The document describes a probabilistic ab initio method for protein structure prediction using coarse grain force fields. It introduces a probabilistic score function that considers sequence, structure, and solvation as mixtures of probabilities without energies. A biased fragment assembly search method generates conformations by combining fragments from a statistical fragment library. Results on several proteins show the method generates protein-like folds. Future work will introduce hydrogen bonding as a probabilistic term to improve results.

1. Protein Structure Prediction
using Coarse Grain Force Fields
Nasir Mahmood
12.02.2010

2. Overview
• Introduction
• Probabilistic Ab Initio – Standard
– Score function
– Search Method
– Results
• Probabilistic Ab Initio - Extended
– Score Function : Introducing Solvation
– Search Method: Bias Fix
– Results
• Outlook
• Summary
2

3. “All the information required
by protein to adopt its final
conformation is encoded in
its sequence”
• information he referred to has not
been decoded yet
• interestingly, these days we also
know about proteins like ‘prions’ Christian B. Anfinsen (1916 - 1995)
Source: http://nobelprize.org/
3

4. X-Ray
Crystallography
Experimental
NMR
Methods
Spectroscopy
N
Cryo-EM
Time (year)

5. X-Ray
Crystallography
Experimental
Methods NMR
Spectroscopy
N
Cryo-EM
Time (year)
More than 3 decades and
only 60000+ structures
5

6. 100 × 10 6
Sequence
90 × 10 6
Database Growth
80 × 10 6 X-Ray
Crystallography
70 × 10 6 Experimental
NMR
Methods
Spectroscopy
60 × 10 6
Cryo-EM
N 50 × 10 6
40 × 10 6
30 × 10 6
20 × 10 6
10 × 10 6
Time (year) 6

7. Experimental Data
X-Ray
Experimental Crystallography
Methods
NMR
Spectroscopy
PDB
Methods
Accuracy
Cryo-EM
Computation cost
Homology
PDB dependence
Computational
Modeling
Methods
Fold
Recognition
Ab Initio
Modeling
Physical Principles 7

8. • Monte Carlo Methods
• Molecular Dynamics
• Physics-based
• Best but most difficult (Force fields)
• Computationally expensive
• Statistics-based Pi = e - ∆E/kBT
• Boltzmann distributions
• Statistical mechanical ensembles
• We use Descriptive Statistics
Ab Initio • Bayesian formulation
• No hidden approximations
Methods • No energies but find distributions
8

9. • Simulated Annealing /
• Coarse Grained Monte Carlo
• reduced dimensionality • Move set: biased & unbiased
• relies on dihedral angles • Acceptance criterion: ratio
of probabilities
• no side chains
• 5-atoms representation
• Fragment Assembly
• Purely Probabilistic Force Field
• Mixture of Probabilities:
• Sequence, Structure, Solvation
Our Ab Initio • No energies
Method • No Boltzmann statistics
9

10. Probabilistic
Score Function
10

11. 1. Sequence • Multi-way Bernoulli
E MP
N S A
W
Y F I D
KG Q H T S L C
2. Structure • Representation :
• Reduced, Simplified
• 5-atoms per amino acid
• dihedral angles (phi, psi)
• Bivariate Gaussian 11

12. i
i+1
i+2
1.5 × 10 6 (B)
(A)
Sequence Structure
-3.1 -2.0 -0.5 -1.7 -2.0 -1.5 -2.2
i A S T C W R I -1.1 -0.9 -0.7 -0.5 -0.3 -0.8 -1.0
-2.0 -0.5 -1.7 -2.0 -1.5 -2.2 -1.1
i+1 S T C W R I M -0.9 -0.7 -0.5 -0.3 -0.8 -1.0 -1.1
-0.5 -1.7 -2.0 -1.5 -2.2 -1.1 -2.1
i+2 T C W R I M F -0.7 -0.5 -0.3 -0.8 -1.0 -1.1 -0.4
…
…
3.1 2.0 1.5 1.7 -2.0 -1.5 -1.2
N P L E N R R V 1.1 0.9 -2.5 2.3 -0.9 -1.2 -0.8
(C)
12

13. Fragment Generation Classified
ACAD .. CCAD .. WFTG .. STST.. STDC ..
WFDC .. DCWF .. GAEG .. GAEG .. GGGG ..
Expectation
Maximization
Fragment Bayesian
Library Statistical Models Classifier
13

