Rapid Global Alignments

CS262 Lecture 9, Win07, Batzoglou

Rapid Global Alignments

How to align genomic sequences in (more or less) linear time

CS262 Lecture 9, Win07, Batzoglou

CS262 Lecture 9, Win07, Batzoglou

Saving cells in DP

1. Find local alignments

2. Chain -O(NlogN) L.I.S.

3. Restricted DP

CS262 Lecture 9, Win07, Batzoglou

Methods to CHAIN Local Alignments

Sparse Dynamic ProgrammingO(N log N)

CS262 Lecture 9, Win07, Batzoglou

The Problem: Find a Chain of Local Alignments

(x,y) (x’,y’)

requires

x < x’y < y’

Each local alignment has a weight

FIND the chain with highest total weight

CS262 Lecture 9, Win07, Batzoglou

Sparse Dynamic Programming

15 3 24 16 20 4 24 3 11 18

4

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• Imagine a situation where the number of hits is much smaller than O(nm) – maybe O(n) instead

CS262 Lecture 9, Win07, Batzoglou

Sparse Dynamic Programming – L.I.S.

• Longest Increasing Subsequence

• Given a sequence over an ordered alphabet

x = x1, …, xm

• Find a subsequence

s = s1, …, sk

s1 < s2 < … < sk

CS262 Lecture 9, Win07, Batzoglou

Sparse Dynamic Programming – L.I.S.Let input be w: w1,…, wn

INITIALIZATION:L: last LIS elt. array L[0] = -inf

L[1] = w1 L[2…n] = +inf

B: array holding LIS elts; B[0] = 0P: array of backpointers// L[j]: smallest jth element wi of j-long LIS seen so far

ALGORITHMfor i = 2 to n { Find j such that L[j – 1] < w[i] ≤ L[j] L[j] w[i]

B[j] iP[i] B[j – 1]

}

That’s it!!!• Running time?

CS262 Lecture 9, Win07, Batzoglou

Sparse LCS expressed as LIS

Create a sequence w

• Every matching point (i, j), is inserted into w as follows:

• For each column j = 1…m, insert in w the points (i, j), in decreasing row i order

• The 11 example points are inserted in the order given

• a = (y, x), b = (y’, x’) can be chained iff

a is before b in w, and y < y’

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CS262 Lecture 9, Win07, Batzoglou

Sparse LCS expressed as LIS

Create a sequence w

w = (4,2) (3,3) (10,5) (2,5) (8,6) (1,6) (3,7) (4,8) (7,9) (5,9) (9,10)

Consider now w’s elements as ordered lexicographically, where

• (y, x) < (y’, x’) if y < y’

Claim: An increasing subsequence of w is a common subsequence of x and y

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CS262 Lecture 9, Win07, Batzoglou

Sparse Dynamic Programming for LIS

Example:w = (4,2) (3,3) (10,5) (2,5) (8,6)

(1,6) (3,7) (4,8) (7,9) (5,9) (9,10)

L = [L1] [L2] [L3] [L4] [L5] …

1. (4,2)2. (3,3)3. (3,3) (10,5)4. (2,5) (10,5)5. (2,5) (8,6)6. (1,6) (8,6)7. (1,6) (3,7)8. (1,6) (3,7) (4,8)9. (1,6) (3,7) (4,8) (7,9)10. (1,6) (3,7) (4,8) (5,9)11. (1,6) (3,7) (4,8) (5,9) (9,10) Longest common subsequence:

s = 4, 24, 3, 11, 18

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CS262 Lecture 9, Win07, Batzoglou

Sparse DP for rectangle chaining

• 1,…, N: rectangles

• (hj, lj): y-coordinates of rectangle j

• w(j): weight of rectangle j

• V(j): optimal score of chain ending in j

• L: list of triplets (lj, V(j), j)

L is sorted by lj: smallest (North) to largest (South) value L is implemented as a balanced binary tree

y

h

l

CS262 Lecture 9, Win07, Batzoglou

Sparse DP for rectangle chaining

Main idea:

• Sweep through x-coordinates

• To the right of b, anything chainable to a is chainable to b

• Therefore, if V(b) > V(a), rectangle a is “useless” for subsequent chaining

• In L, keep rectangles j sorted with increasing lj-coordinates sorted with increasing V(j) score

V(b)V(a)

CS262 Lecture 9, Win07, Batzoglou

Sparse DP for rectangle chaining

Go through rectangle x-coordinates, from lowest to highest:

1. When on the leftmost end of rectangle i:

a. j: rectangle in L, with largest lj < hi

b. V(i) = w(i) + V(j)

2. When on the rightmost end of i:

a. k: rectangle in L, with largest lk lib. If V(i) > V(k):

i. INSERT (li, V(i), i) in Lii. REMOVE all (lj, V(j), j) with V(j) V(i) & lj li

i

j

k

Is k ever removed?

