Overview of Genome Assembly Algorithms

Introduction
OLC
Graph theory and assembly
deBruijn - Euler

Genome Assembly Algorithms and Software
(or...what to do with all that sequence data ?)

Konstantinos Krampis

Asst. Professor, Informatics
J. Craig Venter Institute

George Washington University, Nov. 2nd 2011

Konstantinos Krampis Genome Assembly Algorithms and Software

Introduction
OLC
deBruijn - Euler

Introduction
Why do we need genome assembly
Deﬁnitions of genome assembly
OLC
Overlap
Layout
Consensus
OLC assembly software and publications
Deﬁnition of a graph
Graphs and genome assembly
deBruijn - Euler
An alternative assembly graph
Constructing a de Bruijn graph from reads
Genome assembly from de Bruijn graphs
deBruijn assembly software and publications

Introduction
OLC Why do we need genome assembly
Graph theory and assembly Deﬁnitions of genome assembly
deBruijn - Euler

Cannot read the complete genome
with the sequencer from one end to
the other !

DNA isolated from a cell is
ampliﬁed

Broken into fragments (shearing)

Fragments are ”read” with the
sequencer

Use the fragments - reads to
reconstruct the genome from
Credit: Masahiro Kasahara, Large-Scale Genome Sequence
sequencing reads
Processing, Imprerial College Press


Introduction
deBruijn - Euler

Assembly: hierarchical process
to reconstruct genome from
reads

Assemble the puzzle of the
genome from the reads:
overlaps connect the pieces

Oversample the genome so that
reads overlap

Key approach: data structure
representing overlaps, and
algorithms operating on that Credit: Masahiro Kasahara, Large-Scale Genome Sequence

data structure Processing, Imprerial College Press


Introduction
deBruijn - Euler

Two major algorithmic paradigms for genome assembly

Overlap - Layout - Consensus (OLC): well established,
more powerful method, but more diﬃcult to implement

OLC: ﬁrst to be used successfully for complex Eucaryotic
genomes (Drosophila,H.sapiens)

deBruijn - Euler: newer, easier to implement, problematic
in complex genomes (for current implementations)


Introduction Overlap
OLC Layout
Graph theory and assembly Consensus
deBruijn - Euler OLC assembly software and publications

Find Overlaps by aligning
the sequence of the reads

Layout the reads based
on which aligns to which

Get Consensus by joining
all read sequences,
merging overlaps

Sequencer reads in
random direction,
left-to-right or Credit: Masahiro Kasahara, Large-Scale Genome Sequence Processing,

right-to-left Imprerial College Press


OLC Layout

Sequence alignment,
all-against-all reads
(Smith-Watermann,
BLAST, other?)

Computationally intensive
but easily parallelizable

Represent read overlap by
connecting with directed Credit: Kececioglu and Myers 1995, Algorithmica 13:7-51
link

First step in creating the
genome assembly graph
(more later)

OLC Layout

Create a consistent linear
(ideally) ordering of the
reads

Remove redundancy, so
no two dovetails leave
the same edge

No containment edge is
followed by a dovetail
edge

Remove cycles, one link
in, one out


OLC Layout

Multiple Sequence
Alignment (ClustalW)
algorithms ? No
phylogeny here...

Vote for the most abundant
nucleotide for each position

Incorporate read quality data

Create pre-consensus from
high-quality reads, and align
remaining reads to it


OLC Layout

Celera Assembler

Developed at Celera Genomics for ﬁrst Drosophila and human genome
assemblies

Continuoued development at J. Craig Venter Inst. as open source project

http://wgs-assembler.SourceForge.net (Licence: GPL)

Plently of wiki (developer + user) documentation, examples, user forums

Other OLC implementations: Arachne, PCAP, Newbler, Phrap, TIGR
Assembler


OLC Layout

Celera Assembler publications

Myers et al (2000) A whole-genome assembly of Drosophila
Levy et al (2007) The diploid genome sequence of an individual human
Zimin et al (2009) The domestic cow, Bos taurus
Dalloul et al (2010) The domestic turkey, Meleagris gallopavo
Lorenzi et al (2010) New assembly of Entamoeba histolytica
Lawniczak et al (2010) Divergence in Anopheles gambiae
Jones et al (2011) The marine ﬁlamentous cyanobacterium Lyngbya
majuscula
Miller et al The Tasmanian devil, Sarcophilus harrisii
Prfer et al The great ape bonobo, Pan paniscus
Gordon et al The cotton bollworm moth, Helicoverpa

Introduction
OLC Deﬁnition of a graph
Graph theory and assembly Graphs and genome assembly
deBruijn - Euler

and now a bit of Graph Theory...


