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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).

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Scoring Matrices

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Scoring matrices l.jpg

Scoring Matrices


Diff scoring rules lead to diff alignments l.jpg

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 l.jpg

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 s ij in a scoring matrix as log likelihood ratio l.jpg

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


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  • 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 l.jpg

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 l.jpg

Likelihood Ratio of Aligning Two Sequences


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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


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  • 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 l.jpg

Constructing BLOSUM Matrices

Blocks Substitution Matrices


Blosum matrices of specific similarities l.jpg

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 l.jpg

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


Constructing a blosum matr 1 counting mutations l.jpg

Constructing a BLOSUM matr.1. Counting mutations


2 tallying mutation frequencies l.jpg

2. Tallying mutation frequencies


3 matrix of mutation probs l.jpg

3. Matrix of mutation probs.


4 calculate abundance of each residue marginal prob l.jpg

4. Calculate abundance of each residue (Marginal prob)


5 obtaining a blosum matrix l.jpg

5. Obtaining a BLOSUM matrix


Constructing the real blosum62 matrix l.jpg

Constructing the real BLOSUM62 Matrix


1 2 3 mutation frequency table l.jpg

1.2.3.Mutation Frequency Table


4 calculate amino acid abundance l.jpg

4. Calculate Amino Acid Abundance


5 obtaining blosum62 matrix l.jpg

5. Obtaining BLOSUM62 Matrix


Blosum matrices reference l.jpg

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


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Break

  • Homework


Pam matrices point accepted mutations l.jpg

PAM Matrices (Point Accepted Mutations)

Mutations accepted by natural selection


Constructing pam matrix training data l.jpg

Constructing PAM Matrix: Training Data


Pam phylogenetic tree l.jpg

PAM: Phylogenetic Tree


Pam accepted point mutation l.jpg

PAM: Accepted Point Mutation


Mutability of residue j l.jpg

Mutability of Residue j


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Total Mutation Rate

is the total mutation rate of all amino acids


Normalize total mutation rate to 1 l.jpg

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)


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Mutation Probability Matrix Normalized

Such that the

Total Mutation Rate is 1%


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Mutation Probability Matrix (transposed) M*10000


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

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


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PAM Matrix: Assumptions


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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}


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


Pam k mutation prob matrix l.jpg

PAM-k Mutation Prob. Matrix


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PAM-k log-likelihood matrix


Slide42 l.jpg

PAM-250


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  • 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 l.jpg

PAM Matrices: Reference

  • Atlas of Protein Sequence and Structure,

    Suppl 3, 1978, M.O. Dayhoff.

    ed. National Biomedical Research Foundation, 1


Slide45 l.jpg

Choice of Scoring Matrix


Comparing scoring matrix l.jpg

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

Comparing Scoring Matrix


Sources of error in pam l.jpg

Sources of Error in PAM


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