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Poisson process approximation for sequence repeats, and sequencing by hybridization

R Arratia1, D Martin, G Reinert

  • 1Department of Mathematics, University of Southern California, Los Angeles 90089-1113, USA.

Journal of Computational Biology : a Journal of Computational Molecular Cell Biology
|January 1, 1996
PubMed
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This study analyzes DNA sequencing by hybridization, determining if a DNA sequence is uniquely recoverable from its l-tuple list. We developed Poisson process approximations to assess the probability of unique sequence reconstruction.

Area of Science:

  • Bioinformatics
  • Computational Biology
  • Genomics

Background:

  • Sequencing by hybridization (SbH) reconstructs DNA sequences from l-tuple lists.
  • Unique sequence reconstruction depends on the absence of specific repeat patterns (Ukkonen transformations).

Purpose of the Study:

  • To develop a probabilistic model for unique DNA sequence recovery in SbH.
  • To analyze the impact of repeats on the unique determination of DNA sequences.

Main Methods:

  • Modeling DNA as an independent and identically distributed (i.i.d.) sequence.
  • Applying Poisson process approximations and the Chen-Stein method to analyze repeat occurrences.
  • Investigating the spatial patterns of repeats within DNA sequences.

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Main Results:

  • Poisson process approximations for repeat indicators (with and without self-overlap) were established.
  • Error bounds for these approximations were derived using the Chen-Stein method.
  • An approximation for the probability of unique sequence recoverability was proven.

Conclusions:

  • The study provides a theoretical framework for understanding unique DNA sequence reconstruction in SbH.
  • Probabilistic methods offer insights into the challenges posed by sequence repeats.
  • Numerical examples and error bounds validate the theoretical findings.