In ococrook/bandle: An R package for the Bayesian analysis of differential subcellular localisation experiments

BiocStyle::markdown()

knitr::opts_chunk$set(dpi=40,fig.width=7)

Introduction

In this vignette we use a real-life biological use-case to demonstrate how to analyse mass-spectrometry based proteomics data using the Bayesian ANalysis of Differential Localisation Experiments (BANDLE) method.

The data

As mentioned in "Vignette 1: Getting Started with BANDLE" data from mass spectrometry based proteomics methods most commonly yield a matrix of measurements where we have proteins/peptides/peptide spectrum matches (PSMs) along the rows, and samples/fractions along the columns. To use bandle the data must be stored as a MSnSet, as implemented in the Bioconductor r Biocpkg("MSnbase") package. Please see the relevant vignettes in r Biocpkg("MSnbase") for constructing these data containers.

The data used in this vignette has been published in @thplopit and is currently stored as MSnSet instances in the the r Biocpkg("pRolocdata") package. We will load it in the next section.

Spatialtemporal proteomic profiling of a THP-1 cell line

In this workflow we analyse the data produced by @thplopit. In this experiment triplicate hyperLOPIT experiments [@Mulvey:2017] were conducted on THP-1 human leukaemia cells where the samples were analysed and collected (1) when cells were unstimulated and then (2) following 12 hours stimulation with LPS (12h-LPS).

In the following code chunk we load 4 of the datasets from the study: 2 replicates of the unstimulated and 2 replicates of the 12h-LPS stimulated samples. Please note to adhere to Bioconductor vignette build times we only load 2 of the 3 replicates for each condition to demonstrate the BANDLE workflow.

library("pRolocdata")
data("thpLOPIT_unstimulated_rep1_mulvey2021")
data("thpLOPIT_unstimulated_rep3_mulvey2021")
data("thpLOPIT_lps_rep1_mulvey2021")
data("thpLOPIT_lps_rep3_mulvey2021")

By typing the names of the datasets we get a MSnSet data summary. For example,

thpLOPIT_unstimulated_rep1_mulvey2021
thpLOPIT_lps_rep1_mulvey2021

We see that the datasets thpLOPIT_unstimulated_rep1_mulvey2021 and thpLOPIT_lps_rep1_mulvey2021 contain 5107 and 4879 proteins respectively, across 20 TMT channels. The data is accessed through different slots of the MSnSet (see str(thpLOPIT_unstimulated_rep1_mulvey2021) for all available slots). The 3 main slots which are used most frequently are those that contain the quantitation data, the features i.e. PSM/peptide/protein information and the sample information, and these can be accessed using the functions exprs, fData, and pData, respectively.

Preparing the data

First, let us load the bandle package along with some other R packages needed for visualisation and data manipulation,

library("bandle")
library("pheatmap")
library("viridis")
library("dplyr")
library("ggplot2")
library("gridExtra")

To run bandle there are a few minimal requirements that the data must fulfill.

• the same number of channels across conditions and replicates
• the same proteins across conditions and replicates
• data must be a list of MSnSet instances

If we use the dim function we see that the datasets we have loaded have the same number of channels but a different number of proteins per experiment.

dim(thpLOPIT_unstimulated_rep1_mulvey2021)
dim(thpLOPIT_unstimulated_rep3_mulvey2021)
dim(thpLOPIT_lps_rep1_mulvey2021)
dim(thpLOPIT_lps_rep3_mulvey2021)

We use the function commonFeatureNames to extract proteins that are common across all replicates. This function has a nice side effect which is that it also wraps the data into a list, ready for input into bandle.

thplopit <- commonFeatureNames(c(thpLOPIT_unstimulated_rep1_mulvey2021,  ## unstimulated rep
                                 thpLOPIT_unstimulated_rep3_mulvey2021,  ## unstimulated rep
                                 thpLOPIT_lps_rep1_mulvey2021,           ## 12h-LPS rep
                                 thpLOPIT_lps_rep3_mulvey2021))          ## 12h-LPS rep

We now have our list of MSnSets ready for bandle with 3727 proteins common across all 4 replicates/conditions.

