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Alignment methods and database searching. April 14, 2005 Quiz#1 today

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Alignment methods and database searching

- April 14, 2005
- Quiz#1 today
- Learning objectives- Finish Dotter Program analysis. Understand how to use the program to assess regions of similarity between sequences. Understand how to use the PAM matrices. Understand the theory behind the design of BLOSUM matrices. Database searching algorithms. Understand how the Needleman-Wunsch method of optimal sequence alignment works.
- Homework due on Tuesday, April 19.

Assumptions in the PAM model

1. Replacement at any site depends only on the amino acid at that site and the probability given by the table (Markov model).

2. Sequences compared have should have “average” amino acid composition as derived from Dayhoff’s protein families.

Practical aspects to PAMs

- Good choice for sequences that are closely related (85% or greater).
- First substitution matrix created

Sources of error in PAM model

1. Many sequences depart from average aa composition.

2. Rare replacements were observed too infrequently to determine probabilities accurately. For 36 aa pairs (out of 400 aa pairs) no replacements were observed!

3. The idea that each amino acid is acting independently is an imperfect representation of evolution. Actually, distantly related sequences usually have islands (blocks) of conserved residues implying that replacement is not equally probable over entire sequence.

Where distance is the percent of “non-identity. PAM value

is the PAM Matrix number. Note that PAM250 equates to

point mutations that result in 80% distance.

BLOSUM Matrices (Blocks Substitution Matrix)

- BLOSUM matrices are built from distantly related sequences whereas PAM is built from closely related sequences
- The conserved blocks of aligned protein segments were extracted from the BLOCKS database. The BLOCKS database is a secondary database derived from the PROSITE Family database.

BLOSUM Matrices (cont.1)

- Version 8.0 of the Blocks Database consists of 2884 blocks based on 770 protein families documented in PROSITE.

}

Hypothetical entry in red box in BLOCK record:

AABCDA...BBCDA

DABCDA.A.BBCBB

BBBCDABA.BCCAA

AAACDAC.DCBCDB

CCBADAB.DBBDCC

AAACAA...BBCCC

This block is part of

a motif

Used for creation of BLOSUM

matrix

Building BLOSUM Matrices

1. To build the BLOSUM 62 matrix one must replace sequences that are identical in more than 62% of their amino acid sequences by a single representative sequence.

2. Next, the probability for a pair of amino acids to be in the same column is calculated. In the previous page this would be the probability of replacement of A with A, A with B, A with C, and B with C. This gives the value qij.

3. Next, one calculates the probability that a certain amino acid frequency exists, fi.

4. Finally, we calculate the log odds ratio si,j= log2 (qij/fi). This value is entered into the scoring matrix.

Building BLOSUM Matrices (cont.)

Which BLOSUM to use?

BLOSUM Identity (up to)

80 80%

62 62% (usually default value)

35 35%

If you are comparing sequences that are very similar, use

BLOSUM 80. Sequences that are more divergent (dissimilar)

than 20% are given very low scores in this matrix.

PAM-1

BLOSUM-100

Small evolutionary distance

High identity within short sequences

Which Scoring Matrix to use?PAM-250

BLOSUM-20

- Large evolutionary distance
- Low identity within long sequences

Database Searching

- Learning objectives-Understand the principles behind the Needleman-Wunsch method of alignment. Understand how software operates to optimally align two sequences
- Homework-Use of N-W method for the optimal alignment of two sequences.

Needleman-Wunsch Method (1970)

Output:

An alignment of two sequences is represented by three lines

The first line shows the first sequence.

The second line has a row of symbols.

The third line shows the second sequence.

The symbol is a vertical bar wherever characters in

the two sequences match, and a space where ever they do not.

Dots may be inserted in either sequence to represent gaps.

Needleman-Wunsch Method (cont. 1)

For example, the two hypothetical sequences

abcdefghajklm

abbdhijk

could be aligned like this

abcdefghajklm

|| | | ||

abbd...hijk

As shown, there are 6 matches,

2 mismatches, and one gap of length 3.

Needleman-Wunsch Method (cont. 2)

The alignment is scored according to a payoff matrix

$payoff = { match => $match,

mismatch => $mismatch,

gap_open => $gap_open,

gap_extend => $gap_extend };

For correct operation in this simplified version, match must be positive,

and the other entries must be negative.

Needleman-Wunsch Method (cont. 3)

- Example
- Given the payoff matrix
- $payoff = { match => 4,
- mismatch => -3,
- gap_open => -2,
- gap_extend => -1 };

Needleman-Wunsch Method (cont. 4)

The sequences

abcdefghajklm

abbdhijk

are aligned and scored like this

a b c d e f g h a j k l m

| | | | | |

a b b d . . . h i j k

match 4 4 4 4 4 4

mismatch -3 -3

gap_open -2

gap_extend -1-1-1

for a total score of 24-6-2-3 = 13.

Needleman-Wunsch Method (cont. 5)

The algorithm guarantees that no other

alignment of these two sequences has a

higher score under this payoff matrix.

Needleman-Wunsch Method (cont. 6) Dynamic Programming

Potential difficulty. How does one come up with the optimal

alignment in the first place? We now introduce the concept

of dynamic programming (DP).

DP can be applied to a large search space that can be structured

into a succession of stages such that:

1) the initial stage contains trivial solutions to sub-problems

2) each partial solution in a later stage can be calculated

by recurring on only a fixed number of partial solutions in an

earlier stage.

3) the final stage contains the overall solution.

Three steps in Dynamic Programming

1. Initialization

2 Matrix fill or scoring

3. Traceback and alignment

Two sequences will be aligned.

