Sequence Assembly for Single Molecule Methods

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Sequence Assembly for Single Molecule Methods

• Steven Skiena, Alexey Smirnov
• Department of Computer Science
• SUNY at Stony Brook
• skiena, alexey_at_cs.sunysb.edu

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The State of Sequence Assembly

• The success of full genome sequencing implies
  that shotgun sequence assembly with current
  technologies is largely a solved problem
• With conventional sequence technologies
• read length about 500 base pairs
• error rate under 2
• coverage about 10 times for bacteria, about 30
  times for humans
• But single molecule sequencing methods promise to
  change these parameters significantly

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Single Molecule Sequencing Methods

• Single molecule sequencing methods, such as being
  developed by U.S. Genomics, promise much longer
  read lengths
• read length hundreds of thousands of bases ?
• error rate ?
• "No free lunch hypothesis" - we anticipate that
  the new technologies will (at least initially)
  have significantly higher error rates than
  current sequencing machines.
• Our assumption long lousy reads.

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Our Problems

• What levels of coverage will be needed to get
  accurate sequence informationfrom long noisy
  reads?
• How do we efficiently assemble such long noisy
  reads?

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Sequencing from Subsequences

• Why subsequences?
• We anticipate that certain single molecule
  sequencing technologies will be prone to having
  many base deletion errors
• Example in the U.S. Genomics technology,
  sequence bases are replaced by tagged bases.
  Untagged bases are invisible, generating
  subsequences.
• We study the effect of per base deletion
  frequencies on our ability to accurately
  reconstruct long sequences. Our study revolves
  around this theoretical error model. But our
  algorithm can be easily generalized.

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Notation

• n length of the original sequence
• p base deletion rate
• k number of reads
• Ri a read of the original sequence

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Quality of Reconstruction Metric

• Our score function is

• where ED is the edit distance, s is the target
  sequence of length n, s sequence reconstructed
  from the reads.
• An empty string has a score of 0
• The target string has a score of 1

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Lower Bounds on Reconstruction Quality

• k0 -gt report a random string of some length.
  Computational experiments showed that reporting a
  string of length 0.6n gives best results
  (score0.37)
• k1 -gt report this read score1-p (because
  (1-p)n characters will be matched and the rest
  will be inserted).

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Lower Bounds on Reconstruction Quality
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Information Theory Bounds

• What is the minimal number of reads that we need
  to reconstruct the sequence?
• First, we need to know the number of sequences of
  length n in which a given read of length k occurs

Each of reads gives us at most this number of
bits of information
Therefore, we will need at least this many reads
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Bounds on the Number of Reads
Conclusion reconstruction becomes impossible for
error rates higher than 75, but possible for 50
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Sequence Assembly Algorithm

• We use a two phase procedure
• Insertion align a read Ri with consensus
  sequence Ci-2 and build a new consensus Ci-1
• Refining and Cleanup delete/reorder characters
  from current consensus to better reflect the
  reads and delete unused characters

C3
refine cleanup
C2
R4
refine cleanup
C1
R3
refine cleanup
R1
R2
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Read Insertion

• How to choose the optimal alignment to insert a
  new read into current consensus Ci?
• Pairwise align all reads against Ci and for each
  position of Ci, compute the number of times each
  particular character was inserted into it at this
  position.
• Align the read being inserted against the
  weighted consensus sequence using the insertion
  weights generated before.

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Consensus Refining

• Pairwise alignment from reads is prone to two
  types of errors inserting a pair of characters
  in a wrong order and undersampling

ATA
R1
refine
ATCA
ACTAA
ACTAA
ACA
R2
Solution Try to make a swap and a character
doubling at each position and see if it improves
the alignment score for some reads.
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Clean up Procedure

• Pairwise align all reads against the target to
  weight the positions of S by frequency of use.
• Update weights after each alignment to bias
  matches toward frequently used positions.
• Delete all characters matched fewer than a
  certain number of times.

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Complexity Analysis

• Each insertion step takes O(knn) time
• Each refining step takes O(knn) time
• Each cleanup step takes O(knn) time
• Total O(niterknn) where niter is the number
  of iterations

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Results

• For base deletion rates as high as 40, we can
  completely reconstruct sequences with high enough
  coverage (50 times coverage)
• For larger error rates, our algorithm finds
  shorter supersequences, i.e. there are multiple
  answers so exact reconstruction is impossible.
• Here we ignored the possibility of
  insertion/substitution errors, but it is clear
  our methods can adapt to different error models
  at lower error rates.

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Results
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Future Work

• We want to build your single molecule sequence
  assembler!
• Our Stroll shotgun sequence assembler (Chen and
  Skiena) was used by Brookhaven National
  Laboratory to sequence the bacterial Borrelia
  burgdorferi.
• We are particularly interested in identifying
  better error models for sequencing technologies
  under current development.

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The End

• Questions?