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-################# Linear model: Least-Squares Fit #################
-g.breaks <- g.hist$breaks[-c(1)] # remove 0
-g.probs <- g.hist$density[-1] # make lengths match
-# Need to clean up probabilities that are 0
-nz.probs.mask <- g.probs!=0
-g.breaks.clean <- g.breaks[nz.probs.mask]
-g.probs.clean <- g.probs[nz.probs.mask]
-plot(log(g.breaks.clean), log(g.probs.clean))
-g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
-summary(g.fit)
-alpha.LM <- coef(g.fit)[2]
-lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3, lwd=3)
-################# Max-Log-Likelihood #################
-n <- length(g.breaks.clean)
-kmin <- g.breaks.clean[1]
-alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
-alpha.ML
-lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4, lwd=3)
-plot(log(g.breaks.clean), log(g.probs.clean))
-g.breaks.clean <- g.breaks[nz.probs.mask]
-g.probs.clean <- g.probs[nz.probs.mask]
-plot(log(g.breaks.clean), log(g.probs.clean))
-# Lab 9 for the University of Tulsa's CS-6643 Bioinformatics Course
-# Pairwise Sequence Alignment with Dynamic Programming
-# Professor: Dr. McKinney, Fall 2022
-# Noah L. Schrick - 1492657
-## Set Working Directory to file directory - RStudio approach
-setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
-#### Part A: Specifying the Input
-## Score Rules and Seqs
-x_str <- "ATAC"   # side sequence
-y_str <- "GTGTAC" # top sequence
-match_score <- 3
-mismatch_score <- -1
-gap_penalty <- -4
-## Substitution Matrix
-dna.letters<-c("A","C","G","T")
-num.letters <- length(dna.letters)
-S<-data.frame(matrix(0,nrow=num.letters,ncol=num.letters))  # data frame
-rownames(S)<-dna.letters; colnames(S)<-dna.letters
-for (i in 1:4){
-for (j in 1:4){
-if(dna.letters[i]==dna.letters[j]){
-S[i,j]<- match_score
-}
-else{
-S[i,j]<- mismatch_score
-}
-}
-}
-#### Part B: Alignment Score Matrix (F) and Traceback Matrix (T)
-x <- unlist(strsplit(x_str, ""))
-y <- unlist(strsplit(y_str, ""))
-x.len <- length(x)
-y.len <- length(y)
-Fmat<-matrix(0,nrow=x.len+1,ncol=y.len+1)
-Tmat<-Fmat # 0's to start
-rownames(Fmat)<-c("-",x); colnames(Fmat)<-c("-",y)
-rownames(Tmat)<-c("-",x); colnames(Tmat)<-c("-",y)
-# create first row and column
-Fmat[,1]<- seq(from=0,len=x.len+1,by=-abs(gap_penalty))
-Fmat[1,]<- seq(from=0,len=y.len+1,by=-abs(gap_penalty))
-Tmat[,1]<- rep(2,x.len+1)  # 2 means align with a gap in the upper seq
-Tmat[1,]<- rep(3,y.len+1)  # 3 means align with a gap in the side seq
-x
-T
-Tmat
-Fmat
-#### Part C: Building Fmat and Tmat
-my.numbers <- c(7,9,-4)
-max(my.numbers)
-which.max(my.numbers)
-#### Part C: Building Fmat and Tmat
-my.numbers <- c(9,9,-4)
-which.max(my.numbers)
-S[1,1]
-S
-S[1,2]
-rowname(Fmat[i])
-(Fmat[1])
-(Fmat[2])
-(Fmat[2,])
-rownames(Fmat)
-rownames(Fmat[1])
-rownames(Fmat[2])
-rownames(Fmat[2,1])
-rownames(Fmat)[1]
