1. molecule's structure prediction

2. Outline RNA Protein RNA folding
Dynamic programming for RNA secondary structure prediction
Protein
Secondary Structure Prediction
Homology Modeling
Protein Threading
ab-initio

3. RNA Basics RNA bases A,C,G,U Canonical Base Pairs A-U G-C G-U
2 Hydrogen Bonds
3 Hydrogen Bonds – more stable
RNA bases A,C,G,U
Canonical Base Pairs
A-U
G-C
G-U
“wobble” pairing
Bases can only pair with one other base.
Image:

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

5. RNA secondary structure representation
Circular representation:
Bacillus Subtilis RNase P RNA

6. RNA secondary structure representation
DotPlot representation
of the same Bacillus
Subtilis RNA folding:
A dot is placed to represent
a base pair

7. RNA secondary structure definition
An RNA sequence is represented as:
R = r1, r2, r3, …, rn (ri is the i-th nucleotide).
Each ri belongs to the set {A, C, G, U}.
A secondary structure on R is a set S of ordered pairs, written as i•j,
1≤i<j≤n, satisfying:

8. Computing RNA secondary structure
Working hypothesis:
The native secondary structure of a RNA molecule is the one with the minimum free energy
Restrictions:
No knots (ri,rj) , (rk,rl), i<k<j<l
No close base pairs: (ri,rj) j – i > 3 (exclude “close” base pairs)
Base pairs: A-U, C-G and G-U

9. Computing RNA secondary structure
Tinoco-Uhlenbeck postulate:
Assumption: the free energy of each base pair is independent of all the other pairs and the loop structures
Consequence: the total free energy of an RNA is the sum of all of the base pair free energies

10. Independent Base Pairs Approach
Use solution for smaller strings to find solutions for larger strings
This is precisely the basic principle behind dynamic programming algorithms!

11. RNA folding: Dynamic Programming
Notation:
e(ri,rj) : free energy of a base pair joining ri and rj
Bij : secondary structure of the RNA strand from base ri to base rj. Its energy is E(Bij)
S(i,j) : optimal free energy associated with segment ri…rj
S(i,j) = max -E(Bij) B

12. RNA folding: Dynamic Programming
There are only four possible ways that a secondary structure of
nested base pair can be constructed on a RNA strand from position i to j:
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)

13. RNA folding: Dynamic Programming
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

14. RNA folding: Dynamic Programming
Since there are only four cases, the optimal score S(i,j) is just the
maximum of the four possibilities:
To compute this efficiently, we need to make sure that the scores for
the smaller sub-regions have already been calculated
Dynamic Programming !!

15. RNA folding: Dynamic Programming
Notes:
S(i,j) = 0 if j-i < 4: do not allow “close” base pairs
Reasonable values of e are -3, -2, and -1 kcal/mole
for GC, AU and GU, respectively. In the DP procedure,
we use 3, 2, 1 (or replace max with min)
Build upper triangular part of DP matrix:
- start with diagonal – all 0
- works outward on larger and larger regions
- ends with S(1,n)
Traceback starts with S(1,n), and finds optimal path that lead there.

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

17. j A U C G 2 3 1 Propagation: C5….U9 : C5 unpaired: S(6,9) = 010 5 A U C G 2 3 1
Propagation: 1
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 5 10

18. j A U C G 2 3 5 6 1 Propagation: C5….G11 : C5 unpaired: S(6,11) = 310 A U C G 2 3 5 6 1
Propagation: 1
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 5 10

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

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

21. FINAL PREDICTION AUACCCUGUGGUAU Total free energy: -12 kcal/mol U G
C G
C U
U G
AUACCCUGUGGUAU
Total free energy: -12 kcal/mol

22. Protein structure prediction

23. The sequence-structure gap The gap is getting bigger
200000
180000
160000
140000
120000
Sequences
100000
Structures
80000
60000
40000
20000

24. The protein folding problem
The information for 3D structures is coded in the protein sequence
Proteins fold in their native structure in seconds

25. Secondary Structure Prediction
Given a primary sequence
ADSGHYRFASGFTYKKMNCTEAA
what secondary structure will it adopt ?

26. Backbone
佛爱和普西
A polypeptide chain. The R1 side chains identify the component amino acids.
Atoms inside each quadrilateral are on the same plane, which can rotate according
to angles  and  .

