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Genome

Genome. Nucleus. Tissue. Cell. The chromosomes contains the set of instructions for alive beings. The chromosomes are the volumes of an encyclopedia called Genome. Chromosome. >human chromosome

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Genome

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  1. Genome Nucleus Tissue Cell • The chromosomes contains the set of instructions for alive beings • The chromosomes are the volumes of an encyclopedia called Genome

  2. Chromosome >human chromosome TACGTATACTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGCGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGATGCTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCCGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGATGCTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGATCGATGCTATACGACGATCGTAGCTAGCTGCATGCTAGCGATGCTACGATCGATGCTATACGACGATCGTAGCTTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTCGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGATGCTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGATCGATGCTATACGACGATCGTAGCTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGATGCTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGATCGATGCTATACGACGATCGTAGCTGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGGTACGATCGTCGATCGTCAGCTCGATACGTTACGATCTACGATTACGATCATCTATACTATACTATACGATATATCTAGATATCGATCTA.ACTCCATTCTTTAAACCGTACTACACACACTACTGATCGACGATTACGACGACGAAAGGGCCATATCGGCTAACTACATCATAGACAACATCACGGATCGTCTAAGGCCGAGTTAGGTACGATTAACGTACGACTACCTATCGTATATACATCACGGATATAACCTATCTACTACGATTAACACGATCTATCGTACGGCATATGCATCGTATAGCATCGATTAGAATACGTATACGTACGATCGTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGATGCTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGATCGCGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGATGCTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGATCGATGCTATACGACGATCGTAGCTATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGCTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGATGCATGCTAGCGATGCTACGACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGATGCTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACTGCATCGATGCTATACGACGATCGTAGCTACGTACGATCGTACGACGTACGTTACGTACGATCGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTGTCACGTAGCATGCTGACGTACGATCGATTCGATCGATCGTACGATCGTAGCTAGCTAGTCGTAGCGACGTAGGATTCACGTAGCGATGCGTAGCGTAGCATGCTGACGATGCATCGATCGATGCATCATGCTAGCGTAGCTAGCTAGCATGACTGATCGATTAACGGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGTACGGTACACCGCGCACGATCACACGATGCGACGATGCGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGCTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGACGATCGTACGACTGCTAGCTACGCATGCCTACGTACGTATCCTACGTACGATCGTGCAGCATCGATGCTACGTACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGACGACGATCGATATTAATGCAATCATGCAGCTGCATGCTAGCGATGCTACGTACGATCGTATGCTAGCTAGCATGCATGCATGCATGCAT ………..

  3. Recuperació de la informació • Bioinformatics. Sequence and genome analysis • David W. Mount • Flexible Pattern Matching in Strings (2002) • Gonzalo Navarro and Mathieu Raffinot • Algorithms on strings (2001) • M. Crochemore, C. Hancart and T. Lecroq • http://www-igm.univ-mlv.fr/~lecroq/string/index.html

  4. String Matching String matching: definition of the problem (text,pattern) depends on what we have: text or patterns • Exact matching: • The patterns ---> Data structures for the patterns • 1 pattern ---> The algorithm depends on |p| and || • k patterns ---> The algorithm depends on k, |p| and || • Extensions • Regular Expressions • The text ----> Data structure for the text (suffix tree, ...) • Approximate matching: • Dynamic programming • Sequence alignment (pairwise and multiple) • Sequence assembly: hash algorithm • Probabilistic search: Hidden Markov Models

  5. Exact string matching: one pattern How does the string algorithms made the search? For instance, given the sequence CTACTACTACGTCTATACTGATCGTAGCTACTACATGC search for the pattern ACTGA. and for the pattern TACTACGGTATGACTAA

  6. Exact string matching: Brute force algorithm A T G T A A T G T A A T G T A A T G T A A T G T A A T G T A Example: Given the pattern ATGTA, the search is G T A C T A G A G G A C G T A T G T A C T G ...

  7. Exact string matching: Brute force algorithm • How the comparison is made? From left to right: prefix • Which is the next position of the window? The window is shifted only one cell Text : Pattern : Text : Pattern :

  8. Exact string matching: one pattern Text : Pattern : How does the matching algorithms made the search? There is a sliding window along the text against which the pattern is compared: At each step the comparison is made and the window is shifted to the right. Which are the facts that differentiate the algorithms? • How the comparison is made. • The length of the shift.

  9. Exact string matching: one pattern (text on-line) Experimental efficiency (Navarro & Raffinot) BNDM : Backward Nondeterministic Dawg Matching | | BOM : Backward Oracle Matching 64 32 16 Horspool 8 BOM BNDM 4 Long. pattern 2 w 2 4 8 16 32 64 128 256

  10. Horspool algorithm • How the comparison is made? Text : Pattern : Sufix search • Which is the next position of the window? a Text : Pattern : Shift until the next ocurrence of “a” in the pattern: a a a a a a We need a preprocessing phase to construct the shift table.

