Properties of words on four letters from those on two letters with an application to DNA sequences
type: Item
instance of: scholarly article
title: Properties of words on four letters from those on two letters with an application to DNA sequences
zbMATH Open document ID: 0810.92009
author: R. L. Bivins
author: N. Metropolis
author: George I. Bell
author: J. D. Louck
author: Myron L. Stein
published in: Advances in Applied Mathematics
publication date: 1994-02-07T00:00:00Z
review text: The rapid growth of DNA-sequence databases in the last few years makes it increasingly possible to identify biologically interesting sequence motifs by mathematical and statistical methods. Some special patterns, the tandem repeats of short sequence fragments, deserve great attention in the DNA sequence analysis. The article starts with the definition of an equivalence class consisting of a repeated word, all of its cyclic permutations, together with the reverse complements of each. In connection with such a construction the authors put the question: How many equivalence classes are there and how can they be characterised? Results already found for two letter words are used to infer certain properties of words on four letters. By a surjective mapping \(\varphi\) each letter \(A,C,G,T\) in DNA sequences is replaced by a pair of letters, say \(A \to RL\), \(C \to RR\), \(G \to LR\), \(T \to LL\). As a main result it is shown how a set of cycle class labels for words of length \(n\) on four letters can be constructed from the analogue on two letters using the bijection \(\varphi\). It is shown that the Möbius formulas for \(k = 2\) and \(k = 4\) give the number of cycle classes into which a set of primitive words is partitioned under conjugacy.
reviewed by: R.-D.Recknagel
Mathematics Subject Classification ID: 92C40
Mathematics Subject Classification ID: 68R15
Mathematics Subject Classification ID: 92D20
zbMATH DE Number: 495491
zbMATH Keywords: combinatorics
zbMATH Keywords: order relations
zbMATH Keywords: Möbius inversion formula
zbMATH Keywords: growth of DNA-sequence databases
zbMATH Keywords: DNA sequence analysis
zbMATH Keywords: cyclic permutations
zbMATH Keywords: reverse complements
zbMATH Keywords: equivalence classes
zbMATH Keywords: number of cycle classes
zbMATH Keywords: conjugacy
MaRDI profile type: Publication
full work available at URL: aama.1993.1017
OpenAlex ID: W2078777827
DOI: 10.1006/AAMA.1993.1017
description: scientific article; zbMATH DE number 495491