-rownames(Fmat)[2]
-S[rownames(Fmat)[2], colnames(Fmat)[2])
-S[rownames(Fmat)[2], colnames(Fmat)[2]]
-#### Part C: Building Fmat and Tmat
-for (i in 2:nrow(Fmat)){
-for (j in 2:ncol(Fmat)){    # use F recursive rules
-test_three_cases <- c(Fmat[i-1, j-1] + S[rownames(Fmat)[i], colnames(Fmat)[j]],   # 1 mis/match
-# Fmat[i-1, j] + gap_penalty,    # 2 up-gap
-Fmat[i, j-1] + gap_penalty)  # 3 left-gap
-Fmat[i,j]=max(test_three_cases)
-Tmat[i,j]=which.max(test_three_cases)
-}
-}
-final_score <- Fmat[nrow(Fmat),ncol(Fmat)]
-Fmat
-final_score
-#### Part C: Building Fmat and Tmat
-for (i in 2:nrow(Fmat)){
-for (j in 2:ncol(Fmat)){    # use F recursive rules
-test_three_cases <- c(Fmat[i-1, j-1] + S[rownames(Fmat)[i], colnames(Fmat)[j]],   # 1 mis/match
-Fmat[i-1, j] + gap_penalty,    # 2 up-gap
-Fmat[i, j-1] + gap_penalty)  # 3 left-gap
-Fmat[i,j]=max(test_three_cases)
-Tmat[i,j]=which.max(test_three_cases)
-}
-}
-final_score <- Fmat[nrow(Fmat),ncol(Fmat)]
-Fmat
-gap_penalty
-Fmat[1,5]
-Fmat[1,6]
-Tmat
-final_score
-## Aligning from Tmat
-m <- nrow(Fmat)
-n <- ncol(Fmat)
-top_seq <- list()
-side_seq <- list()
-while (m>0 && n>0){
-if (Tmat[m,n] == 3){
-top_seq.append(rownames(Tmat)[m])
-side_seq.append("-")
-m--
-}  else if (Tmat[m,n] == 2){
-while (m>0 && n>0){
-if (Tmat[m,n] == 3){
-top_seq.append(rownames(Tmat)[m])
-side_seq.append("-")
-m--
-}
-else if (Tmat[m,n] == 2){
-while (m>0 && n>0){
-if (Tmat[m,n] == 3){
-top_seq.append(rownames(Tmat)[m])
-side_seq.append("-")
-m--
-}
-while (m>0 && n>0){
-if (Tmat[m,n] == 3){
-top_seq.append(rownames(Tmat)[m])
-side_seq.append("-")
-m--
-}  else if (Tmat[m,n] == 2){
-n <- n-1
-while (m>0 && n>0){
-if (Tmat[m,n] == 3){
-top_seq.append(rownames(Tmat)[m])
-side_seq.append("-")
-m <- m-1
-}  else if (Tmat[m,n] == 2){
-top_seq.append("-")
-side_seq.append(colnames(Tmat)[n])
-n <- n-1
-}  else{
-top_seq.append(rownames(Tmat)[m])
-side_seq.append(colnames(Tmat)[n])
-m <- m-1
-n <- n-1
-}
-}
-while (m>0 && n>0){
-if (Tmat[m,n] == 3){
-top_seq <- append(top_seq, rownames(Tmat)[m])
-side_seq <- append(side_seq, "-")
-m <- m-1
-}  else if (Tmat[m,n] == 2){
-top_seq <- append(top_seq, "-")
-side_seq <- append(side_seq, colnames(Tmat)[n])
-n <- n-1
-}  else{
-top_seq <- append(top_seq, rownames(Tmat)[m])
-side_seq <- append(side_seq, colnames(Tmat)[n])
-m <- m-1
-n <- n-1
-}
-}
-top_seq
-side_seq
-top_seq[1]
-paste(top_seq, collapse=',')
-paste(top_seq, collapse=',')
-paste(side_seq, collapse=',')
-paste(rev(top_seq), collapse=',')
-paste(rev(side_seq), collapse=',')
-## Aligning from Tmat
-m <- nrow(Fmat)
-n <- ncol(Fmat)
-m
-Tmat[5,5]
-rownames(Tmat)[5]
-colnames(Tmat)[5]
-n
-rownames(Tmat)[5,7]
-rownames(Tmat)[7]
-colnames(Tmat)[7]
-paste(rev(top_seq), collapse=',')
-paste(rev(side_seq), collapse=',')
-side_seq <- list()
-top_seq <- list()
-top_seq <- append(top_seq, rownames(Tmat)[m])
