愈來愈多的蛋白在蛋白質資料庫中被發現具有拓樸扭結的結構，至今，有許多科學家致力於研究蛋白質如何形成如此複雜的扭結構造。其中，EcYbeA是一種31扭結蛋白，並在先前研究中發現即便是在高濃度的化學變性環境下，扭結構造依然存在。為了更加了解拓樸結在結構以及摺疊時的能量貢獻，我們利用環形重組技術來解開扭結構造，將原先蛋白質的N與C端連接起來，再於扭結結構中創造新的N與C端並維持相似的結構。在九個CP的蛋白中，僅有CP74是水溶性佳並能順利被純化的，接著我們利用生物物理與生物化學的方法來觀察CP對結構與摺疊的影響。我們解出了解析度到1.75 Å 的CP74晶體結構，並使用小角度散射技術確認CP74的四級結構與WT相似。然而圓二色光譜以及內生性螢光光譜皆呈現了CP74相較於WT在化學穩定性與熱穩定性中都較不穩定，其中，CP74在熱穩定性實驗中更被觀察到有中間態出現。在動力學實驗中，CP74蛋白展開過程和WT一樣有著兩個階段，而較慢的展開速度卻比WT慢100倍。總體而言，我們的實驗結果觀察到CP74藉由區域交換的方式形成二聚體，維持了和WT相似的整體結構，而扭結構造在穩定結構上扮演了重要的角色。

An increasing number of proteins in Protein Data Bank (PDB) have been discovered to adopt knotted topologies, and tremendous efforts have been devoted to understanding why these proteins attain such intricate structures. It has been demonstrated that the trefoil-knotted EcYbeA cannot be untied even under highly denaturing conditions in concentrated urea. To better understand the potential contributions of knots in protein structures and their associated folding energy landscapes, we generated a library of circular permutants (CPs) of EcYbeA (cpYbeA) to untie the knotted topology through linking the N- and C- termini and introducing new openings elsewhere, while maintaining the same native contacts. Of the nine CPs, CP74 was the only one that could be purified in a soluble form. We examined biophysically and biochemically the impacts of the CP. The X-ray structure of CP74 was solved to a resolution of 1.75 Å. Remarkably, CP74 underwent substantial domain swapping that lead to a similar overall molecular appearance but a completely different dimer interface. The dimeric quaternary structure of CP74 was confirmed by small-angle X-ray scattering (SAXS). Additionally, results from far-UV CD and intrinsic fluorescence indicated that CP74 is chemically and thermally less stable than WT. Furthermore, an additional folding intermediate was observed during thermal unfolding. Similar to WT, CP74 exhibited two unfolding kinetic phases, but the slower phase was 100 times slower than that of WT. Collectively, our data demonstrated that CP74 could fold into a dimeric structure through domain swapping, which maintains the same native contacts as that of the parent WT, and that the knotted structure plays a pivotal role to stabilize the overall structure with minimum frustration.

Contents
Abstract ii
List of Tables ix
List of Figures x
Abbreviations xii
1 Introduction 1
1.1 Topologically knotted protein 1
1.2 Categories of knotted proteins 2
1.3 Protein folding problem 4
1.4 Proteins fold on funnel-shaped energy landscapes 5
1.5 Folding of knotted proteins 6
1.6 SPOUT family 8
1.7 Trefoil knotted protein, EcYbeA 9
1.8 Folding of YbeA 10
1.9 Circular permutation 10
1.10 Motivation 11
2 Materials and methods 13
2.1 CP construct design 13
2.2 Expression and purification 16
2.2.1 Expression test 16
2.2.2 Purification 16
2.3 Mass spectrometry 18
2.4 Size exclusion chromatography-coupled multiple angle light scattering (SEC- MALS) 18
2.5 Spectroscopic measurements 19
2.6 Equilibrium denaturation experiments: 20
2.6.1 Chemical denaturation 20
2.6.2 Thermal denaturation 21
2.6.3 Singular value decomposition (SVD) analysis 21
2.6.4 Two-state dimer denaturation model 22
2.7 Single-jump stopped-flow experiments 23
2.8 Isothermal titration calorimetry (ITC) 24
2.9 Differential scanning calorimeter (DSC) 25
2.10 Hydrogen-deuterium exchange mass spectrometry (HDX-MS) 25
2.11 Small-angle X-ray scattering (SAXS) 28
2.12 Crystallization and data collection 29
2.13 Structure determination and refinement 30
2.14 Protein-related parameters of YbeA WT and CP74 33
3 Results 37
3.1 Construction and expression of YbeA CP variants 37
3.2 Characterization of CP74 and WT 40
3.3 Cofactor binding analyses 44
3.4 Folding dynamics of CP74 and WT 46
3.5 X-ray crystal structure of CP74 52
3.6 HDX of CP74 and WT 62
3.7 Folding kinetics of CP74 68
4 Discussion 73
4.1 Cofactor binding ability 73
4.2 Domain swapping in CP74 74
4.3 Folding dynamics 75
4.4 Possible folding pathway of CP74 76
5 Conclusion 77
Reference 78
Appendix 83
Protein sequence of other YbeA CP variants 83
Crystal picture and diffraction pattern of CP74 88
Supplementary data of HDX-MS 89

1. Adams, C.C., The knot book an elementary introduction to the mathematical theory of knots. 2004, Providence, R.I: American Mathematical Society.
