我們提出一個可以同時折疊出螺旋及平板結構的簡化模型來研究所謂的蛋白質折疊問題。此模型的主要目的是找到一個包含水的效應而且沒有人為外加作用的等效位能，同時，可以在合理的時間內預測出給定序列蛋白質的三維結構。為了達到這個目的，此模型並不考慮整個折疊的動力過程或是原子尺度下的完整結構之描述，而是採用蒙地卡羅方法以及粗粒化的蛋白質結構表現。這粗粒化的蛋白質結構表現是用符合已知結構的特定幾何物件來表示蛋白質的側鏈和骨幹上的胜肽平面。藉此粗粒化的表現，此模型的等效位能可以被設計出來。此外，在這模型中引進了兩個新的交互作用：偶極－偶極交互作用以及局域親疏水性交互作用。這兩個新的交互作用與氫鍵同為形成蛋白質二級結構之關鍵要素。由於這兩種交互作用的加入，此模型可以在不用任何人為外加作用下，同時折疊出螺旋及平板兩種二級結構。進一步的分析指出，此模型亦可以在合理的精確度下折疊出其它的蛋白質。因此，對於解決蛋白質折疊問題，此模型提供了一個可能的起點。

A reduced model, which can fold both helix and sheet structures, is proposed to study the problem of protein folding. The goal of this model is to find an unbiased effective potential that has included the effects of water and at the same time can predict the three dimensional structure of a protein with a given sequence in reasonable time. For this purpose, rather than focusing on the real folding dynamics or full structural details at the atomic scale, we adopt the Monte Carlo method and the coarse-grained representation of the protein in which both side-chains and the backbones are replaced by suitable geometrical objects in consistent with the known structure. On top of the coarse-grained representation, our effective potential can be developed. Two new interactions, the dipole-dipole interactions and the local hydrophobic interactions, are introduced and are shown to be as crucial as the hydrogen bonds for forming the secondary structures. In particular, for the first time, we demonstrate that the resulting reduced model can successfully fold proteins with both helix and sheet structures without using any biased potential. Further analyses show that this model can also fold other proteins in reasonable accuracy and thus provides a promising starting point for the problem of protein folding.

[1] Jens C. Skou. The identification of the Sodium-Potassium Pump. 1997, Nobel Lecture, http://www.nobel.se/chemistry/laureates/1997/illpres/skou.html.
[2] C. B. Anfinsen. Principles that govern the folding of protein chains. Science, 1973, 181, 223-224.
[3] C. Levinthal. Are there pathways for protein folding? J. Chim. Phys., 1968, 65, 44-45.
[4] C. Dobson, A. Sali, and M. Karplus. Protein folding: A perspective from theory and experiment. Angew. Chem. Int. Ed., 1998, 37, 868-893.
[5] P. E. Leopold, M. Montal and J. N. Onuchic. Protein folding funnels - A kinetic approach to the sequence structure relationship. Proc. Nat. Acad. Sci. USA, 1992, 89, 8721-8725.
[6] J. D. Bryngelson, J. N. Onuchic, N. D. Socci, and P. G. Wolynes. Funnels, pathways, and the energy landscape of protein folding - A synthesis. Protein: Struct. Funct. Genet., 1995, 21, 167-195.
[7] P. G. Wolynes, J. N. Onuchic, and D. Thirumalai. Navigating the folding routes. Science, 1995, 267, 1619-1629.
[8] V. I. Abkevich, A. M. Gutin, and E. I. Shakhnovich. Specific nucleus as the transition-state for protein-folding - Evidence from the lattice model. Biochemistry, 1994, 33, 10026-10036.
[9] K. A. Dill, S. Bromberg, K. Z. Yue, K. M. Fiebig, D. P. Yee, P. D. Thomas, and H. S. Chan. Principles of protein folding - A perspective from simple exact models. Protein Sci., 1995, 4, 561-602.
[10] D. K. Klimov and D. Thirumalai. Linking rates of folding in lattice models of proteins with underlying thermodynamics characteristics. J. Chem. Phys., 1998, 109, 4119-4125.
[11] Y. Duan, L. Wang, and P. A. Kollman. The early stage of folding of villin headpiece subdomain observed in a 200-nanosecond fully solvated molecular dynamics simulation. Proc. Nat. Acad. Sci. USA, 1998, 95, 9897-9902.
[12] Y. Duan and P. A. Kollman. Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution. Science, 1998, 282, 5389, 740-744.
[13] H. Nymeyer, A. E. Garcia, and J. N. Onuchic. Folding funnels and frustration in off-lattice minimalist protein landscapes. Proc. Nat. Acad. Sci. USA, 1998, 95, 5921-5928.
[14] Y. Zhou and M. Karplus. Folding thermodynamics of a model three-helix-bundle protein. Proc. Nat. Acad. Sci. USA, 1997, 94, 14429-14432.
