New unit and associated FASTA files
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# Purpose: A Bioinformatics Course:
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# R code accompanying the BIN-ALI-Similarity unit.
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#
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# Version: 0.1
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# Version: 1.0
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#
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# Date: 2017 08 28
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# Date: 2017 10 20
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# Author: Boris Steipe (boris.steipe@utoronto.ca)
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#
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# Versions:
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# 1.0 Refactored for 2017; add aaindex, ternary plot.
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# 0.1 First code copied from 2016 material.
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#
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#
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# TODO:
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#
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#
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# == DO NOT SIMPLY source() THIS FILE! =======================================
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#
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# If there are portions you don't understand, use R's help system, Google for an
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# answer, or ask your instructor. Don't continue if you don't understand what's
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# going on. That's not how it works ...
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#
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# ==============================================================================
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#TOC> ==========================================================================
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#TOC>
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#TOC> Section Title Line
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#TOC> ----------------------------------------
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#TOC> 1 Amino Acid Properties 40
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#TOC> 2 Mutation Data matrix 150
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#TOC> 3 Background score 188
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#TOC>
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#TOC> ==========================================================================
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# = 1 Mutation Data matrix
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# First, we install and load the Biostrings package.
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# = 1 Amino Acid Properties ===============================================
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# A large collection of amino acid property tables is available via the seqinr
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# package:
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if (!require(seqinr)) {
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install.packages("seqinr")
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library(seqinr)
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}
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# A true Labor of Love has gone into the compilation of the seqinr "aaindex"
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# data:
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?aaindex
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data(aaindex) # load the aaindex list from the package
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length(aaindex)
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# Here are all the index descriptions
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for (i in 1:length(aaindex)) {
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cat(paste(i, ": ", aaindex[[i]]$D, "\n", sep=""))
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}
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# It's a bit cumbersome to search through the descriptions ... here is a
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# function to make this easier:
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searchAAindex <- function(patt) {
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# Searches the aaindex descriptions for regular expression "patt"
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# and prints index number and description.
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hits <- which(sapply(aaindex, function(x) length(grep(patt, x$D)) > 0))
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for (i in seq_along(hits)) {
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cat(sprintf("%3d\t%s\n", hits[i], aaindex[[ hits[i] ]]$D))
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}
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}
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searchAAindex("free energy") # Search for "free energy"
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searchAAindex("(size)|(volume)") # Search for "size" or "volume":
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# Let's examine ...
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# ... a hydrophobicity index
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(Y <- aaindex[[528]][c("D", "I")])
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# ... a volume index
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(V <- aaindex[[150]][c("D", "I")])
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# ... and one of our own: side-chain pK values as reported by
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# Pace et al. (2009) JBC 284:13285-13289, with non-ionizable pKs set
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# to 7.4 (physiological pH)
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K <- list(I = c( 7.4, # Ala
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12.3, # Arg
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7.4, # Asn
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3.9, # Asp
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8.6, # Cys
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7.4, # Gln
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4.3, # Glu
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7.4, # Gly
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6.5, # His
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7.4, # Ile
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7.4, # Leu
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10.4, # Lys
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7.4, # Met
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7.4, # Phe
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7.4, # Pro
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7.4, # Ser
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7.4, # Thr
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7.4, # Trp
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9.8, # Tyr
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7.4)) # Val
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names(K$I) <- c("Ala","Arg","Asn","Asp","Cys","Gln","Glu","Gly","His","Ile",
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"Leu","Lys","Met","Phe","Pro","Ser","Thr","Trp","Tyr","Val")
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# Given these biophysical indices, how similar are the amino acids? We have three-dimensions of measures here. Scatterplots can only display two dimensions ...
