Interactome reconstruction from co-elution data with PrInCE
Introduction: What is PrInCE?
Proteins are the central players of life at the molecular level. Yet cellular functions are rarely accomplished by single proteins acting in isolation. Instead, most biological processes are accomplished by the dynamic organization of proteins and other biological macromolecules, such as RNA and DNA, into networks of physical interactions. Systematic maps of these protein interaction networks can provide a “wiring diagram” to complement the “parts list” revealed by genome sequencing, placing each protein into a functional context. However, historically, protein interaction networks were mapped primarily using labour-intensive methods that involved tagging each protein for affinity purification, or heterologously expressing them in yeast. Besides being labour intensive, these approaches also yielded static pictures of cellular networks that offered little insight into how these networks are rewired by stimulation or in differentiation.
Recently, a family of proteomic approaches, variously referred to as co-elution, co-migration, co-fractionation, or protein correlation profiling, has been developed that allow high-throughput mapping of protein interaction networks in native cellular conditions (1–3). A subset of these even enable investigators to identify dynamic rearrangements in the protein-protein interactome in response to cellular stimulation (1, 4), or across in vivo samples, such as mouse tissues (5). The underlying principle that unifies different experimental protocols is to separate protein complexes into a number of fractions, on the basis of their size (diameter) or biochemical properties, and to perform quantitative proteomic analysis of the fractions. Proteins with similar “profiles” across fractions can be inferred to physically interact. However, because the number of potential pairs grows quadratically with the number of proteins quantified, and the number of potential complexes grows even faster, specialized bioinformatic approaches are required to infer protein interaction networks from the raw proteomics data.
PrInCE is an R package that uses a machine learning approach to infer protein-protein interaction networks at a user-defined level of precision from co-elution proteomics data. The input to PrInCE consists of a matrix derived from a co-elution proteomics experiment, with quantitations for each protein in each fraction (PrInCE can also handle more than one such matrix, in the case of biological replicates). PrInCE also requires a set of ‘gold standard’ protein complexes to learn from. It then calculates a series of features for each possible protein pair; importantly, these are derived directly from the data, without incorporating any external knowledge, a step that minimizes bias towards the rediscovery of known interactions (6). These features, and the accompanying gold standard, are used as input to the classifier, which learns to distinguish interacting and non-interacting pairs. A cross-validation procedure is then used to score every potential protein pair in the dataset, which are then ranked by their score in descending order, and the precision (defined as the ratio of true positives to true positives plus false positives) is calculated at every point in this ranked list. The user can then apply a precision threshold of their choice to this ranked list to infer the protein-protein interaction network from their experiment.
Example 1: Interactome rearrangements in apoptosis
To demonstrate the use of PrInCE, we will work through a small example that is derived from a subset of the data presented in Scott et al., 2017 (4). In this paper, the authors mapped rearrangements in the cytoplasmic and membrane interactome during Fas-mediated apoptosis. Control and stimulated cytoplasmic and membrane interactomes were quantified in three replicates each, meaning the complete dataset consists of twelve replicates. In practice, each set of replicates would be analyzed together (for a total of four networks). However, such a complete analysis of the dataset would take over an hour, so for this vignette we focus on a single replicate. The replicate in question is the first cytoplasmic replicate from the Fas-stimulated condition, and is bundled with the PrInCE package; it can be loaded with the following command:
The dataset consists of ratiometric protein quantitations, achieved by SILAC (stable isotope labelling by amino acids in cell culture), for 1,560 proteins in 55 size exclusion chromatography (SEC) fractions:
## [1] 1560 55Each protein was quantified in at least one fraction; however, many measurements are missing:
## SEC_1 SEC_2 SEC_3 SEC_4 SEC_5
## A0AVT1 NaN NaN NaN NaN NaN
## A0MZ66-5 NaN NaN NaN NaN NaN
## A3KN83 NaN NaN NaN NaN NaN
## A5YKK6 NaN NaN NaN NaN NaN
## A6NDG6 NaN NaN NaN NaN NaN
## A6NG79 NaN NaN NaN NaN NaN
## A6NHL2-2 NaN NaN NaN NaN NaN
## A6NHR9 NaN NaN NaN 2.5125 1.8817
## A6NIH7 NaN NaN NaN NaN NaN
## A6NN80 0.22313 NaN NaN NaN NaNThis scenario is common in co-elution data: for example, a protein will be absent entirely from a given SEC fraction if it does not form a complex with a molecular weight in the mass range of that fraction.