  11. Horspool algorithm : example Given the pattern ATGTA A C G T • The shift table is:

  12. Horspool algorithm : example Given the pattern ATGTA A 4 C G T • The shift table is:

  13. Horspool algorithm : example Given the pattern ATGTA A 4 C 5 G T • The shift table is:

  14. Horspool algorithm : example Given the pattern ATGTA A 4 C 5 G 2 T • The shift table is:

  15. Horspool algorithm : example Given the pattern ATGTA A 4 C 5 G 2 T 1 • The shift table is:

  16. Horspool algorithm : example Given the pattern ATGTA A 4 C 5 G 2 T 1 • The shift table is: • The searching phase: G T A C T A G A G G A C G T A T G T A C T G ... A T G T A A T G T A A T G T A A T G T A A T G T A A T G T A

  17. Exemple algorisme de Horspool Given the pattern ATGTA A 4 C 5 G 2 T 1 • The shift table is: • The searching phase: G T A C T A G A G G A C G T A T G T A C T G ... A T G T A A T G T A A T G T A A T G T A A T G T A A T G T A A T G T A

  18. Qüestions sobre l’algorisme de Horspool A 4 C 5 G 2 T 1 Given the pattern ATGTA, the shift table is Given a random text over an equally likely probability distribution (EPD): 1.- Determine the expected shift of the window. And, if the PD is not equally likely? 2.- Determine the expected number of shifts assuming a text of length n. 3.- Determine the expected number of comparisons in the suffix search phase

  19. Exact string matching: one pattern (text on-line) Experimental efficiency (Navarro & Raffinot) BNDM : Backward Nondeterministic Dawg Matching | | BOM : Backward Oracle Matching 64 32 16 Horspool 8 BOM BNDM 4 Long. pattern 2 w 2 4 8 16 32 64 128 256

  20. BNDM algorithm • How the comparison is made? Search for suffixes of T that are factors of x Text : Pattern : That is denoted as D2 = 1 0 0 0 1 0 0 Once the next character x is read D3 = D2<<1 & B(x) B(x): mask of x in the pattern P. For instance, if B(x) = ( 0 0 1 1 0 0 0) D = (0 0 0 1 0 0 0) & (0 0 1 1 0 0 0 ) = (0 0 0 1 0 0 0 ) • Which is the next position of the window? Depends on the value of the leftmost bit of D

  21. BNDM algorithm: exaple B(A) = ( 1 0 0 0 1 ) B(C) = ( 0 0 0 0 0 ) B(G) = ( 0 0 1 0 0 ) B(T) = ( 0 1 0 1 0 ) • The mask of characters is: • The searching phase: G T A C T A G A G G A C G T A T G T A C T G ... A T G T A A T G T A A T G T A A T G T A Given the pattern ATGTA D1 = ( 0 1 0 1 0 ) D2 = ( 1 0 1 0 0 ) & ( 0 0 0 0 0 ) = ( 0 0 0 0 0 ) D1 = ( 0 0 1 0 0 ) D2 = ( 0 1 0 0 0 ) & ( 0 0 1 0 0 ) = ( 0 0 0 0 0 ) D1 = ( 1 0 0 0 1 ) D2 = ( 0 0 0 1 0 ) & ( 0 1 0 1 0 ) = ( 0 0 0 1 0 ) D3 = ( 0 0 1 0 0 ) & ( 0 0 1 0 0) = ( 0 0 1 0 0 ) D4 = ( 0 1 0 0 0 ) & ( 0 0 0 0 0) = ( 0 0 0 0 0 )

  22. Exemple algorisme BNDM B(A) = ( 1 0 0 0 1 ) B(C) = ( 0 0 0 0 0 ) B(G) = ( 0 0 1 0 0 ) B(T) = ( 0 1 0 1 0 ) • Given the pattern ATGTA • The mask of characters is : • The searching phase: G T A C T A G A G G A C G T A T G T A C T G ... A T G T A A T G T A D1 = ( 1 0 0 0 1 ) D2 = ( 0 0 0 1 0 ) & ( 0 1 0 1 0 ) = ( 0 0 0 1 0 ) D3 = ( 0 0 1 0 0 ) & ( 0 0 1 0 0 ) = ( 0 0 1 0 0 ) D4 = ( 0 1 0 0 0 ) & ( 0 1 0 1 0 ) = ( 0 1 0 0 0 ) D5 = ( 1 0 0 0 0 ) & ( 1 0 0 0 1 ) = ( 1 0 0 0 0 ) D6 = ( 0 0 0 0 0 ) & ( * * * * * ) = ( 0 0 0 0 0 ) Trobat!

  23. Exemple algorisme BNDM B(A) = ( 1 0 0 0 1 ) B(C) = ( 0 0 0 0 0 ) B(G) = ( 0 0 1 0 0 ) B(T) = ( 0 1 0 1 0 ) • The mask of characters is : • The searching phase: G T A C T A G A A T A C G T A T G T A C T G ... A T G T A A T G T A A T G T A Given the pattern ATGTA How the shif is determined? D1 = ( 0 1 0 1 0 ) D2 = ( 1 0 1 0 0 ) & ( 0 0 0 0 0 ) = ( 0 0 0 0 0 ) D1 = ( 0 1 0 1 0 ) D2 = ( 1 0 1 0 0 ) & ( 1 0 0 0 1 ) = ( 1 0 0 0 0 ) D3 = ( 0 0 0 0 0 ) & ( 1 0 0 0 1 ) = ( 0 0 0 0 0 )

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