thplopit

We can visualise the data using the plot2D function from pRoloc

## create a character vector of title names for the plots
plot_id <- c("Unstimulated replicate 1", "Unstimulated replicate 2",
             "12h-LPS replicate 1", "12h-LPS replicate 2")

## Let's set the stock colours of the classes to plot to be transparent
setStockcol(NULL)
setStockcol(paste0(getStockcol(), "90"))

## plot the data
par(mfrow = c(2,2))
for (i in seq(thplopit))
    plot2D(thplopit[[i]], main = plot_id[i])
addLegend(thplopit[[4]], where = "topleft", cex = .75)

By default the plot2D uses principal components analysis (PCA) for the data transformation. Other options such as t-SNE, kernal PCA etc. are also available, see ?plot2D and the method argument. PCA sometimes will randomly flip the axis, because the eigenvectors only need to satisfy $||v|| = 1$, which allows a sign flip. You will notice this is the case for the 3rd plot. If desired you can flip the axis/change the sign of the PCs by specifying any of the arguments mirrorX, mirrorY, axsSwitch to TRUE when you call plot2D.

Data summary:

• LOPIT conducted on THP1 leukaemia cells
• 2 conditions: (1) unstimulated, (2) 12 hours stimulation with THP
• 20 TMT fractions yielded from 2 x 10plex TMT in an interleaved experimental design (see @Mulvey:2017 for details and the associated app http://proteome.shinyapps.io/thp-lopit/)
• 2 replicates selected as a use-case from the original experiment
• 3727 proteins common across the 2 replicates

Preparing the bandle input parameters

As mentioned in the first vignette, bandle uses a complex model to analyse the data. Markov-Chain Monte-Carlo (MCMC) is used to sample the posterior distribution of parameters and latent variables from which statistics of interest can be computed. Again, here we only run a few iterations for brevity but typically one needs to run thousands of iterations to ensure convergence, as well as multiple parallel chains.

Fitting Gaussian processes

First, we need to fit non-parametric regression functions to the markers profiles. We use the function fitGPmaternPC. In general the default penalised complexity priors on the hyperparameters (see ?fitGP), of fitGPmaternPC work well for correlation profiling data with <10 channels (as tested in @bandle). From looking at the help documentation (see, ?fitGPmaternPC) we see the default priors on the hyperparameters are hyppar = matrix(c(10, 60, 250), nrow = 1).

Different priors can be constructed and tested. For example, here, we found that matrix(c(1, 60, 100) worked well. In this experiment we have with several thousand proteins and many more subcellular classes and fractions (channels) than tested in the @bandle paper.

In this example, we require a 11*3 matrix as we have 11 subcellular marker classes and 3 columns to represent the hyperparameters length-scale, amplitude, variance. Generally, (1) increasing the lengthscale parameter (the first column of the hyppar matrix) increases the spread of the covariance i.e. the similarity between points, (2) increasing the amplitude parameter (the second column of the hyppar matrix) increases the maximum value of the covariance and lastly (3) decreasing the variance (third column of the hyppar matrix) reduces the smoothness of the function to allow for local variations. We strongly recommend users start with the default parameters and change and assess them as necessary for their dataset by visually evaluating the fit of the GPs using the plotGPmatern function.

To see the subcellular marker classes in our data we use the getMarkerClasses function from pRoloc.

(mrkCl <- getMarkerClasses(thplopit[[1]], fcol = "markers"))

For this use-case we have K = 11 classes

K <- length(mrkCl)

We can construct our priors, which as mentioned above will be a K*3 matrix i.e. 11x3 matrix.

pc_prior <- matrix(NA, ncol = 3, K)
pc_prior[seq.int(1:K), ] <- matrix(rep(c(1, 60, 100),
                                       each = K), ncol = 3)
head(pc_prior)

Now we have generated these complexity priors we can pass them as an argument to the fitGPmaternPC function. For example,

gpParams <- lapply(thplopit,
                   function(x) fitGPmaternPC(x, hyppar = pc_prior))

By plotting the predictives using the plotGPmatern function we see that the distributions and fit looks sensible for each class so we will proceed with setting the prior on the weights.

par(mfrow = c(4, 3))
plotGPmatern(thplopit[[1]], gpParams[[1]])

For the interest of keeping the vignette size small, in the above chunk we plot only the first dataset and its respective predictive. To plot the second dataset we would execute plotGPmatern(thplopit[[i]], gpParams[[i]]) where i = 2, and similarly for the third i = 3 and so on.

