Evaluation of the hypothesis underlying protein complex detection algorithm
Junyan Lu
2020-06-03
Last updated: 2020-06-03
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Objective
In this analysis, I will evaluate whether the underyling hypotheses for protein complex detection algorithms is true for our CLL proteomic datasets.
There are mainly two assumptions:
The protein pairs in complexes have more conserved stoichiometry than proteins not in complexes. This is the assumption underlying Marija’s algorithm.
The expressions of the protein pairs in complexes are more correlated than proteins not in pairs. This is the assumption underlying differential correlation algorithm.
Conclusion
Based on the analyses below, the hypotheses that proteins in complexes have higher conservativeness of stoichiometry or higher correlation are true in some extent, but the difference is very small. Therefore, I would not rely on either of the hypothesis for detecting differential complexes formation related to trisomy12 or IGHV.
Analyses
Prepare datasets
load("../output/proteomic_LUMOS_20200430.RData")
load("../../var/patmeta_200522.RData")
load("../../var/ddsrna_180717.RData")Preprocessing protein and RNA data
#subset samples and genes
overSampe <- intersect(colnames(dds), colnames(protCLL))
overGene <- intersect(rownames(dds), rowData(protCLL)$ensembl_gene_id)
ddsSub <- dds[overGene, overSampe]
protSub <- protCLL[match(overGene, rowData(protCLL)$ensembl_gene_id),overSampe]
rowData(ddsSub)$uniprotID <- rownames(protSub)[match(rownames(ddsSub),rowData(protSub)$ensembl_gene_id)]
#vst
ddsSub.vst <- varianceStabilizingTransformation(ddsSub)Processing protein complex data
int_pairs <- read_delim("../data/proteins_in_complexes", delim = "\t") %>%
mutate(Reactome = grepl("Reactome",Evidence_supporting_the_interaction),
Corum = grepl("Corum",Evidence_supporting_the_interaction)) %>%
filter(ProtA %in% rownames(protSub) & ProtB %in% rownames(protSub)) %>%
mutate(pair=map2_chr(ProtA, ProtB, ~paste0(sort(c(.x,.y)), collapse = "-"))) %>%
mutate(database = case_when(
Reactome & Corum ~ "both",
Reactome & !Corum ~ "Reactome",
!Reactome & Corum ~ "Corum",
TRUE ~ "other"
)) %>% mutate(inComplex = "yes")Question 1: do proteins in complexes really have more conserved stoichiometry?
I will compare the distribution of the ratio of expressions of proteins pairs in complexes and not in complexes. If there’s a higher conservativeness in stoichiometry, the distribution of ratios should be narrower, i.e, smaller standard deviation.
Calculate the ratios of protein pairs in complexes
stoTab <- int_pairs %>% select(ProtA, ProtB, pair, Reactome, Corum, database, inComplex)
protMat <- assays(protSub)[["QRILC"]]
listA <- int_pairs$ProtA
listB <- int_pairs$ProtB
sdRatio <- rep(NA,nrow(int_pairs))
for (i in seq(length(sdRatio))) {
idA <- listA[i]
idB <- listB[i]
logRatio <- log2(protMat[idA,]) - log2(protMat[idB,])
sdRatio[i] <- sd(logRatio)
}
stoTab$sdRatio <- sdRatio
ggplot(stoTab, aes(x=sdRatio, fill = database, col = database, y=..density..)) +
geom_histogram(position = "identity", alpha = 0.5) +
xlab("standard deviation of ratios")
The knowledge of complexes can be obtained from different databases. They may have different reliability. But based on this plot, there’s no significant difference among different databases.
