Introduction to bioinformatics lecture 8

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Introduction to bioinformaticslecture 8

• Deriving amino acid exchange matrices (II) and
  Multiple sequence alignment (I)

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Summary Dayhoffs PAM-matrices

• Derived from global alignments of closely
  related sequences.
• Matrices for greater evolutionary distances are
  extrapolated from those for lesser ones.
• The number with the matrix (PAM40, PAM100)
  refers to the evolutionary distance greater
  numbers are greater distances.
• Several later groups have attempted to extend
  Dayhoff's methodology or re-apply her analysis
  using later databases with more examples.
• Extensions of Dayhoffs methodology gt Jones,
  Thornton and coworkers used the same methodology
  as Dayhoff but with modern databases
  (CABIOS 8275). gt Gonnett and coworkers
  (Science 2561443) used a slightly different
  (but theoretically equivalent) methodology. gt
  Henikoff Henikoff (Proteins 1749) compared
  these two newer versions of the PAM
  matrices with Dayhoff's originals.

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The BLOSUM matrices(BLOcks SUbstitution Matrix)

• The BLOSUM series of matrices were created by
  Steve Henikoff and colleagues (PNAS 8910915).
• Derived from local, un-gapped alignments of
  distantly related sequences.
• All matrices are directly calculated no
  extrapolations are used.
• Again the observed frequency of each pair is
  compared to the expected frequency (which is
  essentially the product of the frequencies of
  each residue in the dataset). Then Log-odds
  matrix.

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The Blocks Database

• The Blocks Database contains multiple
  alignments of conserved regions in protein
  families.
• Blocks are multiply aligned un-gapped segments
  corresponding to the most highly conserved
  regions of proteins.
• The blocks for the BLOCKS database are made
  automatically by looking for the most highly
  conserved regions in groups of proteins
  represented in the PROSITE database. These blocks
  are then calibrated against the SWISS-PROT
  database to obtain a measure of the random
  distribution of matches. It is these calibrated
  blocks that make up the BLOCKS database.
• The database can be searched by e-mail and
  World Wide Web (WWW) servers (http//blocks.fhcr
  c.org/help) to classify protein and nucleotide
  sequences.

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The Blocks Database
Gapless alignment blocks
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The BLOSUM series

• BLOSUM30, 35, 40, 45, 50, 55, 60, 62, 65, 70,
  75, 80, 85, 90.
• The number after the matrix (BLOSUM62) refers
  to the minimum percent identity of the blocks
  (in the BLOCKS database) used to construct the
  matrix (all blocks have gt62 sequence
  identity)
• No extrapolations are made in going to higher
  evolutionary distances
• High number - closely related sequences Low
  number - distant sequences
• BLOSUM62 is the most popular best for general
  alignment.

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The log-odds matrix for BLOSUM62
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PAM versus BLOSUM

• Based on an explicit evolutionary model
• Derived from small, closely related proteins with
  15 divergence
• Higher PAM numbers to detect more remote sequence
  similarities
• Errors in PAM 1 are scaled 250X in PAM 250

• Based on empirical frequencies
• Uses much larger, more diverse set of protein
  sequences (30-90 ID)
• Lower BLOSUM numbers to detect more remote
  sequence similarities
• Errors in BLOSUM arise from errors in alignment

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Comparing exchange matrices

• To compare amino acid exchange matrices, the
  "Entropy" value can be used. This is a relative
  entropy value (H) which describes the amount of
  information available per aligned residue pair.

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Specialized matrices

• Claverie (J.Mol.Biol 2341140) developed a set
  of substitution matrices designed explicitly
  for finding possible frameshifts in protein
  sequences.These matrices are designed solely
  for use in protein-protein comparisons they
  should not be used with programs which blindly
  translate DNA (e.g. BLASTX, TBLASTN).

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Specialized matrices

• Rather than starting from alignments generated
  by sequence comparison, Rissler et al (1988)
  and later Overington et al (1992) only
  considered proteins for which an experimentally
  determined three dimensional structure was
  available.
• They then aligned similar proteins on the basis
  of their structure rather than sequence and
  used the resulting sequence alignments as their
  database from which to gather substitution
  statistics. In principle, the Rissler or
  Overington matrices should give more reliable
  results than either PAM or BLOSUM. However, the
  comparatively small number of available protein
  structures (particularly in the Rissler et al
  study) limited the reliability of their
  statistics.
• Overington et al (1992) developed further
  matrices that consider the local environment of
  the amino acids.