Setting the prior on the weights

The next step is to set up the matrix Dirichlet prior on the mixing weights. If dirPrior = NULL a default Dirichlet prior is computed see ?bandle. We strongly advise you to set your own prior. In "Vignette 1: Getting Started with BANDLE" we give some suggestions on how to set this and in the below code we try a few different priors and assess the expectations.

As per Vignette 1, let's try a dirPrior as follows,

set.seed(1)
dirPrior = diag(rep(1, K)) + matrix(0.001, nrow = K, ncol = K)
predDirPrior <- prior_pred_dir(object = thplopit[[1]],
                               dirPrior = dirPrior,
                               q = 15)

The mean number of relocalisations is

predDirPrior$meannotAlloc

The prior probability that more than q differential localisations are expected is

predDirPrior$tailnotAlloc

hist(predDirPrior$priornotAlloc, col = getStockcol()[1])

We see that the prior probability that proteins are allocated to different components between datasets concentrates around 0. This is what we expect, we expect subtle changes between conditions for this data. We may perhaps wish to be a little stricter with the number of differential localisations output by bandle and in this case we could make the off-diagonal elements of the dirPrior smaller. In the below code chunk we test 0.0005 instead of 0.001, which reduces the number of re-localisations.

set.seed(1)
dirPrior = diag(rep(1, K)) + matrix(0.0005, nrow = K, ncol = K)
predDirPrior <- prior_pred_dir(object = thplopit[[1]],
                               dirPrior = dirPrior,
                               q = 15)

predDirPrior$meannotAlloc
predDirPrior$tailnotAlloc
hist(predDirPrior$priornotAlloc, col = getStockcol()[1])

Again, we see that the prior probability that proteins are allocated to different components between datasets concentrates around 0.

Running bandle

Now we have computed our gpParams and pcPriors we can run the main bandle function.

Here for convenience of building the vignette we only run 2 of the triplicates for each condition and run the bandle function for a small number of iterations and chains to minimise the vignette build-time. Typically we'd recommend you run the number of iterations (numIter) in the $1000$s and to test a minimum of 4 chains.

We first subset our data into two objects called control and treatment which we subsequently pass to bandle along with our priors.

control <- list(thplopit[[1]], thplopit[[2]])
treatment <- list(thplopit[[3]], thplopit[[4]])

params <- bandle(objectCond1 = control, 
                 objectCond2 = treatment,
                 numIter = 10,       # usually 10,000
                 burnin = 5L,        # usually 5,000
                 thin = 1L,          # usually 20
                 gpParams = gpParams,
                 pcPrior = pc_prior,
                 numChains = 4,     # usually >=4
                 dirPrior = dirPrior,
                 seed = 1)

• numIter is the number of iterations of the MCMC algorithm. Default is 1000. Though usually much larger numbers are used we recommend 10000+.
• burnin is the number of samples to be discarded from the beginning of the chain. Here we use 5 in this example but the default is 100.
• thin is the thinning frequency to be applied to the MCMC chain. Default is 5.
• gpParams parameters from prior fitting of GPs to each niche to accelerate inference
• pcPrior matrix with 3 columns indicating the lambda parameters for the penalised complexity prior.
• numChains defined the number of chains to run. We recommend at least 4.
• dirPrior as above a matrix generated by dirPrior function.
• seed a random seed for reproducibility

A bandleParams object is produced

params

Processing and analysing the bandle results

Assessing convergence

The bandle method uses of Markov Chain Monte Carlo (MCMC) and therefore before we can extract our classification and differential localisation results we first need to check the algorithm for convergence of the MCMC chains.

As mentioned in Vignette 1 there are two main functions we can use to help us assess convergence are: (1) calculateGelman which calculates the Gelman diagnostics for all pairwise chain combinations and (2) plotOutliers which generates trace and density plots for all chains.

Let's start with the Gelman which allows us to compare the inter and intra chain variances. If the chains have converged the ratio of these quantities should be close to one.

calculateGelman(params)

In this example, to demonstrate how to use bandle we have only run 10 MCMC iterations for each of the r length(params@chains) chains. As already mentioned in practice we suggest running a minimum of 1000 iterations and a minimum of 4 chains.

