Velvet:%20Algorithms%20for%20De%20Novo%20Short%20Assembly%20Using%20De%20Bruijn%20Graphs

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Velvet Algorithms for De Novo Short Assembly
Using De Bruijn Graphs

• March 12, 2008
• Daniel R. Zerbino and Ewan Birney
• Presenter Seunghak Lee

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What is de Bruijn Graphs?

• De Bruijn graph is a directed graph
• An edge represents overlap between sequences of
  symbols
• V(s1, s2, , sm)
• E(v1,v2,, vn),(w1,w2,,wn))v2w1,v3w2, ,
  vnwn-1

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Introduction

• New sequencing techniques are commercially
  available (e.g. 454 Sequencing, Solexa)
• 454 Sequencing 100 200bp
• Solexa 30bp
• Algorithms whole genome shotgun (WGS) assembly
  are not suitable for short reads
• Overlap graph with a node per read is extremely
  large
• More ambiguous connections in assembly

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Introduction (cont)

• Euler assembler (Pevzner 2001) used k-mer for a
  node of de Bruijn graphs
• Reads are mapped as a path through the de Brujin
  graph
• High redundancy does not affect the number of
  nodes
• Velvet effectively deals with experimental
  errors and repeats by using Brujin graphs with
  k-mers

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De Bruijn Graphs - structure

• Structure

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De Bruijn Graphs structure (cont)

• Adjacent k-mers overlap by k-1 nucleotides
• Each node is attached to twin node
• Reverse series of reverse complement k-mers
• Overlap between reads from opposite strand
• Union of a node and its twin node is called a
  block
• Last k-mer overlaps with the first of
• its destination

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De Bruijn Graphs construction (cont)

• Construction
• Reads are hashed with predefined k-mer length
• Small k-mer ? increase connectivity
• ? more ambiguous repeats
• Large k-mer ? increase specificity
• ? decrease connectivity
• Determine k considering sensitivity and
  specificity

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De Bruijn Graphs construction (cont)

• For each k-mer, hash table records ID of the
  first read and its position
• Each k-mer is recorded with reverse complement
• Node is created if there is distinct
• interruption points
• Reads are traced through the graph
• Create a directed arc if necessary

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De Bruijn Graphs simplification

• Simplify the chains of blocks
• No information loss
• If node A has only one outgoing arc to node B,
• and if node B has only one ingoing arc ?
  merge

A
B
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De Bruijn Graphs error removal

• Velvet focuses on topological features of the
  graph
• First step remove tips
• Tip chain of nodes disconnected on one end
• Use two criteria (1) length and (2) minority
  count
• Length remove a tip if lt 2k bp
• since two nearby errors can create a
  tip up to 2k bp

error
error
k
k
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De Bruijn Graphs error removal (cont)

• Minority count multiplicity m lt n
• Starting from node B, going through the tip is an
  alternative to a more common path

m
B
A
tip
C
n
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De Bruijn Graphs error removal (cont)

• Second step remove bubbles using Tour Bus
• Redundant paths start and end at the same nodes
• Bubbles are created by errors or biological
  variants such as SNP

Bubble
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De Bruijn Graphs error removal (cont)
Tour Bus

1. Detect redundant paths

2. Compare them using dynamic
programming methods
3. If similar, merge them
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De Bruijn Graphs error removal (cont)

• Third step remove erroneous connections
• Remove erroneous connections after Tour Bus
  algorithm
• Remove erroneous connections with basic coverage
• cutoff
• Genuine short nodes which cannot be simplified in
  the graph should have high coverage

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Breadcrumb resolution of repeats

• Using read pairs, pair up the long nodes
• Flag paired reads using unambiguous long nodes

unambiguous long nodes
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Breadcrumb resolution of repeats

• Using read pairs, pair up the long nodes
• Flag paired reads using unambiguous long nodes

unambiguous long nodes
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Breadcrumb resolution of repeats

• Extends the nodes as far as possible using
  flagged paired reads
• All nodes between A and B are paired up to
• either A or B

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Experimental Results

• Test error removal pipeline on simulated data
• Simulate reads are from E. coli, S. cerevisiae,
• C.elegans, and H. sapiens
• Coverage density vs N50 for H. sapiens
• Limited by natural repetition of the reference
  genome

Ideal
Error (1)
SNP
N50
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Experimental Results (cont)

• Test error removal pipeline on experimental data
• 173,428 bp human BAC was sequenced using Solexa
  machines
• Reads were 35bp long, and k31
• Tour Bus increased sensitivity by correcting
  errors and
• preserved the integrity of the graph structure

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Experimental Results (cont)
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Experimental Results (cont)
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Conclusions

• Velvet is a de Bruijn graph based sequence
  assembly method for short reads
• Errors are handled by removing tips and Tour Bus
  algorithm
• A large number of repeats are resolved by
  Breadcrumb algorithm
• Velvet was assessed using simulated and real
  datasets and it performed well