New unit and associated FASTA files

BIN-ALI-Similarity.R

@@ -3,67 +3,267 @@
 # Purpose:  A Bioinformatics Course:
 #              R code accompanying the BIN-ALI-Similarity unit.
 #
-# Version:  0.1
+# Version:  1.0
 #
-# Date:     2017  08  28
+# Date:     2017  10  20
 # Author:   Boris Steipe (boris.steipe@utoronto.ca)
 #
 # Versions:
+#           1.0    Refactored for 2017; add aaindex, ternary plot.
 #           0.1    First code copied from 2016 material.
-
+#
 #
 # TODO:
 #
 #
 # == DO NOT SIMPLY  source()  THIS FILE! =======================================
-
+#
 # If there are portions you don't understand, use R's help system, Google for an
 # answer, or ask your instructor. Don't continue if you don't understand what's
 # going on. That's not how it works ...
-
+#
 # ==============================================================================
  
-# = 1 Mutation Data matrix
+#TOC> ==========================================================================
+#TOC> 
+#TOC>   Section  Title                    Line
+#TOC> ----------------------------------------
+#TOC>   1        Amino Acid Properties      40
+#TOC>   2        Mutation Data matrix      150
+#TOC>   3        Background score          188
+#TOC> 
+#TOC> ==========================================================================
+ 
+
+
+
+# =    1  Amino Acid Properties  ===============================================
+
+# A large collection of amino acid property tables is available via the seqinr
+# package:
+
+if (!require(seqinr)) {
+  install.packages("seqinr")
+  library(seqinr)
+}
+
+# A true Labor of Love has gone into the compilation of the seqinr "aaindex"
+#  data:
+
+?aaindex
+data(aaindex)  # load the aaindex list from the package
+
+length(aaindex)
+
+# Here are all the index descriptions
+for (i in 1:length(aaindex)) {
+  cat(paste(i, ": ", aaindex[[i]]$D, "\n", sep=""))
+}
+
+# It's a bit cumbersome to search through the descriptions ... here is a
+# function to make this easier:
+
+searchAAindex <- function(patt) {
+  # Searches the aaindex descriptions for regular expression "patt"
+  # and prints index number and description.
+  hits <- which(sapply(aaindex, function(x) length(grep(patt, x$D)) > 0))
+  for (i in seq_along(hits)) {
+    cat(sprintf("%3d\t%s\n", hits[i], aaindex[[ hits[i] ]]$D))
+  }
+}
+
+
+searchAAindex("free energy")          # Search for "free energy"
+searchAAindex("(size)|(volume)")      # Search for "size" or "volume":
+
+
+
+
+# Let's examine ...
+# ... a hydrophobicity index
+(Y <- aaindex[[528]][c("D", "I")])
+
+# ... a volume index
+(V <- aaindex[[150]][c("D", "I")])
+
+# ... and one of our own: side-chain pK values as reported by
+# Pace et al. (2009) JBC 284:13285-13289, with non-ionizable pKs set
+# to 7.4 (physiological pH)
+K <- list(I = c( 7.4,   # Ala
+                12.3,   # Arg
+                 7.4,   # Asn
+                 3.9,   # Asp
+                 8.6,   # Cys
+                 7.4,   # Gln
+                 4.3,   # Glu
+                 7.4,   # Gly
+                 6.5,   # His
+                 7.4,   # Ile
+                 7.4,   # Leu
+                10.4,   # Lys
+                 7.4,   # Met
+                 7.4,   # Phe
+                 7.4,   # Pro
+                 7.4,   # Ser
+                 7.4,   # Thr
+                 7.4,   # Trp
+                 9.8,   # Tyr
+                 7.4))  # Val
+names(K$I) <- c("Ala","Arg","Asn","Asp","Cys","Gln","Glu","Gly","His","Ile",
+                "Leu","Lys","Met","Phe","Pro","Ser","Thr","Trp","Tyr","Val")
+
+
+# Given these biophysical indices, how similar are the amino acids? We have three-dimensions of measures here. Scatterplots can only display two dimensions ...
+plot(Y$I, V$I, col="white", xlab = "hydrophobicity", ylab = "volume")
+text(Y$I, V$I, names(Y$I))
+
+plot(Y$I, K$I, col="white", xlab = "hydrophobicity", ylab = "pK")
+text(Y$I, K$I, names(Y$I))
+
+# ... but how do we plot 3D data? Plotting into a 3D cube is possible, but such
+# plots are in general unintuitive and hard to interpret. One alternative is a
+# so-called "ternary plot":
+
+if (!require(ggtern)) {
+  install.packages("ggtern")
+  library(ggtern)
+}
+
+# collect into data frame, normalize to (0.05, 0.95)
+myDat <- data.frame("phi" = 0.9*(((Y$I-min(Y$I))/(max(Y$I)-min(Y$I))))+0.05,
+                    "vol" = 0.9*(((V$I-min(V$I))/(max(V$I)-min(V$I))))+0.05,
+                    "pK"  = 0.9*(((K$I-min(K$I))/(max(K$I)-min(K$I))))+0.05,
+                    stringsAsFactors = FALSE)
+rownames(myDat) <- names(Y$I)
+
+ggtern(data = myDat,
+       aes(x = vol,
+           y = phi,
+           z = pK,
+           label = rownames(myDat))) +
+  geom_text()
+
+# This results in a mapping of amino acids relative to each other that is
+# similar to the Venn diagram you have seen in the notes.
+
+
+# =    2  Mutation Data matrix  ================================================
+
+# A mutation data matrix encodes all amino acid pairscores in a matrix.
+
+# The Biostrings package contains the most common mutation data matrices.
 
