An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Combinatorial Pattern Matching
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Extending l-mer Repeats
GCTTACAGATTCAGTCTTACAGATGGT
• Extend these 4-mer matches:
GCTTACAGATTCAGTCTTACAGATGGT
• Maximal repeat: TTACAGAT
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Hashing: Example
• Where do the animals eat?
• Records: each animal
• Keys: where each animal eats
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Hashing: Collisions
• Dealing with collisions: • “Chain” all start locations of l-mers (linked list)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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 Matching Problem
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Exact Pattern Matching: A Brute-Force Algorithm
PatternMatching(p,t) 1 n ß length of pattern p 2 m ß length of text t 3 for i ß 1 to (m – n + 1) 4 if ti…ti+n-1 = p 5 output i
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Exact Pattern Matching: An Example GCAT • PatternMatching CGCATC algorithm for: GCAT CGCATC • Pattern GCAT GCAT CGCATC
• Text CGCATC GCAT CGCATC GCAT CGCATC
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Keyword Trees: Example
• Keyword tree: • Apple
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Keyword Trees: Example (cont’d)
• Keyword tree: • Apple • Apropos
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Keyword Trees: Example (cont’d)
• Keyword tree: • Apple • Apropos • Banana
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Keyword Trees: Example (cont’d)
• Keyword tree: • Apple • Apropos • Banana • Bandana
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Keyword Trees: Example (cont’d)
• Keyword tree: • Apple • Apropos • Banana • Bandana • Orange
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Keyword Trees: Threading (cont’d)
• Thread “appeal” • appeal
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Keyword Trees: Threading (cont’d)
• Thread “appeal” • appeal
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Keyword Trees: Threading (cont’d)
• Thread “appeal” • appeal
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Keyword Trees: Threading (cont’d)
• Thread “appeal” • appeal
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Keyword Trees: Threading (cont’d)
• Thread “apple” • apple
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Keyword Trees: Threading (cont’d)
• Thread “apple” • apple
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Keyword Trees: Threading (cont’d)
• Thread “apple” • apple
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Keyword Trees: Threading (cont’d)
• Thread “apple” • apple
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Keyword Trees: Threading (cont’d)
• Thread “apple” • apple
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Multiple Pattern Matching Problem
• Goal: Given a set of patterns and a text, find all occurrences of any of patterns in text
1 k • Input: k patterns p ,…,p , 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Suffix Tree of a Text
• Suffix trees of a text is constructed for all its suffixes
ATCATG TCATG Keywor Suffix CATG d Tree ATG Tree TG G
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Suffix Tree of a Text
• Suffix trees of a text is constructed for all its suffixes
ATCATG TCATG Keywor Suffix CATG d Tree ATG Tree TG G How much time does it take?
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Suffix Tree of a Text
• Suffix trees of a text is constructed for all its suffixes
ATCATG
TCATG quadratic Keywor Suffix CATG d Tree ATG Tree TG G Time is linear in the total size of all suffixes, i.e., it is quadratic in the length of the text
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Suffix Trees: Advantages
• Suffix trees of a text is constructed for all its suffixes • Suffix trees build faster than keyword trees
ATCATG
TCATG quadratic Keywor Suffix CATG d Tree ATG Tree TG G linear (Weiner suffix tree algorithm)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Pattern Matching with Suffix Trees
SuffixTreePatternMatching(p,t) 2 Build suffix tree for text t 3 Thread pattern p through suffix tree 4 if threading is complete 5 output positions of all p-matching leaves in the tree 6 else 7 output “Pattern does not appear in text”
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Suffix Trees: Example
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Dot Matrices (cont’d)
• Identify diagonals above a threshold length
• Diagonals in the dot matrix indicate exact substring matching
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Approximate Pattern Matching: A Brute- Force Algorithm
ApproximatePatternMatching(p, t, k) 2 n ß length of pattern p 3 m ß length of text t 4 for i ß 1 to m – n + 1 5 dist ß 0 6 for j ß 1 to n 7 if ti+j-1 != pj 8 dist ß dist + 1 9 if dist < k 10 output i
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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 i approximately matches the n-letter substring of t starting at j, with at most k mismatches
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Approximate Pattern Matching vs Query Matching
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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).
