Analysing thermal proteome profiling data with the NPARC package
29 October 2024, 18:37:40
Package
NPARC 1.19.0
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_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. : 0.00 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 :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.
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 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).
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 226.9107 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()| 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()## 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).
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: 39.87 secs## Flagging successful model fits...## ... complete.## Evaluating model fits...## Evaluating models ...## ... complete.## Computing model predictions and residuals ...## ... complete.## Starting model fitting...## ... complete## Elapsed time: 1.01 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 [359,959 × 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$metrics %>%
mutate(modelType = factor(modelType), nCoeffs = factor(nCoeffs), nFitted = factor(nFitted), group = factor((group))) %>%
summary## modelType id tm a
## alternative:9010 Length:13515 Min. : 43.56 Min. : 0.0
## null :4505 Class :character 1st Qu.: 50.20 1st Qu.: 836.8
## Mode :character Median : 52.85 Median : 1102.8
## Mean : 54.09 Mean : 1426.6
## 3rd Qu.: 56.29 3rd Qu.: 1488.8
## Max. :298.81 Max. :15000.0
## NA's :794 NA's :19
## b pl aumc resid_sd
## Min. : 0.00001 Min. :0.00000 Min. : 4.87 Min. :0.007522
## 1st Qu.: 16.11794 1st Qu.:0.05282 1st Qu.:11.56 1st Qu.:0.035037
## Median : 21.43936 Median :0.07973 Median :14.45 Median :0.049778
## Mean : 26.94484 Mean :0.14092 Mean :15.03 Mean :0.064075
## 3rd Qu.: 28.39752 3rd Qu.:0.14430 3rd Qu.:18.06 3rd Qu.:0.074608
## Max. :250.00000 Max. :1.50000 Max. :37.42 Max. :1.896479
## NA's :19 NA's :19 NA's :19 NA's :19
## rss loglik tm_sd nCoeffs
## Min. : 0.00113 Min. :-70.47 Min. :0.000e+00 3 :13496
## 1st Qu.: 0.02921 1st Qu.: 27.32 1st Qu.:0.000e+00 NA's: 19
## Median : 0.06359 Median : 37.22 Median :0.000e+00
## Mean : 0.19822 Mean : 40.01 Mean :8.468e+11
## 3rd Qu.: 0.15060 3rd Qu.: 49.53 3rd Qu.:1.000e+00
## Max. :79.39804 Max. :123.31 Max. :4.718e+15
## NA's :19 NA's :19 NA's :794
## nFitted conv group
## 20 :8995 Mode :logical 0 :4505
## 40 :4501 FALSE:19 20 :4505
## NA's: 19 TRUE :13496 NA's:4505
##
##
##
## fits$predictions %>%
mutate(modelType = factor(modelType), group = factor((group))) %>%
summary## modelType id x y
## alternative:179915 Length:359959 Min. :40.0 Min. :0.0000
## null :180044 Class :character 1st Qu.:46.0 1st Qu.:0.1563
## Mode :character Median :53.5 Median :0.5780
## Mean :53.5 Mean :0.5642
## 3rd Qu.:61.0 3rd Qu.:0.9570
## Max. :67.0 Max. :8.2379
## NA's :19 NA's :19
## .fitted .resid group
## Min. :0.01099 Min. :-1.156426 0 : 89891
## 1st Qu.:0.15950 1st Qu.:-0.025278 20 : 90024
## Median :0.58415 Median : 0.000310 NA's:180044
## Mean :0.55990 Mean : 0.004323
## 3rd Qu.:0.96261 3rd Qu.: 0.028101
## Max. :1.50000 Max. : 7.240277
## NA's :19 NA's :196.2 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")$rss) # Summarize over both experimental groups
rssNull## [1] 1.218132rssAlt## [1] 0.08314745Next, we plot the predicted curves per model and experimental group:
stk4Predictions <- filter(fits$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))