ProteoMM - Multi-Dataset Model-based Differential Expression Proteomics Platform

In ProteoMM: Multi-Dataset Model-based Differential Expression Proteomics Analysis Platform

knitr::opts_chunk$set(echo = TRUE)
library('ProteoMM')
set.seed(135)

\newline

Introduction

ProteoMM is a platform for peptide-level differential expression analysis of single or multiple proteomic datasets simultaneously. ProteoMM provides a single p-value and a single effect size estimate for the differences in protein abundances. A test statistic is computed as a sum of F-statistics produced for each individual dataset. A p-value is then estimated via a permutation test as the distribution of the sum of the F-statistics does not have a closed form solution. Simultaneous utilization of all available peptides within proteins in multiple datasets increases statistical power to detect differences among conditions or treatments. In addition, in ProteoMM package, we build on our previous research and provide functionality for normalization, model-based imputation of missing peptide abundances and peptide-level differential protein expression analysis [1, 2].

Currently, combined analysis of multiple datasets is limited to utilizing a multi-dataset t-test [3]. Since in proteomics, protein abundances are measured in terms of the constitutive peptides a t-test would require averaging or “rolling-up” the peptide abundances into protein abundances prior to analysis with a multi-dataset t-test. We have previously shown that such reduction in the number of observations leads to the reduced statistical power and reduced ability to detect differentially expressed proteins [1]. ProteoMM provides a flexible pipeline from raw peptide abundances to protein quantification for multiple as well as single datasets in bottom-up mass spectrometry-based proteomics studies.

This tutorial will walk the readers through an example analysis of two simulated datasets. For function definitions and descriptions please use "?" command in R.

\newline

Installation

ProteoMM can be installed from Bioconductor:

source("https://bioconductor.org/biocLite.R")
biocLite("ProteoMM")
library(ProteoMM)

Alternatively ProteoMM can be installed from GitHub:

devtools::install_github("YuliyaLab/ProteoMM")
library(ProteoMM)

ProteoMM Analysis Pipeline

ProteoMM Pipeline includes six steps, which we suggest are performed in the following order:

\newline

Load Data -> EigenMS Normalization -> Model-Based Imputation -> Model-Based Differential Expression Analysis & Presence/Absence Analysis -> Visualization & Table Output.

\newline

Individual steps such as normalization, imputation or presence/absence analysis can be skipped but care must be taken to assure that peptides passed into Model-Based Differential Expression Analysis step contain a sufficient number of observations.

The example we provide in this tutorial follows the suggested ProteoMM analysis outline in Figure 1 with additional data visualization that we find useful in proteomics data analysis.

\newline

EigenMS normalization

The data used in this example is a subset of a proteomics experiment where peptide IDs (sequences) have been shuffled and protein and gene IDs were replaced by fake 'Prot_#' name. This document provides an example of the code and data structures that are necessary to run Multi-Matrix analysis, including EigenMS normalization, Model-Based imputation and Multi-Matrix statistical analysis.

For non-proteomics data, such as metabolomics data, 2 columns with identical information can be provided.

Start by loading the data and defining the parameter prot.info, a two column data framewith IDs for metabolites or peptides in case of matabolites the 2 columns are identical. For peptides, 1st column must contain unique peptide ID (usually peptide sequences), 2nd column can contain protein IDs, (not used in EigenMS) and any other metadata columns that will be propagated through the analysis pipeline.

Human

Human dataset contains 695 peptides with 13 columns where 6 columns contain intensities and the rest are metadata describing the proteins/peptides. There are six samples with three samples in each of the two treatment groups: CG and mCG.

We replace 0's with NA's and log2 transform the intensities as 0's should not be used in place of the missing observations. Such replacement will severely skew the distribution of intensities and produce invalid differential expression results. For more information see Karpievitch et al. 2009 [1,2].

