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Combinatorial Pattern Matching. Outline. Hash Tables Repeat Finding Exact Pattern Matching Keyword Trees Suffix Trees Heuristic Similarity Search Algorithms Approximate String Matching Filtration Comparing a Sequence Against a Database Algorithm behind BLAST Statistics behind BLAST

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Combinatorial pattern matching l.jpg

Combinatorial Pattern Matching


Outline l.jpg
Outline

  • Hash Tables

  • Repeat Finding

  • Exact Pattern Matching

  • Keyword Trees

  • Suffix Trees

  • Heuristic Similarity Search Algorithms

  • Approximate String Matching

  • Filtration

  • Comparing a Sequence Against a Database

  • Algorithm behind BLAST

  • Statistics behind BLAST

  • PatternHunter and BLAT


Genomic repeats l.jpg
Genomic Repeats

  • Example of repeats:

    • ATGGTCTAGGTCCTAGTGGTC

  • Motivation to find them:

    • Genomic rearrangements are often associated with repeats

    • Trace evolutionary secrets

    • Many tumors are characterized by an explosion of repeats


Genomic repeats4 l.jpg
Genomic Repeats

  • The problem is often more difficult:

    • ATGGTCTAGGACCTAGTGTTC

  • Motivation to find them:

    • Genomic rearrangements are often associated with repeats

    • Trace evolutionary secrets

    • Many tumors are characterized by an explosion of repeats


L mer repeats l.jpg
l-mer Repeats

  • Long repeats are difficult to find

  • Short repeats are easy to find (e.g., hashing)

  • Simple approach to finding long repeats:

    • Find exact repeats of short l-mers (l is usually 10 to 13)

    • Use l-mer repeats to potentially extend into longer, maximal repeats


L mer repeats cont d l.jpg
l-mer Repeats (cont’d)

  • There are typically many locations where an l-mer is repeated:

    GCTTACAGATTCAGTCTTACAGATGGT

  • The 4-mer TTAC starts at locations 3 and 17


Extending l mer repeats l.jpg
Extending l-mer Repeats

GCTTACAGATTCAGTCTTACAGATGGT

  • Extend these 4-mer matches:

    GCTTACAGATTCAGTCTTACAGATGGT

  • Maximal repeat: TTACAGAT


Maximal repeats l.jpg
Maximal Repeats

  • To find maximal repeats in this way, we need ALL start locations of all l-mers in the genome

  • Hashing lets us find repeats quickly in this manner


Hashing what is it l.jpg
Hashing: What is it?

  • What does hashing do?

    • For different data, generate a unique integer

    • Store data in an array at the unique integer index generated from the data

  • Hashing is a very efficient way to store and retrieve data


Hashing definitions l.jpg
Hashing: Definitions

  • Hash table: array used in hashing

  • Records: data stored in a hash table

  • Keys: identifies sets of records

  • Hash function: uses a key to generate an index to insert at in hash table

  • Collision: when more than one record is mapped to the same index in the hash table


Hashing example l.jpg
Hashing: Example

  • Where do the animals eat?

  • Records: each animal

  • Keys: where each animal eats


Hashing dna sequences l.jpg
Hashing DNA sequences

  • Each l-mer can be translated into a binary string (A, T, C, G can be represented as 00, 01, 10, 11)

  • After assigning a unique integer per l-mer it is easy to get all start locations of each l-mer in a genome


Hashing maximal repeats l.jpg
Hashing: Maximal Repeats

  • To find repeats in a genome:

    • For all l-mers in the genome, note the start position and the sequence

    • Generate a hash table index for each unique l-mer sequence

    • In each index of the hash table, store all genome start locations of the l-mer which generated that index

    • Extend l-mer repeats to maximal repeats


Hashing collisions l.jpg
Hashing: Collisions

  • Dealing with collisions:

    • “Chain” all start locations of l-mers (linked list)


Hashing summary l.jpg
Hashing: Summary

  • When finding genomic repeats from l-mers:

    • Generate a hash table index for each l-mer sequence

    • In each index, store all genome start locations of the l-mer which generated that index

    • Extend l-mer repeats to maximal repeats


Pattern matching l.jpg
Pattern Matching

  • What if, instead of finding repeats in a genome, we want to find all sequences in a database that contain a given pattern?

