A Survey of Protein A Survey of Protein Folding in HP ModelFolding in HP Model

Presented by:

T.K. Yu2003/7/24 tkyu@ntu.edu.tw

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.

Select a Lattice 2D

– Square lattice– Triangular lattice

3D– Square lattice– Triangular lattice– Face-Centered-Cubic lattice

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.

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 ].

E O

(a)(b) ¾, (c)(d) 2/3.

At most ½ are discarded.

So the ratio is 1/3.

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.

3D Square Lattice Model

Hart and Istrail gave a 3/8 approximation algorithm. (‘95)

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

3D FCC Lattice Model

Backofen and Will have studied many properties of this model.

Conclusion and Future Work

Improve the approximation ratio of existent models.

Create new models. Finding some interesting properties of

these models.

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.

The EndThe End

T.K. Yu