pRoloc 1.30.0
Our main data source to study protein sub-cellular localisation are high-throughput mass spectrometry-based experiments such as LOPIT, PCP and similar designs (see (Gatto et al. 2010) for an general introduction). Recent optimised experiments result in high quality data enabling the identification of over 6000 proteins and discriminate numerous sub-cellular and sub-organellar niches (Christoforou et al. 2016). Supervised and semi-supervised machine learning algorithms can be applied to assign thousands of proteins to annotated sub-cellular niches (Breckels et al. 2013,Gatto:2014) (see also the pRoloc-tutorial vignette). These data constitute our main source for protein localisation and are termed thereafter primary data.
There are other sources of data about sub-cellular localisation of proteins, such as the Gene Ontology (Ashburner et al. 2000) (in particular the cellular compartment name space), quantitative features derived from protein sequences (such as pseudo amino acid composition) or the Human Protein Atlas (Uhlen et al. 2010) to cite a few. These data, while not optimised to a specific system at hand and, in the case of annotation feature, not as reliable as our experimental data, constitute an invaluable, often plentiful source of auxiliary information.
The aim of a transfer learning algorithm is to combine different sources of data to improve overall classification. In particular, the goal is to support/complement the primary target domain (experimental data) with auxiliary data (annotation) features without compromising the integrity of our primary data. In this vignette, we describe the application of transfer learning algorithms for the localisation of proteins from the pRoloc package, as described in
Breckels LM, Holden S, Wonjar D, Mulvey CM, Christoforou A, Groen A, Trotter MW, Kohlbacker O, Lilley KS and Gatto L (2016). Learning from heterogeneous data sources: an application in spatial proteomics. PLoS Comput Biol 13;12(5):e1004920. doi: 10.1371/journal.pcbi.1004920.
Two algorithms were developed: a transfer learning algorithm based on the \(k\)-nearest neighbour classifier, coined kNN-TL hereafter, described in section 4, and one based on the support vector machine algorithm, termed SVM-TL, described in section 3.
library("pRoloc")
The auxiliary data is prepared from the primary data’s features. All the GO terms associated to these features are retrieved and used to create a binary matrix where a one (zero) at position \((i,j)\) indicates that term \(j\) has (not) been used to annotate feature \(i\).
The GO terms are retrieved from an appropriate repository using the biomaRt package. The specific Biomart repository and query will depend on the species under study and the type of features. The first step is to prepare annotation parameters that will enable to perform the query. The pRoloc package provides a dedicated infrastructure to set up the query to the annotation resource and prepare the GO data for subsequent analyses. This infrastructure is composed of:
We will demonstrate these steps using a LOPIT experiment on Human
Embryonic Kidney (HEK293T) fibroblast cells (Breckels et al. 2013),
available and documented in the pRolocdata experiment
package as andy2011
.
library("pRolocdata")
data(andy2011)
The query parameters are stored as AnnotationParams objects that are created with the setAnnotationParams function. The function will present a first menu with 373. Once the species has been selected, a set of possible identifier types is displayed.
It is also possible to pass patterns to match against the
species ("Human genes"
) and feature type ("UniProtKB/Swiss-prot ID"
).
ap <- setAnnotationParams(inputs =
c("Human genes",
"UniProtKB/Swiss-Prot ID"))
## Using species Human genes (GRCh38.p12)
## Ensembl site unresponsive, trying uswest mirror
## Using feature type UniProtKB/Swiss-Prot ID(s) [e.g. A0A024RBG1]
## Connecting to Biomart...
ap
## Object of class "AnnotationParams"
## Using the 'ENSEMBL_MART_ENSEMBL' BioMart database
## Using the 'hsapiens_gene_ensembl' dataset
## Using 'uniprotswissprot' as filter
## Created on Tue Oct 27 22:37:28 2020
The setAnnotationParams function automatically sets the annotation
parameters globally so that the ap
object does not need to be
explicitly set later on. The default parameters can be retrieved with
getAnnotationParams.
