Introduction to Sequence Alignment

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Introduction to Sequence Alignment
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Why Align Sequences?

• Find homology within the same species
• Find clues to gene function
• Practical issues in experiments
• Find homology in other species
• Gather info for an evolutionary model
• Gene families

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The Most Visual Way of Aligning Two Sequences
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Dot Matrix Alignment
CACTAGGC AGCTAGGA
Gibbs McIntyre (1970)
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Dot Matrix Alignment
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• Has many variations
• Can be used to find sequence repeats
• Find self-complimentary subsequences of RNA to
  predict secondary structure
• Still used today

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Alignment using Dynamic Programming
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An Example

• GCGCATGGATTGAGCGA
• TGCGCCATTGATGACCA
• A possible alignment
• -GCGC-ATGGATTGAGCGA
• TGCGCCATTGAT-GACC-A

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Alignments

• -GCGC-ATGGATTGAGCGA
• TGCGCCATTGAT-GACC-A
• Three elements
• Perfect matches
• Mismatches
• Gaps

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Choosing Alignments

• There are many possible alignments
• For example, compare
• -GCGC-ATGGATTGAGCGA
• TGCGCCATTGAT-GACC-A
• to
• ------GCGCATGGATTGAGCGA
• TGCGCC----ATTGATGACCA--
• Which one is better?

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Scoring Rule

• Example Score
• ( matches) ( mismatches) ( gaps) x 2

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Example

• -GCGC-ATGGATTGAGCGA
• TGCGCCATTGAT-GACC-A
• Score (1x13) (-1x2) (-2x4) 3
• ------GCGCATGGATTGAGCGA
• TGCGCC----ATTGATGACCA--
• Score (1x5) (-1x6) (-2x11) -23

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Optimal Alignment

• Optimal alignment is achieved at best similarity
  score d, thus is determined by the scoring rule

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Finding the Best Alignment Score

• The additive form of the score allows to perform
  dynamic programming to find the best score
  efficiently
• Guaranteed to find the best alignment

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Assume that an Optimal Score Exists

• d(s,t) Optimal score for globally aligning s
  and t

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The Idea

• The best alignment that ends at a given pair of
  bases the best among best alignments of the
  sequences up to that point, plus the score for
  aligning the two additional bases.

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Dynamic Programming

• Consider the best alignment score of two
  sequences s, t at base/residue i1, j1,
  respectively

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Dynamic Programming

• The best alignment must be in one of three cases
• 1. Last position is (si1,tj 1 )
• 2. Last position is (-, tj 1 )
• 3. Last position is (si 1,-)

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Dynamic Programming

• The best alignment must be in one of three cases
• 1. Last position is (si1,tj 1 )
• 2. Last position is (-, tj 1 )
• 3. Last position is (si 1,-)

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Dynamic Programming

• The best alignment must be in one of three cases
• 1. Last position is (si1,tj 1 )
• 2. Last position is (-, tj 1 )
• 3. Last position is (si 1,-)

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Dynamic Programming
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Dynamic Programming

• Of course, we first need to handle the base cases
  in the recursion

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Dynamic Programming
A G C A A A C
We fill the matrix using the recurrence rule
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Dynamic Programming
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Dynamic Programming
Conclusion d(AAAC,AGC) -1
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Reconstructing the Best Alignment
AAAC AG-C
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More than one best alignment
AAAC A-GC
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Complexity

• Space O(mn)
• Time O(mn)
• Filling the matrix O(mn)
• Backtrace O(mn)

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Needleman Wunsch (1970)

• A General Method Applicable to the Search for
  Similarities in the Amino Acid Sequence of Two
  Proteins
• J. Mol. Biol. 48 443-453

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Local Alignment

• We just introduced global alignment
• Now introduce local alignment
• A local Alignment between sequence s and sequence
  t is an alignment with maximum similarity between
  a substring of s and a substring of t.

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Smith and Waterman (1981)

• Identification of Common Molecular Subsequences
  
• J. Mol. Biol., 147195-197

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Best-aligned Subsequences
The best score or start over
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• Note different scoring rule

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Best aligned subsequences