Analysing thermal proteome profiling data with the NPARC package (original) (raw)
Contents
- 1 Introduction
- 2 Preparation
- 3 Data import
- 4 Data preprocessing and exploration
- 5 Illustrative example
- 6 Extend the analysis to all proteins
- 7 Compute test statistics
- 8 Detect significantly shifted proteins
- 9 Session info
- Bibliography
Preparation
Load necessary packages.
library(dplyr)
library(magrittr)
library(ggplot2)
library(broom)
library(knitr)
library(NPARC)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_tidyLet’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. : 0.000 Min. :40.0
## Class :character 1st Qu.: 0.169 1st Qu.:46.0
## Mode :character Median : 0.573 Median :53.5
## Mean : 0.576 Mean :53.5
## 3rd Qu.: 0.951 3rd Qu.:61.0
## Max. :394.981 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 :63400The 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.compoundConcentrationThe 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.
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 4505We 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).
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.
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)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.
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 .
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 226.9107 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()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)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()## Warning in left_join(., alternativePredictions, by = c("relAbundance", "temperature", : Detected an unexpected many-to-many relationship between `x` and `y`.
## ℹ Row 1 of `x` matches multiple rows in `y`.
## ℹ Row 21 of `y` matches multiple rows in `x`.
## ℹ If a many-to-many relationship is expected, set `relationship =
## "many-to-many"` to silence this warning.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).
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.
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: 27.68 secs## Flagging successful model fits...## ... complete.## Evaluating model fits...## Evaluating models ...## ... complete.## Computing model predictions and residuals ...## ... complete.## Starting model fitting...## ... complete## Elapsed time: 1.02 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 [359,940 × 7] (S3: tbl_df/tbl/data.frame)
## $ metrics : tibble [13,515 × 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$metrics %>%
mutate(modelType = factor(modelType), nCoeffs = factor(nCoeffs), nFitted = factor(nFitted), group = factor((group))) %>%
summary## modelType id tm a
## alternative:9010 Length:13515 Min. : 43.56 Min. : 0.0
## null :4505 Class :character 1st Qu.: 50.21 1st Qu.: 837.2
## Mode :character Median : 52.85 Median : 1103.0
## Mean : 54.09 Mean : 1431.5
## 3rd Qu.: 56.29 3rd Qu.: 1489.3
## Max. :298.81 Max. :15000.0
## NA's :788 NA's :20
## b pl aumc resid_sd
## Min. : 0.00001 Min. :0.00000 Min. : 4.87 Min. :0.007522
## 1st Qu.: 16.12254 1st Qu.:0.05277 1st Qu.:11.56 1st Qu.:0.035036
## Median : 21.44813 Median :0.07969 Median :14.45 Median :0.049776
## Mean : 26.99854 Mean :0.14040 Mean :15.03 Mean :0.064114
## 3rd Qu.: 28.40214 3rd Qu.:0.14403 3rd Qu.:18.06 3rd Qu.:0.074609
## Max. :250.00000 