To predict protein-protein interactions using PrInCE’s machine-learning approach, we also need two additional pieces of information to train the classifier: a set of true positive interactions, and a set of true negative interactions. In practice, we recommend providing a list of experimentally verified protein complexes: PrInCE assumes intra-complex interactions represent true positives, and inter-complex interactions represent true negatives. These can be obtained from a number of sources, such as the CORUM database (7), or our own previously reported custom subset of CORUM that removes complexes which may not remain intact under co-elution conditions (8). In the PrInCE R package, we provide a third option which is distributed under a CC-BY license, consisting of a list of 477 human protein complexes from the Complex Portal (9).
## $`5-hydroxytryptamine-3A/B receptor complex`
## [1] "O95264" "P46098"
##
## $`5-hydroxytryptamine-3A/C receptor complex`
## [1] "P46098" "Q8WXA8"
##
## $`5-hydroxytryptamine-3A/D receptor complex`
## [1] "P46098" "Q70Z44"
##
## $`5-hydroxytryptamine-3A/E receptor complex`
## [1] "P46098" "A5X5Y0"
##
## $`6-phosphofructokinase, M2L2 heterotetramer`
## [1] "P08237" "P17858"
##
## $`ACF complex`
## [1] "Q9NRL2" "O60264"Predicting protein-protein interactions: one-step analysis
The main function of the PrInCE package, PrInCE,
provides an end-to-end workflow for predicting protein-protein
interaction networks from the raw co-elution data. Briefly, this
function first filters proteins with too little information to permit
data analysis, then cleans the profiles for the remaining proteins and
fits a mixture of Gaussians to each cleaned profile. PrInCE then
calculates six features for each protein pair, from either the raw
profiles, the cleaned profiles, or the fitted Gaussian mixture models,
and concatenates features across replicates if more than one replicate
was used. These features are used as input to a machine learning model,
along with the set of ‘gold standard’ true positive and true negative
interactions, which uses a ten-fold cross-validation procedure to assign
scores to each protein pair. Protein pairs are ranked by their
classifier scores and the precision at each point in the ranked list is
calculated. The entire list is returned to a user, who can select a
precision threshold that matches their needs.
Once we have loaded a co-elution matrix and list of gold standard protein complexes into R, inferring the protein-protein interaction network with PrInCE is therefore as simple as the following command:
# set the seed to ensure reproducible output
set.seed(0)
## not evaluated
PrInCE(scott, gold_standard)However, this command is not evaluated in order to provide some
information on a further parameter that the PrInCE function
takes. One of the six features that PrInCE uses to score protein-protein
interactions is derived from fitting a mixture of Gaussians to each
protein’s elution profile. The process of Gaussian fitting also allows
PrInCE to filter proteins with poor-quality elution profiles (i.e.,
proteins for which a Gaussian mixture could not be fit with an
r2 value above some minimum, set to 0.5 by default). However,
the process of fitting Gaussian mixture models to thousands of curves is
one of the more computationally intensive steps in PrInCE and
consequently, the PrInCE function can also take a
pre-computed list of fitted Gaussians, fit using the command
build_gaussians:
In practice, the ability to provide pre-computed Gaussians can also save time when trying different parameters in PrInCE, such as different types of classifiers (described in greater detail in the following section).
