Add base needleman
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sub createFolderStructure{
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system("bash ./createFolderStructure.sh");
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system("bash ./folder-structure.sh");
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}
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createFolderStructure();
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@ -18,7 +18,20 @@ Here we are interested by the distance that is able to represent the transformat
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Example:
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\begin{itemize}
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\item $sub(a, b) = \begin{cases} 0 & \text{if} a = b \\ 1 &\text{otherwise} \end{cases}$.
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\item $sub(a, b) = \begin{cases} 0 & \text{if} a = b \\ 1 &\text{otherwise} \end{cases}$.
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\item $del(a) = 1$
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\item $ins(a) = 1$
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\end{itemize}
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Let $X = x_{0} x_{1} \ldots x_{m-1}$, $Y = y_{0} y_{1} \ldots y_{n-1} $
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An alignment is noted as $z = \begin{pmatrix} \bar{x}_{0} \\ \bar{y}_{0} \end{pmatrix} \ldots \begin{pmatrix} \bar{x}_{p-1} \\ \bar{y}_{p-1} \end{pmatrix}$ of size $p$. $n \leq p \leq n + m$
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$\bar{x}_{i} = x_{j}$ or $\bar{x}_{i} = \varepsilon$ for $0 \leq i \leq p-1$ and $0 \leq j \leq m - 1$
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$\bar{y}_{i} = y_{j}$ or $\bar{y}_{i} = \varepsilon$ for $0 \leq i \leq p-1$ and $0 \leq j \leq n - 1$
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$X' = \bar{x}_{0} \bar{x}_{1} \ldots \bar{x}_{i} \ldots \bar{x}_{p-1}$
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$Y' = \bar{y}_{0} \bar{y}_{1} \ldots \bar{y}_{i} \ldots \bar{y}_{p-1}$
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for $0 \leq i \leq p-1$, $\nexists i$, such that $\bar{x}_{i} = \bar{y}_{i} = \varepsilon$
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@ -0,0 +1,64 @@
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\chapter{Section alignment}
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\section{Needleman - Wunsch algorithm}
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\begin{algorithm}
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\caption{Needleman-Wunsch Algorithm}
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\begin{algorithmic}[1]
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\Procedure{FillMatrix}{$S_{1}$: Array($m$), $S_{2}$: Array($n$)}
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\Comment{$sub(a, b)$ is the substitution score, $del(a)$ and $ins(a)$ are the deletion and insertion penalty, in regard with the reference $S_{1}$ sequence}
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\State $M = $ Array($m+1$, $n+1$)
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\Comment{Initialize the matrix first column and first row}
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\State $P = $ Array($m$, $n$) \Comment{Store the direction of the cell we chose to build the next cell up on.}
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\For {($i = 0$; $i < m+1$; $i++$)}
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\State $M[i][0] = i * del(S_{1}[i])$
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\EndFor
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\For {($j = 0$; $j < n+1$; $j++$)}
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\State $M[0][j] = j * ins(S_{2}[j])$
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\EndFor
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\Comment{Fill the remaining matrix}
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\For {($i = 1$; $i < m+1$; $i++$)}
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\For {($j = 1$; $j < n+1$; $j++$)}
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\State $delete = M[i-1][j] + del(S_{1}[i-1])$
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\State $insert = M[i][j-1] + ins(S_{2}[j-1])$
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\State $substitute = M[i-1][j-1] + sub(S_{1}[i-1], S_{2}[j-1])$
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\State $choice = \max \{delete, insert, substitute\}$
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\If {$substitute = choice$}
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\State $P[i-1][j-1] = '\nwarrow'$
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\ElsIf {$insertion = choice$}
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\State $P[i-1][j-1] = '\uparrow'$
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\Else
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\State $P[i-1][j-1] = '\leftarrow'$
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\EndIf
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\State $M[i][j] = choice$
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\EndFor
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\EndFor
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\EndProcedure
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\Procedure{ShowAlignment}{$S_{1}$: Array($m$), $S_{2}$: Array($n$)}
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\State $extend_{1} = ''$
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\State $extend_{2} = ''$
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\State $i = m$
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\State $j = n$
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\While{$i > 0$ and $j > 0$}
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\If {$P[i-1][j-1] = '\nwarrow'$}
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\State $extend_{1} = S_{1}[i-1] \circ extend_{1}$
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\State $extend_{2} = S_{2}[j-1] \circ extend_{2}$
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\State $i--$
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\State $j--$
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\ElsIf {$P[i-1][j-1] = '\uparrow'$}
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\State $extend_{1} = S_{1}[i-1] \circ extend_{1}$
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\State $extend_{2} =\quad '-' \circ extend_{2}$
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\State $i--$
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\Else
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\State $extend_{1} =\quad '-' \circ extend_{1}$
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\State $extend_{2} = S_{2}[j-1] \circ extend_{2}$
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\State $j--$
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\EndIf
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\EndWhile
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\State \Call{print}{$extend_{1}$}
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\State \Call{print}{$extend_{2}$}
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\EndProcedure
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\State \Call{FillMatrix}{$S_{1}$, $S_{2}$}
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\State \Call ShowAlignment($S_{1}$, $S_{2}$)
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\end{algorithmic}
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\end{algorithm}
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176
figures/part2/*
176
figures/part2/*
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@ -1,176 +0,0 @@
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function lcsq_matrix(seq1, seq2)
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local gap_penalty = 0
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local match_score = 1
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local n1 = string.len(seq1)
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local n2 = string.len(seq2)
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-- Create a n1 x n2 matrix
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local matrix = {}
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for i=0,n1 do
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matrix[i] = {}
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for j=0,n2 do
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matrix[i][j] = 0
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end
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end
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-- Fill the rest of the matrix
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local match, delete, insert
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for i=1,n1 do
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for j=1,n2 do
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if string.sub(seq1, i, i) == string.sub(seq2, j, j) then
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match = matrix[i-1][j-1] + match_score
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else
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match = matrix[i-1][j-1]
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end
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gap1 = matrix[i-1][j] + gap_penalty
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gap2 = matrix[i][j-1] + gap_penalty
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matrix[i][j] = math.max(match, gap1, gap2)
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end
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end
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return matrix
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end
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local function has_value (tab, val)
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for index, value in ipairs(tab) do
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if value == val then
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return true