2. Mansfield, M.L., Are there knots in proteins? Nature Structural Biology, 1994. 1: p. 213.
3. Lai, Y.-L., C.-C. Chen, and J.-K. Hwang, pKNOT v.2: the protein KNOT web server. Nucleic Acids Research, 2012. 40(Web Server issue): p. W228-W231.
4. Lai, Y.-L., et al., pKNOT: the protein KNOT web server. Nucleic Acids Research, 2007. 35(suppl_2): p. W420-W424.
5. Jamroz, M., et al., KnotProt: a database of proteins with knots and slipknots. Nucleic Acids Research, 2015. 43(Database issue): p. D306-D314.
6. Faísca, P.F.N., Knotted proteins: A tangled tale of Structural Biology. Computational and Structural Biotechnology Journal, 2015. 13: p. 459-468.
7. Anantharaman, V., E.V. Koonin, and L. Aravind, SPOUT: a class of methyltransferases that includes spoU and trmD RNA methylase superfamilies, and novel superfamilies of predicted prokaryotic RNA methylases. Journal of molecular microbiology and biotechnology, 2002. 4(1): p. 71-75.
8. Taylor, W.R. and K. Lin, Protein knots: A tangled problem. Nature, 2003. 421: p. 25.
9. Taylor, W.R., A deeply knotted protein structure and how it might fold. Nature, 2000. 406: p. 916.
10. Lou, S.-C., et al., The Knotted Protein UCH-L1 Exhibits Partially Unfolded Forms under Native Conditions that Share Common Structural Features with Its Kinetic Folding Intermediates. Journal of Molecular Biology, 2016. 428(11): p. 2507-2520.
11. Lee, Y.C. and S.D. Hsu, A Natively Monomeric Deubiquitinase UCH-L1 Forms Highly Dynamic but Defined Metastable Oligomeric Folding Intermediates. Journal of Physical Chemistry Letters, 2018. 9(9): p. 2433-2437.
12. Bölinger, D., et al., A Stevedore's Protein Knot. PLOS Computational Biology, 2010. 6(4): p. e1000731.
13. Wang, I., S.Y. Chen, and S.T. Hsu, Folding analysis of the most complex Stevedore's protein knot. Scientific Report, 2016. 6: p. 31514.
14. Dill, K.A., et al., The Protein Folding Problem. Annual review of biophysics, 2008. 37: p. 289-316.
15. Levinthal, C., Are There Pathways For Protein Folding? Extrait du Journal de Chimie Physique, 1968. 65(1).
16. Levinthal, C. How to Fold Graciously. in Mossbauer Spectroscopy in Biological Systems: Proceedings of a meeting held at Allerton House, Monticello, Illinois. 1969. University of Illinois Press.
17. Leopold, P.E., M. Montal, and J.N. Onuchic, Protein folding funnels: a kinetic approach to the sequence-structure relationship. Proceedings of the National Academy of Sciences, 1992. 89(18): p. 8721-8725.
18. Govindarajan, S. and R.A. Goldstein, On the thermodynamic hypothesis of protein folding. Proceedings of the National Academy of Sciences of the United States of America, 1998. 95(10): p. 5545-5549.
19. Arai, M. and K. Kuwajima, Rapid formation of a molten globule intermediate in refolding of α-lactalbumin. Folding and Design, 1996. 1(4): p. 275-287.
20. Vidugiris, G.J.A., J.L. Markley, and C.A. Royer, Evidence for a molten globule-like transition state in protein folding from determination of activation volumes. Biochemistry, 1995. 34(15): p. 4909-4912.
21. Mallam, A.L., How does a knotted protein fold? FEBS Journal, 2009. 276(2): p. 365-75.
22. Sulkowska, J.I., P. Sulkowski, and J. Onuchic, Dodging the crisis of folding proteins with knots. Proc. Natl. Acad. Sci. U. S. A., 2009. 106(9): p. 3119-24.
23. Virnau, P., A.L. Mallam, and S.E. Jackson, Structures and folding pathways of topologically knotted proteins. Journal of Physics: Condensed Matter, 2011. 23(3): p. 033101.