-side_seq <- append(side_seq, colnames(Tmat)[n])
-paste(rev(top_seq), collapse=',')
-paste(rev(side_seq), collapse=',')
-m <- m-1
-n <- n-1
-top_seq <- append(top_seq, rownames(Tmat)[m])
-side_seq <- append(side_seq, colnames(Tmat)[n])
-m <- m-1
-n <- n-1
-paste(rev(top_seq), collapse=',')
-paste(rev(side_seq), collapse=',')
-top_seq <- append(top_seq, rownames(Tmat)[m])
-side_seq <- append(side_seq, colnames(Tmat)[n])
-m <- m-1
-n <- n-1
-paste(rev(top_seq), collapse=',')
-paste(rev(side_seq), collapse=',')
-?rbind
-curr_align_col <- rbind(x[n-1],y[m-1])
-curr_align_col
-## Aligning from Tmat
-m <- nrow(Tmat)
-n <- ncol(Tmat)
-seq_align <- character()
-while ((n+m) != 2){
-if (Tmat[m,n] == 3){
-curr_align_col <- rbind("-",y[m-1])
-alignment <- cbind(curr_align_col,alignment)
-m <- m-1
-}  else if (Tmat[m,n] == 2){
-curr_align_col <- rbind(x[n-1],"-")
-alignment <- cbind(curr_align_col,alignment)
-n <- n-1
-}  else{
-curr_align_col <- rbind(x[n-1], y[m-1])
-alignment <- cbind(curr_align_col, alignment)
-m <- m-1
-n <- n-1
-}
-}
-seq_align <- character()
-while ((n+m) != 2){
-if (Tmat[m,n] == 3){
-curr_align_col <- rbind("-",y[m-1])
-seq_align <- cbind(curr_align_col,seq_align)
-m <- m-1
-}  else if (Tmat[m,n] == 2){
-curr_align_col <- rbind(x[n-1],"-")
-seq_align <- cbind(curr_align_col,seq_align)
-n <- n-1
-}  else{
-curr_align_col <- rbind(x[n-1], y[m-1])
-seq_align <- cbind(curr_align_col, seq_align)
-m <- m-1
-n <- n-1
-}
-}
-?cbind
-## Aligning from Tmat
-n <- nrow(Tmat)
-m <- ncol(Tmat)
-seq_align <- character()
-while ((n+m) != 2){
-if (Tmat[m,n] == 3){
-curr_align_col <- rbind("-",y[m-1])
-seq_align <- cbind(curr_align_col,seq_align)
-m <- m-1
-}  else if (Tmat[m,n] == 2){
-curr_align_col <- rbind(x[n-1],"-")
-seq_align <- cbind(curr_align_col,seq_align)
-n <- n-1
-}  else{
-curr_align_col <- rbind(x[n-1], y[m-1])
-seq_align <- cbind(curr_align_col, seq_align)
-m <- m-1
-n <- n-1
-}
-}
-## Aligning from Tmat
-m <- nrow(Tmat)
-n <- ncol(Tmat)
-seq_align <- character()
-while ((n+m) != 2){
-if (Tmat[m,n] == 3){
-curr_align_col <- rbind("-",y[m-1])
-seq_align <- cbind(curr_align_col,seq_align)
-m <- m-1
-}  else if (Tmat[m,n] == 2){
-curr_align_col <- rbind(x[n-1],"-")
-seq_align <- cbind(curr_align_col,seq_align)
-n <- n-1
-}  else{
-curr_align_col <- rbind(x[n-1], y[m-1])
-seq_align <- cbind(curr_align_col, seq_align)
-m <- m-1
-n <- n-1
-}
-}
-seq_align
-curr_align_col
-x
-y
-n
-m
-## Aligning from Tmat
-n<-nrow(Tmat) # start at bottom right of Tmat
-m<-ncol(Tmat)
-alignment<-character()
-while( (n+m)!=2 ){
-if (Tmat[n,m]==1){
-# subtract 1 from x and y indices because they are
-# one row/col smaller than Tmat
-curr_align_col <- rbind(x[n-1],y[m-1])
-alignment <- cbind(curr_align_col,alignment)
-n=n-1; m=m-1; # move back diagonally
-}else if(Tmat[n,m]==2){
-curr_align_col <- rbind(x[n-1],"-") # put gap in top seq
