雖然一般相信根據Anfinsenm原理，蛋白質的結構會被它們的序列所唯一決定，但在多尺度下，某些複雜的自然態結構轉換表現出難以捉摸的現象。為了闡明多尺度下結構轉換的機制，我們從唯一結構這個問題去重新了解它，特別是從2DX4這個多肽鏈著手。2DX4包含18個胺基酸:INYWLAHAKAGYIVHWTA。基於一個我們全面校準過的第一原理粗粒化模型，我們建立了一個2DX4完整的自由能地形圖，揭示了2DX4天生是一個多結構共存的蛋白質。它的兩個自然態幾乎是簡併的:一個是螺旋結構，另一個是beta髮夾結構。雖然兩者之間存在著轉換的路徑，但是由於一個約10 kcal/mol的能障存在，兩個自然態之間的轉換並沒有很頻繁。這結果提供了一個重要的線索，小蛋白質的自然態可能不是唯一的所以結構轉換可能發生。我們因此把研究的範圍延伸到多肽鏈 A-beta(16-22)纖維化沉澱的模擬。我們展示了 A-beta(16-22)也有兩個自由能的最小值，一個是alpha-螺旋另一個是beta-髮夾彎結構。然而，因為它們兩個之間的能障很小，alpha與 beta之間的轉換變得很頻繁。結果就是，A-beta(16-22)並沒有固定的自然態。這樣的特性使的A-beta(16-22)表現出聚集沉澱和其他多重結構。由A-beta(16-22)的自由能地形圖可發現，它們的雙體乃至於六聚體的自由能完全與單體的自由能形式無關。反平行的 beta-摺板是這些多聚體的最低能量態，同時有幾個暫存態但是並不穩定。為了能模擬大尺度的沉澱，我們設計了一個盒子中間裝了一個結核的晶種讓其他單體與其反應。使用這個新穎的設計，我們能夠模擬不同濃度下A-beta(16-22)的沉澱行為。在低濃度下，模擬顯示了A-beta(16-22)類似奈米線的成長模式，纖維的成長是由擴散速率決定。然在高濃度下，系統傾向於非結晶且有多個最低能量態。我們的分析指出在低濃度下，沉澱的行為特徵可歸類為古典成核理論，包含遲滯期，臨界核，以及有序纖維化；而它們的成長路徑與濃度相依。這些結果讓人更明白蛋白質沉澱的多重態是與生俱來，且為了解蛋白質自組裝的沉澱路徑提供了重要線索。

Although it has been generally believed as the Anfinsen's dogma that protein structures are uniquely determined by their amino acid sequences, complex conformational transformations of native structures that occur in multiscales makes Anfinsen's dogma elusive. To illuminate mechanism behind conformational transformations in
multiscales, we start by revisiting the uniqueness problem of protein native structures by investigating the peptide 2DX4, comprising 18 amino acids: INYWLAHAKAGYIVHWTA. Based on an ab initio coarse-grained model that are comprehensively calibrated, we construct the complete free energy of 2DX4 and demonstrate that 2DX4 is an inherently multi-conformation peptide with two nearly degenerate native structures: one is a helix structure, while the other is a hairpin-like structure.
Although there exist pathways connecting two degenerate native structures, conformation switch between two native structures does not occur often due to the existence of an energy barrier of the order 10kcal/mol between them. These results provide important clues that the native structures for small proteins may not be unique so that conformation transformations may occur. Our investigation is then extended to simulate fibril aggregation of peptide A-beta(16-22). It is shown that A-beta(16-22) also possesses two minimum with alpha-helix and beta-hairpin structures. However, due to small energy barrier between alpha and beta structures, transformations
between these structures occur frequently. As a result, A-beta(16-22) does not exhibit a fixed native structure. This feature enables the aggregation and manifestation of multi-conformations for A-beta(16-22). The energy landscapes of A-beta(16-22) from dimer to hexamer is found to be completely uncorrelated with that of a single A-beta(16-22). Antiparallel beta sheets are found to be the ground state, while several intermediates are minor unstable minima. To simulate large scale aggregation, a box container with a seed in which other monomers start to interact with the seed is implemented. Using this new simulation scheme, we are able to simulate aggregations of A-beta(16-22) in different concentrations. It is shown that similar to the growth of nanowires, when the density of A-beta(16-22) is low. The aggregation is dominated by diffusion limited aggregation, while for high densities, the system tends to be amorphous with multiple ground states. Our analyses indicate that in the low density region, the aggregation can be characterized by classical nucleation theory, including the lag phase, critical nucleation, fibrilization and their pathway dependence on the concentration. These results shed light on the multi-formational nature of aggregated proteins and provide important clues to understand aggregations pathways for amyloid assemblies.

