Alignment Scoring Fuctions                    Dr Avril Coghlan                   alc@sanger.ac.ukNote: this talk contains ...
Alignment scoring functions                  Letter b                           A    R    N    D    C    Q    E    G    H ...
• The choice of scoring function σ determines the             A R N D C Q E G H I L K M F P S T W Y                       ...
Problem• Find the best alignment between “WHAT” & “WHY”  using the BLOSUM45 scoring function & -2 for a gap
Answer• Find the best alignment between “WHAT” & “WHY”  using the BLOSUM45 scoring function & -2 for a gap•   Matrix T loo...
• Using +1 for a match, -1 for mismatch, & -2 for an  insertion/deletion, the best alignment is:           W H A T        ...
• Non-synonymous mutations change the amino acid  sequence   eg. codon TTT encodes Phe (F), & TTA encodes Leu (L), so a   ...
BLOSUM45 gives larger scores to substitutions that occur      frequently, than for substitutions that rarely occur:       ...
Further Reading•   Chapter 3 in Introduction to Computational Genomics Cristianini & Hahn•   Chapter 6 in Deonier et al Co...
Further Reading•   Chapter 3 in Introduction to Computational Genomics Cristianini & Hahn•   Chapter 6 in Deonier et al Co...
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Alignment scoring functions

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  • In R: >library(“Biostrings”) >data(BLOSUM45) >BLOSUM45 A R N D C Q E G H I L K M F P S T W Y V B J Z X * A 5 -2 -1 -2 -1 -1 -1 0 -2 -1 -1 -1 -1 -2 -1 1 0 -2 -2 0 -1 -1 -1 -1 -5 R -2 7 0 -1 -3 1 0 -2 0 -3 -2 3 -1 -2 -2 -1 -1 -2 -1 -2 -1 -3 1 -1 -5 N -1 0 6 2 -2 0 0 0 1 -2 -3 0 -2 -2 -2 1 0 -4 -2 -3 5 -3 0 -1 -5 D -2 -1 2 7 -3 0 2 -1 0 -4 -3 0 -3 -4 -1 0 -1 -4 -2 -3 6 -3 1 -1 -5 C -1 -3 -2 -3 12 -3 -3 -3 -3 -3 -2 -3 -2 -2 -4 -1 -1 -5 -3 -1 -2 -2 -3 -1 -5 Q -1 1 0 0 -3 6 2 -2 1 -2 -2 1 0 -4 -1 0 -1 -2 -1 -3 0 -2 4 -1 -5 E -1 0 0 2 -3 2 6 -2 0 -3 -2 1 -2 -3 0 0 -1 -3 -2 -3 1 -3 5 -1 -5 G 0 -2 0 -1 -3 -2 -2 7 -2 -4 -3 -2 -2 -3 -2 0 -2 -2 -3 -3 -1 -4 -2 -1 -5 H -2 0 1 0 -3 1 0 -2 10 -3 -2 -1 0 -2 -2 -1 -2 -3 2 -3 0 -2 0 -1 -5 I -1 -3 -2 -4 -3 -2 -3 -4 -3 5 2 -3 2 0 -2 -2 -1 -2 0 3 -3 4 -3 -1 -5 L -1 -2 -3 -3 -2 -2 -2 -3 -2 2 5 -3 2 1 -3 -3 -1 -2 0 1 -3 4 -2 -1 -5 K -1 3 0 0 -3 1 1 -2 -1 -3 -3 5 -1 -3 -1 -1 -1 -2 -1 -2 0 -3 1 -1 -5 M -1 -1 -2 -3 -2 0 -2 -2 0 2 2 -1 6 0 -2 -2 -1 -2 0 1 -2 2 -1 -1 -5 F -2 -2 -2 -4 -2 -4 -3 -3 -2 0 1 -3 0 8 -3 -2 -1 1 3 0 -3 1 -3 -1 -5 P -1 -2 -2 -1 -4 -1 0 -2 -2 -2 -3 -1 -2 -3 9 -1 -1 -3 -3 -3 -2 -3 -1 -1 -5 S 1 -1 1 0 -1 0 0 0 -1 -2 -3 -1 -2 -2 -1 4 2 -4 -2 -1 0 -2 0 -1 -5 T 0 -1 0 -1 -1 -1 -1 -2 -2 -1 -1 -1 -1 -1 -1 2 5 -3 -1 0 0 -1 -1 -1 -5 W -2 -2 -4 -4 -5 -2 -3 -2 -3 -2 -2 -2 -2 1 -3 -4 -3 15 3 -3 -4 -2 -2 -1 -5 Y -2 -1 -2 -2 -3 -1 -2 -3 2 0 0 -1 0 3 -3 -2 -1 3 8 -1 -2 0 -2 -1 -5 V 0 -2 -3 -3 -1 -3 -3 -3 -3 3 1 -2 1 0 -3 -1 0 -3 -1 5 -3 2 -3 -1 -5 B -1 -1 5 6 -2 0 1 -1 0 -3 -3 0 -2 -3 -2 0 0 -4 -2 -3 5 -3 1 -1 -5 J -1 -3 -3 -3 -2 -2 -3 -4 -2 4 4 -3 2 1 -3 -2 -1 -2 0 2 -3 4 -2 -1 -5 Z -1 1 0 1 -3 4 5 -2 0 -3 -2 1 -1 -3 -1 0 -1 -2 -2 -3 1 -2 5 -1 -5 X -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 1
  • In R: >library("Biostrings") >data(BLOSUM45) >BLOSUM45 >seq1 <- "WHAT" >seq2 <- "WHY" >pairwiseAlignment(seq1, seq2, substitutionMatrix = BLOSUM45, gapOpening = 0, gapExtension = -2, scoreOnly = FALSE) Global PairwiseAlignedFixedSubject (1 of 1) pattern: [1] WHAT subject: [1] WH-Y score: 22 >source("C:/Documents and Settings/Avril Coughlan/My Documents/BACKEDUP/DeonierBookProblems/Chapter6/MyRfunctions.R") >needlemanwunsch5(seq1, seq2, -2, -2, BLOSUM45) # algorithm by Isaacs et al, correct version, use -2 for gap penalty NA W H A T NA 0 -2 -4 -6 -8 W -2 15 13 11 9 H -4 13 25 23 21 Y -6 11 23 23 22 Also: >source("C:/Documents and Settings/Avril Coughlan/My Documents/Rfunctions.R") >needlemanwunsch(seq1,seq2,gappenalty=-2,type="protein") [,1] [,2] [,3] [,4] [,5] [1,] NA NA NA NA NA [2,] NA "15 >" "13 -" "11 -" "9 -" [3,] NA "13 |" "25 >" "23 -" "21 -" [4,] NA "11 |" "23 |" "23 >" "22 >“
  • Image source: Alanine http://upload.wikimedia.org/wikipedia/commons/thumb/9/90/L-Alanin_-_L-Alanine.svg/140px-L-Alanin_-_L-Alanine.svg.png Threonine: http://upload.wikimedia.org/wikipedia/commons/thumb/a/a0/L-Threonin_-_L-Threonine.svg/180px-L-Threonin_-_L-Threonine.svg.png Tyrosine: http://minimalpotential.files.wordpress.com/2007/11/730px-l-tyrosine-skeletal.png
  • In R: >library(“Biostrings”) >data(BLOSUM45) >BLOSUM45 A R N D C Q E G H I L K M F P S T W Y V B J Z X * A 5 -2 -1 -2 -1 -1 -1 0 -2 -1 -1 -1 -1 -2 -1 1 0 -2 -2 0 -1 -1 -1 -1 -5 R -2 7 0 -1 -3 1 0 -2 0 -3 -2 3 -1 -2 -2 -1 -1 -2 -1 -2 -1 -3 1 -1 -5 N -1 0 6 2 -2 0 0 0 1 -2 -3 0 -2 -2 -2 1 0 -4 -2 -3 5 -3 0 -1 -5 D -2 -1 2 7 -3 0 2 -1 0 -4 -3 0 -3 -4 -1 0 -1 -4 -2 -3 6 -3 1 -1 -5 C -1 -3 -2 -3 12 -3 -3 -3 -3 -3 -2 -3 -2 -2 -4 -1 -1 -5 -3 -1 -2 -2 -3 -1 -5 Q -1 1 0 0 -3 6 2 -2 1 -2 -2 1 0 -4 -1 0 -1 -2 -1 -3 0 -2 4 -1 -5 E -1 0 0 2 -3 2 6 -2 0 -3 -2 1 -2 -3 0 0 -1 -3 -2 -3 1 -3 5 -1 -5 G 0 -2 0 -1 -3 -2 -2 7 -2 -4 -3 -2 -2 -3 -2 0 -2 -2 -3 -3 -1 -4 -2 -1 -5 H -2 0 1 0 -3 1 0 -2 10 -3 -2 -1 0 -2 -2 -1 -2 -3 2 -3 0 -2 0 -1 -5 I -1 -3 -2 -4 -3 -2 -3 -4 -3 5 2 -3 2 0 -2 -2 -1 -2 0 3 -3 4 -3 -1 -5 L -1 -2 -3 -3 -2 -2 -2 -3 -2 2 5 -3 2 1 -3 -3 -1 -2 0 1 -3 4 -2 -1 -5 K -1 3 0 0 -3 1 1 -2 -1 -3 -3 5 -1 -3 -1 -1 -1 -2 -1 -2 0 -3 1 -1 -5 M -1 -1 -2 -3 -2 0 -2 -2 0 2 2 -1 6 0 -2 -2 -1 -2 0 1 -2 2 -1 -1 -5 F -2 -2 -2 -4 -2 -4 -3 -3 -2 0 1 -3 0 8 -3 -2 -1 1 3 0 -3 1 -3 -1 -5 P -1 -2 -2 -1 -4 -1 0 -2 -2 -2 -3 -1 -2 -3 9 -1 -1 -3 -3 -3 -2 -3 -1 -1 -5 S 1 -1 1 0 -1 0 0 0 -1 -2 -3 -1 -2 -2 -1 4 2 -4 -2 -1 0 -2 0 -1 -5 T 0 -1 0 -1 -1 -1 -1 -2 -2 -1 -1 -1 -1 -1 -1 2 5 -3 -1 0 0 -1 -1 -1 -5 W -2 -2 -4 -4 -5 -2 -3 -2 -3 -2 -2 -2 -2 1 -3 -4 -3 15 3 -3 -4 -2 -2 -1 -5 Y -2 -1 -2 -2 -3 -1 -2 -3 2 0 0 -1 0 3 -3 -2 -1 3 8 -1 -2 0 -2 -1 -5 V 0 -2 -3 -3 -1 -3 -3 -3 -3 3 1 -2 1 0 -3 -1 0 -3 -1 5 -3 2 -3 -1 -5 B -1 -1 5 6 -2 0 1 -1 0 -3 -3 0 -2 -3 -2 0 0 -4 -2 -3 5 -3 1 -1 -5 J -1 -3 -3 -3 -2 -2 -3 -4 -2 4 4 -3 2 1 -3 -2 -1 -2 0 2 -3 4 -2 -1 -5 Z -1 1 0 1 -3 4 5 -2 0 -3 -2 1 -1 -3 -1 0 -1 -2 -2 -3 1 -2 5 -1 -5 X -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 1
  • Alignment scoring functions

    1. 1. Alignment Scoring Fuctions Dr Avril Coghlan alc@sanger.ac.ukNote: this talk contains animations which can only be seen bydownloading and using ‘View Slide show’ in Powerpoint
    2. 2. Alignment scoring functions Letter b A R N D C Q E G H I L K M F P S T W Y V A 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1• We define a scoring function σ(S1(i), S2(j)) R -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 N -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 σ(S1(i), S2(j)) is the cost (score) of aligning symbols D -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 S1(i) & S2(j)C -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 Letter a Q -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1• A simple scoring function σ is a score of +1 for E -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 matches, and -1 for mismatches G -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 H -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 I -1 -1 as -1 -1 -1 -1 -1 matrix This can be represented -1 a substitution -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 L -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 Substitution K -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 matrix σ for M -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 protein F -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 alignments P -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 S -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 T -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 W -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 Y -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 V -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1
