Biological Sequence Comparison Database Homology Searching

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Biological Sequence Comparison / Database
Homology Searching

• Aoife McLysaght
• Summer Intern,
• Compaq Computer Corporation
• Ballybrit Business Park, Galway, Ireland

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Database Homology Searching

• Use algorithms to increase efficiency and to
  provide a mathematical basis for searches which
  can be translated into statistical significance
• Assumes that sequence, structure and function are
  inter-related
• BLAST (Basic Local Alignment Search Tool) and
  FastA (Fast Alignment)
• heuristic approximations of Needleman-Wunsch and
  Smith-Waterman algorithms
• reduce computation

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Needleman-Wunsch Algorithm

• General algorithm for sequence comparison
• Maximise a similarity score, to give maximum
  match
• Maximum match largest number of residues of one
  sequence that can be matched with another
  allowing for all possible deletions
• Finds the best GLOBAL alignment of any two
  sequences
• N-W involves an iterative matrix method of
  calculation
• All possible pairs of residues (bases or amino
  acids) - one from each sequence - are represented
  in a 2-dimensional array
• All possible alignments (comparisons) are
  represented by pathways through this array

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Needleman-Wunsch Algorithm (cont.)

• Three main steps
• 1. Assign similarity values
• 2. For each cell, look at all possible pathways
  back to the beginning of the sequence (allowing
  insertions and deletions) and give that cell the
  value of the maximum scoring pathway
• 3. Construct an alignment (pathway) back from the
  highest scoring cell to give the highest scoring
  alignment

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Needleman-Wunsch Algorithm (cont.)

• Similarity values
• A numerical value is assigned to every cell in
  the array depending on the similarity/dissimilarit
  y of the two residues
• These may be simple scores or more complicated,
  e.g. related to chemical similarities or
  frequency of observed substitutions
• The example shown has
• match 1
• mismatch 0

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Needleman-Wunsch Algorithm (cont.)

• Score pathways through array
• For each cell want to know the maximum possible
  score for an alignment ending at that point
• Searches subrow and subcolumn, as shown, for the
  highest score
• Adds this to the score for the current cell
• Proceeds row by row through the array
• Gap penalty for the introduction of gaps in the
  alignment (presumed insertions or deletions into
  one sequence) here 0

HijmaxHi-1, j-1 s(ai,bj), maxHi-k,j-1 -Wk
s(ai,bj), maxHi-1, j-l -Wl s(ai,bj)
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Needleman-Wunsch Algorithm (cont.)

• Construct alignment
• The alignment score is cumulative by adding along
  a path through the array
• The best alignment has the highest score i.e. the
  maximum match
• Maximum match largest number resulting from
  summing the cell values of every pathway
• The maximum match will ALWAYS be somewhere in the
  outer row or column shown
• The alignment is constructed by working backwards
  from the maximum match

MP-RCLCQR-JNCBA -PBRCKC-RNJ-CJA
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Needleman-Wunsch Algorithm (cont.)

• Statistical Significance
• Maximum match is a function of sequence
  relationship and composition
• Would like to know probability of obtaining
  result (maximum match) from a pair of random
  sequences
• Estimate this experimentally
• form pairs of random sequences by randomly
  drawing one member from each set (I.e. have same
  composition as the real proteins)
• if the value found for the real proteins is
  significantly different from that for the random
  proteins then the difference is a function of the
  sequences alone and not of their composition

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Smith-Waterman Algorithm

• Instead of looking at each sequence in its
  entirety this compares segments of all possible
  lengths (LOCAL alignments) and chooses whichever
  maximise the similarity measure
• For every cell the algorithm calculates ALL
  possible paths leading to it. These paths can be
  of any length and can contain insertions and
  deletions

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Smith-Waterman Algorithm (cont.)

• Only works effectively when gap penalties are
  used
• In example shown
• match 1
• mismatch -1/3
• gap -11/3k (kextent of gap)
• Start with all cell values 0
• Looks in subcolumn and subrow shown and in direct
  diagonal for a score that is the highest when you
  take alignment score or gap penalty into account

HijmaxHi-1, j-1 s(ai,bj), maxHi-k,j -Wk,
maxHi, j-l -Wl, 0
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Smith-Waterman Algorithm (cont.)

• Four possible ways of forming a path
• For every residue in the query sequence
• 1. Align with next residue of db sequence score
  is previous score plus similarity score for the
  two residues
• 2. Deletion (i.e. match residue of query with a
  gap) score is previous score minus gap penalty
  dependent on size of gap
• 3. Insertion (i.e. match residue of db sequence
  with a gap) score is previous score minus gap
  penalty dependent on size of gap
• 4. Stop score is zero
• Choose whichever of these is the highest

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Smith-Waterman Algorithm (cont.)

• Construct Alignment
• The score in each cell is the maximum possible
  score for an alignment of ANY LENGTH ending at
  those coordinates
• Trace pathway back from highest scoring cell
• This cell can be anywhere in the array
• Align highest scoring segment

GCC-UCG GCCAUUG
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Differences

• Needleman-Wunsch
• 1. Global alignments
• 2. Requires alignment score for a pair of
  residues to be gt0
• 3. No gap penalty required
• 4. Score cannot decrease between two cells of a
  pathway

• Smith-Waterman
• 1. Local alignments
• 2. Residue alignment score may be positive or
  negative
• 3. Requires a gap penalty to work effectively
• 4. Score can increase, decrease or stay level
  between two cells of a pathway