Calculate the ratios of protein pairs not in complexes
Here, I will calculate the ratios of 5000 random protein pairs that are not involved in complexes
n <- nrow(int_pairs)
n <- 5000
allProt <- unique(c(int_pairs$ProtA, int_pairs$ProtB))
randSto <- tibble(ProtA = rep("",n), ProtB = rep("",n), sdRatio = rep(0,n), inComplex ="no")
i <- 0
while (i <= n-1) {
ProtA <- sample(allProt, 1)
ProtB <- sample(allProt, 1)
pair <- paste0(sort(c(ProtA, ProtB)),collapse = "-")
if (!pair %in% stoTab$pair) {
#accept
i <- i + 1
randSto[i, 1] <- ProtA
randSto[i, 2] <- ProtB
logRatio <- log2(protMat[ProtA,]) - log2(protMat[ProtB,])
randSto[i, 3] <- sd(logRatio)
}
}Compare the standard deviation of expression ratios of pairs in and not in complexes
For all protein pairs
compareTab <- bind_rows(stoTab, randSto)
ggplot(compareTab, aes(x=sdRatio, fill = inComplex, col = inComplex, y=..density..)) +
geom_histogram(position = "identity", alpha = 0.5) +
xlab("standard deviation of ratios")
There’s a trend that the protein pairs in complexes have slightly lower standard deviations of expression ratio, indicating more conserved stoichiometry, but the difference is very small.
For all protein pairs with stronger evidence of complex (present in both Corum and Reactome databases)
compareTab <- bind_rows(stoTab, randSto) %>%
filter(database %in% c("both",NA))
ggplot(compareTab, aes(x=sdRatio, fill = inComplex, col = inComplex, y=..density..)) +
geom_histogram(position = "identity", alpha = 0.5)
Not too much difference.
Question 2: do protein pairs in complexes really have higher correlation of expression?
I will compare the Pearson correlation coefficients of protein pairs in complexes and not in complexes. A larger coefficient means higher correlation.
Calculate correlations for protein pairs in complexes
corTab <- int_pairs %>% select(ProtA, ProtB, pair, Reactome, Corum, database, inComplex)
protMat <- assays(protSub)[["QRILC"]]
listA <- int_pairs$ProtA
listB <- int_pairs$ProtB
coefList <- rep(NA,nrow(int_pairs))
for (i in seq(length(sdRatio))) {
idA <- listA[i]
idB <- listB[i]
coef <- cor(protMat[idA,], protMat[idB,])
coefList[i] <- coef
}
corTab$coef <- coefList
ggplot(corTab, aes(x=coef, fill = database, col = database, y=..density..)) +
geom_histogram(position = "identity", alpha = 0.5)
It seems if the protein pairs are annotated as complexes in both Corum and Reactome databases (stronger evidence), they tend to have higher correlation coefficient.
Calculate correlations for random protein pairs not in complexes
n <- nrow(int_pairs)
n <- 5000
allProt <- unique(c(int_pairs$ProtA, int_pairs$ProtB))
randCoef <- tibble(ProtA = rep("",n), ProtB = rep("",n), coef = rep(0,n), inComplex ="no")
i <- 0
while (i <= n-1) {
ProtA <- sample(allProt, 1)
ProtB <- sample(allProt, 1)
pair <- paste0(sort(c(ProtA, ProtB)),collapse = "-")
if (!pair %in% corTab$pair) {
#accept
i <- i + 1
randCoef[i, 1] <- ProtA
randCoef[i, 2] <- ProtB
coef <- cor(protMat[ProtA,], protMat[ProtB,])
randCoef[i, 3] <- coef
}
}Compare the correlation coefficients of pairs in and not in complexes
For all protein pairs
compareTab <- bind_rows(corTab, randCoef)
ggplot(compareTab, aes(x=coef, fill = inComplex, col = inComplex, y=..density..)) +
geom_histogram(position = "identity", alpha = 0.5)
There’s indeed a trend that protein pairs in complex have higher coefficient than protein pairs that not in complexes.