# Load data for human, then mouse 
data("hs_peptides") # loads variable hs_peptides
dim(hs_peptides)  # 695 x 13   
intsCols = 8:13   # column indices that contain intensities
m_logInts = make_intencities(hs_peptides, intsCols)  

# replace 0's with NA's, NA's are more appropriate for analysis & log2 transform
m_logInts = convert_log2(m_logInts) 
metaCols = 1:7 # column indices for metadata such as protein IDs and sequences
m_prot.info = make_meta(hs_peptides, metaCols)

# m_prot.info - 2+ column data frame with peptide IDs and protein IDs
head(m_prot.info) 
dim(m_logInts) # 695 x 6
grps = as.factor(c('CG','CG','CG', 'mCG','mCG','mCG')) # 3 samples for CG & mCG

# check the number of missing values
m_nummiss = sum(is.na(m_logInts)) 
m_nummiss
m_numtot = dim(m_logInts)[1] * dim(m_logInts)[2] #  total # of observations
m_percmiss = m_nummiss/m_numtot  # % missing observations
m_percmiss # 38.29% missing values, representative of the true larger dataset
# plot number of missing values for each sample
par(mfcol=c(1,1))
barplot(colSums(is.na(m_logInts)), 
        main="Numbers of missing values in Human samples (group order)")

Note that the mCG treatment group has more missing values. Next identify bias trends with eig_norm1().

hs_m_ints_eig1 = eig_norm1(m=m_logInts,treatment=grps,prot.info=m_prot.info)

names(hs_m_ints_eig1)

Our simulated dataset is small, and only 1 bias trend was identified in the peptides with no missing values. But visually it seems that there are at least 2.

hs_m_ints_eig1$h.c

Run EigenMS normalization to eliminate 1 bias trend

hs_m_ints_norm_1bt = eig_norm2(rv=hs_m_ints_eig1) 

There is a 15% increase in percent variance explained by the trend as is indicated by the percentage in the upper right corner. But the next (middle) trend explains 18% of variation, so bias effect of this trend may need to be removed.

names(hs_m_ints_eig1)
# how many peptides with no missing values (complete) are in the data? 
dim(hs_m_ints_eig1$complete)# bias trend identification is based on 196 peptides

Our simulated dataset is small, with only 196 peptides with no missing values, which are used to identify bias trends. Only one bias trend was identified, but visually it seems that there are at least two. So here we manually set h.c to 2 trestnds that are going to be eliminated.

hs_m_ints_eig1$h.c = 2 # visually there are more than 1 bias trend, set to 2

hs_m_ints_norm = eig_norm2(rv=hs_m_ints_eig1)  

Figure 4 shows a 28% increase in percent variance explained by the trend where differences between the groups explaining 71% of total variation in the data as is indicated by the percentage in the upper right corner. The next (middle) trend explains 16% of variation, but removing the effect of more trends may overnormalize, thus this we will use normalized data with two bias trends eliminated.

cat("\\newpage")

Mouse

The mouse dataset contains 1102 peptides with 13 columns where 6 column contain intensities and the rest are metadata describing the proteins/peptides.

There are six samples with three samples in each of the two treatment groups: CG and mCG. The data preparation is similar to what we have done for Human data.

data("mm_peptides") # loads variable mm_peptides
dim(mm_peptides)

dim(mm_peptides) # 1102 x 13  
head(mm_peptides) 

intsCols = 8:13 # may differ for each dataset, users need to adjust  
m_logInts = make_intencities(mm_peptides, intsCols)  # reuse the name m_logInts
m_logInts = convert_log2(m_logInts) 
metaCols = 1:7 
m_prot.info = make_meta(mm_peptides, metaCols)

head(m_prot.info) 
dim(m_logInts)# 1102 x 6

# check numbers of missing values in Mouse samples
m_nummiss = sum(is.na(m_logInts)) 
m_nummiss
m_numtot = dim(m_logInts)[1] * dim(m_logInts)[2] #  total observations
m_percmiss = m_nummiss/m_numtot  # % missing observations
m_percmiss # 40.8% missing values, representative of the true larger dataset
# plot number of missing values for each sample
par(mfcol=c(1,1))
barplot(colSums(is.na(m_logInts)), 
        main="Numbers of missing values in Mouse samples (group order)")

mm_m_ints_eig1 = eig_norm1(m=m_logInts,treatment=grps,prot.info=m_prot.info)

