Linguistic sequence complexity: Difference between revisions

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<math>C = U_1 U_2...U_i....U_w </math>
 
Vocabulary usage for [[oligomers]] of a given size {{math|<var>i</var>}} can be defined as the ratio of the actual vocabulary size of a given sequence to the maximal possible vocabulary size for a sequence of that length. For example, U<sub>2</sub> for the sequence ACGGGAAGCTGATTCCA = 14/16, as it contains 14 of 16 possible different dinucleotides; U<sub>3</sub> for the same sequence = 15/15, and U<sub>4</sub>=14/14. For the sequence ACACACACACACACACA, U<sub>1</sub>=1/2; U<sub>2</sub>=2/16=0.125, as it has a simple vocabulary of only two dinucleotides; U<sub>3</sub> for this sequence = 2/15. k-tuples with k from two to W considered, while W depends on RW. For RW values less than 18, W is equal to 3; for RW less than 67, W is equal to 4; for RW<260, W=5; for RW<1029, W=6, and so on.{{Clarify|post-text=W looks like a logarithmic measure, but the numbers don't check out very well on a calculator.|date=March 2012}} The value of {{math|<var>C</var>}} provides a measure of sequence complexity in the range 0<C<1 for various DNA sequence fragments of a given length. <ref name=Gabrielian1999></ref>
This novel formula is different from the previous LC measure in two respects: in the way vocabulary usage U<sub>i</sub> is calculated, and because {{math|<var>i</var>}} is not in the range of 2 to N-1 but only up to W. This new limitation on the range of U<sub>i</sub> makes the algorithm substantially more effective without loss of power.<ref name=Gabrielian1999></ref>
 
This sequence analysis complexity calculation can be used to search for conserved regions between compared sequences for the detection of low-complexity regions including simple sequence repeats, imperfect [[Direct_repeat|direct]] or [[Inverted_repeat|inverted repeats]], polypurine and polypyrimidine [[Triple-stranded_DNA|triple-stranded DNA structures]], and four-stranded structures (such as [[G-quadruplex|G-quadruplexes]]).<ref name=Kalendar2011>{{cite doi|10.1016/j.ygeno.2011.04.009|noedit}}}</ref>