Suffix trees

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Suffix trees

• ALGGEN Algorithmics and genetics group
• Dep. Llenguatges i Sistemes Informàtics
• Universitat Politècnica de Catalunya

Dr. Xavier Messeguer
http//www.lsi.upc.es/alggen
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Suffix trees
Given string ababaas
Suffixes
3 abaas
1 ababaas
4 baas
2 babaas
What kind of queries?
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Queries on Suffix trees

• Does the sequence ababaas contain any ocurrence
  of patterns abab, aab, and ab?

• Find repeats within the sequence ababaas.

What about MUMs?
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Search for MUMs
Given strings ababaabs and aabaat
1st Bottom-up traversal
(Through the tree)
List of UM aab,abaa,baa.
2nd Search for maximals
(through the list of UM)
MUMs aab,abaa.
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Suffix tree implementation
Given sequence ababaas
E.Ukkonen implementation MUMER, MGA
MALGEN implementation
On-line linear insertion algorithm!
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Meaning of suffix-links
?
a?
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Suffix links
Given Suffix tree of ababaas
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Search for MUMs
Given Suffix tree of ababaas
and the sequence
b b a b b a a a b a a ...

• bab

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Search for MUMs
Given Suffix tree of ababaas
and the sequence
b b a b b a a a b a a ...

• bab

Quadratic cost!

• baa

• aa

• aa

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Search for MUMs
Linear cost!
Quadratic cost!

• abaa

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Search for MUMs
Linear cost
Quadratic cost!

• baa

• aa

Two improvements

• Decrease quadratic cost!

• Useless candidates!

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Search for MUMs
Given Suffix tree of ababaas
and the sequence
b b a b b a a a b a a ...
Linear cost

• bab

Quadratic cost!

• abaa

• baa

• aa

Two improvements

• Decrease quadratic cost!

?

• Useless candidates!

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Tsuffix tree
Given Suffix tree of ababaas
and the sequence
b b a b b a a a b a a ...
Linear cost

• bab

• abaa

Quadratic cost!
Two improvments
?

• Decrease quadratic cost!

?

• Useless candidates!

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Searching MUMs on-line
Number of the leaf
Length of the MUM
First character into the second sequence
2, 3(bab), 2
b b a b b a a a b a b b
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Searching MUMs on-line
4, 3(baa), 5
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Searching MUMs on-line
4, 3(baa), 5
5, 2(aa), 6
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Searching MUMs on-line
4, 3(baa), 5
5, 2(baa), 6
1, 4(abab), 8
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Methodology for a preview with two genomes

• Construct the TSuffix of the first genome

• Search the MUMs respect to the other genome

Construction of TSuffix tree
Reading the second sequence
Only one TSuffix tree
-50
What about more genomes?
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Computational and biological background (3)
Chlamydophila pneumoniae AR39 1.247420bps Chlamyd
ia pneumoniae 1.247.805 Chlamidia muridarum
1.084.689bps Chlamidia trachomatis1057413bps
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Alignment revisited
Pyrococcus abyssis 1.790.334 Pyrococcus
horikoshu 1.763.341 bps