1. Prediction of Secondary Structure of RNA
Swetha Nandyala

2. Overview Introduction How RNA Secondary Structure is obtained ?
Various types of loops possible in RNA Secondary Structure
Motivation
Resource
Implements the Algorithms to be Understood
Algorithm
Nussinovs RNA Folding
Example

3. RNA Secondary Structure
Primary Structure of RNA : A sequence of the bases A,G,C and U.
Due to hydrogen bonds, the bases of the RNA may form base pairs
a) Watson-Click base pairs:
G≡C : formed by a triple hydrogen bond
A=U : formed by a double hydrogen bond
b) Wooble base pairs:
G-U : formed by single hydrogen bond
Secondary Structure of an RNA : The W-C and Wooble base pairs occurring in an RNA Fold

4. Structural Features Of RNA
Hairpin Loop
Multibranched Loop
Stem
Bulge
Internal Loop
External Base

5. MOTIVATION Why is Prediction of RNA Secondary Structure important?
Tertiary Structure Prediction
Identify highly conserved Motifs
Design and Testing of Pharmaceutical products.

6. Algorithm Input an alignment of RNA sequence Output
single common structure for the sequence
The Model
The evolutionary model (Nussinovs)
The SCFG

7. Resource:
Questions:
Is this the only Secondary Structure possible? No
How to distinguish the correct structure?
Need for both a function and an algorithm arises at this point, Hence Dynamic Programming
Key Idea of Nussinovs algorithm
Recursive and only 4 possible ways

8. Nussinovs’ Dynamic Programming
j-1 j i
Unpaired base i
Unpaired base j j
j-1
i+1 i j k
k+1 i j
Bifurcation
paired i,j

9. Energy Matrix
E(i,j)=maximum energy for sub chain starting at i and ending at j and
s(ri,rj)=energy of pair ri, rj(rj=base at position j)
i is unpaired E(i,j)=E(i+1,j)
j is unpaired E(i,j)=E(i,j-1)
i,j is paired E(i,j)=E(i+1,j-1)+s(ri,rj)
Bifurcation E(i,j)=E(i,k)+E(k+1,j)

10. RNA Secondary Structure Algorithm
Given: RNA Sequence x1,x2,x3…….,xL
Initialization:
E(i,i-1)=0 for i=2 to L
E(i,i)=0 for i=1 to L
Recursion:
for n=2 to L //iteration over length
E(i,j)=max{ E(i+1,j),
E(i,j-1),
E(i+1,j-1)+s(ri,rj)
max i<k<j {E(i,k)+E(k+1,j)} }

11. Example Let s(ri,rj)=1 if ri, rj form a base pair and 0 otherwise
Input : GGGAAAUCC j
E(i,j)=maximum energy conformation for sub chain from i to j G A U C i
Here we should have max energy for AAAUC

12. GGG (i=1,j=3)
max { 0, 0,
0+s(G,G)
}=0 G A U C 1
AAU (i=5,j=7)
max {0, 0,
0+s(A,U)
}=1

13. Recovering the Structure
Main difference to sequence Alignment-We are tracing back a tree like structure not a single optimal path (Bifurcation introduces branch points)
Method 1: Leave pointers as you compute the table:for each element of the table store(atmost two) pointers the subsequences used in solution
Method2: Recover history based on numerical values in the table
-Stacking- check value along diagonal
-Bifurcation-find k such that E(i,k)+E(k+1,j)=E(i,j)

14. Trace back Algorithm Initialization: Push(1,L) onto stack Recursion:
Repeat until stack is empty
pop(i,j)
if i>=j continue;
else if E(i+1,j)=E(i,j) push(i+1,j)
else if E(i+1,j)=E(i,j) push(i,j-1)
else if E(i+1,j)=E(i,j)
push(i,j)
record i,j base pair
push(i+1,j-1)
else for k=i+1 to j-1 : if E(i,k)+E(k+1,j)=E(i,j);
push(k+1,j)
push(i,k)
break

15. G A U C 1 2 3
A A
A • U
G • C G

16. Problems and Improvements
Advantages:
Accurate Output can be obtained if able to provide certain basic details
Cost: O(n3)
Success rate was 70%
Main Drawbacks:
Hairpin loops could be of any length.
Developed in 1978.Therefore, it is not state of art today, but is a good starting point
Improvements:
Minimization Gibbs’ Free energy
SCFGs’

17. References: http://ludwig-sun2.unil.ch/~bsondere/nussinov/
Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids- R.Durbin, S.Eddy, A.Korgh, G.Mitchison. University of Cambridge Press,1998

18. THANK YOU