We provide a list of fitted Gaussians for the scott
dataset in the scott_gaussians object:
## List of 5
## $ n_gaussians: int 3
## $ R2 : num 0.95
## $ iterations : num 1
## $ coefs :List of 3
## ..$ A : Named num [1:3] 2.9 1.59 1.21
## .. ..- attr(*, "names")= chr [1:3] "A1" "A2" "A3"
## ..$ mu : Named num [1:3] 16.05 4.91 40.95
## .. ..- attr(*, "names")= chr [1:3] "mu1" "mu2" "mu3"
## ..$ sigma: Named num [1:3] 6.74 3.11 3.32
## .. ..- attr(*, "names")= chr [1:3] "sigma1" "sigma2" "sigma3"
## $ curveFit : num [1:55] 0.348 0.701 1.161 1.581 1.789 ...We therefore run PrInCE using our precomputed Gaussian curves with
the following command, allowing PrInCE to print information about the
status of the analysis (verbose = TRUE) and limiting the
number of cross-validation folds for the sake of time:
# set the seed to ensure reproducible output
set.seed(0)
# one-step analysis
interactions <- PrInCE(scott, gold_standard,
gaussians = scott_gaussians,
cv_folds = 3,
verbose = TRUE)## generating features for replicate 1 ...## fit mixtures of Gaussians to 970 of 1560 profiles## concatenating features across replicates ...## making labels ...## training classifiers ...## protein_A protein_B score label precision
## P12956_P13010 P12956 P13010 0.9977337 1 1.0
## P36578_P40429 P36578 P40429 0.9966806 NA 1.0
## P62258_Q04917 P62258 Q04917 0.9966630 NA 1.0
## P36578_P46778 P36578 P46778 0.9966609 NA 1.0
## P40429_P46778 P40429 P46778 0.9966256 NA 1.0
## D3YTB1_P62424 D3YTB1 P62424 0.9966104 NA 1.0
## P18124_P46778 P18124 P46778 0.9965548 NA 1.0
## P25786_P28066 P25786 P28066 0.9964794 NA 1.0
## P11940_Q08211 P11940 Q08211 0.9964540 0 0.5
## P14868_P41252 P14868 P41252 0.9964416 NA 0.5
## P43686_P62195 P43686 P62195 0.9964398 NA 0.5
## O00231_Q9UNM6 O00231 Q9UNM6 0.9964243 NA 0.5
## P05388_P36578 P05388 P36578 0.9964118 NA 0.5
## E7EPB3_P05388 E7EPB3 P05388 0.9963531 NA 0.5
## P05388_P40429 P05388 P40429 0.9962900 NA 0.5
## C9J4Z3_P36578 C9J4Z3 P36578 0.9962752 NA 0.5
## P62424_Q9Y3U8 P62424 Q9Y3U8 0.9962596 NA 0.5
## P47914_P62913 P47914 P62913 0.9962394 NA 0.5
## P54136_Q15046 P54136 Q15046 0.9962349 NA 0.5
## P24534_P26641 P24534 P26641 0.9962061 NA 0.5
## P62750_P84098 P62750 P84098 0.9961731 NA 0.5
## P35998_Q13200 P35998 Q13200 0.9961714 NA 0.5
## P13796_Q96KP4 P13796 Q96KP4 0.9961656 NA 0.5
## P18124_P36578 P18124 P36578 0.9961590 NA 0.5
## O15067_Q9UNZ2 O15067 Q9UNZ2 0.9961433 NA 0.5
## P61254_P62241 P61254 P62241 0.9961293 NA 0.5
## P07195_P63104 P07195 P63104 0.9961071 NA 0.5
## C9J4Z3_D3YTB1 C9J4Z3 D3YTB1 0.9961065 NA 0.5
## P04075_P31946 P04075 P31946 0.9960961 NA 0.5
## D3YTB1_P36578 D3YTB1 P36578 0.9960820 NA 0.5
## P49207_P62906 P49207 P62906 0.9960814 NA 0.5
## C9J4Z3_P05388 C9J4Z3 P05388 0.9960643 NA 0.5
## P46778_P61313 P46778 P61313 0.9960462 NA 0.5
## P62249_P62263 P62249 P62263 0.9960311 NA 0.5
## E7EPB3_P05387 E7EPB3 P05387 0.9960072 NA 0.5
## D3YTB1_P47914 D3YTB1 P47914 0.9959959 NA 0.5
## P13796_P22392-2 P13796 P22392-2 0.9959923 NA 0.5
## P30520_Q9NY33 P30520 Q9NY33 0.9959870 NA 0.5
## P05387_P05388 P05387 P05388 0.9959828 NA 0.5
## P47914_P62424 P47914 P62424 0.9959807 NA 0.5
## P18124_P40429 P18124 P40429 0.9959782 NA 0.5
## P07814_P54136 P07814 P54136 0.9959722 NA 0.5
## P40429_P62906 P40429 P62906 0.9959695 NA 0.5
## P18124_P61313 P18124 P61313 0.9959678 NA 0.5
## P05388_P46778 P05388 P46778 0.9959540 NA 0.5
## D3YTB1_P05388 D3YTB1 P05388 0.9959445 NA 0.5
## P08590_P60660-2 P08590 P60660-2 0.9959252 NA 0.5
## P26373_P32969 P26373 P32969 0.9959108 NA 0.5
## P13639_P27348 P13639 P27348 0.9959085 NA 0.5
## P05387_P46778 P05387 P46778 0.9958969 NA 0.5The columns in the output are as follows:
protein_A: the identifier of the first protein in the pair;protein_B: the identifier of the second in the pair;score: the score assigned to the protein pair by the classifierlabel: if the protein pair is in the reference set, this value will be1(for true positives) or0(for true negatives); for all other pairs, the value isNAprecision: the precision at this point in the ranked list