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A note on reliability

• All these matrices are designed using standard
  evolutionary models.
• It is important to understand that evolution is
  not the same for all proteins, not even for the
  same regions of proteins.
• No single matrix performs best on all
  sequences. Some are better for sequences with
  few gaps, and others are better for sequences
  with fewer identical amino acids.
• Therefore, when aligning sequences, applying a
  general model to all cases is not ideal. Rather,
  re-adjustment can be used to make the general
  model better fit the given data.

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Pair-wise alignment quality versus sequence
identity(Vogt et al., JMB 249, 816-831,1995)
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Summary

• If ORF exists, then align at protein level.
• Amino acid substitution matrices reflect the
  log-odds ratio between the evolutionary and
  random model and can therefore help in
  determining homology via the alignment score.
• The evolutionary and random models depend on
  the generalized data used to derive them. This
  not an ideal solution.
• Apart from the PAM and BLOSUM series, a great
  number of further matrices have been developed.
• Matrices have been made based on DNA, protein
  structure, information content, etc.
• For local alignment, BLOSUM62 is often
  superior for distant (global) alignments,
  BLOSUM50, GONNET, or (still) PAM250 work well.
• Remember that gap penalties are always a
  problem unlike the matrices themselves, there
  is no formal way to calculate their values --
  you can follow recommended settings, but these
  are based on trial and error and not on a
  formal framework.

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Biological definitions for related sequences

• Homologues are similar sequences in two different
  organisms that have been derived from a common
  ancestor sequence. Homologues can be described
  as either orthologues or paralogues.
• Orthologues are similar sequences in two
  different organisms that have arisen due to a
  speciation event. Orthologs typically retain
  identical or similar functionality throughout
  evolution.
• Paralogues are similar sequences within a single
  organism that have arisen due to a gene
  duplication event.
• Xenologues are similar sequences that do not
  share the same evolutionary origin, but rather
  have arisen out of horizontal transfer events
  through symbiosis, viruses, etc.

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So this means
Source http//www.ncbi.nlm.nih.gov/Education/BLAS
Tinfo/Orthology.html
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Multiple sequence alignment

• Sequences can be conserved across species and
  perform similar or identical functions.gt hold
  information about which regions have high
  mutation rates over evolutionary time and
  which are evolutionarily conservedgt
  identification of regions or domains that are
  critical to functionality.
• Sequences can be mutated or rearranged to perform
  an altered function.gt which changes in the
  sequences have caused a change in the
  functionality.

Multiple sequence alignment the idea is to take
three or more sequences and align them so that
the greatest number of similar characters are
aligned in the same column of the alignment.
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What to ask yourself

• How do we get a multiple alignment?(three or
  more sequences)
• What is our aim? Do we go for max accuracy,
  least computational time or the best
  compromise?
• What do we want to achieve each time

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Sequence-sequence alignment
sequence
sequence
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Multiple alignment methods

• Multi-dimensional dynamic programminggt extension
  of pairwise sequence alignment.
• Progressive alignmentgt incorporates phylogenetic
  information to guide the alignment process
• Iterative alignmentgt correct for problems with
  progressive alignment by repeatedly realigning
  subgroups of sequence

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Simultaneous multiple alignmentMulti-dimensional
dynamic programming

• The combinatorial explosion
• 2 sequences of length n
• n2 comparisons
• Comparison number increases exponentially
• i.e. nN where n is the length of the sequences,
  and N is the number of sequences
• Impractical for even a small number of short
  sequences

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Multi-dimensional dynamic programming (Murata et
al., 1985)
Sequence 1
Sequence 3
Sequence 2
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The MSA approach

• MSA (Lipman et al., 1989, PNAS 86, 4412)
• MSA restricts the amount of memory by computing
  bounds that approximate the centre of a
  multi-dimensional hypercube.
• Calculate all pair-wise alignment scores.
• Use the scores to to predict a tree.
• Calculate pair weights based on the tree (lower
  bound).
• Produce a heuristic alignment based on the tree.
• Calculate the maximum weight for each sequence
  pair (upper bound).
• Determine the spatial positionsthat must be
  calculated to obtain the optimal alignment.
• Perform the optimal alignment.
• Report the weight found comparedto the maximum
  weight previouslyfound (measure of divergence).
• Extremely slow and memory intensive.
• Max 8-9 sequences of 250 residues.