The feature names of the andy2011
data are UniProt identifiers, as
defined in the ap
accession parameters.
data(andy2011)
head(featureNames(andy2011))
## [1] "O00767" "P51648" "Q2TAA5" "Q9UKV5" "Q12797" "P16615"
The makeGoSet function takes an MSnSet class (from which the
feature names will be extracted) or, directly a vector of characters
containing the feature names of interest to retrieve the associated GO
terms and construct an auxiliary MSnSet
. By default, it downloads
cellular component terms and does not do any filtering on the terms
evidence codes (see the makeGoSet manual for details). Unless passed
as argument, the default, globally set AnnotationParams are used to
define the Biomart server and the query.
andygoset <- makeGoSet(andy2011)
andygoset
## MSnSet (storageMode: lockedEnvironment)
## assayData: 1371 features, 889 samples
## element names: exprs
## protocolData: none
## phenoData: none
## featureData
## featureNames: O00767 P51648 ... O75312 (1371 total)
## fvarLabels: Accession.No. Protein.Description ...
## UniProtKB.entry.name (10 total)
## fvarMetadata: labelDescription
## experimentData: use 'experimentData(object)'
## Annotation:
## - - - Processing information - - -
## Constructed GO set using cellular_component namespace [Tue Oct 27 22:37:34 2020]
## MSnbase version: 2.16.0
exprs(andygoset)[1:7, 1:4]
## GO:0016020 GO:0016021 GO:0005783 GO:0005789
## O00767 1 1 1 1
## P51648 1 1 1 1
## Q2TAA5 1 1 1 1
## Q9UKV5 1 1 1 1
## Q12797 1 1 1 1
## P16615 1 1 1 1
## Q96SQ9 1 0 1 1
We now have a primary data set, composed of 1371 protein quantitative profiles for 8 fractions along the density gradient and an auxiliary data set for 889 cellular compartment GO terms for the same 1371 features.
The generation of the auxiliary data relies on specific Biomart server Mart instances in the AnnotationParams class and the actual query to the server to obtain the GO terms associated with the features. The utilisation of online servers, which undergo regular updates, does not guarantee reproducibility of feature/term association over time. It is recommended to save and store the AnnotationParams and auxiliary MSnSet instances. Alternatively, it is possible to use other Bioconductor infrastructure, such as specific organism annotations and the GO.db package to use specific versioned (and thus traceable) annotations.
The feature names of our LOPIT experiment are UniProt identifiers,
while the Human Protein Atlas uses Ensembl gene identifiers. This
first code chunk matches both identifier types using the Ensembl
Biomart server and left_join
from the dplyr
package. In this section, we copy the experimental data to andyhpa
.
andyhpa <- andy2011
fvarLabels(andyhpa)[1] <- "accession" ## for left_join matching
## convert protein accession numbers to ensembl gene identifiers
library("biomaRt")
mart <- useMart("ensembl", dataset = "hsapiens_gene_ensembl")
filter <- "uniprotswissprot"
attrib <- c("uniprot_gn_symbol", "uniprotswissprot", "ensembl_gene_id")
bm <- getBM(attributes = attrib,
filters = filter,
values = fData(andyhpa)[, "accession"],
mart = mart)
head(bm)
## uniprot_gn_symbol uniprotswissprot ensembl_gene_id
## 1 ESYT2 A0FGR8 ENSG00000117868
## 2 ILVBL A1L0T0 ENSG00000105135
## 3 NBAS A2RRP1 ENSG00000151779
## 4 MTMR11 A4FU01 ENSG00000014914
## 5 C2orf72 A6NCS6 ENSG00000204128
## 6 RTL1 A6NKG5 ENSG00000254656
## HPA data
library("hpar")
