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Needleman-Wunch, Waterman-Smith-Beyer, and Gotoh's Algorithms for Alignment and Repeats, Study notes of Bioinformatics

George Mason University (GMU)Bioinformatics

Sequence alignment algorithms, including the needleman-wunch, waterman-smith-beyer, and gotoh's algorithms. The concepts behind these methods, their efficiency, and how they can be extended to align sequences with tandem repeats. The document also introduces the concept of tandem repeats and their significance in dna.

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Uploaded on 02/12/2009

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1

BINF 730 – Lecture 4

Finish Sequence Alignment and

Multiple Sequence Alignment

Sequence Alignment

• Needleman-Wunch Algorithm – global

alignment, fixed gap penalty

• Waterman-Smith-Beyer Algorithm– local

alignment, affine gap penalty function

• Gotoh’s algorithm – local alignment, affine

gap penalty function

Efficiency of Algorithms

• Needleman-Wunch Algorithm – O(nm) =

O(n2) for n >= m

• Waterman-Smith-Beyer Algorithm–

O(nm(n+m) = O(n3) for n >= m

• Gotoh’s algorithm – O(nm) = O(n2) for n

>= m

Needleman-Wunch Algorithm

(Global Alignment)

gapaofweighttheiswwhere

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Waterman-Smith-Beyer Algorithm

(Local Alignment)

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Gotoh’s Algorithm – (Local Alignment)

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Consider the gapless sequences

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affine gap penalty function and

let w(ai,bj) be a cost function.

D is the distance matrix.

P is the matrix with the minimal

distances for all alignments with

boending in a gap.

Q is the matrix with the minimal

distances for all alignments with

aoending in a gap.

Discover Study notes of Bioinformatics George Mason University (GMU)

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Download Needleman-Wunch, Waterman-Smith-Beyer, and Gotoh's Algorithms for Alignment and Repeats and more Study notes Bioinformatics in PDF only on Docsity!

BINF 730 – Lecture 4

Finish Sequence Alignment and

Multiple Sequence Alignment

Sequence Alignment

• Needleman-Wunch Algorithm – global

alignment, fixed gap penalty

• Waterman-Smith-Beyer Algorithm– local

alignment, affine gap penalty function

• Gotoh’s algorithm – local alignment, affine

gap penalty function

Efficiency of Algorithms

• Needleman-Wunch Algorithm – O(nm) =

O(n

) for n >= m

• Waterman-Smith-Beyer Algorithm–

O(nm(n+m) = O(n

) for n >= m

• Gotoh’s algorithm – O(nm) = O(n

) for n

>= m

Needleman-Wunch Algorithm

(Global Alignment)

wherewistheweightofa gap

D wa

D wab

D w b

ij D

D wa

D w b

D

i j i

i j i j

ij j

ij

i

k

i k

j

k

j k

−

−−

−

=

, 0 min

1 ,

1 , 1

, 1

,

1

, 0

1

0 ,

0 , 0

Waterman-Smith-Beyer Algorithm

(Local Alignment)

wisthesimilarityscore function

wheregkisthegappenaltyfunctionand

D gk

D wab

D gk

ij D

D gi

D gj

D

kj ikj

i j i j

kj ijk

ij

i

j

min( ())

, 0 min

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1 ,

,

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≤≤ −

−−

≤≤ −

Gotoh’s Algorithm – (Local Alignment)

−

−−

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min

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and P

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Q

D wab

P

D

D gi

D gj

Consider the gapless sequences D

a and b. Let g(k) = α + kβ be an

affine gap penalty function and

let w(ai ,b j ) be a cost function.

D is the distance matrix.

P is the matrix with the minimal

distances for all alignments with

b

o

ending in a gap.

Q is the matrix with the minimal

distances for all alignments with

a

o

ending in a gap.

Gotoh’s Algorithm

• Uses dynamic programming with three

matrices (instead of 1) to store information

so they do not have to be recaculated.

• Traceback – need to track movement

through all three matrices.

Tandem Repeats

• A tandem repeat or tandem duplication is a

subsequence of characters that repeats itself

multiple times in a sequence with the copies

adjacent to each other.

Example

ACGAG CCGTAGAA TACCG

ACGAG CCGTAGAA CCGTAGAA CCGTAGAA TACCG

Tandem Repeats

• Tandem repeats are found throughout prokaryote

and eukaryote DNA.

• In humans, they are known to cause at least 10

inherited neurogical diseases, Huntington’s

disease, and myotonic dystrophy.

• They are also implicated in diabetes, epilepsy, and

ovarian and other cancers.

• They are used in DNA fingerprinting and can

differentiate between bacterial strains (including

anthrax).

Tandem Repeats

If we assume that

1. There is no removal of copies of the duplicated

tandem repeat region.

2. Tandem duplication occurs before the other types

of operations

Benson showed that Gotoh’s algorithm can be

extended to align sequences with tandem repeats.

The duplication cost is d(l)=γ+δl

Tandem Repeats

and D dk Da b

D dk Da b

Duplij

i a j b

Duplij

Q

D wab

P

D

D gi

D gj

D

js j

k ir i k

irjs

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irjs

ij

i j i j

ij

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j

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− −

−+ −+ ∈

− −

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min

1 ... 1 ... { 01 ,, 2 ...}

,

1 ... 1 ... { 0 , 1 , 2 ...}

,

1 , 1

,

, 0

0 ,

0 , 0

min

K copies of the word b j-s+1…j

Wraparound Method

• When aligning a sequence with tandem repeats,

use the ‘wrap around’ method to minimize

calculations.

• When implementing the wrap around method,

look at the section with tandem repeats

separately.

• Write the repeated sequence only once in the

similarity matrix.