Note that at the very top of the list, the precision is not defined if no true positives and no true negatives have yet been encountered.
In this toy example, the small size of our dataset and the small size of our gold-standard complexes mean that the precision curve is unstable below about 2,000 interactions:
In most real examples, the precision curve shows a smoother decline.
For illustrative purposes, we here threshold the network at 50%
precision using the threshold_precision function:
## [1] 7607This results in an unweighted protein-protein interaction network with 7607 interactions.
Predicting protein-protein interactions: step-by-step analysis
The PrInCE function accepts a large number of arguments
that were omitted from the preceding discussion. We have strived to set
reasonable defaults for each of these parameters, based on analyses that
have involved much of the human co-elution proteomics data in the public
domain. However, users may wish to change some of these defaults, based
on the properties of their dataset or the biological questions
motivating their investigation. Here, we provide an alternative workflow
for analyzing the scott dataset in a step-by-step manner,
and a discussion of some of the most important parameters.
build_gaussians
The build_gaussians function in PrInCE can be broken
down into three steps. First, profiles are preprocessed by basic
filtering and cleaning operations. Single missing values are imputed as
the mean of their two neighboring points, and profiles with fewer than
five consecutive points are filtered from further analysis. Profiles are
then cleaned by replacing missing values with near-zero noise, and
smoothed with a moving average filter. Finally, mixtures of one to five
Gaussians are fit to each profile using nonlinear least squares, and
model selection is performed to retain the best mixture model for each
curve. Proteins that could not be fit with a mixture of Gaussians
without an r2 value above some minimum are omitted.
This function takes the following parameters:
min_consecutive: the minimum number of consecutive points, after imputing single missing values, to retain a profile; defaults to5min_points: the minimum number of total points to retain a profile; defaults to1so that only the number of consecutive points is used to filter profilesimpute_NA: ifFALSE, skip imputation of single missing valuessmooth: ifFALSE, skip curve smoothing with the moving average filtersmooth_width: width of the moving average filter, in fractions; defaults to4max_gaussians: the maximum number of Gaussians with which to fit each profile; defaults to5criterion: the criterion used for model selection; defaults toAICc, the corrected Akaike information criterion; other options areBIC(Bayesian information criterion) orAIC(Akaike information criterion)max_iterations: the maximum number of iterations to use for curve fitting with random restartsmin_R_squared: the minimum r2 value to retain the fitted curve; defaults to0.5. Profiles that cannot be fit by a mixture of Gaussians are assumed to be low-quality and excluded from further analysis by default.method: method used to select initial conditions fornls; can select either random parameters (random) or make an educated guess based on the maximum values in the profile (guess, the default)filter_gaussians_center,filter_gaussians_height,filter_gaussians_variance_min,filter_gaussians_variance_max: heuristics used to filter poor-quality Gaussian fits. IfTRUE(default),filter_gaussians_centerwill remove Gaussians whose mean falls outside the bounds of the chromatogram.filter_gaussians_heightcontrols the minimum height of the Gaussians, whilefilter_gaussians_variance_minandfilter_gaussians_variance_maxcontrol the range of their standard deviation.