[15] C. Micheletti, J. R. Banavor, A. Martian, and F. Seno. Protein structures and optimal folding from a geometrical variational principle. Phys. Rev. Lett., 1999, 82, 3372-3375.
[16] J. E. Shea, J. N. Onuchic, and C. L. Brooks III, Exploring the origins of topological frustration: Design of a minimally frustrated model of fragment B of protein A. Proc. Nat. Acad. Sci. USA, 1999, 96, 12512-12517.
[17] Y. Zhou and M. Karplus. Interpreting the folding kinetics of helical proteins. Nature, 1999, 401, 400-403.
[18] C. Clementi, P. A. Jennings, and J. N. Onuchic. How native-state topology affect the folding of dihydrofolate reductase and interleukin-1 . Proc. Nat. Acad. Sci. USA, 2000, 97, 5871-5876.
[19] N. Go and H. Taketomi. Respective roles of short- and long-range interactions in protein folding. Proc. Nat. Acad. Sci. USA, 1978, 75, 559-563.
[20] Z. Guo and D. Thirumalai. Kinetics and thermodynamics of folding of a de Novo designed four-helix bundle protein. J. Mol. Biol., 1996, 263, 323-343.
[21] S. Takada, Z. L. Schulten and P. G. Wolynes. Folding dynamics with nonadditive forces: A simulation study of a designed helical protein and a random heteropolymer. J. Chem. Phys., 1999, 110, 11616-11629.
[22] A. Irbäck, F. Sjunnesson, and S. Wallin. Three-helix-bundle protein in a Ramachandran model. Proc. Nat. Acad. Sci. USA, 2000, 97, 13614-13618.
[23] G. Favrin, A. Irbäck, and S. Wallin. Folding of a small helical protein using hydrogen bonds and hydrophobicity forces. Protein: Struct. Funct. Genet., 2002, 47, 99-105.
[24] J.-E. Shea, Y. D. Nochomovitz, Z. Guo, and C. L. Brooks III. Exploring the space of protein folding Hamiltonians: The balance of forces in a minimalist -barrel model. J. Chem. Phys., 1998, 109, 2895-2903.
[25] D. K. Klimov and D. Thirumalai. Mechanisms and kinetics of -hairpin formation. Proc. Nat. Acad. Sci. USA, 2000, 97, 2544-2549.
[26] S. Miyazawa and R. L. Jernigan. Residue–residue potentials with a favorable contact pair term and an unfavorable high packing density term, for simulation and threading. J. Mol. Biol., 1996, 256, 623-644.
[27] Z.-H. Wang and H. C. Lee. Origin of the native driving force for protein folding. Phys. Rev. Lett., 2000, 84, 574-577.
[28] C. K. Mathews, K. E. van Holde, and K. G. Ahern. Biochemistry, 3rd Ed., 2000.
[29] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and E. Teller, Equation of state calculations by fast computing machines. J. Chem. Phys., 1953, 21, 1087-1092.
[30] D. P. Landau and K. Binder. A Guide to Monte Carlo Simulations in Statistical Physics, 2000.
[31] G. Humer, S. Garde, A. E. Garcia, A. Pohorille, and L. R. Pratt. An information theory model of hydrophobic interactions. Proc. Nat. Acad. Sci. USA, 1996, 93, 8951-8955.
[32] G. Humer, S. Garde, A. E. Garcia, M. E. Paulaitis, and L. R. Pratt. The pressure dependence of hydrophobic interactions is consistent with the observed pressure denaturation of proteins. Proc. Nat. Acad. Sci. USA, 1998, 95, 1552-1555.
[33] N. Hillson, J. N. Onuchic, and A. E. Garcia. Pressure-induced protein-folding / unfolding kinetics. Proc. Nat. Acad. Sci. USA, 1999, 96, 14848-14853.
[34] M. S. Cheung, A. E. Garcia, and J. N. Onuchic. Protein folding mediated by solvation: Water expulsion and formation of the hydrophobic core occur after the structural collapse. Proc. Nat. Acad. Sci. USA, 2002, 99, 685-690.
[35] G. Solomons and C. Fryhle. Organic Chemistry, 7th Ed., 2000.
[36] A. M. Lesk. Introduction to Protein Architecture, 2001.
[37] A. V. Finkelstein and O. B. Ptitsyn. Protein Physics A Course of Lectures, 2002.
[38] C. Branden an J. Tooze. Introduction to Protein Structure, 2nd Ed., 1999.
[39] The standard form with the threefold symmetry is , where .
[40] M. Daune. Molecular Biophysics Structures in Motion, 1993.
[41] http://www.umass.edu/microbio/rasmol/
[42] L. Regan and W. F. DeGrado. Characterization of a helical protein designed from first principles. Science, 1988, 241, 976-978.