This document discusses RNA secondary structure prediction. It begins by defining RNA and its primary and secondary structures. The problem of predicting secondary structure given a primary sequence is introduced. Approaches include physical/chemical experiments and computational prediction using a single sequence. The Nussinov and Zuker algorithms are described. Nussinov finds the structure with maximum base pairs using dynamic programming. Zuker finds the minimum free energy structure also using dynamic programming. Addressing pseudoknots and other interactions is discussed as future work.

1. RNA Secondary Structure
Prediction
C SC 550 - Spring 2012
Muhammad J. Alam
Sumin Byeon

2. RNA
Ribonucleic acid
Single-stranded molecule
Consists of nucleotides
Each nucleotide contains
a base (A, C, G, U)

3. RNA Structures
Primary structure:
Linear sequence of
nucleotide bases
Secondary structure:
Hydrogen bonds
between bases forming
base pairs

4. RNA Structures
Hairpin loop
Stacked pair
Internal loop
Bulge
Multi loop

5. Problem Definition
Input: primary structure of an RNA
Goal: to predict the secondary structure
Given a primary structure of an RNA, find a secondary
structure that maximizes the number of base pairs

6. Practical Applications
Function classification
Evolutionary studies
Pseudogene detection

7. Different Approaches
Physical methods (Kim et al)
X-ray diffraction, Nuclear Magnetic Resonance (NMR)
Chemical/enzymatic methods (Ehresmann et al)
Mutational analysis (Tang and Draper)

8. Prediction with
Sequence Only
Structure prediction based on multiple RNA
sequences which are structurally similar
(Sankoff, Gary and Stormo)
Structure prediction based on a single RNA
sequence
Nussinov Folding Algorithm, Zuker Algorithm

9. Assumptions
Three base pairs
(A-U, C-G, G-U)
One base forms at most one base pair
Pseudoknots do not occur

10. Pseudoknots
c
a u
g
a c g u g u

11. Pseudoknots
c
a u
g
a c g u g u

12. Nussinov Folding
Algorithm
...
1 2 n
Case 1: (1) and (n) form a pair
Case 2: There is (k) that is not crossed by any pair
where 1 < k < n

13. Nussinov Folding
Algorithm
...
1 2 n
Case 1: (1) and (n) form a pair
V(1, n) = V(2, n-1) + δ(S[1], S[n])

14. Nussinov Folding
Algorithm
...
1 2 n
Case 1: (1) and (n) form a pair
V(1, n) = V(2, n-1) + δ(S[1], S[n])
⇢
1, if(x, y) 2 (a, u), (u, a), (c, g), (g, c), (g, u), (u, g)
(x, y) =
0, otherwise

15. Nussinov Folding
Algorithm
...
1 2 k n
Case 1: (1) and (n) form a pair
Case 2: There is (k) that is not crossed by any pair
where 1 < k < n
V(1, n) = V(1, k) + V(k+1, n)

16. Nussinov Folding
Algorithm
⇢
V (i + 1, j 1) + (S[i], S[j])
V (i, j) = max
maxik<i {V (i, k) + V (k + 1, j)}
j
i
Dynamic programming
...
...

17. Nussinov Folding
Algorithm
⇢
V (i + 1, j 1) + (S[i], S[j])
V (i, j) = max
maxik<i {V (i, k) + V (k + 1, j)}
. ..
Dynamic programming

18. Alternate Optimization Goal
Find the most stable structure: Zuker Algorithm
The hydrogen bond at a base pair tries to stabilize the
structure
Free bases inside a loop tries to disrupt the structure
Difference between these two is the destabilizing energy
Given a primary structure of an RNA, find the
secondary structure with least total energy

19. Destabilizing Energy Measure
Stacked Pair : eS(i, j)
Stabilizes the structure
eS(i, j) is negative
Hairpin : eH(i, j)
The bigger the loop, the more unstable the structure is
eH(i, j) depends on |j-i+1|

20. Destabilizing Energy Measure
Internal Loop or Bulge : eL(i, j, i', j')
The bigger the loop is and the more asymmetric the two
sides are, the more unstable is the structure
eL(i, j, i', j') depends on (|i'-i+1|+|j'-j+1|) and the asymmetry
Multi-loop : eM(i1, j1, i2, j2, ..., ik, jk)
The structure is more unstable if the loop size and k is big

21. Zuker Algorithm
Finds a secondary structure with minimum total
destabilizing energy
Uses a dynamic Programming
Running Time Exponential

22. Demo

23. Conclusion
Summary
An algorithm that finds a secondary structure
with the maximum number of base pairs
Future works
Develop an algorithm that does not make the
assumption of absence of pseudoknots
(Gary and Stormo)
Develop an algorithm that addresses base
triples and other types of base pairs

24. Thank you