Introduction
deBruijn - Euler

Graph G with set of vertices (nodes)
V: {P,T,Q,S,R}

set of edges (links between nodes)
E: {(P,T),(P,Q),(P,S),(Q,T),
(S,T),(Q,S),(S,Q),(Q,R),(R,S)}

walk from P to R:(P,Q),(Q,R)

walk from R to T:(R,S),(S,Q),(Q,T)
or (R,S),(S,T) Credit: Introduction to Graph Theor
Robert J. Wilson
walk from R to P: not possible


Introduction
deBruijn - Euler

Trail: a walk of the graph where
each edge is visited only once

Example Trail: (P,Q), (Q,R),
(R,S), (S,Q), (Q,S), (S,T)

Path: a walk where each vertice
is visited once

Example Path: (P,Q), (Q,R),
(R,S), (S,T)


Introduction
deBruijn - Euler

Credit: Saad Mneimneh, CUNY


Introduction
deBruijn - Euler

Represent sequence overlaps as
a graph with weighted edges

SCS solution: ﬁnd Path (visit
all edges and vertices once) that
maximizes weight sum

Hamiltonian Cycle or Traveling
Saleman Problem


Introduction
deBruijn - Euler

Which edge to start from?

NO: misses a vertex NO: misses edge with large weight


Introduction
deBruijn - Euler

YES!: all vertices and edge with large weight


Introduction
deBruijn - Euler

A more realistic version of a read / string overlap graph (C. jejuni)
Credit: Eugene W. Myers Bioinformatics 21:79-85


Introduction
deBruijn - Euler

Computational Complexity

SCS solution by searching for a
Hamiltonian Cycle on a graph is a
diﬃcult algorithmic problem
(NP-hard)

Using approximation or greedy
algorithms can yield a 2 to
4-aprroximation solutions (twice or
four times the length of the
optimal-shortest string)

Transformation of Overlap Graph
to String Graph leads to
Polynomial time solution. No Polynomial(P) : O(n), O(n2 ), O(n3 )etc.
assembler implementation yet. (1)

Introduction An alternative assembly graph
OLC Constructing a de Bruijn graph from reads
Graph theory and assembly Genome assembly from de Bruijn graphs
deBruijn - Euler deBruijn assembly software and publications

Pevzner, Tang and
Waterman, An
Eulerian path
approach to DNA
fragment assembly,
PNAS 98 2001
9748-9753.



deBruijn graph: a directed graph representing overlaps between
sequences of symbols
Credit: Wikipedia



In a real genome scenario...

Credit: Flicek and Birney 2009, Nature Methods 6, S6 - S12



Euler’s algorithm

Using Euler’s algorithm we can ﬁnd a path that visits each edge of the de
Bruijn genome assembly graph once, in order to concatenate the edge
labels and ”spell out” the assembly. Polynomial time!
Credit: Wikipedia



Euler assembler (the very ﬁrst), Pevzner et al 2001 PNAS
98:9748-9753

Velvet assembler (more user friendly),

Both those assemlers store the complete graph on the computer
memory 512GB-1024GB for human genomes

At JCVI we have two 1024GB (1TB) RAM servers for assembly

others: ABYSS, YAGA, Contrail-Bio, PASHA parallel (distributed
memory) assemblers on computer clusters



Thank you!

contact: kkrampis@jcvi.org

We hire interns at the J. Craig Venter Institute:
http://www.jcvi.org/cms/education/internship-program/

Some of my other projects - Cloud Computing:
http://tinyurl.com/cloudbiolinux-jcvi
http://www.cloudbiolinux.org


Overview of Genome Assembly Algorithms

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