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Motif Statistics

Abstract

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Algorithms - ESA’ 99 (ESA 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1643))

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Abstract

We present a complete analysis of the statistics of number of occurrences of a regular expression pattern in a random text. This covers “motifs” widely used in computational biology. Our approach is based on: (i) classical constructive results in theoretical computer science (automata and formal language theory); (ii) analytic combinatorics to compute asymptotic properties from generating functions; (iii) computer algebra to determine generating functions explicitly, analyse generating functions and extract coefficients efficiently. We provide constructions for overlapping or non-overlapping matches of a regular expression. A companion implementation produces: multivariate generating functions for the statistics under study; a fast computation of their Taylor coefficients which yields exact values of the moments with typical application to random texts of size 30,000; precise asymptotic formulæ that allow predictions in texts of arbitrarily large sizes. Our implementation was tested by comparing predictions of the number of occurrences of motifs against the 7 megabytes aminoacid database Prodom. We handled more than 88% of the standard collection of Prosite motifs with our programs. Such comparisons help detect which motifs are observed in real biological data more or less frequently than theoretically predicted.

This work has been partially supported by the Long Term Research Project Alcom-IT (#20244) of the European Union.

An extended version of this abstract is available as INRIA Research Report 3606.

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Author information

Authors and Affiliations

  1. DKFZ Theoretische Bioinformatik, Germany

    Pierre Nicodème

  2. Algorithms Project. Inria Rocquencourt, France

    Bruno Salvy & Philippe Flajolet

Authors
  1. Pierre Nicodème
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  2. Bruno Salvy
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  3. Philippe Flajolet
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Editor information

Editors and Affiliations

  1. Department of Applied Mathematics and DIMATIA Centre, Charles University, Malostranská nám. 25, CZ-11800, Prague 1, Czech Republic

    Jaroslav Nešetřil

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© 1999 Springer-Verlag Berlin Heidelberg

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Nicodème, P., Salvy, B., Flajolet, P. (1999). Motif Statistics. In: Nešetřil, J. (eds) Algorithms - ESA’ 99. ESA 1999. Lecture Notes in Computer Science, vol 1643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48481-7_18

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  • DOI: https://doi.org/10.1007/3-540-48481-7_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66251-8

  • Online ISBN: 978-3-540-48481-3

  • eBook Packages: Springer Book Archive

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