1. Pairwise Sequence Alignment:
Summary of Previous Lesson
Global Alignment
Local Alignment
Blast
Fasta
Scoring Matrices
Pam
BLOSUM
Multiple Alignment (If Time Allows)

2. Global Alignment Needleman-Wunsch 1970
Idea: Build up optimal alignment from optimal alignments of subsequences
HEAG
--P-
-25
Add score from table
HEAG-
--P-A
-33
HEAGA
--P-A
-20
HEAGA
--P—
-33
Gap with bottom
Top and bottom
Gap with top

3. Global Alignment Notation xi – ith letter of string x
yj – jth letter of string y
x1..i – Prefix of x from letters 1 through I
F – matrix of optimal scores
F(i,j) represents optimal score lining up x1..i with y1..j
d – gap penalty
s – scoring matrix

4. Global Alignment The work is to build up S
Initialize: S(0,0) = 0, S(i,0) = d(i), S(0,j)=d(j)
Fill from top left to bottom right using the recursive relation
F(I,0) and F(0,j) represents aligning x to all gaps and y to all gaps respectively.

5. Global Alignment F(i-1,j-1) F(i,j-1) F(i-1,j) F(i,j) s(xi,yj) d d
yj aligned to gap
F(i-1,j-1)
F(i,j-1)
F(i-1,j)
F(i,j)
Move ahead in both
s(xi,yj) d
X represents the top string, y the bottom string d
xi aligned to gap
While building the table, keep track of where optimal score came from, reverse arrows

6. Completed Table H E A G W -8 -16 -24 -32 -40 -48 -56 -64 -72 -80 P -2-8
-16
-24
-32
-40
-48
-56
-64
-72
-80 P -2 -9
-17
-25
-33
-42
-49
-57
-65
-73
-10 -3 -4
-12
-20
-28
-36
-44
-52
-60
-18
-11 -6 -7
-15 -5
-13
-21
-29
-37
-14
-19
-22 3
-30 2
-38 1

7. Traceback Trace arrows back from the lower right to top left
Diagonal – both
Up – upper gap
Left – lower gap H E A G W -8
-16
-24
-32
-40
-48
-56
-64
-72
-80 P -2 -9
-17
-25
-33
-42
-49
-57
-65
-73
-10 -3 -4
-12
-20
-28
-36
-44
-52
-60
-18
-11 -6 -7
-15 -5
-13
-21
-29
-37
-14
-19
-22 3
-30 2
-38 1
Diagonal means use one letter from both, up means one letter from bottom and gap on top, left means one letter from top and gap on bottom.
HEAGAWGHE-E
--P-AW-HEAE

8. Local Alignment Problem
First formulated:
Smith and Waterman (1981)
Problem definition:
Find subsequences in S1 and S2 whose similarity is maximum over all pairs of subsequences from S1 and S2

9. Motivation
Searching for unknown domains or motifs within proteins from different families
Proteins encoded from Homeobox genes (only conserved in 1 region called the Homeodomain – 60 Aminoacids long, 50-95% alignment across certain insect and mammalian genes)
Identifying active sites of enzymes
Comparing long stretches of anonymous DNA
Querying databases where query word much smaller than sequences in database

10. Repeat and Overlap Matches
Repeat matches allow for sections of a sequence to match repeatedly
Repeated domain or motif
Overlap matches
Matching when the two sequences overlap
Does not penalize overhanging ends x x y y

11. Changes to DP algorithm
Interpretation of array values:
S(i,j) = score of best alignment of a suffix of G1(1..i) and a suffix of G2(1..j)
Recurrence relation:
S(i,j) = Max { 0,
S(i-1,j-1) + s(G1(i), G2(j)), S(i-k, j) + d(k), S(i, j-k) + d(k)}
Empty substrings value:
Restriction on scoring scheme

12. Changes to DP algorithm
Initialization of matrix:
First row and column with 0’s
Traceback:
Find maximum value of S(i,j)
Traceback pointers until you hit cell with value 0

13. Example Let d = -2 Let s(a,b) = 1 if a=b, and –1 otherwise
Alignment: G T G T
V(i,j) C G T A 1 2

14. Gap cost or penalty functions
Observation:
Gap of length k more probable than k gaps of length 1
Cause might be single mutational event
Separated gaps probably arose due to different events
Gap penalty functions:
Linear cost: Treats both cases uniformly
Common to use a higher cost for h for opening a gap and a lower cost g for extending a gap

15. Pairwise Alignment on the Web
The ALIGN global alignment program is available at several servers:
LFASTA uses FASTA for local alignment of 2 sequences:
BLAST 2 Sequences (NCBI)

16. End of Summary Now to a new interesting discussion on alignment.
First on alignment algorithms on the net, mainly FASTA and BLAST.

17. FASTA-Stages
Find k-tups in the two sequences (k=1,2 for proteins, 4-6 for DNA sequences)
Score and select top 10 scoring “local diagonals”
For proteins, each k-tup found is scored using the PAM250 matrix
For DNA, the number of k-tups found
Penalize intervening gaps

18. Finding k-tups position 1 2 3 4 5 6 7 8 9 10 11
protein 1 n c s p t a
protein a c s p r k
position in offset
amino acid protein A protein B pos A - posB a c k n p r s t
Note the common offset for the 3 amino acids c,s and p
A possible alignment is thus quickly found -
protein 1 n c s p t a
| | |
protein 2 a c s p r k

19. FASTA, K-tups with common offset

20. FASTA-Stages
Rescan top 10 regions, score with PAM250 (proteins) or DNA scoring matrix. Trim off the ends of the regions to achieve highest scores.
Try to join regions with gapped alignments. Join if similarity score is one standard deviation above average expected score
After finding the best initial region, FASTA performs a global alignment of a 32 residue wide region centered on the best initial region, and uses the score as the optimized score.