14. 14
20 05 -32 80
W E W C
87 -71 15 -07
20 05 -32 80
W W E W
87 -71 15 -07
20 05 -32 80
Q W W E
87 -71 15 -07
20 05 -32 80
87 -71 15 -07
A Q W W
20 05 -32 80
87 -71 15 -07
Structure
20 05 -32 80
T A Q W
87 -71 15 -07
20 05 -32 80
T T A T
87 -71 15 -07
20 05 -32 80
L T T A
87 -71 15 -07
20 05 -32 80
T L T I
87 -71 15 -07
T
Sequence
20 05 -32 80
L T L T
87 -71 15 -07
L
20 05 -32 80
S L T M
87 -71 15 -07
S
20 05 -32 80
A S L T
87 -71 15 -07
A
class 0
class 1
class 2
class 3
class 4
class 5
class 6
DCWF ..
GAEG ..
WFDC ..
GGGG ..
GAEG ..
Classified
ACAD ..
CCAD ..
WFTG ..
STDC ..
STST..

15. Search Method
15

16. Initial (random) p(x i )
conformation Relative probabilities: Pi = p(x )
i -1
Probability
• Normal methods : Pi = e - ∆E/kBT
(i)
(i-1) Final
Model
Conformational space 16

17. 180
Random Angle
0
Generator PDB
-180 0 180 180
phi psi
0
psi
93 177 66 14 167 73 31 54
-180
-180 0 180
phi
Fragment ≈ 2 × 10 6
fragments
Library
Unbiased Biased 17

18. Interplay of Cartesian Coordinates
& Dihedral Angles
Choi, V.: 2005, On Updating torsion angles of molecular conformations, 18
J Chem Inf Model 46, 438–444.

19. Results
19

20. Results
2hfq
Model Native
20

21. Results 2hd3
Model Native
21

22. Results 2gzv
Psi
Phi
Model Native
22

23. Results 2hj1
Score
Time
Temperature
Model
Native 23

24. Results
Psi
Phi
Score
Time
Temperature 24

25. Score Function:
Introducing Solvation
25

26. 26

27. PDB
27

28. Trp
PDB
Gly Lys Ser
28

29. 1. Sequence
• Multi-way Bernoulli
E MP
N S A
W
Y F I
KG QH T S D L C
2. Structure 3. Solvation
• Representation : • Simple Gaussian
• Reduced, Simplified
• 5-atoms per amino acid
• dihedral angles (phi, psi)
• Bivariate Gaussian
29

30. • Mixture Models: Re-Classified
 Connections
ACAD .. CCAD .. WFTG .. STST.. STDC ..
 Residues
PDB 

Geometry
Location in protein
WFDC .. DCWF .. GAEG .. GAEG .. GGGG ..
Sequence Structure Solvation
-3.1 -2.0 -0.5 -1.7
A S L T 12 07 08 11
-1.1 -0.9 -0.7 -0.5
-2.0 -0.5 -1.7 -1.2
S L T I 07 08 11 09
-0.9 -0.7 -0.5 -0.4
Expectation
Maximization
Fragment Bayesian
Library Statistical Models Classifier
30

31. Search Method:
Bias Fix & Combining
Fragments
31

32. Bias Fix
32

33. Combining Fragments and
Probabilities
33

34. Results
34

35. Results
1fsv
2hep
Native Model 35

36. Results
2k4x
1agt
Model
Native 36

37. Results
2k53
2k4n
Native Model 37

38. Results
2hf1
Native Model
38

39. Future Outlook
• Introduce hydrogen
bonds – as a
probabilistic term
• Hydrogen bond N
energies have normal
distribution
• Use Simple Gaussian
model Hydrogen bond energy
(kcal/mol)
39

40. Summary
• Purely Probabilistic Approach for Protein Structure
Prediction
• Score function consists of a set of probability distributions
• Conformation probabilities - mixture of probabilities, no
energies at all
• generates protein/protein-like conformations
• long-range interactions not well represented
• In future, hydrogen bond term could improve results
• Application to sequence optimization
• Rapid sampling – combine with other score functions
40

41. Thanks for your attention!