蛋白质折叠的格子链Monte Carlo模拟

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英文题名：Lattice Monte Carlo Simulation of Protein Folding 作者：陈彦涛 论文级别：博士 学科专业名称：高分子化学与物理 中文关键词：蛋白质折叠 ; α-螺旋 ; 螺旋周期 ; 取向相关函数 ; 相关长度 ; helix-coil转变 ; Zimm-Bragg理论 ; 成核 ; 增长 ; 计算机模拟 ; Monte ; Carlo模拟 ; 键长涨落模型 ; 格子链 ; 大分子链构象 ; 膜蛋白 英文关键词：protein folding ; α-helix ; helical period ; orientational correlation function ; correlation length ; helix-coil transition ; Zimm-Bragg theory ; nucleation ; propagation ; computer simulation ; dynamic Monte Carlo simulation ; bond fluctuation model ; lattice chain ; macromolecular conformation 学位年度：2006 导师：丁建东 学科代码：070305 学位授予单位：复旦大学 论文提交日期：2006-10-18

摘要

蛋白质折叠的理论与模拟研究是分子生物学、高分子科学与统计物理相交叉的领域。从高分子科学的角度来看，蛋白质的折叠过程可以理解为一类特殊的高分子从其无规线团状态演变为相对紧致有序的熔球状态的过程。链状分子的折叠过程复杂，而且伴随了较大的熵变，对理论处理提出了很高的要求；另一方面，这一过程发生于纳米空间尺度和纳秒至微秒时间尺度，也限制了大多数实验测试工具的应用。由此，“计算机模拟”成为此领域中一种不可替代的重要研究手段。
     相比连续空间下的全原子模型，粗粒化格子模型虽然忽略了部分结构细节，但是从计算机模拟速度看更为高效，能够以不太长的计算机机时获得链状大分子整体的构象信息。格子模型特别适合于进行Monte Carlo模拟。
     α-螺旋是蛋白质结构最基本的二级结构之一，而且含量最高。本博士论文中，我们以此为重点研究对象，发展了相应的格子链模型，并通过动态Monte Carlo方法对helix-coil转变过程进行了模拟；本论文还拓展了螺旋空间结构的统计参数，并重新考察了经典的螺旋形成理论。
     本博士论文的主要创新性贡献可以分为以下几个部分：
     (一)、提出了一个适于在简单立方格子空间中对α-螺旋进行动态Monte
     Carlo模拟的的粗粒化模型。简单立方格子空间中的格子链模型虽然在高分子领域以及蛋白质globule-coil转变的研究中广为应用，但由于空间堆积和扭曲方面的要求，α-螺旋并不容易在格子空间中产生。本文将高分子研究中提出的键长涨落模型与反映多肽链和螺旋特征的作用力相结合，每个氨基酸残基为基本运动单元，提出了一个单单元格子链模型，并再现了helix-coil转变，得到了周期为4个氨基酸残基的规整α-螺旋。相比传统的立方格子空间，键长涨落的格子空间中允许更多的键长和键角取向，而且允许支化链的形成，是一个准连续空间，同时又保持了格子模型计算高效的特点。而简化的手性和氢键作用使得相应的模型有效而且简单。
     (二)、对基于简单立方格子的单单元模型进行了适当改进，再现了非整数周期螺旋；并在此基础上提出了四单元格子链模型。在单单元模型的基础上，进
    一步引入虚拟的亚胺基和羰基，构建了改进的单单元模型；由此得到了周期基本为3.6的α-螺旋；把残基粗粒化为α-碳、亚胺基、羰基和侧基四个基本运动单元，则构成了解析度比较高的四单元模型，是目前简单格子空间中分辨率最高的多肽链模型。四单元模型在计算时间和模型分辨率之间做了比较恰当的折衷，在残基内部引入了构象熵和亚单元的堆积效应。形成的α-螺旋结构逼真，亚胺基和羰基处于最内侧，侧基缠绕于螺旋外侧。螺旋形成转变点处，亚胺基、羰基之间距离的热涨落最大，证明了氢键对螺旋形成的主导作用；而螺旋稳定形成后，侧基之间距离的热涨落最大说明了侧基行使生物功能的有效性；整个过程中α-碳之间距离的热涨落最小则证明了其作为骨架的合理性。
     (三)、提出了描述蛋白质二级结构(螺旋)的空间取向相关函数及螺旋持久长度的概念。此函数的特点为：可以定量地描述螺旋结构的周期性和相关长度；所得相关长度与螺旋本身长短无关，如同高分子中的持续长度，从物理本质层次描述了螺旋结构的规整性；同样适用于描述不规整的螺旋结构以及多肽链中多个螺旋并存的情形。
     (四)、借助于计算机模拟和理论推导，重新审视了在helix-coil转变领域中最经典、也是最重要的Zimm-Bragg(ZB)理论，提出了修正意见，并给出了部分修正公式。三维格子空间中的模拟表明，尽管ZB理论的基础是一维Ising模型，且只考虑了最近邻的天然相互作用，该理论基本抓住了helix-coil转变的物理本质。另一方面，发现定量的理论处理中所采用的传统的large-N近似并不适用于较短和中等长度的多肽链；考虑到天然蛋白质中的螺旋片段以中等长度居多，进而提出了large-λ近似，并导出了简单公式。提出了多残基成核假设，模拟表明，相比于ZB理论的单残基成核假设，前者能更准确地描述螺旋成核过程。基于对成核常数和增长常数的各种方法的比较，发现综合考虑螺旋比率和螺旋平均长度获得的结果优于只考虑前者。
     (五)、考察了非天然氢键相互作用在α-螺旋形成过程中的作用。发现序列间隔大于四的非天然氢键相互作用虽然不存在于α-螺旋天然结构中，但是在螺旋形成过程中占有较高比例。非天然氢键的存在使得helix-coil转变过程中多肽链形成了类似中间体的构象，从而改变了螺旋增长常数随温度指数变化的特点，而且多肽链需要再次进行构象调整以形成最终的α-螺旋。这为螺旋相关实验中多指数动力学特性的最新发现提供了一个可能的解释。
Theoretical and simulation research for protein folding is an interdisciplinary field between molecular biology, polymer science and statistical physics. In the light of polymer physics, protein folding can be viewed as the process that a special type of polymer chain proceeds from random coil state to compact and ordered globular state. The folding process is complicate, accompanied with large change of entropy, thus far away from a unified theoretical treatment; on the other hand, it happens usually in a nano-meter spatial scale and nano-to-micro-second temporal scale, thus resulting in much difficulty of direct experimental detection. As an alternate, computer simulation has been an important and useful method in this field.
    Compared with all-atom model in continuous space, the coarse-grained lattice model is, at the cost of spatial resolution, beneficial for CPU time. Lattice model is specifically suitable for Monte Carlo simulation.
    α-helix is a type of fundamental secondary structure, holding the largest content in proteins, α-helix constitutes the major subject of the present Ph. D. thesis. The thesis developed corresponding lattice model, and reproduced the helix-coil transition via dynamic Monte Carlo (DMC) simulation. We have also expanded the statistic order parameter for helix structure, and revisited the classical Zimm-Bragg theory for helix formation.
    The main achievements and original contributions of this thesis are summarized as follows:
    1. A coarse-grained model has been constructed for generating α-helix in the simple cubic lattice space. Though lattice model have been widely employed in polymer research and protein's globule-coil transition, it is difficult for embedding α-helix into simple cubic lattice space because of the requirement of spatial packing and warping. In this thesis, a single-unit lattice model was suggested, in which one amino acid residue is dealt as the basic unit for movement and interaction. This model combines the eight-site bond fluctuation model originally used in polymer simulation
    and the interactions for polypeptide and α-helix. Thus, the helix-coil transition has been reproduced in our DMC, and the regular α-helix with period of integer 4. In comparison with traditional one-site cubic lattice space, the eight-site cubic lattice space allows much more bond lengths and bond orientations, and also the branching point, thus can be considered as a quasi-continuous space, but still holds the advantage of effective computing for lattice model.. What's more, the simplified chirality and hydrogen bonding interaction ensure the corresponding single-unit model simple but effective.
    2. The single-unit model has been improved in the simple cubic lattice space, resulting in α-helix structure with non-integer period; and the four-unit lattice model has also been constructed. Based on the single-unit lattice model, the inclusion of virtual-imino group and virtual-carboxyl group makes an improved single-unit model, thus an α-helix with period of about 3.6 can be embedded into the simple cubic lattice space. As a further step, the explicit representation of α-carbon, imino group, carboxyl group and side-chain group as basic unit for movement and interaction makes a four-unit lattice model with intermediate resolution, which holds the highest resolution in simple cubic lattice space for polypeptide at present. The four-unit model includes conformational entropy into residue and packing effect for the unit, and makes a good compromise between computation consumption and spatial resolution. The formed α-helix is more "realistic", with imino group and carboxyl group inside and side-chain group outside. Around the transition point, the thermal fluctuation of the distance between imino group and carboxyl group is the biggest, indicating the leading role of hydrogen bond for helix formation; after the formation, the thermal fluctuation of the side-chain group's distance is the biggest, indicating the probability for performing biological function; the thermal fluctuation of the α-carbon's distance is the smallest in the whole process, indicating it's role as polypeptide's backbone.
    3. A spatial orientational correlation function for helix structure and the related conception of persistent length have been suggested. This function can quantificationally describe the period and correlation length of helix. The correlation length is independent on helix length, much like the persistent length in polymer science, thus essentially describing the regularity of helix structure. Most importantly, this function works not only for irregular helix structure, but also for the polypeptide
    chain containing more than one helix segment.
    4. The classical Zimm-Bragg (ZB) theory for helix-coil transition has been revisited via DMC simulation and theoretical deduction, thus resulting in a few medications and one new formula. DMC simulations based on the single-unit model in three-dimensional lattice space indicated that the ZB theory captured the main physics of helix-coil transition though it is essentially a one-dimensional Ising model. On the other hand, the traditional large-N approximation for the quantificational treatment of the ZB theory was found not suitable for the polypeptide with short or medium length; as the helical segment in natural protein is largely of medium length, another large-λ approximation and associated simple formula has been suggested by us. A multi-residue-nucleus or block-nucleus assumption has been put forward, which could describe helix nucleation process more precisely than the single-residue-nucleus assumption in the original ZB theory. A detailed comparison has been made between different method for nucleation constant and propagation constant, which indicated that, if both helical ratio and mean length of helix were set as input, the output would be better than the case with only helical ratio as input.
    5. The role of non-native hydrogen bonding interaction in the process of α-helix formation has been explored. Though the non-native hydrogen bonds (i.e., sequence interval is larger than four) can not be found in the natural α-helix structure, they hold a big ratio in all hydrogen bonds during α-helix formation. The inclusion of non-native hydrogen bond results in the formation of intermediate-like conformation in the helix-coil transition, thus another arrangement of conformation for the formation of α-helix. The non-native hydrogen bond also complicates the relationship between propagation constant for helix and temperature, changes the exponential property especially around the transition temperature. Thus, all those "abnormal" phenomena may provide a possible explanation for the latest experimental result about the multi- or stretched- exponential kinetics.

引文

[1] 中华人民共和国国务院．(2006)．国家中长期科学和技术发展规划纲要(2006—2020年). http://www.gov.cn/jrzg/2OO6-O2/O9/content 183787.htm
    [2] 来鲁华．(1993)．蛋白质的结构预测与分子设计[M]．北京大学出版社，北京．
    [3] Creighton, T.E. (1992). Protein Folding [M]. W. H. Freeman and Co., New York.
    [4] Fersht, A.R. (1999). Structure and mechanism in protein science: a guide to enzyme catalysis and protein folding [M]. W.H. Freeman, New York:.
    [5] Pain, R.H. (2000). Mechanisms of Protein Folding [M]. Oxford University Press Inc., New York.
    [6] Anfinsen, C.B., Haber, E., Sela, M., and White, F.H. (1961). The Kinetics of Formation of Native Ribonuclease during Oxidation of the Reduced Polypeptide Chain [J]. Proc. Natl.Acad. Sci. U.S.A. 47: 1309-1314.
    [7] 邹承鲁主编．(1997)．第二遗传密码：新生肽链及蛋白质折叠的研究[M]．湖南科学技术出版社，长沙．
    [8] 王志珍．(2004)．蛋白质的折叠：破译“第二遗传密码”．In 科技日报，北京．
    [9] Radford, S.E., and Dobson, C.M. (1999). From computer simulations to human disease: Emerging themes in protein folding [J]. Cell 97: 291-298.
    [10] Dobson, C.M. (2003). Protein folding and misfolding [J]. Nature 426: 884-890.
    [11] Dobson, C.M. (2004). In the footsteps of alchemists [J]. Science 304: 1259-1262.
    [12] Plotkin, S.S., and Onuchic, J.N. (2002). Understanding protein folding with energy landscape theory-Part Ⅰ: Basic concepts [J]. Q. Rev. Biophys. 35: 111-167.
    [13] Anfinsen, C.B. (1973). Principles that govern the folding of protein chain [J]. Science 181: 223-230.
    [14] Levinthal, C. (1968). Are there pathways for protein folding? [J]. J. Chim. Phys. 65: 44-45.
    [15] 王炜．(2001)．生物物理学与相关蛋白质的物理问题．http://biophy.nju.edu.cn/paper/protein.pdf
    [16] Poland, D., and Scheraga, H.A. (1970). Theory of Helix-Coil Transitions in Biopolymers [M]. Academic Press, New York.
    [17] Taketomi, H., Ueda, Y., and Go, N. (1975). Studies on protein folding, unfolding and fluctuations by computer simulations [J]. Int. J. Peptide and Protein Res. 7: 445-459.
    [18] Ueda, Y., Taketomi, H., and Go, N. (1978). Studies on protein folding, unfolding and fluctuations by computer simulations. Ⅱ. A three-dimensional lattice model of lysozyme [J]. Biopolymers 17: 1531-1548.
    [19] Levitt, M., and Warshel, A. (1975). Computer simulation of protein folding [J]. Nature 253: 694-698.
    [20] McCammon, J.A., Gelin, B.R., and Karplus, M. (1977). Dynamics of Folded Proteins [J]. Nature 267: 585-590.
    [21] Wojcik, J., Altmann, K.H., and Scheraga, H.A. (1990). Helix Coil Stability-Constants For The Naturally-Occurring Amino-Acids In Water .24. Half-Cystine Parameters From Random Poly(Hydroxybutylglutamine-Co-S-Methylthio-L-Cysteine) [J]. Biopolymers 30: 121-134.
    [22] Karplus, M., and Shakhnovich, E.I. (1992). Protein folding: theoretical studies of thermodynamics and dynamics. In Protein Folding [M]. (ed. T.E. Creighton), pp. 127-196. W.H. Freeman and Company, New York.