1. Lührs, T., C. Ritter, M. Adrian, D. Riek-Loher, B. Bohrmann, H. Döbeli,
D. Schubert, and R. Riek, 2005. 3D structure of Alzheimer’s amyloid-beta(1-
42) fibrils. Proceedings of the National Academy of Sciences of the United
States of America 102:17342–7.
2. Petkova, A. T., Y. Ishii, J. J. Balbach, O. N. Antzutkin, R. D. Leapman, F. De-
laglio, and R. Tycko, 2002. A structural model for Alzheimer’s beta -amyloid
fibrils based on experimental constraints from solid state NMR. Proceedings of
the National Academy of Sciences of the United States of America 99:16742–7.
3. Luca, S., W.-M. Yau, R. Leapman, and R. Tycko, 2007. Peptide conformation
and supramolecular organization in amylin fibrils: constraints from solid-state
NMR. Biochemistry 46:13505–22.
4. Booth, D. R., M. Sunde, V. Bellotti, C. V. Robinson, W. L. Hutchinson, P. E.
Fraser, P. N. Hawkins, C. M. Dobson, S. E. Radford, C. C. Blake, and M. B.
Pepys, 1997. Instability, unfolding and aggregation of human lysozyme variants
underlying amyloid fibrillogenesis.
5. Dima, R. I., and D. Thirumalai, 2002. Exploring protein aggregation and self-
propagation using lattice models: phase diagram and kinetics. Protein science
: a publication of the Protein Society 11:1036–49.
6. Chiti, F., and C. M. Dobson, 2006. Protein misfolding, functional amyloid,
and human disease. Annual review of biochemistry 75:333–66.
77
7. Massi, F., D. Klimov, D. Thirumalai, and J. E. Straub, 2002. Charge states
rather than propensity for beta-structure determine enhanced fibrillogenesis in
wild-type Alzheimer’s beta-amyloid peptide compared to E22Q Dutch mutant.
Protein science : a publication of the Protein Society 11:1639–47.
8. Urbanc, B., M. Betnel, L. Cruz, G. Bitan, and D. B. Teplow, 2010. Elucida-
tion of amyloid beta-protein oligomerization mechanisms: discrete molecular
dynamics study. Journal of the American Chemical Society 132:4266–80.
9. Senguen, F. T., T. M. Doran, E. a. Anderson, and B. L. Nilsson, 2011. Clar-
ifying the influence of core amino acid hydrophobicity, secondary structure
propensity, and molecular volume on amyloid-β 16-22 self-assembly. Molecu-
lar bioSystems 7:497–510.
10. Hamada, D., S. Segawa, and Y. Goto, 1996. Non-native α-helical intermediate
in the refolding of β-lactoglobulin, a predominantly β-sheet protein. Nature
Structural Biology 3:868–73.
11. Kuwata, K., M. Hoshino, S. Era, C. Batt, and Y. Goto, 1998. α → β transition
of β-lactoglobulin as evidenced by heteronuclear NMR1. Journal of Molecular
Biology 283:731–739.
12. Zhang, S., K. Iwata, M. J. Lachenmann, J. W. Peng, S. Li, E. R. Stimson,
Y. Lu, a. M. Felix, J. E. Maggio, and J. P. Lee, 2000. The Alzheimer’s peptide
Aβ adopts a collapsed coil structure in water. Journal of structural biology
130:130–41.