CS262 Lecture 9, Win07, Batzoglou

Examplex

y

a: 5

c: 3

b: 6

d: 4e: 2

2

56

91011

12141516

1. When on the leftmost end of rectangle i:a. j: rectangle in L, with largest lj < hi

b. V(i) = w(i) + V(j)

2. When on the rightmost end of i:a. k: rectangle in L, with largest lk lib. If V(i) > V(k):

i. INSERT (li, V(i), i) in Lii. REMOVE all (lj, V(j), j) with V(j) V(i) & lj li

a b c d eV

5

L

li

V(i)

i

55a

8

118c

11 12

911b

1512d

13

16133

CS262 Lecture 9, Win07, Batzoglou

Time Analysis

1. Sorting the x-coords takes O(N log N)

2. Going through x-coords: N steps

3. Each of N steps requires O(log N) time:

• Searching L takes log N• Inserting to L takes log N• All deletions are consecutive, so log N per deletion• Each element is deleted at most once: N log N for all deletions

• Recall that INSERT, DELETE, SUCCESSOR, take O(log N) time in a balanced binary search tree

CS262 Lecture 9, Win07, Batzoglou

Examples

Human Genome BrowserABC

CS262 Lecture 9, Win07, Batzoglou

Gene Recognition

CS262 Lecture 9, Win07, Batzoglou

Gene structure

exon1 exon2 exon3intron1 intron2

transcription

translation

splicing

exon = protein-codingintron = non-coding

Codon:A triplet of nucleotides that is converted to one amino acid

CS262 Lecture 9, Win07, Batzoglou

Where are the genes?

CS262 Lecture 9, Win07, Batzoglou

CS262 Lecture 9, Win07, Batzoglou

Needles in a Haystack

CS262 Lecture 9, Win07, Batzoglou

• Classes of Gene predictors Ab initio

• Only look at the genomic DNA of target genome De novo

• Target genome + aligned informant genome(s)

EST/cDNA-based & combined approaches• Use aligned ESTs or cDNAs + any other kind of evidence

Gene Finding

EXON EXON EXON EXON EXON

Human tttcttagACTTTAAAGCTGTCAAGCCGTGTTCTAGATAAAATAAGTATTGGACAACTTGTTAGTCTCCTTTCCAACAACCTGAACAAATTTGATGAAgtatgtaccta Macaque tttcttagACTTTAAAGCTGTCAAGCCGTGTTCTAGATAAAATAAGTATTGGACAACTTGTTAGTCTCCTTTCCAACAACCTGAACAAATTTGATGAAgtatgtaccta Mouse ttgcttagACTTTAAAGTTGTCAAGCCGCGTTCTTGATAAAATAAGTATTGGACAACTTGTTAGTCTTCTTTCCAACAACCTGAACAAATTTGATGAAgtatgta-cca Rat ttgcttagACTTTAAAGTTGTCAAGCCGTGTTCTTGATAAAATAAGTATTGGACAACTTATTAGTCTTCTTTCCAACAACCTGAACAAATTTGATGAAgtatgtaccca Rabbit t--attagACTTTAAAGCTGTCAAGCCGTGTTCTAGATAAAATAAGTATTGGGCAACTTATTAGTCTCCTTTCCAACAACCTGAACAAATTTGATGAAgtatgtaccta Dog t-cattagACTTTAAAGCTGTCAAGCCGTGTTCTGGATAAAATAAGTATTGGACAACTTGTTAGTCTCCTTTCCAACAACCTGAACAAATTCGATGAAgtatgtaccta Cow t-cattagACTTTGAAGCTATCAAGCCGTGTTCTGGATAAAATAAGTATTGGACAACTTGTTAGTCTCCTTTCCAACAACCTGAACAAATTTGATGAAgtatgta-ctaArmadillo gca--tagACCTTAAAACTGTCAAGCCGTGTTTTAGATAAAATAAGTATTGGACAACTTGTTAGTCTCCTTTCCAACAACCTGAACAAATTTGATGAAgtatgtgccta Elephant gct-ttagACTTTAAAACTGTCCAGCCGTGTTCTTGATAAAATAAGTATTGGACAACTTGTCAGTCTCCTTTCCAACAACCTGAACAAATTTGATGAAgtatgtatcta Tenrec tc-cttagACTTTAAAACTTTCGAGCCGGGTTCTAGATAAAATAAGTATTGGACAACTTGTTAGTCTCCTTTCCAACAACCTGAACAAATTTGATGAAgtatgtatcta Opossum ---tttagACCTTAAAACTGTCAAGCCGTGTTCTAGATAAAATAAGCACTGGACAGCTTATCAGTCTCCTTTCCAACAATCTGAACAAGTTTGATGAAgtatgtagctg Chicken ----ttagACCTTAAAACTGTCAAGCAAAGTTCTAGATAAAATAAGTACTGGACAATTGGTCAGCCTTCTTTCCAACAATCTGAACAAATTCGATGAGgtatgtt--tg

