Bioinformatics

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2 Οκτ 2013 (πριν από 4 χρόνια και 8 μήνες)

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Definitions

Optimal alignment

-

one that exhibits the
most correspondences. It is the alignment
with the
highest score
. May or may not
be biologically meaningful.

Global alignment

-

Needleman
-
Wunsch
(1970) maximizes the number of matches
between the sequences along the entire
length of the sequences.

Local alignment

-

Smith
-
Waterman (1981)
gives the highest scoring local match
between two sequences.

Pairwise Global Alignment

Global alignment

-

Needleman
-
Wunsch (1970)

maximizes the number of matches between the
sequences along the entire length of the sequences.

Reason for making a global alignment:

checking minor difference between two sequences

Analyzing polymorphisms (ex. SNPs) between closely related
sequences

Pairwise Global Alignment

Computationally:

Given:

a pair of sequences (strings of characters)

Output:

an alignment that maximizes the similarity

How can we find an optimal
alignment?

ACGTCTGATACGCCGTATAGTCTATCT

CTGAT
---
TCG
-
CATCGTC
--
T
-
ATCT

How many possible alignments?

C(27,7) gap positions = ~888,000 possibilities

Dynamic programming: The Needleman &
Wunsch algorithm

1

27

Time Complexity

Consider two sequences:

AAGT

AGTC

How many possible alignments the 2 sequences
have?

2n

n

= (2n)!/(n!)
2
=

(
2
2n
/

n ) =

(2
n
)

Scoring a sequence alignment

Match/mismatch score:

+1/+0

Open/extension penalty:

2/

1

ACGTCTGAT
A
CGCCGTAT
A
GTCTATCT

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

----
CTGAT
T
CGC
---
AT
C
GTCTATCT

Matches: 18
×

(+1)

Mismatches: 2
×

0

Open: 2
×

(

2)

Extension: 5
×

(

1)

Score = +9

Pairwise Global Alignment

Computationally:

Given:

a pair of sequences (strings of characters)

Output:

an alignment that maximizes the similarity

Needleman & Wunsch

Place each sequence along one axis

Place score 0 at the up
-
left corner

Fill in 1
st

row & column with gap penalty multiples

Fill in the matrix with max value of 3 possible moves:

Vertical move: Score + gap penalty

Horizontal move: Score + gap penalty

Diagonal move: Score + match/mismatch score

The optimal alignment score is in the lower
-
right corner

To reconstruct the optimal alignment, trace back where the max at
each step came from, stop when hit the origin.

Example

Let gap =
-
2

match = 1

mismatch =
-
1.

C

A

A

A

empty

C

G

A

empty

1

-
1

-
3

-
5

-
1

0

-
3

-
4

-
1

-
1

-
2

-
8

-
6

-
4

-
2

-
2

-
6

-
4

-
2

0

AAAC

A
-
GC

AAAC

-
AGC

Time Complexity Analysis

Initialize matrix values: O(n), O(m)

Filling in rest of matrix: O(nm)

Traceback: O(n+m)

If strings are same length, total time O(n
2
)

Local Alignment

Problem first formulated:

Smith and Waterman (1981)

Problem:

Find an optimal alignment between a substring
of s and a substring of t

Algorithm:

is a variant of the basic algorithm for global
alignment

Motivation

Searching for unknown domains or motifs within
proteins from different families

Proteins encoded from Homeobox genes (only conserved
in 1 region called Homeo domain

60 amino acids long)

Identifying active sites of enzymes

Comparing long stretches of anonymous DNA

Querying databases where query word much smaller
than sequences in database

Analyzing repeated elements within a single sequence

Local Alignment

Let gap =
-
2

match = 1

mismatch =
-
1.

GATCACCT

GATACCC

C

C

C

A

T

A

G

empty

T

C

C

A

C

T

A

G

empty

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

0

0

0

0

1

0

2

1

1

0

0

0

0

0

3

2

2

0

0

0

0

1

4

3

0

0

1

0

0

2

3

2

0

1

0

0

0

0

3

1

0

0

0

0

1

2

2

1

1

GATCACCT

GAT

_

ACCC

Smith & Waterman

Place each sequence along one axis

Place score 0 at the up
-
left corner

Fill in 1
st

row & column with
0s

Fill in the matrix with max value of
4

possible values:

0

Vertical move: Score + gap penalty

Horizontal move: Score + gap penalty

Diagonal move: Score + match/mismatch score

The optimal alignment score is
the max in the matrix

To reconstruct the optimal alignment, trace back where the MAX
at each step came from, stop when a
zero

is hit

exercise

Let:

gap =
-
2

match = 1

mismatch =
-
1.