  • This leads us to a different problem, the Pattern MatchingProblem


Pattern matching problem l.jpg
Pattern Matching Problem

  • Goal: Find all occurrences of a pattern in a text

  • Input: Pattern p = p1…pn and text t = t1…tm

  • Output: All positions 1<i< (m – n + 1) such that the n-letter substring of t starting at i matches p

  • Motivation: Searching database for a known pattern


Exact pattern matching a brute force algorithm l.jpg
Exact Pattern Matching: A Brute-Force Algorithm

PatternMatching(p,t)

  • n length of pattern p

  • m length of text t

  • for i  1 to (m – n + 1)

  • if ti…ti+n-1 = p

  • outputi


Exact pattern matching an example l.jpg
Exact Pattern Matching: An Example

GCAT

  • PatternMatching algorithm for:

    • Pattern GCAT

    • Text CGCATC

CGCATC

GCAT

CGCATC

GCAT

CGCATC

GCAT

CGCATC

GCAT

CGCATC


Exact pattern matching running time l.jpg
Exact Pattern Matching: Running Time

  • PatternMatching runtime: O(nm)

  • Probability-wise, it’s more like O(m)

    • Rarely will there be close to n comparisons in line 4

  • Better solution: suffix trees

    • Can solve problem in O(m) time

    • Conceptually related to keyword trees


Keyword trees example l.jpg
Keyword Trees: Example

  • Keyword tree:

    • Apple


Keyword trees example cont d l.jpg
Keyword Trees: Example (cont’d)

  • Keyword tree:

    • Apple

    • Apropos


Keyword trees example cont d23 l.jpg
Keyword Trees: Example (cont’d)

  • Keyword tree:

    • Apple

    • Apropos

    • Banana


Keyword trees example cont d24 l.jpg
Keyword Trees: Example (cont’d)

  • Keyword tree:

    • Apple

    • Apropos

    • Banana

    • Bandana


Keyword trees example cont d25 l.jpg
Keyword Trees: Example (cont’d)

  • Keyword tree:

    • Apple

    • Apropos

    • Banana

    • Bandana

    • Orange


Keyword trees properties l.jpg
Keyword Trees: Properties

  • Stores a set of keywords in a rooted labeled tree

  • Each edge labeled with a letter from an alphabet

  • Any two edges coming out of the same vertex have distinct labels

  • Every keyword stored can be spelled on a path from root to some leaf


Keyword trees threading cont d l.jpg
Keyword Trees: Threading (cont’d)

  • Thread “appeal”

    • appeal


Keyword trees threading cont d28 l.jpg
Keyword Trees: Threading (cont’d)

  • Thread “appeal”

    • appeal


Keyword trees threading cont d29 l.jpg
Keyword Trees: Threading (cont’d)

  • Thread “appeal”

    • appeal


Keyword trees threading cont d30 l.jpg
Keyword Trees: Threading (cont’d)

  • Thread “appeal”

    • appeal


Keyword trees threading cont d31 l.jpg
Keyword Trees: Threading (cont’d)

  • Thread “apple”

    • apple


Keyword trees threading cont d32 l.jpg
Keyword Trees: Threading (cont’d)

  • Thread “apple”

    • apple


Keyword trees threading cont d33 l.jpg
Keyword Trees: Threading (cont’d)

  • Thread “apple”

    • apple


Keyword trees threading cont d34 l.jpg
Keyword Trees: Threading (cont’d)

  • Thread “apple”

    • apple


Keyword trees threading cont d35 l.jpg
Keyword Trees: Threading (cont’d)

  • Thread “apple”

    • apple


Multiple pattern matching problem l.jpg
Multiple Pattern Matching Problem

  • Goal: Given a set of patterns and a text, find all occurrences of any of patterns in text

  • Input: k patterns p1,…,pk, and text t = t1…tm

  • Output: Positions 1 <i <m where substring of t starting at i matches pj for 1 <j<k

  • Motivation: Searching database for known multiple patterns


Multiple pattern matching straightforward approach l.jpg
Multiple Pattern Matching: Straightforward Approach

  • Can solve as k “Pattern Matching Problems”

    • Runtime:

      O(kmn)

      using the PatternMatching algorithm k times

    • m - length of the text

    • n - average length of the pattern


Multiple pattern matching keyword tree approach l.jpg
Multiple Pattern Matching: Keyword Tree Approach

  • Or, we could use keyword trees:

    • Build keyword tree in O(N) time; N is total length of all patterns

    • With naive threading: O(N + nm)

    • Aho-Corasick algorithm: O(N + m)