ABCNJRQCLCRPM (sequence #1)

AJCJNRCKCRBP (sequence #2)

A simple scoring scheme will be used

Si,j = 1 if the residue at position i of sequence #1 is the same as

the residue at position j of the sequence #2 (called match score)

Si,j = 0 for mismatch score

w = gap penalty

A

J

C

J

N

R

C

K

C

R

B

P

Initialization step: Create Matrix with M columns

and N rows. Fill in matches with 1

Seq 1 (length m)

1

1

1

1

1

1

Seq 2

(length n)

1

1

1

1

1

1

1

1

1

1

1

1

1

A

J

C

J

N

R

C

K

C

R

B

P

Matrix fill step: Place 0’s in last row and last column

Seq 1 (length m)

1

0

1

0

1

0

1

1

1

0

Seq 2

(length n)

1

0

1

1

0

1

1

1

0

0

1

1

1

0

1

0

1

0

1

0

0

0

0

0

0

0

0

0

1

0

0

0

Move one row up and add value of cell plus maximum value in diagonal cell and to right from lower row

A B C N J R Q C L C R P M

A

J

C

J

N

R

C

K

C

R

B

P

Seq 1 (length m)

1

0

1

0

1

0

1

1

1

0

Seq 2

(length n)

1

0

1

1

0

1

1

1

0

0

1

1

1

0

1

0

1

0

1

1

1

1

1

1

1

1

1

0

1

2

0

0

0

0

0

0

0

0

0

1

0

0

0

A

J

C

J

N

R

C

K

C

R

B

P

Seq 1 (length m)

1

0

1

0

1

0

1

1

1

0

Seq 2

(length n)

1

0

1

1

0

1

1

1

0

0

1

1

1

0

2

0

1

1

0

1

1

2

2

1

1

1

1

0

1

1

1

1

1

1

1

1

1

0

1

2

0

0

0

0

0

0

0

0

0

1

0

0

0

A

J

C

J

N

R

C

K

C

R

B

P

Fill in rest of matrix

Seq 1 (length m)

8 7 6 6 5 4 4 3 3 2 1 0

0

0

7 7 6 6 6 4 4 3 3 2 1 0

0

6 6 7 6 5 4 4 4 3 3 1 0

0

6 6 6 5 6 4 4 3 3 2 1 0

Seq 2

(length n)

0

5 5 5 6 5 4 4 3 3 2 1 0

4 4 4 4 4 5 4 3 3 2 2 0

0

3 3 4 3 3 3 3 4 3 3 1 0

0

3 3 3 3 3 3 3 3 3 2 1 0

0

2 2 3 2 2 2 2 3 2 3 1 0

0

2

0

1

1

0

1

1

2

2

1

1

1

1

0

1

1

1

1

1

1

1

1

1

0

1

2

0

0

0

0

0

0

0

0

0

1

0

0

0

A

J

C

J

N

R

C

K

C

R

B

P

Traceback step: Position at high scoring cell and find path down and to right with highest numbers.

Seq 1 (length m)

8 7 6 6 5 4 4 3 3 2 1 0

0

0

7 7 6 6 6 4 4 3 3 2 1 0

0

6 6 7 6 5 4 4 4 3 3 1 0

0

6 6 6 5 6 4 4 3 3 2 1 0

Seq 2

(length n)

0

5 5 5 6 5 4 4 3 3 2 1 0

4 4 4 4 4 5 4 3 3 2 2 0

0

3 3 4 3 3 3 3 4 3 3 1 0

0

3 3 3 3 3 3 3 3 3 2 1 0

0

2 2 3 2 2 2 2 3 2 3 1 0

0

2

0

1

1

0

1

1

2

1

1

1

1

1

0

1

1

1

1

1

1

1

1

1

0

1

2

0

0

0

0

0

0

0

0

0

1

0

0

0

Upper

path

Lower

path

ABC-NJRQCLCR-PM

AJCJN-R-CKCRBP-

ABCNJ-RQCLCR-PM

AJC-JNR-CKCRBP-

Needleman-Wunsch Method Dynamic Programming

The problem with Needleman-Wunsch is the amount of

processor memory resources it requires. Because of this

it is not favored for practical use, despite the guarantee of an

optimal alignment. The other difficulty is that the concept of

global alignment is not used in pairwise sequence comparison

searches.

Needleman-Wunsch Method Typical output file

Global: HBA_HUMAN vs HBB_HUMAN

Score: 290.50

HBA_HUMAN 1 VLSPADKTNVKAAWGKVGAHAGEYGAEALERMFLSFPTTKTYFP 44

|:| :|: | | |||| : | | ||| |: : :| |: :|

HBB_HUMAN 1 VHLTPEEKSAVTALWGKV..NVDEVGGEALGRLLVVYPWTQRFFE 43

HBA_HUMAN 45 HF.DLS.....HGSAQVKGHGKKVADALTNAVAHVDDMPNALSAL 83

| ||| |: :|| ||||| | :: :||:|:: : |

HBB_HUMAN 44 SFGDLSTPDAVMGNPKVKAHGKKVLGAFSDGLAHLDNLKGTFATL 88

HBA_HUMAN 84 SDLHAHKLRVDPVNFKLLSHCLLVTLAAHLPAEFTPAVHASLDKF 128

|:|| || ||| ||:|| : |: || | |||| | |: |

HBB_HUMAN 89 SELHCDKLHVDPENFRLLGNVLVCVLAHHFGKEFTPPVQAAYQKV 133

HBA_HUMAN 129 LASVSTVLTSKYR 141

:| |: | ||

HBB_HUMAN 134 VAGVANALAHKYH 146

%id = 45.32 %similarity = 63.31

Overall %id = 43.15; Overall %similarity = 60.27

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