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Pairwise Sequence Alignment

Pairwise Sequence Alignment. Pairwise Sequence Alignment. The most important class of bioinformatics tools – pairwise alignment of DNA and protein seqs. alignment 1 alignment 2 Seq. 1 ACGCTGA ACGCTGA Seq. 2 A - - CTGT ACTGT - -

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Pairwise Sequence Alignment

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  1. Pairwise Sequence Alignment

  2. Pairwise Sequence Alignment • The most important class of bioinformatics tools – pairwise alignment of DNA and protein seqs. alignment 1 alignment 2 Seq. 1 ACGCTGA ACGCTGA Seq. 2 A - - CTGT ACTGT - - Seeks alignments  high seq. identity, few mismatchs and gaps Assumption – the observed identity in seqs. to be aligned is the result of either random or of a shared evolutionary origin Identity ≠ similarity Sequence identity =Homology (a risky assumption) Sequence identity ≠Homology

  3. Pairwise Sequence Alignment Same true alignment arise through different evolutionary events Scoring scheme: substitution  -1, indel  -5, match  3 indel Score 9 5 4 4 Figure A Common evolutionary events and their effects on alignment

  4. Pairwise Sequence Alignment Find the optimal score  the best guess for the true alignment Find the optimal pairwise alignment of two seqs.  inserted gaps into one or both of them  maximize the total alignment score Dynamic programming (DP) – Needleman and Wunsch (1970), Smith and Waterman (1980), this algorithm guarantees that we find all optimal alignments of two seqs. of lengths m and n BLAST is based on DP with improvement on speed Prof. Waterman http://www.usc.edu/dept/LAS/biosci/faculty/waterman.html

  5. Pairwise Sequence Alignment The score for alignment of i residues of sequence 1 against j residues of sequence 2 is given by where c(i,j) = the score for alignment of residues i and j and takes the value 3 for a match or -1 for a mismatch, c(-,j) = the penalty for aligning a residue with a gap, which takes the value of -5

  6. Pairwise Sequence Alignment • The entry for S(1,1) is the maximum of the following three events: • S(0,0) + c(A,A) = 0 + 3 = 3 [c(A,A) = c(1,1)] • S(0,1) + c(A, -) = -5 + -5 = -10 [c(A, -) = c(1, -)] • S(1,0) + c(-, A) = -5 + -5 = -10 [c(- ,A) = c(-, 1)] • Similarly, one finds S(2,1) as the maximum of three values: (-5)-1=-6; 3-5=-2; and (-10)-5=-15  the best is entry is the addition of the C indel to the A-A match, for a score of -2 (see next page).

  7. Pairwise Sequence Alignment The alignment matrix of sequences 1 and 2 S(2,1) = max {S(1,0) + c(2,1), S(1,1) + c(2,-), S(2,0) + c(-,1)} = max { S(1,0) + c(C,A), S(1,1) + c(C,-), S(2,0) + c(-,A) } = max { -5-1, 3-5, -10-5 } = -2

  8. Pairwise Sequence Alignment Traceback  determine the actual alignment From the top right hand corner  the (7,5) cell For example the 1 in the (7,5) cell could only be reached by the addition of the mismatch A-T ACGCTGA A - - CTGT or ACGCTGA AC - - TGT 4 matches 1 mismatch 2 indels Ambiguity – has to do with which C in seq. 1 aligns with the C in seq. 2

  9. Pairwise Sequence Alignment Parameters settings - Gap penalties • Default settings are the easiest to use but they are not necessarily yield the correct alignment • constant penalty independent of the length of gap, A • proportional penalty penalty is proportional to the length L of the gap, BL (that is what we used in the this lecture) • affine gap penalty gap-opening penalty + gap-extension penalty = A+BL • There is no rule for predicting the penalty that best suits the alignment • Optimal penalties vary from seq. to seq.  it is a matter of trial and error • Usually A > B, because of opening a gap (usually A/B ~ 10) • Hint: (1) compare distantly related seqs. high A and very low B often give the best results  penalized more on their existence than on their length, (2) compare closely related seqs., penalize both of extension and extension