Keyword trees threading l.jpg
Keyword Trees: Threading

  • To match patterns in a text using a keyword tree:

    • Build keyword tree of patterns

    • “Thread” the text through the keyword tree


Keyword trees threading cont d40 l.jpg
Keyword Trees: Threading (cont’d)

  • Threading is “complete” when we reach a leaf in the keyword tree

  • When threading is “complete,” we’ve found a pattern in the text


Suffix trees collapsed keyword trees l.jpg
Suffix Trees=Collapsed Keyword Trees

  • Similar to keyword trees, except edges that form paths are collapsed

    • Each edge is labeled with a substring of a text

    • All internal edges have at least two outgoing edges

    • Leaves labeled by the index of the pattern.


Suffix tree of a text l.jpg
Suffix Tree of a Text

  • Suffix trees of a text is constructed for all its suffixes

ATCATG TCATG CATG ATG TG G

Keyword Tree

Suffix Tree


Suffix tree of a text43 l.jpg
Suffix Tree of a Text

  • Suffix trees of a text is constructed for all its suffixes

ATCATG TCATG CATG ATG TG G

Keyword Tree

Suffix Tree

How much time does it take?


Suffix tree of a text44 l.jpg
Suffix Tree of a Text

  • Suffix trees of a text is constructed for all its suffixes

ATCATG TCATG CATG ATG TG G

Keyword Tree

Suffix Tree

quadratic

Time is linear in the total size of all suffixes, i.e., it is quadratic in the length of the text


Suffix trees advantages l.jpg
Suffix Trees: Advantages

  • Suffix trees of a text is constructed for all its suffixes

  • Suffix trees build faster than keyword trees

ATCATG TCATG CATG ATG TG G

Keyword Tree

Suffix Tree

quadratic

linear (Weiner suffix tree algorithm)


Use of suffix trees l.jpg
Use of Suffix Trees

  • Suffix trees hold all suffixes of a text

    • i.e., ATCGC: ATCGC, TCGC, CGC, GC, C

    • Builds in O(m) time for text of length m

  • To find any pattern of length n in a text:

    • Build suffix tree for text

    • Thread the pattern through the suffix tree

    • Can find pattern in text in O(n) time!

  • O(n + m) time for “Pattern Matching Problem”

    • Build suffix tree and lookup pattern


Pattern matching with suffix trees l.jpg
Pattern Matching with Suffix Trees

SuffixTreePatternMatching(p,t)

  • Build suffix tree for text t

  • Thread pattern p through suffix tree

  • if threading is complete

  • output positions of all p-matching leaves in the tree

  • else

  • output “Pattern does not appear in text”



Multiple pattern matching summary l.jpg
Multiple Pattern Matching: Summary

  • Keyword and suffix trees are used to find patterns in a text

  • Keyword trees:

    • Build keyword tree of patterns, and thread text through it

  • Suffix trees:

    • Build suffix tree of text, and thread patterns through it


Approximate vs exact pattern matching l.jpg
Approximate vs. Exact Pattern Matching

  • So far all we’ve seen exact pattern matching algorithms

  • Usually, because of mutations, it makes much more biological sense to find approximate pattern matches

  • Biologists often use fast heuristic approaches (rather than local alignment) to find approximate matches


Heuristic similarity searches l.jpg
Heuristic Similarity Searches

  • Genomes are huge: Smith-Waterman quadratic alignment algorithms are too slow

  • Alignment of two sequences usually has short identical or highly similar fragments

  • Many heuristic methods (i.e., FASTA) are based on the same idea of filtration

    • Find short exact matches, and use them as seeds for potential match extension

    • “Filter” out positions with no extendable matches


Dot matrices l.jpg
Dot Matrices

  • Dot matrices show similarities between two sequences

  • FASTA makes an implicit dot matrix from short exact matches, and tries to find long diagonals (allowing for some mismatches)


Dot matrices cont d l.jpg
Dot Matrices (cont’d)

  • Identify diagonals above a threshold length

  • Diagonals in the dot matrix indicate exact substring matching


Diagonals in dot matrices l.jpg
Diagonals in Dot Matrices

  • Extend diagonals and try to link them together, allowing for minimal mismatches/indels

  • Linking diagonals reveals approximate matches over longer substrings


Approximate pattern matching problem l.jpg
Approximate Pattern Matching Problem

  • Goal: Find all approximate occurrences of a pattern in a text

  • Input: A pattern p = p1…pn, text t = t1…tm, and k, the maximum number of mismatches

