Nonrandom Clusters of Palindromes in Herpesvirus Genomes

Abstract

Palindromes are symmetrical words of DNA in the sense that they read exactly the same as their reverse complementary sequences. Representing the occurrences of palindromes in a DNA molecule as points on the unit interval, the scan statistics can be used to identify regions of unusually high concentration of palindromes. These regions have been associated with the replication origins on a few herpesviruses in previous studies. However, the use of scan statistics requires the assumption that the points representing the palindromes are independently and uniformly distributed on the unit interval. In this paper, we provide a mathematical basis for this assumption by showing that in randomly generated DNA sequences, the occurrences of palindromes can be approximated by a Poisson process. An easily computable upper bound on the Wasserstein distance between the palindrome process and the Poisson process is obtained. This bound is then used as a guide to choose an optimal palindrome length in the analysis of a collection of 16 herpesvirus genomes. Regions harboring significant palindrome clusters are identified and compared to known locations of replication origins. This analysis brings out a few interesting extensions of the scan statistics that can help formulate an algorithm for more accurate prediction of replication origins.

Scoring schemes of palindrome clusters for more sensitive prediction of replication origins in herpesviruses

“…The compound Poisson distribution is motivated from a marked Poisson process point of view. The occurrence of a palindrome of length 2L and above is modeled by a Poisson process (4), and the actual length of this palindrome is modeled by a geometric distribution.…”

“…Leung et al . (4) propose a procedure, which is based on bench-marking with the well-studied HCMV virus, for the choice of L . This choice takes into account the length of the sequence, as well as the base frequencies in the genome.…”

“…(14), and further discussed in the articles of Leung and Yamashita (17), and Leung et al . (4). Two new scoring schemes, namely, the palindrome length scheme (PLS) and the base-pair weighted scheme (BWS) are introduced as measures of palindrome clusters.…”

Importance Sampling of Word Patterns in DNA and Protein Sequences

“…PALINDROMIC PATTERNS AND INVERTED REPEATS Masse et al (1992) reported clusters of palindromic patterns near origins of replication of viruses. There has been much work done to estimate their significance, for example, using Poisson and compound Poisson approximations (Leung et al, 1994(Leung et al, , 2005. The four nucleotides can be divided into two complementary base pairs with a and t forming a pair and c and g forming the second pair.…”

“…Statistical significance of over-representation of these word patterns provides valuable clues to biologists. Consequently, much work has been done on the use of asymptotic limiting distributions to approximate these pvalues (Prum et al, 1995;Reinert et al, 2000;Régnier, 2000;Robin et al, 2002;Huang et al, 2004;Leung et al, 2005;Mitrophanov and Borodovsky, 2006;Pape et al, 2008). However, the approximations may not be accurate for short words or for words consisting of repeats and most theoretical approximations work only in specific settings.…”