Alignments and Comparative Genomics

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Alignments and Comparative Genomics
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Welcome to CS374!

• Today
• Serafim Alignments and Comparative Genomics
• Omkar Administrivia

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Biology in One Slide Twentieth Century
and today
ACGTGACTGAGGACCGTG CGACTGAGACTGACTGGGT CTAGCTAGAC
TACGTTTTA TATATATATACGTCGTCGT ACTGATGACTAGATTACAG
ACTGATTTAGATACCTGAC TGATTTTAAAAAAATATT
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Complete DNA Sequences
nearly 200 complete genomes have been sequenced
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Evolution
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Evolution at the DNA level
Deletion
Mutation
ACGGTGCAGTTACCA
SEQUENCE EDITS
AC----CAGTCCACCA
REARRANGEMENTS
Inversion
Translocation
Duplication
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Evolutionary Rates



next generation
OK



OK



OK



X



X



Still OK?



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Sequence conservation implies function

• Alignment is the key to
• Finding important regions
• Determining function
• Uncovering the evolutionary forces

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Sequence Alignment
AGGCTATCACCTGACCTCCAGGCCGATGCCC TAGCTATCACGACCGCGG
TCGATTTGCCCGAC
-AGGCTATCACCTGACCTCCAGGCCGA--TGCCC--- TAG-CTATCAC-
-GACCGC--GGTCGATTTGCCCGAC
Definition Given two strings x x1x2...xM, y
y1y2yN, an alignment is an assignment of
gaps to positions 0,, N in x, and 0,, N in y,
so as to line up each letter in one sequence
with either a letter, or a gap in the other
sequence
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What is a good alignment?

• Alignment
• The best way to match the letters of one
  sequence with those of the other
• How do we define best?
• Alignment
• A hypothesis that the two sequences come from a
  common ancestor through sequence edits
• Parsimonious explanation
• Find the minimum number of edits that transform
  one sequence into the other

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Scoring Function

• Sequence edits AGGCCTC
• Mutations
  
• AGGACTC
• Insertions
• AGGGCCTC
• Deletions
• AGG.CTC
• Scoring Function
• Match m
• Mismatch -s
• Gap -d
• Score F ( matches) ? m - ( mismatches) ? s
  (gaps) ? d

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How do we compute the best alignment?
AGTGCCCTGGAACCCTGACGGTGGGTCACAAAACTTCTGGA
Too many possible alignments O( 2MN)
AGTGACCTGGGAAGACCCTGACCCTGGGTCACAAAACTC
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Dynamic Programming

• Given two sequences x x1xM and y y1yN
• Let F(i, j) Score of best alignment of x1xi
  to y1yj
• Then, F(M, N) Score of best alignment
• Idea
• Compute F(i, j) for all i and j
• Do this by using F(i1 , j), F(i, j1), F(i1,
  j1)

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Dynamic Programming (contd)

• Notice three possible cases
• xi aligns to yj
• x1xi-1 xi
• y1yj-1 yj
• 2. xi aligns to a gap
• x1xi-1 xi
• y1yj -
• yj aligns to a gap
• x1xi -
• y1yj-1 yj

m, if xi yj F(i,j) F(i-1, j-1)
-s, if not
F(i,j) F(i-1, j) - d
F(i,j) F(i, j-1) - d
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Dynamic Programming (contd)

• How do we know which case is correct?
• Inductive assumption
• F(i, j-1), F(i-1, j), F(i-1, j-1) are optimal
• Then,
• F(i-1, j-1) s(xi, yj)
• F(i, j) max F(i-1, j) d
• F( i, j-1) d
• Where s(xi, yj) m, if xi yj -s, if not

i-1, j-1
i-1, j
i, j-1
i, j
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Example

• x AGTA m 1
• y ATA s -1
• d -1

F(i,j) i 0 1 2 3 4
Optimal Alignment F(4,3) 2 AGTA A - TA
j 0
1
2
3
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The Needleman-Wunsch Matrix
x1 xM
Every nondecreasing path from (0,0) to (M, N)
corresponds to an alignment of the two
sequences
y1 yN
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The Needleman-Wunsch Algorithm