  10. Exercise - Computing an optimal sequence alignment • Two score schemes • Gap penalty = -5, mismatch = -1, match =3 • Gap penalty = -1, mismatch = -1, match =3 • First alignment score = 5*3 + 2*(-1) =13 • Second/Third alignment score = 6*3 + 2*(-5) = 8 • (2) First alignment score = 5*3 + 2*(-1) =13 • Second/Third alignment score = 6*3 + 2*(-1) = 16 • A more serious problem – identify the wrong alignment

  11. Exercise Computing an optimal sequence alignment Gap penalty = -5 Gap penalty = -1

  12. BLAST (Scoring matrices) • Dynamic Programming do notprovide the user with a measure of statistical similarity when regions of local similarity when regions of local similarity are found • Take into account not just the position-position overlap between two seqs. but the characteristics of the a.a being aligned  define scoring matrices • Protein scoring matrices take three major biological factors into account: • Conservation – the numbers within the scoring matrix provide a way of representing what a.a. are capable of substituting for other a.a. (characteristics such as charge, size, hydrophobicity) • Frequency – a.a cannot freely substitute for one another, the matrices need to reflect how often particular a.a occur among the entire proteins. • Evolution – scoring matrices implicitly represent evolutionary patterns, and matrices can be adjusted to favor the detection of closely related or more distantly related proteins.

  13. BLAST (Scoring matrices) Scoring matrices and the Log Odds Ratio where pi[pj] = probability with which a.a i [j] occurs among all proteins qi,j = how often the two a.a i and j are seen to align with one another in MSA of protein families or in seqs. that are known to have a biological relationship.

  14. BLAST (PAM matrices) Amino acid substitution matrix (PAMand BLOSUM) • Leave most adjustable parameters to the default value except the scoring matrix • Box 2.1  a simple scheme for scoring seq. matches and mismatches (all mismatches received the same penalty) • Scoring matrix allows some mismatches to be penalized less then others • Leucine-isoleucine mismatch < leucine-tryptophan mismatch • PAM (Point Accepted Mutations) scoring matrices – derived from closely related species (evolutionary point of view, avoid the complications of unobserved multiple substitutions at a single position) • PAM derived from the likelihood of amino acids substitution during the evolutionary process • PAM matrices with a smaller numberrepresent shorter evolutionary distance • PAM1 – one a.a change per 100 a.a, or roughly 1% divergence

  15. PAM Asp  Glu 0.95%

  16. BLAST (BLOSUM matrices) BLOSUM (BLOck SUM) – there are evidence it outperform PAM • Block  proteins in the same family can be aligned without introducing a gap (not the individual seqs.) • So any given protein can contain one or more blocks, corresponding to each of its functional or structural motif • With these protein blocks, it is possible to look for substitution patterns only in the most conserved regions of a protein  block substitution matrices are generated • BLOSUM scoring matrix – based on data from distantly related seqs. (default BLOSUM62 for general use) • The most commonly used matrices are PAM120, PAM250, BLOSUM50 and BLOSUM 62 • BLOSUM matrices with a smaller numberrepresent a longer evolutionary distance

  17. BLAST (BLOSUM matrices) The BLOSUM62 substitution matrix Values below zero indicate amino acid changes that are more likely to have a functional effect than values of zero and above.

  18. BLAST (relating PAM to BLOSUM) PAM250 equivalent to BLOSUM45 PAM160 equivalent to BLOSUM62 PAM120 equivalent to BLOSUM80 Selecting an appropriate scoring matrix

  19. BLAST (Sensitivity and Specificity)

  20. BLAST (Sensitivity and Specificity)

  21. BLAST (Sensitivity and Specificity)

  22. BLAST (Sensitivity and Specificity)

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