1 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.

2 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 MSnbase package. Please see the relevant vignettes in MSnbase for constructing these data containers.

The data used in this vignette has been published in Mulvey et al. (2021) and is currently stored as MSnSet instances in the the pRolocdata package. We will load it in the next section.

2.1 Spatialtemporal proteomic profiling of a THP-1 cell line

In this workflow we analyse the data produced by Mulvey et al. (2021). In this experiment triplicate hyperLOPIT experiments (Mulvey et al. 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
## MSnSet (storageMode: lockedEnvironment)
## assayData: 5107 features, 20 samples 
##   element names: exprs 
## protocolData: none
## phenoData
##   sampleNames: unstim_rep1_set1_126_cyto unstim_rep1_set1_127N_F1.4 ...
##     unstim_rep1_set2_131_F24 (20 total)
##   varLabels: Tag Treatment ... Fraction (5 total)
##   varMetadata: labelDescription
## featureData
##   featureNames: A0AVT1 A0FGR8-2 ... Q9Y6Y8 (5107 total)
##   fvarLabels: Checked_unst.r1.s1 Confidence_unst.r1.s1 ... markers (107
##     total)
##   fvarMetadata: labelDescription
## experimentData: use 'experimentData(object)'
## Annotation:  
## - - - Processing information - - -
## Loaded on Tue Jan 12 14:46:48 2021. 
## Normalised to sum of intensities. 
##  MSnbase version: 2.14.2
thpLOPIT_lps_rep1_mulvey2021
## MSnSet (storageMode: lockedEnvironment)
## assayData: 4879 features, 20 samples 
##   element names: exprs 
## protocolData: none
## phenoData
##   sampleNames: lps_rep1_set1_126_cyto lps_rep1_set1_127N_F1.4 ...
##     lps_rep1_set2_131_F25 (20 total)
##   varLabels: Tag Treatment ... Fraction (5 total)
##   varMetadata: labelDescription
## featureData
##   featureNames: A0A0B4J2F0 A0AVT1 ... Q9Y6Y8 (4879 total)
##   fvarLabels: Checked_lps.r1.s1 Confidence_lps.r1.s1 ... markers (107
##     total)
##   fvarMetadata: labelDescription
## experimentData: use 'experimentData(object)'
## Annotation:  
## - - - Processing information - - -
## Loaded on Tue Jan 12 14:46:57 2021. 
## Normalised to sum of intensities. 
##  MSnbase version: 2.14.2

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.

2.2 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")

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)
## [1] 5107   20
dim(thpLOPIT_unstimulated_rep3_mulvey2021)
## [1] 5733   20
dim(thpLOPIT_lps_rep1_mulvey2021)
## [1] 4879   20
dim(thpLOPIT_lps_rep3_mulvey2021)
## [1] 5848   20

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
## 3727 features in common

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

thplopit
## Instance of class 'MSnSetList' containig 4 objects.

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 1st rep", "Unstimulated 2nd rep",
             "12h-LPS 1st rep", "12h-LPS 2nd rep")

## 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.

3 Preparing bandle: fitting GPs and setting the priors

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.

3.1 Fitting Gaussian processes

First, we need to fit non-parametric regression functions to the markers profiles. We use the fitGPmaternPC function using the default penalised complexity priors (see ?fitGP), which work well.

gpParams <- lapply(thplopit, function(x) fitGPmaternPC(x))

We apply the fitGPmaternPC function on to each dataset by using lapply over the thplopit list of data. The posterior predictive means, standard deviations and MAP hyperparamters for the GP are returned. If desired we can visualise the predictives overlaid onto the marker profiles of the data by using the plotGPmatern function.

