Jacques'van'Heldenulb'ac'be

1
Sequence analysisPart 1. Dot plots and
substitution matrices

• Introduction to Bioinformatics

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Contents

• Pairwise sequence alignment
• Dot plots (dottup, dotmatcher)
• Substitution matrices
• Gapless alignment
• Alignment with gaps
• Global alignment (Needleman-Wunsch)
• Local alignment (Smith-Waterman)
• Matching a sequence against a database (Fasta,
  BLAST)
• Multiple sequence alignment (ClustalX)
• Matching motifs against sequences

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Dot plots

• Bioinformatics

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Dot plot

• A dot plot is a simple graphical representation
  of identical residues between two sequences.
• The X axis represents the first sequence (PHO5),
• The Y axis represents the second sequence (PHO3)
• A dot is plotted for each match between two
  residues of the sequences.
• Diagonal lines reveal regions of identity between
  the two sequences.

Example protein sequences of the Pho5p and Pho3p
phosphatases in the yeast Saccharomyces
cerevisiae
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Dot plot with word matches

• With nucleic sequences, each residue is expected
  every 4 positions on average. A letter-based dot
  plot is thus very confusing.
• The dot plot can be adapted to display only word
  matches, which correspond to a diagonal of dots
  in the letter-based dot plot.
• Example alignment of PHO5 and PHO3 coding
  sequences, with different word sizes.

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Detecting repeats with a dot plot

• Sequence repeats are easily detected in a dot
  plot when a sequence is compared to itself.
• The main diagonal is completely marked (by
  definition, since the sequence is identical do
  itself)
• Repeats appear as segments of lines parallel to
  the diagonal.

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Gray scale dottups

• Word matches require a perfect match over the
  whole word length.
• A more refined way to show partial similarities
  is to use windows.
• For each point, the window score is the sum of
  matches of its neighbours on the diagonal.
• The gray level reflects the window similarity
  score.

Source ?
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Alignment matrices and substitution matrices

• Bioinformatics

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Alignment matrix

• An alignment matrix is conceptually related to a
  dot plot
• One sequence is pasted horizontally, the other
  vertically
• A score is assigned to each match
• In the case of dot plots, the scoring scheme was
  very simple
• match 1
• mismatch 0

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Substitution matrix

• One could decide to give a lower cost to A-T
  substitutions, if we assume that these are more
  likely to occur in our sequences
• Example
• match 2
• A-T mismatch -1
• other mismatch -2
• The scoring scheme can be represented as a
  substitution matrix

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Scoring an alignment matrix with a substitution
matrix

• Let us come back to our previous alignment matrix
• For each cell of the alignment matrix, we compare
  the residue in sequences A and B, and take the
  score for this pair of residues in the
  substitution matrix.

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Substitution counts in 71 groups of aligned
proteins (Dayhoff, 1978)
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Substitution matrices for proteins

• Margaret Dayhoff (1978) measured the rate of
  substitutions between each pair of amino acids,
  in a collection of aligned proteins.
• Scores are calculated as log-odds
• Positive values reflect frequent ("accepted")
  substitutions, i.e. substitutions that occur more
  frequently than expected by chance.
• Negative values reflect rare ("unfavourable")
  mutations, i.e. substitutions that occur less
  frequently than expected by chance
• The diagonal reflect residue conservation

Reference Dayhoff et al. (1978). A model of
evolutionary change in proteins. In Atlas of
Protein Sequence and Structure, vol. 5, suppl. 3,
345352. National Biomedical Research Foundation,
Silver Spring, MD, 1978.
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PAM scoring matrices

• The alignments used by Dayhoff had 85 identity
• However, frequencies of substitutions are
  expected to depend on the rate of divergence
  between sequences the number of substitutions
  increases with time.
• In order to take into account the divergence
  rate, Margaret Dayhoff calculated a series of
  scoring matrices, each reflecting a certain level
  of divergence
• PAM001 rates of substitutions between amino-acid
  pairs expected for proteins with an average of 1
  substitution per position
• PAM050 rates of substitutions between amino-acid
  pairs expected for proteins with an average of
  50 substitution per position
• PAM250 250 mutations/position (note a position
  could mutate several times)
• The substitution matrix must this be chosen
  according to the relatedness of the sequences to
  be aligned

Reference Dayhoff et al. (1978). A model of
evolutionary change in proteins. In Atlas of
Protein Sequence and Structure, vol. 5, suppl. 3,
345352. National Biomedical Research Foundation,
Silver Spring, MD, 1978.
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Extrapolation of the PAM series from PAM001
Mi,3P(XArg)
M17,jP(ThrX)
Ala
0.0009
0.0022
Arg
0.0001
0.0002
Asn
Asn
0.9822
0.0013
Asp
0.0042
0.0004
Cys
0.0000
0.0001
Gln
0.0004
0.0003
...
...
...
Thr
0.0013
0.9871
Trp
Thr
0.0000
0.0000
Tyr
0.0003
0.0002
Val
0.0001
0.0009
P(Asn -gt Thr) P(Asn -gt Ala -gt Thr) P(Asn -gt
Arg -gt Thr) ... P(Asn -gt Val -gt Thr)
(0.0009)(0.0001) (0.0001)(0.0002) ...
(0.0001)(0.009)
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PAM250 matrix
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Hinton diagram of the PAM250 matrix

• Yellow boxes indicate positive values (accepted
  mutations)
• Red boxes indicate negative values (avoided
  mutations).
• The area of each box is proportional to the
  absolute value of the log-odds score.

