Eric Coissac
39 lines
1.4 KiB
Markdown
39 lines
1.4 KiB
Markdown
# DNA encoding
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## 2-bit nucleotide encoding
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All nucleotides are encoded on 2 bits, MSB-first within each word. Nucleotides are numbered 0-based from the 5′ end across all sequence types:
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| Base | Encoding |
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|------|----------|
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| A | `00` |
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| C | `01` |
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| G | `10` |
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| T | `11` |
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The Watson-Crick complement of any base is its bitwise NOT on 2 bits: `complement(base) = ~base & 0b11`.
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## Kmer encoding
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A kmer fits in a single `u64`. Nucleotide 0 occupies bits 63–62, nucleotide i occupies bits 63−2i and 62−2i, and the low 64−2k bits are zero. Extraction of nucleotide i (0 ≤ i < k): `(kmer >> (62 - 2*i)) & 0b11`.
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Reverse complement is computed via a **16-bit lookup table** (65 536 entries × 2 bytes = 128 KB, fits in L2 cache) storing the reverse-complement of every 8-base chunk.
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!!! abstract "Algorithm — Kmer reverse complement"
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```text
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procedure KmerRevcomp(kmer, k):
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raw ← TABLE16[kmer & 0xFFFF] << 48
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| TABLE16[(kmer >> 16) & 0xFFFF] << 32
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| TABLE16[(kmer >> 32) & 0xFFFF] << 16
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| TABLE16[(kmer >> 48) & 0xFFFF]
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return raw << (64 - 2*k)
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```
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The **canonical form** is the lexicographic minimum of the kmer and its reverse complement:
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```
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canonical(kmer) = min(kmer, revcomp(kmer))
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```
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This halves the kmer space and ensures strand-independent counting.
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