    [23] Sali, A., Shakhnovich, E., and Karplus, M. (1994). How Does a Protein Fold [J]. Nature 369: 248-251.
    [24] Chakrabartty, A., and Baldwin, R.L. (1995). Stability of Alpha-Helices [J]. Advances in Protein Chemistry 46: 141-176.
    [25] Wolynes, EG., Onuchic, J.N., and Thirumalai, D. (1995). Navigating The Folding Routes [J]. Science 267: 1619-1620.
    [26] Baker, D. (2000). A surprising simplicity to protein folding [J]. Nature 405: 39-42.
    [27] Daggett, V., and Fersht, A. (2003). The present view of the mechanism of protein folding [J]. Nat. Rev. Mol. Cell Biol. 4: 497-502.
    [28] Wang, Z.X. (1996). How many fold types of protein are there in nature? [J]. Proteins-Structure Function and Genetics 26: 186-191.
    [29] Zhang, C.T. (1997). Relations of the numbers of protein sequences, families and folds [J]. Protein Eng. 10: 757-761.
    [30] Wang, J., and Wang, W. (1999). A computational approach to simplifying the protein folding alphabet[J]. Nature Structural Biology 6: 1033-1038.
    [31] Hamada, D., Segawa, S., and Goto, Y. (1996). Non-native alpha-helical intermediate in the refolding of beta-lactoglobulin, a predominantly beta-sheet protein [J]. Nat. Struct. Biol. 3: 868-873.
    [32] Plaxco, K.W., Simons, K.T., and Baker, D. (1998). Contact order, transition state placement and the refolding rates of single domain proteins [J]. J. Mol. Biol. 277: 985-994.
    [33] Bryngelson, J.D., Onuchic, J.N., Socci, N.D., and Wolynes, P.G. (1995). Funnels, Pathways, And The Energy Landscape Of Protein Folding - A Synthesis [J]. Proteins 21: 167-195.
    [34] Dill, K.A., and Chan, H.S. (1997). From Levinthal to pathways to funnels [J]. Nat. Struct. Biol. 4: 10-19.
    [35] Kim, P.S., and Baldwin, R.L. (1982). Specific intermediates in the folding reactions of small proteins and the mechanism of protein folding [J]. Annu. Rev. Biochem. 51: 459-489.
    [36] Karplus, M., and Weaver, D.L (1976). Protein folding dynamics [J]. Nature 260: 404-406.
    [37] Tanford, C. (1962). Contribution of hydrophobic interactions to the stability of globular confirmation of proteins [J]. J. Am. Chem. Soc. 84: 4240.
    [38] Baldwin, R.L. (1989). How does protein folding get started? [J]. Trends Biochem. Sci. 14: 291-294.
    [39] Fersht, A.R., and Proc. Natl. Acad. Sci. U.S.A.. (1995). Optimization of rates of protein folding: the nucleation-condensation mechanism and its implications[J]. Proc. Natl. Acad. Sci. U.S.A. 92: 10869-10873.
    [40] Wetlaufer, D.B. (1973). Nucleation, rapid folding, and globular intrachain regions in proteins [J]. Proc. Natl. Acad. Sci. U.S.A. 70: 697-701.
    [41] 阎隆飞，孙之荣．(1999)．蛋白质分子结构[M]．清华大学出版社，北京．
    [42] Pauling, L., and Corey, R.B. (1950). Two Hydrogen-bonded Spiral Configuration of The Polypeptide Chain [J]. J. Am. Chem. Soc. 72: 5349-5349.
    [43] Pauling, L., Corey, R.B., and Barnson, H.R. (1951). The Structure of Proteins: Two Hydrogen-Bonded Helical Configurations of the Polypeptide Chain [J]. Proc. Natl.Acad. Sci. U.S.A. 37: 205-211.
    [44] Barlow, D.J., and Thornton, J.M. (1988). Helix geometry in proteins [J]. J. Mol. Biol. 201: 601-619.
    [45] Lehninger, A.L., Nelson, D.L., and Cox, M.M. (2000). Lehninger Principles of Biochemistry [M], 4th ed. W.H. Freeman, New York
    [46] Zimm, B.H., and Bragg, J.K. (1959). Theory of the phase transition between helix and random coil in polypeptide chains [J]. J. Chem. Phys. 31: 526-535.
    [47] Lifson, S., and Roig, A. (1961). On the theory of helix-coil transition in polypeptides [J]. J. Chem. Phys. 34: 1963-1974.
    [48] Kabsch, W., and Sander, C. (1983). Dictionary of protein secondary structure: Pattern recognition of hydrogen-bonded and geometrical features [J]. Biopolymers 22: 2577-2637.
    [49] Doty, P., and Yang, J.T. (1956). Polypeptide. Ⅵ. Poly-benzyl-L-glutamate: the Helix-coil Transition in Solution [J]. J. Am. Chem. Soc. 78: 498-499.
    [50] Schellman, J.A. (1958). The Factors Affecting the Stability of Hydrogen-bonded Polypeptide Structures in Solution [J]. J. Phys. Chem. 62: 1485-1494.
    [51] Qian, H., and Schellman, J.A. (1992). Helix-Coil Theories: A Comparative Study for Finite Length Polypeptides [J]. J. Phys. Chem. 96: 3987-3994.
    [52] von Dreele, P.H., Poland, D., and Scheraga, H.A. (1971). Helix-coil stability constants for the naturally occurring amino acids in water Ⅰ. Properties of copolymers and approximate theories [J]. Macromolecules 4: 396-407.
    [53] Doig, A.J., Chakrabartty, A., Klingler, T.M., and Baldwin, R.L. (1994). Determination Of Free-Energies Of N-Capping In Alpha-Helices By Modification Of The Lifson-Roig Helix-Coil Theory To Include N-Capping And C-Capping [J]. Biochemistry 33: 3396-3403.
    [54] Stapley, B.J., Rohl, C.A., and Doig, A.J. (1995). Addition Of Side-Chain Interactions To Modified Lifson-Roig Helix-Coil Theory-Application To Energetics Of Phenylalanine-Methionine Interactions [J]. Protein Sci. 4: 2383-2391.
    [55] Scheraga, H.A., Vile, J.A., and Ripoll, D.R. (2002). Helix-coil transitions re-visited [J]. Biophys. Chem. 101: 255-265.
    [56] Chakrabartty, A., Kortemme, T., and Baldwin, R.L. (1994). Helix Propensities Of The Amino-Acids Measured In Alanine-Based Peptides Without Helix-Stabilizing Side-Chain Interactions [J]. Protein Sci. 3: 843-852.
    [57] Oneil, K.T., and Degrado, W.E (1990). A Thermodynamic Scale For The Helix-Forming Tendencies Of The Commonly Occurring Amino-Acids [J]. Science 250: 646-651.
    [58] Lyu, P.C., Lift, M.I., Marky, L.A., and Kallenbach, N.R. (1990). Side-Chain Contributions To The Stability Of Alpha-Helical Structure In Peptides [J]. Science 250: 669-673.
    [59] Scholtz, J.M., Hong, Q., York, E.J., Stewart, J.M., and Baldwin, R.L. (1991). Parameters Of Helix-Coil Transition Theory For Alanine-Based Peptides Of Varying Chain Lengths In Water [J]. Biopolymers 31: 1463-1470.
    [60] Pace, C.N., and Scholtz, J.M. (1998). A helix propensity scale based on experimental studies of peptides and proteins [J]. Biophys. J. 75: 422-427.
    [61] Munoz, V., and Serrano, L. (1994). Elucidating The Folding Problem Of Helical Peptides Using Empirical Parameters [J]. Nat. Struct. Biol. 1: 399-409.
    [62] Wu, Y.D., and Zhao, Y.L. (2001). A theoretical study on the origin of cooperativity in the formation of 3(10)-and alpha-helices [J]. J. Am. Chem. Soc. 123: 5313-5319.
    [63] Levy, Y., Jortner, J., and Becker, O.M. (2001). Solvent effects on the energy landscapes and folding kinetics of polyalanine [J]. Proc. Natl. Acad. Sci. U. S. A. 98: 2188-2193.
    [64] Yang, A.S., and Honig, B. (1995). Free-Energy Determinants Of Secondary Structure Formation. 1. Alpha-Helices [J]. J. Mol. Biol. 252:351-365.
    [65] Takano, M., Yamato, T., Higo, J., Suyama, A., and Nagayama, K. (1999). Molecular dynamics of a 15-residue poly(L-alanine) in water: Helix formation and energetics [J]. J.Am. Chem. Soc. 121: 605-612.
    [66] Makhatadze, G.I. (2006). Thermodynamics of alpha-helix formation [J]. Advances in Protein Chemistry 72: 199-223.
    [67] Williams, S., Causgrove, T.P., Gilmanshin, R., Fang, K.S., Callender, R.H., Woodruff, W.H., and Dyer, R.B. (1996). Fast events in protein folding: Helix melting and formation in a small peptide [J]. Biochemistry 35: 691-697.
    [68] Thompson, P.A., Eaton, W.A., and Hofrichter, J. (1997). Laser temperature jump study of the helix reversible arrow coil kinetics of an alanine peptide interpreted with a 'kinetic zipper' model [J]. Biochemistry 36: 9200-9210.
    [69] Huang, C.Y., Getahun, Z., Zhu, Y.J., Klemke, J.W., DeGrado, W.E, and Gai, E (2002). Helix formation via conformation diffusion search [J]. Proc. Natl. Acad. Sci. U.S.A. 99: 2788-2793.
    [70] Bredenbeck, J., Helbing, J., Kumita, J.R., Woolley, G.A., and Hamm, P. (2005). alpha-Helix formation in a photoswitchable peptide tracked from picoseconds to microseconds by time-resolved IR spectroscopy [J]. Proc. Natl. Acad. Sci. U. S. A. 102: 2379-2384.
    [71] Schwarz, G. (1965). On the kinetics of the helix-coil transition of polypeptides in solution [J]. J. Mol. Biol. 11: 64-77.
    [72] Brooks III, C.L. (1996). Helix-coil kinetics: Folding time scales for helical peptides from a sequential kinetic model [J]. J. Phys. Chem. 100: 2546-2549.
    [73] Buchete, N.V., and Straub, J.E. (2001). Mean first-passage time calculations for the coil-to-helix transition: The active helix Ising model [J]. J. Phys. Chem. B 105：6684-6697．
    [74] 杨玉良，张红东．(1992)．高分子科学中的Monte Carlo方法[M]．复旦大学出版社，上海．
    [75] 王骏，王炜．(1997)．蛋白质动力学理论研究中的计算机模拟方法[J]．物理学进展 17：289-318．
    [76] Levinthal, C. (1969). How to fold graciously. In Mossbauer Spectroscopy in Biological Systems: Proceedings of a meeting held at Allerton House, Monticello, Illinois [M]. (eds. P. DeBrunner, J. Tsibris, and E. Munck), pp. 22-24. University of Illinois Press, Urbana, Illinois.
    [77] de Gennes, P.G. (1992). Soft Matter (Nobel Lecture) [J]. Angew. Chem.-Int. Edit. Engl. 31: 842-845.
    [78] 马红孺，陆坤权．(2000)．软凝聚态物质物理学[J]．物理学进展 9：516-524．
    [79] Leach, A.R. (2001). Molecular Modeling: Principles and Applications [M], 2nd ed. Longman, London.
    [80] Brooks, C.L. (2002). Protein and peptide folding explored with molecular simulations [J]. Accounts Chem. Res. 35: 447-454.
    [81] Boczko, E.M., and Brooks, C.L. (1995). First-Principles Calculation Of The Folding Free-Energy Of A 3-Helix Bundle Protein [J]. Science 269: 393-396.
    [82] Duan, Y., and Kollman, P.A. (1998). Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution [J]. Science 282: 740-744.
    [83] Snow, C.D., Nguyen, N., Pande, V.S., and Gruebele, M. (2002). Absolute comparison of simulated and experimental protein-folding dynamics [J]. Nature 420: 102-106.
    [84] Mayor, U., Guydosh, N.R., Johnson, C.M., Grossmann, J.G., Sato, S., Jas, G.S., Freund, S.M.V., Alonso, D.O.V., Daggett, V., and Fersht, A.R. (2003). The complete folding pathway of a protein from nanoseconds to microseconds [J]. Nature 421: 863-867.
    [85] Shirts, M., and Pande, V.S. (2000). Computing-Screen savers of the world unite! [J]. Science 290: 1903-1904.
    [86] Head-Gordon, T., and Brown, S. (2003). Minimalist models for protein folding and design [J]. Curt. Opin. Struct. Biol. 13: 160-167.
    [87] Tozzini, V. (2005). Coarse-grained models for proteins [J]. Curr. Opin. Struct. Biol. 15: 144-150.
    [88] Dokholyan, N.V. (2006). Studies of folding and misfolding using simplified models [J]. Curr. Opin. Struct. Biol. 16: 79-85.
    [89] Levitt, M. (1976). A Simplified Representation of Protein Conformations for Rapid Simulation of Protein Folding [J]. J. Mol. Biol. 104: 59-107.
    [90] Thirumalai, D., and Klimov, D.K. (1999). Deciphering the timescales and mechanisms of protein folding using minimal off-lattice models [J]. Curr. Opin. Struct. Biol. 9: 197-207.
    [91] McCammon, J.A., Northrup, S.H., Karplus, M., and Levy, R.M. (1980). Helix-coil transitions in a simple polypeptide model [J]. Biopolymers 19: 2033-2045.
    [92] Lau, K.E, and Dill, K.A. (1989). A lattice statistical mechanics model of the conformational and sequence spaces of proteins [J]. Macromolecules 22: 3986-3997.
    [93] Sali, A., Shakhnovich, E., and Karplus, M. (1994). Kinetics Of Protein-Folding-A Lattice Model Study Of The Requirements For Folding To The Native-State [J]. J. Mol. Biol. 235: 1614-1636.
    [94] Hinds, D.A., and Levitt, M. (1994). Exploring Conformational Space With A Simple Lattice Model For Protein-Structure [J]. J. Mol. Biol. 243: 668-682.
    [95] Dill, K.A., Bromberg, S., Yue, K.Z., Fiebig, K.M., Yee, D.P., Thomas, P.D., and Chan, H.S. (1995). Principles Of Protein Folding-A Perspective From Simple Exact Models [J]. Protein Sci. 4: 561-602.
    [96] Li, H., Helling, R., Tang, C., and Wingreen, N. (1996). Emergence of preferred structures in a simple model of protein folding [J]. Science 273: 666-669.
    [97] Zhou, Y.Q., and Karplus, M. (1999). Interpreting the folding kinetics of helical proteins [J]. Nature 401: 400-403.