24. Noel, J.K., J.I. Sulkowska, and J.N. Onuchic, Slipknotting upon native-like loop formation in a trefoil knot protein. Proc. Natl. Acad. Sci. U. S. A., 2010. 107(35): p. 15403-8.
25. Mallam, A.L., J.M. Rogers, and S.E. Jackson, Experimental detection of knotted conformations in denatured proteins. Proc. Natl. Acad. Sci. U. S. A., 2010. 107(18): p. 8189-94.
26. Hori, H., Transfer RNA methyltransferases with a SpoU-TrmD (SPOUT) fold and their modified nucleosides in tRNA. Biomolecules, 2017. 7(1).
27. Christian, T., et al., Methyl transfer by substrate signaling from a knotted protein fold. Nature Structural & Molecular Biology, 2016. 23(10): p. 941-948.
28. Shao, Z., et al., Crystal structure of tRNA m1G9 methyltransferase Trm10: insight into the catalytic mechanism and recognition of tRNA substrate. Nucleic Acids Research, 2014. 42(1): p. 509-25.
29. Purta, E., et al., YbeA is the m3Psi methyltransferase RlmH that targets nucleotide 1915 in 23S rRNA. RNA, 2008. 14(10): p. 2234-44.
30. Koh, C.S., et al., Small methyltransferase RlmH assembles a composite active site to methylate a ribosomal pseudouridine. Scientific Report, 2017. 7(1): p. 969.
31. Mallam, A.L. and S.E. Jackson, A comparison of the folding of two knotted proteins: YbeA and YibK. Journal of Molecular Biology, 2007. 366(2): p. 650-65.
32. Mallam, A.L. and S.E. Jackson, Probing nature's knots: the folding pathway of a knotted homodimeric protein. Journal of Molecular Biology, 2006. 359(5): p. 1420-36.
33. Yu, Y. and S. Lutz, Circular permutation: a different way to engineer enzyme structure and function. Trends in Biotechnology, 2011. 29(1): p. 18-25.
34. Pan, T. and O.C. Uhlenbeck, Circularly permuted DNA, RNA and proteins — a review. Gene, 1993. 125(2): p. 111-114.
35. Goldenberg, D.P. and T.E. Creighton, Circular and circularly permuted forms of bovine pancreatic trypsin inhibitor. Journal of Molecular Biology, 1983. 165(2): p. 407-413.
36. Haglund, E., M.O. Lindberg, and M. Oliveberg, Changes of protein folding pathways by circular permutation. Overlapping nuclei promote global cooperativity. Journal of Biological Chemistry, 2008. 283(41): p. 27904-15.
37. Iwakura, M., et al., Systematic circular permutation of an entire protein reveals essential folding elements. Nature Structural Biology, 2000. 7: p. 580.
38. Lo, W.C., et al., CPred: a web server for predicting viable circular permutations in proteins. Nucleic Acids Research, 2012. 40(Web Server issue): p. W232-7.
39. Lo, W.-C. and P.-C. Lyu, CPSARST: an efficient circular permutation search tool applied to the detection of novel protein structural relationships. Genome Biology, 2008. 9(1): p. R11.
40. Tkaczuk, K.L., et al., Structural and evolutionary bioinformatics of the SPOUT superfamily of methyltransferases. BMC Bioinformatics, 2007. 8: p. 73.
41. Wall, M.E., A. Rechtsteiner, and L.M. Rocha Singular Value Decomposition and Principal Component Analysis. ArXiv e-prints, 2002.
42. Pace, C.N., Determination and analysis of urea and guanidine hydrochloride denaturation curves. Methods in enzymology, 1986. 131: p. 266-280.
43. Tanford, C., Protein Denaturation: Part C.**Parts A and B were published in Volume 23 of Advances in Protein Chemistry (1968), starting on p. 121 Theoretical Models for The Mechanism of Denaturation, in Advances in Protein Chemistry, C.B. Anfinsen, J.T. Edsall, and F.M. Richards, Editors. 1970, Academic Press. p. 1-95.
44. Franke, D., et al., ATSAS 2.8: a comprehensive data analysis suite for small-angle scattering from macromolecular solutions. Journal of Applied Crystallography, 2017. 50(4): p. 1212-1225.
45. Schneidman-Duhovny, D., et al., Accurate SAXS profile computation and its assessment by contrast variation experiments. Biophysical Journal, 2013. 105(4): p. 962-74.
46. Schneidman-Duhovny, D., et al., FoXS, FoXSDock and MultiFoXS: Single-state and multi-state structural modeling of proteins and their complexes based on SAXS profiles. Nucleic Acids Research, 2016. 44(Web Server issue): p. W424-W429.