All of these parameters except the last four are exposed through the
PrInCE function.
As an example, we will re-analyze the scott dataset with
stricter filtering criteria, requiring the presence of at least ten
(non-imputed) data points in addition to five consecutive points;
fitting with a maximum of three Gaussians, instead of five; and
requiring a better fit than the default settings. For the sake of time,
we allow only 10 iterations for the curve-fitting algorithm here, and we
elect to fit only the first 500 profiles.
data(scott)
# set the seed to ensure reproducible output
set.seed(0)
# fit Gaussians
gauss <- build_gaussians(scott[seq_len(500), ],
min_points = 10, min_consecutive = 5,
max_gaussians = 3, min_R_squared = 0.75,
max_iterations = 10)## .. fitting Gaussian mixture models to 255 profilesBy default, the profile matrix is filtered to exclude proteins whose elution profiles could not be fit by a mixture of Gaussians prior to featurization.
calculate_features
Having fitted our co-elution profiles with Gaussians and filtered
them accordingly, the next step is to calculate features for each
protein pair. This is done using the calculate_features
function. By default, PrInCE calculates six features from each pair of
co-elution profiles as input to the classifier, including conventional
similarity metrics but also several features specifically adapted to
co-elution proteomics. The complete set of features includes:
- the Pearson correlation between raw co-elution profiles;
- the p-value of the Pearson correlation between raw co-elution profiles;
- the Pearson correlation between cleaned profiles, which are
generated by imputing single missing values with the mean of their
neighbors, replacing remaining missing values with random near-zero
noise, and smoothing the profiles using a moving average filter (see
clean_profile); - the Euclidean distance between cleaned profiles;
- the ‘co-peak’ score, defined as the distance, in fractions, between the maximum values of each profile; and
- the ‘co-apex’ score, defined as the minimum Euclidean distance between any pair of fit Gaussians
In addition to the profile matrix and list of fitted Gaussian
mixtures, the calculate_features function takes six
parameters that enable the user to enable or disable each of these six
features (in order, pearson_R_raw, pearson_P,
pearson_R_cleaned, euclidean_distance,
co_peak, and co_apex). By default, all six are
enabled.
Continuing our example, if we wanted the classifier to omit the Euclidean distance, we could disable this feature using the following command:
## protein_A protein_B cor_R_raw cor_R_cleaned cor_P co_peak co_apex
## 1 A0AVT1 B3KNT8 1.239943e+00 1.097955 0.504313944 11 10.405282
## 2 B3KNT8 B4DQ14 1.264748e+00 1.262210 0.382046523 32 31.566148
## 3 A0AVT1 B4DQJ8 2.851543e-06 1.018199 0.001520321 2 2.714134
## 4 B3KNT8 B4DQJ8 1.045782e+00 1.110313 0.827969878 13 7.815383
## 5 B4DQ14 B4DQJ8 3.928140e-01 1.064420 0.110395487 45 23.819433
## 6 B3KNT8 B4DVY1 1.577634e+00 1.114307 0.001033478 27 9.042853If we had multiple replicates, we would here concatenate them into a
single feature data frame using the concatenate_features
function:
predict_interactions
With our features in hand and a list of gold standard protein
complexes, we can now provide these to a machine-learning classifier to
rank potential interactions. This is accomplished using the
predict_interactions function. In order to score
interactions that are also part of the reference set, PrInCE uses a
cross-validation strategy, randomly splitting the reference data into
ten folds, and using each split to score interactions in one of the
folds without including them in the training data. For interactions that
are not part of the training set, the median score over all ten folds is
returned. In addition, to ensure that the results are not sensitive to
the way in which the dataset is split, PrInCE averages predictions over
an ensemble of ten classifiers, each with different cross-validation
splits. By default, PrInCE uses a naive Bayes classifier. However, the
PrInCE R package also implements three other types of classifiers:
support vector machine, random forest, and logistic regression. In
addition, PrInCE offers an option to ensemble results over multiple
different classifiers (sometimes called “heterogeneous classifier
fusion” (10)). In this option,
cross-validation and ensembling is performed for all four types of
classifiers independently, then the ranks of each protein pair across
all four classifiers are averaged to return the final ranked list.
