1. Chap. 4: Multiple Sequence Alignment
Pairwise Alignment
Dynamic Programming
Multi-sequence Alignment
FASTA (Fast Alignment)
BLAST (Basic Local Alignment Search Tool)

2. FASTA Pearson and Lipman, 1988, Fast Alignment
Steps
Perform exact match of a subsequences in the query sequence of at least length ktup to subsequences of database sequences
ktup: default – 2 AA
Search diagonal regions in the alignment matrix that contain as many of subsequence matches with small distances between subsequences
Then, see if initial regions can be joined by allowing gaps
Time saved
By performing dynamic programming on initially filtered sequences which are already similar
Only considers pathways through the alignment matrix that remain within a band centered around the highest-scoring initial regions

4. Blast
Exact methods are good and can pick up very distant relationships
Approximate methods can detect only close relationships well
Maybe OK when the probe sequence is fairly similar to one or more sequences in the databank
Take a small k residues in the probe sequence, find all instances of the k-tuple in the database
For the selected candidate sequences, approximate optimal alignment is performed
Particularly useful in multi-sequence alignments

5. Blast
Detect
the best region of local alignment between a query and the target
and if there are other plausible alignments
Computational efficiency comes from “seeding” the search with a small subset of substrings in the query
Substrings from two sequences may be highly conserved in biological applications
Temple Smith and Michael Waterman, 1981
Biologically relevant diagonal matches are likely to have a higher score

6. Word Length and Threshold
Select word length, w (similar to ktup, default is 3 AA), and a threshold T
Given word length of w, scan database for words of length w that score higher than a threshold T
Example: for a human RBP query
…FSGTWYA… (query word in red)
A list of words (w=3) is:
FSG SGT GTW TWY WYA
YSG TGT ATW SWY WFA
FTG SVT GSW TWF WYS

7. (T=11) According to Blosum62 GTW 6,5,11 22 neighborhood GSW 6,1,11 18
word hits ATW 0,5,11 16
> threshold NTW 0,5,11 16
GTY 6,5,2 13
GNW 10
neighborhood GAW 9
word hits
< below threshold
(T=11)

8. Effect of Threshold You can modify the threshold parameter.
The default value for blastp is 11.
To change it, enter “-f 16” or “-f 5” in the
advanced options of BLAST+.
(To find BLAST+ go to BLAST  help  download.)

9. extend extend Hit! KENFDKARFSGTWYAMAKKDPEG 50 RBP (query)
2. Scan the database for entries matching compiled list
3. In each direction, extension terminates when the score falls more than a certain distance below the best score reached so far
KENFDKARFSGTWYAMAKKDPEG 50 RBP (query)
MKGLDIQKVAGTWYSLAMAASD. 44 lactoglobulin (hit)
extend
extend
Hit!

11. Identify all exact matches of k-tuple words (no gaps, no mismatches)
Extend exact matches in both directions (no gaps, no mismatches)
Put extended matches together with mismatches and gaps, only in limited regions containing preliminary matches

14. Blast, 1997 Refined to require two independent hits
The hits must occur in close proximity to each other.
With this modification, only one seventh as many extensions occurred
greatly speeding the time required for a search

15. Comparison of Search Methods
FASTA vs. BLAST
FASTA is more sensitive for DNA-DNA searches, especially for highly diverged sequences.
BLAST is better at finding short regions of high similarity, while FAST is better at finding long regions of lower similarity BLAST will miss similar sequences if they do not have a single identical word
Protein similarity search can find more distant similarities
DNA has four letters and thus the prob. of chancy matches is much greater
Protein databanks are much smaller, and searches can be more sensitive
William Pearson (FASTA author):
“The number one thing that you should learn is that in general, you should try not do DNA sequence comparison.”
Protein-protein search from BLASTX produces more sensitive results than DNA-DNA search

16. Blast (Basic Local Alignment Search Tool)
Program Input Database 1
blastn DNA DNA
blastp protein protein 6
blastx DNA protein
tblastn protein DNA 36
tblastx DNA DNA

17. DNA can encode six Proteins
5’ CAT CAA
5’ ATC AAC
5’ TCA ACT
5’ CATCAACTACAACTCCAAAGACACCCTTACACATCAACAAACCTACCCAC 3’
3’ GTAGTTGATGTTGAGGTTTCTGTGGGAATGTGTAGTTGTTTGGATGGGTG 5’
5’ GTG GGT
5’ TGG GTA
5’ GGG TAG

18. Effect of word size
For blastn, the word size is typically 7, 11, or 15 (EXACT match). Changing word size is like changing threshold of proteins.
w=15 gives fewer matches and is faster than w=11 or w=7.
For megablast, the word size is 28 and can be adjusted to 64. What will this do? Megablast is VERY fast for finding closely related DNA sequences!

