Topic 3: PAM, BLOSUM, and Scoring Matrices

Why are biologically meaningful scoring matrices needed?

Amino acid substitutions have different biological likelihoods, so they should not all receive the same score.

What is a scoring matrix?

A table assigning scores to aligned nucleotide or amino acid pairs.

What is a substitution?

Replacement of one nucleotide or amino acid by another.

What is a diagonal matrix element?

A score for aligning a residue with itself, such as A with A.

What is an off-diagonal element?

A score for aligning two different residues.

What does a symmetric scoring matrix mean?

S(i,j)=S(j,i).

What are the two models behind log-odds scoring?

Related/common-ancestor model and unrelated/random model.

What is the related-sequence model?

Aligned residue pairs are assumed to derive from a common ancestor.

What is the random model?

Aligned residues are assumed unrelated and occur by background frequencies.

What is the random-model probability of ordered residues i and j?

Q(i,j)=p(i)×p(j).

What is the related-model probability given in class?

P(i,j)=p(j)×P(i|j).

What is a log-odds substitution score?

The logarithm of the ratio of related-model probability to random-model probability.

What does a positive substitution score mean?

The pair is more common under the related model than expected by chance.

What does a zero substitution score mean?

The pair occurs about as often as expected by chance.

What does a negative substitution score mean?

The pair is less common under the related model than expected by chance.

What does PAM stand for?

Point Accepted Mutation.

Who developed PAM matrices?

Margaret Dayhoff and colleagues.

How are PAM matrices derived?

Use closely related proteins, infer accepted mutations, estimate a PAM1 substitution model, then extrapolate using matrix powers.

What does PAM1 represent?

One accepted point mutation per 100 amino acids on average.

What does XX mean in PAM-XX?

Evolutionary distance in PAM1 steps.

What does a larger PAM number mean?

Greater evolutionary distance; generally useful for more divergent sequences.

What does PAM250 mean?

The PAM1 mutation probability matrix is applied for 250 evolutionary steps, not 250 observed differences per 100 sites.

What does BLOSUM stand for?

BLOcks SUbstitution Matrix.

Who developed BLOSUM matrices?

Henikoff and Henikoff.

How are BLOSUM matrices derived?

Count amino acid pairs in conserved ungapped blocks, cluster highly similar sequences, calculate observed and expected pair frequencies, then log-odds scores.

Does BLOSUM use an explicit evolutionary tree?

No; it uses observed substitutions in conserved protein blocks.

What does XX mean in BLOSUM-XX?

The sequence identity threshold used to cluster similar sequences.

What does BLOSUM62 mean?

Sequences above 62% identity are grouped when building the matrix.

What does a larger BLOSUM number generally mean?

A matrix more appropriate for closely related sequences.

Which matrices are generally used for more divergent sequences?

Higher PAM numbers and lower BLOSUM numbers.

What is observed pair frequency q(i,j)?

Count of amino acid pair i,j divided by the total pair count.

What is expected frequency for an identical unordered pair?

e(i,i)=p(i)^2.

What is expected frequency for different unordered pairs?

e(i,j)=2p(i)p(j).

What is the BLOSUM half-bit score equation?

S(i,j)=round[2 log2(q(i,j)/e(i,j))].

How do you calculate sequence identity?

(Number of identical aligned residue pairs / number of compared aligned positions)×100%.