From f5256e331a2301f2774366bfed13512b3373e1db Mon Sep 17 00:00:00 2001 From: =?utf8?q?Jean-Fran=C3=A7ois=20Couchot?= Date: Thu, 21 Mar 2013 08:25:31 +0100 Subject: [PATCH] t --- biblio.bib | 4 ++-- classEquiv.tex | 35 ++++++++++++++++++++++------------- main.tex | 3 +++ 3 files changed, 27 insertions(+), 15 deletions(-) diff --git a/biblio.bib b/biblio.bib index 79c455d..b141f05 100644 --- a/biblio.bib +++ b/biblio.bib @@ -52,7 +52,7 @@ pages={1-12} doi = {10.1371/journal.pone.0052841} } @Article{17623808, -AUTHOR = {Gómez-Valero, Laura and Rocha, Eduardo P C and Latorre, Amparo and Silva, Francisco J} +AUTHOR = {Gomez-Valero, Laura and Rocha, Eduardo P C and Latorre, Amparo and Silva, Francisco J}, TITLE = {Reconstructing the ancestor of Mycobacterium leprae: the dynamics of gene loss and genome reduction.}, JOURNAL = {Genome Res}, VOLUME = {17}, @@ -61,5 +61,5 @@ NUMBER = {8}, PAGES = {1178-85}, URL = {http://www.biomedsearch.com/nih/Reconstructing-ancestor-Mycobacterium-leprae-dynamics/17623808.html}, PubMedID = {17623808}, -ISSN = {1088-9051}, +ISSN = {1088-9051} } \ No newline at end of file diff --git a/classEquiv.tex b/classEquiv.tex index 5d9f19d..cdc1280 100644 --- a/classEquiv.tex +++ b/classEquiv.tex @@ -2,8 +2,8 @@ This step considers as input the set $\{((g_1,g_2),r_{12}), (g_1,g_3),r_{13}), (g_{n-1},g{n}),r_{n-1.n})\}$ of $\frac{n(n-1)}{2}$ elements. Each one $(g_i,g_j),r_{ij})$ where $i < j$, -is a pair that gives the similarity rate $r_{ij}$ between the genes -$g_{i}$ and $g_{j}$ in $G$. +is a pair that gives the similarity rate $r_{ij}$ between the two genes +$g_{i}$ and $g_{j}$. The first step of this stage consists in building the following non-oriented graph furthere denoted as to \emph{similarity graphe}. @@ -11,30 +11,29 @@ In this one, the vertices are the genes. There is an edge between $g_{i}$ and $g_{j}$ if the rate $r_{ij}$ is greater than a given similarity treeshold $t$. -We then define the relation $\sim \in G \times G $ such that +We then define the relation $\sim$ such that $ x \sim y$ if $x$ and $y$ belong in the same connected component. Mathematically speaking, it is obvious that this defines an equivalence relation. -Let $\dot{x}= \{y \in G | x \sim y\}$ +Let $\dot{x}= \{y | x \sim y\}$ denotes the equivalence class to which $x$ belongs. -All the elements of $G$ which are equivalent to each other +All the genes which are equivalent to each other are also elements of the same equivalence class. -Let us then consider the set of all equivalence classes of $G$ -by $\sim$, denoted $X/\sim = \{\dot{x} | x \in G\}$. -We then consider the projection $\pi: G \to G/\mathord{\sim}$ +Let us then consider the set of all equivalence classes of the set of genes +by $\sim$, denoted $X/\sim = \{\dot{x} | x \textrm{ is a gene}\}$. defined by \pi(x) = \dot{x} -which maps elements of $G$ into their respective equivalence classes by $\sim$. +which maps each gene into it respective equivalence classe by $\sim$. -For each genome $G=[g_l,\ldot,g{l+m}]$, the second step computes +For each genome $[g_l,\ldot,g{l+m}]$, the second step computes the projection of each gene according to $\pi$. -Let $G'$ the resulting genome which is +The resulting genome which is $$ -G'=[\pi(g_l),\ldot,\pi(g{l+m})] +[\pi(g_l),\ldot,\pi(g{l+m})] $$ -is of size $m$. +is again of size $m$. Intuitivelly speaking, for two genes $g_i$ and $g_j$ in the same equivalence class, there is path from $g_i$ and $g_j$. @@ -44,3 +43,13 @@ has produced a gene s.t. the similarity with the previous one is greater than $t$. Genes $g_i$ and $g_j$ may thus have a common ancestor. + +We compute the core genome as follow. +Each genome is projected according to $\pi$. We then consider the +intersection of all the projected genomes which are considered as sets of genes +and not as sequences of genes. +This results as the set of all the class representents $\dot{x}$ +such that each geneome has an gene $x$ in $\dot{x}$. +The pan genome is computed similarly: the union of all the +projected genomes in computed here. + diff --git a/main.tex b/main.tex index b6e9569..4a7c86b 100755 --- a/main.tex +++ b/main.tex @@ -56,8 +56,11 @@ \section{First Stage: Genomes as Lists of Homologous Classes} +\input{classEquiv} \section{Second Stage: to Find Closed Genomes} +\input{closedgenomes} + \section{Third Stage: Reconstruction of Ancestral Synteny Blocs for the two Closest Genomes} -- 2.39.5