13. Serpell, L. C., 2000. Alzheimer’s amyloid fibrils: structure and assembly.
Biochim Biophys Acta. 1502:16–30.
78
14. Sticht, H., P. Bayer, D. Willbold, S. Dames, C. Hilbich, K. Beyreuther,
R. W. Frank, and P. Rosch, 1995. Structure of amyloid A4-(1-40)-peptide
of Alzheimer’s disease. European Journal of Biochemistry 233:293–298.
15. Coles, M., W. Bicknell, A. Watson, D. Fairlie, and D. Craik, 1998. Solution
structure of amyloid β-peptide (1-40) in a water-micelle environment. Is the
membrane-spanning domain where we think it is? Biochemistry 37:11064–
11077.
16. Xu, Y., J. Shen, X. Luo, W. Zhu, K. Chen, J. Ma, and H. Jiang, 2005. Con-
formational transition of amyloid beta-peptide. Proceedings of the National
Academy of Sciences 102:5403–7.
17. Cerpa, R., F. Cohen, and I. Kuntz, 1996. Conformational switching in designed
peptides: the helix/sheet transition. Folding and Design 1:91–101.
18. Zhang, S., and A. Rich, 1997. Direct conversion of an oligopeptide from a
β-sheet to an α-helix: A model for amyloid formation. Proceedings of the
National Academy of Sciences 94:23–28.
19. Murayama, K., and M. Tomida, 2004. Heat-induced secondary structure and
conformation change of bovine serum albumin investigated by Fourier trans-
form infrared spectroscopy. Biochemistry 43:11526–32.
20. Montserret, R., M. McLeish, A. Böckmann, C. Geourjon, and F. Penin, 2000.
Involvement of electrostatic interactions in the mechanism of peptide folding
induced by sodium dodecyl sulfate binding. Biochemistry 39:8362–8373.
21. Kabsch, W., and C. Sander, 1984. On the use of sequence homologies to pre-
dict protein structure: identical pentapeptides can have completely different
79
conformations. Proceedings of the National Academy of Sciences of the United
States of America 81:1075–8.
22. Cohen, B., S. Presnell, and F. Cohen, 1993. Origins of structural diversity
within sequentially identical hexapeptides. Protein Science 2:2134–2145.
23. Minor, D., and P. Kim, 1996. Context-dependent secondary structure forma-
tion of a designed protein sequence. Nature 380:730–734.
24. Cordes, M., R. Burton, and N. Walsh, 2000. An evolutionary bridge to a new
protein fold. Nature Structural Biology; 7:1129–1132.
25. Alexander, P. A., Y. He, Y. Chen, J. Orban, and P. N. Bryan, 2009. A minimal
sequence code for switching protein structure and function. Proceedings of the
National Academy of Sciences 106:21149–54.
26. Araki, M., and A. Tamura, 2007. Transformation of an α-helix peptide into a
β-hairpin induced by addition of a fragment results in creation of a coexisting
state. Proteins: Structure, Function, and Bioinformatics 66:860–868.
27. Bernstein, F. C., T. F. Koetzle, G. J. Williams, E. F. Meyer, M. D. Brice,
J. R. Rodgers, O. Kennard, T. Shimanouchi, and M. Tasumi, 1978. The Pro-
tein Data Bank: a computer-based archival file for macromolecular structures.
Archives of Biochemistry and Biophysics 185:584–91.
28. Chen, N.-Y., Z.-Y. Su, and C.-Y. Mou, 2006. Effective potentials for folding
proteins. Physical Review Letters 96:078103.
29. Balbach, J. J., Y. Ishii, O. N. Antzutkin, R. D. Leapman, N. W. Rizzo,
F. Dyda, J. Reed, and R. Tycko, 2000. Amyloid fibril formation by A beta
16-22, a seven-residue fragment of the Alzheimer’s beta-amyloid peptide, and
structural characterization by solid state NMR. Biochemistry 39:13748–59.
