The energy landscape, folding pathways and the kinetics of a knotted protein

PLoS Computational Biology

Volumn 6, Issue 7, 2010, Pages 30-

  Prentiss, Michael C ^a,b   Wales, David J ^c   Wolynes, Peter G ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

MOLECULAR PHYSICS; POTENTIAL ENERGY; POTENTIAL ENERGY SURFACES; QUANTUM CHEMISTRY;

C-TERMINUS; DISCRETE PATH SAMPLINGS; ENERGY LANDSCAPE; FOLDING PATHWAY; FOLDING PROCESS; FOLDING RATES; FOLDINGS; KINETIC TRANSITION; N TERMINUS; RATE COEFFICIENTS;

PROTEIN FOLDING;

TRANSFER RNA METHYLTRANSFERASE; PROTEIN;

AMINO ACID SEQUENCE; AMINO TERMINAL SEQUENCE; ARTICLE; ASSOCIATIVE MEMORY; CARBOXY TERMINAL SEQUENCE; CONTROLLED STUDY; GEOMETRY; KERNEL METHOD; PHASE TRANSITION; PROTEIN CONFORMATION; PROTEIN FOLDING; PROTEIN STRUCTURE; CHEMISTRY; KINETICS; MOLECULAR DYNAMICS; THERMODYNAMICS;

KINETICS; MOLECULAR DYNAMICS SIMULATION; PROTEIN CONFORMATION; PROTEIN FOLDING; PROTEINS; THERMODYNAMICS;

EID: 78049271422     PISSN: 1553734X     EISSN: 15537358     Source Type: Journal    
DOI: 10.1371/journal.pcbi.1000835     Document Type: Article

References (74)