Max. :1.50000 Max. :37.42 Max. :1.896479
## NA's :20 NA's :20 NA's :20 NA's :20
## rss loglik tm_sd nCoeffs
## Min. : 0.001131 Min. :-70.47 Min. :0.000e+00 3 :13495
## 1st Qu.: 0.029207 1st Qu.: 27.32 1st Qu.:0.000e+00 NA's: 20
## Median : 0.063571 Median : 37.22 Median :0.000e+00
## Mean : 0.198649 Mean : 40.01 Mean :1.253e+12
## 3rd Qu.: 0.150597 3rd Qu.: 49.53 3rd Qu.:1.000e+00
## Max. :79.398036 Max. :123.31 Max. :5.589e+15
## NA's :20 NA's :20 NA's :788
## nFitted conv group
## 20 :8994 Mode :logical 0 :4505
## 40 :4501 FALSE:20 20 :4505
## NA's: 20 TRUE :13495 NA's:4505
##
##
##
## fits$predictions %>%
mutate(modelType = factor(modelType), group = factor((group))) %>%
summary## modelType id x y
## alternative:179896 Length:359940 Min. :40.0 Min. :0.0000
## null :180044 Class :character 1st Qu.:46.0 1st Qu.:0.1563
## Mode :character Median :53.5 Median :0.5779
## Mean :53.5 Mean :0.5642
## 3rd Qu.:61.0 3rd Qu.:0.9570
## Max. :67.0 Max. :8.2379
## NA's :20 NA's :20
## .fitted .resid group
## Min. :0.01099 Min. :-1.1566785 0 : 89910
## 1st Qu.:0.15948 1st Qu.:-0.0252733 20 : 89986
## Median :0.58405 Median : 0.0003096 NA's:180044
## Mean :0.55986 Mean : 0.0043428
## 3rd Qu.:0.96259 3rd Qu.: 0.0281027
## Max. :1.50000 Max. : 7.2402768
## NA's :20 NA's :20Check 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")$rss) # Summarize over both experimental groups
rssNull## [1] 1.218132rssAlt## [1] 0.08314745Next, we plot the predicted curves per model and experimental group:
stk4Predictions <- filter(fits$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))Compute test statistics
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()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: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.## Warning: Removed 178 rows containing non-finite outside the scale range
## (`stat_density()`).## Warning: Removed 178 rows containing missing values or values outside the scale range
## (`geom_line()`).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()## Warning: The dot-dot notation (`..density..`) was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(density)` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.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 111 rows containing non-finite outside the scale range
## (`stat_density()`).## Warning: Removed 111 rows containing missing values or values outside the scale range
## (`geom_line()`).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.
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)Session info
devtools::session_info()## ─ Session info ───────────────────────────────────────────────────────────────
## setting value
## version R version 4.5.0 beta (2025-04-02 r88102)
## os Ubuntu 24.04.2 LTS
## system x86_64, linux-gnu
## ui X11
## language (EN)
## collate C
## ctype en_US.UTF-8
## tz America/New_York
## date 2025-04-15
## pandoc 2.7.3 @ /usr/bin/ (via rmarkdown)
## quarto 1.6.43 @ /usr/local/bin/quarto
##
## ─ Packages ───────────────────────────────────────────────────────────────────
## package * version date (UTC) lib source
## backports 1.5.0 2024-05-23 [2] CRAN (R 4.5.0)
## BiocManager 1.30.25 2024-08-28 [2] CRAN (R 4.5.0)
## BiocParallel 1.43.0 2025-04-15 [2] Bioconductor 3.22 (R 4.5.0)
## BiocStyle * 2.37.0 2025-04-15 [2] Bioconductor 3.22 (R 4.5.0)
