1. RNA Secondary Structure Prediction
Dong Xu
Computer Science Department
271C Life Sciences Center
1201 East Rollins Road
University of Missouri-Columbia
Columbia, MO
(O)

2. Final Report
Due on Dec. 8.
A numerical score (0-15) will be assigned for based on
Clear formulation of the project (2)
Method (4)
Significant results achieved (4)
Discussion (3)
Writing of the project (2)

3. Final Presentation Preferably shown in powerpoint file, pdf is fine
Preferably 20 minutes (up to 25 min), plus 5min for questions
15 points for the presentation (introduction, methods, results, discussions)
15 points for software demo
Implementation of the software
Major functionalities
Documentation
Perform a test run

4. Presentation Evaluation
A numerical score (0-15) will be assigned based on
Did the student put enough effort? (3)
Is the work interesting or novel? (3)
Is the method technically sound? (3)
Is the discussion insightful? (3)
Is the presentation clear? (3)

5. Software Demo A numerical score (0-15) will be assigned based on
Whether the program can run using actual biological data (3)
Documentations (3)
Whether it is easy to use (3)
Performance in accuracy (3)
Performance in computing time and memory usage (3)

6. Outline RNA Secondary Structure Comparative Approach
Base-Pair Maximization
Free Energy Minimization
Local Structure Prediction

7. RNA Types siRNA, short interfering RNA; miRNA, microRNA;
small temporal RNA stRNA; snoRNA small nucleolar RNA ;
snRNA: Small nuclear RNA.

8. Features of RNA
RNA: polymer composed of a combination of four nucleotides
adenine (A)
cytosine (C)
guanine (G)
uracil (U)

9. Features of RNA
G-C and A-U form complementary hydrogen bonded base pairs (canonical Watson-Crick)
G-C base pairs being more stable (3 hydrogen bonds) A-U base pairs less stable (2 bonds)
non-canonical pairs can occur in RNA -- most common is G-U

10. RNA Pairs
A-U
G-C
G-U

11. RNA Structure Hierarchy
Primary structure:
5’ ACCACCUGCUGA 3’
Secondary Structure
Tertiary structure:

12. Secondary Structure Categories
Hairpin loop
Hairpin loop
Stem
Stem
Internal loop
Internal loop
Bulge loop
Bulge loop
Pseudoknots

13. tRNA structure

14. Circular Representation

15. Assumptions in Secondary Structure Prediction
Most likely structure similar to energetically most stable structure
Energy associated with any position is only influenced by local sequence and structure
Structure formed does not produce pseudoknots

16. Exceptions Pseudoknot Kissing hairpins Hairpin-bulge
Do not obey “parentheses rule”

17. Outline RNA Secondary Structure Comparative Approach
Base-Pair Maximization
Free Energy Minimization
Local Structure Prediction

18. Inferring Structure By Comparative Sequence Analysis
First step is to calculate a multiple sequence alignment
Requires sequences be similar enough so that they can be initially aligned
Sequences should be dissimilar enough for correlated mutation to be detected

19. Mutual Information fxi : frequency of a base in column i
fxixj : joint (pairwise) frequency of a base pair between columns i and j
Information ranges from 0 and 2 bits
If i and j are uncorrelated, mutual information is 0

20. Mutual Information Plot

21. Mutual Information Plot

22. Outline RNA Secondary Structure Comparative Approach
Base-Pair Maximization
Free Energy Minimization
Local Structure Prediction

23. Dot Plot

24. Base-Pair Maximization
Find structure with the most base pairs
Efficient dynamic programming approach to this problem introduced by Nussinov (1970s).
Four ways to get the best structure between position i and j from the best structures of the smaller subsequences

25. Nussinov Algorithm
1)      Add i,j pair onto best structure found for subsequence i+1, j-1
2)      add unpaired position i onto best structure for subsequence i+1, j
3)      add unpaired position j onto best structure for subsequence i, j-1
4)      combine two optimal structures i,k and k+1, j

26. Dynamic Programming - 1
Notation:
e(ri,rj) : free energy of a base pair joining ri and rj
S(i,j) : optimal free energy associated with segment ri…rj

27. Dynamic Programming - 2 i is unpaired, added on to
a structure for i+1…j
S(i,j) = S(i+1,j)
j is unpaired, added on to
a structure for i…j-1
S(i,j) = S(i,j-1)