1. Fersht A (1999) Structure and Mechanism in Protein Science. New York: Freeman.
2. Kubelka J, Hofrichter J, Eaton WA (2004) The protein folding speed limit. Curr Opin Struct Biol 14: 76-88.
3. Dietz H, Rief M (2004) Exploring the energy landscape of gfp by single-molecule mechanical experiments. Proc Natl Acad Sci U S A 101: 16192-16197.
4. Takasugawa F, Kamitori A (1996) A real knot in protein. J Am Chem Soc 118: 8945-8946.
5. Gosavi S, Chavez LL, Jennings PA, Onuchic JN (2006) Topological frustration and the folding of interleukin-1 beta. J Mol Biol 357: 986-996.
6. Wales DJ (2003) Energy Landscapes. Cambridge, UK: Cambridge University Press.
7. Ahn HJ, Kim HW, Yoon HJ, Lee BI, Suh SW, et al. (2003) Crystal structure of trna(m1g37)methyltransferase: insights into trna recognition. EMBO J 22: 2593-2603.
8. Virnau P, Mirny LA, Kardar M (2006) Intricate knots in proteins: Function and evolution. PLoS Comput Biol 2: e122.
9. Kolesov G, Virnau P, Kardar M, Mirny LA (2007) Protein knot server: detection of knots in protein structures. Nucl Acids Res 35: W425-428.
10. Taylor WR (2000) A deeply knotted protein structure and how it might fold. Nature 406: 916-919.
11. Lua RC, Grosberg AY (2006) Statistics of knots, geometry of conformations, and evolution of proteins. PLoS Comput Biol 2: e45.
12. Raymer DM, Smith DE (2007) Spontaneous knotting of an agitated string. Proc Nat Acad Sci USA 104: 16432-16437.
13. Bois JS, Venkataraman S, Choi HMT, Spakowitz AJ, Wang ZG, et al. (2005) Topological constraints in nucleic acid hybridization kinetics. Nucl Acids Res 33: 4090-4095.
14. Wales DJ. PATHSAMPLE: A program for generating connected stationary point databases and extracting global kinetics. http://www-wales.ch.cam.ac.uk/software.html.
15. Wales DJ. OPTIM: A program for optimising geometries and calculating pathways. http://www-wales.ch.cam.ac.uk/software.html.
16. Wales DJ (2006) Energy landscapes: calculating pathways and rates. Int Rev Phys Chem 25: 237-282.
17. Wales DJ (2009) Calculating rate constants and committor probabilities for transition networks by graph transformation. J Chem Phys 130: 204111.
18. Strodel B, Whittleston CS, Wales DJ (2007) Thermodynamics and kinetics of aggregation for the gnnqqny peptide. J Am Chem Soc 129: 16005-16014.
19. Carr JM, Wales DJ (2005) Global optimization and folding pathways of selected alpha-helical proteins. J Chem Phys 123: 234901.
20. Wales DJ (2002) Discrete path sampling. Mol Phys 100: 3285-3306.
21. Carr JM, Wales DJ (2008) Folding pathways and rates for the three-stranded b-sheet peptide beta3s using discrete path sampling. J Phys Chem B 112: 8760-8769.
22. Carr JM, Wales DJ (2009) Refined kinetic transition networks for the gb1 hairpin peptide. Phys Chem Chem Phys 11: 3341-3354.
23. Bryngelson JD, Wolynes PG (1987) Spin glasses and the statistical mechanics of protein folding. Proc Natl Acad Sci USA 84: 7524.
24. Goldstein RA, Luthey-Schulten ZA, Wolynes PG (1992) Optimal proteinfolding codes from spin-glass theory. Proc Natl Acad Sci USA 89: 4918-4922.
25. Becker OM, Karplus M (1997) The topology of multidimensional potential energy surfaces: Theory and application to peptide structure and kinetics. J Chem Phys 106: 1495.
26. Wales DJ, Miller MA, Walsh TR (1998) Archetypal energy landscapes. Nature 394: 758.
27. Humphrey W, Dalke A, Schulten K (1996) VMD- Visual Molecular Dynamics. J Molec Graphics 14: 33-38.
28. Chandler D (1978) Statistical mechanics of isomerization dynamics in liquids and the transition state approximation. J Chem Phys 68: 2959.
29. Dellago C, Bolhuis PG, Chandler D (1999) On the calculation of reaction rate constants in the transition path ensemble. J Chem Phys 110: 6617-6625.
30. Trygubenko SA, Wales DJ (2006) Graph transformation method for calculating waiting times in markov chains (16 pages). J Chem Phys 124: 234110.
31. Miller MA, Wales DJ (1999) Energy landscape of a model protein. J Chem Phys 111: 6610-6616.
32. Evans DA, Wales DJ (2003) Free energy landscapes of model peptides and proteins. J Chem Phys 118: 3891-3897.
33. Wales DJ, Dewsbury PEJ (2004) Effect of salt bridges on the energy landscape of a model protein. J Chem Phys 121: 10284-10290.
34. Friedrichs MS, Wolynes PG (1989) Toward protein tertiary structure recognition by means of associative memory hamiltonians. Science 246: 371-373.
