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{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-02T21:29:24","documenter_version":"1.6.0"}}
{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-02T21:30:58","documenter_version":"1.6.0"}}
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Definitions · PlotPWM.jl</title><meta name="title" content="Definitions · PlotPWM.jl"/><meta property="og:title" content="Definitions · PlotPWM.jl"/><meta property="twitter:title" content="Definitions · PlotPWM.jl"/><meta name="description" content="Documentation for PlotPWM.jl."/><meta property="og:description" content="Documentation for PlotPWM.jl."/><meta property="twitter:description" content="Documentation for PlotPWM.jl."/><meta property="og:url" content="https://kchu25.github.io/PlotPWM.jl/definitions/"/><meta property="twitter:url" content="https://kchu25.github.io/PlotPWM.jl/definitions/"/><link rel="canonical" href="https://kchu25.github.io/PlotPWM.jl/definitions/"/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" 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href="../assets/themes/catppuccin-mocha.css" data-theme-name="catppuccin-mocha"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-macchiato.css" data-theme-name="catppuccin-macchiato"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">PlotPWM.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li class="is-active"><a class="tocitem" href>Definitions</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Definitions</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Definitions</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/kchu25/PlotPWM.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/kchu25/PlotPWM.jl/blob/main/docs/src/definitions.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h3 id="Definition-of-Information-Content-in-Position-Weight-Matrices-(PWM)"><a class="docs-heading-anchor" href="#Definition-of-Information-Content-in-Position-Weight-Matrices-(PWM)">Definition of Information Content in Position Weight Matrices (PWM)</a><a id="Definition-of-Information-Content-in-Position-Weight-Matrices-(PWM)-1"></a><a class="docs-heading-anchor-permalink" href="#Definition-of-Information-Content-in-Position-Weight-Matrices-(PWM)" title="Permalink"></a></h3><p>In a position weight matrix (PWM), the &quot;letter height&quot;, or more formally, the <em>information content</em> <span>$IC(\cdot)$</span> of the <span>$i$</span>-th column <span>$c_i$</span>, quantifies how conserved the nucleotides are at that position compared to a background model. It is calculated using the formula:</p><p class="math-container">\[IC(c_i) = \sum_{\alpha}f_{\alpha i}\log_2 (f_{\alpha i} / \beta_\alpha)\]</p><p>where <span>$f_{\alpha i}$</span> is the frequency of nucleotide <span>$\alpha\in\Set{A,C,G,T}$</span> at the <span>$i$</span>-th column of a PWM and <span>$\beta_\alpha$</span> denotes the genomic background frequency of nucleotide <span>$\alpha$</span>.</p><h3 id="Default-genomic-background"><a class="docs-heading-anchor" href="#Default-genomic-background">Default genomic background</a><a id="Default-genomic-background-1"></a><a class="docs-heading-anchor-permalink" href="#Default-genomic-background" title="Permalink"></a></h3><p>By default, the background model assumes a uniform distribution of nucleotides, with each nucleotide having a frequency of <span>$\beta=(0.25, 0.25,0.25,0.25)$</span>. In this case, the information content <span>$IC(c_i)$</span> simplifies to:</p><p class="math-container">\[IC(c_i)=2+\sum_{\alpha}f_{\alpha i}\log_2 f_{\alpha i}\]</p><p>This formula illustrates why the y-axis of the logo-plot ranges from <span>$0$</span> to <span>$2$</span>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.6.0 on <span class="colophon-date" title="Monday 2 September 2024 21:29">Monday 2 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Definitions · PlotPWM.jl</title><meta name="title" content="Definitions · PlotPWM.jl"/><meta property="og:title" content="Definitions · PlotPWM.jl"/><meta property="twitter:title" content="Definitions · PlotPWM.jl"/><meta name="description" content="Documentation for PlotPWM.jl."/><meta property="og:description" content="Documentation for PlotPWM.jl."/><meta property="twitter:description" content="Documentation for PlotPWM.jl."/><meta property="og:url" content="https://kchu25.github.io/PlotPWM.jl/definitions/"/><meta property="twitter:url" content="https://kchu25.github.io/PlotPWM.jl/definitions/"/><link rel="canonical" href="https://kchu25.github.io/PlotPWM.jl/definitions/"/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../search_index.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-mocha.css" data-theme-name="catppuccin-mocha"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-macchiato.css" data-theme-name="catppuccin-macchiato"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">PlotPWM.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li class="is-active"><a class="tocitem" href>Definitions</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Definitions</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Definitions</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/kchu25/PlotPWM.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/kchu25/PlotPWM.jl/blob/main/docs/src/definitions.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h3 id="Definition-of-Information-Content-in-Position-Weight-Matrices-(PWM)"><a class="docs-heading-anchor" href="#Definition-of-Information-Content-in-Position-Weight-Matrices-(PWM)">Definition of Information Content in Position Weight Matrices (PWM)</a><a id="Definition-of-Information-Content-in-Position-Weight-Matrices-(PWM)-1"></a><a class="docs-heading-anchor-permalink" href="#Definition-of-Information-Content-in-Position-Weight-Matrices-(PWM)" title="Permalink"></a></h3><p>In a position weight matrix (PWM), the &quot;letter height&quot;, or more formally, the <em>information content</em> <span>$IC(\cdot)$</span> of the <span>$i$</span>-th column <span>$c_i$</span>, quantifies how conserved the nucleotides are at that position compared to a background model. It is calculated using the formula:</p><p class="math-container">\[IC(c_i) = \sum_{\alpha}f_{\alpha i}\log_2 (f_{\alpha i} / \beta_\alpha)\]</p><p>where <span>$f_{\alpha i}$</span> is the frequency of nucleotide <span>$\alpha\in\Set{A,C,G,T}$</span> at the <span>$i$</span>-th column of a PWM and <span>$\beta_\alpha$</span> denotes the genomic background frequency of nucleotide <span>$\alpha$</span>.</p><h3 id="Default-genomic-background"><a class="docs-heading-anchor" href="#Default-genomic-background">Default genomic background</a><a id="Default-genomic-background-1"></a><a class="docs-heading-anchor-permalink" href="#Default-genomic-background" title="Permalink"></a></h3><p>By default, the background model assumes a uniform distribution of nucleotides, with each nucleotide having a frequency of <span>$\beta=(0.25, 0.25,0.25,0.25)$</span>. In this case, the information content <span>$IC(c_i)$</span> simplifies to:</p><p class="math-container">\[IC(c_i)=2+\sum_{\alpha}f_{\alpha i}\log_2 f_{\alpha i}\]</p><p>This formula illustrates why the y-axis of the logo-plot ranges from <span>$0$</span> to <span>$2$</span>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.6.0 on <span class="colophon-date" title="Monday 2 September 2024 21:30">Monday 2 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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