1. Heuristic Approaches for Sequence Alignments

2. Outline Sequence Alignment Database Search FASTA BLAST
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3. Sequence Alignment Dynamic Programming (give optimal solution(s))
Needleman-Wunsch (Global Alignment)
Smith-Waterman (Local Alignment)
Heuristics (give approximate solution(s))
Trade speed for precision (good for DB search)
FASTA (finds local alignments)
BLAST (Basic Local Alignment Search Tool)
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4. Database Search
One of the major uses of alignments is to find similar sequences in a database, i.e. compare one input sequence with all sequences in the database and obtain the most similar ones;
Current databases contain massive number of sequences;
Finding homologies in these databases optimally with dynamic programming can take long.
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5. Database Search using Heuristic Sequence Comparison Algorithms
Most database search algorithms relay on heuristic procedures
These are not guaranteed to find the best match
Sometimes, they will completely miss a high-scoring match
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6. Database Search and PAM Matrices - Motivation
Simple scoring scheme (e.g. +1 for match, 0 for mismatch, -1 for mismatch) is not enough, especially for protein sequences
Amino Acids: must consider their relative replacement features in an evolutionary scenario
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7. (Cont’d)
Factors affecting such mutual substitution are numerous (size, chemical properties, etc.)
PAM (Point Accepted Mutations) matrices are widely used – they are derived by direct observation of actual substitution rates.
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8. PAM Matrices (Contn’d)
1-PAM Matrix: reflect an amount of evolution producing on average one mutation per hundred amino acids
How to build a 1-PAM matrices?
A probability transition matrix M: each entry Mab denotes the probability of a changing into b
A scoring matrix S
S is derived from M
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9. How to Build a Probability Transition Matrix M?
We need:
A list of accepted mutations
The probability of occurrence Pa for each amino acid a
M1 (M for 1-PAM) can be computed by simple probability arguments
Mk (M for K-PAM) = M1k
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10. How to Derive S from M?
Question: Assuming pairing an amino acid a with b what is the probability (called a likelihood ratio) this pair is a mutation, not a random occurrence?
Answer:
This ratio =
Where Pb is the probability of a random occurrence of b.
Mab Pb
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11. How to Pick Up a PAM Matrix to Use
Use default one – but should know what it is
Select several to cover a wide range if little is known for the sequences
In general low PAM numbers are good for finding local, strong similarities, while large PAM numbers good for detecting long, weak ones.
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12. A Note on FAST Algorithms
Fast is a family of algorithm, e.g. FASTP, FASTA, TFASTA, LFASTA, ...
In this lecture we use FAST or FASTA interchangeably
References: [Pearson90,91, PearsonLipman88, etc.]
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13. FASTA (Pearson and Lipman, 1988)
Determine k-tuples (exact matches) common to both sequences (with two parameters: ktup and offset).
Join k-tuples that are in the same diagonal and not very far apart – creates regions;
Find region with best score – “initial score” to rank the sequences;
Compute an “optimized score”, using DP, restricted to a band around the region.
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14. Parameters ktup and offset
ktup (k = 1, 2) specify the length of a common segment
offset determines a relative displacement between the query sequence and a database sequence (hint: under a DP method, an offset can be viewed as a diagnal in the similarity matrix)
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15. FASTA - Determine k-tuples
H A R F Y A A Q I V L
query
sequence
Ktup = 1
V D M A A Q I A
Database
sequence
lookup
table
offsets +9 -2 +2 +3 -3 +1 -6 -1
A 2, 6, 7
F 4
H 1 I
L 11
Q 8
R 3
V 10
Y 5
Offset vector 2 1 4
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16. FASTA – Diagonal method
Database
sequence
H A R F Y A A Q I V L V D M A Q I -1 -2 -3 -4 -5 -6 -7
V D M A A Q I A +9 -2 +2 +3 -3 +1 +2
offsets +2 +2 -6 -2 -1
Offset vector 2 1 4
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17. FASTA - Join k-tuples Note: region should be
Determine k-tuples (exact matches) common to both sequences;
Join k-tuples that are in the same diagonal and not very far apart – creates regions;
The larger ktup,
the faster the program
Typically ktup=1 or 2 for proteins
and ktup=4 or 6 for DNA sequence
Note: region should be
gapless, and is created by
certain heuristic
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18. FASTA - Compute an optimized score for highest score region
Find region with best score – “initial score”;
Compute an “optimized score”, using DP, restricted to a band around the region.