The eigentrend that explains most of the variation (45%) in the Mouse data is not representative of the treatment group differences (Figure 5). The second trend in the raw data explains only 22% of the total variation that resembles treatment group differences necessitating normalization. Variation in the data as is indicated by the percentage in the upper right corner.

mm_m_ints_eig1$h.c 

mm_m_ints_norm_1bt = eig_norm2(rv=mm_m_ints_eig1) 

The eigentrend that explains most of the variation (43%) in the normalized mouse data is representative of the treatment group differences. The second trend in the raw data explains only 27% of the total variation and should be considered as bias.

mm_m_ints_eig1$h.c = 2

mm_m_ints_norm = eig_norm2(rv=mm_m_ints_eig1)  
# 190 petides with no missing values were used to id bais trends ($complete)

The eigentrend that explains most of the variation in the normalized mouse data representative of the treatment group differences now explains 58% of variation. The second trend in the normalized data explains less of variation that in Figure 6 (24%) which is still a bit high, but we will use these data for analysis to avoid overfitting.

length(mm_m_ints_eig1$prot.info$MatchedID)          # 1102 - correct
length(hs_m_ints_eig1$prot.info$MatchedID)          # 695 - can normalize all
length(unique(mm_m_ints_eig1$prot.info$MatchedID) ) # 69
length(unique(hs_m_ints_eig1$prot.info$MatchedID) ) # 69

# 787 peptides were normalized, rest eliminated due to low # of observations
dim(mm_m_ints_norm$norm_m) 
dim(hs_m_ints_norm$norm_m) # 480 peptides were normalized

cat("\\newpage")

\newline

Model-based imputation

Model-based imputation uses a statistical model that accounts for the informative missingness in peptide intensities and provides an unbiased, model-based, protein-level differential expression analysis performed at peptide level [1].

Model-based imputation models two missingness mechanisms, one missing completely at random and the other abundance-dependent. Completely random missingness occurs when the fact that a peptide was unobserved in a sample has nothing to do with its abundance or the abundance of any other peptides. This usually affects a small proportion of the peptides considered in the analysis. From our past experience it is near 5% or all observations. Abundance-dependent missingness occurs due to left-censoring, where a peptide is either not present or is present at too low concentration to be detected by the instrument. In this case, we have partial information for the peptide intensity, in that we know it must be less than the rest of the observed peptide intensities.

Human

We need to set up metadata and intensities to use for the imputation. We will impute based on ProtID - position in the matrix for the Protein Identifier. In this example datasets, ProtID and MatchedID can be used interchangeably.

hs_prot.info = hs_m_ints_norm$normalized[,metaCols]
hs_norm_m =  hs_m_ints_norm$normalized[,intsCols]
head(hs_prot.info)
head(hs_norm_m)
dim(hs_norm_m) # 480 x 6, raw: 695, 215 peptides were eliminated due to lack of 
               # observations
length(unique(hs_prot.info$MatchedID)) # 59
length(unique(hs_prot.info$ProtID))    # 59

imp_hs = MBimpute(hs_norm_m, grps, prot.info=hs_prot.info, pr_ppos=3, 
                  my.pi=0.05, compute_pi=FALSE) # use default pi
# historically pi=.05 has been representative of the % missing 
# observations missing completely at random

# check some numbers after the imputation
length(unique(imp_hs$imp_prot.info$MatchedID)) # 59 - MatchedID IDs
length(unique(imp_hs$imp_prot.info$ProtID))    # 59 - Protein IDs
length(unique(imp_hs$imp_prot.info$GeneID))    # 59 

dim(imp_hs$imp_prot.info) # 480 x 7 imputed peptides
dim(imp_hs$y_imputed)     # 480 x 6 


# plot one of the protiens to check normalization and imputation visually
mylabs = c( 'CG','CG','CG', 'mCG','mCG','mCG') # same as grps this is a string
prot_to_plot = 'Prot32' # 43
gene_to_plot = 'Gene32'  
plot_3_pep_trends_NOfile(as.matrix(hs_m_ints_eig1$m), hs_m_ints_eig1$prot.info, 
                         as.matrix(hs_norm_m), hs_prot.info, imp_hs$y_imputed,
                         imp_hs$imp_prot.info, prot_to_plot, 3, gene_to_plot, 
                         4, mylabs)