  • Output: All positions 1 <i< (m – n +1) such that ti…ti+n-1 and p1…pn have at most k mismatches (i.e., Hamming distance between ti…ti+n-1 and p <k)


Approximate pattern matching a brute force algorithm l.jpg
Approximate Pattern Matching: A Brute-Force Algorithm

ApproximatePatternMatching(p, t, k)

  • n length of pattern p

  • m  length of text t

  • fori  1 to m – n + 1

  • dist  0

  • forj  1 to n

  • ifti+j-1 != pj

  • dist dist + 1

  • ifdist<k

  • outputi


Approximate pattern matching running time l.jpg
Approximate Pattern Matching: Running Time

  • That algorithm runs in O(nm).

  • Landau-Vishkin algorithm: O(kn)

  • We can generalize the “Approximate Pattern Matching Problem” into a “Query Matching Problem”:

    • We want to match substrings in a query to substrings in a text with at most k mismatches

    • Motivation: we want to see similarities to some gene, but we may not know which parts of the gene to look for


Query matching problem l.jpg
Query Matching Problem

  • Goal: Find all substrings of the query that approximately match the text

  • Input: Query q = q1…qw,

    text t = t1…tm,

    n (length of matching substrings),

    k (maximum number of mismatches)

  • Output: All pairs of positions (i, j) such that the

    n-letter substring of q starting at iapproximately matches the

    n-letter substring of t starting at j,

    with at most k mismatches



Query matching main idea l.jpg
Query Matching: Main Idea

  • Approximately matching strings share some perfectly matching substrings.

  • Instead of searching for approximately matching strings (difficult) search for perfectly matching substrings (easy).


Filtration in query matching l.jpg
Filtration in Query Matching

  • We want all n-matches between a query and a text with up to k mismatches

  • “Filter” out positions we know do not match between text and query

  • Potential match detection: find all matches of l-tuples in query and text for some small l

  • Potential match verification: Verify each potential match by extending it to the left and right, until (k + 1) mismatches are found


Filtration match detection l.jpg
Filtration: Match Detection

  • If x1…xn and y1…yn match with at most k mismatches, they must share an l-tuple that is perfectly matched, with l = n/(k + 1)

  • Break string of length n into k+1 parts, each each of length n/(k + 1)

    • k mismatches can affect at most k of these k+1 parts

    • At least one of these k+1 parts is perfectly matched


Filtration match detection cont d l.jpg
Filtration: Match Detection(cont’d)

  • Suppose k = 3. We would then have l=n/(k+1)=n/4:

  • There are at most k mismatches in n, so at the very least there must be one out of the k+1 l–tuples without a mismatch

1…l

l+1…2l

2l+1…3l

3l+1…n

1

2

k

k+ 1


Filtration match verification l.jpg
Filtration: Match Verification

  • For each l -match we find, try to extend the match further to see if it is substantial

Extend perfect match of lengthl

until we find an approximate match of length n with k mismatches

query

text


Filtration example l.jpg
Filtration: Example

Shorter perfectmatches required

Performance decreases


Local alignment is to slow l.jpg
Local alignment is to slow

  • Quadratic local alignment is too slow while looking for similarities between long strings (e.g. the entire GenBank database)


Local alignment is to slow67 l.jpg
Local alignment is to slow

  • Quadratic local alignment is too slow while looking for similarities between long strings (e.g. the entire GenBank database)


Local alignment is to slow68 l.jpg
Local alignment is to slow

  • Quadratic local alignment is too slow while looking for similarities between long strings (e.g. the entire GenBank database)


Local alignment is to slow69 l.jpg
Local alignment is to slow

  • Quadratic local alignment is too slow while looking for similarities between long strings (e.g. the entire GenBank database)

  • Guaranteed to find the optimal local alignment

  • Sets the standard for sensitivity


Local alignment is to slow70 l.jpg
Local alignment is to slow

  • Quadratic local alignment is too slow while looking for similarities between long strings (e.g. the entire GenBank database)

  • Basic Local Alignment Search Tool

    • Altschul, S., Gish, W., Miller, W., Myers, E. & Lipman, D.J.

