1. A Survey of Protein Folding in HP Model Presented by: T.K. Yu 2003/7/24 tkyu@ntu.edu.tw

2. Introduction  Protein folding in HP model is an interesting problem in computational biology introduced by Dill.  We classify 20 types of amino acids into 2 types: hydrophobic (H), hydrophilic (P).  We want to make a conformation of an HP sequence such that most HH pairs without covalent are neighboring on some lattice.

3. Select a Lattice  2D – Square lattice – Triangular lattice  3D – Square lattice – Triangular lattice – Face-Centered-Cubic lattice

4. 2D Square Lattice Model  The upper bound: – Parity property, only two nodes have different parity may contact. Thus the upper bound is bounded by the M=2*min(E[S], O[S]).  Cresenzi et al prove that finding the optimal solution in general case is NP-hard.

5. 2D Square Lattice Model  Aichholzer et al present some sequences with only one folding type reaching optimal solutions.  Newman presents a 1/3 approximation algorithm. – Upper bound: M=2*min(E[S], O[S]) – We first assume that the length of S is even; E[S]=O[S} – Make S as a chain. – There exists a point p=s i s.t. for every j, s i ~s j through clockwise is O[s i ~s j ]  E[s i ~s j ], and s i ~s j \s i through counter-clockwise is E[s i ~s j ]  O[s i ~s j ].

6. E O (a)(b) ¾, (c)(d) 2/3. At most ½ are discarded. So the ratio is 1/3.

7. 2D Triangular Lattice Model  Upper bound: 2*s.  Arrow-folding method (Agarwala et al): – Every node own a contact backward. – ½ approximation. – With some improvement, it can be 6/11 approximation.

8. 3D Square Lattice Model  Hart and Istrail gave a 3/8 approximation algorithm. (‘95)

9.  Upper bound: 5*s.  Star-folding method: 9 + 13 – 6 = 16  16/6  5 = 16/30 approximation.  With some modify, it can be 3/5 approximation. 3D Triangulation Lattice Model

10. 3D FCC Lattice Model  Backofen and Will have studied many properties of this model.

11. Conclusion and Future Work  Improve the approximation ratio of existent models.  Create new models.  Finding some interesting properties of these models.

12. References  O. Aichholzer, D. Bremner, E.D. Demaine, H. Meijer, V. Sacristán, M. Soss, “Long proteins with unique foldings in the H-P model”, Computational Geometry Theory and Application, 2003, 139-159.  R. Agarwala, S. Batzoglou, V. Dančík, S.E. Decatur, M. Farach, S. Hannenhalli, S. Skiena, “Local rules for protein folding on a triangular lattice and generalized hydrophobicity in the HP model”, J Comput. Biology, 1997, 275-296.  R. Backfen, “Upper bound for number of contacts in the model on the face- centered-cubic lattice (FCC)”, proceedings of the 11 th annual Symposium on Combinatorial Pattern Matching, Montreal, in: Lecture Notes of Computer Science, 2001, 257-271.  P. Crescenzi, D. Goldman, C. Papadimitriou, A. Piccoboni, M. Yannakakis, “On the complexity of protein folding”, J. Comput. Biol., 1998.  W.E. Hart and S.C. Istrail, “Fast protein folding in the hydrophobic- hytrophilic model within three-eighths of optimal”, Journal of Computational Biology, 1996, 53-96.  A. Newman, “A new Algorithm for protein folding in the HP model”, SODA, 2002, 876-884.

13. The End T.K. Yu