19. Word-matching problem
Consider two sequences of lengths N and M
A simple local alignment algorithm looks for the longest exactly matching word
Score for alignment = the length of the longest match (l)
e.g., l=6
Let n denote the length of matching words starting at two random sites (in red, for example, n = 3 for ‘TCC’)
Then, l=max(n)
F(l) has EVD distribution
G G A T A T C C A G C G C T C C T
A T C C G A T A T C T T G G
G G A T A T C C A G C G C T C C T
A T C C G A T A T C T T G G

20. Word-matching problem -theory
Prob[two bases at randomly selected sites are equal] = a
N: length of matching bases starting at these random sites
P[n ≥ l] = al
Define  = -ln(a) = ln(1/a) => P[n ≥ l] = e -l
Compute E[l]
N ways of choosing the first starting sites, and M ways for the 2nd
If NM selected sites are independent, E[l] = NM e -l
However, words starting at different sites overlap, and are not independent
Thus, E[l] = kNM e -l with k < 1
Since P[n < l] = 1- e -l, from the exponential distribution,
P[n = l] = e -l
Prob. of longest matching words of length l:
F(l) = e-(l-u)exp(e-(l –u) ), u = ln(kMN)/ 

21. EVD Distribution
Thus, F(mmax) does NOT have the same distribution as Gaussian
F(mmax) is of an extreme value distribution (EVD) or Gumbel distribution
F(mmax) = *e- (mmax-u)exp(e- (mmax - u))
Single peak skewed to one side
EVD arises whenever dealing with the maximum value taken from a large number of independent alternatives
Thus, it is likely to be considerably higher than the value of m obtained from just two typical sequences
e.g., # of sequences, S=2000; length of seq., N=200, only two bases C and G with equal prob.
m has a binomial distribution
mmax is EVD distributed

22. EVD distribution
A r.v. x with distribution P(x), and a large sample of S
Find F(xmax)
xmax
Prob[x <xmax] = - P(x) dx
F(xmax) = Prob[choose one with xmax and the rest < xmax ]
= S*P(xmax)*{Prob[x <xmax]}S-1
When P(x) =  e-x, Prob[x <xmax] = 1 – e- xmax,
F(mmax) = S e- xmax (1-e- xmax ) S-1
= Se- xmaxe- Sxmax ((1-a)n exp(-na))
Set u = ln(S)/  , S = exp( u)
F(mmax) = e-(xmax-u)exp(e-(xmax –u))
Single peak at xmax = u
Width of the peak is controlled by 

23. The probability density function of EVD
(characteristic value u=0, decay constant l=1)
0.40
0.35
0.30
0.25
normal
distribution
extreme
value
distribution
probability
0.20
0.15
0.10
0.05 -5 -4 -3 -2 -1 1 2 3 4 5 x

24. Significance of matches
Consider the significance of a match
The observed value of the top-hit score for the query is mobs
Prob. of obtaining a value mmax ≥ mobs by chance is given by the area under the tail of the distribution p(mobs) = 1 – exp(-exp(-  (mobs - u)))
Small p implies that it is less likely the match is to arise by chance (greater the significance)
In the same example, mobs = 130, p=3.3% (just big enough to be significant)
Significance increases as S increases as F(mmax) shifts to the right

25. Alignment stats (reality)
BLAST, etc. works by looking for high-scoring local alignments
When gaps are not allowed, pairwise local alignment scores are shown to be EVD distributed (Karlin and Altschul, 1990)
With gaps, scores are believed to be also EVD distributed
But EVD parameters  and u are not known, and has to be computed empirically
Once the scoring system and EVD parameters for a given search algorithm are known, one can estimate the significance of a match
E: expected number of sequences with a score ≥ observed score S
E(S) = kMNexp(-  S) (N: length of query sequence; M: total length of all the sequences in the database)

26. Blast Result: E value
The expect value E is the number of alignments with scores greater than or equal to score S that are expected to occur by chance in a database search.
An E value is related to a probability value p.
The key equation describing an E value is:
E = Kmn e-lS

27. E = Kmn e-lS
This equation is derived from a description of the extreme value distribution
S = the score
E = the expect value = the number of high-scoring segment pairs (HSPs) expected to occur with a score of at least S
m, n = the length of two sequences
l, K = Karlin Altschul statistics

28. Properties
The value of E decreases exponentially with increasing S (higher S values correspond to better alignments). Very high scores correspond to very low E values.
The E value for aligning a pair of random sequences must be negative! Otherwise, long random alignments would acquire great scores
Parameter K describes the search space (database).
For E=1, one match with a similar score is expected to occur by chance. For a very much larger or smaller database, you would expect E to vary accordingly

29. From Raw scores to Bit scores
There are two kinds of scores:
raw scores (calculated from a substitution matrix) and
bit scores (normalized scores)
Bit scores are comparable between different searches because they are normalized to account for the use of different scoring matrices and different database sizes
S’ = bit score = (lS - lnK) / ln2
The E value corresponding to a given bit score is:
E = mn 2 -S’
Bit scores allow you to compare results between different database searches, even using different scoring matrices.

