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# Scoring Matrices - PowerPoint PPT Presentation

Scoring Matrices. Diff. Scoring Rules Lead to Diff. Alignments. 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).

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Scoring Matrices

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## Scoring Matrices

### Diff. Scoring Rules Lead to Diff. Alignments

• 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)

### Scoring Rules/Matrices

• 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 Sij in a Scoring Matrix (as log likelihood ratio)

• The alignment score of aligning two sequences is the log likelihood ratio of the alignment under two models

• Common ancestry

• By chance

### Likelihood Ratio for Aligning a Single Pair of Residues

• 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)

### Likelihood Ratio of Aligning Two Sequences

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

### BLOSUM Matrices of Specific Similarities

• 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

### 5. Obtaining a BLOSUM matrix

Constructing the real BLOSUM62 Matrix

### BLOSUM matrices reference

• 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

### Mutability of Residue j

Total Mutation Rate

is the total mutation rate of all amino acids

### Normalize Total Mutation Rate to 1%

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

### In two PAM1 periods:

• {AR} = {AA and AR} or

{AN and NR} or

{AD and DR} or

… or

{AV and VR}

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

### PAM-k Mutation Prob. Matrix

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

### PAM Matrices: Reference

• 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