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L3: Blast: Keyword match basics

L3: Blast: Keyword match basics. Silly Quiz. TRUE or FALSE: In New York City at any moment, there are 2 people (not bald) with exactly the same number of hairs!. Assignment 1 is online. Due 10/6 (Thursday) in class. An O(nm) algorithm for score computation. For i = 1 to n

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L3: Blast: Keyword match basics

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  1. L3: Blast: Keyword match basics CSE 182

  2. Silly Quiz • TRUE or FALSE: • In New York City at any moment, there are 2 people (not bald) with exactly the same number of hairs! CSE 182

  3. Assignment 1 is online • Due 10/6 (Thursday) in class. CSE 182

  4. An O(nm) algorithm for score computation For i = 1 to n For j = 1 to m • The iteration ensures that all values on the right are computed in earlier steps. • How much space do you need? CSE 182

  5. Alignment? • Is O(nm) space too much? • What if the query and database are each 1Mbp? CSE 182

  6. Alignment (Linear Space) • Score computation For i = 1 to n For j = 1 to m CSE 182

  7. Linear Space • In Linear Space, we can do each row of the D.P. • We need to compute the optimum path from the origin (0,0) to (m,n) CSE 182

  8. Linear Space (cont’d) • At i=n/2, we know scores of all the optimal paths ending at that row. • Define F[j] = S[n/2,j] • One of these j is on the true path. Which one? CSE 182

  9. Backward alignment • Let S’[i,j] be the optimal score of aligning s[i..n] with t[j..m] • Define B[j] = S’[n/2,j] • One of these j is on the true path. Which one? CSE 182

  10. Forward, Backward computation • At the optimal coordinate, j • F[j]+B[j]=S[n,m] • In O(nm) time, and O(m) space, we can compute one of the coordinates on the optimum path. CSE 182

  11. Linear Space Alignment • Align(1..n,1..m) • For all 1<=j <= m • Compute F[j]=S(n/2,j) • For all 1<=j <= m • Compute B[j]=Sb(n/2,j) • j* = maxj {F[j]+B[j] } • X = Align(1..n/2,1..j*) • Y = Align(n/2..n,j*..m) • Return X,j*,Y CSE 182

  12. Linear Space complexity • T(nm) = c.nm + T(nm/2) = O(nm) • Space = O(m) CSE 182

  13. Why is Blast Fast? CSE 182

  14. Database (n) Query (m) Large database search Database size n=10M, Querysize m=300. O(nm) = 3. 109 computations CSE 182

  15. Observations • Much of the database is random from the query’s perspective • Consider a random DNA string of length n. • Pr[A]=Pr[C] = Pr[G]=Pr[T]=0.25 • Assume for the moment that the query is all 1’s (length m). • What is the probability that an exact match to the query can be found? CSE 182

  16. Basic probability • Probability that there is a match starting at a fixed position i = 0.25m • What is the probability that some position i has a match. • Dependencies confound probability estimates. CSE 182

  17. Total money you expect to earn Basic Probability:Expectation • Q: Toss a coin: each time it comes up heads, you get a dollar • What is the money you expect to get after n tosses? • Let Xi be the amount earned in the i-th toss CSE 182

  18. Expected number of matches • Expected number of matches can still be computed. i • Let Xi=1 if there is a match starting at position i, Xi=0 otherwise • Expected number of matches = CSE 182

  19. Expected number of exact Matches is small! • Expected number of matches = n*0.25m • If n=107, m=10, • Then, expected number of matches = 9.537 • If n=107, m=11 • expected number of hits = 2.38 • n=107,m=12, • Expected number of hits = 0.5 < 1 • Bottom Line: An exact match to a substring of the query is unlikely just by chance. CSE 182

  20. Suppose we are looking for a database string with greater than 90% identity to the query (length 100) • Partition the query into size 10 substrings. At least one much match the database string exactly Observation 2 • What is the pigeonhole principle? CSE 182

  21. Why is this important? • Suppose we are looking for sequences that are 80% identical to the query sequence of length 100. • Assume that the mismatches are randomly distributed. • What is the probability that there is no stretch of 10 bp, where the query and the subject match exactly? • Rough calculations show that it is very low. Exact match of a short query substring to a truly similar subject is very high. • The above equation does not take dependencies into account • Reality is better because the matches are not randomly distributed CSE 182

  22. Just the Facts • Consider the set of all substrings of the query string of fixed length W. • Prob. of exact match to a random database string is very low. • Prob. of exact match to a true homolog is very high. • Keyword Search (exact matches) is MUCH faster than sequence alignment CSE 182

  23. BLAST Database (n) • Consider all (m-W) query words of size W (Default = 11) • Scan the database for exact match to all such words • For all regions that hit, extend using a dynamic programming alignment. • Can be many orders of magnitude faster than SW over the entire string CSE 182

  24. Why is BLAST fast? • Assume that keyword searching does not consume any time and that alignment computation the expensive step. • Query m=1000, random Db n=107,no TP • SW = O(nm) = 1000*107 = 1010 computations • BLAST, W=11 • E(#11-mer hits)= 1000* (1/4)11 * 107=2384 • Number of computations = 2384*100*100=2.384*107 • Ratio=1010/(2.384*107)=420 • Further speed improvements are possible CSE 182

  25. Keyword Matching • How fast can we match keywords? • Hash table/Db index? What is the size of the hash table, for m=11 • Suffix trees? What is the size of the suffix trees? • Trie based search. We will do this in class. AATCA 567 CSE 182

  26. Related notes • How to choose the alignment region? • Extend greedily until the score falls below a certain threshold • What about protein sequences? • Default word size = 3, and mismatches are allowed. • Like sequences, BLAST has been evolving continuously • Banded alignment • Seed selection • Scanning for exact matches, keyword search versus database indexing CSE 182

  27. P-value computation • How significant is a score? What happens to significance when you change the score function • A simple empirical method: • Compute a distribution of scores against a random database. • Use an estimate of the area under the curve to get the probability. • OR, fit the distribution to one of the standard distributions. CSE 182

  28. Z-scores for alignment • Initial assumption was that the scores followed a normal distribution. • Z-score computation: • For any alignment, score S, shuffle one of the sequences many times, and recompute alignment. Get mean and standard deviation • Look up a table to get a P-value CSE 182

  29. Blast E-value • Initial (and natural) assumption was that scores followed a Normal distribution • 1990, Karlin and Altschul showed that ungapped local alignment scores follow an exponential distribution • Practical consequence: • Longer tail. • Previously significant hits now not so significant CSE 182

  30. Exponential distribution • Random Database, Pr(1) = p • What is the expected number of hits to a sequence of k 1’s • Instead, consider a random binary Matrix. Expected # of diagonals of k 1s CSE 182

  31. As you increase k, the number decreases exponentially. • The number of diagonals of k runs can be approximated by a Poisson process • In ungapped alignments, we replace the coin tosses by column scores, but the behaviour does not change (Karlin & Altschul). • As the score increases, the number of alignments that achieve the score decreases exponentially CSE 182

  32. Blast E-value • Choose a score such that the expected score between a pair of residues < 0 • Expected number of alignments with a particular score • For small values, E-value and P-value are the same CSE 182

  33. Blast Variants Longer seeds. Seeds with don’t care values Later Database pre-processing Seeds with don’t care values • What is mega-blast? • What is discontiguous mega-blast? • Phi-Blast/Psi-Blast? • BLAT? • PatternHunter? CSE 182

  34. l l l c c c c c c c c c c c c c P M T S Keyword Matching P O T A S T P O T A T O O T A T O T S I U A E CSE 182

  35. CSE 182

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