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The DCA approach

• DCA (Stoye et al., 1997, Appl. Math. Lett. 10(2),
  67-73)
• Each sequence is cut in two behinda suitable cut
  position somewhere close to its midpoint.
• This way, the problem of aligningone family of
  (long) sequences is divided into the two
  problems of aligning two families of (shorter)
  sequences.
• This procedure is re-iterated untilthe sequences
  are sufficiently short.
• Optimal alignment by MSA.
• Finally, the resulting short alignments are
  concatenated.

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So in effect
Sequence 1
Sequence 3
Sequence 2
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Multiple alignment methods

• Multi-dimensional dynamic programminggt extension
  of pairwise sequence alignment.
• Progressive alignmentgt incorporates phylogenetic
  information to guide the alignment process
• Iterative alignmentgt correct for problems with
  progressive alignment by repeatedly realigning
  subgroups of sequence

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The progressive alignment method

• Underlying idea usually we are interested in
  aligning families of sequences that are
  evolutionary related.
• Principle construct an approximate phylogenetic
  tree for the sequences to be aligned and than to
  build up the alignment by progressively adding
  sequences in the order specified by the tree.
• But before going into details, some notices of
  multiple alignment profiles

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How to represent a block of sequences?

• Historically consensus sequence single
  sequence that best represents the amino acids
  observed at each alignment position.
• Modern methods Alignment profile
  representation that retains the information about
  frequencies of amino acids observed at each
  alignment position.

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Multiple alignment profiles (Gribskov et al. 1987)

• Gribskov created a probe group of typical
  sequences of functionally related proteins that
  have been aligned by similarity in sequence or
  three-dimensional structure (in his case globins
  immunoglobulins).
• Then he constructed a profile, which consists of
  a sequence position-specific scoring matrix
  M(p,a) composed of 21 columns and N rows (N
  length of probe).
• The first 20 columns of each row specify the
  score for finding, at that position in the
  target, each of the 20 amino acid residues. An
  additional column contains a penalty for
  insertions or deletions at that position
  (gap-opening and gap-extension).

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Multiple alignment profiles
Core region
Core region
Gapped region
i
A C D ? ? ? W Y
fA.. fC.. fD.. ? ? ? fW.. fY..
fA.. fC.. fD.. ? ? ? fW.. fY..
fA.. fC.. fD.. ? ? ? fW.. fY..
-
Gapo, gapx
Gapo, gapx
Gapo, gapx
Position dependent gap penalties
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Profile building

• Example each aa is represented as a frequency
  penalties as weights.

i
A C D ? ? ? W Y
0.3 0.1 0 ? ? ? 0.3 0.3
0.5 0 0 ? ? ? 0 0.5
0 0.5 0.2 ? ? ? 0.1 0.2
Gap penalties
0.5
1.0
1.0
Position dependent gap penalties
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Profile-sequence alignment
sequence
ACDVWY
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Sequence to profile alignment
A A V V L
0.4 A 0.2 L 0.4 V
Score of amino acid L in sequence that is aligned
against this profile position Score 0.4
s(L, A) 0.2 s(L, L) 0.4 s(L, V)
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Profile-profile alignment
profile
A C D . . Y
profile
ACDVWY
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Profile to profile alignment
0.4 A 0.2 L 0.4 V
0.75 G 0.25 S
Match score of these two alignment columns using
the a.a frequencies at the corresponding profile
positions Score 0.40.75s(A,G)
0.20.75s(L,G) 0.40.75s(V,G)
0.40.25s(A,S) 0.20.25s(L,S)
0.40.25s(V,S) s(x,y) is value in amino acid
exchange matrix (e.g. PAM250, Blosum62) for amino
acid pair (x,y)
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So, for scoring profiles

• Think of sequence-sequence alignment.
• Same principles but more information for each
  position.
• Reminder
• The sequence pair alignment score S comes from
  the sum of the positional scores M(aai,aaj) (i.e.
  the substitution matrix values at each alignment
  position minus penalties if applicable)
• Profile alignment scores are exactly the same,
  but the positional scores are more complex