80
30. Ma, B., and R. Nussinov, 2002. Stabilities and conformations of Alzheimer’s
beta -amyloid peptide oligomers (Abeta 16-22, Abeta 16-35, and Abeta 10-
35): Sequence effects. Proceedings of the National Academy of Sciences of the
United States of America 99:14126–31.
31. Huang, T. H., D. S. Yang, N. P. Plaskos, S. Go, C. M. Yip, P. E. Fraser, and
a. Chakrabartty, 2000. Structural studies of soluble oligomers of the Alzheimer
beta-amyloid peptide. Journal of molecular biology 297:73–87.
32. Bitan, G., M. D. Kirkitadze, A. Lomakin, S. S. Vollers, G. B. Benedek, and
D. B. Teplow, 2003. Amyloid beta -protein (Abeta) assembly: Abeta 40 and
Abeta 42 oligomerize through distinct pathways. Proceedings of the National
Academy of Sciences of the United States of America 100:330–5.
33. Klimov, D. K., and D. Thirumalai, 2003. Dissecting the assembly of Abeta16-
22 amyloid peptides into antiparallel beta sheets. Structure (London, England
: 1993) 11:295–307.
34. Santini, S., G. Wei, N. Mousseau, and P. Derreumaux, 2004. Pathway com-
plexity of Alzheimer’s beta-amyloid Abeta16-22 peptide assembly. Structure
(London, England : 1993) 12:1245–55.
35. Santini, S., N. Mousseau, and P. Derreumaux, 2004. In silico assembly of
Alzheimer’s Abeta16-22 peptide into beta-sheets. Journal of the American
Chemical Society 126:11509–16.
36. Gnanakaran, S., R. Nussinov, and A. E. García, 2006. Atomic-level description
of amyloid beta-dimer formation. Journal of the American Chemical Society
128:2158–9.
81
37. Röhrig, U. F., A. Laio, N. Tantalo, M. Parrinello, and R. Petronzio, 2006.
Stability and structure of oligomers of the Alzheimer peptide Abeta16-22: from
the dimer to the 32-mer. Biophysical journal 91:3217–29.
38. Mohanty, S., G. Favrin, and A. Irba, 2004. Oligomerization of Amyloid Ab 16
??22 Peptides Using Hydrogen Bonds and Hydrophobicity Forces. Biophysical
Journal 87:3657–3664.
39. Nguyen, P. H., M. S. Li, G. Stock, J. E. Straub, and D. Thirumalai, 2007.
Monomer adds to preformed structured oligomers of Abeta-peptides by a two-
stage dock-lock mechanism. Proceedings of the National Academy of Sciences
of the United States of America 104:111–6.
40. Petty, S. A., and S. M. Decatur, 2005. Experimental evidence for the reorgani-
zation of beta-strands within aggregates of the Abeta(16-22) peptide. Journal
of the American Chemical Society 127:13488–9.
41. Senguen, F. T., N. R. Lee, X. Gu, D. M. Ryan, T. M. Doran, E. a. Anderson,
and B. L. Nilsson, 2011. Probing aromatic, hydrophobic, and steric effects
on the self-assembly of an amyloid-β fragment peptide. Molecular bioSystems
7:486–96.
42. Irbäck, A., S. A. Jónsson, N. Linnemann, B. Linse, and S. Wallin, 2013. Aggre-
gate geometry in amyloid fibril nucleation. Physical review letters 110:058101.
43. Zhang, J., and M. Muthukumar, 2009. Simulations of nucleation and elonga-
tion of amyloid fibrils. The Journal of chemical physics 130:035102.
44. Lin, C.-Y., N.-Y. Chen, and C. Mou, 2012. Folding a Protein with Equal
Probability of Being Helix or Hairpin. Biophysical Journal 103:99–108.
82
45. Miyazawa, S., and R. Jernigan, 1985. Estimation of effective interresidue con-
tact energies from protein crystal structures: quasi-chemical approximation.
Macromolecules 18:534–552.
46. Miyazawa, S., and R. Jernigan, 1996. Residue-residue potentials with a fa-
vorable contact pair term and an unfavorable high packing density term, for
simulation and threading. Journal of Molecular Biology 256:623–644.
