1. 謝孫源 (Sun-Yuan Hsieh) 成功大學 電機資訊學院 資訊工程系 hsiehsy@mail.ncku.edu.tw
A New Branch and Bound Method for the Protein Folding Problem in the HP model
　　謝孫源 (Sun-Yuan Hsieh)
成功大學 電機資訊學院 資訊工程系
2019/4/16

2. Outline Bioinformatics Background Motivation & Purpose Related Works
Preliminaries
New Branch and Bound
Experiment Result
Conclusion
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3. Background Amino acid Protein protein fundamental unit.
Twenty kinds of different amino acid.
e.g.
纈胺酸 (Valine) => 促進腦力，改善肌肉協調功能及安定情緒。
Protein
　Proteins are large organic compounds made of amino acids arranged in a linear chain
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4. Background(1/2)
Protein structure
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5. Background(2/2) Protein folding problem (PFP)
Every two years, the performance of current methods is assessed in the CASP (Critical Assessment of Techniques for Protein Structure Prediction) experiment.
Protein structure prediction is high importance in medicine (for example, in drug design) and biotechnology.
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6. Motivation & Purpose(1/2)
Experiment method
NMR & X-ray crystallography (Protein Data Bank)
Computing model
Homology modeling
Ab initio
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7. Motivation & Purpose(2/2)
Prediction structure methods compare
Our purpose is to design an efficient algorithm with HP model to find minimal-energy conformations (native structure) easily.
COST
TIME
Experiment
High
Computing
Low
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8. Related Works(1/2)
HP model (Hydrophobic-polar model) was introduced by K.A. Dill (1985).
親水性
疏水性 P H
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9. Related Works(2/2) Other computing methods for the PFP in HP model
Ant Colony Optimization 　[A. Smygelska 05]
Branch and bound 　　　 [M. Chen 05]
Evolutionary Monte Carlo [F. Liang 01]
Genetic Algorithms 　　 　[R. Unger 93] …
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10. Preliminaries(1/9)
In general, PFP can be reduced to the following three steps:
Design a simple model with a desired level of accuracy. (Dill)
Define an energy function that can effectively discriminate native states form nonnative states. (Dill)
Design an efficient algorithm to find minimal-energy conformations easily.
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11. Preliminaries(2/9)
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12. Preliminaries(3/9) Conformation process Input sequence (1D)
binding edges
Input sequence (1D)
2D HP lattice model
contact edges
Ex: PPHHPPHHPPHPPHPP
cost (free energy)=-5
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13. Preliminaries(4/9)
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14. Preliminaries(5/9) Proof.
Note that the least number of binding edges contributed by h H monomers occur when p1=H and pm=H . Without loss of generality ,assume that
where P+ represents a substring composed by at least one P. Then, the
number of binding edges contributed by h H monomers equals
h1 + (h2+1) + (h3+1) + … + (hk-1+1) + hk = h+k-2 => h+1-2 = h □
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15. Preliminaries(6/9)
Proof.
Note that every H monomers in has exactly four neighbors which contribute
at most two contact edges. (endpoint contribute at most three)
Therefore, any conformation in has at most contacts edges,
the cost of a conformation equals －(number of contact edges),－(h+1) is a low bound of the cost
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16. Preliminaries(7/9)
A conformation with the cost –(h+1), where s and t represent two endpoints of the path.
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17. Preliminaries(8/9) Proof. contact edges => 2(h’-1)+3 = 2h’+1
cost => －(2h’+1)
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18. Preliminaries(/99) h = The number of H monomers in p
Contact edges at most h+1
Cost at least - (h+1) (lemma 2)
h’= Residues of numbers of H monomers in p
Contact edges at most 2h’+1
Cost at least - (2h’+1) (theorem 1)
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19. New Branch and Bound(1/9)
Use case
NBB method
Folding to 2D/3D
in the HP model
Input
Protein sequence (1D)
Output
time: faster
cost: minimum
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20. New Branch and Bound(2/9)
Search Tree
2D lattice HP model H
Energy function=> Cost = -1 P P P H 向右 向前 向左 P
開始方向 H P H H H H P H P
Cost = -1 P
H monomers的數量和集中度，
是影響cost之主因
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21. New Branch and Bound(3/9)
Fully branch
It will consider all conformation completely
Time cost is high
Bound (pruning)
It may be miss match some best solution
Threshold is utilized to establish the boundary for bounding.
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22. New Branch and Bound(4/9)
Dynamic threshold
R-step checking
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23. New Branch and Bound(5/9)
Dynamic threshold
Use potential score function to predict the future cost in the residues monomers.
Theorem 1
α: compensation coefficient
當α值很低代表目前的path無法取得較樂觀的cost，但不代表最後的cost不是solution，因此我們利用（2h’+1）*(1- α) 來幫它補強 。
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24. New Branch and Bound(6/9)
An illustration of potential score function
The path from the root to v corresponds to a partial conformation formed by p1p2…pk, where v is associated with ps(k).
In (a), we will branch out from v because ps(k) Cmin
In (b), we will prune the branch v because ps(k)>Cmin
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25. New Branch and Bound(7/9)
R-step checking s D D D
若在半徑r的圓中，存在H(1)的vertex則代表在未來的r step的folding process中會有可能產生cost. H D r
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26. New Branch and Bound(8/9)
The concept of NBB method
When,
ratio=1 => with threshold ps(k)
ratio=0 => with threshold –(Ek+h’+1) lemma1
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27. New Branch and Bound(9/9)
The algorithm of NBB method
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28. Experiment Result(1/6) PC: Parameter: Benchmark sequence CPU: 3.4 GHz
Memory: 512 MB
Parameter:
r = (2)
ratio = (0.5)
For the most experiments
Benchmark sequence
S1 - S10 (length from 20 ~ 100) (
eports/compbio/tortilla-hp-benchmarks.htm.)
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29. Experiment Result(2/6)
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30. Experiment Result(3/6)
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31. Experiment Result(4/6)
Cost comparison of various algorithms
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32. Experiment Result(5/6)
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33. Experiment Result(6/6)
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34. Conclusion
our method can obtain a near-optimal energy conformation by running once for each benchmark sequence
Using protein biochemical property to construct the conformation are different from BB method.
To extend the work to the 3D HP model.
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