Classifying Pseudoknots Kyle L. Spafford

Classifying Pseudoknots -- Kyle Spafford 2 Recap – What’s a pseudoknot again? Substructure with non- nested base pairings Makes RNA secondary structure prediction NP- complete Looks pretty simple…

Classifying Pseudoknots -- Kyle Spafford 3 Not so simple... Quite a complex space Some simpler examples  Should they be treated as equals?

Classifying Pseudoknots -- Kyle Spafford 4 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

Classifying Pseudoknots -- Kyle Spafford 5 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

Classifying Pseudoknots -- Kyle Spafford 6 My Project Examined 3 approaches to classifying pseudoknots Looked at prevalence results for what’s been found in nature Formed an argument which explains which approach should be used in different scenarios

Classifying Pseudoknots -- Kyle Spafford 7 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.

Classifying Pseudoknots -- Kyle Spafford 8 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

Classifying Pseudoknots -- Kyle Spafford 9 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

Classifying Pseudoknots -- Kyle Spafford 10 Dual Graphs (from Gan et al) Represent RNA SS’s as dual graphs –Vertex - stem –Edge – single strand that may occur in segments, connects other secondary elements

Classifying Pseudoknots -- Kyle Spafford 11 Dual Graphs Classification idea – work with topological characteristics from dual graphs

Classifying Pseudoknots -- Kyle Spafford 12 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

Classifying Pseudoknots -- Kyle Spafford 13 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

Classifying Pseudoknots -- Kyle Spafford 14 Bottom-Up Start basic – bonds –Orthodox or knotted Hairpin – P 2 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

Classifying Pseudoknots -- Kyle Spafford 15 Knot-Components Optional second superscript when non-unique (double hairpin vs. pseudotrefoil

Classifying Pseudoknots -- Kyle Spafford 16 Top-Down

Classifying Pseudoknots -- Kyle Spafford 17 Knot-component Pros –Precise biological information –No overlap (like Condon’s system) –Mapping to Condon’s categories Cons –High learning curve –Not so easy to implement –Mapping has loss of specificity

Classifying Pseudoknots -- Kyle Spafford 18 A Brief Word on Prevalence Most pseudoknots in nature are P 5 and below Probability of finding more complex pseudoknots drops almost exponentially as superscript grows –Exception: Group II introns

Classifying Pseudoknots -- Kyle Spafford 19 When to use each system Condon’s Patterns – Large scale analysis Gan’s Dual Graphs – When you need a lot of biological information (including substructures) Rodland’s Knot-Components – Any other time

Classifying Pseudoknots -- Kyle Spafford 20 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 Rodland’s knot- component system

Classifying Pseudoknots -- Kyle Spafford 21 Thank You Questions? Dying to read the paper?