47. Davis, M. E., and J. A. McCammon, 1990. Electrostatics in biomolecular
structure and dynamics. Chemical Reviews 90:509–521.
48. Ibarra-Molero, B., V. V. Loladze, G. I. Makhatadze, and J. M. Sanchez-Ruiz,
1999. Thermal versus guanidine-induced unfolding of ubiquitin. An analysis in
terms of the contributions from charge-charge interactions to protein stability.
Biochemistry 38:8138–49.
49. Sham, Y. Y., Z. T. Chu, and A. Warshel, 1997. Consistent Calculations of
p K a ’s of Ionizable Residues in Proteins: Semi-microscopic and Microscopic
Approaches. The Journal of Physical Chemistry B 101:4458–4472.
50. Doig, a. J., and M. J. Sternberg, 1995. Side-chain conformational entropy in
protein folding. Protein science : a publication of the Protein Society 4:2247–
51.
51. Chaikin, P. M., and T. C. Lubensky, 1995. Principles of condensed matter
physics. Cambridge University Press, Cambridge, first edition.
52. Cheung, M., A. Garcìa, and J. Onuchic, 2002. Protein folding mediated by
solvation: water expulsion and formation of the hydrophobic core occur af-
ter the structural collapse. Proceedings of the National Academy of Sciences
99:685–690.
83
53. Shimizu, S., and H. S. Chan, 2001. Configuration-dependent heat capacity of
pairwise hydrophobic interactions. Journal of the American Chemical Society
123:2083–2084.
54. Dias, C., M. Karttunen, and H. S. Chan, 2011. Hydrophobic interactions in
the formation of secondary structures in small peptides. Physical Review E
84:1–9.
55. Betancourt, M. R., and J. Skolnick, 2001. Finding the needle in a haystack:
educing native folds from ambiguous ab initio protein structure predictions.
Journal of Computational Chemistry 22:339–353.
56. Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and
E. Teller, 1953. Equation of State Calculations by Fast Computing Machines.
The Journal of Chemical Physics 21:1087.
57. Wang, F., and D. Landau, 2001. Efficient, multiple-range random walk algo-
rithm to calculate the density of states. Physical Review Letters 86:2050–2053.
58. Rathore, N., T. A. Knotts, and J. J. de Pablo, 2003. Density of states simu-
lations of proteins. The Journal of Chemical Physics 118:4285.
59. Ojeda, P., M. Garcia, A. Londoño, and N. Chen, 2009. Monte Carlo simulations
of proteins in cages: influence of confinement on the stability of intermediate
states. Biophysical Journal 96:1076–1082.
60. Betancourt, M. R., and J. Skolnick, 2004. Local propensities and statistical po-
tentials of backbone dihedral angles in proteins. Journal of Molecular Biology
342:635–49.
61. Matsuo, Y., and K. Nishikawa, 1994. Protein structural similarities predicted
by a sequence-structure compatibility method. Protein Science 3:2055–63.
84
63. Itoh, S. G., A. Tamura, and Y. Okamoto, 2010. Helix-hairpin transitions of
a designed peptide studied by a generalized-ensemble simulation. Journal of
Chemical Theory and Computation 6:979–983.
64. Mccallister, E. L., E. Alm, and D. Baker, 2000. Critical role of β-hairpin
formation in protein G folding. Nature Structural Biology 7:669–673.
65. Kim, D. E., C. Fisher, and D. Baker, 2000. A breakdown of symmetry in the
folding transition state of protein L. Journal of Molecular Biology 298:971–984.
66. Auer, S., C. M. Dobson, and M. Vendruscolo, 2007. Characterization of the nu-
cleation barriers for protein aggregation and amyloid formation. HFSP journal
1:137–46.
67. Knowles, T., C. Waudby, and G. Devlin, 2009. An analytical solution to the
kinetics of breakable filament assembly. Science 1533.
68. Powers, E. T., and D. L. Powers, 2006. The kinetics of nucleated polymer-
izations at high concentrations: amyloid fibril formation near and above the
"supercritical concentration". Biophysical journal 91:122–32.