Mouse

mm_prot.info = mm_m_ints_norm$normalized[,1:7]
mm_norm_m =  mm_m_ints_norm$normalized[,8:13]
head(mm_prot.info)
head(mm_norm_m)
dim(mm_norm_m) # 787 x 6, raw had: 1102 peptides/rows

length(unique(mm_prot.info$MatchedID)) # 56 
length(unique(mm_prot.info$ProtID))    # 56

set.seed(12131) # set random number generator seed for reproducibility, 
# otherwise will get various imputed values for repeated attempts
# as for Human, impute based on ProtID - position in the matrix for the Protein Identifier 
imp_mm = MBimpute(mm_norm_m, grps, prot.info=mm_prot.info, pr_ppos=3, 
                  my.pi=0.05, compute_pi=FALSE) 
                  # pi =.05 is usually a good estimate

Check if returned number of rows corresponds to the same number of rows in normalized data.

dim(imp_mm$imp_prot.info) # 787 x 7 - imputed peptides & 787 were normalized
dim(imp_mm$y_imputed)     # 787 x 6

cat("\\newpage")

\newline

Model-Based Differential Expression Analysis

We will do combined model-based differential expression analysis for proteins detected in both mouse and human datasets. For proteins that were only identified in one of the two datasets analysis will be performed for that particular species separately. Combined analysis of multiple datasets will have higher sensitivity to detect differentially expressed proteins due to the increase in the numbers of observations.

Combined Model-Based Differential Expression Analysis

Multi Matrix analysis is generalizable to 2 or more datasets thus parallel lists are used to store intensities, metadata, and treatment group information. Second column metadata data frame must be a protein identifier that is present in both datasets. In this simulated dataset ProtIDs as well as matchedID, will match across Human and Mouse, in reality, protein IDs will differ, as human and mouse protein IDs are different for the same protein. Gene IDs will generally differ by only by upper vs. lower case, with a few genes having different IDs for the unknown to us reason. Thus when comparing protein abundances across different organisms ProtID is not a good identifier to use across different organisms, instead, protein IDs can be matched based on Ensembl IDs.

We will start by making parallel lists to pass as parameters to teh differential expression function prot_level_multi_part(). Start by dividing the data into a list of proteins that are common to both datasets (can be more than 2) and proteins present only in one or the other (unique to one or the other). Here we will analyze the proteins that were observed only in one of the datasets, Note that "grps"" variable is the same for both simulated dataset here, but for useres number and order of samples ned to checked and grps variable set to the appropriate factors for each dataset. Also note that treatment group order should be the same in all datasets. Do not set groups to

contr contr contr treat treat treat

in one sample and

treat treat treat contr contr contr

in the other.

# make parallel lists to pass as parameters  
mms = list()
treats = list()
protinfos = list()
mms[[1]] = imp_mm$y_imputed
mms[[2]] = imp_hs$y_imputed 
treats[[1]] = grps
treats[[2]] = grps

protinfos[[1]] = imp_mm$imp_prot.info 
protinfos[[2]] = imp_hs$imp_prot.info

subset_data = subset_proteins(mm_list=mms, prot.info=protinfos, 'MatchedID')
names(subset_data)

mm_dd_only = subset_data$sub_unique_prot.info[[1]]
hs_dd_only = subset_data$sub_unique_prot.info[[2]] 

ugene_mm_dd = unique(mm_dd_only$MatchedID) 
ugene_hs_dd = unique(hs_dd_only$MatchedID)
length(ugene_mm_dd) # 24 - in Mouse only
length(ugene_hs_dd) # 27 - Human only

nsets = length(mms)
nperm = 50   # number of permutations should be 500+ for publication quality

ptm = proc.time()
set.seed=(12357)
comb_MBDE = prot_level_multi_part(mm_list=mms, treat=treats,prot.info=protinfos, 
                                  prot_col_name='ProtID', nperm=nperm, 
                                  dataset_suffix=c('MM', 'HS'))
proc.time() - ptm  # shows how long it takes to run the test

