Download Substitution matrices

Burkhard Morgenstern
Grundlagen der Bioinformatik
Subsitutionsmatrizen
SS 07
Substitution matrices
All protein alignment programs depend on similarity
scores s(a,b)
Similarity score s(a,b) for amino acids a and b is based
on probability pa,b of substitution a -> b
Idea: it is more reasonable to align amino acids that are
frequently (with high probability) replaced by each
other!
Substitution matrices
Compute similarity score s(a,b) for amino acids a and b:
 Probability pa,b of substitution
a → b (or b → a),
 Frequency qa of a
Define
s(a,b) = log (pa,b / qa qb)
Substitution matrices
1.
Estimate probability pa as relative frequency of a
(possibly with pseudo counts)
2.
Estimate probability pa,b of substitution a -> b based
on observed substitutions in real-world sequences
Substitution matrices
Simplifying assumptions:
 Consider evolution as a random process: substitution




a -> b occurs with probability pa,b depending on a
and b
pa,b = pa,b (t), i.e. probability depends on time span t
in evolution since sequences originated from
common ancester
pa,b does not depend on sequence position
Sequence positions independent of each other
pa,b = pb,a (symmetry!)
Substitution matrices
Result: PAM matrix (Dayhoff et al.)
Substitution matrices
To calculate pa,b:
Consider alignments of related proteins and count
substitutions
a → b (or b → a)
Substitution matrices
To calculate pa,b:
Consider alignments of related proteins and count
substitutions
a → b (or b → a)
ESWTSRQWERYTIALMSDQRREVLYWIALY
ERWTSERQWERYTLALMSQRREALYWIALY
Substitution matrices
To calculate pa,b:
Consider alignments of related proteins and count
substitutions
a → b (or b → a)
ESWTS-RQWERYTIALMSDQRREVLYWIALY
ERWTSERQWERYTLALMS-QRREALYWIALY
Substitution matrices
To calculate pa,b:
Consider alignments of related proteins and count
substitutions
a → b (or b → a)
ESWTS-RQWERYTIALMSDQRREVLYWIALY
ERWTSERQWERYTLALMS-QRREALYWIALY
Substitution matrices
Problems involved:
Probability pa,b depends on time t since sequences
separated in evolution: pa,b = pa,b (t). But: pa,b (t) not
linear in t for large t
2. Alignment of protein families must be known!
3. Multiple mutations at one sequence position
4. Protein families contain multiple sequences:
phylogenetic tree must be known!
1.
Substitution matrices

Solution for 1. – 3. (time dependence, alignment,
multiple mutations)



Look at small evolutionary distances first, normalize
for distance = 1 PAM (= percentage accepted
mutations)
Calculate substitution matrices for larger distances
based on small distances
Solution for 4 (tree must be known): Use parsimony
to find tree
M. Dayhoff et al. (1978), Atlas of Protein sequence and
Structure: PAM matrices
Substitution matrices
Calculation of pa,b(t) :
 Consider multiple alignments of closely related
protein families
 Count substitutions a->b (or b->a) in alignments
based on phylogenetic tree
 Estimate pa,b(t) for small times t
 Normalize to distance t = 1 PAM (percentage of
accepted mutations)
 Calculate conditional probabilities p(a|b,t) for small t
 Calculate p(a|b,t) for larger evolutionary distances by
matrix multiplication
 Calculate pa,b(t) for larger evolutionary distances
Substitution matrices
Substitution matrices
Alternative: BLOSUM matrices
S. Henikoff and J.G. Henikoff, PNAS, 1992
Basis: BLOCKS database, gap-free regions of multiple
alignments.
 Cluster of sequences if percentage of similarity > L
 Estimate pa,b(t) directly.
Default values: L = 62, L = 50