Waiting times for clumps of patterns and for structured motifs in random sequences

Authors:
V. T. Stefanov;S. Robin;S. Schbath
Affiliations:
School of Mathematics and Statistics, The University of Western Australia, Crawley (Perth) 6009, W.A., Australia;ENGREF / INA PG / INRA unit of Applied Mathematics and Computer Sciences, 16, rue Claude Bernard, 75005, Paris, France;Unité Mathématique, Informatique & Géénome, Institut National de la Recherche Agronomique, 78352 Jouy-en-Josas, France
Venue:
Discrete Applied Mathematics
Year:
2007

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Abstract

This paper provides exact probability results for waiting times associated with occurrences of two types of motifs in a random sequence. First, we provide an explicit expression for the probability generating function of the interarrival time between two clumps of a pattern. It allows, in particular, to measure the quality of the Poisson approximation which is currently used for evaluation of the distribution of the number of clumps of a pattern. Second, we provide explicit expressions for the probability generating functions of both the waiting time until the first occurrence, and the interarrival time between consecutive occurrences, of a structured motif. Distributional results for structured motifs are of interest in genome analysis because such motifs are promoter candidates. As an application, we determine significant structured motifs in a data set of DNA regulatory sequences.