These options are controlled using the following parameters:
classifier: the type of classifier to use; one ofNB,SVM,RF,LR, orensemble, corresponding to the options described abovemodels: the size of the ensemble for each classifier type, i.e., the number of models to train, each with a different train-test splitcv_folds: the number of folds to use in k-fold cross-validationtrees: for random forest and heterogeneous classifier fusion only, the number of trees in each RF model
Continuing our example, we will demonstrate the use of a support
vector machine to rank potential interactions
(classifier = "SVM"). For the sake of time, we use a single
model (omitting ensembling; models = 1) and only three-fold
cross-validation folds (cv_folds = 3). To use our list of
protein complexes as a gold standard, we must first convert it to an
adjacency matrix; this is done using the helper function
adjacency_matrix_from_list (see also the related function
adjacency_matrix_from_data_frame).
data(gold_standard)
reference <- adjacency_matrix_from_list(gold_standard)
# set the seed to ensure reproducible output
set.seed(0)
# predict interactions
ppi <- predict_interactions(feat, reference, classifier = "SVM",
models = 1, cv_folds = 3)We can now plot the precision curve over the first 20,000 interactions:
Finally, we will likely want to keep only the set of high-confidence
interactions for further analysis, where “confidence” is quantified
using precision. This is accomplished using the
threshold_precision function. For example, the following
command constructs a protein-protein interaction network at 70%
precision:
## [1] 4110Identifying co-eluting protein complexes
The core functionality of PrInCE involves the use of a
machine-learning framework to predict binary interactions from
co-elution data, with discovery of novel interactions being a primary
goal. However, PrInCE also implements one alternative to this analytical
framework, which asks whether statistically significant co-elution is
observed for known protein complexes.
This is achieved using a permutation-based approach, inspired by methods
developed for another proteomic method for interactome profiling,
thermal proximity co-aggregation (TPCA) (11). Briefly, given a list of known complexes,
PrInCE calculates the median Pearson correlation between all pairs of
complex members. (To reduce the effect of spurious correlations between
proteins that are rarely observed in the same fractions, PrInCE requires
a certain minimum number of paired observations to include any given
correlation in this analysis—by default, 10 pairs). Then, PrInCE
simulates a large number of complexes of equivalent size (by default,
100), and calculates the median Pearson correlation between pairs of
random ‘complexes’. The resulting null distribution is used to assess
the statistical significance of the observed co-elution profile at the
protein complex level.
To identify complexes from the Complex Portal dataset that are
significantly co-eluting in this replicate, we first use PrInCE’s
filter_profiles and clean_profiles
functions:
# analyze cleaned profiles
data(scott)
filtered = filter_profiles(scott)
chromatograms = clean_profiles(filtered)The filter_profiles function uses a permissive set of
filters to discard chromatograms that do not contain enough information
to make inferences about that protein’s interaction partners. Similarly,
the clean_profiles applies some simple preprocessing steps
to the filtered chromatograms. By default, this function is applied to
calculate Pearson correlations during interaction prediction in PrInCE.
It imputes single missing values as the average of the two neighbors,
remaining missing values with near-zero noise, then passes a
moving-average filter over the chromatogram to smooth it.
We can now test for complex co-elution in the preprocessed
chromatogram matrix using the detect_complexes
function:
# detect significantly co-eluting complexes
set.seed(0)
z_scores = detect_complexes(chromatograms, gold_standard)Complexes that could not be tested (that is, with fewer than three
complex members present in the elution matrix) are given NA
values, which we remove.
