\STATE $geneList=\text{empty list}$
\STATE $common=set(dir(NCBI\_Genes)) \cap set(dir(Dogma\_Genes))$
\FOR{$\text{gene in common}$}
- \STATE $gen1 \leftarrow open(NCBI\_Genes(gene)).read()$
- \STATE $gen2 \leftarrow open(Dogma\_Genes(gene)).read()$
- \STATE $score \leftarrow geneChk(gen1,gen2)$
+ \STATE $g1 \leftarrow open(NCBI\_Genes(gene)).read()$
+ \STATE $g2 \leftarrow open(Dogma\_Genes(gene)).read()$
+ \STATE $score \leftarrow geneChk(g1,g2)$
\IF {$score > Threshold$}
\STATE $geneList \leftarrow gene$
\ENDIF
geneChk subroutine.
\begin{algorithm}[H]
-\caption{Find the maximum similarity score between two sequences}
+\caption{Find the Maximum Similarity Score between two sequences}
\label{Alg3:genechk}
\begin{algorithmic}
-\REQUIRE $gen1,gen2 \leftarrow \text{NCBI gene sequence, Dogma gene sequence}$
+\REQUIRE $g1,g2 \leftarrow \text{NCBI gene sequence, Dogma gene sequence}$
\ENSURE $\text{Maximum similarity score}$
-\STATE $Score1 \leftarrow needle(gen1,gen2)$
-\STATE $Score2 \leftarrow needle(gen1,Reverse(gen2))$
-\STATE $Score3 \leftarrow needle(gen1,Complement(gen2))$
-\STATE $Score4 \leftarrow needle(gen1,Reverse(Complement(gen2)))$
-\RETURN $max(Score1, Score2, Score3, Score4)$
+\STATE $score1 \leftarrow needle(g1,g2)$
+\STATE $score2 \leftarrow needle(g1,Reverse(g2))$
+\STATE $score3 \leftarrow needle(g1,Complement(g2))$
+\STATE $score4 \leftarrow needle(g1,Reverse(Complement(g2)))$
+\RETURN $max(score1,score2,score3,score4)$
\end{algorithmic}
\end{algorithm}
the \textit{Intersection Score} (IS): the cardinality of the core
genes set obtained by intersecting one genome with another
one. Maximum cardinality results in selecting the two genomes having
-the maximum score. Mathematically speaking, if we have an $n \times n$
-matrix where $n$ is the number of genomes in local database, then let
-us consider:
-
+the maximum score. Mathematically speaking, if we have $n$ genomes in
+local database, the ICM is an $n \times n$ matrix whose elements
+satisfy:
\begin{equation}
-Score=\max_{i<j}\vert x_i \cap x_j\vert
+score_{ij}=\vert g_i \cap g_j\vert
\label{Eq1}
\end{equation}
-
-% TO BE CONTINUED
-
-\noindent where $x_i, x_j$ are elements in the matrix. The generation of
-a new core genes is depending on the cardinality value of intersection
-scores, we call it \textit{Score}:
-$$
-\text{New Core} =
-\begin{cases}
-\text{Ignored} & \text{if $\textit{Score}=0$;} \\
-\text{new Core id} & \text{if $\textit{Score}>0$.}
-\end{cases}
-$$
-
-if $\textit{Score}=0$ then we have \textit{disjoint
-relation} \emph{i.e.}, no common genes between two genomes. In this
-case the system ignores the genome that annul the core gene
-size. Otherwise, The system removes these two genomes from ICM and add
-new core genome with a \textit{coreID} of them to ICM for the
-calculation in next iteration. This process reduces the size of ICM
-and repeats until all genomes are treated \emph{i.e.} ICM has no more
-genomes. We observe that ICM is very large because of the amount of
-data that it stores. This results to be time and memory consuming for
-calculating the intersection scores. To increase the speed of
-calculations, it is sufficient to only calculate the upper triangle
-scores. The time complexity for this process after enhancement is thus
-$O(\frac{n.(n-1)}{2})$. Algorithm \ref{Alg1:ICM} illustrates the
-construction of the ICM matrix and the extraction of the core genes
-where \textit{GenomeList}, represents the database where all genomes
-data are stored. At each iteration, it computes the maximum core genes
-with its two genomes parents.
+\noindent where $1 \leq i \leq n$, $1 \leq j \leq n$, and $g_i, g_j$ are
+genomes. The generation of a new core gene depends obviously on the
+value of the intersection scores $score_{ij}$. More precisely, the
+idea is to consider a pair of genomes such that their score is the
+largest element in ICM. These two genomes are then removed from matrix
+and the resulting new core genome is added for the next iteration.
+The ICM is then updated to take into account the new core gene: new IS
+values are computed for it. This process is repeated until no new core
+gene can be obtained.
+
+We can observe that the ICM is very large due to the amount of
+data. As a consequence, the computation of the intersection scores is
+both time and memory consuming. However, since ICM is a symetric
+matrix we can reduce the computation overhead by considering only its
+triangular upper part. The time complexity for this process after
+enhancement is thus $O(\frac{n.(n-1)}{2})$. Algorithm ~\ref{Alg1:ICM}
+illustrates the construction of the ICM matrix and the extraction of
+the core genes, where \textit{GenomeList} represents the database
+storing all genomes data. At each iteration, it computes the maximum
+core genes with its two genomes parents.