    [98] Skolnick, J., and Kolinski, A. (1990). Simulations of the Folding of a Globular Protein [J]. Science 250: 1121-1125.
    [99] Kolinski, A., and Skolnick, J. (1994). Monte-Carlo Simulations Of Protein-Folding. 1. Lattice Model And Interaction Scheme [J]. Proteins-Structure Function And Genetics 18: 338-352.
    [100] Klimov, D.K., and Thirumalai, D. (1998). Cooperativity in protein folding: from lattice models with sidechains to real proteins [J]. Fold. Des. 3: 127-139.
    [101] Li, L., Mirny, L.A., and Shakhnovich, E.I. (2000). Kinetics, thermodynamics and evolution of non-native interactions in a protein folding nucleus [J]. Nat. Struct. Biol. 7: 336-342.
    [102] Mukherjee, A., and Bagchi, B. (2004). Contact pair dynamics during folding of two small proteins: Chicken villin head piece and the Alzheimer protein beta-amyloid [J].J. Chem. Phys. 120: 1602-1612.
    [103] Wallqvist, A., and Ullner, M. (1994). A Simplified Amino-Acid Potential For Use In Structure Predictions Of Proteins [J]. Proteins 18: 267-280.
    [104] Zhang, Y., Kolinski, A., and Skolnick, J. (2003). TOUCHSTONE Ⅱ: A new approach to ab initio protein structure prediction [J]. Biophys. J. 85:1145-1164.
    [105] Liwo, A., Oldziej, S., Pincus, M.R., Wawak, R.J., Rackovsky, S., and Scheraga, H.A. (1997). A united-residue force field for off-lattice protein-structure simulations. 1. Functional forms and parameters of long-range side-chain interaction potentials from protein crystal data [J]. J. Comput. Chem. 18: 849-873.
    [106] Klimov, D.K., Betancourt, M.R., and Thirumalai, D. (1998). Virtual atom representation of hydrogen bonds in minimal off-lattice models of alpha helices: effect on stability, cooperativity and kinetics [J]. Fold. Des. 3: 481-496.
    [107] Chen, J.Z.Y., and Imamura, H. (2003). Universal model for alpha-helix and beta-sheet structures in protein [J]. Physica A 321: 181-188.
    [108] Sun, S.J. (1993). Reduced Representation Model of Protein-Structure Prediction-Statistical Potential and Genetic Algorithms [J]. Protein Sci. 2: 762-785.
    [109] Takada, S., Luthey-Schulten, Z., and Wolynes, P. G. (1999). Folding dynamics with nonadditive forces: A simulation study of a designed helical protein and a random heteropolymer [J]. J. Chem. Phys. 110: 11616-11629.
    [110] Smith, A.V., and Hall, C.K. (2001). alpha-Helix formation: Discontinuous molecular dynamics on an intermediate-resolution protein model [J]. Proteins 44: 344-360.
    [111] Ding, E, Borreguero, J.M., Buldyrey, S.V., Stanley, H.E., and Dokholyan, N.V. (2003). Mechanism for the alpha-helix to beta-hairpin transition [J]. Proteins 53: 220-228.
    [112] Irback, A., Sjunnesson, F., and Wallin, S. (2000). Three-helix-bundle protein in a Ramachandran model [J]. Proc. Natl.Acad. Sci. U.S.A. 97: 13614-13618.
    [113] Ding, F., Buldyrev, S.V., and Dokholyan, N.V. (2005). Folding Trp-cage to NMR resolution native structure using a coarse-grained protein model [J]. Biophys. J. 88: 147-155.
    [114] Shimada, J., Kussell, E.L., and Shakhnovich, E.I. (2001). The folding thermodynamics and kinetics of crambin using an all-atom Monte Carlo simulation [J]. Jo Mol. Biol. 308: 79-95.
    [115] Zhou, Y.Q., and Linhananta, A. (2002). Thermodynamics of an all-atom off-lattice model of the fragment B of Staphylococcal protein A: Implication for the origin of the cooperativity of protein folding [J]. J. Phys. Chem. B 106: 1481-1485.
    [116] Kolinski, A., and Skolnick, J. (2004). Reduced models of proteins and their applications [J]. Biomacromolecules 45: 511-524.
    [117] Wunderlich, B. (1975). Crystallization of Linear Macromolecules [M]. Rensselaer Polytechnic, New York.
    [1] Binder, K., and Heermann, D.W. (2002). Monte Carlo simulation in statistical physics: an introduction [M], 4th ed. Springer, Berlin & New York.
    [2] Raabe, D. (1998). Computational Materials Science [M]. Wiley-VCH, Weinheim.
    [3] 杨玉良，张红东．(1992)．高分子科学中的Monte Carlo方法[M]．复旦大学出版社，上海．
    [4] Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. (1953). Equation of state calculations by fast computing machines [J]. J. Chem. Phys. 21: 1087-1092.
    [5] Leach, A.R. (2001). Molecular Modelling: Principles and Applications [M]. Longman, London.
    [6] 杨小震．(2002)．分子模拟与高分子材料[M]．科学出版社，北京．
    [7] Wall, F.T. (1953). Mean Dimensions of Rubber-Like Polymer Molecules [J]. J. Chem. Phys. 21: 1914.
    [8] Wall, F.T., Hiller, J.L.A., and Wheeler, D.J. (1954). Statistical Computation of Mean Dimensions of Macromolecules. Ⅰ[J]. J. Chem. Phys. 22: 1036.
    [9] Wall, F.T., Hiller, J.L.A., and Atchison, W.E (1955). Statistical Computation of Mean Dimensions of Macromolecules. Ⅱ[J]. J. Chem. Phys. 23: 913.
    [10] Wall, F.T., Hiller, J.L.A., and Atchison, W.F. (1955). Statistical Computation of Mean Dimensions of Macromolecules. Ⅲ [J]. J. Chem. Phys. 23: 2314.
    [11] Taketomi, H., Ueda, Y., and Go, N. (1975). Studies on protein folding, unfolding and fluctuations by computer simulations [J]. Int. J. Peptide and Protein Res. 7:445-459.
    [12] Ueda, Y., Taketomi, H., and Go, N. (1978). Studies on protein folding, unfolding and fluctuations by computer simulations. Ⅱ. A three-dimensional lattice model of lysozyme [J]. Biopolymers 17: 1531-1548.
    [13] Lau, K.E, and Dill, K.A. (1989). A lattice statistical mechanics model of the conformational and sequence spaces of proteins [J]. Macromolecules 22: 3986-3997.
    [14] Kolinski, A., and Skolnick, J. (1992). Discretized Model Of Proteins .1. Monte-Carlo Study Of Cooperativity In Homopolypeptides [J]. J. Chem. Phys. 97: 9412-9426.
    [15] Kolinski, A., and Skolnick, J. (1994). Monte-Carlo Simulations Of Protein-Folding .1. Lattice Model And Interaction Scheme [J]. Proteins 18: 338-352.
    [16] Sali, A., Shakhnovich, E., and Karplus, M. (1994). Kinetics Of Protein-Folding-A Lattice Model Study Of The Requirements For Folding To The Native-State [J]. J. Mol. Biol. 235: 1614-1636.
    [17] Dill, K.A., Bromberg, S., Yue, K.Z., Fiebig, K.M., Yee, D.P., Thomas, P.D., and Chan, H.S. (1995). Principles Of Protein Folding-A Perspective From Simple Exact Models [J]. Protein Sci. 4: 561-602.
    [18] Li, H., Helling, R., Tang, C., and Wingreen, N. (1996). Emergence of preferred structures in a simple model of protein folding [J]. Science 273: 666-669.
    [19] Hansmann, U.H.E., and Okamoto, Y. (1999). New Monte Carlo algorithms for protein folding [J]. Curr. Opin. Struct. Biol. 9: 177-183.
    [20] Li, L., Mirny, L.A., and Shakhnovich, E.I. (2000). Kinetics, thermodynamics and evolution of non-native interactions in a protein folding nucleus [J]. Nat. Struct. Biol. 7: 336-342.
    [21] Shimada, J., and Shakhnovich, E.I. (2002). The ensemble folding kinetics of protein G from an all-atom Monte Carlo simulation [J]. Proc. Natl. Acad. Sci. U.S.A. 99: 11175-11180.
    [22] Landau, D.P., and Binder, K. (2000). A Guide to Monte Carlo Simulations in Statistical Physics [M]. Cambridge University, Cambridge.
    [23] Berg, B.A., and Neuhaus, T. (1991). Multicanonical Algorithms for 1st Order Phase-Transitions [J]. Phys. Lett. B 267: 249-253.
    [24] Berg, B.A., and Neuhaus, T. (1992). Multicanonical Ensemble-a New Approach to Simulate 1st-Order Phase-Transitions [J]. Phys. Rev. Lett. 68: 9-12.
    [25] Hansmann, U.H.E., and Okamoto, Y. (1993). Prediction of Peptide Conformation by Multicanonical Algorithm-New Approach to the Multiple-Minima Problem [J].J. Comput. Chem. 14: 1333-1338.
    [26] Kemp, J., and Chen, Z. (1998). Formation of helical states in wormlike polymer chains [J]. Phys. Rev. Lett. 81: 3880-3883.
    [27] 翁辛．(1997)．高分子线团塌缩转变的Monte Carlo模拟——正则系综法与巨正则系统法[D]．学士学位论文．复旦大学，上海．
    [28] Shimada, J., Kussell, E.L., and Shakhnovich, E.I. (2001). The folding thermodynamics and kinetics of crambin using an all-atom Monte Carlo simulation [J]. J. Mol. Biol. 308: 79-95.
    [29] Rey, A., and Skolnick, J. (1991). Comparison of lattice Monte Carlo dynamics and Brownian dynamics folding pathways of alpha-helical hairpins [J]. Chem. Phys. 158: 199-219.
    [30] Verdier, P.H., and Stockmayer, W.H. (1962). Monte Carlo Calculations on the Dynamics of Polymers in Dilute Solution [J]. J. Chem. Phys. 36: 227.
    [31] Hilhorst, H.J., and Deutch, J.M. (1975). Analysis of Monte Carlo results on the kinetics of lattice polymer chains with excluded volume [J]. J. Chem. Phys. 63: 5153.
    [32] Larson, R.G., Scriven, L.E., and Davis, H.T. (1985). Monte Carlo simulation of model amphiphile-oil-water systems [J]. J. Chem. Phys. 83: 2411-2420.
    [33] Larson, R.G. (1988). Monte Carlo lattice simulation of amphiphilic systems in two and three dimensions [J]. J. Chem. Phys. 89: 1642-1650.
    [34] Carmesin, I., and Kremer, K. (1988). The bond fluctuation method: a new effective algorithm for the dynamics of polymers in all spatial dimensions [J]. Macromolecules 21: 2819-2823.
    [35] Carmesin, I., and Kremer, K. (1990). Static and Dynamic Properties of 2-Dimensional Polymer Melts[J]. J Phys-Paris 51: 915-932.
    [36] Hinds, D.A., and Levitt, M. (1994). Exploring Conformational Space With A Simple Lattice Model For Protein-Structure [J]. J. Mol. Biol. 243: 668-682.
    [37] Deutsch, H.P., and Binder, K. (1991). Interdiffusion And Self-Diffusion In Polymer Mixtures: A Monte-Carlo Study [J]. J. Chem. Phys. 94: 2294-2304.
    [38] Pakula, T. (1987). [J]. Macromolecules 20: 679.
    [39] Pakula, T., and Geyler, S. (1987). [J]. Macromolecules 20: 2909.
    [40] Pakula, T., and Geyler, S. (1988). [J]. Macromolecules 21: 1665.
    [41] Hu, W.B. (1998). Structural transformation in the collapse transition of the single flexible homopolymer model [J]. Journal of Chemical Physics 109: 3686-3690.
    [42] Ding, J., Carver, T.J., and Windle, A.H. (2001). Self-assembled structures of block copolymers in selective solvents reproduced by lattice Monte Carlo simulation [J]. Comput. Theor. Polym. Sci. 11: 483-490.
    [43] de Gennes, P.G. (1979). Scaling concepts in polymer physics [M]. Cornell University Press, Ithaca, New York.
    [44] 张琦．(2001)．链状大分子的coil-globule转发及coil-helix转发的Monte Carlo模拟[D]．学士学位论文．复旦大学，上海．
    [45] Deutsch, H.P., and Binder, K. (1991). Interdiffusion And Self-Diffusion In Polymer Mixtures-A Monte-Carlo Study [J]. Journal Of Chemical Physics 94: 2294-2304.
    [46] 吕文琦．(2006)．聚合反应及大单体凝胶化的动态蒙特卡罗模拟[D]．博士学位论文．复旦大学，上海．
    [47] Dill, K.A. (1990). Dominant Forces In Protein Folding [J]. Biochemistry 29:7133-7155.
    [48] Leach, A.R. (2001). Molecular Modeling: Principles and Applications [M], 2nd ed. Longman, London.
    [49] 阎隆飞，孙之荣．(1999)．蛋白质分子结构[M]．清华大学出版社，北京．
    [50] 徐筱杰等．(2004)．计算机辅助药物分子设计[M]．化学工业出版社，北京．
    [51] Kirkpatrick, S., Gelat Jr, C.D., and Vecchi, M.P. (1983). Optimization by simulated annealing [J]. Science 220: 671-680.
    [52] Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. (1953). Equation of state calculations by fast computing machines [J]. J. Chem. Phys. 21: 1087-1092.
    [53] Onuchic, J.N., Nymeyer, H., Garcia, A.E., Chahine, J., and Socci, N.D. (2000). The energy landscape theory of protein folding: Insights into folding mechanisms and scenarios [J]. Advances In Protein Chemistry 53: 87-152.
    [1] Levinthal, C. (1969). How to fold graciously. In Mossbauer Spectroscopy in Biological Systems: Proceedings of a meeting held at Allerton House, Monticello, Illinois [M]. (eds. P. DeBrunner, J. Tsibris, and E. Munck), pp. 22-24. University of Illinois Press, Urbana, Illinois.
    [2] Levinthal, C. (1968). Are there pathways for protein folding? [J]. J. Chim. Phys. 65: 44-45.
    [3] Anfinsen, C.B. (1973). Principles that govern the folding of protein chain [J]. Science 181: 223-230.
    [4] Wolynes, P.G., Onuchic, J.N., and Thirumalai, D. (1995). Navigating The Folding Routes [J]. Science 267: 1619-1620.
    [5] Dill, K.A., and Chan, H.S. (1997). From Levinthal to pathways to funnels [J]. Nat. Struct. Biol. 4: 10-19.
    [6] Gross, M., and Plaxco, K.W. (1997). Protein engineering-Reading, writing and redesigning [J]. Nature 388: 419-420.