# remove complexes that could not be analyzed
z_scores = na.omit(z_scores)
# how many could be tested?
length(z_scores)## [1] 23## [1] 13## COP9 signalosome variant 1
## 9.083072
## COP9 signalosome variant 2
## 6.744865
## CRD-mediated mRNA stability complex
## 5.806526
## MCM complex
## 5.779922
## Condensin I complex
## 4.568462
## Embryonic stem cell-specific SWI/SNF ATP-dependent chromatin remodeling complex
## 4.256243Of the 23 complexes that could be tested in this (unusually sparse) replicate, 13 were significant at an uncorrected, two-tailed p-value threshold of 0.05
Example 2: Interactome of HeLa cells
As a second example, we can reanalyze another dataset bundled with the PrInCE R package. This dataset consists of a subset of the data presented by Kristensen et al., 2012 (1), who applied SEC-PCP-SILAC to monitor the interactome of HeLa cell lysates, then mapped interactome rearrangements induced by epidermal growth factor (EGF) stimulation. Three biological replicate experiments were performed, and in practice, all three replicates from each condition would be analyzed together. However, for the purposes of demonstrating the use of the PrInCE R package, we limit our analysis to the first replicate from the unstimulated condition.
We first load the data matrix and fitted Gaussians, provided with the PrInCE R package:
## [1] 1875 48## [1] 1117The co-elution matrix contains quantifications for 1,875 proteins across 48 SEC fractions. Mixtures of Gaussians were fit to 1,117 of these. For the sake of time, we subset this matrix further to the first 500 proteins:
kristensen <- kristensen[names(kristensen_gaussians), ]
kristensen <- kristensen[seq_len(500), ]
kristensen_gaussians <- kristensen_gaussians[rownames(kristensen)]We also have to load our reference set of binary interactions or protein complexes, which in this case is derived from the Complex Portal human complexes.
## $`5-hydroxytryptamine-3A/B receptor complex`
## [1] "O95264" "P46098"
##
## $`5-hydroxytryptamine-3A/C receptor complex`
## [1] "P46098" "Q8WXA8"
##
## $`5-hydroxytryptamine-3A/D receptor complex`
## [1] "P46098" "Q70Z44"
##
## $`5-hydroxytryptamine-3A/E receptor complex`
## [1] "P46098" "A5X5Y0"
##
## $`6-phosphofructokinase, M2L2 heterotetramer`
## [1] "P08237" "P17858"We can predict interactions in a single step using the main
PrInCE function, here using a single model (instead of the
default ensemble of ten) and five cross-validation folds (instead of the
default of ten) for time:
# set seed for reproducibility
set.seed(0)
# predict interactions
interactions <- PrInCE(profiles = kristensen,
gold_standard = gold_standard,
gaussians = kristensen_gaussians,
models = 1,
cv_folds = 5)Finally, we can subset our list of interactions to obtain set of high-confidence interactions for further analysis, using a relaxed precision cutoff of 50%.