-alignment <- cbind(curr_align_col,alignment)
-n=n-1 # move up
-}else{
-curr_align_col <- rbind("-",y[m-1]) # put gap in side seq
-alignment <- cbind(curr_align_col,alignment)
-m=m-1 # move left
-}
-} # end while
-alignment
-## Aligning from Tmat
-n <- nrow(Tmat)
-m <- ncol(Tmat)
-seq_align <- character()
-while( (n+m)!=2 ){
-if (Tmat[n,m]==1){
-curr_align_col <- rbind(x[n-1],y[m-1])
-seq_align <- cbind(curr_align_col,seq_align)
-n <- n-1
-m <- m-1
-}else if(Tmat[n,m]==2){
-curr_align_col <- rbind(x[n-1],"-") # put gap in top seq
-seq_align <- cbind(curr_align_col,seq_align)
-n=n-1 # move up
-}else{
-curr_align_col <- rbind("-",y[m-1]) # put gap in side seq
-seq_align <- cbind(curr_align_col,seq_align)
-m=m-1 # move left
-}
-} # end while
-alignment
-## Aligning from Tmat
-n <- nrow(Tmat)
-m <- ncol(Tmat)
-seq_align <- character()
-while( (n+m)!=2 ){
-if (Tmat[n,m]==1){
-curr_align_col <- rbind(x[n-1],y[m-1])
-seq_align <- cbind(curr_align_col,seq_align)
-n <- n-1
-m <- m-1
-}else if(Tmat[n,m]==2){
-curr_align_col <- rbind(x[n-1],"-")
-seq_align <- cbind(curr_align_col,seq_align)
-n <- n-1
-}else{
-curr_align_col <- rbind("-",y[m-1])
-seq_align <- cbind(curr_align_col,seq_align)
-m <- m-1
-}
-} # end while
-alignment
-seq_align
-#### Part D: Convert to functions
-make.alignment.matrices <- function(x_str, y_str, match_score, mismatch_score,
-gap_penalty){
-## Substitution Matrix
-dna.letters<-c("A","C","G","T")
-num.letters <- length(dna.letters)
-S<-data.frame(matrix(0,nrow=num.letters,ncol=num.letters))  # data frame
-rownames(S)<-dna.letters; colnames(S)<-dna.letters
-for (i in 1:4){
-for (j in 1:4){
-if(dna.letters[i]==dna.letters[j]){
-S[i,j]<- match_score
-}
-else{
-S[i,j]<- mismatch_score
-}
-}
-}
-## F Matrix and T Matrix
-x <- unlist(strsplit(x_str, ""))
-y <- unlist(strsplit(y_str, ""))
-x.len <- length(x)
-y.len <- length(y)
-Fmat<-matrix(0,nrow=x.len+1,ncol=y.len+1)
-Tmat<-Fmat # 0's to start
-rownames(Fmat)<-c("-",x); colnames(Fmat)<-c("-",y)
-rownames(Tmat)<-c("-",x); colnames(Tmat)<-c("-",y)
-# create first row and column
-Fmat[,1]<- seq(from=0,len=x.len+1,by=-abs(gap_penalty))
-Fmat[1,]<- seq(from=0,len=y.len+1,by=-abs(gap_penalty))
-Tmat[,1]<- rep(2,x.len+1)  # 2 means align with a gap in the upper seq
-Tmat[1,]<- rep(3,y.len+1)  # 3 means align with a gap in the side seq
-## Building Fmat and Tmat
-for (i in 2:nrow(Fmat)){
-for (j in 2:ncol(Fmat)){    # use F recursive rules
-test_three_cases <- c(Fmat[i-1, j-1] + S[rownames(Fmat)[i], colnames(Fmat)[j]],   # 1 mis/match
-Fmat[i-1, j] + gap_penalty,    # 2 up-gap
-Fmat[i, j-1] + gap_penalty)  # 3 left-gap
-Fmat[i,j]=max(test_three_cases)
-Tmat[i,j]=which.max(test_three_cases)
-}
-}
-final_score <- Fmat[nrow(Fmat),ncol(Fmat)]
-return(list(Fmat=Fmat, Tmat=Tmat, score_out=final_score))
-}
-# load new input
-x_str2 <- "GATTA"  # side sequence
