tècniques i eines bioinformàtiques

Tècniques i Eines Bioinformàtiques

•Bioinformatics, Sequence and Genome AnalysisDavid 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

Algorismes i estructures eficients de cerca

String matching: definition of the problem (text,pattern) depends on what we have: text or patterns• Exact matching:

• 1 pattern ---> The algorithm depends on |p| and || • k patterns ---> The algorithm depends on k, |p| and ||

• The text ----> Data structure for the text (suffix tree, ...)

• The patterns ---> Data structures for the patterns

Exact string matching: one pattern

For instance, given the sequence

CTACTACTACGTCTATACTGATCGTAGCTACTACATGC

search for the pattern ACTGA.

How does the string algorithms made the search?

and for the pattern TACTACGGTATGACTAA

Exact string matching: Brute force algorithm

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 ...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:

Exact string matching: Brute force algorithm

Text :

Pattern :

From left to right: prefix

• Which is the next position of the window?

• How the comparison is made?

Pattern :

Text :

The window is shifted only one cell

Exact string matching: one pattern

There is a sliding window along the text against which the pattern is compared:

How does the matching algorithms made the search?

Pattern :

Text :

Which are the facts that differentiate the algorithms?

1. How the comparison is made.2. The length of the shift.

At each step the comparison is made and the window is shifted to the right.

Exact string matching: one pattern (text on-line)

Experimental efficiency (Navarro & Raffinot)

2 4 8 16 32 64 128 256

64

32

16

8

4

2

| |

Long. pattern

Horspool

BNDMBOM

BNDM : Backward Nondeterministic Dawg Matching

BOM : Backward Oracle Matching

w

Horspool algorithm

Text :

Pattern :Sufix search

• Which is the next position of the window?


Pattern :

Text : a

Shift until the next ocurrence of “a” in the pattern:

aa a

a a a

We need a preprocessing phase to construct the shift table.

Horspool algorithm : example

Given the pattern ATGTA

• The shift table is:

A C G T




A 4C G T




A 4C 5G T




A 4C 5G 2T




A 4C 5G 2T 1




A 4C 5G 2T 1

• 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

Exemple algorisme de Horspool



A 4C 5G 2T 1


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

Qüestions sobre l’algorisme de Horspool

A 4C 5G 2T 1 Given a random text over an

equally likely probability distribution (EPD):

Given the pattern ATGTA, the shift table is

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

Exact string matching: one pattern (text on-line)

Experimental efficiency (Navarro & Raffinot)

2 4 8 16 32 64 128 256

64

32

16

8

4

2

| |

Long. pattern

Horspool

BNDMBOM



w

Text :

Pattern :

Search for suffixes of T that are factors of

BNDM algorithm

• Which is the next position of the window ?


That is denoted as

D2 = 1 0 0 0 1 0 0

Depends on the value of the leftmost bit of D

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 )

x

BNDM algorithm: exaple



A T G T A

A T G T A

A T G T A

• The mask of characters is:

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 )

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 )

Exemple algorisme BNDM

A T G T A

• Given the pattern ATGTA

• The mask of characters is :


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 )

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!

Exemple algorisme BNDM


• 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

• The mask of characters is :

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 )

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 )

How the shif is determined?

Alg. Cerca exacta d’un patró (text on-line)

Algorismes més eficients (Navarro & Raffinot)

2 4 8 16 32 64 128 256

64

32

16

8

4

2

| |

Long. patró

Horspool

BNDMBOM



w

Autòmata Factor Oracle: propietats

Factor Oracle del mot G T A T G T A

GG AT T ATTA

G

Tots els estats són finals ==> Reconeix tots els factors …. i més

GG AT T ATTA

G

Hip: reconeix tots factors de GTA

L’estat reconeix tots els factors que acaben a la quarta lletra T que no eren reconeguts:GTAT, TAT, AT perque T ja ho era.

Reconeix tots els factors de de les primeres 4 lletres

Autòmata Factor Oracle: algorisme

Algorisme: per a i=1 fins p fer Afegir transicions que reconeguin factors acabats a i;

?


Que passa si el següent caràcter existeix?

TT


Que passa si el següent caràcter no existeix?

TT

Autòmata Factor Oracle: exemple d’algorisme

GG AT T ATTA

G

i reconeix mots que no són factors com GTGTA.

Però, si no el reconeix ==> no és factor!

Es l’estratègia de l’algorisme BOM

Algorisme BOM (Backward Oracle Matching)

• Com es determina la següent posició de la finestra?

• Com fa la comparació?

Text :

Patró : Autòmata: Factor Oracle

Comproba si el sufix és factor del patró

a

• Si la a no s’ha trobat

• Si arriben a l’estat final de l’autòmat amb la a

a


• Es construeix l’autòmata del patró invers: Suposem que el patró és ATGTATG

• I la cerca sobre el text : G T A C T A G A A T G T G T A G A C A T G T A T G G T G A...A T G T A T G


GG AT T ATTA

G



• I la cerca sobre el text : G T A C T A G A A T G T G T A G A C A T G T A T G G T GA T G T A T G


GG AT T ATTA

G

A T G T A T G



• I la cerca sobre el text : G T A C T A G A A T G T G T A G A C A T G T A T G G T G A T G T A T G


GG AT T ATTA

G

A T G T A T G A T G T A T G



• I la cerca sobre el text : G T A C T A G A A T G T G T A G A C A T G T A T G G T GA T G T A T G


GG AT T ATTA

G


A T G T A T G



• I la cerca sobre el text : G T A C T A G A A T G T G T A G A C A T G T A T G G T G ...A T G T A T G


GG AT T ATTA

G





• I la cerca sobre el text : G T A C T A G A A T G T G T A G A C A T G T A T G G T G ...A T G T A T G


GG AT T ATTA

G



A T G T A T G

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