The prior needs to form a K*3 matrix (where K is the number of subcellular classes in the data),

(mrkCl <- getMarkerClasses(thplopit[[1]], fcol = "markers"))
##  [1] "40S/60S Ribosome"      "Chromatin"             "Cytosol"              
##  [4] "Endoplasmic Reticulum" "Golgi Apparatus"       "Lysosome"             
##  [7] "Mitochondria"          "Nucleolus"             "Nucleus"              
## [10] "Peroxisome"            "Plasma Membrane"

So for this data we require a 11*3 matrix. Three columns are needed which represent the hyperparameters length-scale, amplitude, variance. We have found that the matrix(c(10, 60, 250), nrow = 1) worked well for the smaller datasets with a few hundred proteins, as tested in Crook et al. (2021). Here, we found that matrix(c(1, 60, 100) worked well. This is a bigger dataset with several thousand proteins and many more subcellular classes. This was visually assessed by passing these values and visualising the GP fit using the plotGPmatern function. 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 recommended parameters and change and assess them as necessary for their dataset by visually evaluating the fit of the GPs using the plotGPmatern function.

K <- length(mrkCl)
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)
##      [,1] [,2] [,3]
## [1,]    1   60  100
## [2,]    1   60  100
## [3,]    1   60  100
## [4,]    1   60  100
## [5,]    1   60  100
## [6,]    1   60  100

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.

3.2 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
## [1] 0.421633

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

predDirPrior$tailnotAlloc
## [1] 0.0016
hist(predDirPrior$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$meannotAlloc
## [1] 0.2308647
predDirPrior$tailnotAlloc
## [1] 6e-04
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.

3.3 The bandle function

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 to minimise the vignette build-time. Typically we’d recommend you run the number of iterations (numIter) in the \(1000\)s.

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]])

bandleres <- bandle(objectCond1 = control,
                    objectCond2 = treatment,
                    numIter = 50,       # usually 10,000
                    burnin = 5L,        # usually 5,000
                    thin = 1L,          # usually 20
                    gpParams = gpParams,
                    pcPrior = pc_prior,
                    numChains = 1,     # usually >=4
                    dirPrior = dirPrior,
                    seed = 1)

A bandleParams object is produced

bandleres
## Object of class "bandleParams"
## Method: bandle 
## Number of chains: 1

4 Processing and analysing the bandle results

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

bandleres <- bandleProcess(bandleres)

These slots have now been populated

summary(summaries(bandleres))
##      Length Class         Mode
## [1,] 1      bandleSummary S4  
## [2,] 1      bandleSummary S4

The posteriorEstimates slot gives posterior quantities of interest for different proteins. The object is of length 2, - 1 slot for control - 1 slot for treatment

length(summaries(bandleres))
## [1] 2

We explicitly extract the posterior estimates and protein allocation predictions as follows

pe1 <- posteriorEstimates(summaries(bandleres)[[1]])
pe2 <- posteriorEstimates(summaries(bandleres)[[2]])

head(pe1)
## DataFrame with 6 rows and 7 columns
##              bandle.allocation bandle.probability bandle.outlier
##                    <character>          <numeric>      <numeric>
## A0AVT1                 Cytosol           1.000000              0
## A0FGR8-2       Golgi Apparatus           0.701717              0
## A0JNW5                 Nucleus           1.000000              1
## A0MZ66-3               Cytosol           1.000000              0
## A0PJW6              Peroxisome           1.000000              0
## A1L0T0   Endoplasmic Reticulum           0.999968              0
##          bandle.probability.lowerquantile bandle.probability.upperquantile
##                                 <numeric>                        <numeric>
## A0AVT1                           1.000000                         1.000000
## A0FGR8-2                         0.388022                         0.962611
## A0JNW5                           1.000000                         1.000000
## A0MZ66-3                         1.000000                         1.000000
## A0PJW6                           0.999999                         1.000000
## A1L0T0                           0.999706                         1.000000
##          bandle.mean.shannon bandle.differential.localisation
##                    <numeric>                        <numeric>
## A0AVT1           0.00000e+00                         0.000000
## A0FGR8-2         0.00000e+00                         0.755556
## A0JNW5           5.60223e-11                         0.000000
## A0MZ66-3         0.00000e+00                         0.000000
## A0PJW6           0.00000e+00                         0.977778
## A1L0T0           0.00000e+00                         0.000000

The full joint probability distribution can be found in the bandle.joint slot e.g. for the control in slot 1 this would be bandleJoint(summaries(bandleres)[[1]]) and the treatment in slot 2 this would be bandleJoint(summaries(bandleres)[[2]]).