28. Dynamic Programming - 3 i j paired, but not to each other;
the structure for i…j adds together
structures for 2 sub regions,
i…k and k+1…j
S(i,j) = max {S(i,k)+S(k+1,j)}
i j paired, added on to
a structure for i+1…j-1
S(i,j) = S(i+1,j-1)+e(ri,rj)
i<k<j

29. Dynamic Programming - 4
Since there are only four cases, the optimal score S(i,j) is just the
maximum of the four possibilities:

30. j A U C G
Initialisation:
No close basepairs i

31. j A U C G 2 3 1 Propagation: C5….U9 : C5 unpaired: S(6,9) = 02 3 1
Propagation:
C5….U9 :
C5 unpaired:
S(6,9) = 0
U10 unpaired:
S(5,8)=0
C5-U10 paired
S(6,8) +e(C,U)=0
C5 paired, U10 paired:
S(5,6)+S(7,9)=0
S(5,7)+S(8,9)=0

32. j A U C G 2 3 5 6 1 Propagation: C5….G11 : C5 unpaired: S(6,11) = 32 3 5 6 1
Propagation:
C5….G11 :
C5 unpaired:
S(6,11) = 3
G11 unpaired:
S(5,10)=3
C5-G11 paired
S(6,10)+e(C,G)=6
C5 paired, G11 paired:
S(5,6)+S(7,11)=1
S(5,7)+S(8,11)=0
S(5,8)+S(9,11)=0
S(5,9)+S(10,11)=0

33. j A U C G 2 3 5 6 8 10 12 1
Propagation: i

34. j A U C G 2 3 5 6 8 10 12 1
Traceback: i

35. Final Prediction AUACCCUGUGGUAU Total free energy: -12 kcal/mol U G
C G
C U
U G
AUACCCUGUGGUAU
Total free energy: -12 kcal/mol

36. Some Notes Computational complexity: N3
Does not work with pseudo-knot (would invalidate DP algorithm)
Methods that include pseudo knots:
Rivas and Eddy, JMB 285, 2053 (1999)
These methods are at least N6

37. Outline RNA Secondary Structure Comparative Approach
Base-Pair Maximization
Free Energy Minimization
Local Structure Prediction

38. Energy Minimization Methods
RNA folding is determined by biophysical properties
Energy minimization algorithm predicts the correct secondary structure by minimizing the free energy (G)
G calculated as sum of individual contributions of:
loops
base pairs
secondary structure elements
Energies of stems calculated as stacking contributions between neighboring base pairs

39. Example for Thermodynamic Parameters

40. Calculating Best Structure
sequence is compared against itself using a dynamic programming approach
similar to the maximum base-paired structure
instead of using a scoring scheme, the score is based upon the free energy values
Gaps represent some form of a loop
The most widely used software that incorporates this minimum free energy algorithm is MFOLD.

41. How well do they perform?
Current RNA folding programs get about 60-70% of base pairs correct, on average: useful, but not yet good.
The problem is the scoring system: thermodynamic model is accurate within 5-10%, and many alternative structures are within 10%.
Possible solution: combination of thermodynamic score with comparative sequence information

42. Outline RNA Secondary Structure Comparative Approach
Base-Pair Maximization
Free Energy Minimization
Local Structure Prediction

43. RNA Motif in HIV
TAR motif:
Transactivating Response Element

44. RNA Motifs Associated with Transcription termination
Rho-independent terminator stop the transcription process via its hairpin structure

45. Algorithm in Rnall Definition 1. A “match” : canonical base pairs
Definition 2. A “mismatch”: non-canonical base pair
Definition 3. An “insertion”/“deletion”: nucleotide unpaired

46. RNA LSS in HIV
TAR (30)
DIS (260)
PolyA (82)
SD (292)
PSI (319)

47. Some RNA Resource Comparative RNA web site
RNA world
RNA page by Michael Suker
RNA structure database
(nucleic acid database)
(non canonical bases)
RNA structure classification
RNA visualisation

48. Suggested reading: Optional reading: Reading Assignments
Chapter 14 in “Current Topics in Computational Molecular Biology, edited by Tao Jiang, Ying Xu, and Michael Zhang. MIT Press ”
Optional reading: