1. Sequence Alignment
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2. Motivation: Types
Two sequences of same length, some characters are different (Database search)
Aagtacggaga
aagcaccgaga
Two seq are of different length, possible gaps in one of them (Database search)
Aaccaccgaga
Aa-caccgaga
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3. Motivation: Types
Match longest prefix of one with the suffix of the other (fragment assembly)
Aaacgtcgata
gatacgatg
Local alignment: longest substring matching over two sequences (homolog search)
Gatacgatgctagtttacg
agagcgatgcataattcgaatga
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4. Motivation: Types Multiple sequence alignment
(page 71) (Comparative studies of sequences)
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5. Formalizing sequence comparison
Either a character matches with the corresponding character in an an alignment (+1),
Or, it does not (-1),
Or, a gap needs to be inserted (-2)
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6. Global Alignment Smith-Waterman (1981) Dynamic programming algorithm
Scoring matrix for alignment ( p 31)
Initializing boundaries of the scoring matrix for gaps in front of either string
Meaning of an entry to the matrix
Corner element is the final score
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7. Global Alignment Three alternatives in each iteration
Ordering of calculation: row or column-wise
The algorithm (p 52)
Recursive recovery process from corner element (constant m and n, the string lengths)
Variable len returned by the algorithm
Convention for tie braking
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8. Local alignment Alignment will stop anywhere
So, the min score is zero, even on boundaries
Best local alignment is where the score is max in the matrix
Recovery starts from that max value, stops at a zero value
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9. Semi-global (as-required alignment) alignment
Four alternatives: penalty-less gaps in front of string s, in front of t, at the back of s, back of t)
Prefix-suffix matching by playing with alternatives
E.g., suffix of s with prefix of t: gaps at the back of s but in the front of t
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10. Semi-global alignment
Example: p 56
Gaps in front: zeros in row or column representing the string
Gaps at the back: recovery starts from the max of row or column representing the string
Above may be combined as required
Exercise: how to combine for matching suffix of s with prefix of t
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11. Generalized gap penalty
Multiple gaps with the same penalty as that of one or by some formula w(k)
Each block matching gaps is to be considered as one unit (like a char)
Boundary (first row and col) initialization with w(k)
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12. Generalized gap penalty
Three matrices interplaying:
one for character matching with p(I,j)
One for gaps in s
One for gaps in t
Formula on p 63
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13. Affine gap penalty Generalized gap penalty, with
W(k) = h + gk, first gap costs more h+g
Formula changes slightly with known w(k)
block gap-matrices compares only previous elements: complexity reduces
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14. Multiple sequence alignment
Function for each column: character or gap for each sequence
Combinatorics: 2^k –1, for k sequences (-1 for not putting gaps in all columns)
But . . .
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15. Multiple sequence alignment
Order of arguments for the function should not matter: f(I,-,v) = f(I,v,-)
Score pairwise on a column
Combinatorics: (k choose 2)
For k=10, 2^k-1 = 1111, kC2=45
We need gap to gap scoring now
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16. Multiple sequence alignment
Total score can be measured either way:
Sum over all columns, Or,
Sum over all pairs of sequences
If p(-, -) = 0, then both the scoring above is same
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17. Multiple sequence alignment
Consider 3 sequence alignment s1, s2, and s3
(I, j, k)-th entry of the scoring matrix is for aligning s1[1..I], s2[1..j], s3[1..k]
3D matrix (n x m x l) dimension, for |s1|=n, |s2|=m, |s3|=l
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18. Multiple sequence alignment
Each entry in scoring matrix will be at a corner of a 3D box
Optimal score is calculated over all other 7 corners (max):
A[I-1, j,k], A[I, j-1, k], A[I,j, k-1],
A[I-1, j-1, k], A[I-1, j, k-1], A[I, j-1, k-1],
A[I-1, j-1, k-1]
[Vector(I,j,k) - bit-vector]
In each case sum-of-pair scores are to be added for the column [EXAMPLE]
Initialization: (-4)I 1<=I<=n, for two gaps against substrings of s1, likewise for s2 and s3
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19. Multiple sequence alignment
For k sequences, k-dimensional matrix
Each entry is a calculation over 2^k –1 other corners of the “box”
Formula page 72
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20. Alignment improvements
Alignment could be from the back also:
S[I+1..n], t[j+1..m]
Front and back alignment could be combined to “cut” alignment: compute the two matrices, add them, align according to the added matrix
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21. Alignment improvements
When the length of two sequences are comparable and expectation is to have good global alignment:
Retrieval is mostly along the diagonal
Computation can focus around a strip (fixed (k) number) around diagonal: k-band
More efficient
Usage of relevant cells only
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22. Multiple sequence alignment: Star alignment
One sequence at center: all others are pairwise aligned against it
Which sequence to put at the center?
Try each:
create a 2D similarity matrix for all pairs, pick up the best (least of summed) row [page 79]
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23. Multiple sequence alignment: Tree alignment
A spanning tree out of the sequences: nodes are sequences
Each edge labels the similarity between pair of nodes
Total tree cost, or aggregate over edges should be max
Star is a special tree
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24. PAM matrix for matching residues
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25. BLAST search engine
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