30. E and p
The expect value E is the number of alignments with scores greater than or equal to score S that are expected to occur by chance in a database search. A p value is a different way of representing the significance of an alignment.
p = 1 - e-E
Default value of E: 10
p>0.05 is considered to be significant

31. Very small E values are very similar to p values.
E values of about 1 to 10 are far easier to interpret
than corresponding p values.
E p
(about 0.1)
(about 0.05)
(about 0.001)

32. Two problems standard BLAST cannot solve
Use human beta globin as a query against human RefSeq proteins, and blastp does not “find” human myoglobin. This is because the two proteins are too distantly related. PSI-BLAST at NCBI as well as hidden Markov models easily solve this problem.
How can we search using 10,000 base pairs as a query, or even millions of base pairs? Many BLAST-like tools for genomic DNA are available such as PatternHunter, Megablast, BLAT, and BLASTZ.
Page 141

33. Position specific iterated BLAST:
PSI-BLAST
The purpose of PSI-BLAST is to look deeper into the database for matches to your query protein sequence by employing a scoring matrix that is customized to your query.
Page 146

34. PSI-BLAST
PSI (Position Specific Iterated) BLAST – Altschul et al., 1997
Use the original BLAST algorithm and retrieve database sequences with significant matches (E < 0.01)
Multiple alignment is performed
Place all locally aligned sections of the database sequences below the query sequence
When a gap is inserted in the query seq., corresponding residue in database seq. is removed, so that all seq.’s are of the same length => for speed and simplicity
Multiple sequences are then used as input to the 2nd run
Use PSSM (Position Specific Scoring Matrix) for scoring
Score is dependent on the frequencies of the residues n the column of the alignment (V is more likely to be aligned with the column with many V’s or other hydrophobic)
Repeat the process until no more new sequences are added

35. Search results During iteration in PSI Blast,
New distantly related sequences can be found, which are not detected in straightforward Blast
Due to the extra info in the aligned group of sequences not in any one sequence
On the other hand, by adding sequences, the range of sequence becomes too broad
Alignment may end up having little relationship to the original query
Ranking of hits gives some info about the degree of relatedness
But, the top hits are not necessarily the most meaningful in terms of evolution
Several top hits to human genes were from bacteria, which led to claims of horizontal gene transfer (dis-proved by phylogenetic methods)
Frequently top hits are not the closest relatives

36. Multiple Sequence Alignment
Based on local sequence alignments
Wants to recognize resemblance even when sequences share only weak similarities
Problem Statement
Given k strings, v1, …, vk of lengths n1,…, nk over an alphabet A (A’ = A U{-}),
And k dimensional score matrix δ
Find kxn matrix, s.t.
Each character in vi is in order
Every column contains at least one symbol from A
The sum of scores of the columns is maximum
Can extend global alignment approach to k dimension

37. PSI-BLAST is performed in five steps
Select a query and search it against a protein database
PSI-BLAST constructs a multiple sequence alignment then
creates a “profile” or specialized position-specific
scoring matrix (PSSM)
Page 146

38. Inspect the blastp output to identify empirical “rules” regarding amino acids tolerated at each position
R,I,K C
D,E,T
K,R,T
N,L,Y,G

39. A R N D C Q E G H I L K M F P S T W Y V
...
37 S
38 G
39 T
40 W
41 Y
42 A
20 amino acids
all the amino acids from position 1 to the end of your PSI-BLAST query protein

40. A R N D C Q E G H I L K M F P S T W Y V
...
37 S
38 G
39 T
40 W
41 Y
42 A
note that a given amino acid (such as alanine) in your query protein can receive different scores for matching alanine—depending on the position in the protein

41. A R N D C Q E G H I L K M F P S T W Y V
...
37 S
38 G
39 T
40 W
41 Y
42 A
note that a given amino acid (such as tryptophan) in your query protein can receive different scores for matching tryptophan—depending on the position in the protein

42. PSI-BLAST is performed in five steps
Select a query and search it against a protein database
PSI-BLAST constructs a multiple sequence alignment then creates a “profile” or specialized position-specific scoring matrix (PSSM)
The PSSM is used as a query against the database
PSI-BLAST estimates statistical significance (E values)
Repeat steps [3] and [4] iteratively, typically 5 times.
At each new search, a new profile is used as the query
Page 146

44. Multiple Sequence Alignment Example: k=3
With three sequences v, w, and u and 3D δ (score of a column with x,y, and z)
In global alignment
In multiple sequences
si-1, j + δ(vi, -)
si, j = max [ si, j δ(-, wj) ]
si-1, j-1 + δ(vi, wj)
si-1, j,k δ(vi, -, -)
si, j-1,k δ(-, wj , -)
si, j,k δ(-, -, uk)
si, j,k = max [ si-1, j-1,k + δ(vi, wj, -) ]
si-1, j,k δ(vi, -, uk)
si, j-1,k δ(vi, wj, -)
si-1, j-1,k δ(vi, wj, uk)

45. Multiple Sequence Alignment
Time complexity is O((2n)k)
Heuristics 1
Compute all (k2) optimal pairwise alignments, and combines them
Does not work all the time

46. Multiple Sequence Alignment
Heuristics 2: Greedy progressive multiple alignment
Select two string with greatest similarities
Merge the two into a new string
Works well for very close sequences
Maybe dependent upon two seed sequences
Clustal uses this approach