69. Oosawa, F., and S. Asakura, 1975. Thermodynamics of the Polymerization of
Protein. Academic Press, London, New York.
70. Sabaté, R., and J. Estelrich, 2005. Evidence of the existence of micelles in the
fibrillogenesis of beta-amyloid peptide. The journal of physical chemistry. B
109:11027–32.
71. Serio, T. R., 2000. Nucleated Conformational Conversion and the Replication
of Conformational Information by a Prion Determinant. Science 289:1317–
1321.
85
72. Nguyen, H. D., and C. K. Hall, 2004. Molecular dynamics simulations of spon-
taneous fibril formation by random-coil peptides. Proceedings of the National
Academy of Sciences of the United States of America 101:16180–5.
73. Pellarin, R., and A. Caflisch, 2006. Interpreting the aggregation kinetics of
amyloid peptides. Journal of molecular biology 360:882–92.
74. Schmit, J. D., K. Ghosh, and K. Dill, 2011. What drives amyloid molecules to
assemble into oligomers and fibrils? Biophysical journal 100:450–8.
75. Ward, J. H., 1963. Hierarchical Grouping to Optimize an Objective Function.
Journal of the American Statistical Association 58:236–244.
76. Harper, J. D., C. M. Lieber, and P. T. Lansbury Jr, 1997. Atomic force
microscopic imaging of seeded fibril formation and fibril branching by the
Alzheimer’s disease amyloid-β protein. Chemistry & Biology 4:951–959.
77. Gosal, W. S., I. J. Morten, E. W. Hewitt, D. A. Smith, N. H. Thomson, and
S. E. Radford, 2005. Competing pathways determine fibril morphology in the
self-assembly of beta2-microglobulin into amyloid. Journal of molecular biology
351:850–64.
78. Morozova-Roche, L. a., V. Zamotin, M. Malisauskas, A. Ohman, R. Chertkova,
M. a. Lavrikova, I. a. Kostanyan, D. a. Dolgikh, and M. P. Kirpichnikov, 2004.
Fibrillation of carrier protein albebetin and its biologically active constructs.
Multiple oligomeric intermediates and pathways. Biochemistry 43:9610–9.
79. Schmit, J. D., 2013. Kinetic theory of amyloid fibril templating. The Journal
of chemical physics 138:185102.
80. Atkins, P., and J. D. Paula, 2006. Atkins’ physical chemistry. Oxford Univer-
sity Press, Oxford .
86
81. Lomakin, a., D. B. Teplow, D. a. Kirschner, and G. B. Benedek, 1997. Kinetic
theory of fibrillogenesis of amyloid beta-protein. Proceedings of the National
Academy of Sciences of the United States of America 94:7942–7.
82. Padrick, S. B., and A. D. Miranker, 2002. Islet amyloid: phase partition-
ing and secondary nucleation are central to the mechanism of fibrillogenesis.
Biochemistry 41:4694–703.
83. Collins, S. R., A. Douglass, R. D. Vale, and J. S. Weissman, 2004. Mechanism
of prion propagation: amyloid growth occurs by monomer addition. PLoS
biology 2:e321.
84. Ruschak, A. M., and A. D. Miranker, 2007. Fiber-dependent amyloid forma-
tion as catalysis of an existing reaction pathway. Proceedings of the National
Academy of Sciences of the United States of America 104:12341–6.
85. a.J Modler, K. Gast, G. Lutsch, and G. Damaschun, 2003. Assembly of Amy-
loid Protofibrils via Critical Oligomers Novel Pathway of Amyloid Formation.
Journal of Molecular Biology 325:135–148.
86. Carrotta, R., M. Manno, D. Bulone, V. Martorana, and P. L. San Biagio, 2005.
Protofibril formation of amyloid beta-protein at low pH via a non-cooperative
elongation mechanism. The Journal of biological chemistry 280:30001–8.
87. Goldstein, R., and L. Stryer, 1986. Cooperative polymerization reactions.
Analytical approximations, numerical examples, and experimental strategy.
Biophysical Journal 50:583–599.