Let’s look at the posterior estimates and allocation predictions found in pe1 and pe2. Each object is a data.frame containing the protein allocations and associated localisation probabilities for each condition. The 7 columns are

  • 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.

We plot the distribution of protein allocations by bandle

par(mfrow = c(1, 2), oma = c(6, 2, 2, 2))
barplot(table(pe1$bandle.allocation), col = getStockcol()[2],
        las = 2, main = "Control: Protein allocation",
        ylab = "Number of proteins")
barplot(table(pe2$bandle.allocation), col = getStockcol()[2],
        las = 2, main = "Treatment: Protein allocation")

The bar plot above tells us for this data bandle has allocated the majority of unlabelled proteins to the nucleus. The allocation result for each condition (found in bandle.allocation) is determined by bandle by looking at which subcellular niche was given the highest probability from the full distribution e.g. from bandle.joint. If we plot the bandle.probability (corresponding to the mean of the distribution) against the protein allocation results we can see that not all protein allocations are confident, this is why it is important to threshold when deducing a protein’s location.

par(mfrow = c(1, 2), oma = c(6, 2, 2, 2))
boxplot(pe1$bandle.probability ~ pe1$ bandle.allocation, 
        col = getStockcol()[2], xlab = "",
        ylab = "BANDLE probability (mean)",
        las = 2, main = "Control: Probability distribution\n by allocation class")
boxplot(pe2$bandle.probability ~ pe1$ bandle.allocation, 
        col = getStockcol()[2], xlab = "", ylab = "",
        las = 2, main = "Treatment: Probability distribution\n by allocation class")

4.1 Predicting subcellular location

As mentioned in Vignette 1, it is 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 use the bandlePredict function to append our results to the original MSnSet datasets.

## Add the bandle results to a MSnSet
xx <- bandlePredict(control, 
                    treatment, 
                    params = bandleres, 
                    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 with the output of bandle e.g. bandle.probability, bandle.allocation, bandle.outlier etc. (as described above) 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. 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]])

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)
## ans
##      40S/60S Ribosome             Chromatin               Cytosol 
##                   255                   208                   505 
## Endoplasmic Reticulum       Golgi Apparatus              Lysosome 
##                   164                   129                   300 
##          Mitochondria             Nucleolus               Nucleus 
##                   386                   113                   671 
##            Peroxisome       Plasma Membrane               unknown 
##                   157                   244                   595
res_12h[[1]] <- getPredictions(res_12h[[1]], 
                               fcol = "bandle.allocation",
                               scol = "bandle.probability", 
                               mcol = "markers",      
                               t = .99)
## ans
##      40S/60S Ribosome             Chromatin               Cytosol 
##                   161                   222                   458 
## Endoplasmic Reticulum       Golgi Apparatus              Lysosome 
##                   276                   303                   201 
##          Mitochondria             Nucleolus               Nucleus 
##                   356                   122                   750 
##            Peroxisome       Plasma Membrane               unknown 
##                   203                   362                   313

