Bioinformatics Algorithms and Data Structures

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Bioinformatics Algorithms and Data Structures

• CLUSTAL W Algorithm
• Lecturer Dr. Rose
• Slides by Dr. Rose
• April 3, 2003

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Multiple Sequence Alignment

• CLUSTAL is an algorithm for aligning multiple
  sequences.
• Reasons for computing multiple alignments
• Characterizing protein families
• Detect homology between sequences and families of
  sequences
• Predict secondary and tertiary structures of new
  sequences.
• Needed for creating of phylogenetic trees.

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Multiple Sequence Alignment

• Recall DP used for 2 sequence alignment
• Guarantees optimal alignment relative to the
  scoring table that is used.
• DP is only practical for small numbers of short
  sequences.
• Impractical for
• large numbers of sequences
• Very long sequences
• i.e., more than 8 proteins of average length.

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Progressive Algorithms

• Progressive Approaches
• Exploit idea that homologous sequences are
  related by evolution.
• Multiple alignments can be built up from pairwise
  alignments.
• The pairwise alignments follow branching in the
  guide tree.
• The most closely related sequences are aligned
  first.
• The more distant related sequences are gradually
  added.

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Progressive Algorithms

• Empirical observations
• For simple cases
• correctly align domains of known secondary and
  tertiary structures.
• closely related sequences are less sensitive to
  parameter settings, i.e., gap penalties and
  weight matrix.
• In all cases
• gaps are preserved, i.e., once a gap always a
  gap.
• progressive alignment gives an idea of the
  variability at each position before more distant
  sequences are added.

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Progressive Algorithms

• Empirical observations
• For more complicated cases
• Progressive approach is less reliable for highly
  divergent sequences (less than 25-30 identity).
• gives a good starting point for further
  manual/automatic refinement.

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Problems with Progressive Algorithms

• Local minimum problem
• Recall this is a greedy algorithm approach
• Sequences are added greedily
• Multiple alignments are built up from pairwise
  alignments.
• The pairwise alignments follow branching in the
  initial guide tree. (more on this later)
• No guarantee of a global optimum
• Any misaligned regions made early on can not be
  corrected later on.

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Problems with Progressive Algorithms

• Sensitivity to alignment parameters
• problematic also for iterative and stochastic
  algorithms.
• Traditional parameters
• weight table
• cost of opening a gap
• cost of extending a gap
• Expectation is one set of parameters works well
  over
• all sequences in the set
• all parts of each sequence

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Problems with Progressive Algorithms

• Sensitivity to alignment parameters continued
• A single weight matrix choice will generally work
  for closely related sequences.
• weight matrices give highest weight to identities
• Any weight matrix will work ok if identities
  dominate
• For divergent sequences
• Nonidentical residues are more significant
• Scores to these residues are critical
• Different weight matrices will be required for
• different evolutionary distances
• Different classes of proteins

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Problems with Progressive Algorithms

• Sensitivity to alignment parameters continued
• A range of gap penalty values will generally work
  for closely related sequences.
• For divergent sequences
• The specific choice of gap penalty value becomes
  critical
• For proteins gaps dont occur randomly.
• Recall our discussion of conserved secondary
  features
• Gaps occur between alpha helices and beta strands
  rather than within them

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CLUSTAL W Contributions

• Dynamically vary gap penalties according to
  position residue
• Local gap opening penalty adjustment
• relative to observed relative frequency of gaps
  next to each of the 20 amino acid.
• reduced for loop or random coil regions (as
  indicated by short stretches of hydrophilic
  residues)
• reduced for gaps found in early alignments
• increased within 8 residues of existing gaps
  (observation gaps tend not to be closer than 8
  residues)

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CLUSTAL W Contributions

• Weight matrices are chosen dynamically
• PAM series and BLOSUM series are main series of
  amino acid weight matrices in use.
• Choice of weight matrix is by estimation of
  divergence of sequences being aligned at each
  step.
• Different weight matrices are appropriate
  depending on similarity of sequences

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CLUSTAL W Contributions

• Different weight matrices are appropriate
  depending on similarity of sequences
• For closely related sequences
• identities predominate
• Only frequent conservative substitutions are
  scored high
• For evolutionary divergent sequences
• Less weight should be given to identities
• Weight matrix should be tuned to greater
  evolutionary distance

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CLUSTAL W Contributions

• Weighting of sequences
• corrects for unequal sampling across the
  evolutionary distance in the data set.
• Downweights similar sequences
• Upweights divergent sequences
• Weight are calculated from the branch lengths of
  the initial guide tree.

