PatternHunter: A Fast and Highly Sensitive Homology Search Method

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PatternHunter A Fast and Highly Sensitive
Homology Search Method

• Bin Ma
• Department of Computer Science
• University of Western Ontario

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A homology between mouse and human genomes
GCNTACACGTCACCATCTGTGCCACCACNCATGTCTCTAGTGATCCCTCA
TAAGTTCCAACAAAGTTTGC

GCCTACACACCGCCAGTTGTG-TTCCTGCTATGTCTCTAGTGAT
CCCTGAAAAGTTCCAGCGTATTTTGC GAGTACTCAACACCAACATTGA
TGGGCAATGGAAAATAGCCTTCGCCATCACACCATTAAGGGTGA----

GAATACTCAACAGCAACATCAAC
GGGCAGCAGAAAATAGGCTTTGCCATCACTGCCATTAAGGATGTGGG -
-----------------TGTTGAGGAAAGCAGACATTGACCTCACCGAGA
GGGCAGGCGAGCTCAGGTA

TTGACAGTACACTCATAGTGTTGAGGAAAGCTGACGTTGACCTCACC
AAGTGGGCAGGAGAACTCACTGA GGATGAGGTGGAGCATATGATCACC
ATCATACAGAACTCAC-------CAAGATTCCAGACTGGTTCTTG

GGATGAGATGGAACGTGTGATGACCAT
TATGCAGAATCCATGCCAGTACAAGATCCCAGACTGGTTCTTG
Smith-Waterman is the most accurate method. Time
complexityO(mn).
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BLAST finds a hit and then extends
GCNTACACGTCACCATCTGTGCCACCACNCATGTCTCTAGTGATCCCTCA
TAAGTTCCAACAAAGTTTGC

GCCTACACACCGCCAGTTGTG-TTCCTGCTATGTCTCTAGTGAT
CCCTGAAAAGTTCCAGCGTATTTTGC GAGTACTCAACACCAACATTGA
TGGGCAATGGAAAATAGCCTTCGCCATCACACCATTAAGGGTGA----

GAATACTCAACAGCAACATCAAC
GGGCAGCAGAAAATAGGCTTTGCCATCACTGCCATTAAGGATGTGGG -
-----------------TGTTGAGGAAAGCAGACATTGACCTCACCGAGA
GGGCAGGCGAGCTCAGGTA

TTGACAGTACACTCATAGTGTTGAGGAAAGCTGACGTTGACCTCACC
AAGTGGGCAGGAGAACTCACTGA GGATGAGGTGGAGCATATGATCACC
ATCATACAGAACTCAC-------CAAGATTCCAGACTGGTTCTTG

GGATGAGATGGAACGTGTGATGACCAT
TATGCAGAATCCATGCCAGTACAAGATCCCAGACTGGTTCTTG
Seed match hit
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Example of missing a target

• Fail
• GAGTACTCAACACCAACATTAGTGGGCAATGGAAAAT
• GAATACTCAACAGCAACATCAATGGGCAGCAGAAAAT
• Dilemma
• Sensitivity needs shorter seeds
• the success rate of finding a homology
• Speed needs longer seeds
• Mega-BLAST uses seeds of length 28.

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PatternHunter uses spaced seeds

• 111010010100110111 (called a model)
• Eleven required matches (weight11)
• Seven dont care positions
• GAGTACTCAACACCAACATTAGTGGCAATGGAAAAT
• GAATACTCAACAGCAACACTAATGGCAGCAGAAAAT
• 111010010100110111
• Hit all the required matches are satisfied.
• BLAST seed model 11111111111

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Observations re. spaced seeds

• Seed models with different shapes can detect
  different homologies.
• Two consequences
• Some models may detect more homologies than
  others
• More sensitive homology search
• PatternHunter I
• Can use several seed models simultaneously to hit
  more homologies
• Approaching 100 sensitive homology search
• PatternHunter II

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Spaced Seed PatternHunter I
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Weight of a seed

• Lemma The expected number of hits of a weight W
  length M seed model within a length L region with
  similarity p is (L-M1)pW
• Proof There are (L-M1) positions a hit can
  occur. At each position, pW hit is expected.
  Q.E.D.
• Seed models with the same weight generate
  approximately the same amount of hits.
• Speed is approximately the same.
• Sensitivity is not necessarily the same.
• num of hits v.s. num of regions that contain
  hits.

GAGTACTCAACACCAACATTAGTGGCAATGGAAAAT
GAATACTCAACAGCAACACTAATGGC
AGCAGAAAAT 111010010100110111
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Simulated sensitivity curves
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Why spaced seeds are better?

