1264 lines
20 KiB
HTML
1264 lines
20 KiB
HTML
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<link rel="prev" href="../kmers_and_superkmers/">
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<link rel="next" href="../entropy_filter/">
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Skip to content
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obikmer — User Guide
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<div class="md-header__topic" data-md-component="header-topic">
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<span class="md-ellipsis">
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DNA encoding
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obikmer — User Guide
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Home
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Installation
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</a>
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<span class="md-ellipsis">
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Theory
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<span class="md-nav__icon md-icon"></span>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="true">
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<span class="md-nav__icon md-icon"></span>
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Theory
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../kmers_and_superkmers/" class="md-nav__link">
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<span class="md-ellipsis">
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Kmers and super-kmers
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</span>
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</a>
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</li>
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<span class="md-ellipsis">
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DNA encoding
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</span>
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<span class="md-nav__icon md-icon"></span>
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</label>
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<a href="./" class="md-nav__link md-nav__link--active">
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<span class="md-ellipsis">
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DNA encoding
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</span>
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</a>
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<nav class="md-nav md-nav--secondary" aria-label="Table of contents">
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<label class="md-nav__title" for="__toc">
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<span class="md-nav__icon md-icon"></span>
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Table of contents
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<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="#2-bit-nucleotide-encoding" class="md-nav__link">
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<span class="md-ellipsis">
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2-bit nucleotide encoding
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="#kmer-encoding" class="md-nav__link">
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<span class="md-ellipsis">
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Kmer encoding
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="#canonical-form" class="md-nav__link">
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<span class="md-ellipsis">
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Canonical form
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</span>
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item">
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<a href="../entropy_filter/" class="md-nav__link">
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<span class="md-ellipsis">
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Low-complexity kmer filter
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||
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../minimizer_selection/" class="md-nav__link">
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<span class="md-ellipsis">
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Minimizer selection
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../indexing_architecture/" class="md-nav__link">
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<span class="md-ellipsis">
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Partitioning and indexing architecture
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</span>
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
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<label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
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<span class="md-ellipsis">
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Usage
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</span>
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<span class="md-nav__icon md-icon"></span>
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</label>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_4">
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<span class="md-nav__icon md-icon"></span>
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Usage
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../usage/superkmer/" class="md-nav__link">
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<span class="md-ellipsis">
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superkmer
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../usage/index_command/" class="md-nav__link">
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<span class="md-ellipsis">
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index
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../usage/merge/" class="md-nav__link">
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||
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||
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<span class="md-ellipsis">
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||
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||
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merge
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||
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||
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||
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</span>
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||
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||
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||
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</a>
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||
</li>
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||
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|
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||
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||
<li class="md-nav__item">
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||
<a href="../../usage/filter/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
filter
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
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||
</li>
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||
|
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|
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|
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|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../usage/select/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
select
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||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
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||
</li>
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||
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<li class="md-nav__item">
|
||
<a href="../../usage/query/" class="md-nav__link">
|
||
|
||
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||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
query
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
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<li class="md-nav__item">
|
||
<a href="../../usage/dump/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
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||
dump
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||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
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||
</a>
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||
</li>
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|
||
|
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<li class="md-nav__item">
|
||
<a href="../../usage/annotate/" class="md-nav__link">
|
||
|
||
|
||
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||
<span class="md-ellipsis">
|
||
|
||
|
||
annotate
|
||
|
||
|
||
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||
</span>
|
||
|
||
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||
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||
</a>
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||
</li>
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|
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<li class="md-nav__item">
|
||
<a href="../../usage/phylo/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
phylo
|
||
|
||
|
||
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2-bit nucleotide encoding
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|
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<h1 id="dna-encoding">DNA encoding</h1>
|
||
<h2 id="2-bit-nucleotide-encoding">2-bit nucleotide encoding</h2>
|
||
<p>Every nucleotide is encoded on 2 bits, most-significant-bit first within each word:</p>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>Base</th>
|
||
<th>Encoding</th>
|
||
</tr>
|
||
</thead>
|
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<tbody>
|
||
<tr>
|
||
<td>A</td>
|
||
<td><code>00</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td>C</td>
|
||
<td><code>01</code></td>
|
||
</tr>
|
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<tr>
|
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<td>G</td>
|
||
<td><code>10</code></td>
|
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</tr>
|
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<tr>
|
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<td>T</td>
|
||
<td><code>11</code></td>
|
||
</tr>
|
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</tbody>
|
||
</table>
|
||
<p>The Watson-Crick complement of a base is its bitwise NOT on 2 bits: <span class="arithmatex">\(\text{complement}(base) = \lnot base \mathbin{\&} \texttt{0b11}\)</span>.</p>
|
||
<h2 id="kmer-encoding">Kmer encoding</h2>
|
||
<p>A kmer of length <span class="arithmatex">\(k\)</span> (<span class="arithmatex">\(k \le 31\)</span>) fits in a single 64-bit word. The first nucleotide occupies the two most significant bits, each following nucleotide occupies the next two bits, and unused low-order bits are zero. Extracting nucleotide i (0-indexed from the 5′ end) is a shift-and-mask operation.</p>
|
||
<p>Reverse complement is computed by bit manipulation directly on the packed word, without any lookup table: complement every base, reverse the byte order, then reverse the order of 2-bit groups within each byte in two more passes, and finally realign the result to the most-significant bits.</p>
|
||
<h2 id="canonical-form">Canonical form</h2>
|
||
<p>The canonical form of a kmer is the lexicographic minimum of the kmer and its reverse complement:</p>
|
||
<div class="arithmatex">\[\text{canonical}(kmer) = \min\big(kmer,\ \text{revcomp}(kmer)\big)\]</div>
|
||
<p>Using the canonical form halves the kmer space and makes counting strand-independent: a kmer and its reverse complement are always treated as the same entity, regardless of which DNA strand was sequenced.</p>
|
||
|
||
|
||
|
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