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CLUSTAL W Contributions

• Neighbor-Joining method used to calculate guide
  tree
• Less sensitive to unequal evolutionary rates in
  different branches.
• Significance branch lengths are used to derive
  sequence weights.
• Accuracy of distance calculations for guide tree
• Tree constructed from pairwise distance matrix
• Fast approximate alignment
• Full dynamic programming
• User selectable

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CLUSTAL W Algorithm

• Basic method
• Distance matrix is calculated
• Distances are pairwise alignment scores
• Gives divergence of each pair of sequences
• Guide tree built from distance matrix
• Progressive alignment according to guide tree
• Branching order of tree specifies alignment order
• Alignment progresses from leaves to root.

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CLUSTAL W Algorithm

• Distance matrix/pairwise alignments phase
• Two choices fast approximation or DP
• Fast approximation
• Defn a k-tuple match is a run of identical
  residues, typically
• 1 to 2 for proteins
• 2 to 4 for nucleotide sequences
• Scores are calculated as (k-tuple matches)
  fixed penalty per gap
• Score is initially calculated as a percent
  identity score.
• Distance 1.0 (score/100)

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CLUSTAL W Algorithm

• Distance matrix/pairwise alignments phase
• Full DP alignment
• Alignment uses
• gap opening penalties
• gap extension penalties
• full amino acid weight matrix.
• Scores are calculated as (identies)/(residues),
  gaps not included
• Score is initially calculated as a percent
  identity score.
• Distance 1.0 (score/100)

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NJ Algorithm

• Neighbor Joining to Calculate the Guide Tree
  Phase
• does not require a uniform molecular clock
• the raw data are provided as a distance matrix
• the initial tree is a star tree
• distance matrix is modified
• distance between node pairs is adjusted on the
  basis of their average divergence from all other
  nodes.
• the least-distant pair of nodes are linked.

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NJ Algorithm

• Neighbor Joining to Calculate the Guide Tree
  Phase
• When two nodes are linked
• Add their common ancestral node to the tree
• delete the terminal nodes with their branches
• the common ancestor is now a terminal node on a
  smaller tree
• At each step, two terminal nodes are replaced by
  one new node
• The process is complete when there are only two
  nodes separated by a single branch

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NJ Algorithm

• Advantages of Neighbor Joining
• Fast.
• Can be used on large datasets
• Can support bootstrap analysis
• Can handle lineages with largely different branch
  lengths (different molecular evolutionary rates)
• Can be used with methods that use correction for
  multiple substitutions

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NJ Algorithm

• Disadvantages of Neighbor Joining
• sequence information is reduced
• Sequences are boiled down to distances
• No secondary or tertiary features used
• gives only one possible tree
• strongly dependent on the model of evolution used

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NJ Algorithm

• NJ example from http//www.icp.ucl.ac.be/opperd/
  private/neighbor.html
• Consider the following tree

• Notice that the branches for D and B are longer.
• This expresses the idea that they have a faster
  molecular clock than the other OTUs.

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NJ Algorithm

• The distance matrix for the tree is

Normally, we create the tree from the
distances. In this example, we use to tree to
derive the distances.
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NJ Algorithm

• We start with a star tree.
• Notice that we have 6 operational taxonomic units
  (OTUs)
• The start tree has a leaf for each OTU

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NJ Algorithm

• Step 1 Calculate the net divergence for each
  OTU.
• The net divergence is the sum of distances from i
  to all other OTUs.

r(A) 5476830 r(B) 42 r(C) 32 r(D)
38 r(E) 34 r(F) 44
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NJ Algorithm

• Step 2 Calculate a new distance matrix based on
  average divergence
• M(ij)d(ij) - r(i) r(j)/(N-2)
• Example A,B
• M(AB)d(AB) -(r(A) r(B)/(N-2) -13

Recall r(A) 30 r(B) 42
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NJ Algorithm

• Step 2 continued
• M(ij)d(ij) - r(i) r(j)/(N-2)

Distance matrix
Average divergence matrix
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NJ Algorithm

• Step 3 choose two OTUs for which Mij is the
  smallest.
• the possible choices are A,B and D,E
• arbitrarily choose A and B
• form a new node called U, the parent of A B.
• calculate the branch length from U to A and B.
• S(AU) d(AB) / 2 r(A)-r(B) / 2(N-2) 1
• S(BU) d(AB) -S(AU) 4

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NJ Algorithm

• The tree after U is added.

