RNA Folding

Xinyu Tang

Bonnie Kirkpatrick

Overview

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

Introduction to RNA

Composition of Ribonucleic Acid

A polymer (sequence) of ribonucleoside-phosphates

Ribose (sugar) Phosphoric Acid Organic bases

– Adenine (A)– Guanine (G)– Cytosine (C)– Uracil (U)

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

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

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:

Representations of RNA

M: Multi-loop I: Internal-loop B: Bulge-loop H: hairpin-loop •: W-C pairs -: GU pairs

Representations (cont.)

Hydrogen bonds between intra-chain pairs are represented by circular arcs

All representations are equivalent

Representations (cont.)

Contact Map

A dot is placed in the ith

row and jth column of a triangular array to represent the intra-chain contact [i, j]

Previous Work

Maximum Matching Problem

Watermann and Nussinnov Algorithms– Finding the conformation with the maximum possibl

e number of intra-chain contacts– Computed using dynamic programming

Minimum Energy Problem

Zuker and Stiegler Algorithm– Predicts the native structure by finding the conformati

on 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 occurr

ences in an ensemble of all possible structures

Problem

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

Elements of the Problem

Model Sampling Pattern Node Connection Methods Analysis Techniques

Hofacker’s Paper

Chen and Dill’s Paper

Modeling RNA Folding with PRM

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 ens

emble of possible tertiary structures

Chen and Dill were able to use a