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 Used for creation of BLOSUM matrix } This block is part of a motif

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 q ij. 3. Next, one calculates the probability that a certain amino acid frequency exists, f i. 4. Finally, we calculate the log odds ratio s i,j = log 2 (q ij /f i ). 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.

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 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 mismatch gap_open -2 gap_extend for a total score of = 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 S i,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) S i,j = 0 for mismatch score w = gap penalty

Initialization step: Create Matrix with M columns and N rows. Fill in matches with 1 AJCJNRCKCRBPAJCJNRCKCRBP A B C N J R Q C L C R P M Seq 1 (length m) Seq 2 (length n)

Matrix fill step: Place 0’s in last row and last column AJCJNRCKCRBPAJCJNRCKCRBP A B C N J R Q C L C R P M Seq 1 (length m) Seq 2 (length n)

Move one row up and add value of cell plus maximum value in diagonal cell and to right from lower row AJCJNRCKCRBPAJCJNRCKCRBP A B C N J R Q C L C R P M Seq 1 (length m) Seq 2 (length n)

AJCJNRCKCRBPAJCJNRCKCRBP A B C N J R Q C L C R P M Seq 1 (length m) Seq 2 (length n)

AJCJNRCKCRBPAJCJNRCKCRBP A B C N J R Q C L C R P M Seq 1 (length m) Seq 2 (length n) Fill in rest of matrix

Traceback step: Position at high scoring cell and find path down and to right with highest numbers. AJCJNRCKCRBPAJCJNRCKCRBP A B C N J R Q C L C R P M Seq 1 (length m) Seq 2 (length n) ABCNJ-RQCLCR-PM AJC-JNR-CKCRBP- ABC-NJRQCLCR-PM AJCJN-R-CKCRBP- Upper path Lower path

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: 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 = %similarity = Overall %id = 43.15; Overall %similarity = 60.27