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end
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end
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return false
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end
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function repr_matrix(matrix)
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repr = ""
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for i=1,#matrix do
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for j=1,#matrix do
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repr = repr .. matrix[i][j] .. " "
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end
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repr = repr .. "\n"
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end
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return repr
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end
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function draw_lcsq_matrix_graph(seq1, seq2)
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local matrix = lcsq_matrix(seq1, seq2)
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local tikz_code = ""
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function coordinate(i, j)
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return i .. "_" .. j
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end
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local steps = {
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{-1, 0},
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{-1, -1},
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{0, -1}
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}
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local n1 = string.len(seq1)
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local n2 = string.len(seq2)
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local path = {}
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local i = n1
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local j = n2
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while i >= 0 and j >= 0 do
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path[#path+1] = coordinate(i, j)
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local min = matrix[i][j]
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local min_step = steps[1]
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for index, step in ipairs(steps) do
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local k = i + step[1]
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local l = j + step[2]
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if k >= 0 and l >= 0 and matrix[k][l] <= min then
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min_step = step
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min = matrix[k][l]
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end
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end
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i = i + min_step[1]
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j = j + min_step[2]
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print(i, j)
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end
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-- Draw the matrix as tikz node with matrix value
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for i=0,n1 do
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for j=0,n2 do
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local options = ""
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if has_value(path, coordinate(i, j)) then
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options = "[fill=gray, draw, minimum size=1]"
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end
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tikz_code = tikz_code .. "\\node" .. options .. " (" .. coordinate(i, j) .. ") at (" .. i .. ", " .. -j .. ")" .. " {" .. matrix[i][j] .. "};"
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end
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end
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-- Add nucleotide labels
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for i=1,n1 do
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local nt = string.sub(seq1, i, i)
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tikz_code = tikz_code .. "\\node at (".. i .. "," .. 1 .. ")" .. "{$" .. nt .."$};"
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end
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for i=1,n2 do
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local nt = string.sub(seq2, i, i)
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tikz_code = tikz_code .. "\\node at (" .. -1 .. ", " .. -i .. ")" .. "{$ ".. nt .."$};"
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end
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-- For seq2
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for i=0,n1 do
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for j=0,n2 do
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local min = math.huge
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for index, step in ipairs(steps) do
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local k = i + step[1]
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local l = j + step[2]
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if k >= 0 and l >= 0 and matrix[k][l] < min then
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min = matrix[k][l]
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end
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end
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local highlighted = false
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for index, step in ipairs(steps) do
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local k = i + step[1]
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local l = j + step[2]
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if k >= 0 and l >= 0 and matrix[k][l] == min then
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tikz_code = tikz_code .. "\\draw[->] (" .. coordinate(i, j) .. ")" .. " -- " .. "(" .. coordinate (k, l) .. ");"
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end
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end
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end
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end
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return tikz_code
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end
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function draw_lcsq_matrix(seq1, seq2)
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-- print(string.format(" Path: %s -> %s", seq1, seq2))
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local matrix = lcsq_matrix(seq1, seq2)
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local n1 = string.len(seq1)
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local n2 = string.len(seq2)
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-- Draw the matrix as tikz nodes
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for i=0,n1-1 do
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for j=0,n2-1 do
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print(string.format("\\node[draw, minimum width=1cm, minimum height=1cm] at (%d, -%d) {};", i, j, matrix[i][j]))
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end
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end
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-- Draw the sequence labels
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for i=1,n1 do
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print(string.format("\\node at (%d, -%d) {%s};", i-1, -1, string.sub(seq1, i, i)))
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end
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for i=1,n2 do
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print(string.format("\\node at (%d, -%d) {%s};", -1, i-1, string.sub(seq2, i, i)))
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end
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-- Add a path from the bottom right corner to the top left corner, following the minimum of the three possible moves at each step
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local i, j, value, previous_value
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i = n1-1
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j = n2-1
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print(string.format("\\draw[-,line width=2, gray] (%d, -%d) --", i, j))
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while i > 0 and j > 0 do
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value = math.min(matrix[i-1][j-1], table[i-1][j], table[i][j-1])
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if value == matrix[i-1][j-1] then
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i = i - 1
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j = j - 1
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elseif value == matrix[i-1][j] then
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i = i - 1
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else
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j = j - 1
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end
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print(string.format(" (%d, -%d) -- ", i, j))
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end
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print(string.format("(0, 0) -- (-1, 1);", i, j))
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end
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function main()
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local seq1 = "ATCTGAT"
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local seq2 = "TGCATA"
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local matrix = lcsq_matrix(seq1, seq2)
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print(repr_matrix(matrix))
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end
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main()
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