Figure 1.
Insertion and deletion errors violate the codeword scheme and reduce the utility of Hamming-based tags.
Panel (A) shows two sequence tags that are different from one another by seven substitutions (Hamming distance = 7) – a distance more than sufficient to differentiate tags in the presence of substitution errors. However, these same two tags have an edit distance of two (B) – meaning that a total of two insertions, substitutions, or deletions can turn Tag 1 into Tag 2 and confuse samples. Although it seems improbable that two indels or substitutions would occur in a sequence tag, consider the third case (C) in which a single deletion event at the 5′ end of a sequence tag adjoining DNA template beginning with 5′ guanine confuses Tag 1 with Tag 2. Edit metric sequence tags of distance three or greater would mitigate this mistake.
Figure 2.
Using Hamming codes to design binary encoded sequence tags when synthesis, replication, or sequencing errors mutate the nucleotide sequence reduces the number of single-base errors that are correctable during downstream demultiplexing.
Here, we show two sequence tags (Tag 1 and Tag 2) and both their nucleotide and binary encodings. Tag 1 and Tag 2 have a Hamming distance of four between their binary representations and a Hamming distance of two between their nucleotide representations. Error 1 is correctable to Tag 2, because a single nucleotide substitution (in purple) results in a single, binary difference (11 versus 01) between Error 1 and Tag 2, and single binary errors are correctable when tags are at least three binary differences from each other. Error 2 and Error 3 tags also exhibit a single nucleotide substitution (in purple) but two binary differences from Tag 1 and two binary differences from Tag 2. Because there is more than a single binary difference, we cannot determine whether the source tag was originally Tag 1 or Tag 2, we cannot correct the error, and we must discard the read. More generally, because of the binary encoding and the Hamming distance between tags (Hamming distance four between binary representations, Hamming distance two between nucleotide representations), we can correct single binary errors seen in the substitutions around the perimeter of inset (B), but we cannot correct double binary errors across the diagonals of inset (B). Because these single nucleotide, double binary substitutions (i.e., across the diagonals) comprise two of six potential substitution mutations, we cannot correct 33% (2/6) of single nucleotide substitution errors.
Table 1.
Commercial and non-commercial sequence tag sets and the conformance of each to the stated or assumed distance metric (edit or Hamming).
Figure 3.
Pairwise edit distance between 25 tags of five nucleotides in length and edit distance three designed using EDITTAG.
Table 2.
Counts of four to 10 nucleotide, ≥3 edit distance sequence tags sets designed using EDITTAG.
Figure 4.
Number of HiSeq reads returned for libraries prepared using Illumina TruSeq adapters versus libraries prepared using adapters integrating edit metric sequence tags designed using EDITTAG.