We do not expect the algorithm to have converged with so little iterations and this is highlighted in the Gelman diagnostics which are > 1. For convergence we expect Gelman diagnostics < 1.2, as discuss in @Crook2019 and general Bayesian literature.

If we plot trace and density plots we can also very quickly see that (as expected) the algorithm has not converged over the 20 test runs.

Example with 5 iterations

plotOutliers(params)

We include a plot below of output from 500 iterations

Example with 500 iterations

knitr::include_graphics("figs/traceplot.png")

In this example where the data has been run for 500 iterations. We get a better idea of what we expect convergence to look like. We would still recommend running for 10000+ iterations for adequate sampling. For convergence we expect trace plots to look like hairy caterpillars and the density plots should be centered around the same number of outliers. For condition 1 we see the number of outliers sits around 1620 proteins and in condition 2 it sits around 1440. If we the number of outliers was wildly different for one of the chains, or if the trace plot has a long period of burn-in (the beginning of the trace looks very different from the rest of the plot), or high serial correlation (the chain is very slow at exploring the sample space) we may wish to discard these chains. We may need to run more chains.

@Taboga2021 provides a nice online book explaining some of the main problems users may encounter with MCMC at, see the chapter "Markov-Chain-Monte-Carlo-diagnostics"

Removing unconverged chains

Although we can clearly see all chains in the example with 5 iterations are bad here as we have not sampled the space with sufficient number of iterations to achieve convergence, let's for sake of demonstration remove chains 1 and 4. In practice, all of these chains would be discarded as (1) none of the trace and density plots show convergence and additionally (2) the Gelman shows many chains have values > 1. Note, when assessing convergence if a chain is bad in one condition, the same chain must be discarded from the second condition too. They are considered in pairs.

Let's remove chains 1 and 4 as an example,

params_converged <- params[-c(1, 4)]

We have now removed chains 1 and 4 and we are left with 2 chains

params_converged

Running bandleProcess and bandleSummary

Following Vignette 1 we populate the bandleres object by calling the bandleProcess function. This may take a few seconds to process.

params_converged <- bandleProcess(params_converged)

The bandleProcess must be run to process the bandle output and populate the bandle object.

The summaries function is a convenience function for accessing the output

bandle_out <- summaries(params_converged)

The output is a list of 2 bandleSummary objects.

length(bandle_out)
class(bandle_out[[1]])

There are 3 slots:

• A posteriorEstimates slot containing the posterior quantities of interest for different proteins.
• A slot for convergence diagnostics
• The joint posterior distribution across organelles see bandle.joint

For the control we would access these as follows,

bandle_out[[1]]@posteriorEstimates
bandle_out[[1]]@diagnostics
bandle_out[[1]]@bandle.joint

Instead of examining these directly we are going to proceed with protein localisation prediction and add these results to the datasets in the fData slot of the MSnSet.

Predicting subcellular location

The bandle method performs both (1) protein subcellular localisation prediction and (2) predicts the differential localisation of proteins. In this section we will use the bandlePredict function to perform protein subcellular localisation prediction and also append all the bandle results to the MSnSet dataset.

We begin by using the bandlePredict function to append our results to the original MSnSet datasets.

## Add the bandle results to a MSnSet
xx <- bandlePredict(control, 
                    treatment, 
                    params = params_converged, 
                    fcol = "markers")
res_0h <- xx[[1]]
res_12h <- xx[[2]]

The BANDLE model combines replicate information within each condition to obtain the localisation of proteins for each single experimental condition.

The results for each condition are appended to the first dataset in the list of MSnSets (for each condition). It is important to familiarise yourself with the MSnSet data structure. To further highlight this in the below code chunk we look at the fvarLabels of each datasets, this shows the column header names of the fData feature data. We see that the first replicate at 0h e.g. res_0h[[1]] has 7 columns updated with the output of bandle e.g. bandle.probability, bandle.allocation, bandle.outlier etc. appended to the feature data (fData(res_0h[[1]])).

