Scoring Matrices

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Scoring Matrices
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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 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

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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

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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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Likelihood Ratio of Aligning Two Sequences
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PAM Accepted Mutations1500 changes in 71
groups w/ gt 85 similarity BLOSUM Blocks
Substitution Matrix2000 blocks from 500
families
Two classes of widely used protein scoring
matrices
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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.

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Constructing BLOSUM Matrices

• Blocks Substitution Matrices

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BLOSUM Matrices of Specific Similarities

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

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

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Constructing a BLOSUM matr.1. Counting mutations
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2. Tallying mutation frequencies
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3. Matrix of mutation probs.
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4. Calculate abundance of each residue (Marginal
prob)
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5. Obtaining a BLOSUM matrix
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• Constructing the real BLOSUM62 Matrix

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1.2.3.Mutation Frequency Table
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4. Calculate Amino Acid Abundance
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5. Obtaining BLOSUM62 Matrix
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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

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PAM Matrices (Point Accepted Mutations)

• Mutations accepted by natural selection

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Constructing PAM Matrix Training Data
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PAM Phylogenetic Tree
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PAM Accepted Point Mutation
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Mutability of Residue j
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Total Mutation Rate
is the total mutation rate of all amino acids
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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) M10000
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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.
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PAM-k Mutation Prob. Matrix
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PAM-k log-likelihood matrix
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PAM-250
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• PAM6060, PAM8050,
• PAM12040
• 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

• 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
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Comparing 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

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Sources of Error in PAM