CS262 Lecture 9, Win07, Batzoglou

Signals for Gene Finding

1. Regular gene structure

2. Exon/intron lengths

3. Codon composition

4. Motifs at the boundaries of exons, introns, etc.Start codon, stop codon, splice sites

5. Patterns of conservation

6. Sequenced mRNAs

7. (PCR for verification)

CS262 Lecture 9, Win07, Batzoglou

Next Exon:Frame 0

Next Exon:Frame 1

CS262 Lecture 9, Win07, Batzoglou

Exon and Intron Lengths

CS262 Lecture 9, Win07, Batzoglou

Nucleotide Composition• Base composition in exons is characteristic due to the genetic code

Amino Acid SLC DNA CodonsIsoleucine I ATT, ATC, ATALeucine L CTT, CTC, CTA, CTG, TTA, TTGValine V GTT, GTC, GTA, GTGPhenylalanine F TTT, TTCMethionine M ATGCysteine C TGT, TGCAlanine A GCT, GCC, GCA, GCG Glycine G GGT, GGC, GGA, GGG Proline P CCT, CCC, CCA, CCGThreonine T ACT, ACC, ACA, ACGSerine S TCT, TCC, TCA, TCG, AGT, AGCTyrosine Y TAT, TACTryptophan W TGGGlutamine Q CAA, CAGAsparagine N AAT, AACHistidine H CAT, CACGlutamic acid E GAA, GAGAspartic acid D GAT, GACLysine K AAA, AAGArginine R CGT, CGC, CGA, CGG, AGA, AGG

CS262 Lecture 9, Win07, Batzoglou

atg

tga

ggtgag

ggtgag

ggtgag

caggtg

cagatg

cagttg

caggccggtgag

CS262 Lecture 9, Win07, Batzoglou

Splice Sites

(http://www-lmmb.ncifcrf.gov/~toms/sequencelogo.html)

CS262 Lecture 9, Win07, Batzoglou

HMMs for Gene Recognition

GTCAGATGAGCAAAGTAGACACTCCAGTAACGCGGTGAGTACATTAA

exon exon exonintronintronintergene intergene

Intergene State

First Exon State

IntronState

CS262 Lecture 9, Win07, Batzoglou

HMMs for Gene Recognition

exon exon exonintronintronintergene intergene

Intergene State

First Exon State

IntronState

GTCAGATGAGCAAAGTAGACACTCCAGTAACGCGGTGAGTACATTAA

CS262 Lecture 9, Win07, Batzoglou

Duration HMMs for Gene Recognition

TAA A A A A A A A A A A AA AAT T T T TT TT T T TT T T TG GGG G G G GGGG G G G GCC C C C C C

Exon1 Exon2 Exon3

Duration d

iPINTRON(xi | xi-1…xi-w)

PEXON_DUR(d)iPEXON((i – j + 2)%3)) (xi | xi-1…xi-w)

j+2

P5’SS(xi-3…xi+4)

PSTOP(xi-4…xi+3)

CS262 Lecture 9, Win07, Batzoglou

Genscan

• Burge, 1997

• First competitive HMM-based gene finder, huge accuracy jump

• Only gene finder at the time, to predict partial genes and genes in both strands

Features– Duration HMM– Four different parameter sets

• Very low, low, med, high GC-content

CS262 Lecture 9, Win07, Batzoglou

Using Comparative Information

CS262 Lecture 9, Win07, Batzoglou

Using Comparative Information

• Hox cluster is an example where everything is conserved

CS262 Lecture 9, Win07, Batzoglou

Patterns of Conservation

30% 1.3%0.14%

58%14%

10.2%

Genes Intergenic

Mutations Gaps Frameshifts

Separation

2-fold10-fold75-fold

CS262 Lecture 9, Win07, Batzoglou

Comparison-based Gene Finders

• Rosetta, 2000• CEM, 2000

– First methods to apply comparative genomics (human-mouse) to improve gene prediction

