Evolution and Scoring Rules

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Evolution and Scoring Rules

• 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 Rules vs. Scoring Matrices

• Nucleotide vs. Amino Acid Sequence
• The choice of a scoring rule can strongly
  influence the outcome of sequence analysis
• 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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Translation - Protein Synthesis Every 3
nucleotides (codon) are translated into one amino
acid
DNA A T G C 11 RNA A U G
C 31 Protein 20 amino acids
Replication
Transcription
Translation
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Nucleotide sequence determines the amino acid
sequence
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Translation - Protein Synthesis
RNA Protein
5 -gt 3 N-term -gt C-term
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Log Likelihoods used as Scoring Matrices PAM
- Accepted Mutations1500 changes in 71 groups
w/ gt 85 similarity BLOSUM Blocks
Substitution Matrix2000 blocks from 500
families
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Log Likelihoods used as Scoring MatricesBLOSUM
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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
  protein sequences (abundance)

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Likelihood Ratio of Aligning Two Sequences
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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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• PAM and BLOSUM matrices are all log likelihood
  matrices
• More specificly
• 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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BLOSUM matrices for Protein

• 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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Constructing BLOSUM Matrices of Specific
Similarities

• Sets of sequences have widely varying similarity.
  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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Constructing a BLOSUM matr.2. Tallying mutation
frequencies
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Constructing a BLOSUM matr.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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PAM Matrices (Point Accepted Mutations)

• Mutations accepted by natural selection

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PAM Matrices

• Accepted Point Mutation
• Atlas of Protein Sequence and Structure,
• Suppl 3, 1978, M.O. Dayhoff.
• ed. National Biomedical Research Foundation,
  1
• Based on evolutionary principles

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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
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Total Mutation Rate
is the total mutation rate of all amino acids
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Normalize Total Mutation Rate
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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-1 log likelihood 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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Sources of Error in PAM
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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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Choice of Scoring Matrix
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Global Alignment with Affine Gaps

• Complex Dynamic Programming

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Problem w/ Independent Gap Penalties

• The occurrence of x consecutive
  deletions/insertions is more likely than the
  occurrence of x isolated mutations
• We should penalize x long gap less than x
• times of the penalty for one gap

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Affine Gap Penalty

• w2 is the penalty for each gap
• w1 is the _extra_ penalty for the 1st gap

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Scoring Rule not Additive!

• We need to know if the current gap is a new gap
  or the continuation of an existing gap
• Use three Dynamic Programming matrices to keep
  track of the previous step

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• S1 is the vertical sequence
• S2 is the horizontal sequence
• (From Diagonal) a(i,j) current position is a
  match
• (From Left) b(i,j) current position is a gap in
  S1
• (From Above) c(i,j) current position is a gap in
  S2
• Filling the next element in each matrix depends
  on the previous step, which is stored in the
  three matrices.

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Last step a match
a gap in S2
a gap in S1
new gap in S2
a continued gap in S2
a gap in S2 following a gap in S1
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Decisions in Seq. Alignment

• Local or global alignment?
• Which program to use
• Type of scoring matrix
• Value of gap penalty

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Aij10
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PAM-k log-likelihood matrix
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