For all protein pairs with stronger evidence of complex (present in both Corum and Reactome databases)
Compare (only from both)
compareTab <- bind_rows(corTab, randCoef) %>%
filter(database %in% c("both",NA))
ggplot(compareTab, aes(x=coef, fill = inComplex, col = inComplex, y=..density..)) +
geom_histogram(position = "identity", alpha = 0.5)
The difference is stronger if I only include proteins with stronger evidence of forming complexes.
However, the correlations observed for protein abundance can also be due to the correlation in RNA expression, not neccessary due to complex formation. I will also test if the RNA expression of protein pairs shows this trend
Correlations on RNA expression level
Correlations of RNA expression levels of proteins in complexs
corTab.rna <- int_pairs %>% select(ProtA, ProtB, pair, Reactome, Corum, database, inComplex)
protMat <- assay(ddsSub.vst)
rownames(protMat) <- rowData(ddsSub.vst)$uniprotID
listA <- int_pairs$ProtA
listB <- int_pairs$ProtB
coefList <- rep(NA,nrow(int_pairs))
for (i in seq(length(coefList))) {
idA <- listA[i]
idB <- listB[i]
coef <- cor(protMat[idA,], protMat[idB,])
coefList[i] <- coef
}
corTab.rna$coef <- coefList
ggplot(corTab.rna, aes(x=coef, fill = database, col = database, y=..density..)) +
geom_histogram(position = "identity", alpha = 0.5)
It seems that the RNA expressions of proteins in complex also have higher correlation. The trend is stronger for proteins with stronger evidences of being in complexes.
Correlations of RNA expression levels of random protein pairs not in complexes
n <- nrow(int_pairs)
n <- 5000
allProt <- unique(c(int_pairs$ProtA, int_pairs$ProtB))
randCoef.rna <- tibble(ProtA = rep("",n), ProtB = rep("",n), coef = rep(0,n), inComplex ="no")
i <- 0
while (i <= n-1) {
ProtA <- sample(allProt, 1)
ProtB <- sample(allProt, 1)
pair <- paste0(sort(c(ProtA, ProtB)),collapse = "-")
if (!pair %in% corTab$pair) {
#accept
i <- i + 1
randCoef.rna[i, 1] <- ProtA
randCoef.rna[i, 2] <- ProtB
coef <- cor(protMat[ProtA,], protMat[ProtB,])
randCoef.rna[i, 3] <- coef
}
}Compare the correlation coefficients of pairs in and not in complexes
For all pairs
compareTab <- bind_rows(corTab.rna, randCoef.rna)
ggplot(compareTab, aes(x=coef, fill = inComplex, col = inComplex, y=..density..)) +
geom_histogram(position = "identity", alpha = 0.5)
For all pairs with stronger evidence of complex (present in both Corum and Reactome databases)
compareTab <- bind_rows(corTab.rna, randCoef.rna) %>%
filter(database %in% c("both",NA))
ggplot(compareTab, aes(x=coef, fill = inComplex, col = inComplex, y=..density..)) +
geom_histogram(position = "identity", alpha = 0.5)
The trend is almost the same as for protein expressions. Which means the higher correlation observed for protein pairs in complexes can simply because their RNA expressions are correlated. Not necessarily because of the complex formation.
Compare the correlation coefficients of protein expression and RNA expression for protein pairs that are annotated as in complexes
compareTab <- bind_rows(mutate(corTab, set = "Protein"), mutate(corTab.rna, set = "RNA"))
ggplot(compareTab, aes(x=coef, fill = set, col = set, y=..density..)) +
geom_histogram(position = "identity", alpha = 0.5)
There’s no strong difference. The RNA expressions of protein pairs in complexes even have higher correlations than the corresponding protein expression. This somewaht contradicts previous report that the proteins expressions are more correlations for proteins in complexes than their RNA expressions. However, one explanation is that, if two proteins are annotated as complexes, there’s also a high chance that they are in the same pathway and therefore, their RNAs are also co-expressed.
sessionInfo()R version 3.6.0 (2019-04-26)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS 10.15.4
Matrix products: default
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