An Eulerian path approach to DNA fragment assembly Pavel A'Pevzner, Haixu Tang, and Michael S' Water

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An Eulerian path approach to DNA fragment
assemblyPavel A.Pevzner, Haixu Tang, and Michael
S. WatermanPNAS 2001

• Mohamed Tikah Marrakchi
• BIN6002
• Summer, 2005

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Genome sequencing

• Analysing DNA using improved technologies opens a
  new era in (but not only in) biomedical research.
  
• In the past few years genome sequences of many
  organisms were generated.
• A yeast (Saccharomyces cerevisiae)
• A nematode (C. elegans)
• A fly (Drosophila melanogaster)
• A plant (Arabidopsis thaliana)
• Human (Homo sapiens)

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Genome sequencing

• Depending on the intended use of the genome
  sequence data, choose a specific sequencing
  strategy.
• a detailed 'blueprint' (to establish a gene
  catalogue...)
• not so detailed to acquire information about
  repetitive sequences, carry simple comparisons
  with other organisms...)

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Genome sequencing

• Central to almost all the past and current genome
  sequencing projects is the 'dideoxy chain
  termination'
• sequencing method (developed by Fred Sanger and
  colleagues in the 70s)
• electrophoretic separation and detection of
  invitro synthesized, single-stranded DNA
  molecules terminated with dideoxynucleotides.

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Genome sequencing

• Many improvements were brought to the Sanger
  sequencing method.
• laser based instrumentation that allows the
  detection of fluorescently labeled DNA-molecules
• development of thermostable polymerases
• development of more robust fluorescent dye
  systems
• robotic systems have been designed to automate
  specific steps in the sequencing process (prepare
  sequencing reactions, load samples on gels ...)

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Genome sequencing

• Improvement of the quality and overall throughput
  of DNA sequencing and decrease in the cost
  (100-fold less in the past decade...)

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Genome sequencing

• Software tools were developed for analysing
  sequence data and for carrying out sequence
  assembly
• calling the nucleotide base at each position and
  assigning a corresponding quality score
• assembling sequences (using the quality score to
  calculate accuracy rates which are helpful for
  analysis and finishing steps)
• user friendly viewers (ex. phred, phrap and
  consed)

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Genome sequencing

• Many strategies were tested for large genomes
  sequencing
• 'Shotgun' sequencing (described in the 80s) was
  found to be very efficient.
• large piece of DNA can be sequenced by first
  fragmenting it into smaller pieces generating
  redundant amounts of sequence
• Obtaining sequence data from random fragments
  data then piecing the sequence reads together

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Genome sequencing

• Strategies in shotgun sequencing
• Strategy using large insert clones and associated
  physical maps
• Strategy taking a whole genome approach (without
  using clone-based physical maps)
• Hybrid strategies involving both approaches

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Clone by clone shotgun sequencing

• Also referred to as hierarchical shotgun
  sequencing or map-based shotgun sequencing
• Map construction pieces of genomic DNA are
  cloned using a host vector system (bacteria or
  yeast)
• Individual clones are analysed for the presence
  of unique DNA landmarks (STS, restriction sites
  ...) used to assemble overlapping clone maps.
• YACs (yeast artificial chromosomes) up to a
  megabase pair in size (used for the first
  physical maps of the human and mouse).
• BACs (100 - 200 kb)

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Clone by clone shotgun sequencing

• 2 Eric D. Green. Nature Review Genetics 2,
  573-583 (2001)

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Clone by clone shotgun sequencing

• Clone selection With the assembled BAC contig
  map, minimally overlapping clones are selected
  for shotgun sequences
• One BAC is usually selected for sequencing if
  each of the restriction fragments in its
  fingerprint is also present in one overlapping
  clone.

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Clone by clone shotgun sequencing

• 2 Eric D. Green. Nature Review Genetics 2,
  573-583 (2001)

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Clone by clone shotgun sequencing

• Subclone library selection Random fragmentation
  of the cloned DNA in each selected BAC. subclone
  it into a plasmid
• even assemblies generated with low coverage (3 -
  5x) can be used for important analysis to provide
  a working draft sequence
• highly accurate sequences (gt99.99 accurate) are
  obtained with 8 - 10x coverage.