21. FASTA FastA is a family of programs: FastA, TFastA, FastX, FastY
Query: DNA Protein
Database: DNA Protein

22. FastA
Blosum50 default.
Lower PAM
higher blosum
to detect close sequences
Higher PAM and lower blosum
to detect distant sequences
Gap opening penalty -12, -16 by default for fasta with proteins and DNA, respectively
Gap extension penalty -2, -4 by default for fasta with proteins and DNA, respectively
The larger the word-length the less sensitive, but faster the search will be
Max number of scores and alignments is 100

23. FastA Output Database code hyperlinked to the SRS database at EBI
Accession number
Description
Length
Initn, init1, opt, z-score calculated during run
E score - expectation value, how many hits are expected to be found by chance with such a score while comparing this query to this database.
E() does not represent the % similarity

24. FASTA Output

25. BLAST Basic Local Alignment Search Tool
Altschul et al. 1990,1994,1997
Heuristic method for local alignment
Designed specifically for database searches
Idea: Good alignments contain short lengths of exact matches

26. Blast – Basic Local Alignment Search Tool
Blast uses a heuristic search algorithm and uses statistical methods of Karlin and Altshul (1990)
Blast programs were designed for fast database searching with minimal sacrifice of sensitivity for distantly related sequences

27. Low-complexity and Gapped Blast Algorithm
The SEG program has been implemented as part of the blast routine in order to mask low-complexity regions
Low-complexity regions are denoted by strings of Xs in the query sequence
In 1997 a modification introduced generation of gapped alignments
The gapped algorithm seeks only ONE ungapped alignment that makes up a significant match and hence speeds the initial database search
Dynamic programming is used to extend a central pair of aligned residues in both directions to yield the final gapped alignment
Gapped blast is 3 times faster than ungapped blast

28. Mathematical Basis of BLAST
Model matches as a sequence of coin tosses
Let p be the probability of a “head”
For a “fair” coin, p = 0.5
(Erdös-Rényi) If there are n throws, then the expected length R of the longest run of heads is
R = log1/p (n).
Example: Suppose n = 20 for a “fair” coin
R=log2(20)=4.32
Trick is how to model DNA (or amino acid) sequence alignments as coin tosses.

29. Mathematical Basis of BLAST
To model random sequence alignments, replace a match with a “head” and mismatch with a “tail”.
For DNA, the probability of a “head” is 1/4
What is it for amino acid sequences?
AATCAT
ATTCAG
HTHHHT

30. Mathematical Basis of BLAST
Model matches as a sequence of coin tosses
Let p be the probability of a “head”
For a “fair” coin, p = 0.5
(Erdös-Rényi) If there are n throws, then the expected length R of the longest run of heads is
R = log1/p (n).
Example: Suppose n = 20 for a “fair” coin
R=log2(20)=4.32
Trick is how to model DNA (or amino acid) sequence alignments as coin tosses.

31. Mathematical Basis of BLAST
So, for one particular alignment, the Erdös-Rényi property can be applied
What about for all possible alignments?
Consider that sequences are being shifted back and forth, dot matrix plot
The expected length of the longest match is
R=log1/p(mn)
where m and n are the lengths of the two sequences.

32. Steps of BLAST Filter out low-complexity regions
where L is length, N is alphabet size, ni is the number of letter i appearing in sequence. Example: AAAT
K=1/4 log4(24/(3!*1!*0!*0!))=0.25

33. Steps of BLAST
Query words of length 3 (for proteins) or 11 (for DNA) are created from query sequence using a sliding window
Expected run length in sequences of ~90 for proteins and 64 for DNA.
MEFPGLGSLGTSEPLPQFVDPALVSS
MEF
EFP
FPG
PGL
GLG
The values 90 and 64 can easily be obtained from the expected run length formula shown earlier.

34. Steps of BLAST
Using BLOSUM62 (for proteins) or scores of +5/-4 (DNA, PAM40), score all possible words of length 3 or 11 respectively against a query word.
Select a neighborhood word score threshold (T) so that only most significant sequences are kept. Approximately 50 hits per query word.
Repeat 3 and 4 for each query word in step 2. Total number of high scoring words is approximately 50 * sequence length.

35. Steps of BLAST Organize the high-scoring words into a search tree
Scan each database sequence for match to high-scoring words. Each match is a seed for an ungapped alignment. M E F G P

36. Steps of BLAST
(Original BLAST) extend matching words to the left and right using ungapped alignments. Extension continues as long as score increases or stays same. This is a HSP (high scoring pair).
(BLAST2) Matches along the same diagonal (think dot plot) within a distance A of each other are joined and then the longer sequence extended as before. (Requires lower T)

37. Steps of BLAST
Using a cutoff score S, keep only the extended matches that have a score at least S.
Determine statistical significance of each remaining match (from last time).
Try to extend the HSPs if possible.
Show Smith-Waterman local alignments.

38. Blast Application
Blast is a family of programs: BlastN, BlastP, BlastX, tBlastN, tBlastX
BlastN - nt versus nt database
BlastP - protein versus protein database
BlastX - translated nt versus protein database
tBlastN - protein versus translated nt database
tBlastX - translated nt versus translated nt database
Query: DNA Protein
Database: DNA Protein

39. Statistical Significance of Blast
Probability (P) – score of the likelihood of its having arisen by chance. The closer the p-value approaches zero, the greater the confidence that the match is real. The closer the value is to unity, the greater the chance that the match is spurious
Expected Frequency (E) value – number of hits one can expect to see by chance (noise) when searching a database of a particular size. E value of 1 – one match with a similar score by chance. E value of 0 – no matches expected by chance