A table of predictions is printed 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)
## ans
##      40S/60S Ribosome             Chromatin               Cytosol 
##                    90                   143                   323 
## Endoplasmic Reticulum       Golgi Apparatus              Lysosome 
##                   161                    63                   225 
##          Mitochondria             Nucleolus               Nucleus 
##                   347                    66                   100 
##            Peroxisome       Plasma Membrane               unknown 
##                   130                   222                  1857
res_12h[[1]] <- getPredictions(res_12h[[1]], 
                               fcol = "bandle.allocation.pred",
                               scol = "bandle.outlier.t", 
                               mcol = "markers",      
                               t = .99)
## ans
##      40S/60S Ribosome             Chromatin               Cytosol 
##                   115                   173                   287 
## Endoplasmic Reticulum       Golgi Apparatus              Lysosome 
##                   251                   222                   163 
##          Mitochondria             Nucleolus               Nucleus 
##                   348                    99                   134 
##            Peroxisome       Plasma Membrane               unknown 
##                   179                   308                  1448

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)

4.2 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 (Crook et al. 2021) 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 bandleParams output.

diffloc_probs <- pe1$bandle.differential.localisation

If we take a 5% FDR and examine how many proteins get a differential probability greater than 0.95 we find there are 638 proteins above this threshold.

length(which(diffloc_probs[order(diffloc_probs, decreasing = TRUE)] > 0.95))
## [1] 694

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

plot(diffloc_probs[order(diffloc_probs, 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.

4.3 Estimating uncertainty

One advantage of using Bayesian methods over classic machine learning is the ability to quantify the uncertainty in our estimates. There are many ways to do this, as discussed in “Vignette 1: Getting Started with BANDLE”. In the below code chunk we use the binomialDiffLocProb function to obtain credible intervals from the binomial distribution and then extract a probability estimate for the differential localisation.

Please note, that in interest of time and for the purpose of demonstration we set nsample = 500 and thus only return 500 samples of the binomial distribution. In practice the minimum recommended number of samples is 5000.

set.seed(1)
bin_t <- binomialDiffLocProb(params = bandleres, top = 500,
                             nsample = 500, decreasing = TRUE)

As we have a large number of proteins as candidates we have chosen to threshold on the interval to reduce the number of differential localisations.

qt <- apply(bin_t, 1, function(x) quantile(x, .025))

This leaves us with 147 proteins to investigate.

candidates <- names(which(qt > 0.95))
head(candidates)
## [1] "A1L170-2" "B2RUZ4"   "O15439"   "O43181"   "O43427"   "O43633"

4.3.1 Add the results to the MSnSet

Let’s add the results to each replicate in the MSnSets. The reason for doing this is so that later on when we wish to visulalise the data we have the information readily accessible to make use of the functions in the pRoloc package.

Let’s double check all datasets have the same proteins,

all(featureNames(res_0h[[1]]) == featureNames(res_0h[[2]]))
## [1] TRUE
all(featureNames(res_0h[[1]]) == featureNames(res_12h[[1]]))
## [1] TRUE
all(featureNames(res_12h[[1]]) == featureNames(res_12h[[2]]))
## [1] TRUE

Now let’s add the differential location estimates,

dl.estimate <- qt[candidates]
fn <- featureNames(control[[1]])
cmn <- fn %in% names(dl.estimate)


## Add results to the 0h time-point (control)
for (i in seq(res_0h)) {
    ## create column called "dl.estimate" in the data
    mcol <- "dl.estimate"
    fData(res_0h[[i]])[, mcol] <- NA
    fData(res_0h[[i]])[cmn, mcol] <- dl.estimate
    ## create column called "dl.candidate" in the data
    mcol <- "dl.candidate"
    fData(res_0h[[i]])[, mcol] <- "unknown"
    fData(res_0h[[i]])[cmn, mcol] <- "DL candidate"
}


## Add results to the 12h time-point (treatment)
for (i in seq(res_12h)) {
    ## create column called "dl.estimate" in the data
    mcol <- "dl.estimate"
    fData(res_12h[[i]])[, mcol] <- NA
    fData(res_12h[[i]])[cmn, mcol] <- dl.estimate
    ## create column called "dl.candidate" in the data
    mcol <- "dl.candidate"
    fData(res_12h[[i]])[, mcol] <- "unknown"
    fData(res_12h[[i]])[cmn, mcol] <- "DL candidate"
}

In the next section we can visualise these results.