mybreaks = seq(0,1, by=.05)
# adjustment for permutation test is done by stretching out values on the 
# interval [0 1]  as expected in a theoretical p-value distribution
par(mfcol=c(1,3)) # always check out p-values
# bunched up on interval [0 .5]
hist(comb_MBDE$P_val, breaks=mybreaks, xlab='unadjusted p-values', main='') 
# adjusted p-values look good
hist(comb_MBDE$BH_P_val, breaks=mybreaks, xlab='adjusted p-values', main='') 
# bunched up on interval [0 .5]
hist(p.adjust(comb_MBDE$P_val, method='BH'), breaks=mybreaks, 
     xlab='BH adjusted p-values', main='') 

# horizontal streaks correspond to where a permutation test produces 0 or 
# very small value, these are reset to improve visualization
par(mfcol=c(1,1)) # Volcano generally look better for larger dataset... 
plot_volcano_wLab(comb_MBDE$FC, comb_MBDE$BH_P_val, comb_MBDE$GeneID, 
                  FC_cutoff=1.2, PV_cutoff=.05, 'CG vs mCG')  

Model-Based Differential Expression Analysis for proteins observed only in Human

There are Human (HS) specific proteins that can be analyzed with Model-Based Differential Expression Analysis, so no analysis for this subset.

Model-Based Differential Expression Analysis for proteins observed only in Mouse

# subset_data contains "sub_unique_mm_list"  "sub_unique_prot.info" lists 
# for each dataset in the order provided to subset function
mms_mm_dd = subset_data$sub_unique_mm_list[[1]] # Mouse
dim(mms_mm_dd)  # 258 x 6, 
protinfos_mm_dd = subset_data$sub_unique_prot.info[[1]] 

length(unique(protinfos_mm_dd$ProtID))    # 24
length(unique(protinfos_mm_dd$GeneID))    # 24
length(unique(protinfos_mm_dd$MatchedID)) # 24

DE_mCG_CG_mm_dd = peptideLevel_DE(mms_mm_dd, grps, prot.info=protinfos_mm_dd, 
                                  pr_ppos=2) 

# volcano plot
FCval = 1.2 # change this value for alternative fold change cutoff
plot_volcano_wLab(DE_mCG_CG_mm_dd$FC, DE_mCG_CG_mm_dd$BH_P_val, 
                  DE_mCG_CG_mm_dd$GeneID, FC_cutoff=FCval, 
                  PV_cutoff=.05, 'Mouse specific - CG vs mCG') 

cat("\\newpage")

\newline

Presence-Absence Analysis

Combined Mouse and Human Analysis

In the Presence-Absence Analysis, we use only proteins that are NOT in the normalized data. For example, some peptides may have been eliminated for some proteins due to many missing values, but if some peptides remained in the Model-Based Differential Expression Analysis, we do not analyze a subset of peptides in the Presence-Absence Analysis as we would obtain 2 p-values. We strongly believe that Model-Based Differential Expression Analysis is a more sensitive approach and thus it is a preferred method of analysis for proteins that have sufficient number of observations in both treatment groups.

# make data structures suitable for get_presAbs_prots() function
raw_list = list()
norm_imp_prot.info_list = list()
raw_list[[1]] = mm_m_ints_eig1$m
raw_list[[2]] = hs_m_ints_eig1$m
norm_imp_prot.info_list[[1]] = mm_m_ints_eig1$prot.info
norm_imp_prot.info_list[[2]] = hs_m_ints_eig1$prot.info

protnames_norm_list = list()
protnames_norm_list[[1]] = unique(mm_m_ints_norm$normalized$MatchedID) #56/69 
protnames_norm_list[[2]] = unique(hs_m_ints_norm$normalized$MatchedID) #59 

