1. We continue where we stopped last week: FASTA – BLAST
Alignment Class III
We continue where we stopped last week: FASTA – BLAST

2. FASTA FastA uses the method of Pearson and Lipman (1985).
Based on the idea of identifying short words, k-tuples, common to both sequences.
K-tuples of 1-2 aa are used in protein searches and up to 6 bases in DNA searches.
Uses a heuristic approach to join k-tuples that lie close together on the same diagonal.
If a significant number of matches is found, FastA uses a dynamic programming algorithm to compute gapped alignments that incorporate the ungapped regions.
E-value approaching zero indicates that no match with a similar score is expected by chance.

3. 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

4. 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

5. FASTA, K-tups with common offset

6. 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.

7. FASTA - E Scores
In evaluating the E scores, the following rules of thumb can be used:
For searches of database, sequences with E less than are almost always found to be homologous.
Sequences with E between 1 and 10 frequently turn out to be related as well.

8. 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

9. 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

10. Ungapped Blast Algorithm
Given two sequences, a segment pair is defined as a pair of sub-sequences of the same length that form an ungapped alignment
Blast calculates all segment pairs between the query and the database sequences, above a scoring threshold
The algorithm searches for fixed length hits, which are extended until certain threshold parameters are achieved
The resulting high-scoring pairs (HSPs) form the basis of the ungapped alignments

11. 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.

12. 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
Same logic applies to amino acids
AATCAT
ATTCAG
HTHHHT

13. 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.

14. 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

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

16. 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.

17. 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

18. 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 within a distance A of each other are joined and then the longer sequence extended as before.

19. 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.

20. Shanon Entropy and information
Information theory
Shanon Entropy and information

21. Entropy X: discrete Random Variable (RV), p(X)
Entropy (or self-information)
Entropy measures the amount of information in a RV
using the optimal code = the entropy will be the minimum

22. Entropy (cont) i.e when the value of X is determinate, hence
H is a weighted average for log(p(X) where the weighting depends on the probability of each x
H INCREASES WITH MESSAGE LENGTH
i.e when the value of X
is determinate, hence
providing no new
information

23. Joint Entropy
The joint entropy of 2 RV X,Y is the amount of the information needed on average to specify both their values

24. Conditional Entropy
The conditional entropy of a RV Y given another X, expresses how much extra information one still needs to supply on average to communicate Y given that the other party knows X

25. Chain Rule

26. Mutual Information
I(X,Y) is the mutual information between X and Y. It is the reduction of uncertainty of one RV due to knowing about the other, or the amount of information one RV contains about the other

27. Mutual Information (cont)
I is 0 only when X,Y are independent: H(X|Y)=H(X)
H(X)=H(X)-H(X|X)=I(X,X) Entropy is the self-information
For 2 dependent variables, I grows not only with the degree of their dependence but only with their entropy
H(X) = I(X<X)
This explain also how mutual information between 2 totally dependent variables is not constant but depends on their entropy

28. Kullback-Leibler Divergence
Relative entropy or KL (Kullback-Leibler) divergence

29. Scoring matrices
Identity
PAM
BLOSUM

30. Scoring Matrices Types
Identity matrix – exact matches receive one score and non-exat matches a different score (say 1 and 0, or 6 and –1 for local alignment.).
Mutation data matrix – a scoring matrix compiled based on observation of protein point mutation (PAM, BLOSUM).
Physical properties matrix – amino acids with with similar properties (e.G. hydrophobicity ) receive high score.
Genetic code matrix – amino acids are scored based on similarities in the coding triple (codons).

31. Substitution Matrix
Amino acids substitute easily for another due to similar physicochemical properties
Isoleucine for Valine (both small, hydrophobic)
Serine for Threonine (both polar)
Such changes – “conservative”
Thus, need a way to increase sensitivity of the alignment algorithm
Solution – substitution matrix
Therefore, we need a range of values that depend on the nature of sequences being compared
Identical amino acids > Conservative substitutions > Nonconservative substitutions

32. Choice of scoring matrix is dictated by the alignment goals
Two proteins are homologous if (and only if) they are evolutionarily related (have a common ancestor)
Homologous proteins are likely to have related functions (and have the same fold)
Scoring matrices must in some way model our understanding of protein evolution.
Based on the result of the search we have to be able to decide if the discovered sequence similarity could happen by chance or is a signature of likely homology.