# Structural Biochemistry/Nucleic Acid/RNA/RNA Secondary Structure

## Basis of RNA

-RNA bases: A,G,C,U
-Base Pairs: A-U, G-C
-non-canonical pairs: G-U
-Stability: G-C > A-U > G-U
-Single Stranded: strand folds upon it to form base pairs; can have a diverse form of secondary structure

## Secondary Structure

### Structure Rules

1. Base pairing stabilize the structure
2. Unpaired sections-loops destabilize the structure
3. When a base in one position changes, the base it pairs to must also change to maintain the same structure-covariation

### Representations

-Most base pairs are non-crossing base pairs: -any two pairs (i, j) and (i’, j’) -> i < i’ <j’ < j or i’ < i < j < j’

### Circular Representation

-Base pairs of a secondary structure represented by a circle
-Arc drawn for each base pairing in the structure

### Combinatorics

-The number of RNA secondary structures for the sequence: (Recurrence Relation)
S(0)=S(1)=S(2)=1
S(n+1)=S(n)+ƩS(j-1)S(n-j), (n≥2)
-There are approximately 1.3 billion RNA structures of length n is 27

### Types of regions

1) Hairpin Loop - 4 or more bases long for each loop
2) Bulge Loop - bases on one side cannot form base pairs
3) Interior Loop - bases on both sides cannot form base pairs
4) Multi Loop (Junctions) – 2 or more double stranded regions converge to form a closed structure

### Structure Prediction Methods

1) Maximize Base Pairs
-Determine set of maximal base pairs
-Align bases based on ability to pair up to determine the optical structure
-Nussinov Algorithm: 4 ways to get the optimal structure between i and j
-Find strucuter with the most base pairs: A-U and G-C
2) Minimize Energy
-Determine maximum of scores for 4 structures at a particular position
-Stacks are the dominant stabilizing force
-Energy minimization algorithm predicts the secondary structure by minimizing the free energy
-Require estimation of energy terms contributing to secondary structure
-Dynamic programming approach:
1) Initialization
2) Recursion
3) Traceback
-Does not require prior sequence alighnment
-Energy associated with any position is only influenced by local sequence and structure

## References

1. How Do RNA Folding Algorithms Work? S.R. Eddy. Nature Biotechnology, 22:1457-1458, 2004.
2. <http://en.wikipedia.org/wiki/Biomolecular_structure>