A Survey of Protein Folding in HP Model

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=si s.t. for every j, si~sj through clockwise is O[si~sj ]E[si~sj], and si~sj\si through counter-clockwise is E[si~sj ]O[si~sj].

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. 3D Triangulation Lattice Model • 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.

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 11th 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