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Expected frequencies of DNA patterns using whittle's formula

Published online by Cambridge University Press:  14 July 2016

Richard Cowan
Richard Cowan*
Affiliation:
University of Hong Kong
*
∗ Postal address: Department of Statistics, University of Hong Kong, Pokfulam Road, Hong Kong.
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Abstract

Given a realisation of a Markov chain, one can count the numbers of state transitions of each type. One can ask how many realisations are there with these transition counts and the same initial state. Whittle (1955) has answered this question, by finding an explicit though complicated formula, and has also shown that each realisation is equally likely. In the analysis of DNA sequences which comprise letters from the set {A, C, G, T}, it is often useful to count the frequency of a pattern, say ACGCT, in a long sequence and compare this with the expected frequency for all sequences having the same start letter and the same transition counts (or ‘dinucleotide counts' as they are called in the molecular biology literature). To date, no exact method exists; this paper rectifies that deficiency.

Keywords

MARKOV CHAINSDNADINUCLEOTIDETRANSITION COUNTS
Type
Short Communications
Information
Journal of Applied Probability , Volume 28 , Issue 4 , December 1991 , pp. 886 - 892
Copyright
Copyright © Applied Probability Trust 1991 

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