1. Lecture 11. RNA Secondary Structure Prediction
The Chinese University of Hong Kong
CSCI3220 Algorithms for Bioinformatics

2. Lecture outline From sequences to functions RNA secondary structures
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

3. From Sequences to Functions
Part 1
From Sequences to Functions

4. From sequences to functions
One of the biggest questions in biology: Can one tell the function of a molecule (DNA/RNA/protein) from its sequence alone?
Sometimes, but usually not
Easier if we also know the structure
Common believe: sequence  structure  function
Of course, also depends on the environment
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

5. Molecular structures Four levels: Primary structures
The sequence
Secondary structures
First formed
Local
Tertiary structures
Global
“Folds”, “domains”
Quaternary structures
Multiple molecules
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Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

6. Primary structures
Connections (strong covalent bonds vs. weak hydrogen bonds)
Which molecules are connected
Which atoms are connected
First-level constraints of the possible structures
Example: Molecules close in primary structure must also be close in secondary, tertiary and quaternary structures
Image credit: Wikibooks
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

7. Primary structures Orientation: DNA, RNA: 5’-3’
Amino acids: Amino (N) terminus to carboxyl (C) terminus
“Residue”: what remains after a water molecule is expelled
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Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

8. DNA secondary structures
Double helix
A-DNA (dehydrated samples)
Right-handed
11bp per turn
Most common: B-DNA
10.5bp per turn
Z-DNA (some methylated DNA)
Left-handed
12bp per turn
Image credit: Wikipedia
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

9. DNA secondary structures
A-DNA
B-DNA
Z-DNA
Image credit: Wikipedia
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

10. RNA secondary structures
Largely possible to be projected onto a 2D plane
Stem/hairpin loop
Stacking pairs
Bulge
Internal loop
Multi-loop
Exterior loop
Dangling nucleotides
Less stable pair
Coaxial stacking
Image credit:
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

11. RNA secondary structures
Pseudoknots: complex structures
Image credit: Wikipedia, Sperschneider and Datta, RNA 14(4): , (2008)
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

12. Protein secondary structures
Three main types:
-helixes
-sheets
Coils (connectors)
Image credit:
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

13. DNA tertiary structures
Wrapped around nucleosomes formed by histone proteins
Condensed form at beginning of mitosis and meiosis
Image credit: Wikipedia
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

14. RNA tertiary structures
Overall structure of an RNA
More studied for RNAs that do not translate into proteins -- “non-coding” RNAs
Example: tRNA
Image credit: Wikipedia
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

15. Protein tertiary structures
Complex structures
Mainly caused by weak forces (hydrogen bonds and hydrophobic interactions)
Occasionally stronger forces (disulfide bonds between cysteines)
The CATH hierarchy
Class: composition of secondary structures
Architecture: overall shape
Topology: connection of secondary structures
Homologous: with common ancestor
Image credit: CATH
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

16. Quaternary structures
Types:
Protein subunit-protein sub-unit
Protein-protein
Protein-DNA
Protein-RNA
(Protein-small molecules)
RNA-RNA
...
Protein-subunit interaction (Hemoglobin)
Protein-DNA interaction
Image credit: Wikipedia,
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

17. Structure and function
Why function depends on structure?
Structure itself is the function (e.g., tubulins)
Binding
Complementarity of interacting structures
Formation of special bonds
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Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

18. Structure and function
Why function depends on structure? (cont’d)
Functional group (e.g., catalytic site)
Determining localization (e.g., transporter membrane proteins)
Image credit: Spudich , Science 288(5470): , 2000
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

19. RNA Secondary Structures
Part 2
RNA Secondary Structures

20. Important RNA classes Coding: Non-coding: Messenger RNAs (mRNAs)
For translating into proteins
Non-coding:
Ribosomal RNAs (rRNAs)
Parts of the ribosome complex
Transfer RNAs (tRNAs)
Delivering free amino acids during translation
Micro RNAs (miRNAs)
Binding mRNA targets to promote RNA degradation or repress translation
Small nucleolar RNAs (snoRNAs)
Guiding chemical modifications of other RNAs
Small nuclear RNAs (snRNAs)
Involved in mRNA splicing
Long non-coding RNAs (lncRNAs)
Some involved in gene regulation
...
Image source:
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

21. Importance of RNA structures
Structure is important to many classes of RNA
Examples:
tRNA
snoRNA
Image sources:
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

22. Representing RNA secondary structures
Formats: (see
Dot-bracket format
Stockholm format
...
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