• Initialization.
• F(0, 0) 0
• F(0, j) - j ? d
• F(i, 0) - i ? d
• Main Iteration. Filling-in partial alignments
• For each i 1M
• For each j 1N
• F(i-1,j) d case 1
• F(i, j) max F(i, j-1) d case
  2
• F(i-1, j-1) s(xi, yj) case 3
• UP, if case 1
• Ptr(i,j) LEFT if case 2
• DIAG if case 3
• Termination. F(M, N) is the optimal score, and
• from Ptr(M, N) can trace back optimal alignment

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Performance

• Time
• O(NM)
• Space
• O(NM)

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Alignment on a Large Scale

• Given a newly sequenced organism,
• Which subregions align with other organisms?
• Potential genes
• Other biological characteristics
• Assume we use Dynamic Programming

Our newly sequenced mammal
3?109
The entire genomic database
1010 - 1011
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Index-based Local Alignment

• Main idea
• Construct a dictionary of all the words in the
  query
• Initiate a local alignment for each word match
  between query and DB
• Running Time
• Theoretical worst case O(MN)
• Fast in practice

query
DB
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Index-based Local Alignment BLAST

• Dictionary
• All words of length k (11)
• Alignment initiated between exact-matching words
  
• (more generally, between words of alignment
  score ? T)
• Alignment
• Ungapped extensions until score
• below statistical threshold
• Output
• All local alignments with score
• gt statistical threshold

query

scan
DB
query
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Index-based Local Alignment BLAST
A C G A A G T A A G G T C
C A G T
Example k 4, T 4 The matching word GGTC
initiates an alignment Extension to the left and
right with no gaps until alignment falls lt
50 Output GTAAGGTCC GTTAGGTCC
C C C T T C C T G G A T T
G C G A
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Gapped BLAST
A C G A A G T A A G G T C
C A G T

• Added features
• Pairs of words can initiate alignment
• Nearby alignments are merged
• Extensions with gaps until score lt T below best
  score so far
• Output
• GTAAGGTCCAGT
• GTTAGGTC-AGT

C T G A T C C T G G A T T
G C G A
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Example

• Query gattacaccccgattacaccccgattaca (29 letters)
  2 mins
• Database All GenBankEMBLDDBJPDB sequences
  (but no EST, STS, GSS, or phase 0, 1 or 2 HTGS
  sequences) 1,726,556 sequences 8,074,398,388
  total letters
• gtgi28570323gbAC108906.9 Oryza sativa
  chromosome 3 BAC OSJNBa0087C10 genomic sequence,
  complete sequence Length 144487 Score 34.2
  bits (17), Expect 4.5 Identities 20/21 (95)
  Strand Plus / Plus
• Query 4 tacaccccgattacaccccga 24
• Sbjct 125138 tacacccagattacaccccga 125158
• Score 34.2 bits (17),
• Expect 4.5 Identities 20/21 (95) Strand
  Plus / Plus
• Query 4 tacaccccgattacaccccga 24
• Sbjct 125104 tacacccagattacaccccga 125124
• gtgi28173089gbAC104321.7 Oryza sativa
  chromosome 3 BAC OSJNBa0052F07 genomic sequence,
  complete sequence Length 139823 Score 34.2
  bits (17), Expect 4.5 Identities 20/21 (95)
  Strand Plus / Plus

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Efficient global alignment
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Global alignment with the chaining approach

• Find local alignments
• Chain them into a rough global map
• Align regions in-between

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LAGAN 1. FIND Local Alignments

• Find Local Alignments
• Chain Local Alignments
• Restricted DP

Mike Brudno, Chuong B Do, et al.
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LAGAN 2. CHAIN Local Alignments

• Find Local Alignments
• Chain Local Alignments
• Restricted DP

Mike Brudno, Chuong B Do, et al.
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LAGAN 3. Restricted DP

• Find Local Alignments
• Chain Local Alignments
• Restricted DP

Mike Brudno, Chuong B Do, et al.
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Restricted DP (contd)

• What if a box is too large?
• Recursive application of LAGAN,
• more sensitive word search

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Multiple Alignment
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(No Transcript)
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Scoring Function Sum Of Pairs