    [7] Ueda, Y., Taketomi, H., and Go, N. (1978). Studies on protein folding, unfolding and fluctuations by computer simulations. Ⅱ. A three-dimensional lattice model of lysozyme [J]. Biopolymers 17: 1531-1548.
    [8] Taketomi, H., Ueda, Y., and Go, N. (1975). Studies on protein folding, unfolding and fluctuations by computer simulations [J]. Int. J. Peptide and Protein Res. 7: 445-459.
    [9] Zhou, Y.Q., and Karplus, M. (1997). Folding thermodynamics of a model three-helix-bundle protein [J]. Proc. Natl. Acad. Sci. U.S.A. 94: 14429-14432.
    [10] Zhou, Y.Q., and Karplus, M. (1999). Folding of a model three-helix bundle protein: A thermodynamic and kinetic analysis [J]. J. Mol. Biol. 293: 917-951.
    [11] Zhou, Y.Q., and Karplus, M. (1999). Interpreting the folding kinetics of helical proteins [J]. Nature 401: 400-403.
    [12] Smith, A.V., and Hall, C.K. (2000). Bridging the gap between homopolymer and protein models: A discontinuous molecular dynamics study [J]. J. Chem. Phys. 113: 9331-9342.
    [13] Smith, A.V., and Hall, C.K. (2001). alpha-Helix formation: Discontinuous molecular dynamics on an intermediate-resolution protein model [J]. Proteins 44: 344-360.
    [14] Zhou, Y.Q., and Linhananta, A. (2002). Thermodynamics of an all-atom off-lattice model of the fragment B of Staphylococcal protein A: Implication for the origin of the cooperativity of protein folding [J]. J. Phys. Chem. B 106: 1481-1485.
    [15] Duan, Y., and Kollman, P.A. (1998). Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution [J]. Science 282: 740-744.
    [16] Sorin, E.J., and Pande, V.S. (2005). Exploring the helix-coil transition via all-atom equilibrium ensemble simulations [J]. Biophys. J. 88: 2472-2493.
    [17] Snow, C.D., Nguyen, N., Pande, V.S., and Gruebele, M. (2002). Absolute comparison of simulated and experimental protein-folding dynamics [J]. Nature 420: 102-106.
    [18] Mayor, U., Guydosh, N.R., Johnson, C.M., Grossmann, J.G., Sato, S., Jas, G.S., Freund, S.M.V., Alonso, D.O.V., Daggett, V., and Fersht, A.R. (2003). The complete folding pathway of a protein from nanoseconds to microseconds [J]. Nature 421: 863-867.
    [19] Daggett, V., and Levitt, M. (1992). Molecular Dynamics Simulations Of Helix Denaturation [J]. J. Mol. Biol. 223: 1121-1138.
    [20] Hansmann, U.H.E., and Okamoto, Y. (1999). Finite-size scaling of helix-coil transitions in poly-alanine studied by multicanonical simulations [J]. J. Chem. Phys. 110: 1267-1276.
    [21] Kemp, J., and Chen, Z. (1998). Formation of helical states in wormlike polymer chains [J]. Phys. Rev. Lett. 81: 3880-3883.
    [22] Kemp, J.P., and Chen, J.Z.Y. (2001). Helical structures in proteins [J]. Biomacromolecules 2: 389-401.
    [23] Kemp, J.P., and Chen, J.Z.Y. (2002). Folding dynamics of the helical structure observed in a minimal model [J]. Europhys. Lett. 59: 721-727.
    [24] Shimada, J., Kussell, E.L., and Shakhnovich, E.I. (2001). The folding thermodynamics and kinetics of crambin using an all-atom Monte Carlo simulation [J]. J. Mol. Biol. 308: 79-95.
    [25] Shimada, J., and Shakhnovich, E.I. (2002). The ensemble folding kinetics of protein G from an all-atom Monte Carlo simulation [J]. Proc. Natl. Acad. Sci. U.S.A. 99: 11175-11180.
    [26] Lau, K.E, and Dill, K.A. (1989). A lattice statistical mechanics model of the conformational and sequence spaces of proteins [J]. Macromolecules 22: 3986-3997.
    [27] Sali, A., Shakhnovich, E., and Karplus, M. (1994). Kinetics Of Protein-Folding-A Lattice Model Study Of The Requirements For Folding To The Native-State [J]. J. Mol. Biol. 235: 1614-1636.
    [28] Baker, D. (2000). A surprising simplicity to protein folding [J]. Nature 405: 39-42.
    [29] Godzik, A., Kolinski, A., and Skolnick, J. (1993). Lattice Representations Of Globular-Proteins-How Good Are They [J]. J. Comput. Chem. 14: 1194-1202.
    [30] Hinds, D.A., and Levitt, M. (1994). Exploring Conformational Space With A Simple Lattice Model For Protein-Structure [J]. J. Mol. Biol. 243: 668-682.
    [31] Dill, K.A., Bromberg, S., Yue, K.Z., Fiebig, K.M., Yee, D.P., Thomas, P.D., and Chan, H.S. (1995). Principles Of Protein Folding-A Perspective From Simple Exact Models [J]. Protein Sci. 4: 561-602.
    [32] Kolinski, A., Galazka, W., and Skolnick, J. (1996). On the origin of the cooperativity of protein folding: Implications from model simulations [J]. Proteins 26: 271-287.
    [33] Li, L., Mirny, L.A., and Shakhnovich, E.I. (2000). Kinetics, thermodynamics and evolution of non-native interactions in a protein folding nucleus [J]. Nat. Struct. Biol. 7: 336-342.
    [34] Kolinski, A., and Skolnick, J. (2004). Reduced models of proteins and their applications [J]. Biomacromolecules 45: 511-524.
    [35] Li, H., Helling, R., Tang, C., and Wingreen, N. (1996). Emergence of preferred structures in a simple model of protein folding [J]. Science 273: 666-669.
    [36] Ivanov, V.A., Paul, W., and Binder, K. (1998). Finite chain length effects on the coil-globule transition of stiff-chain macromolecules: A Monte Carlo simulation [J]. J. Chem. Phys. 109: 5659-5669.
    [37] Chertovich, A.V., Ivanov, V.A., Zavin, B.G., and Khokhlov, A.R. (2002). Conformation-dependent sequence design of HP copolymers: An algorithm based on sequential modifications of monomer units [J]. Macromol. Theory Simul. 11: 751-756.
    [38] Zhang, L.X., and Zhao, D.L. (2001). Folding lattice HP model of proteins using the bond-fluctuation model[J]. Macromol. Theory Simul. 10: 518-522.
    [39] Okamoto, Y., and Hansmann, U.H.E. (1995). Thermodynamics of helix-coil transitions studied by multicanonical algorithms [J]. J. Phys. Chem. 99: 11276-11287.
    [40] Sikorski, A., Kolinski, A., and Skolnick, J. (1998). Computer simulations of de novo designed helical proteins [J]. Biophys. J. 75: 92-105.
    [41] Chen, C.M. (2001). Lattice model of transmembrane polypeptide folding [J]. Phys. Rev. E 6301.
    [42] 张琦．(2001)．链状大分子的coil-globule转变及coil-helix转变的Monte Carlo模拟[D]．学士学位论文．复旦大学，上海．
    [43] Chakrabartty, A., and Baldwin, R.L. (1995). Stability of Alpha-Helices [J]. Advances in Protein Chemistry 46: 141-176.
    [44] Schellman, J.A. (1958). The Factors Affecting the Stability of Hydrogen-bonded Polypeptide Structures in Solution [J]. J. Phys. Chem. 62: 1485-1494.
    [45] Zimm, B.H., and Bragg, J.K. (1959). Theory of the phase transition between helix and random coil in polypeptide chains [J]. J. Chem. Phys. 31: 526-535.
    [46] Lifson, S., and Roig, A. (1961). On the theory of helix-coil transition in polypeptides [J].J. Chem. Phys. 34: 1963-1974.
    [47] Poland, D., and Scheraga, H.A. (1970). Theory of Helix-Coil Transitions in Biopolymers [M]. Academic Press, New York & London.
    [48] Blundell, T.L., and Johnson, L.N. (1976). Protein Crystallography [M]. Academic Press, New York.
    [49] Carmesin, I., and Kremer, K. (1988). The bond fluctuation method: a new effective algorithm for the dynamics of polymers in all spatial dimensions [J]. Macromolecules 21: 2819-2823.
    [50] Deutsch, H.P., and Binder, K. (1991). Interdiffusion And Self-Diffusion In Polymer Mixtures: A Monte-Carlo Study [J]. J. Chem. Phys. 94: 2294-2304.
    [51] Xu, G.Q., Ding, J.D., and Yang, Y.L. (1997). Monte Carlo simulation of self-avoiding lattice chains subject to simple shear flow. I. Model and simulation algorithm [J]. J. Chem. Phys. 107: 4070-4084.
    [52] Dill, K.A. (1990). Dominant Forces In Protein Folding [J]. Biochemistry 29: 7133-7155.
    [53] Pauling, L., and Corey, R.B. (1950). Two Hydrogen-bonded Spiral Configuration of The Polypeptide Chain [J]. J. Am. Chem. Soc. 72: 5349-5349.
    [54] Pauling, L., Corey, R.B., and Barnson, H.R. (1951). The Structure of Proteins: Two Hydrogen-Bonded Helical Configurations of the Polypeptide Chain [J]. Proc. Natl.Acad. Sci. U.S.A. 37: 205-211.
    [55] 阎隆飞，and孙之荣．(1999)．蛋白质分子结构[M]．清华大学出版社，北京．
    [56] Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. (1953). Equation of state calculations by fast computing machines [J]. J. Chem. Phys. 21: 1087-1092.
    [57] Kirkpatrick, S., Gelat Jr, C.D., and Vecchi, M.P. (1983). Optimization by simulated annealing [J]. Science 220: 671-680.
    [58] Leach, A.R. (2001). Heat Capacity and Energy Fluctuations. In Molecular Modeling: Principles and Applications [M], 2nd ed. (ed. A.R. Leach), pp. 348-349. Longman, London.
    [59] 杨玉良，and于同隐．(1986)．高斯链回转椭球主轴分量均方值的近似计算[J]．中国科学A辑 29：651-656．
    [60] Wojcik, J., Altmann, K.H., and Scheraga, H.A. (1990). Helix Coil Stability-Constants For The Naturally-Occurring Amino-Acids In Water .24. Half-Cystine Parameters From Random Poly(Hydroxybutylglutamine-Co-S-Methylthio-L-Cysteine) [J]. Biopolymers 30: 121-134.
    [61] Chakrabartty, A., Kortemme, T., and Baldwin, R.L. (1994). Helix Propensities Of The Amino-Acids Measured In Alanine-Based Peptides Without Helix-Stabilizing Side-Chain Interactions [J]. Protein Sci. 3: 843-852.
    [62] Daggett, V., Kollman, P.A., and Kuntz, I.D. (1991). A Molecular Dynamics Simulation Of Polyalanine: An Analysis Of Equilibrium Motions And Helix-Coil Transitions [J]. Biopolymers 31: 1115-1134.
    [63] Ohkubo, Y.Z., and Brooks III, C.L. (2003). Exploring Flory's isolated-pair hypothesis: Statistical mechanics of helix-coil transitions in polyalanine and the C-peptide from RNase A [J]. Proc. Natl.Acad. Sci. U.S.A. 100: 13916-13921.
    [64] Skolnick, J., and Kolinski, A. (1990). Simulations of the Folding of a Globular Protein [J]. Science 250: 1121-1125.
    [65] Kolinski, A., and Skolnick, J. (1992). Discretized Model Of Proteins .1. Monte-Carlo Study Of Cooperativity In Homopolypeptides [J]. J. Chem. Phys. 97: 9412-9426.
    [1] Pauling, L., and Corey, R.B. (1950). Two Hydrogen-bonded Spiral Configuration of The Polypeptide Chain [J]. J. Am. Chem. Soc. 72: 5349-5349.
    [2] Pauling, L., Corey, R.B., and Barnson, H.R. (1951). The Structure of Proteins: Two Hydrogen-Bonded Helical Configurations of the Polypeptide Chain [J]. Proc. Natl.Acad. Sci. U.S.A. 37: 205-211.
    [3] Doty, P., and Yang, J.T. (1956). Polypeptide. Ⅵ. Poly-benzyl-L-glutamate: the Helix-coil Transition in Solution [J]. J. Am. Chem. Soc. 78: 498-499.
    [4] Wojcik, J., Altmann, K.H., and Scheraga, H.A. (1990). Helix Coil Stability-Constants For The Naturally-Occurring Amino-Acids In Water .24. Half-Cystine Parameters From Random Poly(Hydroxybutylglutamine-Co-S-Methylthio-L-Cysteine) [J]. Biopolymers 30: 121-134.
    [5] Oneil, K.T., and Degrado, W.E (1990). A Thermodynamic Scale For The Helix-Forming Tendencies Of The Commonly Occurring Amino-Acids [J]. Science 250: 646-651.
    [6] Lyu, P.C., Lift, M.I., Marky, L.A., and Kallenbach, N.R. (1990). Side-Chain Contributions To The Stability Of Alpha-Helical Structure In Peptides [J]. Science 250: 669-673.
    [7] Scholtz, J.M., Hong, Q., York, E.J., Stewart, J.M., and Baldwin, R.L. (1991). Parameters Of Helix-Coil Transition Theory For Alanine-Based Peptides Of Varying Chain Lengths In Water [J]. Biopolymers 31: 1463-1470.
    [8] Chakrabartty, A., Kortemme, T., and Baldwin, R.L. (1994). Helix Propensities Of The Amino-Acids Measured In Alanine-Based Peptides Without Helix-Stabilizing Side-Chain Interactions [J]. Protein Sci. 3: 843-852.
    [9] Thompson, P.A., Eaton, W.A., and Hofrichter, J. (1997). Laser temperature jump study of the helix reversible arrow coil kinetics of an alanine peptide interpreted with a 'kinetic zipper' model [J]. Biochemistry 36: 9200-9210.
    [10] Huang, C.Y., Getahun, Z., Zhu, Y.J., Klemke, J.W., DeGrado, W.E, and Gai, E (2002). Helix formation via conformation diffusion search [J]. Proc. Natl. Acad. Sci. U.S.A. 99: 2788-2793.
    [11] Barrett, D.G., Minder, C.M., Mian, M.U., Whittington, S.J., Cooper, W.J., Fuchs, K.M., Tripathy, A., Waters, M.L., Creamer, T.P., and Pielak, G.J. (2006). Pressure perturbation calorimetry of helical peptides [J]. Proteins 63: 322-326.
    [12] Loladze, V.V., and Makhatadze, G.I. (2005). Both helical propensity and side-chain hydrophobicity at a partially exposed site in alpha-helix contribute to the thermodynamic stability of ubiquitin [J]. Proteins 58: 1-6.