## This is hpar version 1.32.0,
## based on the Human Protein Atlas
## Version: 18.1
## Release data: 2018.11.15
## Ensembl build: 88.38
## See '?hpar' or 'vignette('hpar')' for details.
## using old version for traceability
setHparOptions(hpadata = "hpaSubcellularLoc14")
hpa <- getHpa(bm$ensembl_gene_id)
hpa$Reliability <- droplevels(hpa$Reliability)
colnames(hpa)[1] <- "ensembl_gene_id"
hpa <- dplyr::left_join(hpa, bm)
## Joining, by = "ensembl_gene_id"
hpa <- hpa[!duplicated(hpa$uniprotswissprot), ]
## match HPA/LOPIT
colnames(hpa)[7] <- "accession"
fd <- dplyr::left_join(fData(andyhpa), hpa)
## Joining, by = "accession"
rownames(fd) <- featureNames(andyhpa)
fData(andyhpa) <- fd
stopifnot(validObject(andyhpa))
## Let's get rid of features without any hpa data
lopit <- andyhpa[!is.na(fData(andyhpa)$Main.location), ]
Below, we deparse the multiple ‘;’-delimited locations contained in the Human Protein sub-cellular Atlas, create the auxiliary binary data matrix (only localisations with reliability equal to Supportive are considered; Uncertain assignments are ignored - see http://www.proteinatlas.org/about/antibody+validation for details) and filter proteins without any localisation data.
## HPA localisation
hpalocs <- c(as.character(fData(lopit)$Main.location),
as.character(fData(lopit)$Other.location))
hpalocs <- hpalocs[!is.na(hpalocs)]
hpalocs <- unique(unlist(strsplit(hpalocs, ";")))
makeHpaSet <- function(x, score2, locs = hpalocs) {
hpamat <- matrix(0, ncol = length(locs), nrow = nrow(x))
colnames(hpamat) <- locs
rownames(hpamat) <- featureNames(x)
for (i in 1:nrow(hpamat)) {
loc <- unlist(strsplit(as.character(fData(x)[i, "Main.location"]), ";"))
loc2 <- unlist(strsplit(as.character(fData(x)[i, "Other.location"]), ";"))
score <- score2[fData(x)[i, "Reliability"]]
hpamat[i, loc] <- score
hpamat[i, loc2] <- score
}
new("MSnSet", exprs = hpamat,
featureData = featureData(x))
}
hpaset <- makeHpaSet(lopit,
score2 = c(Supportive = 1, Uncertain = 0))
hpaset <- filterZeroRows(hpaset)
## Removing 319 columns with only 0s.
dim(hpaset)
## [1] 669 18
exprs(hpaset)[c(1, 6, 200), 1:3]
## Endoplasmic reticulum Cytoplasm Vesicles
## O00767 1 0 0
## O95302 0 0 1
## P06493 0 1 0
Protein-protein interaction data can also be used as auxiliary data input to the transfer learning algorithm. Several sources can be used to do so directly from R:
The PSICQUIC package provides an R interfaces to the HUPO Proteomics Standard Initiative (HUPO-PSI) project, which standardises programmatic access to molecular interaction databases. This approach enables to query great many resources in one go but, as noted in the vignettes, for bulk interactions, it is recommended to directly download databases from individual PSICQUIC providers.
The STRINGdb package provides a direct interface to
the STRING protein-protein interactions database. This package can
be used to generate a table as the one used below. The exact
procedure is described in the STRINGdb
vignette and involves
mapping the protein identifiers with the map and retrieve the
interaction partners with the get_neighbors method.
Finally, it is possible to use any third-party PPI inference results and adequately prepare these results for transfer learning. Below, we will described this case with PPI data in a tab-delimited format, as retrieved directly from the STRING database.