-y_str2 <- "GAATTC" # top sequence
-match_score <- 2
-mismatch_score <- -1
-gap_penalty <- -2
-align.list2 <- make.alignment.matrices(x_str2, y_str2, match_score,
-mismatch_score, gap_penalty)
-align.list2$Fmat
-align.list2$Tmat
-align.list2$score_out
-if (!require("gplots")) install.packages("gplots")
-library(gplots)
-Fmat2 <- align.list2$Fmat
-col = c("black","blue","red","yellow","green")
-breaks = seq(min(Fmat2),max(Fmat2),len=length(col)+1)
-heatmap.2(Fmat2[-1,-1], dendrogram='none', density.info="none",
-Rowv=FALSE, Colv=FALSE, trace='none',
-breaks = breaks, col = col,
-sepwidth=c(0.01,0.01),
-sepcolor="black",
-colsep=1:ncol(Fmat2),
-rowsep=1:nrow(Fmat2))
-#### Part E: Traceback Matrix
-show.alignment <- function(x_str,y_str,Tmat){
-################ create the alignment
-# input Tmat and the two sequences: x side seq and y is top seq
-# make character vectors out of the strings
-x<-unlist(strsplit(x_str,""))
-y<-unlist(strsplit(y_str,""))
-n<-nrow(Tmat) # start at bottom right of Tmat
-m<-ncol(Tmat)
-alignment<-character()
-while( (n+m)!=2 ){
-if (Tmat[n,m]==1){
-# subtract 1 from x and y indices because they are
-# one row/col smaller than Tmat
-curr_align_col <- rbind(x[n-1],y[m-1])
-alignment <- cbind(curr_align_col,alignment)
-n=n-1; m=m-1; # move back diagonally
-}else if(Tmat[n,m]==2){
-curr_align_col <- rbind(x[n-1],"-") # put gap in top seq
-alignment <- cbind(curr_align_col,alignment)
-n=n-1 # move up
-}else{
-curr_align_col <- rbind("-",y[m-1]) # put gap in side seq
-alignment <- cbind(curr_align_col,alignment)
-m=m-1 # move left
-}
-} # end while
-return(alignment)
-} # end function
-alignment2 <- show.alignment(x_str2,y_str2,align.list2$Tmat)
-alignment2
-write.table(alignment2,row.names=F,col.names=F,quote=F)
-## Input 3
-x_str3 <- "ATCGT"  # side sequence
-y_str3 <- "TGGTG" # top sequence
-match_score <- 1
-mismatch_score <- -2
-gap_penalty <- -1
-align.list3 <- make.alignment.matrices(x_str3, y_str3, match_score,
-mismatch_score, gap_penalty)
-align.list3$Fmat
-align.list3$Tmat
-align.list3$score_out
-col = c("black","blue","red","yellow","green")
-breaks = seq(min(Fmat3),max(Fmat3),len=length(col)+1)
-heatmap.2(Fmat3[-1,-1], dendrogram='none', density.info="none",
-Rowv=FALSE, Colv=FALSE, trace='none',
-breaks = breaks, col = col,
-sepwidth=c(0.01,0.01),
-sepcolor="black",
-colsep=1:ncol(Fmat3),
-rowsep=1:nrow(Fmat3))
-Fmat3 <- align.list3$Fmat
-align.list3$Fmat
-Fmat3 <- align.list3$Fmat
-align.list3$Tmat
-align.list3$score_out
-o
-heatmap.2(Fmat3[-1,-1], dendrogram='none', density.info="none",
-Rowv=FALSE, Colv=FALSE, trace='none',
-breaks = breaks, col = col,
-sepwidth=c(0.01,0.01),
-sepcolor="black",
-colsep=1:ncol(Fmat3),
-rowsep=1:nrow(Fmat3))
-alignment3 <- show.alignment(x_str3,y_str3,align.list3$Tmat)
-alignment3
-write.table(alignment3,row.names=F,col.names=F,quote=F)