    3. 3. • The choice of scoring function σ determines the A R N D C Q E G H I L K M F P S T W Y V score Aof the alignment 5 -2 -1 -2 -1 -1 -1 0 -2 -1 -1 -1 -1 -2 -1 1 0 -2 -2 0 σ determines the 0scores of1different0 possible 3alignments,-1so-1 R -2 7 -1 -3 0 -2 -3 -2 -1 -2 -2 -2 affects -1 -2 which alignment is ‘best’ (highest-scoring)-3 0 -2 -2 -2 1 0 N -1 0 6 2 -2 0 0 0 1 -2 one -4 -2 -3 D We need to-2be-1careful about which scoring function we use..-1 C 2 7 -3 0 2 -1 0 -4 -3 0 -3 -4 -1 0 . -4 -2 -3 -1 -3 -2 -3 12 -3 -3 -3 -3 -3 -2 -3 -2 -2 -4 -1 -1 -5 -3 -1 • MoreQcomplex scoring functions exist that give -1 1 0 0 -3 6 2 -2 1 -2 -2 1 0 -4 -1 0 -1 -2 -1 -3 higher scores to certain matches/mismatches eg. the E G -1 0 0 2 -3 2 6 -2 0 -3 -2 1 -2 -3 0 0 -1 -3 -2 -3 0 -2 0 -1 -3 -2 -2 7 -2 -4 -3 -2 -2 -2 -2 -3 -3 BLOSUM45 0scoring function gives7 a -2 -4 of -2 for H -2 0 -1 -3 -2 -2 score -3 -2 -2 -3 -2 0 -2 -2 -3 -3 aligning ‘Y’ & -2 0 1 0 -3 1 0 -2 10 -3 -2 -1 0 -2 -2 -1 -2 -3 2 -3 ‘A’, but a score-3of-2 -4 -3 -2 -3 ‘Y’ -3 ‘T’ 2 -3 2 I -1 -1 for aligning -4 & 5 0 -2 -2 -1 -2 0 3 LBLOSUM45 K -1 -2 -3 -3 -2 -2 -2 -3 -2 2 5 -3 2 1 -3 -3 -1 -2 0 1 -1 3 0 0 -3 1 1 -2 -1 -3 -3 5 -1 -3 -1 -1 -1 -2 -1 -2 M -1 -1 -2 -3 -2 0 -2 -2 0 2 2 -1 6 0 -2 -2 -1 -2 0 1 F -2 -2 -2 -4 -2 -4 -3 -3 -2 0 1 -3 0 8 -3 -2 -1 1 3 0 P -1 -2 -2 -1 -4 -1 0 -2 -2 -2 -3 -1 -2 -3 9 -1 -1 -3 -3 -3 S 1 -1 1 0 -1 0 0 0 -1 -2 -3 -1 -2 -2 -1 4 2 -4 -2 -1 T 0 -1 0 -1 -1 -1 -1 -2 -2 -1 -1 -1 -1 -1 -1 2 5 -3 -1 0 W -2 -2 -4 -4 -5 -2 -3 -2 -3 -2 -2 -2 -2 1 -3 -4 -3 15 3 -3 Y -2 -1 -2 -2 -3 -1 -2 -3 2 0 0 -1 0 3 -3 -2 -1 3 8 -1 V 0 -2 -3 -3 -1 -3 -3 -3 -3 3 1 -2 1 0 -3 -1 0 -3 -1 5
    4. 4. Problem• Find the best alignment between “WHAT” & “WHY” using the BLOSUM45 scoring function & -2 for a gap
    5. 5. Answer• Find the best alignment between “WHAT” & “WHY” using the BLOSUM45 scoring function & -2 for a gap• Matrix T looks like this, giving 1 traceback: W H A T W H A T 0 -2 -4 -6 -8 0 -2 -4 -6 -8 W -2 15 13 11 9 W -2 15 13 11 9 H -4 13 25 23 21 H -4 13 25 23 21 Y -6 11 23 23 22 Y -6 11 23 23 22• The traceback gives the following best alignment: W H A T | | W H - Y (Pink traceback)
    6. 6. • Using +1 for a match, -1 for mismatch, & -2 for an insertion/deletion, the best alignment is: W H A T W H A T (Two equally highest- | | | | W H - Y W H Y - scoring solutions)• Using BLOSUM45, and -2 for an insertion/deletion, the best alignment is: W H A T | | (The highest- W H - Y scoring solution)• Should we use the simpler scoring scheme (match: +1,mismatch:-1) or BLOSUM45? BLOSUM45, because it takes into account that certain amino acids are more likely to substitute for each other during evolution than others
