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lect4 Keyword matching

# An Introduction to Bioinformatics Algorithms (Computational Molecular Biology)

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Fa05 CSE 182 CSE182-L4: Keyword matching

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Fa05 CSE 182 Backward scoring Defin S b [i,j] : Best scoring alignment of the suffixes s[i+1. .n] and t[j+1. .m] Q: What is the score of the best alignment of the two strings s and t? HW: Write the recurrences for S b
Fa05 CSE 182 Forward/Backward computations F[j] = Score of the best scoring alignment of s[1. .n/2] and t[1. .j] F[j] = S[n/2,j] B[j] = Score of the best scoring alignment of s[n/2+1. .n] and t[j+1. .m] B[j] = S b [n/2,j] n/2 j 1 m

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Fa05 CSE 182 Forward/Backward computations 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. n/2 j 1 m
Fa05 CSE 182 Forward, Backward computation There exists a 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.

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Fa05 CSE 182 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]=S b (n/2,j) j* = max j {F[j]+B[j] } X = Align(1. .n/2,1. .j*) Y = Align(n/2. .n,j*. Return X,j*,Y
Fa05 CSE 182 Linear Space complexity T(nm) = c.nm + T(nm/2) = O(nm) Space = O(m)

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Fa05 CSE 182 Summary We considered the basics of sequence alignment Opt score computation Reconstructing alignments Local alignments Affine gap costs Space saving measures Can we recreate Blast?
Fa05 CSE 182 Blast and local alignment Concatenate all of the database sequences to form one giant sequence. Do local alignment computation with the query.

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Fa05 CSE 182 Large database search Query (m) Database (n) Database size n=100M, Querysize m=1000. O(nm) = 10 11 computations
Fa05 CSE 182 Why is Blast Fast?

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Fa05 CSE 182 Silly Question! True or False: No two people in new york city have the same number of hair
Fa05 CSE 182 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 A’s (length m). What is the probability that an exact match to the query can be found?

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Fa05 CSE 182 Basic probability Probability that there is a match starting at a fixed position i = 0.25 m What is the probability that some position i has a match. Dependencies confound probability estimates.
Fa05 CSE 182 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 X i be the amount earned in the i-th toss E ( X i ) =1. p + 0.(1- p ) = p Total money you expect to earn E ( X i ) = E ( X i ) = i np i

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Fa05 CSE 182 Expected number of matches Expected number of matches can still be computed. Let X i =1 if there is a match starting at position i, X i =0 otherwise Pr(Match at Position i) = p i = 0.25 m E ( X i ) = p i = 0.25 m Expected number of matches = E ( X i ) = E ( X i ) i i = n 1 4 ( ) m i
Fa05 CSE 182 Expected number of exact Matches is small!

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lect4 Keyword matching - CSE182-L4 Keyword matching Fa05...

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