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plot(Y$I, V$I, col="white", xlab = "hydrophobicity", ylab = "volume")
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text(Y$I, V$I, names(Y$I))
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plot(Y$I, K$I, col="white", xlab = "hydrophobicity", ylab = "pK")
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text(Y$I, K$I, names(Y$I))
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# ... but how do we plot 3D data? Plotting into a 3D cube is possible, but such
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# plots are in general unintuitive and hard to interpret. One alternative is a
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# so-called "ternary plot":
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if (!require(ggtern)) {
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install.packages("ggtern")
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library(ggtern)
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}
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# collect into data frame, normalize to (0.05, 0.95)
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myDat <- data.frame("phi" = 0.9*(((Y$I-min(Y$I))/(max(Y$I)-min(Y$I))))+0.05,
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"vol" = 0.9*(((V$I-min(V$I))/(max(V$I)-min(V$I))))+0.05,
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"pK" = 0.9*(((K$I-min(K$I))/(max(K$I)-min(K$I))))+0.05,
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stringsAsFactors = FALSE)
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rownames(myDat) <- names(Y$I)
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ggtern(data = myDat,
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aes(x = vol,
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y = phi,
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z = pK,
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label = rownames(myDat))) +
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geom_text()
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# This results in a mapping of amino acids relative to each other that is
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# similar to the Venn diagram you have seen in the notes.
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# = 2 Mutation Data matrix ================================================
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# A mutation data matrix encodes all amino acid pairscores in a matrix.
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# The Biostrings package contains the most common mutation data matrices.
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if (!require(Biostrings, quietly=TRUE)) {
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source("https://bioconductor.org/biocLite.R")
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biocLite("Biostrings")
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library(Biostrings)
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}
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# Biostrings contains mutation matrices and other useful datasets
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data(package = "Biostrings")
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# Let's load BLOSUM62
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# Let's load the BLOSUM62 mutation data matrix from the package
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data(BLOSUM62)
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# ... and see what it contains. (You've seen this before, right?)
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# ... and see what it contains. (You've seen this matrix before.)
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BLOSUM62
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# We can simply access values via the row/column names to look at the data
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# for the questions I asked in the Assignment on the Wiki:
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BLOSUM62["H", "H"]
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BLOSUM62["S", "S"]
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# We can simply access values via the row/column names.
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# Identical amino acids have high scores ...
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BLOSUM62["H", "H"] # Score for a pair of two histidines
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BLOSUM62["S", "S"] # Score for a pair of two serines
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BLOSUM62["L", "K"]
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BLOSUM62["L", "I"]
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# Similar amino acids have low positive scores ...
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BLOSUM62["L", "I"] # Score for a leucine / lysine pair
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BLOSUM62["F", "Y"] # etc.
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# Dissimilar amino acids have negative scores ...
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BLOSUM62["L", "K"] # Score for a leucine / lysine pair
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BLOSUM62["Q", "P"] # etc.
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BLOSUM62["R", "W"]
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BLOSUM62["W", "R"] # the matrix is symmetric!
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BLOSUM62["R", "W"] # the matrix is symmetric!
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BLOSUM62["W", "R"]
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# = 3 Background score ====================================================
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# The mutation data matrix is designed to give high scores to homologous sequences, low scores to non-homologous sequences. What score on average should we expect for a random sequence?
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# = 1.1 <<<Subsection>>>
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# If we sample amino acid pairs at random, we will get a score that is the
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# average of the individual pairscores in the matrix. Omitting the ambiguity
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# codes and the gap character:
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sum(BLOSUM62[1:20, 1:20])/400
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# But that score could be higher for real sequences, for which the amino acid
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# distribution is not random. For example membrane proteins have a large number
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# of hydrophobic residues - an alignment of unrelated proteins might produce
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# positive scores. And there are other proteins with biased amino acid
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# compositions, in particular poteins that interact with multiple other
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# proteins. Let's test how this impacts the background score by comparing a
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# sequence with shuffled sequences. These have the same composition, but are
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# obvioulsy not homologous. The data directory contains the FASTA file for the
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# PDB ID 3FG7 - a villin headpiece structure with a large amount of
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# low-complexity amino acid sequence ...
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# = 1 Tasks
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aa3FG7 <- readAAStringSet("./data/3FG7.fa")[[1]]
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# ... and the FASTA file for the E. coli OmpG outer membrane porin (PDB: 2F1C)
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# with an exceptionally high percentage of hydrophobic residues.
