Importance sampling of word patterns in DNA and protein sequences.

Monte Carlo methods can provide accurate p-value estimates of word counting test statistics and are easy to implement. They are especially attractive when an asymptotic theory is absent or when either the search sequence or the word pattern is too short for the application of asymptotic formulae. Naive direct Monte Carlo is undesirable for the estimation of small probabilities because the associated rare events of interest are seldom generated. We propose instead efficient importance sampling algorithms that use controlled insertion of the desired word patterns on randomly generated sequences. The implementation is illustrated on word patterns of biological interest: palindromes and inverted repeats, patterns arising from position-specific weight matrices (PSWMs), and co-occurrences of pairs of motifs.

Nonrandom clusters of palindromes in herpesvirus genomes.

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.