Below, we access the PPI spreadsheet file for our test data, that is distributed with the pRolocdata package.
ppif <- system.file("extdata/tabdelimited._gHentss2F9k.txt.gz", package = "pRolocdata")
ppidf <- read.delim(ppif, header = TRUE, stringsAsFactors = FALSE)
head(ppidf)
## X.node1 node2 node1_string_id node2_string_id node1_external_id
## 1 NUDT5 IMPDH2 1861432 1850365 ENSP00000419628
## 2 NOP2 RPL23 1858730 1858184 ENSP00000382392
## 3 HSPA4 ENO1 1848476 1843405 ENSP00000302961
## 4 RPS13 DKC1 1862013 1855055 ENSP00000435777
## 5 RPL35A DDOST 1859718 1856225 ENSP00000393393
## 6 RPL13A RPS6 1857955 1857216 ENSP00000375730
## node2_external_id neighborhood fusion cooccurence homology coexpression
## 1 ENSP00000321584 0.000 0 0 0 0.112
## 2 ENSP00000377865 0.000 0 0 0 0.064
## 3 ENSP00000234590 0.000 0 0 0 0.109
## 4 ENSP00000358563 0.462 0 0 0 0.202
## 5 ENSP00000364188 0.000 0 0 0 0.000
## 6 ENSP00000369757 0.000 0 0 0 0.931
## experimental knowledge textmining combined_score
## 1 0.000 0.0 0.370 0.416
## 2 0.868 0.0 0.000 0.871
## 3 0.222 0.0 0.436 0.575
## 4 0.000 0.0 0.354 0.698
## 5 0.000 0.9 0.265 0.923
## 6 0.419 0.9 0.240 0.996
The file contains 18623 pairwise interactions and the STRING combined interaction score. Below, we create a contingency matrix that uses these scores to encode and weight interactions.
uid <- unique(c(ppidf$X.node1, ppidf$node2))
ppim <- diag(length(uid))
colnames(ppim) <- rownames(ppim) <- uid
for (k in 1:nrow(ppidf)) {
i <- ppidf[[k, "X.node1"]]
j <- ppidf[[k, "node2"]]
ppim[i, j] <- ppidf[[k, "combined_score"]]
}
ppim[1:5, 1:8]
## NUDT5 NOP2 HSPA4 RPS13 RPL35A RPL13A CPS1 CTNNB1
## NUDT5 1 0 0 0 0.000 0.000 0 0
## NOP2 0 1 0 0 0.000 0.000 0 0
## HSPA4 0 0 1 0 0.000 0.000 0 0
## RPS13 0 0 0 1 0.997 0.998 0 0
## RPL35A 0 0 0 0 1.000 0.999 0 0
We now have a contingency matrix reflecting a total of
19910 interactions between 1287
proteins. Below, we only keep proteins that are also available in our
spatial proteomics data (renamed to andyppi
), subset the PPI and
LOPIT data, create the appropriate MSnSet
object, and filter out
proteins without any interaction scores.
andyppi <- andy2011
featureNames(andyppi) <- sub("_HUMAN", "", fData(andyppi)$UniProtKB.entry.name)
cmn <- intersect(featureNames(andyppi), rownames(ppim))
ppim <- ppim[cmn, ]
andyppi <- andyppi[cmn, ]
ppi <- MSnSet(ppim, fData = fData(andyppi),
pData = data.frame(row.names = colnames(ppim)))
ppi <- filterZeroCols(ppi)
## Removing 178 columns with only 0s.
We now have two MSnSet
objects containing respectively
520 primary experimental protein profiles along a
sub-cellular density gradient (andyppi
) and 520 auxiliary
interaction profiles (ppi
).
The SVM-TL method descibed in (Breckels et al. 2016) has not yet been incorporated in the pRoloc package. The code implementing the method is currently available in its own repository:
https://github.com/ComputationalProteomicsUnit/lpsvm-tl-code
The weighted nearest neighbours transfer learning algorithm estimates
optimal weights for the different data sources and the spatial niches
described for the data at hand with the knntlOptimisation
function. For instance, for the human data modelled by the andy2011
and andygoset
objects1 We will use the sub-cellular markers defined in the markers.tl
feature variable, instead of the default markers
.
and the 10 annotated sub-cellular localisations
(Golgi, Mitochondrion, PM, Lysosome, Cytosol, Cytosol/Nucleus, Nucleus, Ribosome 60S, Ribosome 40S and ER), we want to know how
to optimally combine primary and auxiliary data. If we look at figure
1, that illustrates the experimental separation of
the 10 spatial classes on a principal component plot, we
see that some organelles such as the mitochondrion or the cytosol and
cytosol/nucleus are well resolved, while others such as the Golgi or
the ER are less so. In this experiment, the former classes are not
expected to benefit from another data source, while the latter should
benefit from additional information.
