BLAST: Basic Local Alignment Search Tool Altschul et al. J. Mol Bio CS 466 Saurabh Sinha

Transcription

1 BLAST: Basic Local Alignment Search Tool Altschul et al. J. Mol Bio CS 466 Saurabh Sinha

2 Motivation Sequence homology to a known protein suggest function of newly sequenced protein Bioinformatics task is to find homologous sequence in a database of sequences Databases of sequences growing fast

3 Alignment Natural approach to check if the query sequence is homologous to a sequence in the database is to compute alignment score of the two sequences Alignment score counts gaps (insertions, deletions) and replacements Minimizing the evolutionary distance

4 Alignment Global alignment: optimize the overall similarity of the two sequences Local alignment: find only relatively conserved subsequences Local similarity measures preferred for database searches Distantly related proteins may only share isolated regions of similarity

5 Alignment Dynamic programming is the standard approach to sequence alignment Algorithm is quadratic in length of the two sequences Not practical for searches against very large database of sequences (e.g., whole genome)

6 Scoring alignments Scoring matrix: 4 x 4 matrix (DNA) or 20 x 20 matrix (protein) Amino acid sequences: PAM matrix Consider amino acid sequence alignment for very closely related proteins, extract replacement frequencies (probabilities), extrapolate to greater evolutionary distances DNA sequences: match = +5, mismatch = -4

7 BLAST: the MSP Given two sequences of same length, the similarity score of their alignment (without gaps) is the sum of similarity values for each pair of aligned residues Maximal segment pair (MSP): Highest scoring pair of identical length segments from the two sequences The similarity score of an MSP is called the MSP score BLAST heuristically aims to find this

8 Locally maximal segment pair A molecular biologist may be interested in all conserved regions shared by two proteins, not just their highest scoring pair A segment pair (segments of identical lengths) is locally maximal if its score cannot be improved by extending or shortening in either direction BLAST attempts to find all locally maximal segment pairs above some score cutoff.

9 Rapid approximation of MSP score Goal is to report those database sequences that have MSP score above some threshold S. Statistics tells us what is the highest threshold S at which chance similarities are likely to appear Tractability to statistical analysis is one of the attractive features of the MSP score

10 Rapid approximation of MSP score BLAST minimizes time spent on database sequences whose similarity with the query has little chance of exceeding this cutoff S. Main strategy: seek only segment pairs (one from database, one query) that contain a word pair with score >= T Intuition: If the sequence pair has to score above S, its most well matched word (of some predetermined small length) must score above T Lower T => Fewer false negatives Lower T => More pairs to analyze

11 Implementation 1. Compile a list of high scoring words 2. Scan database for hits to this word list 3. Extend hits

12 Step 1: Compiling list of words from query sequence For proteins: List of all w-length words that score at least T when compared to some word in query sequence Question: Does every word in the query sequence make it to the list? For DNA: list of all w-length words in the query sequence, often with w=12

13 Step 2: Scanning the database for hits Find exact matches to list words Can be done in linear time two methods (next slides) Each word in list points to all occurrences of the word in word list from previous step

14 Scanning the database for hits Method 1: Let w=4, so 20 4 possible words Each integer in is an index for an array Array element point to list of all occurrences of that word in query Not all 20 4 elements of array are populated only the ones in word list from previous step

15 Scanning the database for hits Method 2: use deterministic finite automaton or finite state machine. Similar to the keyword trees seen in course. Build the finite state machine out of all words in word list from previous step

16 Step 3: Extending hits Once a word pair with score >= T has been found, extend it in each direction. Extend until score >= S is obtained During extension, score may go up, and then down, and then up again Terminate if it goes down too much (a certain distance below the best score found for shorter extensions) One implementation allows gaps during extension

17 BLAST: approximating the MSP BLAST may not find all segment pairs above threshold S Trying to approximate the MSP Bounds on the error: not hard bounds, but statistical bounds Highly likely to find the MSP

18 Statistics Suppose the MSP has been calculated by BLAST (and suppose this is the true MSP) Suppose this observed MSP scores S. What are the chances that the MSP score for two unrelated sequences would be >= S? If the chances are very low, then we can be confident that the two sequences must not have been unrelated

19 Statistics Given two random sequences of lengths m and n Probability that they will produce an MSP score of >= x?

20 Statistics Number of separate SPs with score >= x is Poisson distributed with mean y(x) = Kmn exp(-λx), where λ is the positive solution of p i p j exp(λs(i,j)) = 1 K is a constant s(i,j) is the scoring matrix, p i is the frequency of i in random sequences

21 Statistics Poisson distribution: Pr(x) = (e - λ λ x )/x! Pr(#SPs >= α) = 1 - Pr(#SPs <= α-1) =1" #"1 $ i= 0 e "y y i i! #"1 $ i= 0 =1" e "y y i i!

22 Statistics For α=1, Pr(#SPs >= 1) = 1-e -y(x) Choose S such that 1-e -y(s) is small Suppose the probability of having at least 1 SP with score >= S is This seems reasonably small However, if you test random sequences, you expect 10 to cross the threshold Therefore, require E-value to be small. That is, expected number of random sequence pairs with score >= S should be small.

23 More statistics We just saw how to choose threshold S How to choose T? BLAST is trying to find segment pairs (SPs) scoring above S If an SP scores S, what is the probability that it will have a w-word match of score T or more? We want this probability to be high

24 More statistics: Choosing T Given a segment pair (from two random sequences) that scores S, what is the probability q that it will have no w-word match scoring above T? Want this q to be low Obtained from simulations Found to decrease exponentially as S increases

25 BLAST is the universally used bioinformatics tool

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