-# First, we install and load the Biostrings package.
 if (!require(Biostrings, quietly=TRUE)) {
   source("https://bioconductor.org/biocLite.R")
   biocLite("Biostrings")
   library(Biostrings)
 }
 
-
-# Biostrings contains mutation matrices and other useful datasets
 data(package = "Biostrings")
 
-# Let's load BLOSUM62
+# Let's load the BLOSUM62 mutation data matrix from the package
 data(BLOSUM62)
 
-# ... and see what it contains. (You've seen this before, right?)
+# ... and see what it contains. (You've seen this matrix before.)
 BLOSUM62
 
-# We can simply access values via the row/column names to look at the data
+# We can simply access values via the row/column names.
-# for the questions I asked in the Assignment on the Wiki:
+# Identical amino acids have high scores ...
-BLOSUM62["H", "H"]
+BLOSUM62["H", "H"]   # Score for a pair of two histidines
-BLOSUM62["S", "S"]
+BLOSUM62["S", "S"]   # Score for a pair of two serines
 
-BLOSUM62["L", "K"]
+# Similar amino acids have low positive scores ...
-BLOSUM62["L", "I"]
+BLOSUM62["L", "I"]   # Score for a leucine / lysine pair
+BLOSUM62["F", "Y"]   # etc.
+
+# Dissimilar amino acids have negative scores ...
+BLOSUM62["L", "K"]   # Score for a leucine / lysine pair
+BLOSUM62["Q", "P"]   # etc.
 
 
-BLOSUM62["R", "W"]
+BLOSUM62["R", "W"]   # the matrix is symmetric!
-BLOSUM62["W", "R"]   # the matrix is symmetric!
+BLOSUM62["W", "R"]
 
 
+# =    3  Background score  ====================================================
 
+# 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?
 
-# = 1.1 <<<Subsection>>>
+# If we sample amino acid pairs at random, we will get a score that is the
+# average of the individual pairscores in the matrix. Omitting the ambiguity
+# codes and the gap character:
 
+sum(BLOSUM62[1:20, 1:20])/400
 
+# But that score could be higher for real sequences, for which the amino acid
+# distribution is not random. For example membrane proteins have a large number
+# of hydrophobic residues - an alignment of unrelated proteins might produce
+# positive scores. And there are other proteins with biased amino acid
+# compositions, in particular poteins that interact with multiple other
+# proteins. Let's test how this impacts the background score by comparing a
+# sequence with shuffled sequences. These have the same composition, but are
+# obvioulsy not homologous. The data directory contains the FASTA file for the
+# PDB ID 3FG7 - a villin headpiece structure with a large amount of
+# low-complexity amino acid sequence ...
 
-# = 1 Tasks
+aa3FG7 <- readAAStringSet("./data/3FG7.fa")[[1]]
 
+# ... and the FASTA file for the E. coli OmpG outer membrane porin (PDB: 2F1C)
+# with an exceptionally high percentage of hydrophobic residues.
 