Let’s define a set of three possible weights: 0, 0.5 and 1. A weight of 1 indicates that the final results rely exclusively on the experimental data and ignore completely the auxiliary data. A weight of 0 represents the opposite situation, where the primary data is ignored and only the auxiliary data is considered. A weight of 0.5 indicates that each data source will contribute equally to the final results. It is the algorithm’s optimisation step task to identify the optimal combination of class-specific weights for a given primary and auxiliary data pair. The optimisation process can be quite time consuming for many weights and many sub-cellular classes, as all combinations (there are \(number~of~classes^{number~of~weights}\) possibilities; see below). One would generally defined more weights (for example 0, 0.25, 0.5, 0.75, 1 or 0, 0.33, 0.67, 1) to explore more fine-grained integration opportunities. The possible weight combinations can be calculated with the thetas function:
head(thetas(3, by = 0.5))
## Weigths:
## (0, 0.5, 1)
## [,1] [,2] [,3]
## [1,] 0 0.0 0.0
## [2,] 0 0.0 0.5
## [3,] 0 0.0 1.0
## [4,] 0 0.5 0.0
## [5,] 0 0.5 0.5
## [6,] 0 0.5 1.0
dim(thetas(3, by = 0.5))
## Weigths:
## (0, 0.5, 1)
## [1] 27 3
dim(thetas(5, length.out = 4))
## Weigths:
## (0, 0.333333333333333, 0.666666666666667, 1)
## [1] 1024 5
andy2011
data, considering 4 weights, there are very
many combinations:## marker classes for andy2011
m <- unique(fData(andy2011)$markers.tl)
m <- m[m != "unknown"]
th <- thetas(length(m), length.out=4)
## Weigths:
## (0, 0.333333333333333, 0.666666666666667, 1)
dim(th)
## [1] 1048576 10
The actual combination of weights to be tested can be defined in
multiple ways: by passing a weights matrix explicitly (as those
generated with thetas above) through the th
argument; or by
defining the increment between weights using by
; or by specifying
the number of weights to be used through the length.out
argument.
Considering the sub-cellular resolution for this experiment, we would anticipate that the mitochondrion, the cytosol and the cytosol/nucleus classes would get high weights, while the ER and Golgi would be assigned lower weights.
As we use a nearest neighbour classifier, we also need to know how many neighbours to consider when classifying a protein of unknown localisation. The knnOptimisation function (see the pRoloc-tutorial vignette and the functions manual page) can be run on the primary and auxiliary data sources independently to estimate the best \(k_P\) and \(k_A\) values. Here, based on knnOptimisation, we use 3 and 3, for \(k_P\) and \(k_A\) respectively.
Finally, to assess the validity of the weight selection, it should be repeated a certain number of times (default value is 50). As the weight optimisation can become very time consuming for a wide range of weights and many target classes, we would recommend to start with a lower number of iterations, pre-analyse the results, proceed with further iterations and eventually combine the optimisation results data with the combineThetaRegRes function before proceeding with the selection of best weights.
topt <- knntlOptimisation(andy2011, andygoset,
th = th,
k = c(3, 3),
fcol = "markers.tl",
times = 50)
The above code chunk would take too much time to be executed in the
frame of this vignette. Below, we pass a very small subset of theta
matrix to minimise the computation time. The knntlOptimisation
function supports parallelised execution using various backends thanks
to the BiocParallel package; an appropriate backend
will be defined automatically according to the underlying architecture
and user-defined backends can be defined through the BPPARAM
argument2 Large scale applications of this algorithms were run on a cluster using an MPI backend defined with SnowParams(256, type="MPI")
..