• Definition Induced pairwise alignment
• A pairwise alignment induced by the multiple
  alignment
• Example
• x AC-GCGG-C
• y AC-GC-GAG
• z GCCGC-GAG
• Induces
• x ACGCGG-C x AC-GCGG-C y AC-GCGAG
• y ACGC-GAC z GCCGC-GAG z GCCGCGAG

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Sum Of Pairs (contd)

• The sum-of-pairs score of an alignment is the
  sum of the scores of all induced pairwise
  alignments
• S(m) ?kltl s(mk, ml)
• s(mk, ml) score of induced alignment (k,l)

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Dynamic Programming for Multiple Alignment
AGTGCCCTGGAACCCTGACGGTGGGTCACAAAACTTCTGGA
AGTGACCTGGGAAGACCCTGACCCTGGGTCACAAAACTC
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Progressive Alignment

• Multiple Alignment is NP-complete
• Most used heuristic Progressive Alignment
• Algorithm
• Until all sequences are aligned
• Align two (multi-)sequences to each other, and
  treat the result as a new sequence
• Example aligning AACTGTA with AATGTC, gives
• AACTGTA
• AA-TGTC, with letters (AA), (AA), (C-), (TT),
  (GG), (TT), (AC)
• Running Time O(NL2), where N seqs, L length
  of a seq

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MLAGAN Progressive Alignment
Human
Baboon
Mouse
Rat

• Given N sequences, phylogenetic tree
• Align pairwise, in order of the tree (LAGAN)
• With needed generalizations for multi-anchoring
  scoring edit distance

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Evolution at the DNA level
Deletion
Mutation
ACGGTGCAGTTACCA
SEQUENCE EDITS
AC----CAGTCCACCA
REARRANGEMENTS
Inversion
Translocation
Duplication
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Local Global Alignment
Global
Local
AGTGCCCTGGAACCCTGACGGTGGGTCACAAAACTTCTGGA
AGTGACCTGGGAAGACCCTGAACCCTGGGTCACAAAACTC
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Glocal Alignment Problem

• Find least cost transformation of one sequence
  into another using shuffle operations

AGTGCCCTGGAACCCTGACGGTGGGTCACAAAACTTCTGGA

• Sequence edits
• Inversions
• Translocations
• Duplications
• Combinations of above

AGTGACCTGGGAAGACCCTGAACCCTGGGTCACAAAACTC
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SLAGAN 1. Find Local Alignments

• Find Local Alignments
• Build Rough Homology Map
• Globally Align Consistent Parts

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SLAGAN 2. Build Homology Map

• Find Local Alignments
• Build Rough Homology Map
• Globally Align Consistent Parts

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SLAGAN 2. Build Homology Map
Chain using Sparse Dynamic Programming

• Penalties
• regular
• translocation

c) inversion d) inverted translocation
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SLAGAN 2. Build Homology Map

• Find Local Alignments
• Build Rough Homology Map
• Globally Align Consistent Parts

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SLAGAN 3. Global Alignment

• Find Local Alignments
• Build Rough Homology Map
• Globally Align Consistent Parts

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SLAGAN Example Chromosome 20

• Human Chromosome 20 versus Mouse Chromosome 2
• 270 Segments of conserved synteny
• 70 Inversions

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SLAGAN example HOX cluster

• 10 paralogous genes
• Conserved order in Human/Mouse/Rat

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SLAGAN example HOX cluster

• 10 paralogous genes
• Conserved order in Human/Mouse/Rat

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Whole-genome alignment with SLAGAN

• Two-step Shuffle
• Shuffle for large-scale synteny map
• Shuffle each syntenic region for
  microrearrangements

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The ENCODE Project
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ENCODE regions shuffled
Hum/Rat
Hum/Mus
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ENCODE regions shuffled
Hum/Mus
Hum/Rat
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ENCODE regions shuffled
Hum/Rat
Hum/Mus
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ENCODE regions shuffled
Hum/Mus
Hum/Rat
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ENCODE regions shuffled
Hum/Rat
Hum/Mus
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Constrained Elements in Alignments
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Human-Mouse-Rat
Berkeley Genome Pipeline http//pipeline.lbl.gov
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Human-Mouse-Rat
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More DNA is coming