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19. Some Issues of FAST Algorithms
Selectivity vs. Sensitivity
Ktup selectivity
Ktup sensitivity
Statistical significance of the scores
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20. BLAST (Altschul et al, 1990)
Compile list of high-scoring words based on the query sequence;
Scanning the database to search for hits – each hit gives a seed;
Extend seeds for each sequence;
Report high scoring segments
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21. BLAST (Basic Local Alignment Search Tool)
A list of high-scoring “segment pairs” between the query and database sequences with scores above a certain threshold
Query
sequence
BLAST
database
Segment: a substring of a sequence
Segment pair: a pair of segments with the same length
Segment pairs are gapless local alignments
[S.F.Altschul, W.Gish, W.Miller, E.Myers and D.Lipman: Basic Local Alignment Search Tool, J. Mol. Biology, (1990) 215, ]
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22. Maximum segment pair (MSP) – is a segment pair of maximum score.
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23. A segment pair is locally optimal if its score cannot be improved by either extending or shortening both segments.
Note: Local similarity is useful for finding conserved regions (e.g. in a protein)
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24. BLAST is interested in finding only those sequences with MSP scores over some cutoff score S.
The main strategy of BLAST is to seek only segment pairs that contain a word pair with a score of at least T.
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25. BLAST- Compile list of high-scoring words
w, T – program parameters N
Query
sequence w
Maximum of N-w+1 words
Typically w=3 for proteins
and w=11 for DNA sequence . w1
Example: w = 3, T = 15 w2 w3
A N S
find the list of words
with score > T w4 w5
= 6 < T .
C R Y wk
= 28 > T
word list
PAM matrices can be used to compute the scores
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26. BLAST- Search for hits, each hit gives a seed
seeds
Database
sequences
Exact matches of words from the
word list to the database sequence
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27. BLAST- Search for hits, each hit gives a seed
Lookup (hash) table: w
F(w)
Database
sequence 1 2 3 4 5 6 7 8 w5 w1 w2 w4 w3 w6 w8
A: 00
C: 01
G: 10
T: 11
Byte
A C G T
DNA sequences w7
word list
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28. BLAST- Extend seeds for each sequence
L P S L D L L QUERY SEQUENCE
M P S L D L L DATABASE SEQUENCE
< WORD> LETTER WORD FOUND INITIALLY
word score = 14
< >
EXTENSION EXTENSION
TO LEFT TO RIGHT
< MAXIMAL SEGMENT PAIR > SCORE = 31
Maximum Segment Pairs (MSPs)
For each exact word match, alignment is extended
in both directions to find high score segments
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29. BLAST- report high scoring segments
Choose high score segments: scores > S
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30. Why BLAST is Fast? Because: the alignments are gapless!
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31. Statistical Significance of BLAST Results
Question: If a match found by BLAST – what is the probability that such match is due to chance alone?
A well-funded statistical theory is used by BLAST in determine the matching scores.
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32. Questions
Q1: What proportion of segment pairs with a given score contain a word pair with a score at least T?
Answer: [Karlin91]
Q2: What probability q of a MSP pair found (under a threshold score S) will fail to contain a seed word W (of score >= T)?
Answer: See Plot [Alschul et.al.90]
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33. Note: PIM-120 scores are used, w=4 and T=8
- ln q
Score S
Note: PIM-120 scores are used, w=4 and T=8
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34. Improvement of The Basic BLAST-Gapped BLAST and PSI-BLAST
[S.F. Altschul, et.al., Gapped BLAST and PSI-BLAST: A New Generation of Protein Database Search Algorithms, Nucleic Acids Research, 1997, Vol25, No. 17, ]
Objectives
Speedup the execution substantially
Enhance the sensitivity to weak similarities
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35. Major Extensions/Changes to BLAST
Add ability to generate gapped alignment using dynamic programming to extend a seed in both directions
Using a “two-hit” method to “filter” out the candidate pairs for extension
The search may be iterated: round i will generate a new position-specific score matrix from significant alignments found to be used for round i+1
(this process involves the construction of a multiple sequence alignment – see Topic 2C)
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36. The Two-Hit Method
Observation: an HSP of interest is much longer than a single word pair, thus may contain multiple hits on the same diagonal within a relatively short distance apart.
Methods: Choose a “window” , and do extension only when two non-overlapping hits are found within distance A of one another on the same diagonal
Effectiveness: reduce candidate pairs for extension substantially (by 86%)
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37. An Example
The BLAST comparison of broad bean leghemoglobin I (87) (SSWISS-PROT accession no.PO2232) and horse beta -globin (88) (SWISS_PROT accession no.P02062). The 15 hits with score at least 13 are indicated by plus signs. An additional 22 non-overlaping hits with score at least 11 are indicated by dots.
Of these 37 hits, only the two indicated pairs are on the same diagonal and within distance 40 of one another. Thus the two-hit heuristic with T=11 triggers two extensions, in place of the 15 extensions invoked by the one-hit heuristic with T=13.
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