• Twinscan, 2001– First HMM for comparative gene prediction in two genomes

• SLAM, 2002– Generalized pair-HMM for simultaneous alignment and gene prediction in two

genomes

• NSCAN, 2006– Best method to-date based on a phylo-HMM for multiple genome gene

prediction

CS262 Lecture 9, Win07, Batzoglou

Twinscan

1. Align the two sequences (eg. from human and mouse)

2. Mark each human base as gap ( - ), mismatch ( : ), match ( | )

New “alphabet”: 4 x 3 = 12 lettersS = { A-, A:, A|, C-, C:, C|, G-, G:, G|, U-, U:, U| }

3. Run Viterbi using emissions ek(b) where b { A-, A:, A|, …, T| }

Emission distributions ek(b) estimated from real genes from human/mouse

eI(x|) < eE(x|): matches favored in exonseI(x-) > eE(x-): gaps (and mismatches) favored in introns

ExampleHuman: ACGGCGACGUGCACGUMouse: ACUGUGACGUGCACUUAlignment: ||:|:|||||||||:|

CS262 Lecture 9, Win07, Batzoglou

SLAM – Generalized Pair HMM

d

e

Exon GPHMM1.Choose exon lengths (d,e).2.Generate alignment of length d+e.

CS262 Lecture 9, Win07, Batzoglou

NSCAN—Multiple Species Gene Prediction• GENSCAN

• TWINSCAN

• N-SCAN

Target GGTGAGGTGACCAAGAACGTGTTGACAGTA

Target GGTGAGGTGACCAAGAACGTGTTGACAGTAConservation |||:||:||:|||||:||||||||......sequence

Target GGTGAGGTGACCAAGAACGTGTTGACAGTAInformant1 GGTCAGC___CCAAGAACGTGTAG......Informant2 GATCAGC___CCAAGAACGTGTAG......Informant3 GGTGAGCTGACCAAGATCGTGTTGACACAA

...

),...,,...,|( 1 oiioiii TTP III),...,|( 1 oiii TTTP

),...,,,...,|,( 11 oiioiiii TTTP III

Target sequence:

Informant sequences (vector):

Joint prediction (use phylo-HMM):