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Clone by clone shotgun sequencing

• Directed Finishing phase
• sequence finishing is a process in which
  remaining problems with the assembly are
  resolved
• discontinuities between sequence contigs (gaps),
  areas of low quality, ambiguous bases in the
  consensus sequence...
• software facilitates the process of sequence
  finishing.
• phred statistical foundation for sequence
  assembly programs (phrap).
• Autofinish automates the finishing process
  (recommends specific additional sequencing
  reactions)

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Clone by clone shotgun sequencing

• 2 Eric D. Green. Nature Review Genetics 2,
  573-583 (2001)

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Whole genome shotgun sequencing

• Assembly of sequence reads generated in a random,
  genome-wide fashion.
• Bypasses the need for a clone-based physical map.
• Pieces of the entire genome are subcloned in
  suitable plasmid vectors.
• Sequence reads are generated from both ends of
  subclones to produce highly redundant sequence
• Coverage to deal with the problem of repetitive
  sequences.

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Whole genome shotgun sequencing

• (drosophilia, Haemophilus influenzae)
• using several size classes of subclone is
  important
• availability of long range mapping data is also
  crutially important
• software tools

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Whole genome shotgun sequencing

• 2 Eric D. Green. Nature Review Genetics 2,
  573-583 (2001)

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Hybrid strategies for shotgun sequencing

• The two strategies clone-by-clone and whole
  genome shotgun sequencing are not mutually
  exclusive.
• Mixed approach that capture the advantages of of
  both the approches.
• provide a rapid insight about the sequence of the
  entire genome
• minimizing the likelihood of serious
  misassemblies
• Finding optimal balance between generating
  sequence reads in a clone-by-clone versus whole
  genome fashion

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Hybrid strategies for shotgun sequencing

• 2 Eric D. Green. Nature Review Genetics 2,
  573-583 (2001)

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Sequencing of genomes from multicellular organisms

• 2 Eric D. Green. Nature Review Genetics 2,
  573-583 (2001)

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DNA Fragment Assembly

• Fragment assembly is trying to assemble a big
  puzzle.
• Follows the "overlap - layout - concensus
  paradigm which is used in almost all available
  assembly tools (phrap, cap, tigr, celera)
• There is no polynomial algorithm for the
  resolution of the layout step
• Finishing step is time consuming

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DNA Fragment Assembly

• fragment assembly problem finding a path in the
  overlap graph.
• Hamiltonian path problem NP-complete difficult
  problem.

1 Pavel A. Pevzner, Haixu Tang, Michael S.
Waterman. PNAS, August 2001.
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DNA Fragment Assembly

• Euler is a new algorithm and software tool that
  solves the repeat problem.
• Uses a counter-intuitive approach which consists
  in breaking the puzzle in more pieces!
• loss of information is minimal (if we still use
  'big' pieces).
• information can be restored in later stages.
• Doesn't have the overlap step
• Reduces the NP-complete Hamiltonian path problem
  to an easy to solve Eulerian path problem.

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DNA Fragment Assembly
1 Pavel A. Pevzner, Haixu Tang, Michael S.
Waterman. PNAS, August 2001.
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DNA Fragment Assembly - EULER

• A repeat corresponds to an edge rather than a
  collection of vertices.
• The problem is transformed into finding a path
  visiting every edge of the graph exactly once.
• Eulerian path problem.

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DNA Fragment Assembly - EULER

• How to construct the de Bruijn graph from
  sequencing reads?
• finished DNA sequence is not available...its
  actually what we are looking for!
• Consensus (error correction in reads) is the
  first step in the proposed approach.
• But again, how could we correct the errors
  without having the final sequence?

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DNA Fragment Assembly - EULER

• Unlike the existing tools. Euler starts with the
  consensus step
• Spectral Alignment Problem
• Error Correction Problem

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DNA Fragment Assembly - EULER

• Spectral Alignment Problem Two types of l-tuples
  (which are subsequences of length l) are defined
• solid l-tuples belonging to more than M reads (M
  is a threshold)
• weak l-tuples otherwise
• Lets T be a set of l-tuples (called a spectrum).