The second dataset at 0h i.e. res_0h[[2]] does not have this information appended to the feature data as it is already in the first dataset. This is the same for the second condition at 12h post LPS stimulation.

fvarLabels(res_0h[[1]])
fvarLabels(res_0h[[2]])

fvarLabels(res_12h[[1]])
fvarLabels(res_12h[[2]])

The bandle results are shown in the columns:

• bandle.joint which is the full joint probability distribution across all subcellular classes
• bandle.allocation which contains the the localisation predictions to one of the subcellular classes that appear in the training data.
• bandle.probability is the allocation probability, corresponding to the mean of the distribution probability.
• bandle.outlier is the probability of being an outlier. A high value indicates that the protein is unlikely to belong to any annotated class (and is hence considered an outlier).
• bandle.probability.lowerquantile and bandle.probability.upperquantile are the upper and lower quantiles of the allocation probability distribution.
• bandle.mean.shannon is the Shannon entropy, measuring the uncertainty in the allocations (a high value representing high uncertainty; the highest value is the natural logarithm of the number of classes).
• bandle.differential.localisation is the differential localisation probability.

Thresholding on the posterior probability

As mentioned in Vignette 1, it is also common to threshold allocation results based on the posterior probability. Proteins that do not meet the threshold are not assigned to a subcellular location and left unlabelled (here we use the terminology "unknown" for consistency with the pRoloc package). It is important not to force proteins to allocate to one of the niches defined here in the training data, if they have low probability to reside there. We wish to allow for greater subcellular diversity and to have multiple location, this is captured essentially in leaving a protein "unlabelled" or "unknown". We can also extract the "unknown" proteins with high uncertainty and examine their distribution over all organelles (see bandle.joint).

To obtain classification results we threshold using a 1% FDR based on the bandle.probability and append the results to the data using the getPredictions function from MSnbase.

## threshold results using 1% FDR
res_0h[[1]] <- getPredictions(res_0h[[1]], 
                              fcol = "bandle.allocation",  
                              scol = "bandle.probability",    
                              mcol = "markers", 
                              t = .99)

res_12h[[1]] <- getPredictions(res_12h[[1]], 
                               fcol = "bandle.allocation",
                               scol = "bandle.probability", 
                               mcol = "markers",      
                               t = .99)

A table of predictions is printed to the screen as a side effect when running getPredictions function.

In addition to thresholding on the bandle.probability we can threshold based on the bandle.outlier i.e. the probability of being an outlier. A high value indicates that the protein is unlikely to belong to any annotated class (and is hence considered an outlier). We wish to assign proteins to a subcellular niche if they have a high bandle.probability and also a low bandle.outlier probability. This is a nice way to ensure we keep the most high confidence localisations.

In the below code chunk we use first create a new column called bandle.outlier.t in the feature data which is 1 - outlier probability. This allows us then to use getPredictions once again and keep only proteins which meet both the 0.99 threshold on the bandle.probability and the bandle.outlier.

Note, that running getPredictions appends the results to a new feature data column called fcol.pred, please see ?getPredictions for the documentation. As we have run this function twice, our column of classification results are found in bandle.allocation.pred.pred.

## add outlier probability
fData(res_0h[[1]])$bandle.outlier.t <- 1 -  fData(res_0h[[1]])$bandle.outlier
fData(res_12h[[1]])$bandle.outlier.t <- 1 -  fData(res_12h[[1]])$bandle.outlier

## threshold again, now on the outlier probability
res_0h[[1]] <- getPredictions(res_0h[[1]], 
                              fcol = "bandle.allocation.pred",  
                              scol = "bandle.outlier.t",    
                              mcol = "markers", 
                              t = .99)

res_12h[[1]] <- getPredictions(res_12h[[1]], 
                               fcol = "bandle.allocation.pred",
                               scol = "bandle.outlier.t", 
                               mcol = "markers",      
                               t = .99)

Appending the results to all replicates

Let's append the results to the second replicate (by default they are appended to the first only, as already mentioned above). This allows us to plot each dataset and the results using plot2D.

