Exceptional Motifs in Different Markov Chain Models for a Statistical Analysis of DNA Sequences

Abstract

Identifying exceptional motifs is often used for extracting information from long DNA sequences. The two difficulties of the method are the choice of the model that defines the expected frequencies of words and the approximation of the variance of the difference T(W) between the number of occurrences of a word W and its estimation. We consider here different Markov chain models, either with stationary or periodic transition probabilities. We estimate the variance of the difference T(W) by the conditional variance of the number of occurrences of W given the oligonucleotides counts that define the model. Two applications show how to use asymptotically standard normal statistics associated with the counts to describe a given sequence in terms of its outlying words. Sequences of Escherichia coli and of Bacillus subtilis are compared with respect to their exceptional tri- and tetranucleotides. For both bacteria, exceptional 3-words are mainly found in the coding frame. E. coli palindrome counts are analyzed in different models, showing that many overabundant words are one-letter mutations of avoided palindromes.

Identification of the Chi site of Haemophilus influenzae as several sequences related to the Escherichia coli Chi site

“…Statistical methods were used to determine whether Chi Hi (compared with Chi Ec ) occurs as a random or non-random sequence on the H. influenzae chromosome when the mono-, di-through heptanucleotide composition of the genome is taken into account (Schbath et al, 1995;see …”

“…Briefly, statistical analyses of genome sequences reveal a non-random organization of nucleotides (Blaisdell, 1984;Pevzner, 1992;Schbath et al, 1995;Karlin and Burge, 1995). Examples of this are seen in dinucleotide occurrence that is non-random and is proposed to be the signature of a particular microorganism (Karlin and Burge, 1995), or trinucleotide representation on the genome, which is determined in part by codon usage (Brendel et al, 1986).…”

“…the di-or trinucleotide composition of the genome) can be used to determine the probability that a given sequence, such as Chi Ec , occurs at random. In these models, the probability that the frequent occurrence of Chi Ec is random proves to be essentially nil (Schbath et al, 1995). Application of statistical analyses to other microorganisms requires biological characterization of Chi, as well as extensive sequence data.…”

Compound Poisson approximation of word counts in DNA sequences

“…This simple model is useful to identify exceptional long words, given (m + 1 ) -w ords frequencies. Prum et al (1995) and Schbath et al (1995) study the normal approximation of N(W) corresponding to the asymptotic frame where the expectation of N(W) c o n verges to in nity with n. If the expectation of N(W) i s bounded when n increases, we t h e n s a y that W is rare, and Poisson approximations are more reasonable. We s h o w here that the number of overlapping occurrences of a rare word can be approximated by a compound Poisson variable, which reduces to a Poisson variable if the word W cannot overlap itself.…”

Palindromes in SARS and Other Coronaviruses

“…Various statistical assessments of unusual abundance and rarity of individual words, including individual palindromes, in nucleotide sequences have been done using randomsequence models in a number of previous studies (Karlin et al 1992;Merkl and Fritz 1996;Rocha et al 1998Rocha et al , 2001Schbath et al 1995, to name just a few). The present study, however, aims at investigating the unusual abundance and rarity of palindromes collectively rather than individually.…”