Reconstruction of DNA sequencing by hybridization

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Reconstruction of DNA sequencing by hybridization

• Ji-Hong Zhang, Ling-Yun Wu and Xiang-Sun Zhang
• ZHANGroup_at_aporc.org
• Institute of Applied Mathematics, AMSS, CAS

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Bioinformatics

• Human Genome Project
• Large molecule data in biology, such as DNA and
  protein
• Knowledge of mathematics, computer science,
  information science, physics, system science,
  management science as well as biology
• Genomics
• DNA sequencing
• Gene prediction
• Sequence alignment

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DNA Sequencing
ACGTGACTGAGGACCGTG CGACTGAGACTGACTGGGT CTAGCTAGAC
TACGTTTTA TATATATATACGTCGTCGT ACTGATGACTAGATTACAG
ACTGATTTAGATACCTGAC TGATTTTAAAAAAATATT
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DNA Sequencing (shotgun)
target DNA
cut many times at random
forward-reverse linked reads
known dist
500 bp
500 bp
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DNA Sequencing (SBH)

• DNA array (DNA chip) with 43 probes
• Target DNA AAATGCG

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Sequencing by Hybridization

• Hybridize target to array containing a spot for
  each possible k-tuple (k-mer)
• The spectrum of a sequence
• multi-set of all its k-long substrings (k-tuples)
• Goal
• reconstruct the sequence from its spectrum
• Pevzner (1989) reconstruction is polynomial
• But

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Uniqueness of Reconstruction

• Different sequences can have the same spectrum
• ACT, CTA, TAC
• ACTAC
• TACTA
• Non-uniqueness Probability

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Experiment Errors

• Hybridization experiments are error prone
• False negative error
• k-tuple appears in target DNA but does not appear
  in its measured spectrum
• Repetition of k-tuple
• False positive error
• k-tuple does not appear in target DNA but does
  appear in its measured spectrum

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Sequencing by Hybridization

• Target DNA TTTTACGC
• 
  ß
• Spectrum
• Errors Positive (misread) / Negative (missing,
  repetition)

TTT TTT TTA TAC
ACG CGC Ideal case
TTT TTT TTA TAC
ACG CGC TGA With
errors
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SBH Reconstruction Problem

• In the case of error-free SBH experiments
• A desired solution of SBH is just a feasible
  solution including all k-tuple in the specturm
• For the general case
• There is no additional information except
  spectrum and the length of target DNA
• A feasible solution composed of a maximum
  cardinality subset of the spectrum shall be a
  reasonable desired solution

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SBH Reconstruction Problem

• Ideal case (without repetitions and errors)
• Equivalent to finding an Eulerian path in a
  corresponding graph (Pevzner, 1989)
• A linear time algorithm (Fleischner, 1990)
• General case is NP-hard problem
• Branch and bound
• Heuristics
• Extensions
• PSBH (Positional SBH)
• SBH with length error

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Motivations

• Give some criteria which can determine the most
  possible k-tuples at both ends and in the middle
  of all possible reconstructions of the target DNA
• These criterions greatly reduce ambiguities in
  the reconstruction of DNA
• Transform the negative errors into the positive
  errors
• These means enables us to handle both types of
  errors easily
• Separate the repetitions from both type of errors

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Methods

• Estimate the number of k-tuples that does not
  occur in a solution
• Adjacency matrix (connection matrix)
• Give a lower bound of k-tuples that does not
  occur in all solutions from k-tuple i to j

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Methods

• Determine the most possible k-tuples at both ends
• Reconstruct from the most possible end pairs to
  get an upper bound of SBH problem
• Purge the end pairs that can not have better
  solution than current upper bound

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Methods

• Transform the negative errors into the positive
  errors
• Artificial k-tuple
• Fill in all the possible gaps due to false
  negative error
• Negative error level
• The maximal number of allowed consecutively
  missing k-tuples
• Reduce the number of artificial k-tuples

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Computational Experiments

• 109 DNA sequence from GenBank
• Simulate the SBH experiments
• Error models
• Randomly (probabilistic model)
• Systematically (one base mismatched model)

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Conclusions

• Ideal case (without repetitions and errors) can
  be solved in polynomial time (Pevzner, 1989)
• General case is NP-hard problem
• Design efficient algorithms
• Ji-Hong Zhang, Ling-Yun Wu and Xiang-Sun Zhang. A
  new approach to the reconstruction of DNA
  sequencing by hybridization. Bioinformatics, vol
  19(1), pages 14-21, 2003.
• Xiang-Sun Zhang, Ji-Hong Zhang and Ling-Yun Wu.
  Combinatorial optimization problems in the
  positional DNA sequencing by hybridization and
  its algorithms. System Sciences and Mathematics,
  vol 3, 2002. (in Chinese)
• Ling-Yun Wu, Ji-Hong Zhang and Xiang-Sun Zhang.
  Application of neural networks in the
  reconstruction of DNA sequencing by
  hybridization. In Proceedings of the 4th ISORA,
  2002.