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BLOSUM scoring matrices

• Henikoff and Henikoff (1992) analyzed
  substitution rates on the basis of aligned
  regions (blocks)
• They calculated scoring matrices from blocks with
  different percentages of protein divergence
• Example
• BLOSUM62 calculated from blocks with 62
  similarity
• BLOSUM80 calculated from blocks with 80
  similarity
• When these substitution matrices are used to
  score sequence alignments, one should always
  choose the matrix appropriate to the expected
  percentage of similarity.

Reference Henikoff, S. and Henikoff, J.G.
(1992). Amino acid substitution matrices from
protein blocks. PNAS 8910915-10919.
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BLOSSUM62
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BLOSSUM62substitutions between acidic residues
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BLOSSUM62substitutions between basic residues
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BLOSSUM62substitutions between aromatic residues
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BLOSSUM62substitutions between polar residues
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BLOSSUM62substitutions between hydrophobic
residues
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Substitution matrices - summary

• Different substitution scoring matrices have been
  established
• PAM (Dayhoff, 1979)
• BLOSSUM (Henikoff Henikoff, 1992)
• Residue categories (Phylip)
• Substitution matrices allow to detect
  similarities between more distant proteins than
  what would be detected with the simple identity
  of residues.
• The matrix must be chosen carefully, depending on
  the expected rate of conservation between the
  sequences to be aligned.
• Beware
• With PAM matrices
• the score indicates the percentage of
  substitution per position-gt higher numbers are
  appropriate for more distant proteins
• With BLOSUM matrices
• the score indicates the percentage of
  conservation-gt higher numbers are appropriate
  for more conserved proteins

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Scoring an alignment with a substitution matrix

• The substitution matrix can be used to assign a
  score to a pair-wise alignment.
• The score of the alignment is the sum, over all
  the aligned positions (i from 1 to L), of the
  scores of the pairs of residues (r1,I and r2,I).
• Gaps are treated by subtracting a penalty, with
  two parameters
• Gap opening (go) penalty
• Typical values between -10 and -15
• Gap extension (ge) penalty
• Typical values between -0.5 and -2

i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 R L A S V E T D M
P - - - - - L T L R Q H . .
. . go ge ge ge ge . . .
. T L T S L Q T T L K N L K
E M A H L G T H S -1 4 0 4 1 2 5 -1
2 -1 -10 -1 -1 -1 -1 -1 -2 4 -2 -1 8 7
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Substitution matrices in dot plots

• Substitution matrices can be used in dot plots
• The user has to specify the following parameters
• Window size (word size)
• Score threshold
• Substitution matrix
• At each position of the plot
• A pair of words of size w are extracted from the
  first and second sequences.
• The score of the word pair is calculated by
  summing the scores of the corresponding pairs of
  residues.
• If the pair of words passes the threshold, a
  black diagonal is displayed at the corresponding
  position of the dot plot.
• The regions of similarity between the two
  sequences are appear as black diagonals on the
  dot plot.

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Aspartokinases dot plot with simple word matches

• Let us compare the peptidic sequences of two
  enzymes from the bacteria Escherichia coli K12.
• LysC aspartokinase involved in lysine
  biosynthesis
• MetL bifunctional enzyme which combines two
  domains
• aspartokinase catalyses the first step of
  methionine biosynthesis
• homoserine dehydrogenase catalyze the third step
  of methionine biosynthesis
• On the dot plot, the region of similarity between
  the two aspartokinase domains is barely visible..

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Aspartokinases dot plot with substitution matrix
(BLOSUM62)

• With dotmatcher, a substitution matrix is used to
  score the similarity between each pair of
  residues.
• This reveals the similarity between the
  aspartokinase domains of MetL and LysC.
• Note that this similarity only covers the N
  terminal half of MetL, because it is a
  bi-functional enzyme the C-terminal domain is a
  homoserine dehydrogenase.
• It is quite tricky to find the appropriate
  parameters, because these can vary from case ot
  case.

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Software tools for displaying dot plot

• DNA Strider
• Marck C (1988) 'DNA Strider' a 'C' program for
  the fast analysis of DNA and protein sequences on
  the Apple Macintosh family of computers. Nucleic
  Acids Res. 161829-36.
• http//www...
• Dotlet
• Junier T, Pagni M (2000) Dotlet diagonal plots
  in a web browser. Bioinformatics. 16178-9.
• http//myhits.isb-sib.ch/cgi-bin/dotlet
• Dotter
• Sonnhammer EL, Durbin R (1995) A dot-matrix
  program with dynamic threshold control suited for
  genomic DNA and protein sequence analysis. Gene.
  167GC1-10.
• http//www.cgb.ki.se/cgb/groups/sonnhammer/Dotter.
  html

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Bibliography

• Substitution matrices
• PAM series
• Dayhoff, M. O., Schwartz, R. M. Orcutt, B.
  (1978). A model of evolutionary change in
  proteins. Atlas of Protein Sequence and Structure
  5, 345--352.
• BLOSUM substitution matrices
• Henikoff, S. Henikoff, J. G. (1992). Amino acid
  substitution matrices from protein blocks. Proc
  Natl Acad Sci U S A 89, 10915-9.
• Gonnet matrices, built by an iterative procedure
• Gonnet, G. H., Cohen, M. A. Benner, S. A.
  (1992). Exhaustive matching of the entire protein
  sequence database. Science 256, 1443-5. 1.