29 lines
1.4 KiB
Markdown
29 lines
1.4 KiB
Markdown
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# DNA encoding
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## 2-bit nucleotide encoding
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Every nucleotide is encoded on 2 bits, most-significant-bit first within each word:
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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 a base is its bitwise NOT on 2 bits: $\text{complement}(base) = \lnot base \mathbin{\&} \texttt{0b11}$.
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## Kmer encoding
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A kmer of length $k$ ($k \le 31$) 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.
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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.
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## Canonical form
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The canonical form of a kmer is the lexicographic minimum of the kmer and its reverse complement:
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$$\text{canonical}(kmer) = \min\big(kmer,\ \text{revcomp}(kmer)\big)$$
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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.
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