5 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", 
                                 "dl.estimate",
                                 "bandle.allocation.pred.pred")],
    fData(msnset_cands[[2]])[, "bandle.allocation.pred.pred"])

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

# order by highest differential localisation estimate
df_cands <- df_cands %>% arrange(desc(bandle.differential.localisation))
head(df_cands)
##          bandle.differential.localisation dl.estimate 0hr_location
## A1L170-2                                1   0.9506301      unknown
## B2RUZ4                                  1   0.9525446     Lysosome
## O15439                                  1   0.9559090      unknown
## O43181                                  1   0.9505633      unknown
## O43427                                  1   0.9528166      unknown
## O43633                                  1   0.9530232      unknown
##             12h_location
## A1L170-2         unknown
## B2RUZ4   Plasma Membrane
## O15439   Plasma Membrane
## O43181        Peroxisome
## O43427           unknown
## O43633           unknown

5.1 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)
## 147 features in common
## ------------------------------------------------
## If length(fcol) == 1 it is assumed that the
## same fcol is to be used for both datasets
## setting fcol = c(bandle.allocation.pred.pred,bandle.allocation.pred.pred)
## ----------------------------------------------
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"))
## 147 features in common
## ------------------------------------------------
## If length(fcol) == 1 it is assumed that the
## same fcol is to be used for both datasets
## setting fcol = c(bandle.allocation.pred.pred, bandle.allocation.pred.pred)
## ----------------------------------------------
##                Condition1            Condition2 value
## 6               Chromatin             Nucleolus     1
## 19                Cytosol               unknown     1
## 23  Endoplasmic Reticulum       Golgi Apparatus     2
## 29  Endoplasmic Reticulum               unknown     2
## 39        Golgi Apparatus               unknown     1
## 44               Lysosome       Golgi Apparatus     4
## 48               Lysosome       Plasma Membrane    15
## 49               Lysosome               unknown     4
## 57           Mitochondria            Peroxisome     5
## 59           Mitochondria               unknown     2
## 69              Nucleolus               unknown     1
## 73             Peroxisome Endoplasmic Reticulum     1
## 76             Peroxisome          Mitochondria     5
## 79             Peroxisome               unknown     1
## 85        Plasma Membrane              Lysosome     1
## 89        Plasma Membrane               unknown     4
## 91                unknown             Chromatin     5
## 93                unknown Endoplasmic Reticulum     6
## 94                unknown       Golgi Apparatus     3
## 95                unknown              Lysosome     3
## 96                unknown          Mitochondria     3
## 97                unknown             Nucleolus     1
## 98                unknown            Peroxisome     6
## 99                unknown       Plasma Membrane     4
## 100               unknown               Nucleus     1

Although this example analysis is limited compared to that of Mulvey et al. (2021), 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)
## 50 features in common
## ------------------------------------------------
## If length(fcol) == 1 it is assumed that the
## same fcol is to be used for both datasets
## setting fcol = c(bandle.allocation.pred.pred,bandle.allocation.pred.pred)
## ----------------------------------------------
secretory_alluvial + ggtitle("Movements of secretory proteins")

5.2 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)
##          bandle.differential.localisation dl.estimate 0hr_location
## A1L170-2                                1   0.9506301      unknown
## B2RUZ4                                  1   0.9525446     Lysosome
## O15439                                  1   0.9559090      unknown
## O43181                                  1   0.9505633      unknown
## O43427                                  1   0.9528166      unknown
## O43633                                  1   0.9530232      unknown
##             12h_location
## A1L170-2         unknown
## B2RUZ4   Plasma Membrane
## O15439   Plasma Membrane
## O43181        Peroxisome
## O43427           unknown
## O43633           unknown

Let’s take the first protein as an 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")