    7. 7. • Non-synonymous mutations change the amino acid sequence eg. codon TTT encodes Phe (F), & TTA encodes Leu (L), so a TTT→TTA mutation causes a F→L mutation (substitution)• Certain amino acids are more likely to substitute for each other than others Because only organisms that carry mutations to similar amino acids tend to survive & reproduce Because a mutation to a dissimilar amino acid (eg. A→Y) is more likely to disrupt a protein’s function (& so kill the organism) than a mutation to a similar amino acid (eg. A→V)Alanine Valine Tyrosine(A) (V) (Y) A & V are small Y is much larger Image source: Wikimedia Commons
    8. 8. BLOSUM45 gives larger scores to substitutions that occur frequently, than for substitutions that rarely occur: A R N D C Q E G H I L K M F P S T W Y V A 5 -2 -1 -2 -1 -1 -1 0 -2 -1 -1 -1 -1 -2 -1 1 0 -2 -2 0eg. the score R -2 7 0 -1 -3 1 0 -2 0 -3 -2 3 -1 -2 -2 -1 -1 -2 -1 -2 Nfor aligning ‘A’ -1 0 6 2 -2 0 0 0 1 -2 -3 0 -2 -2 -2 1 0 -4 -2 -3 Dto ‘V’ (0) is -2 -1 2 7 -3 0 2 -1 0 -4 -3 0 -3 -4 -1 0 -1 -4 -2 -3 Chigher than -1 -3 -2 -3 12 -3 -3 -3 -3 -3 -2 -3 -2 -2 -4 -1 -1 -5 -3 -1 Q -1 1 0 0 -3 6 2 -2 1 -2 -2 1 0 -4 -1 0 -1 -2 -1 -3that for E -1 0 0 2 -3 2 6 -2 0 -3 -2 1 -2 -3 0 0 -1 -3 -2 -3aligning ‘A’ to G 0 -2 0 -1 -3 -2 -2 7 -2 -4 -3 -2 -2 -3 -2 0 -2 -2 -3 -3‘Y’ (-2) H -2 0 1 0 -3 1 0 -2 10 -3 -2 -1 0 -2 -2 -1 -2 -3 2 -3 I -1 -3 -2 -4 -3 -2 -3 -4 -3 5 2 -3 2 0 -2 -2 -1 -2 0 3 L -1 -2 -3 -3 -2 -2 -2 -3 -2 2 5 -3 2 1 -3 -3 -1 -2 0 1BLOSUM45 K -1 3 0 0 -3 1 1 -2 -1 -3 -3 5 -1 -3 -1 -1 -1 -2 -1 -2substitution matrix M -1 -1 -2 -3 -2 0 -2 -2 0 2 2 -1 6 0 -2 -2 -1 -2 0 1σ for protein F -2 -2 -2 -4 -2 -4 -3 -3 -2 0 1 -3 0 8 -3 -2 -1 1 3 0alignments P -1 -2 -2 -1 -4 -1 0 -2 -2 -2 -3 -1 -2 -3 9 -1 -1 -3 -3 -3 S 1 -1 1 0 -1 0 0 0 -1 -2 -3 -1 -2 -2 -1 4 2 -4 -2 -1 T 0 -1 0 -1 -1 -1 -1 -2 -2 -1 -1 -1 -1 -1 -1 2 5 -3 -1 0 W -2 -2 -4 -4 -5 -2 -3 -2 -3 -2 -2 -2 -2 1 -3 -4 -3 15 3 -3 Y -2 -1 -2 -2 -3 -1 -2 -3 2 0 0 -1 0 3 -3 -2 -1 3 8 -1 V 0 -2 -3 -3 -1 -3 -3 -3 -3 3 1 -2 1 0 -3 -1 0 -3 -1 5
    9. 9. Further Reading• Chapter 3 in Introduction to Computational Genomics Cristianini & Hahn• Chapter 6 in Deonier et al Computational Genome Analysis• Practical on pairwise alignment in R in the Little Book of R for Bioinformatics: https://a-little-book-of-r-for- bioinformatics.readthedocs.org/en/latest/src/chapter4.html
    10. 10. Further Reading• Chapter 3 in Introduction to Computational Genomics Cristianini & Hahn• Chapter 6 in Deonier et al Computational Genome Analysis• Practical on pairwise alignment in R in the Little Book of R for Bioinformatics: https://a-little-book-of-r-for- bioinformatics.readthedocs.org/en/latest/src/chapter4.html

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