Also, in the interest of time, the weights optimisation is repeated
only 5 times below.
set.seed(1)
i <- sample(nrow(th), 12)
topt <- knntlOptimisation(andy2011, andygoset,
th = th[i, ],
k = c(3, 3),
fcol = "markers.tl",
times = 5)
## Removing 481 columns with only 0s.
## Note: vector will be ordered according to classes: Cytosol Cytosol/Nucleus ER Golgi Lysosome Mitochondrion Nucleus PM Ribosome 40S Ribosome 60S (as names are not explicitly defined)
topt
## Object of class "ThetaRegRes"
## Algorithm: theta
## Theta hyper-parameters:
## weights: 0 0.3333333 0.6666667 1
## k: 3 3
## nrow: 12
## Design:
## Replication: 5 x 5-fold X-validation
## Partitioning: 0.2/0.8 (test/train)
## Results
## macro F1:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.7950 0.8101 0.8220 0.8519 0.8881 0.9446
## best theta:
## Cytosol Cytosol.Nucleus ER Golgi Lysosome Mitochondrion Nucleus PM
## weight:0 0 0 4 4 0 1 0 1
## weight:0.33 1 4 0 0 0 0 0 4
## weight:0.67 0 1 0 1 1 0 1 0
## weight:1 4 0 1 0 4 4 4 0
## Ribosome.40S Ribosome.60S
## weight:0 5 1
## weight:0.33 0 4
## weight:0.67 0 0
## weight:1 0 0
The optimisation is performed on the labelled marker examples
only. When removing unlabelled non-marker proteins (the unknowns
),
some auxiliary GO columns end up containing only 0 (the GO-protein
association was only observed in non-marker proteins), which are
temporarily removed.
The topt
result stores all the result from the optimisation step,
and in particular the observed theta weights, which can be directly
plotted as shown on the bubble plot below. These bubble
plots give the proportion of best weights for each marker class that
was observed during the optimisation phase. We see that the
mitochondrion, the cytosol and cytosol/nucleus classes predominantly
are scored with height weights (2/3 and 1), consistent with high
reliability of the primary data. The Golgi and the ribosomal clusters
(and to a lesser extend the ER) favour smaller scores, indicating a
substantial benefit of the auxiliary data.
A set of best weights must be chosen and applied to the classification
of the unlabelled proteins (formally annotated as unknown
). These
can be defined manually, based on the pattern observed in the weights
bubble plot, or automatically extracted with the
getParams
method3 Note that the scores extracted here are based on the random subsest of weights.. See
?getParams for details and the favourPrimary function, if it is
desirable to systematically favour the primary data (i.e. high
weights) when different weight combinations perform equally well.
getParams(topt)
## Cytosol Cytosol/Nucleus ER Golgi Lysosome
## 1.0000000 0.3333333 0.0000000 0.0000000 1.0000000
## Mitochondrion Nucleus PM Ribosome 40S Ribosome 60S
## 1.0000000 1.0000000 0.3333333 0.0000000 0.3333333
We provide the best parameters for the extensive parameter optimisation search, as provided by getParams:
(bw <- experimentData(andy2011)@other$knntl$thetas)
## Cytosol Cytosol/Nucleus ER Golgi Lysosome
## 0.6666667 0.6666667 0.3333333 0.3333333 0.6666667
## Mitochondrion Nucleus PM Ribosome 40S Ribosome 60S
## 0.6666667 0.3333333 0.3333333 0.0000000 0.3333333
To apply our best weights and learn from the auxiliary data
accordingly when classifying the unlabelled proteins to one of the
sub-cellular niches considered in markers.tl
(as displayed on figure
1), we pass the primary and auxiliary data sets, best
weights, best k’s (and, on our case the marker’s feature variable we
want to use, default would be markers
) to the knntlClassification
function.