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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 = ën/(k + 1)û • Break string of length n into k+1 parts, each each of length ën/(k + 1)û • k mismatches can affect at most k of these k+1 parts • At least one of these k+1 parts is perfectly matched
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Filtration: Match Detection (cont’d)
• Suppose k = 3. We would then have l=n/(k+1)=n/4:
1…l l +1…2l 2l +1…3l 3l +1…n 1 2 k k + 1
• 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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 length l query until we find an approximate match of length n with k text mismatches
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Filtration: Example
k = 0 k = 1 k = 2 k = 3 k = 4 k = 5 l -tuple n n/2 n/3 n/4 n/5 n/6 length
Shorter perfect matches required
Performance decreases
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Local alignment is to slow…
• Quadratic local alignment is too slow while looking for similarities between long strings (e.g. the entire GenBank database)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Local alignment is to slow…
• Quadratic local alignment is too slow while looking for similarities between long strings (e.g. the entire GenBank database)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Local alignment is to slow…
• Quadratic local alignment is too slow while looking for similarities between long strings (e.g. the entire GenBank database)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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”
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info What Similarity Reveals
• BLASTing a new gene
• Evolutionary relationship
• Similarity between protein function
• BLASTing a genome
• Potential genes
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
BLAST algorithm (cont’d)
keyword
Query: KRHRKVLRDNIQGITKPAIRRLARRGGVKRISGLIYEETRGVLKIFLENVIRD GVK 18 GAK 16 GIK 16 Neighborhood GGK 14 words neighborhood GLK 13 score threshold GNK 12 (T = 13) GRK 11 GEK 11 GDK 11 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)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Original BLAST: Example A C G A A G T A A G G T C C A G T • w = 4 A
• Exact keyword match of GGTC • Extend
diagonals with T G C A mismatches until score is under 50%
• Output result
GTAAGGTCC T C G
A GTTAGGTCC
From lectures by Serafim Batzoglou
(Stanford) C T G An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Gapped BLAST : Example A C G A A G T A A G G T C C A G T • Original BLAST A exact keyword
search, THEN: • Extend with gaps around ends of T G C A exact match until score < threshold • Output result
GTAAGGTCCA GT T C G A GTTAGGTC- AGT
From lectures by Serafim Batzoglou (Stanford) C T G An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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=1 d(xi, yi)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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: d(x,y) S x,y in A(pxpye ) = 1, where px and py are frequenceies of amino acids x and y, and A is the twenty letter amino acid alphabet An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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 Ð e-E
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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 An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info PatternHunter: faster and even more sensitive • BLAST: matches short • PatternHunter: matches consecutive sequences short non-consecutive (consecutive seed) sequences (spaced seed) • Increases sensitivity by • Length = k locating homologies that • Example (k = 11): would otherwise be missed • Example (a spaced seed of length 18 w/ 11 “matches”): 11111111111 111010010100110111
Each 1 represents a “match” Each 0 represents a “don’t care”, so there can be a match or a mismatch
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Spaced seeds
Example of a hit using a spaced seed:
How does this result in better sensitivity?
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Why is PH better?
• BLAST: redundant PatternHunter hits
This results in > 1 hit and This results in very few creates clusters of redundant hits redundant hits
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Why is PH better?
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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Advantage of Gapped Seeds
11 positions 11 positions
10 positions
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Why is PH better?
• Higher hit probability • Lower expected number of random hits
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Use of Multiple Seeds
Basic Searching Algorithm 2. Select a group of spaced seed models 3. For each hit of each model, conduct extension to find a homology.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Another method: BLAT
• BLAT (BLAST-Like Alignment Tool) • Same idea as BLAST - locate short sequence hits and extend
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info BLAT vs. BLAST: Differences
• 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info BLAT: Fast cDNA Alignments
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.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info BLAT: Indexing
• 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Indexing: An Example
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 Multiple instances map to single index cDNA (query sequence): aattctcac 3-mers (overlapping): aat att ttc tct ctc tca cac 0 1 2 3 4 5 6 Position of 3-mer in query, genome
Hits: aat 0,3 cac 6,0 cac 6,9 clump: cacAATtatCACgaccgc
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info However…
• BLAT was designed to find sequences of 95% and greater similarity of length >40; may miss more divergent or shorter sequence alignments
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info PatternHunter and BLAT vs. BLAST
• 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Resources
• 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