## Add results to second replicate at 0h
res_alloc_0hr <- fData(res_0h[[1]])$bandle.allocation.pred.pred
fData(res_0h[[2]])$bandle.allocation.pred.pred <- res_alloc_0hr

## Add results to second replicate at 12h
res_alloc_12hr <- fData(res_12h[[1]])$bandle.allocation.pred.pred
fData(res_12h[[2]])$bandle.allocation.pred.pred <- res_alloc_12hr

We can plot these results on a PCA plot and compare to the original subcellular markers.

par(mfrow = c(5, 2))

plot2D(res_0h[[1]], main = "Unstimulated - replicate 1 \n subcellular markers", 
       fcol = "markers")
plot2D(res_0h[[1]], main = "Unstimulated - replicate 1 \nprotein allocations (1% FDR)", 
       fcol = "bandle.allocation.pred.pred")

plot2D(res_0h[[2]], main = "Unstimulated - replicate 2 \nsubcellular markers", 
       fcol = "markers")
plot2D(res_0h[[2]], main = "Unstimulated - replicate 2 \nprotein allocations (1% FDR)", 
       fcol = "bandle.allocation.pred.pred")

plot2D(res_0h[[1]], main = "12h LPS - replicate 1 \nsubcellular markers", 
       fcol = "markers")
plot2D(res_0h[[1]], main = "12h LPS - replicate 1 \nprotein allocations (1% FDR)", 
       fcol = "bandle.allocation.pred.pred")

plot2D(res_0h[[2]], main = "12h LPS - replicate 2 \nsubcellular markers", 
       fcol = "markers")
plot2D(res_0h[[2]], main = "12h LPS - replicate 2 \nprotein allocations (1% FDR)", 
       fcol = "bandle.allocation.pred.pred")

plot(NULL, xaxt='n',yaxt='n',bty='n',ylab='',xlab='', xlim=0:1, ylim=0:1)
addLegend(res_0h[[1]], where = "topleft", cex = .8)

Distribution on allocations

We can examine the distribution of allocations that (1) have been assigned to a single location with high confidence and, (2) those which did not meet the threshold and thus have high uncertainty i.e. are labelled as "unknown".

Before we can begin to examine the distribution of allocation we first need to subset the data and remove the markers. This makes it easier to assess new prediction.

We can use the function unknownMSnSet to subset as we did in Vignette 1,

## Remove the markers from the MSnSet
res0hr_unknowns <- unknownMSnSet(res_0h[[1]], fcol = "markers")
res12h_unknowns <- unknownMSnSet(res_12h[[1]], fcol = "markers")

Proteins assigned to one main location

In this example we have performed an extra round of filtering when predicting the main protein subcellular localisation by taking into account outlier probability in addition to the posterior. As such, the column containing the predictions in the fData is called bandle.allocation.pred.pred.

Extract the predictions,

res1 <- fData(res0hr_unknowns)$bandle.allocation.pred.pred
res2 <- fData(res12h_unknowns)$bandle.allocation.pred.pred

res1_tbl <- table(res1)
res2_tbl <- table(res2)

We can visualise these results on a barplot,

par(mfrow = c(1, 2))
barplot(res1_tbl, las = 2, main = "Predicted location: 0hr",
        ylab = "Number of proteins")
barplot(res2_tbl, las = 2, main = "Predicted location: 12hr",
        ylab = "Number of proteins")

The barplot tells us for this example that after thresholding with a 1% FDR on the posterior probability bandle has allocated many new proteins to subcellular classes in our training data but also many are still left with no allocation i.e. they are labelled as "unknown". As previously mentioned the class label "unknown" is a historic term from the pRoloc package to describe proteins that are left unassigned following thresholding and thus proteins which exhibit uncertainty in their allocations and thus potential proteins of mixed location.

The associated posterior estimates are located in the bandle.probabilitycolumn and we can construct a boxplot to examine these probabilities by class,

pe1 <- fData(res0hr_unknowns)$bandle.probability
pe2 <- fData(res12h_unknowns)$bandle.probability

par(mfrow = c(1, 2))
boxplot(pe1 ~ res1, las = 2, main = "Posterior: control",
        ylab = "Probability")
boxplot(pe2 ~ res2, las = 2, main = "Posterior: treatment",
        ylab = "Probability")

We see proteins in the "unknown" "unlabelled" category with a range of different probabilities. We still have several proteins in this category with a high probability, it is likely that proteins classed in this category also have a high outlier probability.