andy2011 <- knntlClassification(andy2011, andygoset,
bestTheta = bw,
k = c(3, 3),
fcol = "markers.tl")
This will generate a new instance of class MSnSet, identical to the
primary data, including the classification results and classifications
scores of the transfer learning classification algorithm (as knntl
and knntl.scores
feature variables respectively). Below, we extract
the former with the getPrediction function and plot the results of
the classification.
andy2011 <- getPredictions(andy2011, fcol = "knntl")
## ans
## Chromatin associated Cytosol Cytosol/Nucleus
## 11 282 49
## ER Endosome Golgi
## 198 12 63
## Lysosome Mitochondrion Nucleus
## 60 254 122
## PM Ribosome 40S Ribosome 60S
## 240 19 61
setStockcol(paste0(getStockcol(), "80"))
ptsze <- exp(fData(andy2011)$knntl.scores) - 1
plot2D(andy2011, fcol = "knntl", cex = ptsze)
setStockcol(NULL)
addLegend(andy2011, where = "topright",
fcol = "markers.tl",
bty = "n", cex = .7)
Please read the pRoloc-tutorial vignette, and in particular the classification section, for more details on how to proceed with exploration the classification results and classification scores.
This vignette describes the application of a weighted \(k\)-nearest neighbour transfer learning algorithm and its application to the sub-cellular localisation prediction of proteins using quantitative proteomics data as primary data and Gene Ontology-derived binary data as auxiliary data source. The algorithm can be used with various data sources (we show how to compile binary data from the Human Protein Atlas in section 2.2) and have successfully applied the algorithm (Breckels et al. 2016) on third-party quantitative auxiliary data.
All software and respective versions used to produce this document are listed below.
## R version 4.0.3 (2020-10-10)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.5 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.12-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.12-bioc/R/lib/libRlapack.so
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_US.UTF-8 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
##
## attached base packages:
## [1] stats4 parallel stats graphics grDevices utils datasets
## [8] methods base
##
## other attached packages:
## [1] hpar_1.32.0 biomaRt_2.46.0 class_7.3-17
## [4] pRolocdata_1.27.1 pRoloc_1.30.0 BiocParallel_1.24.0
## [7] MLInterfaces_1.70.0 cluster_2.1.0 annotate_1.68.0
## [10] XML_3.99-0.5 AnnotationDbi_1.52.0 IRanges_2.24.0
## [13] MSnbase_2.16.0 ProtGenerics_1.22.0 S4Vectors_0.28.0
## [16] mzR_2.24.0 Rcpp_1.0.5 Biobase_2.50.0
## [19] BiocGenerics_0.36.0 knitr_1.30 BiocStyle_2.18.0
##
## loaded via a namespace (and not attached):
## [1] colorspace_1.4-1 ellipsis_0.3.1 mclust_5.4.6
## [4] proxy_0.4-24 farver_2.0.3 hexbin_1.28.1
## [7] affyio_1.60.0 bit64_4.0.5 lubridate_1.7.9
## [10] prodlim_2019.11.13 mvtnorm_1.1-1 xml2_1.3.2
## [13] codetools_0.2-16 splines_4.0.3 ncdf4_1.17
## [16] doParallel_1.0.16 impute_1.64.0 LaplacesDemon_16.1.4
## [19] pROC_1.16.2 caret_6.0-86 GO.db_3.12.0
## [22] kernlab_0.9-29 