      Journal of Mol. Biol., 1990

  • Search sequence databases for local alignments to a query


Blast l.jpg
BLAST

  • Great improvement in speed, with a modest decrease in sensitivity

  • Minimizes search space instead of exploring entire search space between two sequences

  • Finds short exact matches (“seeds”), only explores locally around these “hits”


What similarity reveals l.jpg
What Similarity Reveals

  • BLASTing a new gene

    • Evolutionary relationship

    • Similarity between protein function

  • BLASTing a genome

    • Potential genes


Blast algorithm l.jpg
BLAST algorithm

  • Keyword search of all words of length w from the query of length n in database of length m with score above threshold

    • w = 11 for DNA queries, w =3 for proteins

  • Local alignment extension for each found keyword

    • Extend result until longest match above threshold is achieved

  • Running time O(nm)


Blast algorithm cont d l.jpg
BLAST algorithm (cont’d)

keyword

Query: KRHRKVLRDNIQGITKPAIRRLARRGGVKRISGLIYEETRGVLKIFLENVIRD

GVK 18

GAK 16

GIK 16

GGK 14

GLK 13

GNK 12

GRK 11

GEK 11

GDK 11

Neighborhood

words

neighborhood

score threshold

(T = 13)

extension

Query: 22 VLRDNIQGITKPAIRRLARRGGVKRISGLIYEETRGVLK 60

+++DN +G + IR L G+K I+ L+ E+ RG++K

Sbjct: 226 IIKDNGRGFSGKQIRNLNYGIGLKVIADLV-EKHRGIIK 263

High-scoring Pair (HSP)


Original blast l.jpg
Original BLAST

  • Dictionary

    • All words of length w

  • Alignment

    • Ungapped extensions until score falls below some statistical threshold

  • Output

    • All local alignments with score > threshold


Original blast example l.jpg
Original BLAST: Example

A C G A A G T A A G G T C C A G T

  • w = 4

  • Exact keyword match of GGTC

  • Extend diagonals with mismatches until score is under 50%

  • Output result

    • GTAAGGTCC

    • GTTAGGTCC

C T G A T C C T G G A T T G C G A

From lectures by Serafim Batzoglou (Stanford)


Gapped blast example l.jpg
Gapped BLAST : Example

A C G A A G T A A G G T C C A G T

  • Original BLAST exact keyword search, THEN:

  • Extend with gaps around ends of exact matchuntil score < threshold

  • Output result

    GTAAGGTCCAGT

    GTTAGGTC-AGT

C T G A T C C T G G A T T G C G A

From lectures by Serafim Batzoglou (Stanford)


Incarnations of blast l.jpg
Incarnations of BLAST

  • blastn: Nucleotide-nucleotide

  • blastp: Protein-protein

  • blastx: Translated query vs. protein database

  • tblastn: Protein query vs. translated database

  • tblastx: Translated query vs. translated

    database (6 frames each)


Incarnations of blast cont d l.jpg
Incarnations of BLAST (cont’d)

  • PSI-BLAST

    • Find members of a protein family or build a custom position-specific score matrix

  • Megablast:

    • Search longer sequences with fewer differences

  • WU-BLAST: (Wash U BLAST)

    • Optimized, added features


Assessing sequence similarity l.jpg
Assessing sequence similarity

  • Need to know how strong an alignment can be expected from chance alone

  • “Chance” relates to comparison of sequences that are generated randomly based upon a certain sequence model

  • Sequence models may take into account:

    • G+C content

    • Poly-A tails

    • “Junk” DNA

    • Codon bias

    • Etc.


Blast segment score l.jpg
BLAST: Segment Score

  • BLAST uses scoring matrices (d) to improve on efficiency of match detection

    • Some proteins may have very different amino acid sequences, but are still similar

  • For any two l-mers x1…xl and y1…yl :

    • Segment pair: pair of l-mers, one from each sequence

    • Segment score: Sli=1d(xi, yi)


Blast locally maximal segment pairs l.jpg
BLAST: Locally Maximal Segment Pairs

  • A segment pair is maximal if it has the best score over all segment pairs

  • A segment pair is locally maximal if its score can’t be improved by extending or shortening

  • Statistically significant locally maximal segment pairs are of biological interest

  • BLAST finds all locally maximal segment pairs with scores above some threshold

    • A significantly high threshold will filter out some statistically insignificant matches


Blast statistics l.jpg
BLAST: Statistics

  • Threshold: Altschul-Dembo-Karlin statistics

    • Identifies smallest segment score that is unlikely to happen by chance

  • # matches above q has mean E(q) = Kmne-lq; K is a constant, m and n are the lengths of the two compared sequences

    • Parameter l is positive root of:

      Sx,y in A(pxpyed(x,y)) = 1, where px and py are frequenceies of amino acids x and y, and A is the twenty letter amino acid alphabet


P values l.jpg
P-values

  • The probability of finding b HSPs with a score ≥S is given by:

    • (e-EEb)/b!

