1. A Hidden Markov Model for Protein Secondary Structure Prediction
Wei-Mou Zheng
Institute of Theoretical Physics
Academia Sinica
PO Box 2735, Beijing

2. Outline
Protein structure
A brief review of secondary structure prediction
Hidden Markov model: simple-minded
Hidden Markov model: realistic
Discussion
References

3. Hydrophobic Charged+- Polar
Protein sequences are written in 20 letters (20 Naturally-occurring amino acid residues): AVCDE FGHIW KLMNY PQRST
Hydrophobic
Charged+-
Polar

4. Residues form a directed chain
Cis-
Trans-

5. H: E: C = 34.9: 21.8: 43.3 Rasmol ribbon diagram of GB1
Helix (pink), sheets (yellow) and coil (grey)
Hydrogen-bond network
3D structure → secondary structure written in three letters:H, E, C.
H: E: C = 34.9: 21.8: 43.3

6. Bayes formula
Count of
Generally, P(x, y) = P(x|y)P(y),

7. Protein sequence A, {ai}, i=1,2,…,n
Secondary structure sequence S, {si}, i=1,2,…,n
Secendary structure prediction:
1D amino acid sequences → 1D secondary structure sequence
An old problem for more than 30 years
Inference of S from A: P(S |A )
1. Simple Chou-fasman approach
Chou-Fasman’s propensity of amino acid to conformational state
+ independence approximation

8. Parameter Training
Propensities q(a,s)
Counts (20x3) from a database: N(a, s)
sum over a → N(s),
sum over s → N(a),
sum over a and s → N
q(a,s) = [N(a,s) N] / [N(a) N(s)].

9. 2. Garnier-Osguthorpe-Robson (GOR) window version
Conditional
Independency
Weight matrix (20x17)x3 P(W|s)
3. Improved GOR (20x20x16x3, to include pair correlation)

10. Hidden Markov Model (HMM): simple-minded
Bayesian formula: P(S|A) = P(S,A)/P(A) ~ P(S,A) = P(A|S) P(S)
Simple version
emitting ai at si
Markov chain according to P(a|s)
For hidden sequence
Forward and backward functions a1 a2 a3 s1 s2 s3

11. Initial conditions and recursion relations
Partition function
Linear algorithm: Dynamic programming
Baum-Welch (sum) & Viterbi (max)

12. Prob(si=s, si+1=s’) = Ai(s) tss’ P(ai+1|s’) Bi+1(s’)/Z
Prob(si:j)

13. Hidden Markov Model: Realistic
1) Strong correlation in conformational states: at least two consicutive E and three consicutive H
refined conformational states (243 → 75)
2) Emission probabilities → improved window scores
Proportion of accurately predicted sites ~ 70% (compared with < 65% for prediction based on a single sequence)
No post-prediction filtering
Integrated (overall) estimation of refined conformation states
Measure of prediction confidence

14. Discussions
HMM using refined conformational states and window scores is efficient for protein secondary structure prediction.
Better score system should cover more correlation between conformation and sequence.
Combining homologous information will improve the prediction accuracy.
From secondary structure to 3D structure (structure codes: discretized 3D conformational states)

15. References
Lawrence R Rabiner,
A tutorial on hidden Markov models and selected appllications in speech recognition
Proceeding of the IEEE, 77 (1989)
Burkhard Rost
Protein Secondary Structure Prediction Continues to Rise
Journal of Structural Biology 134, 204–218 (2001)

16. The End

17. Small P
Tiny G I A V
Aliphatic L C S N T D Q M E Y K F H R
Negative W
Positive
Aromatic
Hydrophobic
Polar