Sequence Alignment

1
Sequence Alignment

• Csc 487/687 Computing for bioinformatics

2
Refining the Scoring Scheme- Scoring Matrix

• To measure the relative probability of any
  particular substitution.
• The relative frequencies of such changes to form
  a scoring matrix for substitution
• A likely change will score higher than a rare one.

3
Scoring matrix for nucleic acid sequences

• A simple scheme for substitutions
• 1 for a match, -1 for a mismatch.
• A more complicated scheme based on the higher
  frequency of transition mutations than
  transversion mutations
• a g and t c
• (a or g) (t or c)

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Refining the Scoring Scheme- Scoring Matrix

• The scheme should return high values for
  alignment of homologous proteins
• Should reward higher alignment of amino acids
  often seen in corresponding positions in
  homologous proteins

5
Scoring Matrices

• Importance of scoring matrices
• Scoring matrices appear in all analyses involving
  sequence comparisons.
• The choice of matrix can strongly influence the
  outcome of the analysis.
• Scoring matrices implicitly represent a
  particular theory of relationships.
• Understanding theories underlying a given scoring
  matrix can aid in making proper choice.

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Identity Matrix
1
A
1
0
C
1
0
0
I
1
0
0
0
L
L
I
C
A
Simplest type of scoring matrix
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Similarity
It is easy to score if an amino acid is identical
to another (the score is 1 if identical and 0 if
not). However, it is not easy to give a score
for amino acids that are somewhat similar.
CO2-
CO2-
NH3
NH3
Isoleucine
Leucine
Should they get a 0 (non-identical) or a 1
(identical) or Something in between?
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Scoring matrices

• Gives scores between each pair of amino acids
• Should reflect
• The degree of biological relatedness
• The probability that two amino acids occurring
  in different sequences have common ancestor
• Should be symmetric
• Substitution matrices
• The probability that an amino acid a is changed
  to amino acid b (in a certain evolutionary time)
• Is generally not symmetric

9
Scoring matrices

• Identity matrix (scoring 0/1)
• Use of the distances in the genetic codes
• Use of the amino acid similarities based on
  physico-chemical properties
• Scoring matrices based on experimental data (PAM
  BLOSUM)

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DAYHOFFs PAM-MATRICES

• Based on experimental data
• t evolutionary time interval
• Sequences from 34 superfamilies were used
• Divide the sequences into groups (71) of
  homologous sequences, and make a multiple
  alignment for each of them
• Construct evolutionary trees for each group, and
  estimate the mutations that have occurred
• Define an evolutionary model to explain the
  evolution
• Construct substitution matrices, for each amino
  acid pairs (a,b) an estimate of the probability
  that an amino acid a has mutated to an amino acid
  b in time interval t
• Construct scoring matrices from the substitution
  matrices.
• Note that a and b are variables that mean any
  amino acid.

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Example
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The model of the evolution

• The probability of a mutation in a position is
  independent on
• Position and neighbour residues
• Previous mutations in the position
• The biological (evolutionary) clock is assumed
  (meaning constant rate of mutations)
• This means that evolutionary time can be measured
  in number of mutations (here substitutions)
• The measure is PAM (Point Accepted Mutations)
• 1 PAM is one accepted mutation per 100 residues

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The Point-Accepted-Mutation (PAM) model of
evolution and the PAM scoring matrix
A 1-PAM unit is equivalent to 1 mutation found in
a stretch of 2 sequences each containing 100
amino acids that are aligned Example 1
..CNGTTDQVDKIVKILNEGQIASTDVVEVVVSPPYVFLPVVKSQLRPE
IQV..
..CNGTTDQVDKIVKIRNEGQIASTDVVEVVVSPPYVFLPV
VKSQLRPEIQV.. length 100, 1 Mismatch, PAM
distance 1 A k-PAM unit is equivalent to k
1-PAM units (or Mk).
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Substitution matrix M1
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Calculate Mz by matrix multiplication, show for
z2

• Z2 mean two mutations per 100 residues
• A residue a can be changed to residue b after 2
  PAM of following reasons
• a is mutated to b in first PAM, unchanged in the
  next, with probability MabMbb
• a is unchanged in first PAM, changed in the next,
  probability MaaMab
• a is mutated to an amino acid x in the first PAM,
  and then to b in the next, probability MaxMxb, x
  being any amino acid unequal (a,b)
• These three cases are disjunctive, hence

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Final Scoring Matrix is the Log-Odds Scoring
Matrix

• S (a,b) 10 log10(Mab/Pb)

Replacement amino acid
Original amino acid
Frequency of amino acid b
Mutational probability matrix number
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M250
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PAM-250 scoring matrix
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BLOSUM (Henikoff Henikoff)

• Perform best in identifying distant relationships
• Making use of the much larger amount of data that
  become available since Dayhoffs work
• Based on BLOCKS database of aligned protein
  sequence

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BLOSUM (Henikoff Henikoff)

• Make multiple alignments and discover blocks not
  containing gaps (used over 2,000 blocks)
• ...KIFIMK.......GDEVK...
• ...NLFKTR GDSKK...
• KIFKTK GDPKA
• KLFESR GDAER
• KIFKGR GDAAK
• For each column in each block they counted the
  number of occurrences of each pair of amino acids
  (210 different pairs (2021/2) )
• A block of length w from an alignment of n
  sequences has wn(n-1)/2 occurrences of amino acid
  pairs
• Let hab be the number of occurrences of the pair
  (ab) in all blocks (habhba)
• T total number of pairs
• fabhab/T

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Gap weighting

• CLUSTAL-W
• For aligning DNA sequences
• Use of identity matrix for substitution
• Gap penalties 10 for gap initiation and 0.1 for
  gap extension by one residue
• For aligning protein sequences
• BLOSUM62 matrix
• Gap penalties 11 for gap initiation and 1 for gap
  extension by one residue