  • For b = 0, that chance is:

    • e-E

  • Thus the probability of finding at least one HSP with a score ≥S is:

    • P = 1 – e-E


Sample blast output l.jpg
Sample BLAST output

  • Blast of human beta globin protein against zebra fish

Score E

Sequences producing significant alignments: (bits) Value

gi|18858329|ref|NP_571095.1| ba1 globin [Danio rerio] >gi|147757... 171 3e-44

gi|18858331|ref|NP_571096.1| ba2 globin; SI:dZ118J2.3 [Danio rer... 170 7e-44

gi|37606100|emb|CAE48992.1| SI:bY187G17.6 (novel beta globin) [D... 170 7e-44

gi|31419195|gb|AAH53176.1| Ba1 protein [Danio rerio] 168 3e-43

ALIGNMENTS

>gi|18858329|ref|NP_571095.1| ba1 globin [Danio rerio]

Length = 148

Score = 171 bits (434), Expect = 3e-44

Identities = 76/148 (51%), Positives = 106/148 (71%), Gaps = 1/148 (0%)

Query: 1 MVHLTPEEKSAVTALWGKVNVDEVGGEALGRLLVVYPWTQRFFESFGDLSTPDAVMGNPK 60

MV T E++A+ LWGK+N+DE+G +AL R L+VYPWTQR+F +FG+LS+P A+MGNPK

Sbjct: 1 MVEWTDAERTAILGLWGKLNIDEIGPQALSRCLIVYPWTQRYFATFGNLSSPAAIMGNPK 60

Query: 61 VKAHGKKVLGAFSDGLAHLDNLKGTFATLSELHCDKLHVDPENFRLLGNVLVCVLAHHFG 120

V AHG+ V+G + ++DN+K T+A LS +H +KLHVDP+NFRLL + + A FG

Sbjct: 61 VAAHGRTVMGGLERAIKNMDNVKNTYAALSVMHSEKLHVDPDNFRLLADCITVCAAMKFG 120

Query: 121 KE-FTPPVQAAYQKVVAGVANALAHKYH 147

+ F VQ A+QK +A V +AL +YH

Sbjct: 121 QAGFNADVQEAWQKFLAVVVSALCRQYH 148


Sample blast output cont d l.jpg
Sample BLAST output (cont’d)

  • Blast of human beta globin DNA against human DNA

Score E

Sequences producing significant alignments: (bits) Value

gi|19849266|gb|AF487523.1| Homo sapiens gamma A hemoglobin (HBG1... 289 1e-75

gi|183868|gb|M11427.1|HUMHBG3E Human gamma-globin mRNA, 3' end 289 1e-75

gi|44887617|gb|AY534688.1| Homo sapiens A-gamma globin (HBG1) ge... 280 1e-72

gi|31726|emb|V00512.1|HSGGL1 Human messenger RNA for gamma-globin 260 1e-66

gi|38683401|ref|NR_001589.1| Homo sapiens hemoglobin, beta pseud... 151 7e-34

gi|18462073|gb|AF339400.1| Homo sapiens haplotype PB26 beta-glob... 149 3e-33

ALIGNMENTS

>gi|28380636|ref|NG_000007.3| Homo sapiens beta globin region (HBB@) on chromosome 11

Length = 81706

Score = 149 bits (75), Expect = 3e-33

Identities = 183/219 (83%)

Strand = Plus / Plus

Query: 267 ttgggagatgccacaaagcacctggatgatctcaagggcacctttgcccagctgagtgaa 326

|| ||| | || | || | |||||| ||||| ||||||||||| ||||||||

Sbjct: 54409 ttcggaaaagctgttatgctcacggatgacctcaaaggcacctttgctacactgagtgac 54468

Query: 327 ctgcactgtgacaagctgcatgtggatcctgagaacttc 365

||||||||| |||||||||| ||||| ||||||||||||

Sbjct: 54469 ctgcactgtaacaagctgcacgtggaccctgagaacttc 54507


Timeline l.jpg
Timeline

  • 1970: Needleman-Wunsch global alignment algorithm

  • 1981: Smith-Waterman local alignment algorithm

  • 1985: FASTA

  • 1990: BLAST (basic local alignment search tool)

  • 2000s: BLAST has become too slow in “genome vs. genome” comparisons - new faster algorithms evolve!

