Heuristic Approaches for Sequence Alignments

Heuristic Approaches forSequence Alignments

/course/eleg667-01-f/Topic-2b.ppt 2

Outline

Sequence Alignment Database Search FASTA BLAST


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)


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.


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


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


(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.


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


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


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


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.


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.]


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.


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)


Ktup = 1

FASTA - Determine k-tuples

H A R F Y A A Q I V L 1 2 3 4 5 6 7 8 9 10 11query

sequence

V D M A A Q I A1 2 3 4 5 6 7 8Database

sequence

A 2, 6, 7F 4H 1I 9L 11Q 8R 3V 10Y 5

lookuptable

offsets+9

-2+2+3

-3+1+2

+2+2

-6-2-1

Offset vector

-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10

21 1 1 1 1 14


FASTA – Diagonal method

H A R F Y A A Q I V L

VDMAAQ IA

0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10

-1

-2

-3

-4

-5

-6

-7

Offset vector

-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10

21 1 1 1 1 14

V D M A A Q I A1 2 3 4 5 6 7 8

Databasesequence

offsets

+9

-2+2+3

-3+1+2

+2+2

-6-2-1


FASTA - Join k-tuples

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 proteinsand ktup=4 or 6 for DNA sequence

Note: region should be gapless, and is created bycertain heuristic


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.


Some Issues of FAST Algorithms

Selectivity vs. Sensitivity Ktup selectivity Ktup sensitivity

Statistical significance of the scores


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


BLAST (Basic Local Alignment Search Tool)

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, 403-410]

Querysequence BLAST

database

A list of high-scoring “segment pairs” between the query and database sequences with scores above a certain threshold


Maximum segment pair (MSP) – is a segment pair of maximum score.


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)


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.


BLAST- Compile list of high-scoring words

Querysequence

.

.

.

. . .

word list

find the list of wordswith score > T

Maximum of N-w+1 wordsTypically w=3 for proteinsand w=11 for DNA sequence

Nw

A N SA N S

2 2 2 = 6 < T

w, T – program parameters

C R YC R Y

12 6 10= 28 > T

Example: w = 3, T = 15

wk

w4

w3

w2

w1

w5

PAM matrices can be used to compute the scores


Databasesequences

Exact matches of words from the word list to the database sequence

BLAST- Search for hits, each hit gives a seed

seeds


BLAST- Search for hits, each hit gives a seed

w5 w1

w2

w4

w3 w6 w8

w7

Lookup (hash) table:

1

2

3

4

5

6

7

8

w

F(w)

Databasesequence

A: 00C: 01G: 10T: 11Byte

A C G T

0 0 0 1 1 0 1 1

DNA sequences

word list


For each exact word match, alignment is extendedin both directions to find high score segments

Maximum Segment Pairs (MSPs)

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> 3-LETTER WORD FOUND INITIALLY 4 4 6 word score = 14 <------- ------->EXTENSION EXTENSION TO LEFT TO RIGHT

2 7 4 4 6 4 4 < MAXIMAL SEGMENT PAIR > SCORE 14 + 9 + 8 = 31


BLAST- report high scoring segments

Choose high score segments: scores > S


Why BLAST is Fast?

Because:

the alignments are gapless!


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.


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]

Questions


Note: PIM-120 scores are used, w=4 and T=8

Score S

- ln q


Improvement of The Basic BLAST-Gapped BLAST and PSI-BLAST

Objectives Speedup the execution substantially Enhance the sensitivity to weak similarities

[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, 3389-3402]


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)


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%)


An ExampleThe 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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Heuristic Approaches for Sequence Alignments