1. RNA Secondary Structure Prediction
Dynamic Programming Approaches
Sarah Aerni

2. Outline
RNA folding
Dynamic programming for RNA secondary structure prediction

3. RNA Basics RNA bases A,C,G,U Canonical Base Pairs A-U G-C
Bases can only pair with one other base.
Image:

4. Basics of RNA Structure

5. RNA Secondary Structure
Pseudoknot
Stem
Interior Loop
Single-Stranded
Bulge Loop
Junction (Multiloop)
Hairpin loop
Image– Wuchty

6. Nesting

7. Circle Plot All loops must have at least 3 bases in them
Images – David Mount
Linear RNA strand folded back on itself to create secondary structure
Circularized representation uses this requirement
Arcs represent base pairing
All loops must have at least 3 bases in them
Equivalent to having 3 base pairs between all arcs
Exception: Location where the beginning and end of RNA come together in circularized representation

8. Pseudoknots

9. Trouble with Pseudoknots
Images – David Mount
Pseudoknots cause a breakdown in the Dynamic Programming Algorithm.
In order to form a pseudoknot, checks must be made to ensure base is not already paired – this breaks down the recurrence relations

10. Base Pair MaximizationC C
Problem:
Find the RNA structure with the maximum (weighted) number of nested pairings A G C C G G C A U A U U A A A C U G U G A C A C A A A A C U C G G C U G U G U C G G A G C C U U G A G G C G G A G C G A U G C A U C A A U U G A
ACCACGCUUAAGACACCUAGCUUGUGUCCUGGAGGUCUAUAAGUCAGACCGCGAGAGGGAAGACUCGUAUAAGCG

11. Base Pair Maximization – Dynamic Programming Algorithm
S(i,j) is the folding of the subsequence of the RNA strand from index i to index j which results in the highest number of base pairs
Simple Example:
Maximizing Base Pairing
Bifurcation
Unmatched at i
Umatched at j
Base pair at i and j
Images – Sean Eddy

12. S(i, j – 1) S(i + 1, j) S(i + 1, j – 1) +1
Base Pair Maximization – Dynamic Programming Algorithm
Alignment Method
Align RNA strand to itself
Score increases for feasible base pairs
Each score independent of overall structure
Bifurcation adds extra dimension
S(i, j – 1)
S(i + 1, j)
Initialize first two diagonal arrays to 0
Fill in squares sweeping diagonally
Bases cannot pair, similar
to unmatched alignment
Bases can pair, similar
to matched alignment
Dynamic Programming – possible paths
S(i + 1, j – 1) +1
Images – Sean Eddy

13. k = 0 : Bifurcation max in this case
Base Pair Maximization – Dynamic Programming Algorithm
Alignment Method
Align RNA strand to itself
Score increases for feasible base pairs
Each score independent of overall structure
Bifurcation adds extra dimension
k = 0 : Bifurcation max in this case
S(i,k) + S(k + 1, j)
Reminder:
For all k
S(i,k) + S(k + 1, j)
Reminder:
For all k
S(i,k) + S(k + 1, j)
Initialize first two diagonal arrays to 0
Fill in squares sweeping diagonally
Bases cannot pair, similar
Bases can pair, similar
to matched alignment
Dynamic Programming – possible paths
Bifurcation – add values for all k
Images – Sean Eddy

14. Example

15. Base Pair Maximization - Drawbacks
Base pair maximization will not necessarily lead to the most stable structure
May create structure with many interior loops or hairpins which are energetically unfavorable
Not biologically reasonable

16. References
How Do RNA Folding Algorithms Work?. S.R. Eddy. Nature Biotechnology, 22: , 2004.