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CMSC423: Bioinformatic Algorithms, Databases and Tools
Lecture 15
Genome assembly
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Admin• Project questions?
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Questions/answers• Why do you need a multiple alignment for phylogeny?• What is the running time of the neighbor-joining
algorithm, given k sequences of length L?• What is the parsimony score of the following tree, and
what are the labels at internal nodes?
C T AG T T
ACTG2112
ACTG2211
ACTG2322
ACTG4434
ACTG5535
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Reading assignment• http://www.cbcb.umd.edu/research/assembly_primer.shtml• Chapter 4.5 – coverage statistics• Chapter 8 – genome assembly
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Shotgun sequencing
shearing
sequencing
assemblyoriginal DNA (hopefully)
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Overview of terms
Assembly
Scaffolding
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Shortest common superstring problem
Given a set of strings, Σ=(s1, ..., sn), determine the shortest string Ssuch that every si is a sub-string of S. NP-hardapproximations: 4, 3, 2.89, ...
Greedy algorithm (4-approximation)
phrap, TIGR Assembler, CAP
...ACAGGACTGCACAGATTGATAG ACTGCACAGATTGATAGCTGA...
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Greedy algorithm detailsCompute all pairwise overlaps*Pick best (e.g. in terms of alignment score) overlapJoin corresponding readsRepeat from * until no more joins possible
• How do you compute an overlap alignment?• Hint: modify Smith-Waterman dynamic programming
algorithm
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Repeats (where greedy fails)
AAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAA AAAAAA
AAAAAA AAAAAAAAAAAA AAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
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Impact of randomness – non-uniform coverage
1 2 3 4 5 6 C
over
age
Contig
Reads
Imagine raindrops on a sidewalk
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Lander-Waterman statistics
L = read lengthT = minimum overlapG = genome sizeN = number of readsc = coverage (NL / G)σ = 1 – T/L
E(#islands) = Ne-cσ E(island size) = L(ecσ – 1) / c + 1 – σcontig = island with 2 or more reads
See chapter 4.5
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All pairs alignment• Needed by the assembler• Try all pairs – must consider ~ n2 pairs• Smarter solution: only n x coverage (e.g. 8) pairs are
possible– Build a table of k-mers contained in sequences (single pass
through the genome)– Generate the pairs from k-mer table (single pass through k-
mer table)
k-mer
A
B
C
D H I
F
G E
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Additional pairwise-alignment details• 4 types of overlaps• Often – assume first read is “forward”
• Representing the alignment
• Why not store length of overlap?
Normal
Innie
Outie
Anti-normal
A-hang B-hang
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Overlap-layout-consensus
Main entity: readRelationship between reads: overlap
12
3
45
6
78
9
1 2 3 4 5 6 7 8 9
1 2 3
1 2 3
1 2 3 12
3
1 3
2
13
2
ACCTGAACCTGAAGCTGAACCAGA
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Paths through graphs and assembly• Hamiltonian circuit: visit each node (city) exactly once,
returning to the start
A
B D C
E
H G
I
F
A
B
C
D H I
F
G E
Genome
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Sequencing by hybridization
AAAAAAACAAAGAAATAACAAACGAACTAAGA...
probes - all possible k-mers
AACAGTAGCTAGATGAACA TAGC AGAT ACAG AGCT GATG CAGT GCTA AGTA CTAG GTAG TAGA
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Assembling SBH data
Main entity: oligomer (overlap)Relationship between oligomers: adjacency
ACCTGATGCCAATTGCACT...
CTGAT follows CCTGA (they share 4 nucleotides: CTGA)
Problem: given all the k-mers, find the original string
In assembly: fake the SBH experiment - break the reads into k-mers
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Eulerian circuit
• Eulerian circuit: visit each edge (bridge) exactly once and come back to the start
ACCTAGATTGAGGTCG
CCTAGATTGAGGTCGACCTAGATTGAGGTC
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deBruijn graph• Nodes – set of k-mers obtained from the reads• Edges – link k-mers that overlap by k-1 lettersACCAGTGCA
CCAGTGCAT
• This formulation particularly useful for very short reads• Solution – Eulerian path through the graph• Note – multiple Eulerian paths possible (exponential
number) due to repeats
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deBruijn graph of Mycoplasma genitalium
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Read-length vs. genome complexity
