1. RNA Folding Xinyu Tang Bonnie Kirkpatrick

2. Overview Introduction to RNA Previous Work Problem Hofacker ’ s Paper Chen and Dill ’ s Paper Modeling RNA Folding with PRM

3. Introduction to RNA

4. Composition of Ribonucleic Acid A polymer (sequence) of ribonucleoside- phosphates Ribose (sugar) Phosphoric Acid Organic bases – Adenine (A) – Guanine (G) – Cytosine (C) – Uracil (U)

5. Complementary Base Pairs Canonical base pairs – Watson-Crick base pairs C-G A-U Stable base pairs Hydrogen bonds – Weaker G-U wobble pair Non-canonical base pairs – Some of them stable

6. RNA Tertiary Structure A complex folding in 3-dimensions (similar to protein tertiary structure) A specific folding is referred to as a conformation Pseudo knots are considered a tertiary structure, rather than a secondary structure

7. RNA Secondary Structure A secondary structure conformation is specified by a set of intra-chain contacts (base pairs) that follow certain rules Given any two intra-chain contacts [i, j] with i < j and [i ’, j ’ ] with i ’ < j ’, then: 1) If i = i ’, then j = j ’ Each base can appear in only one contact pair 2) If i ’ < j, then i < i ’ < j ’ < j No pseudo-knots Can be represented as planar graphs:

8. Representations of RNA M: Multi-loop I: Internal-loop B: Bulge-loop H: hairpin-loop : W-C pairs -: GU pairs

9. Representations (cont.) Hydrogen bonds between intra-chain pairs are represented by circular arcs All representations are equivalent

10. Representations (cont.) Contact Map A dot is placed in the i th row and jth column of a triangular array to represent the intra- chain contact [i, j]

11. Previous Work

12. Maximum Matching Problem Watermann and Nussinnov Algorithms – Finding the conformation with the maximum possible number of intra-chain contacts – Computed using dynamic programming

13. Minimum Energy Problem Zuker and Stiegler Algorithm – Predicts the native structure by finding the conformation with the minimum energy Modified Zuker Algorithm – Generates a set of conformations that lie within some energy range of the predicted native conformation McCaskill Algorithm – Calculates the frequency of intra-chain contact occurrences in an ensemble of all possible structures

14. Problem

15. Energy Landscapes Native conformations of RNA can be predicted with accuracy But the not much is known about the kinetics and thermodynamics of the folding Energy landscapes show us what different conformations the RNA goes through as it folds

16. Elements of the Problem Model Sampling Pattern Node Connection Methods Analysis Techniques

17. Hofacker ’ s Paper

18. Chen and Dill ’ s Paper

19. Modeling RNA Folding with PRM

20. Secodary vs Tertiary Structure Tertiary structure can only be determined for tRNA Secondary structure predictions only approximate tertiary structure – For each set of intra-chain contacts, there is an ensemble of possible tertiary structures Chen and Dill were able to use a