    [13] Schellman, J.A. (1955). The Stability of Hydrogen-bonded Peptide Structures in Aqueous Solution [J]. Compt. Rend. Trav. Lab. Carlsburg, Ser. Chim. 29: 230-259.
    [14] Zimm, B.H., and Bragg, J.K. (1959). Theory of the phase transition between helix and random coil in polypeptide chains [J]. J. Chem. Phys. 31: 526-535.
    [15] Lifson, S., and Roig, A. (1961). On the theory of helix-coil transition in polypeptides [J]. J. Chem. Phys. 34: 1963-1974.
    [16] Flory, P.J., and Miller, W.G. (1966). A General Treatment of Helix-coil Equilibria in Macromolecular Systems [J]. J. Mol. Biol. 15: 284.
    [17] Fixman, M., and Zeroka, D. (1968). Helix-Coil Transition in Heterogeneous Chains. I. Protein Model [J]. J. Chem. Phys. 48: 5223-5230.
    [18] Poland, D., and Scheraga, H.A. (1970). Theory of Helix-Coil Transitions in Biopolymers [M]. Academic Press, New York & London.
    [19] Qian, H., and Schellman, J.A. (1992). Helix-Coil Theories: A Comparative Study for Finite Length Polypeptides [J]. J. Phys. Chem. 96: 3987-3994.
    [20] Doig, A.J., Chakrabartty, A., Klingler, T.M., and Baldwin, R.L. (1994). Determination Of Free-Energies Of N-Capping In Alpha-Helices By Modification Of The Lifson-Roig Helix-Coil Theory To Include N-Capping And C-Capping [J]. Biochemistry 33: 3396-3403.
    [21] Munoz, V., and Serrano, L. (1994). Elucidating The Folding Problem Of Helical Peptides Using Empirical Parameters [J]. Nat. Struct. Biol. 1: 399-409.
    [22] Brooks III, C.L. (1996). Helix-coil kinetics: Folding time scales for helical peptides from a sequential kinetic model [J]. J. Phys. Chem. 100: 2546-2549.
    [23] Avbelj, F., Luo, P.Z., and Baldwin, R.L. (2000). Energetics of the interaction between water and the helical peptide group and its role in determining helix propensities [J]. Proc. Natl.Acad. Sci. U.S.A. 97: 10786-10791.
    [24] Buchete, N.V., and Straub, J.E. (2001). Mean first-passage time calculations for the coil-to-helix transition: The active helix Ising model [J]. J. Phys. Chem. B 105: 6684-6697.
    [25] McCammon, J.A., Northrup, S.H., Karplus, M., and Levy, R.M. (1980). Helix-coil transitions in a simple polypeptide model [J]. Biopolymers 19: 2033-2045.
    [26] Daggett, V., Kollman, P.A., and Kuntz, I.D. (1991). A Molecular Dynamics Simulation Of Polyalanine: An Analysis Of Equilibrium Motions And Helix-Coil Transitions [J]. Biopolymers 31: 1115-1134.
    [27] Daggett, V., and Levitt, M. (1992). Molecular Dynamics Simulations Of Helix Denaturation [J]. J. Mol. Biol. 223: 1121-1138.
    [28] Yang, A.S., and Honig, B. (1995). Free-Energy Determinants Of Secondary Structure Formation. 1. Alpha-Helices [J]. J. Mol. Biol. 252: 351-365.
    [29] Okamoto, Y., and Hansmann, U.H.E. (1995). Thermodynamics of helix-coil transitions studied by multicanonical algorithms [J]. J. Phys. Chem. 99: 11276-11287.
    [30] Young, W.S., and Brooks III, C.L. (1996). A microscopic view of helix propagation: N and C-terminal helix growth in alanine helices [J]. J. Mol. Biol. 259: 560-572.
    [31] Ohkubo, Y.Z., and Brooks III, C.L. (2003). Exploring Flory's isolated-pair hypothesis: Statistical mechanics of helix-coil transitions in polyalanine and the C-peptide from RNase A [J]. Proc. Natl. Acad. Sci. U.S.A. 100: 13916-13921.
    [32] Zhou, Y.Q., and Karplus, M. (1997). Folding thermodynamics of a model three-helix-bundle protein [J]. Proc. Natl. Acad. Sci. U.S.A. 94: 14429-14432.
    [33] Zhou, Y.Q., and Linhananta, A. (2002). Thermodynamics of an all-atom off-lattice model of the fragment B of Staphylococcal protein A: Implication for the origin of the cooperativity of protein folding [J]. J. Phys. Chem. B 106: 1481-1485.
    [34] Kemp, J., and Chen, Z. (1998). Formation of helical states in wormlike polymer chains [J]. Phys. Rev. Lett. 81: 3880-3883.
    [35] Sikorski, A., Kolinski, A., and Skolnick, J. (1998). Computer simulations of de novo designed helical proteins [J]. Biophys. J. 75: 92-105.
    [36] Takano, M., Yamato, T., Higo, J., Suyama, A., and Nagayama, K. (1999). Molecular dynamics of a 15-residue poly(L-alanine) in water: Helix formation and energetics [J]. J.Am. Chem. Soc. 121: 605-612.
    [37] Takano, M., Nagayama, K., and Suyama, A. (2002). Investigating a link between all-atom model simulation and the Ising-based theory on the helix-coil transition: Equilibrium statistical mechanics [J]. J. Chem. Phys. 116: 2219-2228.
    [38] Vila, J.A., Ripoll, D.R., and Scheraga, H.A. (2000). Physical reasons for the unusual alpha-helix stabilization afforded by charged or neutral polar residues in alanine-rich peptides [J]. Proc. Natl. Acad. Sci. U.S.A. 97: 13075-13079.
    [39] Smith, A.V., and Hall, C.K. (2001). alpha-Helix formation: Discontinuous molecular dynamics on an intermediate-resolution protein model [J]. Proteins 44: 344-360.
    [40] Wu, Y.D., and Zhao, Y.L. (2001). A theoretical study on the origin of cooperativity in the formation of 3(10)- and alpha-helices [J]. J. Am. Chem. Soc. 123: 5313-5319.
    [41] Knott, M., and Chan, H.S. (2004). Exploring the effects of hydrogen bonding and hydrophobic interactions on the foldability and cooperativity of helical proteins using a simplified atomic model [J]. Chem. Phys. 307: 187-199.
    [42] Sorin, E.J., and Pande, V.S. (2005). Exploring the helix-coil transition via all-atom equilibrium ensemble simulations [J]. Biophys. J. 88: 2472-2493.
    [43] Shental-Bechor, D.S., Kirca, S., Ben-Tal, N., and Haliloglu, T. (2005). Monte Carlo studies of folding, dynamics, and stability in alpha-helices [J]. Biophys. J. 88: 2391-2402.
    [44] van Giessen, A.E., and Straub, J.E. (2005). Monte Carlo simulations of polyalanine using a reduced model and statistics-based interaction potentials [J]. J. Chem. Phys. 122: 024904.
    [45] Salvatella, X., Dobson, C.M., Fersht, A.R., and Vendruscolo, M. (2005). Determination of the folding transition states of barnase by using Phi(I)-value-restrained simulations validated by double mutant Phi(IJ)-values [J]. Proc. Natl.Acad. Sci. U.S.A. 102: 12389-12394.
    [46] Gnanakaran, S., and Garcia, A.E. (2005). Helix-coil transition of alanine peptides in water: Force field dependence on the folded and unfolded structures [J]. Proteins 59: 773-782.
    [47] Podtelezhnikov, A.A., and Wild, D.L. (2005). Exhaustive metropolis Monte Carlo sampling and analysis of polyalanine conformations adopted under the influence of hydrogen bonds [J]. Proteins 61: 94-104.
    [48] Chen, Y.T., Zhang, Q., and Ding, J.D. (2004). A coarse-grained model and associated lattice Monte Carlo simulation of the coil-helix transition of a homopolypeptide [J]. J. Chem. Phys. 120: 3467-3474.
    [49] Zimm, B.H., and Bragg, L.K. (1959). Theory of the phase transition between helix and random coil in polypeptide chains [J]. J. Chem. Phys. 31: 526-535.
    [50] Cantor, C.R., and Schimmel, P.R. (1980). Biophysical Chemistry [M]. Freeman, New York, pp. 1041-1073.
    [51] Applequist, J. (1963). On the Helix-Coil Equilibrium in Polypeptides [J]. J. Chem. Phys. 38: 934-941.
    [52] Cantor, C.R., and Schimmel, P.R. (1980). Biophysical Chemistry[M], pp. 1041-1073. Freeman, New York.
    [53] Taketomi, H., Ueda, Y., and Go, N. (1975). Studies on protein folding, unfolding and fluctuations by computer simulations [J]. Int. J. Peptide and Protein Res. 7: 445-459.
    [54] Chen, Y.T., Zhang, Q., and Ding, J.D. (2006). A coarse-grained model for the formation of alpha-helix with a non-integer period on simple cubic lattices [J]. J. Chem. Phys. 124: 184903.
    [55] Wang, L., Oconnell, T., Tropsha, A., and Hermans, J. (1995). Thermodynamic Parameters For The Helix-Coil Transition Of Oligopeptides Molecular-Dynamics Simulation With The Peptide Growth Method [J]. Proc. Natl. Acad. Sci. U.S.A. 92: 10924-10928.
    [56] Armen, R., Alonso, D.O.V., and Daggett, V. (2003). The role of alpha-, 3(10)-, and pi-helix in helix -> coil transitions [J]. Protein Sci. 12: 1145-1157.
    [57] van Giessen, A.E., and Straub, J.E. (2006). Coarse-Grained Model of Coil-to-Helix Kinetics Demonstrates the Importance of Multiple Nucleation Sites in Helix Folding [J]. J. Chem. Theory Comput. 2: 674-684.
    [58] Nymeyer, H., and Garcia, A.E. (2003). Simulation of the folding equilibrium of alpha-helical peptides: A comparison of the generalized born approximation with explicit solvent [J]. Proc. Natl. Acad. Sci. U.S.A. 100: 13934-13939.
    [59] Hansmann, U.H.E., and Okamoto, Y. (1999). Finite-size scaling of helix-coil transitions in poly-alanine studied by multicanonical simulations [J]. J. Chem. Phys. 110: 1267-1276.
    [60] Peng, Y., Hansmann, U.H.E., and Alves, N.A. (2003). Solution effects and the order of the helix-coil transition in polyalanine [J]. J. Chem. Phys. 118: 2374-2380.
    [61] Kemp, J.P., and Chen, J.Z.Y. (2001). Helical structures in proteins [J]. Biomacromolecules 2: 389-401.
    [62] Scheraga, H.A., Vile, J.A., and Ripoll, D.R. (2002). Helix-coil transitions re-visited [J]. Biophys. Chem. 101: 255-265.
    [63] von Dreele, P.H., Poland, D., and Scheraga, H.A. (1971). Helix-coil stability constants for the naturally occurring amino acids in water. Ⅰ. Properties of copolymers and approximate theories [J]. Macromolecules 4: 396-407.
    [64] Ptitsyn, O.B. (1972). Thermodynamic parameters of helix-coil transitions in polypeptide chains [J]. Pure Appl. Chem. 31: 227-244.
    [65] Rohl, C.A., Scholtz, J.M., York, E.J., Stewart, J.M., and Baldwin, R.L. (1992). Kinetics of Amide Proton-Exchange in Helical Peptides of Varying Chain Lengths-Interpretation by the Lifson-Roig Equation [J]. Biochemistry 31: 1263-1269.
    [66] von Dreele, P.H., Lotan, N., Ananthanarayanan, V.S., Andreatta, R.H., Poland, D., and Scheraga, H.A. (1971). Helix-coil stability constants for the naturally occurring amino acids in water. Ⅱ. Characterization of the host polymers and application of the host-guest technique to random poly(hydroxypropylglutamine-co-hydroxybutylglutamine) [J]. Macromolecules 4: 408-417.
    [67] Pace, C.N., and Scholtz, J.M. (1998). A helix propensity scale based on experimental studies of peptides and proteins [J]. Biophys. J. 75: 422-427.
    [68] Kumar, S., and Bansal, M. (1996). Structural and sequence characteristics of long alpha helices in globular proteins [J]. Biophys. J. 71: 1574-1586.
    [69] Flory, P.J. (1953). Principles of polymer chemistry [M]. Cornell University Press, Ithaca and London.
    [70] Kabsch, W., and Sander, C. (1983). Dictionary of protein secondary structure: Pattern recognition of hydrogen-bonded and geometrical features [J]. Biopolymers 22: 2577-2637.
    [1] Hao, M.H., and Scheraga, H.A. (1999). Designing potential energy functions for protein folding [J]. Curr. Opin. Struct. Biol. 9: 184-188.
    [2] Mirny, L.A., and Shakhnovich, E.I. (1996). How to derive a protein folding potential? A new approach to an old problem [J].J. Mol. Biol. 264: 1164-1179.
    [3] Taketomi, H., Ueda, Y., and Go, N. (1975). Studies on protein folding, unfolding and fluctuations by computer simulations [J]. Int. J. Peptide and Protein Res. 7: 445-459.
    [4] Ueda, Y., Taketomi, H., and Go, N. (1978). Studies on protein folding, unfolding and fluctuations by computer simulations. Ⅱ. A three-dimensional lattice model of lysozyme [J]. Biopolymers 17: 1531-1548.
    [5] Clementi, C., Jennings, P.A., and Onuchic, J.N. (2000). How native-state topology affects the folding of dihydrofolate reductase and interleukin-1 beta [J]. Proc. Natl. Acad. Sci. U.S.A. 97: 5871-5876.
    [6] Plaxco, K.W., Simons, K.T., Ruczinski, I., and David, B. (2000). Topology, stability, sequence, and length: Defining the determinants of two-state protein folding kinetics [J]. Biochemistry 39:11177-11183.
    [7] Plaxco, K.W., Simons, K.T., and Baker, D. (1998). Contact order, transition state placement and the refolding rates of single domain proteins [J]. J. Mol. Biol. 277: 985-994.
    [8] Itzhaki, L.S., Otzen, D.E., and Fersht, A.R. (1995). The Structure Of The Transition-State For Folding Of Chymotrypsin Inhibitor-2 Analyzed By Protein Engineering Methods-Evidence For A Nucleation-Condensation Mechanism For Protein-Folding [J]. J. Mol. Biol. 254: 260-288.
    [9] Onuchic, J.N., Nymeyer, H., Garcia, A.E., Chahine, J., and Socci, N.D. (2000). The energy landscape theory of protein folding: Insights into folding mechanisms and scenarios [J]. Adv. Protein Chem. 53: 87-152.
