Sequence Analysis

1
Sequence Analysis

• CSC 487/687 Introduction to computing for
  Bioinformatics

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Aligning Sequences

• Sequences
• Representing proteins or nucleic acid (DNA/RNA)
  molecules
• Order of amino acids (for proteins nucleotides
  for DNA/RNA) along one chain
• Sequence alignment
• The identification of residue-residue
  correspondences
• Any assignment of correspondences that preserves
  the order of residues within the sequences

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Evolutionary Basis of Sequence Alignment

• Identity Quantity that describes how much
• two sequences are alike in the strictest
  terms.
• Similarity Quantity that relates how much
• two amino acid sequences are alike.
• Homology a conclusion drawn from data
• suggesting that two genes share a common
• evolutionary history.

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Evolutionary Basis of Sequence Alignment

• Homologous sequences
• Related by evolution (common ancestors)
• Alignment of homologous sequences
• Identifying relationship between the sequence
  elements
• Match up characters coming from same characters
  in ancestor

5
Alignment and Evolution

• Assume we know evolutionary history relating q
  and d
• The true alignment can be found using h as a
  template
• h GLVS T
• q GLISVT
• d GIV--T

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Alignment Evolution

• Given an alignment, several different
  evolutionary histories may be (equally) plausible
• Example
• Alignment
• q GLISVT
• d G-I-VT
• One possible history
• HGLIVT
• /\
• -gtS / \ L-gt
• / \
• qGLISVT dGIVT

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Global and Local Alignment

• Global
• Assuming that the complete sequences are the
  results of evolution from the same ancestor
  sequence
• Local
• Align segments of the sequences so that the
  segments are evolutionarily related

8
Pairwise sequence alignments Vs Multiple sequence
alignments

• Pairwise sequence alignment two sequence
• Multiple sequence alignments a mutual alignment
  of more than two sequences

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The dotplot
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The dotplot

• Captures not only the overall similarity of two
  sequences, but also the complete set and relative
  quality of different possible alignments
• Diagonal ?
• Horizontal ? a gap is introduced in the sequence
  indexing the rows
• Vertical ? a gap is introduced in the sequence
  indexing the columns

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Dotplots and alignments

• A path through the dotplot is as an edit script
• Each move performs an operation ? a
  substitution, an insertion or a deletion.
• When the end of the path is reached, the effect
  will change one sequence into the other.
• Several different sequences of edit operations
  may convert one string to the other in the same
  number of steps.

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Dotplots and alignments

• Although a sequence of edit operations derived
  from an optimal alignment may correspond to an
  actual evolutionary pathway
• Impossible to prove that it does.
• The larger the edit distance, the larger the
  number of reasonable evolutionary pathways
  between two sequences.

13
Dotplots and alignments

• The dotplots between pairs of proteins with
  increasingly more distant relationships.
• The dotplot comparisons of the sulphydryl
  proteinase papain from papaya, with four
  homologues ? the close relative, kiwi fruit
  actinidin, the more distant relatives, human
  procathepsin L, human cathepsin B, and
  staphyloccus anueus.

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Example
15
Example
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Example
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Example
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Measures of sequence similarity

• Hamming distance ? the number of positions with
  mismatching characters.
• Edit distance ? the minimum number of edit
  operations required to change one string into
  the other.

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What is an Alignment?

• A global alignment of two sequences A and B
  contains all characters of A and B in the same
  order
• one symbol from A can be aligned with one symbol
  from B
• a symbol can be aligned with a blank, written as
  -
• two blanks cannot be aligned
• Every symbol from A and from B must be aligned
• Example
• AINVEST, BINTEREST
• IN--VEST INV--EST IN-V--EST
• INTEREST INTEREST IN-TEREST

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Computing Alignments

• There exist a large number of alignments for a
  pair of sequences
• In order to use a computer to do the alignment
  process in a meaningful way, we need
• Scoring scheme mathematical way to calculate
  goodness of candidate alignments
• Search method algorithm able to identify high
  scoring alignments

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Choosing Scoring Scheme

• Scoring scheme should be
• Simple to allow for
• efficient calculation and
• search for best alignment
• Biologically meaningful (give score to
  biologically good alignments)

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Simple Scoring Scheme

• Assign score to each column in the alignment
• Columns are of the following sorts
• Alignment score sum of score over all columns
• R matrix giving score for all possible character
  pairs (e.g., all pairs of amino acid symbols)

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Alignment Score Example

• R identity matrix identical characters score1,
  unequal 0,
• g1
• ALIGN1
• V - E I T G E I S T
• P R E - T E R I - T
• 0 -1 1 -1 1 0 0 1 -1 1 Score 1
• ALIGN2
• V E I T G E I S T
• P R E T - E R I T
• 0 0 0 1 -1 1 0 0 1 Score 2

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Finding the Minimum Scoring Alignment

• Large number of possible alignments cannot
  generate all and score them to find the best
• Task align
• Aa1a2...am and
• Bb1b2...bn

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Independence Between Sub-alignments

• Observations
• The score of the alignment up to and including
  character i from A and character j from B is
  independent of how the rest of the sequences are
  aligned
• The best solution to (i,j) can be locked, its
  score recorded in Di,j
• Dm,n is the score of the best global alignment
• Amenable to dynamic Programming

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Dynamic programming algorithm

• Individual edit operations include
• Substitution of bj for ai ? represented (ai, bj)
• Deletion of ai from sequence A? represented
  (ai,?)
• Deletion of bj from sequence B? represented
  (?,bj)

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Dynamic programming algorithm

• A cost function d is defined on edit operations
• d(ai, bj)cost of a mutation in an alignment in
  which position i of sequence A corresponds to
  position j of sequence B
• d(ai,?) or d(? bj) cost of a deletion or
  insertion
• The minimum weighted distance between sequences A
  and B as
• D(A,B)min (?d(x,y))

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Three Alternative Alignment Ends

• The alignment between a1a2...ai and b1b2...bi
  ends in one of three ways

a1..i-1 b1..j
ai -
To calculate Di,j we pick the one thatgives the
lowest cost
a1..i-1 b1..j-1
ai bj
a1..i b1..j-1
- bj
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Recurrence Relation
Assume that Di-1,j, Di-1,j-1, Di,j-1 have been
calculated already
a1..i-1 b1..j
ai -
d(ai,?)
a1..i-1 b1..j-1
ai bj
d(ai,bj)
a1..i b1..j-1
d(?,bj)
- bj
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Basis of Recursion

• Align empty string to string of length i (resp.
  j) can be done by aligning to i (resp. j)
  blanks

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Calculating Score of Best Alignment Using Matrix
H matrix
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Time Complexity

• Sequences of lengths n and m
• Two sequences of length l