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Lecture 8: Multiple Sequence Alignment
CS 5263 Bioinformatics Lecture 8: Multiple Sequence Alignment
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Roadmap Homework? Review of last lecture Multiple sequence alignment
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Homework #1: dsDNA => mRNA => protein Coding strand
Template strand The genetic code mRNA Template strand mRNA protein
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Problem #2 For two strings of lengths m and n, the number of alignment is equal to the number of paths from (0, 0) to (m, n) How many ways we can get to (i, j) depend on how many ways we can get to its preceding neighbors
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Problem #3 Similar to problem #2
But there are some limitations on certain paths (i-1, j-1)→(i-1, j)→(i, j) is illegal So is (i-1, j-1)→(i, j-1)→(i, j) How many ways to get to (i-1, j) without using (i-1, j-1)→(i-1, j)? How many ways to get to (i, j-1) without using (i-1, j-1)→(i, j-1)?
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Problem #4 Implementation is easy
Histogram: how you bin it may affect your results bin for each discrete value you observed in your scores Scores related to base frequency? Scores differ between global and local alignments? Score distribution?
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BLAST Main idea: Construct a dictionary of all the words in the query
Alignment initiated between words of alignment score T Alignment: Ungapped extensions until score below statistical threshold Output: All local alignments with score > statistical threshold …… query …… scan DB query
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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 < 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 Added features: Pairs of words can initiate alignment
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 Extensions with gaps in a band around anchor 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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Advantages Disadvantages Fast!!!!
A few minute to search a database of 1011 bases Disadvantages Sensitivity may be low Often misses weak homologies
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New improvement Make it even faster Make it more sensitive
But even less sensitive Mainly for aligning very similar sequences or really long sequences E.g. whole genome vs whole genome Make it more sensitive PSI-BLAST: iteratively add more homologous sequences PatternHunter: discontinuous seeds
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Things we’ve covered so far
Global alignment Needleman-Wunsch and variants Improvement on space and time Local Alignment Smith-Waterman Heuristic algorithms BLAST families Statistics for sequence alignment Extreme value distribution
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Commonality They all deal with aligning two sequences
Pair-wise sequence alignment
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Today Aligning multiple sequences all together
Multiple sequence alignment
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Motivation A faint similarity between two sequences becomes very significant if present in many Protein domains Motifs responsible for gene regulation
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Definition Given N sequences x1, x2,…, xN:
Insert gaps (-) in each sequence xi, such that All sequences have the same length L Score of the global map is maximum Pairwise alignment: a hypothesis on the evolutionary relationship between the letters of two sequences Same for a multiple alignment!
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Scoring Function Ideally:
Find alignment that maximizes probability that sequences evolved from common ancestor x y ? z Phylogenetic tree or evolution tree w v
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Scoring Function (cont’d)
Unfortunately: too many parameters Compromises: Ignore phylogenetic tree Compute from pair-wise scores Based on sum of all pair-wise scores Based on scores with a consensus sequence
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First assumption Columns are independent
Similar in pair-wise alignment Therefore, the score of an alignment is the sum of all columns Need to decide how to score a single column
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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 (cont’d) The sum-of-pairs score of an alignment is the sum of the scores of all induced pairwise alignments S(m) = k<l s(mk, ml) s(mk, ml): score of induced alignment (k,l)
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Example: x: AC-GCGG-C y: AC-GC-GAG z: GCCGC-GAG A C G T - 1 -1
(A,A) + (A,G) x 2 = -1 (C,C) x 3 = 3 (-,A) x 2 + (A,A) = -1 Total score = (-1) (-2) (-2) (-1) + (-1) = 5
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Sum Of Pairs (cont’d) Drawback: no evolutionary characterization
Every sequence derived from all others Heuristic way to incorporate evolution tree Weighted Sum of Pairs: S(m) = k<l wkl s(mk, ml) wkl: weight decreasing with distance Human Mouse Duck Chicken
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Consensus score -AGGCTATCACCTGACCTCCAGGCCGA--TGCCC---
TAG-CTATCAC--GACCGC--GGTCGATTTGCCCGAC CAG-CTATCAC--GACCGC----TCGATTTGCTCGAC CAG-CTATCAC--GACCGC--GGTCGATTTGCCCGAC Consensus sequence: Find optimal consensus string m* to maximize S(m) = i s(m*, mi) s(mk, ml): score of pairwise alignment (k,l)
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Multiple Sequence Alignments
Algorithms
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Multidimensional Dynamic Programming (MDP)