    [10] Riddle, D.S., Grantcharova, V.P., Santiago, J.V., Alm, E., Ruczinski, I., and Baker, D. (1999). Experiment and theory highlight role of native state topology in SH3 folding [J]. Nat. Struct. Biol. 6: 1016-1024.
    [11] Galzitskaya, O.V., and Finkelstein, A.V. (1999). A theoretical search for folding/unfolding nuclei in three-dimensional protein structures [J]. Proc. Natl. Acad. Sci. U.S.A. 96: 11299-11304.
    [12] Alm, E., and Baker, D. (1999). Prediction of protein-folding mechanisms from free-energy landscapes derived from native structures [J]. Proc. Natl. Acad. Sci. U.S.A. 96: 11305-11310.
    [13] Munoz, V., and Eaton, W.A. (1999). A simple model for calculating the kinetics of protein folding from three-dimensional structures [J]. Proc. Natl. Acad. Sci. U.S.A. 96: 11311-11316.
    [14] Zhou, Y.Q., and Karplus, M. (1999). Interpreting the folding kinetics of helical proteins [J]. Nature 401: 400-403.
    [15] Zhou, Y.Q., and Linhananta, A. (2002). Thermodynamics of an all-atom off-lattice model of the fragment B of Staphylococcal protein A: Implication for the origin of the cooperativity of protein folding [J]. J. Phys. Chem. B 106: 1481-1485.
    [16] Shimada, J., Kussell, E.L., and Shakhnovich, E.I. (2001). The folding thermodynamics and kinetics of crambin using an all-atom Monte Carlo simulation [J]. J. Mol. Biol. 308: 79-95.
    [17] Shimada, J., and Shakhnovich, E.I. (2002). The ensemble folding kinetics of protein G from an all-atom Monte Carlo simulation [J]. Proc. Natl. Acad. Sci. U.S.A. 99: 11175-11180.
    [18] Viguera, A.R., Vega, C., and Serrano, L. (2002). Unspecific hydrophobic stabilization of folding transition states [J]. Proc. Natl. Acad. Sci. U.S.A. 99: 5349-5354.
    [19] Blanco, F.J., Serrano, L., and Forman-Kay, J.D. (1998). High populations of non-native structures in the denatured state are compatible with the formation of the native folded state [J]. J. Mol. Biol. 284: 1153-1164.
    [20] Hamada, D., and Goto, Y. (1997). The equilibrium intermediate of beta-lactoglobulin with non-native alpha-helical structure [J]. J. Mol. Biol. 269: 479-487.
    [21] Hamada, D., Segawa, S., and Goto, Y. (1996). Non-native alpha-helical intermediate in the refolding of beta-lactoglobulin, a predominantly beta-sheet protein [J]. Nat. Struct. Biol. 3: 868-873.
    [22] Clementi, C., and Plotkin, S.S. (2004). The effects of nonnative interactions on protein folding rates: Theory and simulation [J]. Protein Sci. 13: 1750-1766.
    [23] Fan, K., Wang, J., and Wang, W. (2002). Folding of lattice protein chains with modified G(o)over-bar potential [J]. Eur. Phys. J. B 30: 381-391.
    [24] Paci, E., Vendruscolo, M., and Karplus, M. (2002). Native and non-native interactions along protein folding and unfolding pathways [J]. Proteins 47: 379-392.
    [25] Plotkin, S.S. (2001). Speeding protein folding beyond the Go model: How a little frustration sometimes helps [J]. Proteins 45: 337-345.
    [26] Treptow, W.L., Barbosa, M.A.A., Garcia, L.G., and de Araujo, A.F.P. (2002). Non-native interactions, effective contact order, and protein folding: A mutational investigation with the energetically frustrated hydrophobic model [J]. Proteins 49: 167-180.
    [27] Li, L., Mirny, L.A., and Shakhnovich, E.I. (2000). Kinetics, thermodynamics and evolution of non-native interactions in a protein folding nucleus [J]. Nat. Struct. Biol. 7: 336-342.
    [28] Barlow, D.J., and Thornton, J.M. (1988). Helix geometry in proteins [J]. J. Mol. Biol. 201: 601-619.
    [29] Pauling, L., and Corey, R.B. (1950). Two Hydrogen-bonded Spiral Configuration of The Polypeptide Chain [J]. J. Am. Chem. Soc. 72: 5349-5349.
    [30] Pauling, L., Corey, R.B., and Barnson, H.R. (1951). The Structure of Proteins: Two Hydrogen-Bonded Helical Configurations of the Polypeptide Chain [J]. Proc. Natl.Acad. Sci. U.S.A. 37: 205-211.
    [31] Zimm, B.H., and Bragg, L.K. (1959). Theory of the phase transition between helix and random coil in polypeptide chains [J]. J. Chem. Phys. 31: 526-535.
    [32] Lifson, S., and Roig, A. (1961). On the theory of helix-coil transition in polypeptides [J]. J. Chem. Phys. 34: 1963-1974.
    [33] Poland, D., and Scheraga, H.A. (1970). Theory of Helix-Coil Transitions in Biopolymers [M]. Academic Press, New York & London.
    [34] Qian, Q., and Schellman, J.A. (1992). Helix-Coil Theories: A Comparative Study for Finite Length Polypeptides [J]. J. Phys. Chem. 96: 3987-3994.
    [35] Chen, Y.T., Zhang, Q., and Ding, J.D. (2004). A coarse-grained model and associated lattice Monte Carlo simulation of the coil-helix transition of a homopolypeptide [J]. J. Chem. Phys. 120: 3467-3474.
    [36] Wu, X.W., and Wang, S.M. (2001). Helix folding of an alanine-based peptide in explicit water [J]. J. Phys. Chem. B 105: 2227-2235.
    [37] Okamoto, Y., and Hansmann, U.H.E. (1995). Thermodynamics of helix-coil transitions studied by multicanonical algorithms [J]. J. Phys. Chem. 99: 11276-11287.
    [38] Sung, S.S. (1994). Helix Folding Simulations With Various Initial Conformations [J]. Biophys. J. 66: 1796-1803.
    [39] Daggett, V., Kollman, P.A., and Kuntz, I.D. (1991). A Molecular Dynamics Simulation Of Polyalanine: An Analysis Of Equilibrium Motions And Helix-Coil Transitions [J]. Biopolymers 31: 1115-1134.
    [40] Kemp, J.P., and Chen, J.Z.Y. (2001). Helical structures in proteins [J]. Biomacromolecules 2: 389-401.
    [41] Hummer, G., Garcia, A.E., and Garde, S. (2001). Helix nucleation kinetics from molecular simulations in explicit solvent [J]. Proteins 42: 77-84.
    [42] Duan, Y., and Kollman, P.A. (1998). Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution [J]. Science 282: 740-744.
    [43] Mayor, U., Guydosh, N.R., Johnson, C.M., Grossmann, J.G., Sato, S., Jas, G.S., Freund, S.M.V., Alonso, D.O.V., Daggett, V., and Fersht, A.R. (2003). The complete folding pathway of a protein from nanoseconds to microseconds [J]. Nature 421: 863-867.
    [44] Snow, C.D., Nguyen, N., Pande, V.S., and Gruebele, M. (2002). Absolute comparison of simulated and experimental protein-folding dynamics [J]. Nature 420: 102-106.
    [45] Thompson, P.A., Eaton, W.A., and Hofrichter, J. (1997). Laser temperature jump study of the helix reversible arrow coil kinetics of an alanine peptide interpreted with a 'kinetic zipper' model [J]. Biochemistry 36: 9200-9210.
    [46] Williams, S., Causgrove, T.P., Gilmanshin, R., Fang, K.S., Callender, R.H., Woodruff, W.H., and Dyer, R.B. (1996). Fast events in protein folding: Helix melting and formation in a small peptide [J]. Biochemistry 35: 691-697.
    [47] Wang, T., Zhu, Y.J., Getahun, Z., Du, D.G., Huang, C.Y., DeGrado, W.E, and Gai, F. (2004). Length dependent helix-coil transition kinetics of nine alanine-based peptides [J]. J. Phys. Chem. B 108: 15301-15310.
    [48] Brooks III, C.L. (1996). Helix-coil kinetics: Folding time scales for helical peptides from a sequential kinetic model [J]. J. Phys. Chem. 100: 2546-2549.
    [49] Buchete, N.V., and Straub, J.E. (2001). Mean first-passage time calculations for the coil-to-helix transition: The active helix Ising model [J]. J. Phys. Chem. B 105: 6684-6697.
    [50] Richardson, J.M., and Makhatadze, G.I. (2004). Temperature dependence of the thermodynamics of helix-coil transition [J]. J. Mol. Biol. 335:1029-1037.
    [51] Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. (1953). Equation of state calculations by fast computing machines [J]. J. Chem. Phys. 21: 1087-1092.
    [52] Rudnick, J., and Gaspari, G. (1986). [J]. J. Phys. A: Math. Gen. 19: L191.
    [53] Zifferer, G., and Olaj, O.F. (1994). Shape Asymmetry of Random-Walks and Nonreversal Random-Walks[J]. J. Chem. Phys. 100: 636-639.
    [54] Kabsch, W., and Sander, C. (1983). Dictionary of protein secondary structure: Pattern recognition of hydrogen-bonded and geometrical features [J]. Biopolymers 22: 2577-2637.
    [55] Armen, R., Alonso, D.O.V., and Daggett, V. (2003). The role of alpha-, 3(10)-, and pi-helix in helix -> coil transitions [J]. Protein Sci. 12: 1145-1157.
    [56] Daggett, V., and Levitt, M. (1992). Molecular Dynamics Simulations Of Helix Denaturation [J]. J. Mol. Biol. 223: 1121-1138.
    [57] Ohkubo, Y.Z., and Brooks III, C.L. (2003). Exploring Flory's isolated-pair hypothesis: Statistical mechanics of helix-coil transitions in polyalanine and the C-peptide from RNase A [J]. Proc. Natl.Acad. Sci. U.S.A. 100: 13916-13921.
    [58] Chen, Y.T., Zhang, Q., and Ding, J.D. (2006). A coarse-grained model for the formation of alpha-helix with a non-integer period on simple cubic lattices [J]. J. Chem. Phys. 124: 184903.
    [59] Elmer, S., and Pande, V.S. (2001). A new twist on the helix-coil transition: A non-biological helix with protein-like intermediates and traps [J]. J. Phys. Chem. B105: 482-485.
    [60] Hamm, P., Helbing, J., and Bredenbeck, J. (2006). Stretched versus compressed exponential kinetics in alpha-helix folding [J]. Chem. Phys. 323: 54-65.
    [61] Huang, C.Y., Getahun, Z., Zhu, Y.J., Klemke, J.W., DeGrado, W.F., and Gai, E (2002). Helix formation via conformation diffusion search [J]. Proc. Natl. Acad. Sci. U.S.A. 99: 2788-2793.
    [62] Chowdhury, S., Zhang, W., Wu, C., Xiong, G.M., and Duan, Y. (2003). Breaking non-native hydrophobic clusters is the rate-limiting step in the folding of an alanine-based peptide [J]. Biopolymers 68: 63-75.
    [63] Huang, C.Y., Klemke, J.W., Getahun, Z., DeGrado, W.F., and Gai, F. (2001). Temperature-dependent helix-coil transition of an alanine based peptide [J]. J. Am. Chem. Soc. 123: 9235-9238.
    [64] Carmesin, I., and Kremer, K. (1988). The bond fluctuation method: a new effective algorithm for the dynamics of polymers in all spatial dimensions [J]. Macromolecules 21: 2819-2823.
    [65] Deutsch, H.P., and Binder, K. (1991). Inter-diffusion and self-diffusion in polymer mixtures: A Monte Carlo study [J]. J. Chem. Phys. 94: 2294-2304.
    [1] Pauling, L., and Corey, R.B. (1950). Two Hydrogen-bonded Spiral Configuration of The Polypeptide Chain [J]. J. Am. Chem. Soc. 72: 5349-5349.
    [2] Pauling, L., Corey, R.B., and Barnson, H.R. (1951). The Structure of Proteins: Two Hydrogen-Bonded Helical Configurations of the Polypeptide Chain [J]. Proc. Natl.Acad. Sci. U.S.A. 37: 205-211.
    [3] Barlow, D.J., and Thornton, J.M. (1988). Helix geometry in proteins [J]. J. Mol. Biol. 201: 601-619.
    [4] Doty, P., and Yang, J.T. (1956). Polypeptide. Ⅳ. Poly-benzyl-L-glutamate: the Helix-coil Transition in Solution [J]. J. Am. Chem. Soc. 78: 498-499.
    [5] Schellman, J.A. (1958). The Factors Affecting the Stability of Hydrogen-bonded Polypeptide Structures in Solution [J]. J. Phys. Chem. 62: 1485-1494.
    [6] Zimm, B.H., and Bragg, L.K. (1959). Theory of the phase transition between helix and random coil in polypeptide chains [J]. J. Chem. Phys. 31: 526-535.
    [7] Lifson, S., and Roig, A. (1961). On the theory of helix-coil transition in polypeptides [J]. J. Chem. Phys. 34: 1963-1974.
    [8] Fixman, M., and Zeroka, D. (1968). Helix-Coil Transition in Heterogeneous Chains. I. Protein Model [J]. J. Chem. Phys. 48: 5223-5230.
    [9] Poland, D., and Scheraga, H.A. (1970). Theory of Helix-Coil Transitions in Biopolymers [M]. Academic Press, New York & London.
    [10] Qian, Q., and Schellman, J.A. (1992). Helix-Coil Theories: A Comparative Study for Finite Length Polypeptides [J]. J. Phys. Chem. 96: 3987-3994.
    [11] Chakrabartty, A., and Baldwin, R.L. (1995). Stability of Alpha-Helices [J]. Adv. Protein Chem. 46: 141-176.
    [12] Yang, A.S., and Honig, B. (1995). Free-Energy Determinants Of Secondary Structure Formation .1. Alpha-Helices [J]. J. Mol. Biol. 252: 351-365.
    [13] Takano, M., Yamato, T., Higo, J., Suyama, A., and Nagayama, K. (1999). Molecular dynamics of a 15-residue poly(L-alanine) in water: Helix formation and energetics [J]. J.Am. Chem. Soc. 121: 605-612.
    [14] Brooks Ⅲ, C.L. (1996). Helix-coil kinetics: Folding time scales for helical peptides from a sequential kinetic model [J]. J. Phys. Chem. 100: 2546-2549.
    [15] Buchete, N.V., and Straub, J.E. (2001). Mean first-passage time calculations for the coil-to-helix transition: The active helix Ising model [J]. J. Phys. Chem. B 105: 6684-6697.
    [16] Richardson, J.M., and Makhatadze, G.I. (2004). Temperature dependence of the thermodynamics of helix-coil transition [J]. J. Mol. Biol. 335: 1029-1037.
