Corn Hoogendoorn

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Multiple sequence alignment methods

• Corné Hoogendoorn
• Denis Miretskiy

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Overview

• What a multiple alignment means
• Scoring a multiple alignment
• Break
• Multidimensional dynamic programming
• Progressive alignment methods

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What a multiple alignment means

• Homologous residues are aligned in columns
• Structurally homologous
• Evolutionarily homologous
• Similar 3D structural positions
• Diverging from a common ancestral residue

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Multiple alignment - issues

• Identifying unambiguously homologous positions is
  not possible
• A need to identify which alignment is best
• Protein structures and sequences evolve
• Sequences not entirely superposable

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Multiple alignment - issues

• There always is an unambiguously correct
  evolutionary alignment
• Common ancestral sequence
• Sheerly impossible to infer the evolutionary
  history
• Usually easier to construct a structural alignment

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Multiple alignment - issues

• Sequence diverges even faster than structure
• Structurally unalignable protein parts cannot be
  aligned by sequence either
• Some parts are very well alignable
• Use these parts to align whatever can be aligned
• Disregard the rest to assess alignment quality
• Supposedly meaningless biases are omitted

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Scoring an alignment

• Some positions are more conserved than others
• Position-specific scoring
• Sequences are not independent
• Related to each other by a phylogenetic tree
• Specify a complete probabilistic model of
  molecular sequence evolution

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Complete probabilistic model

• Probabilities of all evolutionary events
• Prior probability of root ancestral sequence
• Probabilities of evolutionary change depend on
  evolutionary time
• Position-specific structural and functional
  constraints
• We just dont have all the necessary data

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Workable approximations

• Assume that all columns are statistically
  independent

Score for multiple alignment m
Gap score/penalty
Score for column i in the multiple alignment m
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Scoring an alignment

• Notations

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Minimum EntropyFurther simplification

• We already assumed independence between columns
• Complex statistical dependence between sequences
  (within columns) if their phylogenetic tree has
  many intermediate ancestors
• We assume independence between and within columns

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Minimum entropy

• Probability of column mi
• Score of column mi can be defined as the negative
  logarithm

A regularized probability estimate as used in
chapter 5
An entropy measure directly related to the
Shannon entropy (chapter 11)
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Example (1)
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Example (2)
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Example (3)
Will this ever be 0 in reality? Why (not)?
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Example (4)
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Minimum entropy

• Very near to the HMM formulation
• Choose the sequences carefully
• Usually the sample of sequences is biased
• Weighting schemes as discussed in chapter 5 are
  necessary
• This partially compensates for the defects of the
  assumption of sequence independence

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Sum of pairs

• Also assumes statistical independence between
  columns
• Uses substitution matrices
• For simple linear gap costs, s(a,-) s(-,a) and
  s(-,-) are defined, with s(-,-) 0

Scores s(a,b) come from substitution matrices
like PAM or BLOSUM
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Sum of pairs

• Substitution scores are usually log-odds scores
  for pairwise comparisons
• log(pab/qaqb) log(pbc/qbqc) log(pac/qaqc)
• log(pabc/qaqbqc)
• Each sequence is scored as if it descended from
  the N-1 other sequences
• Evolutionary events are over-counted

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Problem with SP scores

• Consider an alignment of N sequences
• All have leucine (L) at position i

Number of symbol pairs in the column
Score for an L-L alignment according to the
BLOSUM50 matrix
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Problem with SP scores

• What if one sequence has glycine (G) at i?
• G-L pair scores -4, difference with L-L is 9
• The score is worse than the all-leucine column by
  a fraction

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What a multiple alignment meansScoring a
multiple alignment

• Questions?
• Break

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Multidimensional dynamic programming

• We assume that columns of an alignment are
  statistically independent
• Gaps are scored with a linear gap cost
• Now we can calculate overall score S(m)
• Where S(mi) is a score for column i

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Calculating the overall score

• Define as the maximum score of an
  alignment up to the subsequences ending with

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Simple notation

• Introduce Di which is 0 or 1 and define the
  product
• Now recursion can be written as follows

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Complexity of algorithm

• The algorithm requires the computation of the
  whole dynamic programming matrix with L1, L2,,LN
  entries.
• We have to view 2N - 1 combinations of gaps in a
  column.
• All sequences have roughly the same length
• Memory complexity of algorithm is
• Time complexity is

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MSA

• Let akl denote the pairwise alignment between
  sequences k and l
• the score of the complete alignment is given
• Let âkl be the optimal pairwise alignment of k,
  l
• Obviously

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Lower bound

• Assume that we have a lower bound of the optimal
  multiple alignment, so
• In other words
• Where

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Lower bound

• Now we can look only at pairwise alignments of k
  and l that score better bkl
• We need to obtain s(a), and this can be done by
  using a progressive alignment algorithm

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Restricted algorithm

• For each pair k, l we can find the complete set
  Bkl of coordinate pairs (ik, il) such that the
  best alignment of xk to xl through (ik, il)
  scores more than bkl
• Now we only have to look at cells (i1, i2,, iN)
  which meet the following condition
• (ik, il) is in Bkl for all k, l

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Progressive alignment methods

• The algorithms differ in several ways
• Choice of order to do the alignment
• Whether the progression involves only alignment
  of sequences to a single growing alignment or
  whether subfamilies are built upon a tree
  structure

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Feng-Doolittle progressive multiple alignment

• Calculate a diagonal matrix of N(N-1)/2 distances
  between all pairs of N sequences by standard
  pairwise alignment
• Construct a guide tree from the distance matrix
  using the FitchMargoliash clustering algorithm
• Starting from the first node added to the tree,
  align the child nodes
• Repeat until all sequences have been aligned.

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Converting scores to distances

• Where
• Smax is the maximum score
• Sobs is the observed pairwise alignment score
• Srand is the expected score for aligning two
  random sequences

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Profile alignment

• Linear gap scores can be included in the SP
  score
• Global alignment score

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CLUSTALW progressive alignment

• Construct a distance matrix of all N(N-1)/2 pair
  by pairwise dynamic programming alignment.
• Construct a guide tree by a neighbor-joining
  clustering algorithm (Saitou Nei).
• Progressively align at nodes in order of
  decreasing similarity, using sequence-sequence,
  sequence-profile and profile-profile alignment.

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CLUSTALW properties

• Sequences are weighted to compensate for biased
  representation.
• The substitution matrix used to score an
  alignment is chosen based on the expected
  similarity of the sequences
• Position-specific gap-open profile penalties are
  multiplied by a modifier that is a function of
  the residues observed at the position.

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CLUSTALW properties

• Gap-open penalties are also decreased if the
  position is spanned by a consecutive stretch of
  five or more hydrophilic residues.
• Both gap-open and gap-extend penalties are
  increased if there are also no gaps occur nearby
  in the alignment.
• In the progressive alignment stage, if the score
  of an alignment is low, we have to accumulate
  profile information

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Iterative refinement methodsBarton-Stenberg
multiple alignment

• Find two sequences with the highest pairwise
  similarity and align them using standard pairwise
  dynamic programming alignment.
• Find the sequence that is most similar to a
  profile of the alignment of the first two and
  align it to the first two by profile-sequence
  alignment. Repeat until all sequences have been
  included in the multiply alignment.

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Iterative refinement methodsBarton-Stenberg
multiple alignment

• Remove sequence and realign it to a profile of
  the other aligned sequences by profile-sequence
  alignment. Repeat for sequences.
• Repeat the previous realignment step a fixed
  number of times or until the alignment score
  converges.