## bookdown 0.43 2025-04-15 [2] CRAN (R 4.5.0)
## broom * 1.0.8 2025-03-28 [2] CRAN (R 4.5.0)
## bslib 0.9.0 2025-01-30 [2] CRAN (R 4.5.0)
## cachem 1.1.0 2024-05-16 [2] CRAN (R 4.5.0)
## cli 3.6.4 2025-02-13 [2] CRAN (R 4.5.0)
## codetools 0.2-20 2024-03-31 [3] CRAN (R 4.5.0)
## colorspace 2.1-1 2024-07-26 [2] CRAN (R 4.5.0)
## crayon 1.5.3 2024-06-20 [2] CRAN (R 4.5.0)
## devtools 2.4.5 2022-10-11 [2] CRAN (R 4.5.0)
## digest 0.6.37 2024-08-19 [2] CRAN (R 4.5.0)
## dplyr * 1.1.4 2023-11-17 [2] CRAN (R 4.5.0)
## ellipsis 0.3.2 2021-04-29 [2] CRAN (R 4.5.0)
## evaluate 1.0.3 2025-01-10 [2] CRAN (R 4.5.0)
## farver 2.1.2 2024-05-13 [2] CRAN (R 4.5.0)
## fastmap 1.2.0 2024-05-15 [2] CRAN (R 4.5.0)
## fs 1.6.6 2025-04-12 [2] CRAN (R 4.5.0)
## generics 0.1.3 2022-07-05 [2] CRAN (R 4.5.0)
## ggplot2 * 3.5.2 2025-04-09 [2] CRAN (R 4.5.0)
## glue 1.8.0 2024-09-30 [2] CRAN (R 4.5.0)
## gtable 0.3.6 2024-10-25 [2] CRAN (R 4.5.0)
## htmltools 0.5.8.1 2024-04-04 [2] CRAN (R 4.5.0)
## htmlwidgets 1.6.4 2023-12-06 [2] CRAN (R 4.5.0)
## httpuv 1.6.15 2024-03-26 [2] CRAN (R 4.5.0)
## jquerylib 0.1.4 2021-04-26 [2] CRAN (R 4.5.0)
## jsonlite 2.0.0 2025-03-27 [2] CRAN (R 4.5.0)
## knitr * 1.50 2025-03-16 [2] CRAN (R 4.5.0)
## labeling 0.4.3 2023-08-29 [2] CRAN (R 4.5.0)
## later 1.4.2 2025-04-08 [2] CRAN (R 4.5.0)
## lifecycle 1.0.4 2023-11-07 [2] CRAN (R 4.5.0)
## magick 2.8.6 2025-03-23 [2] CRAN (R 4.5.0)
## magrittr * 2.0.3 2022-03-30 [2] CRAN (R 4.5.0)
## MASS 7.3-65 2025-02-28 [3] CRAN (R 4.5.0)
## memoise 2.0.1 2021-11-26 [2] CRAN (R 4.5.0)
## mime 0.13 2025-03-17 [2] CRAN (R 4.5.0)
## miniUI 0.1.1.1 2018-05-18 [2] CRAN (R 4.5.0)
## munsell 0.5.1 2024-04-01 [2] CRAN (R 4.5.0)
## NPARC * 1.21.0 2025-04-15 [1] Bioconductor 3.22 (R 4.5.0)
## pillar 1.10.2 2025-04-05 [2] CRAN (R 4.5.0)
## pkgbuild 1.4.7 2025-03-24 [2] CRAN (R 4.5.0)
## pkgconfig 2.0.3 2019-09-22 [2] CRAN (R 4.5.0)
## pkgload 1.4.0 2024-06-28 [2] CRAN (R 4.5.0)
## profvis 0.4.0 2024-09-20 [2] CRAN (R 4.5.0)
## promises 1.3.2 2024-11-28 [2] CRAN (R 4.5.0)
## purrr 1.0.4 2025-02-05 [2] CRAN (R 4.5.0)
## R6 2.6.1 2025-02-15 [2] CRAN (R 4.5.0)
## Rcpp 1.0.14 2025-01-12 [2] CRAN (R 4.5.0)
## remotes 2.5.0 2024-03-17 [2] CRAN (R 4.5.0)
## rlang 1.1.6 2025-04-11 [2] CRAN (R 4.5.0)
## rmarkdown 2.29 2024-11-04 [2] CRAN (R 4.5.0)
## sass 0.4.10 2025-04-11 [2] CRAN (R 4.5.0)
## scales 1.3.0 2023-11-28 [2] CRAN (R 4.5.0)
## sessioninfo 1.2.3 2025-02-05 [2] CRAN (R 4.5.0)
## shiny 1.10.0 2024-12-14 [2] CRAN (R 4.5.0)
## tibble 3.2.1 2023-03-20 [2] CRAN (R 4.5.0)
## tidyr 1.3.1 2024-01-24 [2] CRAN (R 4.5.0)
## tidyselect 1.2.1 2024-03-11 [2] CRAN (R 4.5.0)
## tinytex 0.57 2025-04-15 [2] CRAN (R 4.5.0)
## urlchecker 1.0.1 2021-11-30 [2] CRAN (R 4.5.0)
## usethis 3.1.0 2024-11-26 [2] CRAN (R 4.5.0)
## vctrs 0.6.5 2023-12-01 [2] CRAN (R 4.5.0)
## withr 3.0.2 2024-10-28 [2] CRAN (R 4.5.0)
## xfun 0.52 2025-04-02 [2] CRAN (R 4.5.0)
## xtable 1.8-4 2019-04-21 [2] CRAN (R 4.5.0)
## yaml 2.3.10 2024-07-26 [2] CRAN (R 4.5.0)
##
## [1] /tmp/RtmpotOTHv/Rinst1e2bbe39b8d394
## [2] /home/biocbuild/bbs-3.22-bioc/R/site-library
## [3] /home/biocbuild/bbs-3.22-bioc/R/library
## * ── Packages attached to the search path.
##
## ──────────────────────────────────────────────────────────────────────────────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.