Applications of the Scan Statistic in DNA Sequence Analysis

Advances of biochemical techniques have made available large databases of long DNA sequences. These sequences reflect conglomerates of random and nonrandom letter strings from the nucleotide alphabet {A, C, G, T}. As the databases expand, mathematical methods play an increasingly important role in analyzing and interpreting the rapidly accumulating DNA data. In this chapter, we discuss a specific example of identifying nonrandom clusters of palindromes in a family of herpesvirus genomes using the r-scan statistic. Palindrome positions on the genome are modeled by i.i.d. random variables uniformly distributed on the unit interval (0,1). After a comparison of three Poisson-type approximations, the r-scan distribution is computed by a compound Poisson approximation proposed by Glaz (1994). Some of the significant palindrome clusters are located at genome regions containing origins of replication and regulatory signals of the herpesviruses.

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