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Real-world protein aligners

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Real-world protein aligners. MUSCLE High throughput One of the best in accuracy ProbCons High accuracy Reasonable speed. MUSCLE at a glance. Fast measurement of all pairwise distances between sequences D DRAFT (x, y) defined in terms of # common k-mers (k~3) – O(N 2 L logL) time - PowerPoint PPT Presentation
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262 Lecture 9, Win07, Batzoglou Real-world protein aligners MUSCLE High throughput One of the best in accuracy ProbCons High accuracy Reasonable speed
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Page 1: Real-world protein aligners

CS262 Lecture 9, Win07, Batzoglou

Real-world protein aligners

• MUSCLE High throughput One of the best in accuracy

• ProbCons High accuracy Reasonable speed

Page 2: Real-world protein aligners

CS262 Lecture 9, Win07, Batzoglou

MUSCLE at a glance

1. Fast measurement of all pairwise distances between sequences • DDRAFT(x, y) defined in terms of # common k-mers (k~3) – O(N2 L logL) time

2. Build tree TDRAFT based on those distances, with UPGMA

3. Progressive alignment over TDRAFT, resulting in multiple alignment MDRAFT• Only perform alignment steps for the parts of the tree that have changed

4. Measure new Kimura-based distances D(x, y) based on MDRAFT

5. Build tree T based on D

6. Progressive alignment over T, to build M

7. Iterative refinement; for many rounds, do:• Tree Partitioning: Split M on one branch and realign the two resulting profiles• If new alignment M’ has better sum-of-pairs score than previous one, accept

Page 3: Real-world protein aligners

CS262 Lecture 9, Win07, Batzoglou

PROBCONS at a glance

1. Computation of all posterior matrices Mxy : Mxy(i, j) = Prob(xi ~ yj), using a HMM

2. Re-estimation of posterior matrices M’xy with probabilistic consistency• M’xy(i, j) = 1/N sequence z k Mxz(i, k) Myz (j, k); M’xy = Avgz(MxzMzy)

3. Compute for every pair x, y, the maximum expected accuracy alignment• Axy: alignment that maximizes aligned (i, j) in A M’xy(i, j)• Define E(x, y) = aligned (i, j) in Axy M’xy(i, j)

4. Build tree T with hierarchical clustering using similarity measure E(x, y)

5. Progressive alignment on T to maximize E(.,.)

6. Iterative refinement; for many rounds, do:• Randomized Partitioning: Split sequences in M in two subsets by flipping a coin for each

sequence and realign the two resulting profiles

Page 4: Real-world protein aligners

CS262 Lecture 9, Win07, Batzoglou

Some Resources

Genome Resources

Annotation and alignment genome browser at UCSChttp://genome.ucsc.edu/cgi-bin/hgGateway

Specialized VISTA alignment browser at LBNLhttp://pipeline.lbl.gov/cgi-bin/gateway2

ABC—Nice Stanford tool for browsing alignmentshttp://encode.stanford.edu/~asimenos/ABC/

Protein Multiple Aligners

http://www.ebi.ac.uk/clustalw/ CLUSTALW – most widely used

http://phylogenomics.berkeley.edu/cgi-bin/muscle/input_muscle.py MUSCLE – most scalable

http://probcons.stanford.edu/ PROBCONS – most accurate

Page 5: Real-world protein aligners

CS262 Lecture 9, Win07, Batzoglou

Rapid Global Alignments

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

Page 6: Real-world protein aligners

CS262 Lecture 9, Win07, Batzoglou

Page 7: Real-world protein aligners

CS262 Lecture 9, Win07, Batzoglou

Motivation

• Genomic sequences are very long:

Human genome = 3 x 109 –long Mouse genome = 2.7 x 109 –long

• Aligning genomic regions is useful for revealing common gene structure

It is useful to compare regions > 1,000,000-long

Page 8: Real-world protein aligners

CS262 Lecture 9, Win07, Batzoglou

The UCSC Browser

• http://genome.ucsc.edu/cgi-bin/hgGateway

Page 9: Real-world protein aligners

CS262 Lecture 9, Win07, Batzoglou

Main Idea

Genomic regions of interest contain islands of similarity, such as genes

1. Find local alignments2. Chain an optimal subset of them3. Refine/complete the alignment

Systems that use this idea to various degrees:MUMmer, GLASS, DIALIGN, CHAOS, AVID, LAGAN, TBA, & others

Page 10: Real-world protein aligners

CS262 Lecture 9, Win07, Batzoglou

Saving cells in DP

1. Find local alignments

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

3. Restricted DP

Page 11: Real-world protein aligners

CS262 Lecture 9, Win07, Batzoglou

Methods to CHAIN Local Alignments

Sparse Dynamic ProgrammingO(N log N)

Page 12: Real-world protein aligners

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

Page 13: Real-world protein aligners

CS262 Lecture 9, Win07, Batzoglou

Quadratic Time Solution

• Build Directed Acyclic Graph (DAG): Nodes: local alignments [(xa,xb) (ya,yb)] & score Directed edges: local alignments that can be chained

• edge ( (xa, xb, ya, yb) , (xc, xd, yc, yd) )• xa < xb < xc < xd

• ya < yb < yc < yd

Each local alignmentis a node vi with alignment score si

Page 14: Real-world protein aligners

CS262 Lecture 9, Win07, Batzoglou

Quadratic Time Solution

Initialization:Find each node va s.t. there is no edge (u, va)Set score of V(a) to be sa

Iteration:For each vi, optimal path ending in vi has total score:

V(i) = maxj s.t. there is edge (vj, vi) ( weight(vj, vi) + V(j) )

Termination:Optimal global chain: j = argmax ( V(j) ); trace chain from vj

Worst case time: quadratic

Page 15: Real-world protein aligners

CS262 Lecture 9, Win07, Batzoglou

Sparse Dynamic Programming

Back to the LCS problem:

• Given two sequences x = x1, …, xm

y = y1, …, yn

• Find the longest common subsequence Quadratic solution with DP

• How about when “hits” xi = yj are sparse?

Page 16: Real-world protein aligners

CS262 Lecture 9, Win07, Batzoglou

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

Page 17: Real-world protein aligners

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

Page 18: Real-world protein aligners

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?

Page 19: Real-world protein aligners

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’

15 3 24 16 20 4 24 3 11 18

6

42 7

1 8

10

95

113

4

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24

3

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11

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x

y

Page 20: Real-world protein aligners

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

15 3 24 16 20 4 24 3 11 18

6

42 7

1 8

10

95

113

4

20

24

3

11

15

11

4

18

20

x

y

Page 21: Real-world protein aligners

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

15 3 24 16 20 4 24 3 11 18

6

42 7

1 8

10

95

113

4

20

24

3

11

15

11

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x

y

Page 22: Real-world protein aligners

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

Page 23: Real-world protein aligners

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)

Page 24: Real-world protein aligners

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?

Page 25: Real-world protein aligners

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

Page 26: Real-world protein aligners

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

Page 27: Real-world protein aligners

CS262 Lecture 9, Win07, Batzoglou

Examples

Human Genome BrowserABC


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