23. Dot-bracket format
Sequence (nucleotides 10, 20, 30, etc. marked in red): GUGAAUGAUGAAUUUAAUUCUUUGGUCCGUGUUUAUGAUGGGAAGUAAGACCCCCGAUAUGAGUGACAAAAGAGAUGUGGUUGACUAUCACAGUAUCUGACG
Structure: (((( ((((((.(((....((((((.(((( )))).)))))).))).)))))).((((((.....)))))).)))).....
Image credit: Xihao Hu
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

24. Predicting RNA secondary structures
A basic assumption in structure predictions:
Real structure has the lowest free energy
In a simplified view, more stable bonds  lower free energy
In the case of RNA secondary structures:
Good to form more pairs
A-U
C-G
Sometimes G-U (a “wobble base pair”)
Good to form more stable pairs
C-G > A-U > G-U
Good to have stable sub-structures
E.g., stacking pairs
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

25. Predicting RNA secondary structures
We will assume there are no pseudoknots
With pseudoknots, currently there is no known algorithm that can find the optimal solution efficiently
We need two things:
A thermodynamic model for computing the free energy of a structure
A method for finding the structure with the minimum free energy
This setting sounds familiar?
A pseudoknot
Image credit: Wikipedia
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

26. Further assumptions
The free energy of a secondary structure is the sum of the free energies of the sub-structures
Not the sum of individual bases/base pairs, as one base pair can participate in multiple sub-structures
The free energies of the sub-structures are independent
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

27. Problem definition
Given an RNA sequence, find a set of base pairs so that each base is paired at most once
Example:
Input sequence: GUGAAUGAUGAAUUU...ACG
Output set of base pairs:
(7, 97)
(8, 96)
...
(18, 74)
(81, 87)
Image credit: Xihao Hu
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

28. Linear view Last update: 21-Nov-2015
... 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
... 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97
... .
... ( ( ( ( . . . . . . . ( ( ( ( ( ( . (
... ) . ) ) ) ) ) ) . ( ( ( ( ( ( . . . . . ) ) ) ) ) ) . ) ) ) )
...
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

29. Thermodynamics model
We will consider four types of sub-structures here:
Stacking pairs: both (i, j) and (i+1, j-1) are in the set
Hairpin loop: there is a pair (i, j), where all bases from i+1 to j-1 are not paired
Bulge/Internal loop: there are two pairs (i, j) and (i1, j1), where i<i1<j1<j, and all bases from i+1 to i1-1 and from j1+1 to j-1 are not paired
Multi-loop: there are pairs (i, j), (i1, j1), ..., (ik, jk), where i<i1<j1<...<ik<jk<j, and all bases from i+1 to i1-1, from j1+1 to i2-1, ..., jk-1+1 to ik-1 and from jk+1 to j-1 are unpaired
One base pair can participate in multiple structures
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

30. Stacking pairs Both (i, j) and (i+1, j-1) are in the set
E.g., i:20, j:72 1
... 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
... 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97
... i
i+1
j-1 j
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

31. Hairpin loop
There is a pair (i, j), where all bases from i+1 to j-1 are not paired
E.g., i: 81, j: 87 1
... 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
... 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97
... i j
Image source:
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

32. Bulge/Internal loop
Internal loop: There are two pairs (i, j) and (i1, j1), where i<i1<j1<j, and all bases from i+1 to i1-1 and from j1+1 to j-1 are not paired
Called a bulge if only one side has unpaired bases
E.g., i:23, j:69, i1:25, j1:67 1
... 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
... 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97
... i i1 j1 j
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

33. Multi-loop
Multi-loop: There are pairs (i, j), (i1, j1), ..., (ik, jk), where i<i1<j1<...<ik<jk<j, and all bases from i+1 to i1-1, from j1+1 to i2-1, ..., jk-1+1 to ik-1 and from jk+1 to j-1 are unpaired
E.g., k=2, i:10, j:94, i1:18, j1:74, i2:76, j2:92 1
... 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
... 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97
... i i1 j1 i2 j2 j
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

34. One possible thermodynamic model
Unpaired bases have 0 free energy and all the terms below have negative free energy
eS(i, j): for the stacking pairs (i, j) and (i+1, j-1)
eH(i, j): for the hairpin loop closed at (i, j)
eBI(i, j, i1, j1): for a bulge or internal loop enclosed by the pairs (i, j) and (i1, j1)
eM(i, j, i1, j1, ..., ik, jk): for a multi-loop that consists of the pairs (i, j), (i1, j1), ..., (ik, jk) and satisfying i<i1<j1<...<ik<jk<j
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

35. Finding the optimal structure
Dynamic programming
Let s be the RNA sequence with n nucleotides
Tables:
V(j): free energy of the optimal structure for s[1..j]
Final answer is based on V(n)
VP(i, j): free energy of the optimal structure for s[i..j] with i and j forming a pair
VBI(i, j): free energy of the optimal structure for s[i..j] with i and j forming a pair that closes a budge or internal loop
VM(i, j): free energy of the optimal structure for s[i..j] with i and j forming a pair that closes a multi-loop
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

