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Scoring Matrices

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Scoring Matrices

- Example Score =
5 x (# matches) + (-4) x (# mismatches) +

+ (-7) x (total length of all gaps)

- Example Score =
5 x (# matches) + (-4) x (# mismatches) +

+ (-5) x (# gap openings) + (-2) x (total length of all gaps)

- Why are they important?
- The choice of a scoring rule can strongly influence the outcome of sequence analysis

- What do they mean?
- Scoring matrices implicitly represent a particular theory of evolution
- Elements of the matrices specify the similarity of one residue to another

- The alignment score of aligning two sequences is the log likelihood ratio of the alignment under two models
- Common ancestry
- By chance

- Above: the probability that two residues are aligned by evolutionary descent
- Below: the probability that they are aligned by chance
- Pi, Pj are frequencies of residue i and j in all sequences (abundance)

Two classes of widely used protein scoring matrices

PAM = % Accepted Mutations:1500 changes in 71 groups w/ > 85% similarityBLOSUM = Blocks Substitution Matrix:2000 “blocks” from 500 families

- PAM and BLOSUM matrices are all log likelihood matrices
- More specifically:
- An alignment that scores 6 means that the alignment by common ancestry is 2^(6/2)=8 times as likely as expected by chance.

Constructing BLOSUM Matrices

Blocks Substitution Matrices

- Sequences with above a threshold similarity are clustered.
- If clustering threshold is 62%, final matrix is BLOSUM62

A toy example of constructing a BLOSUM matrix from 4 training sequences

Constructing the real BLOSUM62 Matrix

- S. Henikoff and J. Henikoff (1992). “Amino acid substitution matrices from protein blocks”. PNAS 89: 10915-10919
- Training Data: ~2000 conserved blocks from BLOCKS database. Ungapped, aligned protein segments. Each block represents a conserved region of a protein family

- Homework

PAM Matrices (Point Accepted Mutations)

Mutations accepted by natural selection

Total Mutation Rate

is the total mutation rate of all amino acids

This defines an evolutionary period: the period during which the 1% of all sequences are mutated (accepted of course)

Mutation Probability Matrix Normalized

Such that the

Total Mutation Rate is 1%

Mutation Probability Matrix (transposed) M*10000

-- PAM1 mutation prob. matr. -- PAM2 Mutation Probability Matrix?

-- Mutations that happen in twice the evolution period of that for a PAM1

- {AR} = {AA and AR} or
{AN and NR} or

{AD and DR} or

… or

{AV and VR}

Entries in a PAM-2 Mut. Prob. Matr.

PAM-k log-likelihood matrix

PAM-250

- PAM60—60%, PAM80—50%,
- PAM120—40%
- PAM-250 matrix provides a better scoring alignment than lower-numbered PAM matrices for proteins of 14-27% similarity

- Atlas of Protein Sequence and Structure,
Suppl 3, 1978, M.O. Dayhoff.

ed. National Biomedical Research Foundation, 1

Choice of Scoring Matrix

PAM

Based on extrapolation of a small evol. Period

Track evolutionary origins

Homologous seq.s during evolution

BLOSUM

Based on a range of evol. Periods

Conserved blocks

Find conserved domains