Proteins with uncertainty

We can use the unknownMSnSet function once again to extract proteins in the "unknown" category.

res0hr_mixed <- unknownMSnSet(res0hr_unknowns, fcol = "bandle.allocation.pred.pred")
res12hr_mixed <- unknownMSnSet(res12h_unknowns, fcol = "bandle.allocation.pred.pred")

We see we have r nrow(res0hr_mixed) and r nrow(res12hr_mixed) proteins for the 0hr and 12hr conditions respectively, which do not get assigned one main location. This is approximately 40% of the data.

nrow(res0hr_mixed)
nrow(res12hr_mixed)

Let's extract the names of these proteins,

fn1 <- featureNames(res0hr_mixed)
fn2 <- featureNames(res12hr_mixed)

Let's plot the the first 9 proteins that did not meet the thresholding criteria. We can use the mcmc_plot_probs function to generate a violin plot of the localisation distribution.

Let's first look at these proteins in the control condition,

g <- vector("list", 9)
for (i in 1:9) g[[i]] <- mcmc_plot_probs(params_converged, fn1[i], cond = 1)
do.call(grid.arrange, g)

Now the treated,

g <- vector("list", 9)
for (i in 1:9) g[[i]] <- mcmc_plot_probs(params_converged, fn1[i], cond = 2)
do.call(grid.arrange, g)

We can also get a summary of the full probability distribution by looking at the joint estimates stored in the bandle.joint slot of the MSnSet.

head(fData(res0hr_mixed)$bandle.joint)

Or visualise the joint posteriors on a heatmap

bjoint_0hr_mixed <- fData(res0hr_mixed)$bandle.joint
pheatmap(bjoint_0hr_mixed, cluster_cols = FALSE, color = viridis(n = 25), 
         show_rownames = FALSE, main = "Joint posteriors for unlabelled proteins at 0hr")

bjoint_12hr_mixed <- fData(res12hr_mixed)$bandle.joint
pheatmap(bjoint_12hr_mixed, cluster_cols = FALSE, color = viridis(n = 25),
         show_rownames = FALSE, main = "Joint posteriors for unlabelled proteins at 12hr")

Differential localisation

The differential localisation probability tells us which proteins are most likely to differentially localise, that exhibit a change in their steady-state subcellular location. Quantifying changes in protein subcellular location between experimental conditions is challenging and Crook et al [@bandle] have used a Bayesian approach to compute the probability that a protein differentially localises upon cellular perturbation, as well quantifying the uncertainty in these estimates. The differential localisation probability is found in the bandle.differential.localisation column of the MSnSet or can be extracted directly with the diffLocalisationProb function.

dl <- diffLocalisationProb(params_converged)
head(dl)

If we take a 5% FDR and examine how many proteins get a differential probability greater than 0.95 we find there are r length(which(dl[order(dl, decreasing = TRUE)] > 0.99)) proteins above this threshold.

length(which(dl[order(dl, decreasing = TRUE)] > 0.95))

On a rank plot we can see the distribution of differential probabilities.

plot(dl[order(dl, decreasing = TRUE)],
     col = getStockcol()[2], pch = 19, ylab = "Probability",
     xlab = "Rank", main = "Differential localisation rank plot")

This indicated that most proteins are not differentially localised and there are a few hundred confident differentially localised proteins of interest.

candidates <- names(dl)

Visualising differential localisation

There are several different ways we can visualise the output of bandle. Now we have our set of candidates we can subset MSnSet datasets and plot the the results.

To subset the data,

msnset_cands <- list(res_0h[[1]][candidates, ], 
                     res_12h[[1]][candidates, ])

We can visualise this as a data.frame too for ease,

# construct data.frame
df_cands <- data.frame(
    fData(msnset_cands[[1]])[, c("bandle.differential.localisation", 
                                 "bandle.allocation.pred.pred")],
    fData(msnset_cands[[2]])[, "bandle.allocation.pred.pred"])

colnames(df_cands) <- c("differential.localisation", 
                        "0hr_location", "12h_location")

# order by highest differential localisation estimate
df_cands <- df_cands %>% arrange(desc(differential.localisation))
head(df_cands)

Alluvial plots

We can now plot this on an alluvial plot to view the changes in subcellular location. The class label is taken from the column called "bandle.allocation.pred.pred" which was deduced above by thresholding on the posterior and outlier probabilities before assigning BANDLE's allocation prediction.