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DNA Fragment Assembly - EULER

• given a string s and a spectrum T find the
  minimum number of mutations in s that transform s
  into a T-string (e.g all l-tuples of s belong to
  T)
• solve the problem using dynamic programming
• Use spectral alignment of a read against all
  solid l-tuples
• Use iterative spectral alignments with the set of
  reads reduces the number of weak l-tuples (and
  increases the number of solid l-tuples)

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DNA Fragment Assembly - EULER

• Error Correction Problem
• Given a collection of reads S and a maximum of d
  errors per read, introduce d corrections in each
  read in such a way that Sl is minimised where
  Sl is the spectrum of S (all l-tuples of the
  reads and their reverse complement).
• An error in a read s affects at most 2l l-tuples
  that point to the same error
• or 2x for position within a distance xltl from
  endpoints of read.

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DNA Fragment Assembly - EULER

• Error Correction Problem
• Look for error corrections that reduce the size
  of Sl by 2l (or 2x)
• Euler uses a more evolved approach. It eliminates
  97.7 of sequencing errors (in some case going
  from 4.8 errors per read to 0.11 errors per read)
• Error correction is not perfect. It can introduce
  errors but as long as the errors are
  consistent.
• Errors introduced are corrected in a later stage.
  Eliminating the false edges in the de Bruijn
  graph being built is more important.

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DNA Fragment Assembly - EULER

• Eulerian Superpath
• S is a set of reads. The de Bruijn graph is
  defined as follows
• Sl is the set l-tuples of S
• vertices in the graph are the set S(l-1).
• if Sl contains a l-tuple whose first
  (l-1)-elements are the vertex v and last
  (l-1)-elements are the vertex w then join v and w
  in the graph.
• If S is only one read then the assembly problem
  is finding the Chinese Postman path which can be
  easily transformed to the Eulerian path problem.

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DNA Fragment Assembly - EULER

• Definitions
• source vertex
• sink vertex
• branching vertex
• repeat
• entrance
• exit

1 Pavel A. Pevzner, Haixu Tang, Michael S.
Waterman. PNAS, August 2001.
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DNA Fragment Assembly - EULER

• de Bruijn graph is very complicated even in error
  free cases.
• use the information about which l-tuples belong
  to the same reads
• covering reads (reads containing an entrance and
  an exit) reveal information about the pairing
  between entrances and exits
• tangles are repeats that do not have a covering
  read.

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DNA Fragment Assembly - EULER

• Eulerian Superpath Problem find in a given graph
  G an Eulerian path which contains a given set of
  paths P as subpaths.
• the graph G is the de Bruijn graph
• the subpaths in P are the reads.

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DNA Fragment Assembly - EULER

• Solving the subpath problem
• carry k consecutive transformations of the graph
  G and the system of paths P in order to obtain
  new 'equivalent' graph Gk and system of paths Pk.
• where every path is a single edge.
• Every solution of the Eulerian path problem in
  (Gk, Pk) provides a solution of the Eulerian
  superpath problem in (G, P)

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DNA Fragment Assembly - EULER

• Definition Px,y, P-gtx, Py-gt
• x,y-detachment reduces the number of edges in G
  to eventually 1 path per edge.
• However, in the case of multiple edges some extra
  work has to be done.

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DNA Fragment Assembly - EULER
1 Pavel A. Pevzner, Haixu Tang, Michael S.
Waterman. PNAS, August 2001.
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DNA Fragment Assembly - EULER

• resolvable path, resolvable edge
• some edges cannot be resolved even after
  detachment of all resolvable edges
• usually this situation corresponds to tangles
  (x-cuts)

1 Pavel A. Pevzner, Haixu Tang, Michael S.
Waterman. PNAS, August 2001.
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DNA Fragment Assembly - EULER

• Neseira meningitidis (NM) project
• Better results with real sequencing data than
  those obtained with other tools sing error free
  sequencing data.

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DNA Fragment Assembly - EULER
1 Pavel A. Pevzner, Haixu Tang, Michael S.
Waterman. PNAS, August 2001.
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Bibliography

• 1 An Eulerian path approach to DNA fragment
  assembly, Pavel A. Pevzner, Haixu Tang, Michael
  S. Waterman. PNAS, August 2001.
• 2 Strategies for the systematic sequencing of
  complex genomes. Eric D. Green. Nature Review
  Genetics 2, 573-583 (2001)
• 3 Eulerian Cycle / Chinese Postman. The Stony
  Brook Algorithm Repository. Steven S. Skiena.
  http//www.cs.sunysb.edu/algorith/