• Align as usual except when reaching the end of

the repeated sequence, use that value as the

first value in the next row and repeat this

procedure.

Wraparound Method Wraparound Method

3 4 5

Similarity Methods

a) Maximize the similarity between two

sequences rather than minimizing the

distance.

b) Use similarity score function s(x,y) to

compare characters x and y with s(x,y) > 0 for

x = y and s(x,y) < 0 for x ><y. The score for

a gap can be different than the score for a

mismatch.

c) transition = a substitution of a purine for a

purine or a pyrmidine for a pyrimidine if the

alignment for a random sequence is negative

(which is guaranteed by the PAM matrices).

Similarity Methods

d) tranversion = a substitution of a pyr for a

pur or a pur for a pyr

e) Once again use dynamic programming

algorithm.

f) This can be used for local or global

alignments

Multiple Sequence Alignment

• Up until now we have aligned two sequence

at a time.

• There are times when we would want to

align more than two sequences

simultaneously – i.e. looking for consensus

sequences, or looking for homology in a

family of proteins

Multiple Sequence Alignment

The text presents five methods

• Dynamic Programming

• Gibbs Sampler

• Maximum-Weight Trace

• Hidden Markov Models

• Steiner Sequences.

Multiple Sequence Alignment –

Dynamic Programming

• This is an extension of the pairwise

sequence alignment we have discussed.

• Assume we want to align k sequences of

length at most k

• Develop a cost function w(a

,…a

k

) that will

align multiple letters at a time.

• Same as before except the distance matrix is

(k dimensional) and the weight function

compares k letters.

Dynamic Programming for

Multiple Sequence Alignment

•Assume that we are trying to align three

sequence a,b, and c.

•Also assume that we have a cost function

w(x,y,z) that computes the cost of comparing

x, y, and z in sequences a, b, and c

respectively.

x y z

of symbolsarethesame

x y z

wxyz

Dynamic Programming for

Multiple Sequence Alignment

−

−−

− −

− −−

,, 0 min

,, 1

, 1 ,

1 ,,

1 , 1 ,

1 ,, 1

, 1 , 1

1 , 1 , 1

,,

ijk k

ij k j

i jk i

i j k i j

i jk i k

ij k j k

i j k i j k

ijk

D w c

D w b

D wa

D wab

D wa c

D w bc

D wab c

ijk D

• Alternatvively we can define our

distance matrix D by

Multiple Sequence Alignment –

Dynamic Programming

• This would take n

k

time with can be long if

for large n and k.

• NP-complete problem – this means that is it

the length of the sequence or number of

sequences get large if is extremely

computationally expensive to solve.

• Need more efficient methods.

Gibbs Sampler

• The Gibbs Sampler is based on the Gibbs

Distribution (pages 47-52).

• Basically, perform local alignments on

windows (subsequences) of fixed size.

• The optimal alignment is found after

varying the window size and repeating.

• Original Gibbs Sampler looks for motifs in

a protein.

Gibbs Sampler Algorithm

1. Identify random size w segments, or

windows, from m amino acid sequences.

2. Choose one of the m proteins at random

and temporarily call it P, where r

,…,r

n

is

its amino acid sequence.

3. Define a 20 x m frequency matrix Q where

Q

r,j

= N

r,j

/(m-1) and N

r,j

Needleman-Wunch, Waterman-Smith-Beyer, and Gotoh's Algorithms for Alignment and Repeats, Study notes of Bioinformatics

Related documents

Partial preview of the text

Download Needleman-Wunch, Waterman-Smith-Beyer, and Gotoh's Algorithms for Alignment and Repeats and more Study notes Bioinformatics in PDF only on Docsity!

BINF 730 – Lecture 4

Finish Sequence Alignment and

Multiple Sequence Alignment

Sequence Alignment

• Needleman-Wunch Algorithm – global

alignment, fixed gap penalty

• Waterman-Smith-Beyer Algorithm– local

alignment, affine gap penalty function

• Gotoh’s algorithm – local alignment, affine

gap penalty function

Efficiency of Algorithms

• Needleman-Wunch Algorithm – O(nm) =

O(n

) for n >= m

• Waterman-Smith-Beyer Algorithm–

O(nm(n+m) = O(n

) for n >= m

• Gotoh’s algorithm – O(nm) = O(n

) for n

>= m

Needleman-Wunch Algorithm

(Global Alignment)

wherewistheweightofa gap

D wa

D wab

D w b

ij D

D wa

D w b

D

, 0 min

Waterman-Smith-Beyer Algorithm

(Local Alignment)

D

Gotoh’s Algorithm – (Local Alignment)

Q

Q

P

Q

P

D

Consider the gapless sequences D

a and b. Let g(k) = α + kβ be an

affine gap penalty function and

let w(ai ,b j ) be a cost function.

D is the distance matrix.

P is the matrix with the minimal

distances for all alignments with

b

ending in a gap.

Q is the matrix with the minimal

distances for all alignments with

a

ending in a gap.

Gotoh’s Algorithm

• Uses dynamic programming with three

matrices (instead of 1) to store information

so they do not have to be recaculated.

• Traceback – need to track movement

through all three matrices.

Tandem Repeats

• A tandem repeat or tandem duplication is a

subsequence of characters that repeats itself

multiple times in a sequence with the copies

adjacent to each other.

Example

ACGAG CCGTAGAA TACCG

ACGAG CCGTAGAA CCGTAGAA CCGTAGAA TACCG

Tandem Repeats

• Tandem repeats are found throughout prokaryote

and eukaryote DNA.

• In humans, they are known to cause at least 10

inherited neurogical diseases, Huntington’s

disease, and myotonic dystrophy.

• They are also implicated in diabetes, epilepsy, and

ovarian and other cancers.