+aa2F1C <- readAAStringSet("./data/2F1C.fa")[[1]]
+
+# Here is a function that takes two sequences and
+# returns their average pairscore.
+
+averagePairScore <- function(a, b, MDM = BLOSUM62) {
+  # Returns average pairscore of two sequences.
+  # Parameters:
+  #    a, b   chr   amino acid sequence string
+  #    MDM          mutation data matrix. Default is BLOSUM62
+  # Value:    num   average pairscore.
+  a <- unlist(strsplit(a, ""))
+  b <- unlist(strsplit(b, ""))
+  v <- 0
+  for (i in seq_along(a)) {
+    v <- v + MDM[ a[i], b[i] ]
+  }
+  return(v / length(a))
+}
+
+orig3FG7 <- toString(aa3FG7)
+orig2F1C <- toString(aa2F1C)
+N <- 1000
+scores3FG7 <- numeric(N)
+scores2F1C <- numeric(N)
+for (i in 1:N) {
+  scores3FG7[i] <- averagePairScore(orig3FG7, toString(sample(aa3FG7)))
+  scores2F1C[i] <- averagePairScore(orig2F1C, toString(sample(aa2F1C)))
+}
+
+# Plot the distributions
+hist(scores3FG7,
+     col="#5599EE33",
+     breaks = seq(-1.5, 0, by=0.1),
+     main = "Pairscores for randomly shuffled sequences",
+     xlab = "Average pairscore from BLOSUM 62")
+hist(scores2F1C,
+     col="#55EE9933",
+     breaks = seq(-1.5, 0, by=0.1),
+     add = TRUE)
+abline(v = sum(BLOSUM62[1:20, 1:20])/400, col = "firebrick", lwd = 2)
+legend('topright',
+       c("3FG7 (villin)", "2F1C (OmpG)"),
+       fill = c("#5599EE33", "#55EE9933"), bty = 'n',
+       inset = 0.1)
+
+# This is an important result: even though we have shuffled significantly biased
+# sequences, and the average scores trend above the average of the mutation data
+# matrix, the average scores still remain comfortably below zero. This means
+# that we can't (in general) improve a high-scoring alignment by simply
+# extending it with randomly matched residues. We will only improve the score if
+# the similarity of newly added residues is larger than what we expect to get by
+# random chance!
 
 
 # [END]

data/2F1C.fa

@@ -0,0 +1,5 @@
+>2F1C:X|PDBID|CHAIN|SEQUENCE
+EERNDWHFNIGAMYEIENVEGYGEDMDGLAEPSVYFNAANGPWRIALAYYQEGPVDYSAGKRGTWFDRPELEVHYQFLEN
+DDFSFGLTGGFRNYGYHYVDEPGKDTANMQRWKIAPDWDVKLTDDLRFNGWLSMYKFANDLNTTGYADTRVETETGLQYT
+FNETVALRVNYYLERGFNMDDSRNNGEFSTQEIRAYLPLTLGNHSVTPYTRIGLDRWSNWDWQDDIEREGHDFNRVGLFY
+GYDFQNGLSVSLEYAFEWQDHDEGDSDKFHYAGVGVNYSFHHHHHH

data/3FG7.fa

@@ -0,0 +1,6 @@
+>3FG7:A|PDBID|CHAIN|SEQUENCE
+MAEEHHHHHHHHLEVLFQGPGRPKTHTVGSVAKVEQVKFDATSMHVKPQVAAQQKMVDDGSGEVQVWRIENLELVPVDSK
+WLGHFYGGDCYLLLYTYLIGEKQHYLLYVWQGSQASQDEITASAYQAVILDQKYNGEPVQIRVPMGKEPPHLMSIFKGRM
+VVYQGGTSRTNNLETGPSTRLFQVQGTGANNTKAFEVPARANFLNSNDVFVLKTQSCCYLWCGKGCSGDEREMAKMVADT
+ISRTEKQVVVEGQEPANFWMALGGKAPYANTKRLQEENLVITPRLFECSNKTGRFLATEIPDFNQDDLEEDDVFLLDVWD
+QVFFWIGKHANEEEKKAAATTAQEYLKTHPSGRDPETPIIVVKQGHEPPTFTGWFLAWDPFKWSGIHVVPNLSPLSNN