1. Pairwise Sequence Analysis-III
Amino-acid substitution matrices
PAM matrices
Derivation
Limitation
BLOSUM matrices
Lecture 4 CS566

2. Amino-acid substitution matrix
Goal
To find log [Pjoint(xy)/Pindependent(xy)]
To find probabilistic measures of “interchangeability” between amino acids
Concepts
Accepted mutation
Replacement that does not disrupt function
Markov chain (1st order)
Next state (amino-acid) in time decided entirely by current value of state
“Odds of winning for team in play-offs” (Does not matter how the team got there!)
Lecture 4 CS566

3. Point Accepted Mutation (PAM) Matrix
Pioneering work by Margaret Dayhoff et al (1978)
Based on Evolutionary model
PAM n matrix
Scores based on allowing for average substitution in n% of residues
Larger the value of n, greater the evolutionary distance between residues
Lecture 4 CS566

4. PAM Matrix Generation Assumption
Based on atomic substitutions (“What you see is what you got”) A=>G and not A=>S=>G
Sets of highly related sequences (>85% similarity)
Lecture 4 CS566

5. PAM Matrix Generation
Build phylogenetic (“family”) tree for each set of sequences to establish sequence of atomic changes
Count residue populations and substitutions
Estimate probability of replacements for each pair of residues
Normalize to 1% average replacement and generate Mutation probability matrix
Generate PAM1 matrix
Generate other PAM matrices (e.g., PAM250)
Lecture 4 CS566

6. Phylogenetic trees Tree for set of 4 sequences that have either C or D
at a certain position in the alignment
Typically double-counted as C=>D as well as D=>C
Counts to keep track of
Frequency of each residue
Frequency of each kind of substitution
Frequency of each residue’s involvement in substitution
Lecture 4 CS566

7. PAM n% mutation matrix generation
Square PAM 1 mutation matrix n times to obtain PAM n% matrix
Helps to model “what is you see is not what you got” by representing longer evolutionary distances
PAM 250 implies 250% average substitutions, i.e., average of 2.5 transitions between aligned residues – and NOT a completely different pair of protein sequences
Lecture 4 CS566

8. PAM n% matrix generation
A given PAM n% mutation matrix is converted to the log odds form by dividing each entry by the relative abundance of each residue, taking the log, rounding and averaging x=>y and y<=x scores
Lecture 4 CS566

9. Point Accepted Mutation (PAM) Matrix
Limitation
Based on only one type of mutational event
Ignores rarer types of mutations that are observed only over longer periods of time
Because of the above, model does not fit as well for the more divergent sequences
Lecture 4 CS566

10. BLOSUMx matrices
Matrix scores for different evolutionary distances derived independently
Much larger dataset (better sampling)
Sequences clustered into BLOCKS; x represents % similarity within block
Intrablock substitutions used to characterize log odds
Lecture 4 CS566

11. Choice of appropriate matrix
Matrix should be chosen based on percent similarity of sequences being analyzed
PAM250 for 20% similarity
PAM120 for 40% similarity
PAM80 for 50% similarity
PAM60 for 60% similarity
BLOSUM?
Lecture 4 CS566