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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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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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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)



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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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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



Constructing a blosum matr 1 counting mutations l.jpg
Constructing a BLOSUM matr. training sequences1. Counting mutations



3 matrix of mutation probs l.jpg
3. Matrix of mutation probs. training sequences



5 obtaining a blosum matrix l.jpg
5. Obtaining a BLOSUM matrix training sequences



1 2 3 mutation frequency table l.jpg
1.2.3.Mutation Frequency Table training sequences



5 obtaining blosum62 matrix l.jpg
5. Obtaining BLOSUM62 Matrix training sequences


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BLOSUM matrices reference training sequences

  • 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 training sequences

  • Homework


Pam matrices point accepted mutations l.jpg

PAM Matrices training sequences(Point Accepted Mutations)

Mutations accepted by natural selection



Pam phylogenetic tree l.jpg
PAM: Phylogenetic Tree training sequences


Pam accepted point mutation l.jpg
PAM: Accepted Point Mutation training sequences


Mutability of residue j l.jpg
Mutability of Residue training sequencesj


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Total Mutation Rate training sequences

is the total mutation rate of all amino acids


Normalize total mutation rate to 1 l.jpg
Normalize Total Mutation Rate to training sequences1%

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 training sequences

Such that the

Total Mutation Rate is 1%



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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 Probability Matrix?


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In two PAM1 periods: Probability Matrix?

  • {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}



Pam k mutation prob matrix l.jpg
PAM-k Mutation Prob. Matrix Probability Matrix?


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PAM-k log-likelihood matrix Probability Matrix?


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PAM-250 Probability Matrix?


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  • PAM60—60%, PAM80—50%, Probability Matrix?

  • PAM120—40%

  • PAM-250 matrix provides a better scoring alignment than lower-numbered PAM matrices for proteins of 14-27% similarity


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PAM Matrices: Reference Probability Matrix?

  • Atlas of Protein Sequence and Structure,

    Suppl 3, 1978, M.O. Dayhoff.

    ed. National Biomedical Research Foundation, 1


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Choice of Scoring Matrix Probability Matrix?


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PAM Probability Matrix?

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 Probability Matrix?