Find the best local alignment:

CGATG

AAATGGA

Semi
-
global Alignment

Example:

CAGCA
-
CTTGGATTCTCGG

–––
CAGCGTGG
––––––––

CAGCACTTGGATTCTCGG

CAGC
––––
G
––
T
––––
GG

We like the first alignment much better. In semiglobal
comparison, we score the alignments ignoring some of
the
end spaces
.

Global Alignment

Example:

AAACCC

A


CCC

Prefer to see:

AAACCC

ACCC

Do not want to penalize

the end spaces

empty

A

A

A

C

C

C

empty

0

-
2

-
4

-
6

-
8

-
10

-
12

A

-
2

1

-
1

-
3

-
5

-
7

-
9

C

-
4

-
1

0

-
2

-
2

-
4

-
6

C

-
6

-
3

-
2

-
1

-
1

-
1

-
3

C

-
8

-
5

-
4

-
3

0

0

0

SemiGlobal Alignment

Example:

s = AAACCC

t =

ACCC

empty

A

A

A

C

C

C

empty

0

0

0

0

0

0

0

A

-
2

1

1

1

-
1

-
1

-
1

C

-
4

-
1

0

0

2

0

0

C

-
6

-
3

-
2

-
1

1

3

1

C

-
8

-
5

-
4

-
3

0

2

4

SemiGlobal Alignment

Example:

s = AAACCC
G

t =

ACCC

empty

A

A

A

C

C

C

empty

0

0

0

0

0

0

0

A

-
2

1

1

1

-
1

-
1

-
1

C

-
4

-
1

0

0

2

0

0

C

-
6

-
3

-
2

-
1

1

3

1

C

-
8

-
5

-
4

-
3

0

2

4

2

-
2

-
1

0

G

-
1

SemiGlobal Alignment

Summary of end space charging procedures:

Place where spaces are not
penalized for

Action

Beginning of 1
st

sequence

End of 1
st

sequence

Beginning of 2
nd

sequence

End of 2
nd

sequence

Initialize 1
st

row with zeros

Look for max in last row

Initialize 1
st

column with zeros

Look for max in last column

Pairwise Sequence Comparison over Internet

lalign

www.ch.embnet.org/software/LALIGN_form.html

Global/Local

lalign

fasta.bioch.virginia.edu/fasta_www/plalign.htm

Global/Local

USC

www
-
hto.usc.edu/software/seqaln/seqaln
-
query.html

Global/Local

alion

fold.stanford.edu/alion

Global/Local

genome.cs.mtu.edu/align.html

Global/Local

align

www.ebi.ac.uk/emboss/align

Global/Local

xenAliTwo

www.soe.ucsc.edu/~kent/xenoAli/xenAliTwo.html

Local for DNA

blast2seqs

www.ncbi.nlm.nih.gov/blast/bl2seq/bl2.html

Local BLAST

blast2seqs

web.umassmed.edu/cgi
-
bin/BLAST/blast2seqs

Local BLAST

lalnview

www.expasy.ch/tools/sim
-
prot.html

Visualization

Evaluation

Evaluation

graph
-
align

Darwin.nmsu.edu/cgi
-
bin/graph_align.cgi

Evaluation

Bioinformatics for Dummies

Significance of Sequence Alignment

Consider randomly generated sequences.
What distribution do you think the best local
alignment score of two sequences of sample
length should follow?

1.
Uniform distribution

2.
Normal distribution

3.
Binomial distribution (n Bernoulli trails)

4.
Poisson distribution (n

, np=

)

5.
others

Extreme Value Distribution

Y
ev

= exp(
-

x
-

e
-
x
)

Extreme Value Distribution vs.
Normal Distribution

“Twilight Zone”

Some proteins with less than 15% similarity have exactly
the same 3
-
D structure while some proteins with 20%
similarity have different structures. Homology/non
-
homology is never granted in the twilight zone.