• TTGACCTCACC?
• ?
• TTGACCTCACC?
• 11111111111
• 11111111111

CAA?A??A?C??TA?TGG? ???????? CAA?A??A?C
??TA?TGG? 111010010100110111 111010010100110111

• BLASTs seed usually uses more than one hits to
  detect one homology (redundant)
• Spaced seeds uses fewer hits to detect one
  homology (efficient)

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PHs seed does not overlap heavily

• PHs seed do not overlap heavily when shifts
• 111010010100110111
• 111010010100110111
• 111010010100110111
• 111010010100110111
• 111010010100110111
• 111010010100110111
• 111010010100110111
• ......
• The hits at different positions are independent.
• The probability of having the second hit is 5p6
  
• compare to BLASTs model p p2 p3 p4

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Indeed

• Indeed, under the condition that there is one hit
  in a length 64, 70 similar homology, the average
  number of hits in that region is
• 2.0 for PHs weight-11 seed
• 3.6 for contiguous weight-11 seed.

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A dynamic programming algorithm to compute
sensitivity

• R1..n Random homology, Pr(Ri1) p We want
  Pr(R is hit by a seed model x)
• DPi,s denotes Pr(R1..i is hit R1..i ends
  with s)
• 1 sx and s is hit
• DPi,s DPi-1,s1..s-1 sx and s is
  not hit
• pDPi,(1s) (1-p)DPi,(0s)
  else
• O(n2x). Better algorithm exists.

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PatternHunter I performance

• Blastn MB28 PH
  
• E.coli (4.7M) v.s. H.inf (1.8M)
• 716s /158M 5s/561M 34s/78M
• Arabidopsis chr2 (19.6M) v.s. chr4 (17.5M)
• -- 21720s/1087M 5020s/279M
• Human chr21 (26.2M) v.s. chr22 (35M)
• -- -- 14512s/419M
  
• All used a 700MHZ PentiumIII PC with 1G byte
  memory.
• Human (3G) v.s. Mouse (3G)
• Using 2-hit, weight 12 seed, PH used 6 days with
  a 1GHZ PentiumIII PC with 2G byte memory.
• With Blast, it would otherwise take months with
  parallel computers to finish.

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Multiple Seeds PatternHunter II
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PatternHunter II Optimized Multiple seeds

• Basic Searching Algorithm
• Select a group of spaced seed models
• For each hit of each model, conduct extension to
  find a homology.
• Selecting optimal multiple seed is NP-hard.

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Seed Selection Algorithm

• Let A be an empty set.
• Let s be the seed such that A?s has the highest
  hit probability.
• AA?s if AltK go to 2.
• Approximation ratio 1-1/e
• Computing the hit probability of multiple seeds
  is NP-hard.
• Efficient algorithm when number of zeros is
  limited.
• PTAS to compute the probability approximately.

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PTAS to compute the probability approximately.

• Randomly generate m homologies independently.
  Suppose n of them are hit by our seeds. Let p be
  the sensitivity of our seeds.
• If , then with probability
• 1-2/K,
• Can be proved by Chernoffs bounds.

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The seeds obtained under a simple homology
distribution

• (homology identity 0.7, homology length64)
• 111011001011010111,
• 1111000100010011010111,
• 1100110100101000110111,
• 1110100011110010001101,

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Simulated sensitivity curves

• Solid curves Multiple (1, 2, 4, 8, 16) weight-12
  spaced seeds.
• Dashed curves Optimal spaced seeds with weight
  11, 10, 9, 8.
• Typically, Doubling the seed number gains
  better sensitivity than decreasing the weight by
  1.

Two weight-12
One weight-11
One weight-12
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Coding region seeds

• The first two bases of a codon is more conserved
  than the third base.
• Coding regions matches have patterns like
  110110
• The seeds trained under a coding region homology
  distribution are called the coding region seeds.
• PHIIs default seeds were trained under a simple
  distribution (0.8, 0.8, 0.5).

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Experiments on real data

• About 30k mouse ESTs (25Mb) and 4k human ESTs
  (3Mb)
• downloaded from NCBI genbank.
• low complexity regions were filtered out.
• SSearch (Smith-Waterman method) finds all pairs
  of ESTs with significant local alignments.
• Check how many percents of those pairs can be
  found by BLAST and different configurations of
  PatternHunter.

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Sensitivity curves
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Recent development

• Can 100 sensitivity be achieved with reasonable
  speed?
• Yes.
• When gt80 similarity, 100 sensitivity can be
  achieved with approximately 40 weight-9 seeds.

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Open questions

• Can the hit probability of one (or constant
  number of) seed be computed in polynomial time?
• Current Polynomial time algorithms exist when
  num of 0s in one seed is O(log n).
• PTAS.
• Can the optimal seed (or set of seeds) be found
  in polynomial time?
• For general distributions of the homologies,
  these are NP-hard.

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How the hits are found efficiently?

• Put all the seeds of database in a lookup table.
• For each seed in the query, find all the
  occurrences of the seed in the database by
  looking at the lookup table.