47. Guinier, A. and G. Fournet, Small-angle scattering of X-rays. 1955, New York: John Wiley and Sons.
48. Adams, P.D., et al., PHENIX: a comprehensive Python-based system for macromolecular structure solution. Acta Crystallographica Section D, 2010. 66(Partt 2): p. 213-221.
49. Murshudov, G.N., et al., REFMAC5 for the refinement of macromolecular crystal structures. Acta Crystallographica Section D, 2011. 67(Pt 4): p. 355-67.
50. Emsley, P. and K. Cowtan, Coot: model-building tools for molecular graphics. Acta Crystallographica Section D, 2004. 60(12 Part 1): p. 2126-2132.
51. Laskowski, R.A., et al., PROCHECK: a program to check the stereochemical quality of protein structures. Journal of Applied Crystallography, 1993. 26(2): p. 283-291.
52. Micsonai, A., et al., Accurate secondary structure prediction and fold recognition for circular dichroism spectroscopy. Proc. Natl. Acad. Sci. U. S. A., 2015. 112(24): p. E3095-103.
53. Hoffman, J.L., Chromatographic analysis of the chiral and covalent instability of S-adenosyl-L-methionine. Biochemistry, 1986. 25(15): p. 4444-4449.
54. Dhulesia, A., et al., Local Cooperativity in an Amyloidogenic State of Human Lysozyme Observed at Atomic Resolution. Journal of the American Chemical Society, 2010. 132(44): p. 15580-15588.
55. Myers, J.K., C.N. Pace, and J.M. Scholtz, Denaturant m values and heat capacity changes: relation to changes in accessible surface areas of protein unfolding. Protein Science : A Publication of the Protein Society, 1995. 4(10): p. 2138-2148.
56. Liu, Y. and D. Eisenberg, 3D domain swapping: as domains continue to swap. Protein Science, 2002. 11(6): p. 1285-99.
57. García De La Torre, J., M.L. Huertas, and B. Carrasco, Calculation of hydrodynamic properties of globular proteins from their atomic-level structure. Biophysical Journal, 2000. 78(2): p. 719-730.
58. Kikhney, A.G. and D.I. Svergun, A practical guide to small angle X-ray scattering (SAXS) of flexible and intrinsically disordered proteins. FEBS Letters, 2015. 589(19, Part A): p. 2570-2577.
59. Engen, J.R., Analysis of Protein Conformation and Dynamics by Hydrogen/Deuterium Exchange MS. Analytical chemistry, 2009. 81(19): p. 7870-7875.
60. Morgan, C.R. and J.R. Engen, Investigating solution-phase protein structure and dynamics by hydrogen exchange mass spectrometry. Current Protocols in Protein Science, 2009. Chapter 17: p. Unit 17 6 1-17.
61. Konermann, L., J. Pan, and Y.H. Liu, Hydrogen exchange mass spectrometry for studying protein structure and dynamics. Chemical Society Review, 2011. 40(3): p. 1224-34.
62. Frauenfelder, H., et al., A unified model of protein dynamics. Proc. Natl. Acad. Sci. U. S. A., 2009. 106(13): p. 5129-34.
63. Fersht, A., Structure and mechanism in protein science : a guide to enzyme catalysis and protein folding. 1999, New York : W.H. Freeman, c1999 1998 printing.
64. Bennett, M.J., M.P. Schlunegger, and D. Eisenberg, 3D domain swapping: a mechanism for oligomer assembly. Protein Science : A Publication of the Protein Society, 1995. 4(12): p. 2455-2468.
65. Fruchter, R.G. and A.M. Crestfield, Preparation and Properties of Two Active Forms of Ribonuclease Dimer. Journal of Biological Chemistry, 1965. 240(10): p. 3868-3874.
66. Gotte, G., M. Bertoldi, and M. Libonati, Structural versatility of bovine ribonuclease A. European Journal of Biochemistry, 2001. 265(2): p. 680-687.
67. Libonati, M., M. Bertoldi, and S. Sorrentino, The activity on double-stranded RNA of aggregates of ribonuclease A higher than dimers increases as a function of the size of the aggregates. Biochemical Journal, 1996. 318(Pt 1): p. 287-290.
68. Liu, Y., et al., The crystal structure of a 3D domain-swapped dimer of RNase A at a 2.1-Å resolution. Proceedings of the National Academy of Sciences, 1998. 95(7): p. 3437-3442.
69. Liu, Y., et al., A domain-swapped RNase A dimer with implications for amyloid formation. Nature Structural Biology, 2001. 8: p. 211.
70. Mallam, A.L. and S.E. Jackson, The dimerization of an alpha/beta-knotted protein is essential for structure and function. Structure, 2007. 15(1): p. 111-22.
71. Ha, J.H., et al., Engineered Domain Swapping as an On/Off Switch for Protein Function. Chemical Biology, 2015. 22(10): p. 1384-93.