vsn_3.58.0 dbplyr_1.4.4
## [25] BiocManager_1.30.10 compiler_4.0.3 httr_1.4.2
## [28] sampling_2.8 assertthat_0.2.1 Matrix_1.2-18
## [31] limma_3.46.0 htmltools_0.5.0 prettyunits_1.1.1
## [34] tools_4.0.3 coda_0.19-4 gtable_0.3.0
## [37] glue_1.4.2 affy_1.68.0 reshape2_1.4.4
## [40] dplyr_1.0.2 rappdirs_0.3.1 MALDIquant_1.19.3
## [43] vctrs_0.3.4 gdata_2.18.0 preprocessCore_1.52.0
## [46] nlme_3.1-150 iterators_1.0.13 timeDate_3043.102
## [49] xfun_0.18 gower_0.2.2 stringr_1.4.0
## [52] lpSolve_5.6.15 lifecycle_0.2.0 gtools_3.8.2
## [55] dendextend_1.14.0 zlibbioc_1.36.0 MASS_7.3-53
## [58] scales_1.1.1 ipred_0.9-9 pcaMethods_1.82.0
## [61] hms_0.5.3 RColorBrewer_1.1-2 yaml_2.2.1
## [64] curl_4.3 memoise_1.1.0 gridExtra_2.3
## [67] ggplot2_3.3.2 rpart_4.1-15 segmented_1.3-0
## [70] stringi_1.5.3 RSQLite_2.2.1 highr_0.8
## [73] randomForest_4.6-14 foreach_1.5.1 e1071_1.7-4
## [76] lava_1.6.8 rlang_0.4.8 pkgconfig_2.0.3
## [79] mzID_1.28.0 evaluate_0.14 lattice_0.20-41
## [82] purrr_0.3.4 labeling_0.4.2 recipes_0.1.14
## [85] bit_4.0.4 tidyselect_1.1.0 plyr_1.8.6
## [88] magrittr_1.5 bookdown_0.21 R6_2.4.1
## [91] magick_2.5.0 generics_0.0.2 DBI_1.1.0
## [94] withr_2.3.0 pillar_1.4.6 mixtools_1.2.0
## [97] survival_3.2-7 nnet_7.3-14 tibble_3.0.4
## [100] crayon_1.3.4 BiocFileCache_1.14.0 rmarkdown_2.5
## [103] viridis_0.5.1 progress_1.2.2 grid_4.0.3
## [106] data.table_1.13.2 blob_1.2.1 FNN_1.1.3
## [109] ModelMetrics_1.2.2.2 digest_0.6.27 xtable_1.8-4
## [112] openssl_1.4.3 munsell_0.5.0 viridisLite_0.3.0
## [115] askpass_1.1
Ashburner, M, C A Ball, J A Blake, D Botstein, H Butler, J M Cherry, A P Davis, et al. 2000. “Gene Ontology: Tool for the Unification of Biology. The Gene Ontology Consortium.” Nat Genet 25 (1):25–29. https://doi.org/10.1038/75556.
Breckels, L M, S B Holden, D Wojnar, C M Mulvey, A Christoforou, A Groen, M W Trotter, O Kohlbacher, K S Lilley, and L Gatto. 2016. “Learning from Heterogeneous Data Sources: An Application in Spatial Proteomics.” PLoS Comput Biol 12 (5):e1004920. https://doi.org/10.1371/journal.pcbi.1004920.
Breckels, Lisa M, Laurent Gatto, Andy Christoforou, Arnoud J Groen, Kathryn S Lilley, and Matthew W B Trotter. 2013. “The Effect of Organelle Discovery Upon Sub-Cellular Protein Localisation.” J Proteomics, March. https://doi.org/10.1016/j.jprot.2013.02.019.
Christoforou, A, C M Mulvey, L M Breckels, A Geladaki, T Hurrell, P C Hayward, T Naake, et al. 2016. “A Draft Map of the Mouse Pluripotent Stem Cell Spatial Proteome.” Nat Commun 7:8992. https://doi.org/10.1038/ncomms9992.
Gatto, Laurent, Juan Antonio Vizcaíno, Henning Hermjakob, Wolfgang Huber, and Kathryn S Lilley. 2010. “Organelle Proteomics Experimental Designs and Analysis.” Proteomics. https://doi.org/10.1002/pmic.201000244.
Uhlen, Mathias, Per Oksvold, Linn Fagerberg, Emma Lundberg, Kalle Jonasson, Mattias Forsberg, Martin Zwahlen, et al. 2010. “Towards a knowledge-based Human Protein Atlas.” Nature Biotechnology 28 (12). Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.:1248–50. https://doi.org/10.1038/nbt1210-1248.