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Characterizing the D2 Statistic: Word Matches in Biological Sequences
1Australian National University & James Cook University
1Australian National University & University of New South Wales
1Australian National University
Citation Information: Statistical Applications in Genetics and Molecular Biology. Volume 8, Issue 1, Pages 1–21, ISSN (Online) 1544-6115, DOI: 10.2202/1544-6115.1447, October 2009
- Published Online:
Word matches are often used in sequence comparison methods, either as a measure of sequence similarity or in the first search steps of algorithms such as BLAST or BLAT. The D2 statistic is the number of matches of words of k letters between two sequences. Recent advances have been made in the characterization of this statistic and in the approximation of its distribution. Here, these results are extended to the case of approximate word matches.
We compute the exact value of the variance of the D2 statistic for the case of a uniform letter distribution, and introduce a method to provide accurate approximations of the variance in the remaining cases. This enables the distribution of D2 to be approximated for typical situations arising in biological research. We apply these results to the identification of cis-regulatory modules, and show that this method detects such sequences with a high accuracy.
The ability to approximate the distribution of D2 for both exact and approximate word matches will enable the use of this statistic in a more precise manner for sequence comparison, database searches, and identification of transcription factor binding sites.