27. Protein structure

28. Secondary Structure Prediction Methods
Chou-Fasman / GOR Method
Based on amino acid frequencies
Machine learning methods
PHDsec and PSIpred

29. Chou and Fasman (1974) Success rate of 50%
Name P(a) P(b) P(turn) Alanine
Arginine
Aspartic Acid
Asparagine
Cysteine
Glutamic Acid
Glutamine
Glycine
Histidine
Isoleucine
Leucine
Lysine
Methionine
Phenylalanine
Proline
Serine
Threonine
Tryptophan
Tyrosine
Valine
The propensity of an amino acid to be part of a certain secondary structure (e.g. – Proline has a low propensity of being in an alpha helix or beta sheet  breaker)
Success rate of 50%

30. Secondary Structure Method Improvements
‘Sliding window’ approach
Most alpha helices are ~12 residues long Most beta strands are ~6 residues long
Look at all windows, calculate a score for each window. If >threshold  predict this is an alpha helix/beta sheet
TGTAGPOLKCHIQWMLPLKK

31. Improvements since 1980’s Success -> 75%-80%
Adding information from conservation in MSA
Smarter algorithms (e.g. Machine learning).
Success -> 75%-80%

32. Machine learning approach for predicting Secondary Structure (PHD, PSIpred)
Query
SwissProt
Step 1:
Generating a multiple sequence alignment
Query
Subject
Subject
Subject
Subject

33. Step 2:
Additional sequences are added using a profile. We end up with a MSA which represents the protein family.
Query
seed
MSA
Query
Subject
Subject
Subject
Subject

34. Step 3:
The sequence profile of the protein family is compared (by machine learning methods) to sequences with known secondary structure.
Query
seed
Machine
Learning
Approach
MSA
Known
structures
Query
Subject
Subject
Subject
Subject

35. Neural Network architecture used in BetaTPred2

36. Predicting protein 3d structure
Goal: 3d structure from 1d sequence
An existing fold
A new fold
Fold recognition
ab-initio
Homology modeling

37. Homology Modeling Simplest, reliable approach
Basis: proteins with similar sequences tend to fold into similar structures
Has been observed that even proteins with 25% sequence identity fold into similar structures
Does not work for remote homologs (< 25% pairwise identity)

38. Homology Modeling Given:
A query sequence Q
A database of known protein structures
Find protein P such that P has high sequence similarity to Q
Return P’s structure as an approximation to Q’s structure

39. Homology modeling needs three items of input:
The sequence of a protein with unknown 3D structure, the "target sequence."
A 3D “template” – a structure having the highest sequence identity with the target sequence ( >25% sequence identity)
An sequence alignment between the target sequence and the template sequence

40. Fold recognition = Protein Threading
Which of the known folds is likely to be similar to the (unknown) fold of a new protein when only its amino-acid sequence is known?

41. MTYKLILN …. NGVDGEWTYTE
Protein Threading
The goal: find the “correct” sequence-structure alignment between a target sequence and its native-like fold in PDB
Energy function – knowledge (or statistics) based rather than physics based
Should be able to distinguish correct structural folds from incorrect structural folds
Should be able to distinguish correct sequence-fold alignment from incorrect sequence-fold alignments
MTYKLILN …. NGVDGEWTYTE

42. Protein Threading Basic premise
Statistics from Protein Data Bank (~2,000 structures)
Chances for a protein to have a structural fold that already exists in PDB are quite good.
The number of unique structural (domain) folds in nature is fairly small (possibly a few thousand)
90% of new structures submitted to PDB in the past three years have similar structural folds in PDB

43. Protein Threading Basic components: Structure database Energy function
Sequence-structure alignment algorithm
Prediction reliability assessment

44. ab-initio folding Goal: Predict structure from “first principles”
Requires:
A free energy function, sufficiently close to the “true potential”
A method for searching the conformational space
Advantages:
Works for novel folds
Shows that we understand the process
Disadvantages:
Applicable to short sequences only

45. Qian et al. (Nature: 2007) used distributed computing
Qian et al. (Nature: 2007) used distributed computing* to predict the 3D structure of a protein from its amino-acid sequence. Here, their predicted structure (grey) of a protein is overlaid with the experimentally determined crystal structure (color) of that protein. The agreement between the two is excellent.
*70,000 home computers for about two years.

46. Overall Approach No Yes Yes No Protein Sequence Multiple Sequence
Alignment
Database Searching
Homologue in PDB No
Secondary
Structure
Prediction
Fold Recognition
Yes
Predicted Fold
Yes
Homology
Modelling
Sequence-Structure
Alignment
Ab-initio Structure
Prediction No
3-D Protein Model

47. Thank you for learning with me!