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aa2F1C <- readAAStringSet("./data/2F1C.fa")[[1]]
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# Here is a function that takes two sequences and
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# returns their average pairscore.
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averagePairScore <- function(a, b, MDM = BLOSUM62) {
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# Returns average pairscore of two sequences.
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# Parameters:
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# a, b chr amino acid sequence string
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# MDM mutation data matrix. Default is BLOSUM62
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# Value: num average pairscore.
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a <- unlist(strsplit(a, ""))
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b <- unlist(strsplit(b, ""))
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v <- 0
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for (i in seq_along(a)) {
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v <- v + MDM[ a[i], b[i] ]
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}
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return(v / length(a))
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}
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orig3FG7 <- toString(aa3FG7)
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orig2F1C <- toString(aa2F1C)
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N <- 1000
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scores3FG7 <- numeric(N)
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scores2F1C <- numeric(N)
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for (i in 1:N) {
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scores3FG7[i] <- averagePairScore(orig3FG7, toString(sample(aa3FG7)))
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scores2F1C[i] <- averagePairScore(orig2F1C, toString(sample(aa2F1C)))
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}
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# Plot the distributions
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hist(scores3FG7,
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col="#5599EE33",
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breaks = seq(-1.5, 0, by=0.1),
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main = "Pairscores for randomly shuffled sequences",
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xlab = "Average pairscore from BLOSUM 62")
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hist(scores2F1C,
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col="#55EE9933",
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breaks = seq(-1.5, 0, by=0.1),
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add = TRUE)
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abline(v = sum(BLOSUM62[1:20, 1:20])/400, col = "firebrick", lwd = 2)
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legend('topright',
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c("3FG7 (villin)", "2F1C (OmpG)"),
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fill = c("#5599EE33", "#55EE9933"), bty = 'n',
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inset = 0.1)
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# This is an important result: even though we have shuffled significantly biased
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# sequences, and the average scores trend above the average of the mutation data
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# matrix, the average scores still remain comfortably below zero. This means
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# that we can't (in general) improve a high-scoring alignment by simply
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# extending it with randomly matched residues. We will only improve the score if
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# the similarity of newly added residues is larger than what we expect to get by
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# random chance!
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# [END]
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5
data/2F1C.fa
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5
data/2F1C.fa
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>2F1C:X|PDBID|CHAIN|SEQUENCE
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EERNDWHFNIGAMYEIENVEGYGEDMDGLAEPSVYFNAANGPWRIALAYYQEGPVDYSAGKRGTWFDRPELEVHYQFLEN
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DDFSFGLTGGFRNYGYHYVDEPGKDTANMQRWKIAPDWDVKLTDDLRFNGWLSMYKFANDLNTTGYADTRVETETGLQYT
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FNETVALRVNYYLERGFNMDDSRNNGEFSTQEIRAYLPLTLGNHSVTPYTRIGLDRWSNWDWQDDIEREGHDFNRVGLFY
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GYDFQNGLSVSLEYAFEWQDHDEGDSDKFHYAGVGVNYSFHHHHHH
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6
data/3FG7.fa
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6
data/3FG7.fa
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>3FG7:A|PDBID|CHAIN|SEQUENCE
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MAEEHHHHHHHHLEVLFQGPGRPKTHTVGSVAKVEQVKFDATSMHVKPQVAAQQKMVDDGSGEVQVWRIENLELVPVDSK
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WLGHFYGGDCYLLLYTYLIGEKQHYLLYVWQGSQASQDEITASAYQAVILDQKYNGEPVQIRVPMGKEPPHLMSIFKGRM
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VVYQGGTSRTNNLETGPSTRLFQVQGTGANNTKAFEVPARANFLNSNDVFVLKTQSCCYLWCGKGCSGDEREMAKMVADT
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ISRTEKQVVVEGQEPANFWMALGGKAPYANTKRLQEENLVITPRLFECSNKTGRFLATEIPDFNQDDLEEDDVFLLDVWD
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QVFFWIGKHANEEEKKAAATTAQEYLKTHPSGRDPETPIIVVKQGHEPPTFTGWFLAWDPFKWSGIHVVPNLSPLSNN
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