    • Pattern Hunter

    • BLAT


Patternhunter faster and even more sensitive l.jpg

BLAST: matches short consecutive sequences (consecutive seed)

Length = k

Example (k = 11):

11111111111

Each 1 represents a “match”

PatternHunter: matches short non-consecutive sequences (spaced seed)

Increases sensitivity by locating homologies that would otherwise be missed

Example (a spaced seed of length 18 w/ 11 “matches”):

111010010100110111

Each 0 represents a “don’t care”, so there can be a match or a mismatch

PatternHunter: faster and even more sensitive


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Example of a hit using a spaced seed: seed)

Spaced seeds

How does this result in better sensitivity?


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Why is PH better? seed)

  • BLAST: redundant hits

  • PatternHunter

This results in > 1 hit and creates clusters of redundant hits

This results in very few redundant hits


Why is ph better91 l.jpg
Why is PH better? seed)

BLAST may also miss a hit

GAGTACTCAACACCAACATTAGTGGGCAATGGAAAAT

|| ||||||||| |||||| | |||||| ||||||

GAATACTCAACAGCAACATCAATGGGCAGCAGAAAAT

9 matches

In this example, despite a clear homology, there is no sequence of continuous matches longer than length 9. BLAST uses a length 11 and because of this, BLAST does not recognize this as a hit!

Resolving this would require reducing the seed length to 9, which would have a damaging effect on speed


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Advantage of Gapped Seeds seed)

11 positions

11 positions

10 positions


Why is ph better93 l.jpg
Why is PH better? seed)

  • Higher hit probability

  • Lower expected number of random hits


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Use of Multiple Seeds seed)

Basic Searching Algorithm

  • Select a group of spaced seed models

  • For each hit of each model, conduct extension to find a homology.


Another method blat l.jpg
Another method: BLAT seed)

  • BLAT (BLAST-Like Alignment Tool)

  • Same idea as BLAST - locate short sequence hits and extend


Blat vs blast differences l.jpg
BLAT vs. BLAST: Differences seed)

  • BLAT builds an index of the database and scans linearly through the query sequence, whereas BLAST builds an index of the query sequence and then scans linearly through the database

  • Index is stored in RAM which is memory intensive, but results in faster searches


Blat fast cdna alignments l.jpg
BLAT: Fast cDNA Alignments seed)

Steps:

1. Break cDNA into 500 base chunks.

2. Use an index to find regions in genome similar to each chunk of cDNA.

3. Do a detailed alignment between genomic regions and cDNA chunk.

4. Use dynamic programming to stitch together detailed alignments of chunks into detailed alignment of whole.


Blat indexing l.jpg
BLAT: Indexing seed)

  • An index is built that contains the positions of each k-mer in the genome

  • Each k-mer in the query sequence is compared to each k-mer in the index

  • A list of ‘hits’ is generated - positions in cDNA and in genome that match for k bases


Indexing an example l.jpg
Indexing: An Example seed)

Here is an example with k = 3:

Genome:cacaattatcacgaccgc

3-mers (non-overlapping): cac aat tat cac gac cgc

Index: aat 3 gac 12

cac 0,9 tat 6

cgc 15

cDNA (query sequence): aattctcac

3-mers (overlapping): aat att ttc tct ctc tca cac

0 1 2 3 4 5 6

Hits: aat 0,3

cac 6,0

cac 6,9

clump: cacAATtatCACgaccgc

Multiple instances map to single index

Position of 3-mer in query, genome


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However… seed)

  • BLAT was designed to find sequences of 95% and greater similarity of length >40; may miss more divergent or shorter sequence alignments


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PatternHunter and BLAT vs. BLAST seed)

  • PatternHunter is 5-100 times faster than Blastn, depending on data size, at the same sensitivity

  • BLAT is several times faster than BLAST, but best results are limited to closely related sequences


Resources l.jpg
Resources seed)

  • tandem.bu.edu/classes/ 2004/papers/pathunter_grp_prsnt.ppt

  • http://www.jax.org/courses/archives/2004/gsa04_king_presentation.pdf

  • http://www.genomeblat.com/genomeblat/blatRapShow.pps


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