    [17] Daggett, V., Kollman, P.A., and Kuntz, I.D. (1991). A Molecular Dynamics Simulation Of Polyalanine: An Analysis Of Equilibrium Motions And Helix-Coil Transitions [J]. Biopolymers 31: 1115-1134.
    [18] Sung, S.S. (1994). Helix Folding Simulations With Various Initial Conformations [J]. Biophys. J. 66: 1796-1803.
    [19] Okamoto, Y., and Hansmann, U.H.E. (1995). Thermodynamics of helix-coil transitions studied by multicanonical algorithms [J]. J. Phys. Chem. 99: 11276-11287.
    [20] Kemp, J., and Chen, Z. (1998). Formation of helical states in wormlike polymer chains [J]. Phys. Rev. Lett. 81: 3880-3883.
    [21] Hansmann, U.H.E., and Okamoto, Y. (1999). Finite-size scaling of helix-coil transitions in poly-alanine studied by multicanonical simulations [J]. J. Chem. Phys. 110: 1267-1276.
    [22] Hummer, G., Garcia, A.E., and Garde, S. (2001). Helix nucleation kinetics from molecular simulations in explicit solvent [J]. Proteins 42: 77-84.
    [23] Ohkubo, Y.Z., and Brooks Ⅲ, C.L. (2003). Exploring Flory's isolated-pair hypothesis: Statistical mechanics of helix-coil transitions in polyalanine and the C-peptide from RNase A [J]. Proc. Natl.Acad. Sci. U.S.A. 100: 13916-13921.
    [24] Peng, Y., Hansmann, U.H.E., and Alves, N.A. (2003). Solution effects and the order of the helix-coil transition in polyalanine [J]. J. Chem. Phys. 118: 2374-2380.
    [25] Chen, J.Z.Y., Lemak, A.S., Lepock, J.R., and Kemp, J.P. (2003). Minimal model for studying prion-like folding pathways [J]. Proteins 51: 283-288.
    [26] Chen, J.Z.Y., and Imamura, H. (2003). Universal model for alpha-helix and beta-sheet structures in protein [J]. Physica A 321: 181-188.
    [27] Imamura, H., and Chen, J.Z.Y. (2004). Conformational conversion of proteins due to mutation [J]. Europhys. Lett. 67: 491-497.
    [28] Chen, Y.T., Zhang, Q., and Ding, J.D. (2004). A coarse-grained model and associated lattice Monte Carlo simulation of the coil-helix transition of a homopolypeptide [J]. J. Chem. Phys. 120: 3467-3474.
    [29] van Giessen, A.E., and Straub, J.E. (2005). Monte Carlo simulations of polyalanine using a reduced model and statistics-based interaction potentials [J]. J. Chem. Phys. 122: 024904.
    [30] Shental-Bechor, D.S., Kirca, S., Ben-Tal, N., and Haliloglu, T. (2005). Monte Carlo studies of folding, dynamics, and stability in alpha-helices [J]. Biophys. J. 88: 2391-2402.
    [31] Duan, Y., and Kollman, P.A. (1998). Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution [J]. Science 282: 740-744.
    [32] Snow, C.D., Nguyen, N., Pande, V.S., and Gruebele, M. (2002). Absolute comparison of simulated and experimental protein-folding dynamics [J]. Nature 420: 102-106.
    [33] Zhou, Y.Q., and Linhananta, A. (2002). Thermodynamics of an all-atom off-lattice model of the fragment B of Staphylococcal protein A: Implication for the origin of the cooperativity of protein folding [J]. J. Phys. Chem. B 106: 1481-1485.
    [34] Mayor, U., Guydosh, N.R., Johnson, C.M., Grossmann, J.G., Sato, S., Jas, G.S., Freund, S.M.V., Alonso, D.O.V., Daggett, V., and Fersht, A.R. (2003). The complete folding pathway of a protein from nanoseconds to microseconds [J]. Nature 421: 863-867.
    [35] Thirumalai, D., Klimov, D.K., and Dima, R.I. (2002). Insights into specific problems in protein folding using simple concepts [J]. Adv. Chem. Phys. 120: 35-76.
    [36] Head-Gordon, T., and Brown, S. (2003). Minimalist models for protein folding and design [J]. Curr. Opin. Struct. Biol. 13: 160-167.
    [37] Taketomi, H., Ueda, Y., and Go, N. (1975). Studies on protein folding, unfolding and fluctuations by computer simulations [J]. Int. J. Peptide and Protein Res. 7: 445-459.
    [38] Lau, K.E, and Dill, K.A. (1989). A lattice statistical mechanics model of the conformational and sequence spaces of proteins [J]. Macromolecules 22: 3986-3997.
    [39] Dill, K.A., Bromberg, S., Yue, K.Z., Fiebig, K.M., Yee, D.P., Thomas, P.D., and Chan, H.S. (1995). Principles Of Protein Folding-A Perspective From Simple Exact Models [J]. Protein Sci. 4: 561-602.
    [40] Sali, A., Shakhnovich, E., and Karplus, M. (1994). Kinetics Of Protein-Folding-A Lattice Model Study Of The Requirements For Folding To The Native-State [J]. J. Mol. Biol. 235: 1614-1636.
    [41] Li, L., Mirny, L.A., and Shakhnovich, E.I. (2000). Kinetics, thermodynamics and evolution of non-native interactions in a protein folding nucleus [J]. Nat. Struct. Biol. 7: 336-342.
    [42] Kolinski, A., and Skolnick, J. (2004). Reduced models of proteins and their applications [J]. Polymer 45: 511-524.
    [43] Kolinski, A., and Skolnick, J. (1992). Discretized Model Of Proteins .1. Monte-Carlo Study Of Cooperativity In Homopolypeptides [J]. J. Chem. Phys. 97: 9412-9426.
    [44] Godzik, A., Kolinski, A., and Skolnick, J. (1993). Lattice Representations Of Globular-Proteins-How Good Are They [J]. J. Comput. Chem. 14: 1194-1202.
    [45] Carmesin, I., and Kremer, K. (1988). The bond fluctuation method: a new effective algorithm for the dynamics of polymers in all spatial dimensions [J]. Macromolecules 21: 2819-2823.
    [46] Deutsch, H.P., and Binder, K. (1991). Inter-diffusion and self-diffusion in polymer mixtures: A Monte Carlo study [J]. J. Chem. Phys. 94: 2294-2304.
    [47] Verdier, P.H., and Stockmayer, W.H. (1962). Monte Carlo Calculations on the Dynamics of Polymers in Dilute Solution [J]. J. Chem. Phys. 36: 227-235.
    [48] Hilhorst, H.J., and Deutch, J.M. (1975). Analysis of Monte Carlo results on the kinetics of lattice polymer chains with excluded volume [J]. J. Chem. Phys. 63: 5153-5161.
    [49] Xu, G.Q., Ding, J.D., and Yang, Y.L. (1997). Monte Carlo simulation of self-avoiding lattice chains subject to simple shear flow. I. Model and simulation algorithm [J]. J. Chem. Phys. 107: 4070-4084.
    [50] Chen, Y.T., Luo, Z.L., and Ding, J.D. (2003). Preliminary computer simulation of spatial structure of SARS coronavirus E-protein [J]. Chem. J. Chin. Univ.-Chin. 24: 1406-1409.
    [51] Klimov, D.K., Betancourt, M.R., and Thirumalai, D. (1998). Virtual atom representation of hydrogen bonds in minimal off-lattice models of alpha helices: effect on stability, cooperativity and kinetics [J]. Fold. Des. 3: 481-496.
    [52] Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. (1953). Equation of state calculations by fast computing machines [J]. J. Chem. Phys. 21: 1087-1092.
    [53] Rudnick, J., and Gaspari, G. (1986). [J]. J. Phys. A: Math. Gen. 19: L191.
    [54] Zifferer, G., and Olaj, O.E (1994). Shape Asymmetry of Random-Walks and Nonreversal Random-Walks [J]. J. Chem. Phys. 100: 636-639.
    [55] Kabsch, W., and Sander, C. (1983). Dictionary of protein secondary structure: Pattern recognition of hydrogen-bonded and geometrical features [J]. Biopolymers 22: 2577-2637.
    [56] Zhang, W., Lei, H.X., Chowdhury, S., and Duan, Y. (2004). Fs-21 peptides can form both single helix and helix-turn-helix [J]. J. Phys. Chem. B 108: 7479-7489.
    [57] DeGrado, W.E, Wasserman, Z.R., and Lear, J.D. (1989). Protein design, a minimalist approach [J]. Science 243: 622-628.
    [58] Bragg, L., Kendrew, J.C., and Perutz, M.E (1950). [J]. Proc. Roy. Soc. A203: 321.
    [59] Ji, S.C., and Ding, J.D. (2005). Nonequilibrium Monte Carlo simulation of lattice block copolymer chains subject to oscillatory shear flow [J]. J. Chem. Phys. 122: 164901.
    [60] Cellmer, T., Bratko, D., Prausnitz, J.M., and Blanch, H. (2005). Thermodynamics of folding and association of lattice-model proteins [J]. J. Chem. Phys. 122: 174908.
    [1] Levitt, M., and Warshel, A. (1975). Computer simulation of protein folding [J]. Nature 253: 694-698.
    [2] McCammon, J.A., Gelin, B.R., and Karplus, M. (1977). Dynamics of Folded Proteins [J]. Nature 267: 585-590.
    [3] Ueda, Y., Taketomi, H., and Go, N. (1978). Studies on protein folding, unfolding and fluctuations by computer simulations. Ⅱ. A three-dimensional lattice model of lysozyme [J]. Biopolymers 17: 1531-1548.
    [4] Lau, K.F., and Dill, K.A. (1989). A lattice statistical mechanics model of the conformational and sequence spaces of proteins [J]. Macromolecules 22: 3986-3997.
    [5] Skolnick, J., and Kolinski, A. (1990). Simulations of the Folding of a Globular Protein [J]. Science 250: 1121-1125.
    [6] Daggett, V., and Levitt, M. (1992). Molecular Dynamics Simulations Of Helix Denaturation [J]. J. Mol. Biol. 223: 1121-1138.
    [7] Sali, A., Shakhnovich, E., and Karplus, M. (1994). Kinetics Of Protein-Folding-A Lattice Model Study Of The Requirements For Folding To The Native-State [J]. J. Mol. Biol. 235: 1614-1636.
    [8] Boczko, E.M., and Brooks, C.L. (1995). First-Principles Calculation Of The Folding Free-Energy Of A 3-Helix Bundle Protein [J]. Science 269: 393-396.
    [9] Wolynes, P.G., Onuchic, J.N., and Thirumalai, D. (1995). Navigating The Folding Routes [J]. Science 267: 1619-1620.
    [10] Li, H., Helling, R., Tang, C., and Wingreen, N. (1996). Emergence of preferred structures in a simple model of protein folding [J]. Science 273: 666-669.
    [11] Duan, Y., and Kollman, P.A. (1998). Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution [J]. Science 282: 740-744.
    [12] Zhou, Y.Q., and Karplus, M. (1999). Interpreting the folding kinetics of helical proteins [J]. Nature 401: 400-403.
    [13] Li, L., Mirny, L.A., and Shakhnovich, E.I. (2000). Kinetics, thermodynamics and evolution of non-native interactions in a protein folding nucleus [J]. Nat. Struct. Biol. 7: 336-342.
    [14] Snow, C.D., Nguyen, N., Pande, V.S., and Gruebele, M. (2002). Absolute comparison of simulated and experimental protein-folding dynamics [J]. Nature 420: 102-106.
    [15] Mayor, U., Guydosh, N.R., Johnson, C.M., Grossmann, J.G., Sato, S., Jas, G.S., Freund, S.M.V., Alonso, D.O.V., Daggett, V., and Fersht, A.R. (2003). The complete folding pathway of a protein from nanoseconds to microseconds [J]. Nature 421: 863-867.
    [16] Kemp, J., and Chen, Z. (1998). Formation of helical states in wormlike polymer chains [J]. Phys. Rev. Lett. 81: 3880-3883.
    [17] Taketomi, H., Ueda, Y., and Go, N. (1975). Studies on protein folding, unfolding and fluctuations by computer simulations [J]. Int. J. Peptide and Protein Res. 7: 445-459.
    [18] Dill, K.A., Bromberg, S., Yue, K.Z., Fiebig, K.M., Yee, D.P., Thomas, P.D., and Chan, H.S. (1995). Principles Of Protein Folding-A Perspective From Simple Exact Models [J]. Protein Sci. 4: 561-602.
    [19] Kolinski, A., and Skolnick, J. (2004). Reduced models of proteins and their applications [J]. Biomacromolecules 45: 511-524.
    [20] Kolinski, A., and Skolnick, J. (1994). Monte-Carlo Simulations Of Protein-Folding .1. Lattice Model And Interaction Scheme [J]. Proteins 18: 338-352.
    [21] Klimov, D.K., and Thirumalai, D. (1998). Cooperativity in protein folding: from lattice models with sidechains to real proteins [J]. Fold. Des. 3: 127-139.
    [22] Chen, Y.T., Zhang, Q., and Ding, J.D. (2004). A coarse-grained model and associated lattice Monte Carlo simulation of the coil-helix transition of a homopolypeptide [J]. J. Chem. Phys. 120: 3467-3474.
    [23] Deutsch, H.P., and Binder, K. (1991). Interdiffusion And Self-Diffusion In Polymer Mixtures-A Monte-Carlo Study [J]. J. Chem. Phys. 94: 2294-2304.
    [24] Carmesin, I., and Kremer, K. (1988). The bond fluctuation method: a new effective algorithm for the dynamics of polymers in all spatial dimensions [J]. Macromolecules 21: 2819-2823.
    [25] Wittmann, H.P., Kremer, K., and Binder, K. (1992). Glass-Transition Of Polymer Melts-A 2-Dimensional Monte-Carlo Study In The Framework Of The Bond Fluctuation Method [J]. J. Chem. Phys. 96: 6291-6306.
    [26] Barlow, D.J., and Thornton, J.M. (1988). Helix geometry in proteins [J]. J. Mol. Biol. 201: 601-619.
    [27] Pauling, L., and Corey, R.B. (1950). Two Hydrogen-bonded Spiral Configuration of The Polypeptide Chain [J]. J. Am. Chem. Soc. 72: 5349-5349.
    [28] Pauling, L., Corey, R.B., and Barnson, H.R. (1951). The Structure of Proteins: Two Hydrogen-Bonded Helical Configurations of the Polypeptide Chain [J]. Proc. Natl.Acad. Sci. U.S.A. 37: 205-211.
    [29] Zimm, B.H., and Bragg, J.K. (1959). Theory ofthephase transition between helix and random coil in polypeptide chains [J]. J. Chem. Phys. 31: 526-535.
