- The document discusses alignment scoring functions used to score alignments of protein sequences. - A simple scoring function gives a score of +1 for matches and -1 for mismatches. This can be represented as a substitution matrix. - More complex scoring functions like BLOSUM45 take into account that certain amino acid substitutions are more likely than others based on evolution. - The choice of scoring function determines which alignments are considered "best" or highest scoring.

1. Alignment Scoring Fuctions
Dr Avril Coghlan
alc@sanger.ac.uk
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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. • 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
L
BLOSUM45 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. Problem
• Find the best alignment between “WHAT” & “WHY”
using the BLOSUM45 scoring function & -2 for a gap

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. • 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. • 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. 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 0
eg. the score R -2 7 0 -1 -3 1 0 -2 0 -3 -2 3 -1 -2 -2 -1 -1 -2 -1 -2
N
for aligning ‘A’ -1 0 6 2 -2 0 0 0 1 -2 -3 0 -2 -2 -2 1 0 -4 -2 -3
D
to ‘V’ (0) is -2 -1 2 7 -3 0 2 -1 0 -4 -3 0 -3 -4 -1 0 -1 -4 -2 -3
C
higher 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 -3
that for E -1 0 0 2 -3 2 6 -2 0 -3 -2 1 -2 -3 0 0 -1 -3 -2 -3
aligning ‘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 1
BLOSUM45 K -1 3 0 0 -3 1 1 -2 -1 -3 -3 5 -1 -3 -1 -1 -1 -2 -1 -2
substitution matrix
M -1 -1 -2 -3 -2 0 -2 -2 0 2 2 -1 6 0 -2 -2 -1 -2 0 1
σ for protein F -2 -2 -2 -4 -2 -4 -3 -3 -2 0 1 -3 0 8 -3 -2 -1 1 3 0
alignments 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. 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. 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