+
+% ALGORITHM HAS BEEN REWRITTEN
\begin{algorithm}[H]
\caption{Extract Maximum Intersection Score}
\label{Alg1:ICM}
\begin{algorithmic}
\REQUIRE $L \leftarrow \text{genomes vectors}$
-\ENSURE $B1 \leftarrow Max core vector$
+\ENSURE $B1 \leftarrow Max Core Vector$
\FOR{$i \leftarrow 0:len(L)-1$}
+ \STATE $score \leftarrow 0$
\STATE $core1 \leftarrow set(GenomeList[L[i]])$
- \STATE $score1 \leftarrow 0$
- \STATE $g1,g2 \leftarrow$ " "
+ \STATE $g1 \leftarrow L[i]$
\FOR{$j \leftarrow i+1:len(L)$}
- \STATE $core2 \leftarrow set(GenomeList[L[i]])$
- \IF{$i < j$}
- \STATE $Core \leftarrow core1 \cap core2$
- \IF{$len(Core) > score1$}
- \STATE $g1 \leftarrow L[i]$
- \STATE $g2 \leftarrow L[j]$
- \STATE $Score \leftarrow len(Core)$
- \ELSIF{$len(Core) == 0$}
- \STATE $g1 \leftarrow L[i]$
- \STATE $g2 \leftarrow L[j]$
- \STATE $Score \leftarrow -1$
- \ENDIF
- \ENDIF
+ \STATE $core2 \leftarrow set(GenomeList[L[j]])$
+ \STATE $Core \leftarrow core1 \cap core2$
+ \IF{$len(Core) > score$}
+ \STATE $score \leftarrow len(Core)$
+ \STATE $g2 \leftarrow L[j]$
+ \ENDIF
\ENDFOR
- \STATE $B1[score1] \leftarrow (g1,g2)$
+ \STATE $B1[score] \leftarrow (g1,g2)$
\ENDFOR
\RETURN $max(B1)$
\end{algorithmic}
\end{algorithm}
-\subsection{Features Visualization}
+\subsection{Features visualization}
The goal is to visualize results by building a tree of evolution. All
core genes generated represent important information in the tree,
because they provide information about the ancestors of two or more
genomes. Each node in the tree represents one chloroplast genome or
one predicted core called \textit{(Genes count:Family name\_Scientific
-names\_Accession number)}, while an edge is labeled with the number
-genes lost from a leaf genome or an intermediate core gene.
-
-
-The number of lost genes here can represent an important factor
-for evolution: it represents how much is the lost of genes from the
-species belongs to same or different families. By the principle of
-classification, a small number of gene lost among species indicates
+names\_Accession number)}, while an edge is labeled with the number of
+lost genes from a leaf genome or an intermediate core gene. Such
+numbers are very interesting because they give an information about
+the evolution: how many genes were lost between two species whether
+they belong to the same familie or not. By the principle of
+classification, a small number of genes lost among species indicates
that those species are close to each other and belong to same family,
-while big genes lost means that we have an evolutionary relationship
-between species from different families. To see the picture clearly,
-Phylogenetic tree is an evolutionary tree generated also by the
-system. Generating this tree is based on the distances among genes
-sequences. There are many resources to build such tree (for example:
+while a large lost means that we have an evolutionary relationship
+between species from different families. To depict the links between
+species clearly, we built a phylogenetic tree showing the
+relationships based on the distances among genes sequences. Many tools
+are available to obtain a such tree, for example:
PHYML\cite{guindon2005phyml},
-RAxML{\cite{stamatakis2008raxml,stamatakis2005raxml}, BioNJ, and
-TNT\cite{goloboff2008tnt}}.
-
-We use
-RAxML\cite{stamatakis2008raxml,stamatakis2005raxml} because it is fast
-and accurate for build large trees for large count of genomes
-sequences.
-
-The procedure of constructing phylogenetic tree stated in
-the following steps:
+RAxML{\cite{stamatakis2008raxml,stamatakis2005raxml}, BioNJ, and
+TNT\cite{goloboff2008tnt}}. In this work, we chose to use
+RAxML\cite{stamatakis2008raxml,stamatakis2005raxml} because it is
+fast, accurate, and can build large trees when dealing with a large
+number of genomic sequences.
+The procedure used to built a phylogenetic tree is as follows:
\begin{enumerate}
-\item Extract gene sequence for all gene in all core genes, store it in database.
-\item Use multiple alignment tool such as (****to be write after see christophe****) to align these sequences with each others.
-\item aligned genomes sequences then submitted to RAxML program to compute the distances and draw phylogenetic tree.
+\item For each gene in a core gene, extract its sequence and store it in the database.
+\item Use multiple alignment tools such as (****to be write after see christophe****)
+to align these sequences with each others.
+\item Submit the resulting aligned sequences to RAxML program to compute the distances and finally draw the phylogenetic tree.
\end{enumerate}
\begin{figure}[H]
- \centering
- \includegraphics[width=0.7\textwidth]{Whole_system}
- \caption{Total overview of the system pipeline}\label{wholesystem}
+ \centering \includegraphics[width=0.75\textwidth]{Whole_system}
+ \caption{Overview of the pipeline}\label{wholesystem}
\end{figure}
-% STOP HERE
-
\section{Implementation}
We implemented four algorithms to extract maximum core genes from large amount of chloroplast genomes. Two algorithms used to extract core genes based on NCBI annotation, and the others based on dogma annotation tool. Evolutionary tree generated as a result from each method implementation. In this section, we will present the four methods, and how they can extract maximum core genes?, and how the developed code will generate the evolutionary tree.