6 Session information

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

sessionInfo()
## R version 4.3.1 (2023-06-16)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 22.04.3 LTS
## 
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.18-bioc/R/lib/libRblas.so 
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.10.0
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_GB              LC_COLLATE=C              
##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## time zone: America/New_York
## tzcode source: system (glibc)
## 
## attached base packages:
## [1] stats4    stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] ggplot2_3.4.4        dplyr_1.1.3          pRolocdata_1.39.0   
##  [4] viridis_0.6.4        viridisLite_0.4.2    pheatmap_1.0.12     
##  [7] bandle_1.6.0         pRoloc_1.42.0        BiocParallel_1.36.0 
## [10] MLInterfaces_1.82.0  cluster_2.1.4        annotate_1.80.0     
## [13] XML_3.99-0.14        AnnotationDbi_1.64.0 IRanges_2.36.0      
## [16] MSnbase_2.28.0       ProtGenerics_1.34.0  mzR_2.36.0          
## [19] Rcpp_1.0.11          Biobase_2.62.0       S4Vectors_0.40.0    
## [22] BiocGenerics_0.48.0  BiocStyle_2.30.0    
## 
## loaded via a namespace (and not attached):
##   [1] splines_4.3.1               bitops_1.0-7               
##   [3] filelock_1.0.2              tibble_3.2.1               
##   [5] hardhat_1.3.0               preprocessCore_1.64.0      
##   [7] pROC_1.18.4                 rpart_4.1.21               
##   [9] lifecycle_1.0.3             doParallel_1.0.17          
##  [11] globals_0.16.2              lattice_0.22-5             
##  [13] MASS_7.3-60                 dendextend_1.17.1          
##  [15] magrittr_2.0.3              limma_3.58.0               
##  [17] plotly_4.10.3               sass_0.4.7                 
##  [19] rmarkdown_2.25              jquerylib_0.1.4            
##  [21] yaml_2.3.7                  MsCoreUtils_1.14.0         
##  [23] DBI_1.1.3                   RColorBrewer_1.1-3         
##  [25] lubridate_1.9.3             abind_1.4-5                
##  [27] zlibbioc_1.48.0             GenomicRanges_1.54.0       
##  [29] purrr_1.0.2                 mixtools_2.0.0             
##  [31] RCurl_1.98-1.12             nnet_7.3-19                
##  [33] rappdirs_0.3.3              ipred_0.9-14               
##  [35] circlize_0.4.15             lava_1.7.2.1               
##  [37] GenomeInfoDbData_1.2.11     ggrepel_0.9.4              
##  [39] listenv_0.9.0               gdata_3.0.0                
##  [41] parallelly_1.36.0           ncdf4_1.21                 
##  [43] codetools_0.2-19            DelayedArray_0.28.0        
##  [45] xml2_1.3.5                  shape_1.4.6                
##  [47] tidyselect_1.2.0            farver_2.1.1               
##  [49] matrixStats_1.0.0           BiocFileCache_2.10.0       
##  [51] jsonlite_1.8.7              caret_6.0-94               
##  [53] e1071_1.7-13                ggalluvial_0.12.5          
##  [55] survival_3.5-7              iterators_1.0.14           
##  [57] foreach_1.5.2               segmented_1.6-4            
##  [59] tools_4.3.1                 progress_1.2.2             
##  [61] lbfgs_1.2.1.2               glue_1.6.2                 
##  [63] prodlim_2023.08.28          gridExtra_2.3              
##  [65] SparseArray_1.2.0           xfun_0.40                  
##  [67] MatrixGenerics_1.14.0       GenomeInfoDb_1.38.0        
##  [69] withr_2.5.1                 BiocManager_1.30.22        
##  [71] fastmap_1.1.1               fansi_1.0.5                
##  [73] digest_0.6.33               timechange_0.2.0           
##  [75] R6_2.5.1                    colorspace_2.1-0           
##  [77] gtools_3.9.4                lpSolve_5.6.19             
##  [79] biomaRt_2.58.0              RSQLite_2.3.1              
##  [81] utf8_1.2.4                  tidyr_1.3.0                
##  [83] generics_0.1.3              hexbin_1.28.3              
##  [85] data.table_1.14.8           recipes_1.0.8              
##  [87] FNN_1.1.3.2                 class_7.3-22               
##  [89] prettyunits_1.2.0           httr_1.4.7                 
##  [91] htmlwidgets_1.6.2           S4Arrays_1.2.0             
##  [93] ModelMetrics_1.2.2.2        pkgconfig_2.0.3            
##  [95] gtable_0.3.4                timeDate_4022.108          
##  [97] blob_1.2.4                  impute_1.76.0              
##  [99] XVector_0.42.0              htmltools_0.5.6.1          
## [101] bookdown_0.36               MALDIquant_1.22.1          
## [103] clue_0.3-65                 scales_1.2.1               
## [105] png_0.1-8                   gower_1.0.1                
## [107] knitr_1.44                  reshape2_1.4.4             
## [109] coda_0.19-4                 nlme_3.1-163               
## [111] curl_5.1.0                  GlobalOptions_0.1.2        
## [113] proxy_0.4-27                cachem_1.0.8               
## [115] stringr_1.5.0               parallel_4.3.1             
## [117] mzID_1.40.0                 vsn_3.70.0                 
## [119] pillar_1.9.0                grid_4.3.1                 
## [121] vctrs_0.6.4                 pcaMethods_1.94.0          
## [123] randomForest_4.7-1.1        dbplyr_2.3.4               
## [125] xtable_1.8-4                evaluate_0.22              
## [127] magick_2.8.1                mvtnorm_1.2-3              
## [129] cli_3.6.1                   compiler_4.3.1             
## [131] rlang_1.1.1                 crayon_1.5.2               
## [133] future.apply_1.11.0         LaplacesDemon_16.1.6       
## [135] mclust_6.0.0                affy_1.80.0                
## [137] plyr_1.8.9                  stringi_1.7.12             
## [139] munsell_0.5.0               Biostrings_2.70.0          
## [141] lazyeval_0.2.2              Matrix_1.6-1.1             
## [143] hms_1.1.3                   bit64_4.0.5                
## [145] future_1.33.0               KEGGREST_1.42.0            
## [147] statmod_1.5.0               SummarizedExperiment_1.32.0
## [149] kernlab_0.9-32              memoise_2.0.1              
## [151] affyio_1.72.0               bslib_0.5.1                
## [153] sampling_2.9                bit_4.0.5

References

Crook, Oliver M, Colin TR Davies, Laurent Gatto, Paul DW Kirk, and Kathryn S Lilley. 2021. “Inferring Differential Subcellular Localisation in Comparative Spatial Proteomics Using Bandle.” bioRxiv. doi: https://doi.org/10.1101/2021.01.04.425239.

Mulvey, Claire M., Lisa M. Breckels, Oliver M. Crook, David J. Sanders, Andre L. R. Ribeiro, Aikaterini Geladaki, Andy Christoforou, et al. 2021. “Spatiotemporal Proteomic Profiling of the Pro-Inflammatory Response to Lipopolysaccharide in the THP-1 Human Leukaemia Cell Line.” Nature Communications 12 (1). https://doi.org/10.1038/s41467-021-26000-9.

Mulvey, Claire M, Lisa M Breckels, Aikaterini Geladaki, Nina Kočevar Britovšek, Daniel J H Nightingale, Andy Christoforou, Mohamed Elzek, Michael J Deery, Laurent Gatto, and Kathryn S Lilley. 2017. “Using hyperLOPIT to Perform High-Resolution Mapping of the Spatial Proteome.” Nature Protocols 12 (6): 1110–35. https://doi.org/10.1038/nprot.2017.026.