36. Update formulas V(j): free energy of the optimal structure for s[1..j]
For j > 1, 1
... j
...
j is unpaired 1
...
j-1 j
...
j pairs with i 1
...
i-1 i
... j
...
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

37. Update formulas
VP(i, j): free energy of the optimal structure for s[i..j] with i and j forming a pair
We require that i < j
... i
... j
...
Stacking pairs
... i
i+1
...
j-1 j
...
Hairpin loop
... i
... j
...
All unpaired
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

38. Update formulas
VBI(i, j): free energy of the optimal structure for s[i..j] with i and j forming a pair that closes a budge or internal loop (i.e., i and j take the roles of i1 and j1)
... i
... j
...
Budge or internal loop
... i
... i1
... j1
... j
...
All unpaired
All unpaired
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

39. Update formulas
VM(i, j): free energy of the optimal structure for s[i..j] with i and j forming a pair that closes a multi-loop
... i
... j
...
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

40. Time and space requirements
V: n entries, each takes O(n) time
VP(i, j): O(n2) entries, each takes constant time
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

41. Time and space requirements
VBI: O(n2) entries, each takes O(n2) time
VM: O(n2) entries, each takes O(n2k) time
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

42. Time and space requirements
Summary:
V: n entries, each takes O(n) time
VP: O(n2) entries, each takes constant time
VBI: O(n2) entries, each takes O(n2) time
VM: O(n2) entries, each takes O(n2k) time
Total: O(n2) space, O(n2k+2) time
Exponential if k is unbounded
Some approximations could bring the time down to O(n4) – still huge for large n, but feasible for small or median n
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

43. Some remarks
If we allow general pseudoknots, there is currently no efficient way to find the optimal RNA secondary structure with the minimum free energy
Other methods to predict RNA secondary structures:
Conservation and covariation
High conservation: 2 and 4
Strong covariation: 1 and 5
Experimental methods (e.g., RNA footprinting)
12345
ACGGU
ACUGU
CCAGG
UCCGA
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

44. Representing pseudoknots
Without pseudoknots, RNA secondary structures can be unambiguously represented by dots (single bases) and brackets (base pairs)
What if there are pseudoknots?
Need more types of brackets 1
... 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
... 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97
... .
... ( ( ( ( . . . . . . . ( ( ( ( ( ( . (
... ) . ) ) ) ) ) ) . ( ( ( ( ( ( . . . . . ) ) ) ) ) ) . ) ) ) )
...
GAAGUACAAUAUGUAACCG
.{.((((.....))}))..
Image source:
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

45. Case Study, Summary and Further Readings
Epilogue
Case Study, Summary and Further Readings

46. Case study: Drug finding/design
Drugs are mostly chemicals with a specific structure that interacts with some biological objects
Examples:
Inhibiting the activities of an important protein of bacteria
Blocking the interaction between virus and receptors of host cell
Simulating the production of a hormone
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

47. Case study: Drug finding/design
Suppose we want to identify/design a chemical to target a particular object (e.g., a protein), we need to make sure that they have tight bindings through a process called docking
Image source:
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

48. Case study: Drug finding/design
Computational problem:
Input: a target protein and a list of chemicals
Goal: find a chemical that binds the target well
Try different locations and orientations
Binding depends on structure and chemistry
Output: One or more chemicals that bind the target well
Difficulties:
Computational complexity
Large search space for each protein-chemical combination
Need to try many chemicals
Need to ensure specificity (not to target other proteins and cause side effects)
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

49. Case study: Drug finding/design
There is a game for players to try folding proteins called FoldIt (
Score based on free energy
Real time update of scores and ranks
Players can discuss and share solutions
Resulted in some amazingly good folds as compared to automatic predictions by computer programs
Image source:
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

50. Summary Functions depend on structures Different levels of structures:
Primary (sequence)
Secondary (local)
Tertiary (global)
Quaternary (interactions)
RNA secondary structures can be predicted by dynamic programming based on a thermodynamic model
Important sub-structures
Stacking pairs
Hairpin loops
Internal loops/bulges
Multi-loops
Pseoduknots
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015

51. Further readings
Chapter 11 of Algorithms in Bioinformatics: A Practical Introduction
Speed up of algorithm
Algorithm for RNA structure perdition with pseudoknots
Free slides available
Parts VII and VIII of Fundamental Concepts of Bioinformatics
Protein folding and protein structure prediction
Docking
Last update: 21-Nov-2015
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015