cs262 lecture 9, win07, batzoglou rapid global alignments how to align genomic sequences in (more or...

CS262 Lecture 9, Win07, Batzoglou

Rapid Global Alignments

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


Saving cells in DP

1. Find local alignments

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

3. Restricted DP


Methods to CHAIN Local Alignments

Sparse Dynamic ProgrammingO(N log N)


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


Sparse Dynamic Programming

15 3 24 16 20 4 24 3 11 18

4

20

24

3

11

15

11

4

18

20

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


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


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?


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’

15 3 24 16 20 4 24 3 11 18

6

4

2 7

1 8

10

9

5

11

3

4

20

24

3

11

15

11

4

18

20

x

y


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

15 3 24 16 20 4 24 3 11 18

6

4

2 7

1 8

10

9

5

11

3

4

20

24

3

11

15

11

4

18

20

x

y


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

15 3 24 16 20 4 24 3 11 18

6

4

2 7

1 8

10

9

5

11

3

4

20

24

3

11

15

11

4

18

20

x

y


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



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)



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 L

ii. REMOVE all (lj, V(j), j) with V(j) V(i) & lj li

i

j

k

Is k ever removed?


Example

x

y

a: 5

c: 3

b: 6

d: 4e: 2

2

56

9101112141516

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 L

ii. REMOVE all (lj, V(j), j) with V(j) V(i) & lj li

a b c d eV

5

L

li

V(i)

i

5

5

a

8

11

8

c

11 12

9

11

b

15

12

d

13

16

13

3


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


Examples

Human Genome BrowserABC


Gene Recognition


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


Where are the genes?Where are the genes?Where are the genes?Where are the genes?


Needles in a Haystack


• 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


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)


Next Exon:Frame 0

Next Exon:Frame 1


Exon and Intron Lengths


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

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


atgatg

tgatga

ggtgagggtgag

ggtgagggtgag

ggtgagggtgag

caggtgcaggtg

cagatgcagatg

cagttgcagttg

caggcccaggccggtgagggtgag


Splice Sites

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


HMMs for Gene Recognition

GTCAGATGAGCAAAGTAGACACTCCAGTAACGCGGTGAGTACATTAA

exon exon exonintronintronintergene intergene

Intergene State

Intergene State

First Exon State

First Exon State

IntronStateIntronState


HMMs for Gene Recognition

exon exon exonintronintronintergene intergene

Intergene State

Intergene State

First Exon State

First Exon State

IntronStateIntronState

GTCAGATGAGCAAAGTAGACACTCCAGTAACGCGGTGAGTACATTAA


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)


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


Using Comparative Information


Using Comparative Information

• Hox cluster is an example where everything is conserved


Patterns of Conservation

30% 1.3%

0.14%

58%14%

10.2%

Genes Intergenic

Mutations Gaps Frameshifts

Separation

2-fold10-fold75-fold


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


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 letters = { 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: ||:|:|||||||||:|


SLAM – Generalized Pair HMM

d

e

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


NSCAN—Multiple Species Gene Prediction

• GENSCAN

• TWINSCAN

• N-SCAN

Target GGTGAGGTGACCAAGAACGTGTTGACAGTATarget GGTGAGGTGACCAAGAACGTGTTGACAGTA

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

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

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

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):


NSCAN—Multiple Species Gene Prediction

XX

C YY

ZZ H

M R

)|()|()|(

)|()|()|()(

),,,,,,(

1

ZRPZMPYZP

YHPXYPXCPAP

ZYXRMCHP

XX

C

YY

ZZ

H

M R

)|()|()|(

)|()|()|()(

),,,,,,(

ZRPZMPXCP

YZPYXPHYPHP

ZYXRMCHP


Performance Comparison

GENSCANGeneralized HMMModels human sequence

TWINSCANGeneralized HMMModels human/mouse alignments

N-SCANPhylo-HMMModels multiple sequence evolution

GENSCANGeneralized HMMModels human sequence

TWINSCANGeneralized HMMModels human/mouse alignments

N-SCANPhylo-HMMModels multiple sequence evolution

NSCAN human/mouse

>Human/multiple

informants


• 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

SVMSVM SVMSVM

X

Y

a b a b


CONTRAST


• 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


• Accuracy increases as we add informants

• Diminishing returns after ~5 informants

CONTRAST – SVM accuracies

SN SP


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))


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)



De NovoDe Novo

EST-assistedEST-assisted

HumanMacaqueMouseRatRabbitDogCowArmadilloElephantTenrecOpossumChicken

HumanMacaqueMouseRatRabbitDogCowArmadilloElephantTenrecOpossumChicken

cs262 lecture 9, win07, batzoglou rapid global alignments how to align genomic sequences in (more or...

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