Generalization of Needleman-Wunsh: Find the longest path in a high-dimensional cube As opposed to a two-dimensional grid Uses a N-dimensional matrix As apposed to a two-dimensional array Entry F(i1, …, ik) represents score of optimal alignment for s1[1..i1], … sk[1..ik] F(i1,i2,…,iN) = max(all neighbors of a cell) (F(nbr)+S(current))
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Multidimensional Dynamic Programming (MDP)
Example: in 3D (three sequences): 23 – 1 = 7 neighbors/cell (i-1,j-1,k-1) (i-1,j,k-1) (i-1,j-1,k) (i-1,j,k) F(i-1,j-1,k-1) + S(xi, xj, xk), F(i-1,j-1,k ) + S(xi, xj, -), F(i-1,j ,k-1) + S(xi, -, xk), F(i,j,k) = max F(i ,j-1,k-1) + S(-, xj, xk), F(i-1,j ,k ) + S(xi, -, -), F(i ,j-1,k ) + S(-, xj, -), F(i ,j ,k-1) + S(-, -, xk) (i,j-1,k-1) (i,j,k-1) (i,j-1,k) (i,j,k)
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Multidimensional Dynamic Programming (MDP)
Running Time: Size of matrix: LN; Where L = length of each sequence N = number of sequences Neighbors/cell: 2N – 1 Therefore………………………… O(2N LN)
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Faster MDP Carrillo & Lipman, 1988
Branch and bound Other heuristics Practical for about 6 sequences of length about
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Progressive Alignment
Multiple Alignment is NP-hard Most used heuristic: Progressive Alignment Algorithm: Align two of the sequences xi, xj Fix that alignment Align a third sequence xk to the alignment xi,xj Repeat until all sequences are aligned Running Time: O(NL2) Each alignment takes O(L2) Repeat N times
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Progressive Alignment
x y z w When evolutionary tree is known: Align closest first, in the order of the tree Example: Order of alignments: 1. (x,y) 2. (z,w) 3. (xy, zw)
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Progressive Alignment: CLUSTALW
CLUSTALW: most popular multiple protein alignment Algorithm: Find all dij: alignment dist (xi, xj) High alignment score => short distance Construct a tree (Neighbor-joining hierarchical clustering. Will discuss in future) Align nodes in order of decreasing similarity + a large number of heuristics
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CLUSTALW example S1 ALSK S2 TNSD S3 NASK S4 NTSD
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CLUSTALW example S1 ALSK S2 TNSD S3 NASK S4 NTSD s1 s2 s3 s4 9 4 7 8 3
9 4 7 8 3 Distance matrix
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CLUSTALW example S1 ALSK S2 TNSD S3 NASK S4 NTSD s1 s1 s2 s3 s4 9 4 7
9 4 7 8 3 s3 s2 s4
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CLUSTALW example S1 ALSK S2 TNSD S3 NASK S4 NTSD s1 s1 s2 s3 s4 9 4 7
9 4 7 8 3 s3 s2 s4
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CLUSTALW example S1 ALSK S2 TNSD S3 NASK S4 NTSD s1 s1 s2 s3 s4 9 4 7
9 4 7 8 3 s3 s2 s4
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CLUSTALW example S1 ALSK S2 TNSD S3 NASK S4 NTSD -ALSK -TNSD NA-SK
Question: how do you align two alignments? S1 ALSK S2 TNSD S3 NASK S4 NTSD -ALSK NA-SK -ALSK -TNSD NA-SK NT-SD -TNSD NT-SD s1 s1 s2 s3 s4 9 4 7 8 3 s3 s2 s4
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Aligning two alignments
You can treat each column in an alignment as a single letter Remember in the case of gene finder, we aligned three nucleic acids at a time How do we score it? Naïve: compute Sum of Pair Better: only compute the cross terms We already have (K, K) and (D, D) Need to add 2x(K, D) -ALSK NA-SK -TNSD NT-SD
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CLUSTALW & the CINEMA viewer
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Iterative Refinement Problems with progressive alignment:
Depend on pair-wise alignments If sequences are very distantly related, much higher likelihood of errors Initial alignments are “frozen” even when new evidence comes Example: x: GAAGTT y: GAC-TT z: GAACTG w: GTACTG Frozen! Now clear: correct y should be GA-CTT
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Iterative Refinement Algorithm (Barton-Stenberg):
Align most similar xi, xj Align xk most similar to (xixj) Repeat 2 until (x1…xN) are aligned For j = 1 to N, Remove xj, and realign to x1…xj-1xj+1…xN Repeat 4 until convergence Note: Guaranteed to converge Running time: O(kNL2), k: number of iterations
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Iterative Refinement (cont’d)
For each sequence y Remove y Realign y (while rest fixed) z x allow y to vary y x,z fixed projection
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Iterative Refinement Example: align (x,y), (z,w), (xy, zw):
x: GAAGTTA y: GAC-TTA z: GAACTGA w: GTACTGA After realigning y: y: G-ACTTA + 3 matches
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Iterative Refinement Example not handled well: x: GAAGTTA y1: GAC-TTA
z: GAACTGA w: GTACTGA Realigning any single yi changes nothing
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Restricted MDP Similar to bounded DP in pair-wise alignment
Construct progressive multiple alignment m Run MDP, restricted to radius R from m z x y Running Time: O(2N RN-1 L)
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Restricted MDP Within radius 1 of the optimal
x: GAAGTTA y1: GAC-TTA y2: GAC-TTA y3: GAC-TTA z: GAACTGA w: GTACTGA Within radius 1 of the optimal Restricted MDP will fix it.
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Other approaches Profile Hidden Markov Models
Statistical learning methods Will discuss in future
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Multiple alignment tools
Clustal W (Thompson, 1994) Most popular PRRP (Gotoh, 1993) HMMT (Eddy, 1995) DIALIGN (Morgenstern, 1998) T-Coffee (Notredame, 2000) MUSCLE (Edgar, 2004) Align-m (Walle, 2004) PROBCONS (Do, 2004)
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In summary Multiple alignment algorithms: MDP (too slow)
B&B doesn’t solve the problem entirely Progressive alignment: clustalW Iterative refinement Restricted MDP
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