CS262 Lecture 9, Win07, Batzoglou

NSCAN—Multiple Species Gene Prediction

X

C Y

Z H

M R

)|()|()|()|()|()|()(

),,,,,,(

1

ZRPZMPYZPYHPXYPXCPAP

ZYXRMCHP

X

C

Y

Z

H

M R

)|()|()|()|()|()|()(

),,,,,,(

ZRPZMPXCPYZPYXPHYPHP

ZYXRMCHP

CS262 Lecture 9, Win07, Batzoglou

Performance Comparison

GENSCANGeneralized HMMModels human sequence

TWINSCANGeneralized HMMModels human/mouse alignments

N-SCANPhylo-HMMModels multiple sequence evolution

NSCAN human/mouse

>Human/multiple

informants

CS262 Lecture 9, Win07, Batzoglou

• 2-level architecture• No Phylo-HMM that models alignments

CONTRAST

Human tttcttagACTTTAAAGCTGTCAAGCCGTGTTCTAGATAAAATAAGTATTGGACAACTTGTTAGTCTCCTTTCCAACAACCTGAACAAATTTGATGAAgtatgtaccta Macaque tttcttagACTTTAAAGCTGTCAAGCCGTGTTCTAGATAAAATAAGTATTGGACAACTTGTTAGTCTCCTTTCCAACAACCTGAACAAATTTGATGAAgtatgtaccta Mouse ttgcttagACTTTAAAGTTGTCAAGCCGCGTTCTTGATAAAATAAGTATTGGACAACTTGTTAGTCTTCTTTCCAACAACCTGAACAAATTTGATGAAgtatgta-cca Rat ttgcttagACTTTAAAGTTGTCAAGCCGTGTTCTTGATAAAATAAGTATTGGACAACTTATTAGTCTTCTTTCCAACAACCTGAACAAATTTGATGAAgtatgtaccca Rabbit t--attagACTTTAAAGCTGTCAAGCCGTGTTCTAGATAAAATAAGTATTGGGCAACTTATTAGTCTCCTTTCCAACAACCTGAACAAATTTGATGAAgtatgtaccta Dog t-cattagACTTTAAAGCTGTCAAGCCGTGTTCTGGATAAAATAAGTATTGGACAACTTGTTAGTCTCCTTTCCAACAACCTGAACAAATTCGATGAAgtatgtaccta Cow t-cattagACTTTGAAGCTATCAAGCCGTGTTCTGGATAAAATAAGTATTGGACAACTTGTTAGTCTCCTTTCCAACAACCTGAACAAATTTGATGAAgtatgta-ctaArmadillo gca--tagACCTTAAAACTGTCAAGCCGTGTTTTAGATAAAATAAGTATTGGACAACTTGTTAGTCTCCTTTCCAACAACCTGAACAAATTTGATGAAgtatgtgccta Elephant gct-ttagACTTTAAAACTGTCCAGCCGTGTTCTTGATAAAATAAGTATTGGACAACTTGTCAGTCTCCTTTCCAACAACCTGAACAAATTTGATGAAgtatgtatcta Tenrec tc-cttagACTTTAAAACTTTCGAGCCGGGTTCTAGATAAAATAAGTATTGGACAACTTGTTAGTCTCCTTTCCAACAACCTGAACAAATTTGATGAAgtatgtatcta Opossum ---tttagACCTTAAAACTGTCAAGCCGTGTTCTAGATAAAATAAGCACTGGACAGCTTATCAGTCTCCTTTCCAACAATCTGAACAAGTTTGATGAAgtatgtagctg Chicken ----ttagACCTTAAAACTGTCAAGCAAAGTTCTAGATAAAATAAGTACTGGACAATTGGTCAGCCTTCTTTCCAACAATCTGAACAAATTCGATGAGgtatgtt--tg

SVM SVM

CRF

X

Y

a b a b

CS262 Lecture 9, Win07, Batzoglou

CONTRAST

CS262 Lecture 9, Win07, Batzoglou

• log P(y | x) ~ wTF(x, y)

• F(x, y) = i f(yi-1, yi, i, x)

• f(yi-1, yi, i, x):

1{yi-1 = INTRON, yi = EXON_FRAME_1} 1{yi-1 = EXON_FRAME_1, xhuman,i-2,…, xhuman,i+3 = ACCGGT) 1{yi-1 = EXON_FRAME_1, xhuman,i-1,…, xdog,i+1 = ACC, AGC) (1-c)1{a<SVM_DONOR(i)<b} (optional) 1{EXON_FRAME_1, EST_EVIDENCE}

CONTRAST - Features

CS262 Lecture 9, Win07, Batzoglou

• Accuracy increases as we add informants

• Diminishing returns after ~5 informants

CONTRAST – SVM accuraciesSN SP

CS262 Lecture 9, Win07, Batzoglou

CONTRAST - Decoding

Viterbi Decoding:

maximize P(y | x)

Maximum Expected Boundary Accuracy Decoding:

maximize i,B 1{yi-1, yi is exon boundary B} Accuracy(yi-1, yi, B | x)

Accuracy(yi-1, yi, B | x) = P(yi-1, yi is B | x) – (1 – P(yi-1, yi is B | x))

CS262 Lecture 9, Win07, Batzoglou

CONTRAST - Training

Maximum Conditional Likelihood Training:

maximize L(w) = Pw(y | x)

Maximum Expected Boundary Accuracy Training:

ExpectedBoundaryAccuracy(w) = i Accuracyi

Accuracyi = B 1{(yi-1, yi is exon boundary B} Pw(yi-1, yi is B | x) -

B’ ≠ B P(yi-1, yi is exon boundary B’ | x)

CS262 Lecture 9, Win07, Batzoglou

N-SCAN(Mouse)

CONTRAST(Mouse)

CONTRAST(Eleven

Informants)Gene Sn 35.6 50.8 58.6Gene Sp 25.1 29.3 35.5

Exon Sn 84.2 90.8 92.8Exon Sp 64.6 70.5 72.5Nucleotide Sn 90.8 96.0 96.9

Nucleotide Sp 67.9 70.0 72.0

Performance Comparison

N-SCAN(Mouse)

CONTRAST(Mouse)

CONTRAST(Eleven

Informants)

Gene Sn 46.8 60.7 65.4Gene Sp 31.7 40.6 46.2Exon Sn 89.7 92.6 93.9Exon Sp 66.9 74.8 76.2

Nucleotide Sn 93.7 95.7 96.7

Nucleotide Sp 69.3 74.3 75.8

De Novo

EST-assisted

HumanMacaqueMouseRatRabbitDogCowArmadilloElephantTenrecOpossumChicken

CS262 Lecture 9, Win07, Batzoglou

Performance Comparison