Editing Subsequence (section)

== Applications ==

Subsequences have applications to [[computer science]],<ref name="substrVsSubseq">In computer science, ''[[string (computer science)|string]]'' is often used as a synonym for ''sequence'', but it is important to note that ''[[substring]]'' and ''subsequence'' are not synonyms. Substrings are ''consecutive'' parts of a string, while subsequences need not be. This means that a substring of a string is always a subsequence of the string, but a subsequence of a string is not always a substring of the string, see: {{cite book | last = Gusfield | first = Dan | orig-year = 1997 | year = 1999 | title = Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology | publisher = Cambridge University Press | location = USA | isbn = 0-521-58519-8 | pages = 4}}</ref> especially in the discipline of [[bioinformatics]], where computers are used to compare, analyze, and store [[DNA]], [[RNA]], and [[protein]] sequences.

Take two sequences of DNA containing 37 elements, say:

:<samp>SEQ<sub>1</sub> = ACGGTGTCGTGCTATGCTGATGCTGACTTATATGCTA</samp>
:<samp>SEQ<sub>2</sub> = CGTTCGGCTATCGTACGTTCTATTCTATGATTTCTAA</samp>

The longest common subsequence of sequences 1 and 2 is:

:<samp>LCS<sub>(SEQ<sub>1</sub>,SEQ<sub>2</sub>)</sub> = '''CGTTCGGCTATGCTTCTACTTATTCTA'''</samp>

This can be illustrated by highlighting the 27 elements of the longest common subsequence into the initial sequences:

:<samp>SEQ<sub>1</sub> = A'''{{font color|red|CG}}'''G'''{{font color|red|T}}'''G'''{{font color|red|TCG}}'''T'''{{font color|red|GCTATGCT}}'''GA'''{{font color|red|T}}'''G'''{{font color|red|CT}}'''G'''{{font color|red|ACTTAT}}'''A'''{{font color|red|T}}'''G'''{{font color|red|CTA}}'''</samp>
:<samp>SEQ<sub>2</sub> = '''{{font color|red|CGTTCGGCTAT}}'''C'''{{font color|red|G}}'''TA'''{{font color|red|C}}'''G'''{{font color|red|TTCTA}}'''TT'''{{font color|red|CT}}'''A'''{{font color|red|T}}'''G'''{{font color|red|ATT}}'''T'''{{font color|red|CTA}}'''A</samp>

Another way to show this is to ''align'' the two sequences, that is, to position elements of the longest common subsequence in a same column (indicated by the vertical bar) and to introduce a special character (here, a dash) for padding of arisen empty subsequences:
:<samp>SEQ<sub>1</sub> = ACGGTGTCGTGCTAT-G--C-TGATGCTGA--CT-T-ATATG-CTA-</samp>
:<samp>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;|&nbsp;||&nbsp;|||&nbsp;|||||&nbsp;|&nbsp;&nbsp;|&nbsp;|&nbsp;&nbsp;|&nbsp;||&nbsp;|&nbsp;&nbsp;||&nbsp;|&nbsp;||&nbsp;|&nbsp;&nbsp;||| </samp>
:<samp>SEQ<sub>2</sub> = -C-GT-TCG-GCTATCGTACGT--T-CT-ATTCTATGAT-T-TCTAA</samp>

Subsequences are used to determine how similar the two strands of DNA are, using the DNA bases: [[adenine]], [[guanine]], [[cytosine]] and [[thymine]].