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NJ Algorithm

• Step 4 define distances from U to other terminal
  nodes
• d(CU) d(AC) d(BC) - d(AB) / 2 3
• d(DU) d(AD) d(BD) - d(AB) / 2 6
• d(EU) d(AE) d(BE) - d(AB) / 2 5
• d(FU) d(AF) d(BF) - d(AB) / 2 7
• Note no change in paired distances C,D,E,F

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NJ Algorithm

• Now N N-1 5
• Repeat steps 1 through 4
• Stop when N 2

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CLUSTAL W Algorithm

• The final result of the tree produced by NJ is an
  unrooted tree.
• The branch lengths are proportional to the
  estimated divergence.
• A mid-point method is used to place the root
• The mid point is defined at the point where the
  means of the branch lengths on either side are
  equal.

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CLUSTAL W Algorithm

• Basic Progressive Alignment Phase
• Use a series of pairwise alignments
• The alignments follow the branching order of the
  guide tree
• The alignments start from the leaves and progress
  towards the root
• Full DP with a residue weight matrix is used
• Gaps are preserved
• Newly created gaps get full opening extension
  penalties

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CLUSTAL W Algorithm

• Basic Progressive Alignment Phase
• Each step involved two existing alignments or
  sequences
• The score at a given position is the average of
  the pairwise weight matrix scores. Example
• aligning 2 alignments with 3 and 4 sequences,
  respectively
• The score at a given position is the average of
  the 3X4 comparisons.
• The weight matrix has only positive scores
• Each gap versus a residue is scored a zero, the
  worst value
• This is the average linkage cluster distance
  metric

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CLUSTAL W Algorithm

• Example
• A B are aligned
• C is aligned with the result of (1)
• D E are aligned
• The results of (2) and (3) are aligned
• F is aligned with the result of (4)

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CLUSTAL W Algorithm

• Improvement to Progressive Alignment Phase
• Sequence weighting
• Calculated from the guide tree
• Normalized so that largest weight is 1.0
• Closely related sequences receive lower weights
• They over-represent their common information
• A lower weight seeks to reduce this influence
• Divergent sequences receive higher weights
• Sequence weight impacts alignment scores
• each weight matrix value is multiplied by the
  weights of the two sequences.

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CLUSTAL W Algorithm

• Improvement to Progressive Alignment Phase
• Two gap penalty types
• Gap opening (GOP)
• Gap extension (GEP)
• Actual assessed penalty depends on
• Weight matrix GOP is scaled by the average score
  of mismatched residues
• Similarity of sequences identity is used to
• increase GOP for similar sequences
• decrease GOP for divergent sequences

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CLUSTAL W Algorithm

• Actual assessed penalty depends on continued
• Length of sequences the logarithm of the length
  of the shorter sequence is used to increase GOP
  with sequence length
• GOP (GOP log(min(N,M))) (ave residue
  mismatch score) ( identity scaling factor)
• Difference in sequence lengths GEP is increased
  to inhibit many long gaps in shorter sequences.
• GEP GEP (1.0 log(N/M))

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CLUSTAL W Algorithm

• Improvement to Progressive Alignment Phase
• Position-specific gap penalties
• Lowered GOP at existing gaps
• if a position already has gaps, GOP is reduced
  relative to the number of sequences with a gap at
  that position
• GOP GOP 0.3 ( sequences w/o gap)/(
  sequences)
• Increased GOP near existing gaps
• New gap within 8 residues of an exisiting gap
• GOP GOP (2 ((8 distance from gap) 2) /
  8)

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CLUSTAL W Algorithm

• Improvement to Progressive Alignment Phase
• Position-specific gap penalties continued
• Reduced GOP in hydrophilic stretches
• 5 or more consecutive hydrophilic residues is a
  stretch ?
• Hydrophilic residues are D,E,G,K,N,Q,P,R S
• GOP reduced by a third if there is no gap in a
  stretch
• Residue specific penalty
• GOP is modified if there is no gap and no
  hydrophilic stretch
• There is an adjustment factor for each of the 20
  residues
• For mixtures, the factor is the average of all
  contributing residues

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• The End