presAbs_dd = get_presAbs_prots(mm_list=raw_list, 
                               prot.info=norm_imp_prot.info_list, 
                               protnames_norm=protnames_norm_list, 
                               prot_col_name=2)
ints_presAbs = list()
protmeta_presAbs = list()
ints_presAbs[[1]] = presAbs_dd[[1]][[1]] # Mouse
ints_presAbs[[2]] = presAbs_dd[[1]][[2]] # HS
protmeta_presAbs[[1]] = presAbs_dd[[2]][[1]] 
protmeta_presAbs[[2]] = presAbs_dd[[2]][[2]]

dim(protmeta_presAbs[[2]]) # 32 x 7 peptides
length(unique(protmeta_presAbs[[2]]$MatchedID))  # 10 - proteins 
dim(protmeta_presAbs[[1]]) # 30 x 7 peptides
length(unique(protmeta_presAbs[[1]]$MatchedID))  # 13 - proteins 

 # grps are the same for all analyses
subset_presAbs = subset_proteins(mm_list=ints_presAbs,
                                 prot.info=protmeta_presAbs,'MatchedID') 
names(subset_presAbs)
dim(subset_presAbs$sub_unique_prot.info[[1]])
dim(subset_presAbs$sub_unique_prot.info[[2]]) 
dim(subset_presAbs$sub_prot.info[[1]]) 
dim(subset_presAbs$sub_prot.info[[2]])  

nperm = 50  # set to 500+ for publication 
ptm = proc.time()
set.seed=(123372)
presAbs_comb=prot_level_multiMat_PresAbs(mm_list=subset_presAbs$sub_mm_list,
                                         treat=treats, 
                                         prot.info=subset_presAbs$sub_prot.info, 
                                         prot_col_name='MatchedID', nperm=nperm,
                                         dataset_suffix=c('MM', 'HS') )
proc.time() - ptm

plot_volcano_wLab(presAbs_comb$FC, presAbs_comb$BH_P_val, presAbs_comb$GeneID, 
                  FC_cutoff=.5, PV_cutoff=.05, 'Combined Pres/Abs CG vs mCG') 

# just checking the numbers here
dim(subset_presAbs$sub_unique_mm_list[[1]]) 
dim(subset_presAbs$sub_unique_mm_list[[2]]) 

unique(subset_presAbs$sub_unique_prot.info[[1]]$ProtID)# 8 
unique(subset_presAbs$sub_unique_prot.info[[2]]$ProtID)# 5 

Presence/Absence analysis for proteins found only in Mouse

mm_presAbs = peptideLevel_PresAbsDE(subset_presAbs$sub_unique_mm_list[[1]], 
                                    treats[[1]], 
                                    subset_presAbs$sub_unique_prot.info[[1]], 
                                    pr_ppos=3) 

plot_volcano_wLab(mm_presAbs$FC, mm_presAbs$BH_P_val, mm_presAbs$GeneID, 
                  FC_cutoff=.5, PV_cutoff=.05, 'MM Pres/Abs CG vs mCG') 

Presence/Absence analysis for proteins found only in Human

hs_presAbs = peptideLevel_PresAbsDE(subset_presAbs$sub_unique_mm_list[[2]], 
                                    treats[[2]], 
                                    subset_presAbs$sub_unique_prot.info[[2]], 
                                    pr_ppos=3) 

plot_volcano_wLab(hs_presAbs$FC, hs_presAbs$BH_P_val, hs_presAbs$GeneID, 
                  FC_cutoff=.5, PV_cutoff=.05, 'HS Pres/Abs CG vs mCG') 

\newline

References

1. Karpievitch, Y.V., et al., A statistical framework for protein quantitation in bottom-up MS-based proteomics. Bioinformatics, 2009. 25(16): p. 2028-34.

2. Karpievitch, Y.V., et al., Normalization of peak intensities in bottom-up MS-based proteomics using singular value decomposition. Bioinformatics, 2009. 25(19): p. 2573-80.

3. Taylor, S.L., et al., Multivariate two-part statistics for analysis of correlated mass spectrometry data from multiple biological specimens. Bioinformatics, 2017. 33(1): p. 17-25.

\newline

R Session Information

sessionInfo()

ProteoMM documentation built on Nov. 8, 2020, 5:57 p.m.