    [30] Lifson, S., and Roig, A. (1961). On the theory of helix-coil transition in polypeptides [J]. J. Chem. Phys. 34: 1963-1974.
    [31] Poland, D., and Scheraga, H.A. (1970). Theory of Helix-Coil Transitions in Biopolymers [M]. Academic Press, New York & London.
    [32] Qian, H., and Schellman, J.A. (1992). Helix-Coil Theories: A Comparative Study for Finite Length Polypeptides [J]. J. Phys. Chem. 96: 3987-3994.
    [33] Scholtz, J.M., and Baldwin, R.L. (1992). The Mechanism Of Alpha-Helix Formation By Peptides [J]. Annu. Rev. Biophys. Biomolec. Struct. 21:95-118.
    [34] Scheraga, H.A., Vile, J.A., and Ripoll, D.R. (2002). Helix-coil transitions re-visited [J]. Biophys. Chem. 101: 255-265.
    [35] Doig, A.J. (2002). Recent advances in helix-coil theory [J]. Biophys. Chem. 101: 281-293.
    [36] Makhatadze, G.I. (2006). Thermodynamics of alpha-helix formation [J]. Advances in Protein Chemistry 72: 199-223.
    [37] 阎隆飞，and孙之荣．(1999)．蛋白质分子结构[M]．清华大学出版社，北京．
    [38] Berman, H., Henrick, K., and Nakamura, H. (2003). Announcing the worldwide Protein Data Bank [J]. Nat. Struct. Biol. 10: 980-980.
    [39] Ramachandran, G.N., and Sasisekharan, V. (1968). Conformation ofpolypeptide and proteins [J].Advances in Protein Chemistry 23: 283-437.
    [40] Takada, S., Luthey-Schulten, Z., and Wolynes, P.G. (1999). Folding dynamics with nonadditive forces: A simulation study of a designed helical protein and a random heteropolymer [J]. J. Chem. Phys. 110: 11616-11629.
    [41] Smith, A.V., and Hall, C.K. (2001). alpha-Helix formation: Discontinuous molecular dynamics on an intermediate-resolution protein model [J]. Proteins 44: 344-360.
    [42] Ding, F., Borreguero, J.M., Buldyrey, S.V., Stanley, H.E., and Dokholyan, N.V. (2003). Mechanism for the alpha-helix to beta-hairpin transition [J]. Proteins 53: 220-228.
    [43] Kwiecinska, J.I., and Cieplak, M. (2005). Chirality and protein folding [J]. J. Phys.-Condes. Matter 17: S1565-S1580.
    [44] Chen, Y.T., Zhang, Q., and Ding, J.D. (2006). A coarse-grained model for the formation of alpha-helix with a non-integer period on simple cubic lattices [J]. J. Chem. Phys. 124: 184903.
    [45] Verdier, P.H., and Stockmayer, W.H. (1962). Monte Carlo Calculations on the Dynamics of Polymers in Dilute Solution [J]. J. Chem. Phys. 36: 227-235.
    [46] Hilhorst, H.J., and Deutch, J.M. (1975). Analysis of Monte Carlo results on the kinetics of lattice polymer chains with excluded volume [J]. J. Chem. Phys. 63: 5153-5161.
    [47] Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. (1953). Equation of state calculations by fast computing machines [J]. J. Chem. Phys. 21: 1087-1092.
    [48] McCammon, J.A., Northrup, S.H., Karplus, M., and Levy, R.M. (1980). Helix-coil transitions in a simple polypeptide model [J]. Biopolymers 19: 2033-2045.
    [49] Hinds, D.A., and Levitt, M. (1994). Exploring Conformational Space With A Simple Lattice Model For Protein-Structure [J]. J. Mol. Biol. 243: 668-682.
    [50] Okamoto, Y., and Hansmann, U.H.E. (1995). Thermodynamics of helix-coil transitions studied by multicanonical algorithms [J]. J. Phys. Chem. 99: 11276-11287.
    [51] Sorin, E.J., and Pande, V.S. (2005). Exploring the helix-coil transition via all-atom equilibrium ensemble simulations [J]. Biophys. J. 88: 2472-2493.
    [52] Kabsch, W., and Sander, C. (1983). Dictionary of protein secondary structure: Pattern recognition of hydrogen-bonded and geometrical features [J]. Biopolymers 22: 2577-2637.
    [53] Ohkubo, Y.Z., and Brooks Ⅲ, C.L. (2003). Exploring Flory's isolated-pair hypothesis: Statistical mechanics of helix-coil transitions in polyalanine and the C-peptide from RNase A [J]. Proc. Natl.Acad. Sci. U.S.A. 100: 13916-13921.
    [54] Zimmerman, S.S., Pottle, M.S., Némethy, G., and Scheraga, H.A. (1977). Conformational Analysis of the 20 Naturally Occurring Amino Acid Residues Using ECEPP [J]. Macromolecules 10: 1-9.
    [55] Irbaick, A., Sjunnesson, E, and Wallin, S. (2000). Three-helix-bundle protein in a Ramachandran model [J]. Proc. Natl.Acad. Sci. U.S.A. 97: 13614-13618.
    [56] Godzik, A., Kolinski, A., and Skolnick, J. (1993). Lattice Representations Of Globular-Proteins-How Good Are They [J]. J. Comput. Chem. 14: 1194-1202.
    [1] Peiris, J.S.M., Lai, S.T., Poon, L.L.M., Guan, Y., Yam, L.Y.C., Lim, W., Nicholls, J., Yee, W.K.S., Yah, W.W., Cheung, M.T., et al. (2003). Coronavirus as a possible cause of severe acute respiratory syndrome [J]. Lancet 361: 1319-1325.
    [2] Marra, M.A., Jones, S.J.M., Astell, C.R., Holt, R.A., Brooks-Wilson, A., Butterfield, Y.S.N., Khattra, J., Asano, J.K., Barber, S.A., Chan, S.Y., et al. (2003). The genome sequence of the SARS-associated coronavirus [J]. Science 300: 1399-1404.
    [3] Ksiazek, T.G., Erdman, D., Goldsmith, C.S., Zaki, S.R., Peter, T., Emery, S., Tong, S.X., Urbani, C., Comer, J.A., Lim, W., et al. (2003). A novel coronavirus associated with severe acute respiratory syndrome [J]. N. Engl. J. Med. 345: 1953-1966.
    [4] Qin, E., Zhu, Q.Y., Yu, M., Fan, B.C., Chang, G.H., Si, B.Y., Yang, B.A., Peng, W.M., Jiang, T., Liu, B.H., et al. (2003). A complete sequence and comparative analysis of a SARS-associated virus (Isolate BJ01) [J]. Chin. Sci. Bull. 48: 941-948.
    [5] Raamsman, M.J.B., Locker, J.K., de Hooge, A., de Vries, A.A.F., Griffiths, G., Vennema, H., and Rottier, P.J.M. (2000). Characterization of the coronavirus mouse hepatitis virus strain A59 small membrane protein E [J]. J. Virol. 74: 2333-2342.
    [6] Maeda, J., Repass, J.F., Maeda, A., and Makino, S. (2001). Membrane topology of coronavirus E protein [J]. Virology 281: 163-169.
    [7] Lau, K.F., and Dill, K.A. (1989). A lattice statistical mechanics model of the conformational and sequence spaces of proteins [J]. Macromolecules 22: 3986-3997.
    [8] Kyte, J., and Doolitle, R.F. (1982). A simple method for displaying the hydropathic character of a protein [J]. J. Mol. Biol. 157: 105-132.
    [9] Carmesin, I., and Kremer, K. (1988). The bond fluctuation method: a new effective algorithm for the dynamics of polymers in all spatial dimensions [J]. Macromolecules 21: 2819-2823.
    [10] Xu, G.Q., Ding, J.D., and Yang, Y.L. (1997). Monte Carlo simulation of self-avoiding lattice chains subject to simple shear flow. I. Model and simulation algorithm [J]. J. Chem. Phys. 107: 4070-4084.
    [11] Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. (1953). Equation of state calculations by fast computing machines [J]. J. Chem. Phys. 21: 1087-1092.
    [12] Binder, K., and Heermann, D.W. (2002). Monte Carlo simulation in statistical physics: an introduction [M], 4th ed. Springer, Berlin & New York.
    [13] Zhang, L.X., and Zhao, D.L. (2001). Folding lattice HP model of proteins using the bond-fluctuation model [J]. Macromol. Theory Simul. 10: 518-522.
    [14] Leach, A.R. (2001). Heat Capacity and Energy Fluctuations. In Molecular Modeling: Principles and Applications [M], 2nd ed. (ed. A.R. Leach), pp. 348-349. Longman, London.
    [15] Wallin, E., and yon Heijne, G. (1998). Genome-wide analysis of integral membrane proteins from eubacterial, archaean, and eukaryotic organisms [J]. Protein Sci. 7: 1029-1038.
    [16] Daley, D.O., Rapp, M., Granseth, E., Melen, K., Drew, D., and yon Heijne, G. (2005). Global topology analysis of the Escherichia coli inner membrane proteome [J]. Science: 1321-1323.
    [17] Woolf, T.B. (1997). Molecular dynamics of individual alpha-helices of bacteriorhodopsin in dimyristoyl phosphatidylcholine. 1. Structure and dynamics [J]. Biophys. J. 73: 2376-2392.
    [18] Korzhnev, D.M., Orekhov, V.Y., Arseniev, A.S., Gratias, R., and Kessler, H. (1999). Mechanism of the unfolding of transmembrane alpha-helical segment (1-36)-bacteriorhodopsin studied by molecular dynamics simulations [J]. J. Phys. Chem. B 103: 7036-7043.
    [19] Woolf, T.B. (1998). Molecular dynamics simulations of individual alpha-helices of bacteriorhodopsin in dimyristoylphosphatidylcholine. Ⅱ. Interaction energy analysis [J]. Biophys. J. 74: 115-131.
    [20] White, S.H., and Wimley, W.C. (1999). Membrane protein folding and stability: Physical principles [J]. Annu. Rev. Biophys. Biomolec. Struct. 28: 319-365.
    [21] Biggin, P.C., and Sansom, M.S.P. (1999). Interactions of alpha-helices with lipid bilayers: a review of simulation studies [J]. Biophys. Chem. 76: 161-183.
    [22] Booth, P.J. (2000). Unravelling the folding of bacteriorhodopsin [J]. Biochim. Biophys. Acta-Bioenerg. 1460: 4-14.
    [23] Baudry, J., Tajkhorshid, E., Molnar, F., Phillips, J., and Schulten, K. (2001). Molecular dynamics study of bacteriorhodopsin and the purple membrane [J]. J. Phys. Chem. B 105: 905-918.
    [24] Ash, W.L., Zlomislic, M.R., Oloo, E.O., and Tieleman, D.P. (2004). Computer simulations of membrane proteins [J]. Biochim. Biophys. Acta-Biomembr. 1666: 158-189.
    [25] Bowie, J.U. (2005). Solving the membrane protein folding problem [J]. Nature 438: 581-589.
    [26] Chen, Z., and Xu, Y. (2006). Energetics and stability of transmembrane helix packing: a replica-exchange simulation with a knowledge-based membrane potential [J]. Proteins 62: 539-552.
    [27] Cieplak, M., Filipek, S., Janovjak, H., and Krzysko, K.A. (2006). Pulling single bacteriorhodopsin out of a membrane: Comparison of simulation and experiment [J]. Biochim. Biophys. Acta-Biomembr. 1758: 537-544.
    [28] MacKenzie, K.R. (2006). Folding and stability of alpha-helical integral membrane proteins [J]. Chem. Rev. 106: 1931-1977.
    [29] Chou, P.Y., and Fasman, G.D. (1974). Conformational parameters for amino acids in helical, beta-sheet, and random coil regions calculated from proteins [J]. Biochemistry 13: 211-222.
    [30] Chou, P.Y., and Fasman, G.D. (1974). Prediction of protein conformation [J]. Biochemistry 13: 222-245.
    [31] http://www.smbs.buffalo.edu/physbio/service1.htm#thumb.
    [32] http://www.ch.embnet.org/software/TMPRED form.html.
    [33] Chen, Y.T., Zhang, Q., and Ding, J.D. (2004). A coarse-grained model and associated lattice Monte Carlo simulation of the coil-helix transition of a homopolypeptide [J]. J. Chem. Phys. 120: 3467-3474.
    [34] 陈彦涛，罗钟琳，and丁建东．(2003)．SARS病毒E蛋白的计算机模拟的初步研究[J]．高等化学学报 24：1406-1409．
    [35] 赵南明，and周海梦．(2000)．生物物理学[M]．高等教育出版社、施普林格出版社，北京．
    [36] Oesterhelt, D., and Stoeckenius, W. (1971). Rhodopsin-like protein from the purple membrane of Halobacterium halobium [J]. Nature New Bio. 233: 149-154.
    [37] Henderson, R., and Unwin, P.N. (1975). Three-dimensional model of purple membrane obtained by electron microscopy, [J]. Nature 257: 28-32.
    [38] 刘坚．(1 999)．含嗜盐菌袖紫红质蛋白的功能材料的制备和初步研究[D]．硕士学位论文．复旦大学，上海．
    [39] 刘嘉．(2002)．基于细菌视紫红质的光学材料的制备及相关功能研究[D]．学士学位论文．复旦大学，上海．
    [40] Liu, J., Ming, M., Liu, J., Huang, L., Li, Q.G., and Ding, J.D. (2002). Preparation and study of bacteriorhodopsin/poly (vinyl alcohol) composite film [J]. Acta Chim. Sin. 60: 2209-2213.
    [41] Wu, J., Huang, L, Liu, J., Ming, M., Li, Q.G., and Ding, J.D. (2005). Directional self-assembly in archaerhodopsin-reconstituted phospholipid liposomes [J]. Chin. J. Chem. 23: 330-333.
    [42] Ming, M., Lu, M., Balashov, S.P., Ebrey, T.G., Li, Q.G., and Ding, J.D. (2006). pH dependence of light-driven proton pumping by an archaerhodopsin from Tibet: Comparison with bacteriorhodopsin [J]. Biophys. J. 90: 3322-3332.
    [43] 明明．(2006)．细菌视紫红质和古紫质蛋白的质子泵机理及其与聚合物复合功能材料的研究[D]．博士学位论文．复旦大学，上海．
    [44] Ji, S.C., and Ding, J.D. (2006). Spontaneous formation of vesicles from mixed amphiphiles with dispersed molecular weight: Monte Carlo simulation [J]. Langmuir 22: 553-559.
    [45] 纪仕辰．(2006)．链状分子软物质的蒙特卡罗模拟和部分实验研穷[D]．博士学位论文．复旦大学，上海．