## [1] 1404PrInCE predicts a total of 1,047 interactions at a precision of 50%.
Session info
## R version 4.4.2 (2024-10-31)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.1 LTS
##
## Matrix products: default
## BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
## LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0
##
## 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
##
## time zone: Etc/UTC
## tzcode source: system (glibc)
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] PrInCE_1.23.0 BiocStyle_2.35.0
##
## loaded via a namespace (and not attached):
## [1] sys_3.4.3 rstudioapi_0.17.1
## [3] jsonlite_1.8.9 MultiAssayExperiment_1.33.1
## [5] magrittr_2.0.3 MALDIquant_1.22.3
## [7] rmarkdown_2.29 zlibbioc_1.52.0
## [9] vctrs_0.6.5 base64enc_0.1-3
## [11] progress_1.2.3 htmltools_0.5.8.1
## [13] S4Arrays_1.7.1 curl_6.0.1
## [15] SparseArray_1.7.2 Formula_1.2-5
## [17] mzID_1.45.0 TTR_0.24.4
## [19] sass_0.4.9 bslib_0.8.0
## [21] naivebayes_1.0.0 htmlwidgets_1.6.4
## [23] plyr_1.8.9 impute_1.81.0
## [25] zoo_1.8-12 cachem_1.1.0
## [27] buildtools_1.0.0 igraph_2.1.1
## [29] lifecycle_1.0.4 iterators_1.0.14
## [31] pkgconfig_2.0.3 Matrix_1.7-1
## [33] R6_2.5.1 fastmap_1.2.0
## [35] GenomeInfoDbData_1.2.13 rbibutils_2.3
## [37] MatrixGenerics_1.19.0 clue_0.3-66
## [39] digest_0.6.37 pcaMethods_1.99.0
## [41] colorspace_2.1-1 S4Vectors_0.45.2
## [43] Hmisc_5.2-1 GenomicRanges_1.59.1
## [45] fansi_1.0.6 httr_1.4.7
## [47] abind_1.4-8 compiler_4.4.2
## [49] doParallel_1.0.17 speedglm_0.3-5
## [51] htmlTable_2.4.3 backports_1.5.0
## [53] tseries_0.10-58 BiocParallel_1.41.0
## [55] DBI_1.2.3 biglm_0.9-3
## [57] LiblineaR_2.10-24 MASS_7.3-61
## [59] DelayedArray_0.33.3 mzR_2.41.1
## [61] tools_4.4.2 ranger_0.17.0
## [63] PSMatch_1.11.0 foreign_0.8-87
## [65] lmtest_0.9-40 quantmod_0.4.26
## [67] nnet_7.3-19 glue_1.8.0
## [69] quadprog_1.5-8 nlme_3.1-166
## [71] QFeatures_1.17.0 grid_4.4.2
## [73] checkmate_2.3.2 cluster_2.1.6
## [75] reshape2_1.4.4 generics_0.1.3
## [77] gtable_0.3.6 preprocessCore_1.69.0
## [79] tidyr_1.3.1 hms_1.1.3
## [81] data.table_1.16.2 utf8_1.2.4
## [83] XVector_0.47.0 BiocGenerics_0.53.3
## [85] foreach_1.5.2 pillar_1.9.0
## [87] stringr_1.5.1 limma_3.63.2
## [89] robustbase_0.99-4-1 dplyr_1.1.4
## [91] lattice_0.22-6 tidyselect_1.2.1
## [93] maketools_1.3.1 knitr_1.49
## [95] gridExtra_2.3 urca_1.3-4
## [97] IRanges_2.41.2 ProtGenerics_1.39.0
## [99] SummarizedExperiment_1.37.0 forecast_8.23.0
## [101] stats4_4.4.2 xfun_0.49
## [103] Biobase_2.67.0 statmod_1.5.0
## [105] MSnbase_2.33.2 timeDate_4041.110
## [107] matrixStats_1.4.1 DEoptimR_1.1-3-1
## [109] stringi_1.8.4 UCSC.utils_1.3.0
## [111] lazyeval_0.2.2 yaml_2.3.10
## [113] evaluate_1.0.1 codetools_0.2-20
## [115] tester_0.2.0 MsCoreUtils_1.19.0
## [117] tibble_3.2.1 BiocManager_1.30.25
## [119] cli_3.6.3 affyio_1.77.0
## [121] rpart_4.1.23 Rdpack_2.6.2
## [123] munsell_0.5.1 jquerylib_0.1.4
## [125] Rcpp_1.0.13-1 GenomeInfoDb_1.43.2
## [127] XML_3.99-0.17 parallel_4.4.2
## [129] fracdiff_1.5-3 ggplot2_3.5.1
## [131] prettyunits_1.2.0 AnnotationFilter_1.31.0
## [133] scales_1.3.0 xts_0.14.1
## [135] affy_1.85.0 ncdf4_1.23
## [137] purrr_1.0.2 crayon_1.5.3
## [139] rlang_1.1.4 vsn_3.75.0