## set colours for organelles and unknown
cols <- c(getStockcol()[seq(mrkCl)], "grey")
names(cols) <- c(mrkCl, "unknown")

## plot
alluvial <- plotTranslocations(msnset_cands, 
                               fcol = "bandle.allocation.pred.pred", 
                               col = cols)
alluvial + ggtitle("Differential localisations following 12h-LPS stimulation")

To view a table of the translocations, we can call the function plotTable,

(tbl <- plotTable(msnset_cands, fcol = "bandle.allocation.pred.pred"))

Although this example analysis is limited compared to that of @thplopit, we do see similar trends inline with the results seen in the paper. For examples, we see a large number of proteins translocating between organelles that are involved in the secretory pathway. We can further examine these cases by subsetting the datasets once again and only plotting proteins that involve localisation with these organelles. Several organelles are known to be involved in this pathway, the main ones, the ER, Golgi (and plasma membrane).

Let's subset for these proteins,

secretory_prots <- unlist(lapply(msnset_cands, function(z) 
    c(which(fData(z)$bandle.allocation.pred.pred == "Golgi Apparatus"),
      which(fData(z)$bandle.allocation.pred.pred == "Endoplasmic Reticulum"),
      which(fData(z)$bandle.allocation.pred.pred == "Plasma Membrane"),
      which(fData(z)$bandle.allocation.pred.pred == "Lysosome"))))
secretory_prots <- unique(secretory_prots)

msnset_secret <- list(msnset_cands[[1]][secretory_prots, ],
                      msnset_cands[[2]][secretory_prots, ])

secretory_alluvial <- plotTranslocations(msnset_secret, 
                                         fcol = "bandle.allocation.pred.pred", 
                                         col = cols)
secretory_alluvial + ggtitle("Movements of secretory proteins")

Protein profiles

In the next section we see how to plot proteins of interest. Our differential localisation candidates can be found in df_cands,

head(df_cands)

We can probe this data.frame by examining proteins with high differential localisation probabilites. For example, protein with accession B2RUZ4. It has a high differential localisation score and it's steady state localisation in the control is predicted to be lysosomal and in the treatment condition at 12 hours-LPS it is predicted to localise to the plasma membrane. This fits with the information we see on Uniprot which tells us it is Small integral membrane protein 1 (SMIM1).

In the below code chunk we plot the protein profiles of all proteins that were identified as lysosomal from BANDLE in the control and then overlay SMIM1. We do the same at 12hrs post LPS with all plasma membrane proteins.

par(mfrow = c(2, 1))

## plot lysosomal profiles
lyso <- which(fData(res_0h[[1]])$bandle.allocation.pred.pred == "Lysosome")
plotDist(res_0h[[1]][lyso], pcol = cols["Lysosome"], alpha = 0.04)
matlines(exprs(res_0h[[1]])["B2RUZ4", ], col = cols["Lysosome"], lwd = 3)
title("Protein SMIM1 (B2RUZ4) at 0hr (control)")

## plot plasma membrane profiles
pm <- which(fData(res_12h[[1]])$bandle.allocation.pred.pred == "Plasma Membrane")
plotDist(res_12h[[1]][pm], pcol = cols["Plasma Membrane"], alpha = 0.04)
matlines(exprs(res_12h[[1]])["B2RUZ4", ], col = cols["Plasma Membrane"], lwd = 3)
title("Protein SMIM1 (B2RUZ4) at 12hr-LPS (treatment)")

We can also visualise there on a PCA or t-SNE plot.

par(mfrow = c(1, 2))
plot2D(res_0h[[1]], fcol = "bandle.allocation.pred.pred",
       main = "Unstimulated - replicate 1 \n predicted location")
highlightOnPlot(res_0h[[1]], foi = "B2RUZ4")

plot2D(res_12h[[1]], fcol = "bandle.allocation.pred.pred",
       main = "12h-LPS - replicate 1 \n predicted location")
highlightOnPlot(res_12h[[1]], foi = "B2RUZ4")

Session information

All software and respective versions used to produce this document are listed below.

sessionInfo()

References {-}

ococrook/bandle documentation built on Jan. 15, 2025, 5:27 a.m.