 | 0.0002667
OSBPL3_IPI00023555 | 25.54331 | 0.0000031 | 0.0002810
HEBP1_IPI00148063 | 25.13118 | 0.0000035 | 0.0003077
RPS6KA1_IPI00477982 | 24.35454 | 0.0000043 | 0.0003730
PIK3CD_IPI00384817 | 24.08274 | 0.0000047 | 0.0003946
MAP3K2_IPI00513803 | 23.86291 | 0.0000049 | 0.0004118
SGK3_IPI00655852 | 23.35040 | 0.0000057 | 0.0004674
PRKCB_IPI00219628 | 23.01663 | 0.0000063 | 0.0005052
IRAK1_IPI00293652 | 22.93129 | 0.0000065 | 0.0005087
CAMK1D_IPI00170508 | 22.10925 | 0.0000082 | 0.0006360
POLR2K_IPI00023975 | 21.44212 | 0.0000100 | 0.0007640
LYN_IPI00298625 | 20.66056 | 0.0000128 | 0.0009556
CDC42BPA_IPI00903296 | 20.15429 | 0.0000150 | 0.0010989
PRKCQ_IPI00029196 | 20.11326 | 0.0000152 | 0.0010989
ALDH6A1_IPI00024990 | 19.89092 | 0.0000163 | 0.0011611
NEDD4L_IPI00304945 | 19.75452 | 0.0000170 | 0.0011942
CCNB2_IPI00028266 | 19.47712 | 0.0000186 | 0.0012864
PRKCD_IPI00329236 | 17.83029 | 0.0000323 | 0.0021980
PRCP_IPI00399307 | 17.79359 | 0.0000328 | 0.0021980
XPOT_IPI00306290 | 17.47422 | 0.0000366 | 0.0024213
MAPK14_IPI00221141 | 17.32712 | 0.0000386 | 0.0025132
CYCS_IPI00465315 | 16.06980 | 0.0000609 | 0.0039089
STK10_IPI00304742 | 15.93821 | 0.0000639 | 0.0040446
FAM96A_IPI00030985 | 15.90307 | 0.0000648 | 0.0040446
DDX54_IPI00152510 | 14.08251 | 0.0001318 | 0.0081148
RPS6KB1_IPI00216132 | 14.03772 | 0.0001342 | 0.0081523
PCTK2_IPI00376955 | 13.94637 | 0.0001393 | 0.0083488
MAP4K5_IPI00294842 | 13.86297 | 0.0001441 | 0.0085251
LLGL1_IPI00105532 | 13.59837 | 0.0001608 | 0.0093853
NQO2_IPI00219129 | 13.56419 | 0.0001631 | 0.0093975
ROCK2_IPI00307155 | 13.44623 | 0.0001713 | 0.0096957
TLK2_IPI00385652 | 13.42865 | 0.0001726 | 0.0096957

# 9 Session info

    devtools::session_info()

