Classifying Pseudoknots

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Classifying Pseudoknots

• Kyle L. Spafford

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Recap Whats a pseudoknot again?

• Substructure with non-nested base pairings
• Makes RNA secondary structure prediction
  NP-complete
• Looks pretty simple

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Not so simple...

• Quite a complex space
• Some simpler examples ?
• Should they be treated as equals?

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Biological Motivation

• In nature, things get complicated

A) Hepatitis Delta B) Diels-Alder Ribozyme C)
Human telomerase D) Mouse mammary tumor virus E)
pea enation mosaic virus F) Simian retrovirus
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Biological Motivation

• Function of these pseudoknots?
• Viral Frameshifting
• SARS, Hep C, MMTV, some HIV
• Catalytically Active
• Genome replication
• Self-cleaving ribozymes
• Break down C-C bonds
• Some things remain a mystery
• Telomeres, aging, and cancer

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My Project

• Examined 3 approaches to classifying pseudoknots
• Looked at prevalence results for whats been
  found in nature
• Formed an argument which explains which approach
  should be used in different scenarios

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Patterns (from Condon et al)

• A pattern is a string P over some alphabet A,
  s.t. every element of A appears exactly twice, or
  not at all in P.

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Patterns

• Classification idea - Sort pseudoknots by the
  algorithm(s) that can predict them
• Algorithms from Uemura Akutsu, Rivas Eddy,
  Lyngso Pederson, Dirks Pierce
• Also, have a pseudoknot-free class

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Patterns

• Pros
• O(n) existence test and classification
• Really easy to implement
• Given a pseudoknot, if is in one of the
  categories (with high probability)
• Cons
• Not very useful for biologists

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Dual Graphs (from Gan et al)

• Represent RNA SSs as dual graphs
• Vertex - stem
• Edge single strand that may occur in segments,
  connects other secondary elements

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Dual Graphs

• Classification idea work with topological
  characteristics from dual graphs

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Dual Graphs

• Pros
• Very useful for biologists
• Topological qualities are easy to compute
• Cons
• Hard to specify in words
• Not efficient to store
• Problems with accuracy

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Knot-Components (from Rodland)

• Simplify the complex space
• Find building blocks of pseudoknots
• Describe structure in a short, precise method
• Ignore nested substructures which complicate
  things

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Bottom-Up

• Start basic bonds
• Orthodox or knotted
• Hairpin P2
• The notation
• Superscript Number of stems involved in the
  pseudoknot
• Subscript (used when not reduced) number of stem
  components replacing a single stem in reduced
  form

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Knot-Components
Optional second superscript when non-unique
(double hairpin vs. pseudotrefoil
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Top-Down
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Knot-component

• Pros
• Precise biological information
• No overlap (like Condons system)
• Mapping to Condons categories
• Cons
• High learning curve
• Not so easy to implement
• Mapping has loss of specificity

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A Brief Word on Prevalence

• Most pseudoknots in nature are P5 and below
• Probability of finding more complex pseudoknots
  drops almost exponentially as superscript grows
• Exception Group II introns

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When to use each system

• Condons Patterns Large scale analysis
• Gans Dual Graphs When you need a lot of
  biological information (including substructures)
• Rodlands Knot-Components Any other time

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Summary

• Pseudoknots range from trivially simple to
  extraordinarily complex.
• They perform a myriad of exciting biological
  roles.
• Classifying them is important in determining
  those roles.
• Almost always, stick with Rodlands
  knot-component system

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Thank You

• Questions?
• Dying to read the paper?
• kls_at_gatech.edu