Alignment: Spaced Seed

2012-03-16 LEAST Seminar

Abner Huang< abnercyh@cs.nthu.edu.tw >

CSBB Lab, NTHU

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Outline

• Introduction

• Theory

• Remarks

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Stringology

• String matching• Pattern matching• Periodicities• Data structure• Text Compression• Alignment

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Alignment

• Spelling correction• Bitext word alignment• File comparison (diff)• Amino acid sequences comparison

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Nature Milestones in DNA: BLAST

Altschul, S. F., Gish, W., Miller, W., Myers, E. W. & Lipman, D. J. Basic local alignment search tool. J. Mol. Biol. 215, 403–410 (1990)

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A. Califano and I. Rigoutsos, “Flash: A fast look-up algorithm for string homology,” in Proceedings of the 1st International Conference on Intelligent Systems for Molecular Biology (ISMB), pp. 56-64, July 1993.

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Spaced seed

Spaced seed, Multiple spaced seeds, Vector

(Relaxed) seed, Neighbor seeds

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Outline

• Introduction

• Theory

• Remarks

Optimal Spaced Seed(Ma, Tromp, Li: Bioinformatics, 18:3, 2002, 440-445)

• Spaced Seed: nonconsecutive matches and optimized match positions.

• Represent BLAST seed by 11111111111• Spaced seed: 111*1**1*1**11*111– 1 means a required match– * means “don’t care” position

• This seemingly simple change makes a huge difference: significantly increases hit prob. to homologous region while reducing bad hits.

Formalization

• Given i.i.d. sequence (homology region) with Pr(1)=p and Pr(0)=1-p for each bit:

1100111011101101011101101011111011101

• Which seed is more likely to hit this region:– BLAST seed: 11111111111– Spaced seed: 111*1**1*1**11*111

111*1**1*1**11*111

Sensitivity: PH weight 11 seed vs Blast 11 & 10

PH 2-hit sensitivity vs Blastn 11, 12 1-hit

Expect Less, Get More• Lemma: The expected number of hits of a weight W length M

seed model within a length L region with similarity p is (L-M+1)pW

Proof: The expected number of hits is the sum, over the L-M+1 possible positions of fitting the seed within the region, of the probability of W specific matches, the latter being pW. ■

• Example: In a region of length 64 with 0.7 similarity, PH has probability of 0.466 to hit vs Blast 0.3, 50% increase. On the other hand, by above lemma, Blast expects 1.07 hits, while PH 0.93, 14% less.

Why Is Spaced Seed Better?A wrong, but intuitive, proof: seed s, interval I, similarity p E(#hits) = Pr(s hits) E(#hits | s hits)Thus: Pr(s hits) = Lpw / E(#hits | s hits)For optimized spaced seed, E(#hits | s hits) 111*1**1*1**11*111 Non overlap Prob 111*1**1*1**11*111 6 p6

111*1**1*1**11*111 6 p6

111*1**1*1**11*111 6 p6 111*1**1*1**11*111 7 p7

…..• For spaced seed: the divisor is 1+p6+p6+p6+p7+ …• For BLAST seed: the divisor is bigger: 1+ p + p2 + p3 + …

Improvements

• Brejova-Brown-Vinar (HMM) and Buhler-Keich-Sun (Markov): The input sequence can be modeled by a (hidden) Markov process, instead of iid.

• Multiple seeds • Brejova-Brown-Vinar: Vector seeds• Csuros: Variable length seeds – e.g. shorter

seeds for rare query words.

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Outline

• Introduction

• Theory

• Remarks

Thank You