Alignment methods and database searching

April 14, 2005Quiz#1 todayLearning 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 valueis the PAM Matrix number. Note that PAM250 equates topoint 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...BBCDADABCDA.A.BBCBBBBBCDABA.BCCAAAAACDAC.DCBCDBCCBADAB.DBBDCCAAACAA...BBCCC

Used for creation of BLOSUMmatrix

}This block is part of a motif

Building BLOSUM Matrices1. 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, useBLOSUM 80. Sequences that are more divergent (dissimilar)than 20% are given very low scores in this matrix.

Which Scoring Matrix to use?

PAM-1

BLOSUM-100

Small evolutionary distance

High identity within short sequences

PAM-250

BLOSUM-20

Large evolutionary distance

Low identity within long sequences

Database SearchingLearning 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 linesThe 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 inthe 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...hijkAs 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 abbdhijkare 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 -1-1-1for a total score of 24-6-2-3 = 13.

Needleman-Wunsch Method (cont. 5)

The algorithm guarantees that no otheralignment of these two sequences has ahigher score under this payoff matrix.

Needleman-Wunsch Method (cont. 6) Dynamic Programming

Potential difficulty. How does one come up with the optimalalignment in the first place? We now introduce the conceptof dynamic programming (DP).

DP can be applied to a large search space that can be structuredinto a succession of stages such that:

1) the initial stage contains trivial solutions to sub-problems2) each partial solution in a later stage can be calculated

by recurring on only a fixed number of partial solutions in anearlier 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 asthe residue at position j of the sequence #2 (called match score)

Si,j = 0 for mismatch score

w = gap penalty

Initialization step: Create Matrix with M columnsand N rows. Fill in matches with 1

AJCJNRCKCRBP

A B C N J R Q C L C R P MSeq 1 (length m)

Seq 2(length n)

11

1 1 11

11 1

111

1 1 111

11

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

AJCJNRCKCRBP

A B C N J R Q C L C R P MSeq 1 (length m)

Seq 2(length n)

11

1 1 11

11 1

111

1 1 111

11

00000000000000000000000

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

AJCJNRCKCRBP

A B C N J R Q C L C R P MSeq 1 (length m)

Seq 2(length n)

11

1 1 11

11 1

111

1 1 111

1

00000000000000000000000

011111111121

AJCJNRCKCRBP

A B C N J R Q C L C R P MSeq 1 (length m)

Seq 2(length n)

11

1 1 11

11 1

111

1 1 122

1

00000000000000000000000

011111111121111111112 0

AJCJNRCKCRBP

A B C N J R Q C L C R P MSeq 1 (length m)

Seq 2(length n)

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

22

1

00000000000000000000000

011111111121111111112 0

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

6 6 7 6 5 4 4 4 3 3 1 06 6 6 5 6 4 4 3 3 2 1 05 5 5 6 5 4 4 3 3 2 1 04 4 4 4 4 5 4 3 3 2 2 03 3 4 3 3 3 3 4 3 3 1 03 3 3 3 3 3 3 3 3 2 1 02 2 3 2 2 2 2 3 2 3 1 0

Fill in rest of matrix

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

AJCJNRCKCRBP

A B C N J R Q C L C R P MSeq 1 (length m)

Seq 2(length n)

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

21

1

00000000000000000000000

011111111121111111112 0

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

6 6 7 6 5 4 4 4 3 3 1 06 6 6 5 6 4 4 3 3 2 1 05 5 5 6 5 4 4 3 3 2 1 04 4 4 4 4 5 4 3 3 2 2 03 3 4 3 3 3 3 4 3 3 1 03 3 3 3 3 3 3 3 3 2 1 02 2 3 2 2 2 2 3 2 3 1 0

ABCNJ-RQCLCR-PMAJC-JNR-CKCRBP-

ABC-NJRQCLCR-PMAJCJN-R-CKCRBP-

Upperpath

Lowerpath

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 anoptimal alignment. The other difficulty is that the concept ofglobal alignment is not used in pairwise sequence comparisonsearches.

Needleman-Wunsch Method Typical output file

Global: HBA_HUMAN vs HBB_HUMANScore: 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 = 63.31Overall %id = 43.15; Overall %similarity = 60.27