Text Comparison of Genetic Sequences

1
Text Comparison of Genetic Sequences

• Shiri Azenkot
• Pomona College
• DIMACS REU 2004

2
Comparing Two Strings

• Definition A string is a set of consecutive
  characters.

• Examples
• hello world
• 0123456
• DNA sequences
• text file

3
Comparing Two Strings

• If X and Y are strings, how similar are they?
• Edit distance, d(X, Y) smallest number of
  operations needed to make X look like Y.
• Allowed operations
• Insert a character
• Delete a character
• Replace a character
• Running time O(mn) with a dynamic programming
  algorithm

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Comparing Two Strings

• If X and Y are strings, how similar are they?
• Edit distance, d(X, Y) smallest number of
  operations needed to make X look like Y.

X abcdef Y defabc d(X, Y) ? operations

5
Comparing Two Strings

• If X and Y are strings, how similar are they?
• Edit distance, d(X, Y) smallest number of
  operations needed to make X look like Y.

X bcdef Y defabc d(X, Y) ? operations
1
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Comparing Two Strings

• If X and Y are strings, how similar are they?
• Edit distance, d(X, Y) smallest number of
  operations needed to make X look like Y.

X cdef Y defabc d(X, Y) ? operations
2
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Comparing Two Strings

• If X and Y are strings, how similar are they?
• Edit distance, d(X, Y) smallest number of
  operations needed to make X look like Y.

X def Y defabc d(X, Y) ? operations
3
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Comparing Two Strings

• If X and Y are strings, how similar are they?
• Edit distance, d(X, Y) smallest number of
  operations needed to make X look like Y.

X defa Y defabc d(X, Y) ? operations
4
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Comparing Two Strings

• If X and Y are strings, how similar are they?
• Edit distance, d(X, Y) smallest number of
  operations needed to make X look like Y.

X defab Y defabc d(X, Y) ? operations
5
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Comparing Two Strings

• If X and Y are strings, how similar are they?
• Edit distance, d(X, Y) smallest number of
  operations needed to make X look like Y.

X defabc Y defabc d(X, Y) 6 operations
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Does this seem too high?
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Edit Distance with Moves

• d(X, Y) smallest number of operations to make X
  look like Y.
• New operation move a substring

X abcdef Y defabc d(X, Y) 1
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Edit Distance with Moves

• d(X, Y) smallest number of operations to make X
  look like Y.
• New operation move a substring
• Some applications
• Computational biology DNA sequences
• Text editing
• Webpage updating

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Edit Distance with Moves

• Edit Sensitive Parsing (ESP) Algorithm
• Parse each string into a 2-3 tree
• Compare nodes (substrings) of the trees to
  compute edit distance approximation

• The problem is NP-hard
• Algorithm approximates d(X, Y) deterministically
• Run time O(n log n)

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Edit Distance with MovesAlgorithm

• Parse each string into a 2-3 tree
• Every node represents a substring
• X bagcabagehead

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Edit Distance with MovesAlgorithm

• Parse each string into a 2-3 tree
• Every node represents aa substring
• Y cabageheadbag

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Edit Distance with MovesAlgorithm

• Compare nodes (substrings) of the trees to
  compute edit distance approximation
• 2.1 Find frequencies of occurrence of each
  substring.
• X

b
a
g
c
a
b
a
g
e
h
e
a
d
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Edit Distance with MovesAlgorithm

• Compare nodes (substrings) of the trees to
  compute edit distance approximation
• 2.1 Find frequencies of occurrence of each
  substring.
• Y

caba gehea dbag
1 1 1
ca ba geh ea db ag
1 1 1 1 1
1
a
c
a
a
e
h
e
a
b
g
b
g
d
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Edit Distance with MovesAlgorithm

• Compare nodes (substrings) of the trees to
  compute edit distance approximation
• 2.1 Find frequencies of occurrence of each
  substring.
• 2.2 Subtract characteristic vectors to get
  approximation for d(X, Y)

Bagca bagehead
caba gehea dbag
-
1 1
1 1 1
ca ba geh ea db ag
bag ca ba geh ead
1 1 1 1 1 1
1 1 1 1 1
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Edit Distance with MovesAlgorithm

• Compare nodes (substrings) of the trees to
  compute edit distance approximation
• 2.1 Find frequencies of occurrence of each
  substring.
• 2.2 Subtract characteristic vectors to get
  approximation for d(X, Y)

Actual edit distance with moves?
1
d(bagcabagehead, cabageheadbag)
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Edit Distance with Moves

• Goals for this project
• Implement this algorithm
• Test algorithm on DNA sequences
• Questions to think about
• How accurate is the approximation?
• How applicable is this technique for comparing
  large biological sequences?
• This algorithm finds repeating structures within
  the sequences when comparing them. Do these
  structures have significance?
• Do such structures exist for real sequences?

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Acknowledgements

• Mentor Graham Cormode, DIMACS Postdoc
• DIMACS REU 2004
• References
• Benedetto, D., Caglioti E., Loreto V., Language
  Trees and Zipping. Physical Review Letters, 2002
• Cormode, G., Muthukrishnan, S., The String Edit
  Distance Matching Problem with Moves.