    ## - Session info ---------------------------------------------------------------
    ##  setting  value
    ##  version  R version 4.1.0 RC (2021-05-10 r80283)
    ##  os       Windows Server x64
    ##  system   x86_64, mingw32
    ##  ui       RTerm
    ##  language (EN)
    ##  collate  C
    ##  ctype    English_United States.1252
    ##  tz       America/New_York
    ##  date     2021-05-19
    ##
    ## - Packages -------------------------------------------------------------------
    ##  package      * version date       lib source
    ##  assertthat     0.2.1   2019-03-21 [2] CRAN (R 4.1.0)
    ##  backports      1.2.1   2020-12-09 [2] CRAN (R 4.1.0)
    ##  BiocManager    1.30.15 2021-05-11 [2] CRAN (R 4.1.0)
    ##  BiocParallel   1.26.0  2021-05-19 [2] Bioconductor
    ##  BiocStyle    * 2.20.0  2021-05-19 [2] Bioconductor
    ##  bookdown       0.22    2021-04-22 [2] CRAN (R 4.1.0)
    ##  broom        * 0.7.6   2021-04-05 [2] CRAN (R 4.1.0)
    ##  bslib          0.2.5.1 2021-05-18 [2] CRAN (R 4.1.0)
    ##  cachem         1.0.5   2021-05-15 [2] CRAN (R 4.1.0)
    ##  callr          3.7.0   2021-04-20 [2] CRAN (R 4.1.0)
    ##  cli            2.5.0   2021-04-26 [2] CRAN (R 4.1.0)
    ##  colorspace     2.0-1   2021-05-04 [2] CRAN (R 4.1.0)
    ##  crayon         1.4.1   2021-02-08 [2] CRAN (R 4.1.0)
    ##  DBI            1.1.1   2021-01-15 [2] CRAN (R 4.1.0)
    ##  desc           1.3.0   2021-03-05 [2] CRAN (R 4.1.0)
    ##  devtools       2.4.1   2021-05-05 [2] CRAN (R 4.1.0)
    ##  digest         0.6.27  2020-10-24 [2] CRAN (R 4.1.0)
    ##  dplyr        * 1.0.6   2021-05-05 [2] CRAN (R 4.1.0)
    ##  ellipsis       0.3.2   2021-04-29 [2] CRAN (R 4.1.0)
    ##  evaluate       0.14    2019-05-28 [2] CRAN (R 4.1.0)
    ##  fansi          0.4.2   2021-01-15 [2] CRAN (R 4.1.0)
    ##  farver         2.1.0   2021-02-28 [2] CRAN (R 4.1.0)
    ##  fastmap        1.1.0   2021-01-25 [2] CRAN (R 4.1.0)
    ##  fs             1.5.0   2020-07-31 [2] CRAN (R 4.1.0)
    ##  generics       0.1.0   2020-10-31 [2] CRAN (R 4.1.0)
    ##  ggplot2      * 3.3.3   2020-12-30 [2] CRAN (R 4.1.0)
    ##  glue           1.4.2   2020-08-27 [2] CRAN (R 4.1.0)
    ##  gtable         0.3.0   2019-03-25 [2] CRAN (R 4.1.0)
    ##  highr          0.9     2021-04-16 [2] CRAN (R 4.1.0)
    ##  htmltools      0.5.1.1 2021-01-22 [2] CRAN (R 4.1.0)
    ##  jquerylib      0.1.4   2021-04-26 [2] CRAN (R 4.1.0)
    ##  jsonlite       1.7.2   2020-12-09 [2] CRAN (R 4.1.0)
    ##  knitr        * 1.33    2021-04-24 [2] CRAN (R 4.1.0)
    ##  labeling       0.4.2   2020-10-20 [2] CRAN (R 4.1.0)
    ##  lifecycle      1.0.0   2021-02-15 [2] CRAN (R 4.1.0)
    ##  magick         2.7.2   2021-05-02 [2] CRAN (R 4.1.0)
    ##  magrittr     * 2.0.1   2020-11-17 [2] CRAN (R 4.1.0)
    ##  MASS           7.3-54  2021-05-03 [2] CRAN (R 4.1.0)
    ##  memoise        2.0.0   2021-01-26 [2] CRAN (R 4.1.0)
    ##  munsell        0.5.0   2018-06-12 [2] CRAN (R 4.1.0)
    ##  NPARC        * 1.4.0   2021-05-19 [1] Bioconductor
    ##  pillar         1.6.1   2021-05-16 [2] CRAN (R 4.1.0)
    ##  pkgbuild       1.2.0   2020-12-15 [2] CRAN (R 4.1.0)
    ##  pkgconfig      2.0.3   2019-09-22 [2] CRAN (R 4.1.0)
    ##  pkgload        1.2.1   2021-04-06 [2] CRAN (R 4.1.0)
    ##  prettyunits    1.1.1   2020-01-24 [2] CRAN (R 4.1.0)
    ##  processx       3.5.2   2021-04-30 [2] CRAN (R 4.1.0)
    ##  ps             1.6.0   2021-02-28 [2] CRAN (R 4.1.0)
    ##  purrr          0.3.4   2020-04-17 [2] CRAN (R 4.1.0)
    ##  R6             2.5.0   2020-10-28 [2] CRAN (R 4.1.0)
    ##  Rcpp           1.0.6   2021-01-15 [2] CRAN (R 4.1.0)
    ##  remotes        2.3.0   2021-04-01 [2] CRAN (R 4.1.0)
    ##  rlang          0.4.11  2021-04-30 [2] CRAN (R 4.1.0)
    ##  rmarkdown      2.8     2021-05-07 [2] CRAN (R 4.1.0)
    ##  rprojroot      2.0.2   2020-11-15 [2] CRAN (R 4.1.0)
    ##  rstudioapi     0.13    2020-11-12 [2] CRAN (R 4.1.0)
    ##  sass           0.4.0   2021-05-12 [2] CRAN (R 4.1.0)
    ##  scales         1.1.1   2020-05-11 [2] CRAN (R 4.1.0)
    ##  sessioninfo    1.1.1   2018-11-05 [2] CRAN (R 4.1.0)
    ##  stringi        1.6.2   2021-05-17 [2] CRAN (R 4.1.0)
    ##  stringr        1.4.0   2019-02-10 [2] CRAN (R 4.1.0)
    ##  testthat       3.0.2   2021-02-14 [2] CRAN (R 4.1.0)
    ##  tibble         3.1.2   2021-05-16 [2] CRAN (R 4.1.0)
    ##  tidyr          1.1.3   2021-03-03 [2] CRAN (R 4.1.0)
    ##  tidyselect     1.1.1   2021-04-30 [2] CRAN (R 4.1.0)
    ##  usethis        2.0.1   2021-02-10 [2] CRAN (R 4.1.0)
    ##  utf8           1.2.1   2021-03-12 [2] CRAN (R 4.1.0)
    ##  vctrs          0.3.8   2021-04-29 [2] CRAN (R 4.1.0)
    ##  withr          2.4.2   2021-04-18 [2] CRAN (R 4.1.0)
    ##  xfun           0.23    2021-05-15 [2] CRAN (R 4.1.0)
    ##  yaml           2.2.1   2020-02-01 [2] CRAN (R 4.1.0)
    ##
    ## [1] D:/biocbuild/bbs-3.13-bioc/tmpdir/RtmpsvwCSp/Rinstcc023897564
    ## [2] D:/biocbuild/bbs-3.13-bioc/R/library

# Bibliography

Childs, Dorothee, Karsten Bach, Holger Franken, Simon Anders, Nils Kurzawa, Marcus Bantscheff, Mikhail Savitski, and Wolfgang Huber. 2019. “Non-Parametric Analysis of Thermal Proteome Profiles Reveals Novel Drug-Binding Proteins.” Molecular & Cellular Proteomics, October. https://doi.org/10.1074/mcp.TIR119.001481.

Marazzi, A. 2002. “Bootstrap Tests for Robust Means of Asymmetric Distributions with Unequal Shapes.” Computational Statistics & Data Analysis 39 (4): 503–28.

Savitski, Mikhail M, Friedrich B M Reinhard, Holger Franken, Thilo Werner, Maria Fälth Savitski, Dirk Eberhard, Daniel Martinez Molina, et al. 2014. “Tracking Cancer Drugs in Living Cells by Thermal Profiling of the Proteome.” Science 346 (6205): 1255784.