35. Friedrichs MS, Goldstein RA, Wolynes PG (1991) Generalized protein tertiary structure recognition using associative memory hamiltonians. J Mol Biol 222: 1013-1034.
36. Wallin S, Zeldovich KB, Shakhnovich EI (2007) The folding mechanics of a knotted protein. J Mol Biol 368: 884-893.
37. Sułkowska JI, Sułkowski P, Onuchic J (2009) Dodging the crisis of folding proteins with knots. Proc Natl Acad Sci USA 106: 3119-3124.
38. Trygubenko SA, Wales DJ (2004) A doubly nudged elastic band method for finding transition states. J Chem Phys 120: 2082.
39. Henkelman G, Jónsson H (1999) A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J Chem Phys 111: 7010-7022.
40. Henkelman G, Uberuaga BP, Jónsson H (2000) A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J Chem Phys 113: 9901-9904.
41. Henkelman G, Jónsson H (2000) Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J Chem Phys 113: 9978-9985.
42. Mallam AL, Jackson SE (2007) A comparison of the folding of two knotted proteins: Ybea and yibk. J Mol Biol 366: 650-665.
43. Mallam AL, Jackson SE (2006) Probing nature's knots: the folding pathway of a knotted homodimeric proteind. J Mol Biol 359: 1420-1436.
44. Clementi C, Plotkin S (2004) The effects of non-native interactions on protein folding rates: Theory and simulation. Prot Sci 13: 1750-1765.
45. Eastwood MP, Wolynes PG (2002) Role of explicitly cooperative interactions in protein folding funnels: A simulation study. J Chem Phys 114: 4702-4716.
46. Mallam AL, Morris ER, Jackson SE (2008) Exploring knotting mechanisms in protein folding. Proc Nat Acad Sci USA 105: 18740-18745.
47. Metzler R, Reisner W, Riehn R, Austin R, Tegenfeldt JO, et al. (2006) Diffusion mechanisms of localised knots along a polymer. Europhys Lett 76: 696-702.
48. Hardin C, Eastwood M, Luthey-Schulten Z, Wolynes PG (2000) Associative memory hamiltonians for structure prediction without homology: Alpha-helical proteins. Proc Natl Acad Sci USA 97: 14235-14240.
49. Eastwood M, Hardin C, Luthey-Schulten Z, Wolynes PG (2002) Statistical mechanical refinement of protein structure prediction schemes i:cumulant expansion approach. J Chem Phys 117: 4602-4615.
50. Papoian G, Ulander J, Eastwood M, Luthey-Schulten Z, Wolynes PG (2004) Water in protein structure prediction. Proc Nat Acad Sci USA 101: 3352-3357.
51. Zong C, Papoian G, Ulander J, Wolynes P (2006) Role of topology, nonadditivity, and water-mediated interactions in predicting the structures of proteins. J Am Chem Soc 128: 5168-5176.
52. Eastwood MP, Hardin C, Luthey-Schulten Z, Wolynes PG (2001) Evaluating protein structure-prediction schemes using energy landscape theory. IBM Systems Research 45: 475-497.
53. Prentiss MC, Hardin C, Eastwood M, Zong C, Wolynes PG (2006) Protein structure prediction: The next generation. J Chem Ther Comp 2:3: 705-716.
54. Ueda Y, Taketomi H, Gō N (1978) Studies on protein folding, unfolding, and fluctuations by computer simulation. ii. a three-dimensional lattice model of lysozyme. Biopolymers 17: 1531.
55. Gō N (1983) Theoretical studies of protein folding. Annu Rev Biophys and Bioeng 12: 183-210.
56. Koga N, Takada S (2001) Roles of native topology and chain-length scaling in protein folding: a simulation study with a gō-like model. J Mol Biol 313: 171-180.
57. Portman JJ, Takada S, Wolynes PG (1998) Variational theory for site resolved protein folding free energy surfaces. Phys Rev Lett 81: 5237-5240.
58. Saven JG, Wolynes PG (1996) Local conformation signals and the statistical thermodynamics of collapsed helical proteins. J Mol Biol 257: 199-216.
59. Kunz RE, Berry RS (1995) Statistical interpretation of topographies and dynamics of multidimensional potentials. J Chem Phys 103: 1904.
60. Noé F, Fischer S (2008) Transition networks for modeling the kinetics of ocnformational change in macromolecules. Curr Op Struct Biol 18: 154-162.
61. Prada-Gracia D, Gómez-Gardenes J, Echenique P, Fernando F (2009) Exploring the free energy landscape: From dynamics to networks and back. PLoS Comput Biol 5: 1-9.
62. Prentiss MC, Wales DJ, Wolynes PG (2008) Protein structure prediction using basin-hopping. J Chem Phys 128: 225106.
63. Li Z, Scheraga HA (1987) Monte carlo-minimization approach to the multipleminima problem in protein folding. Proc Natl Acad Sci USA 84: 6611.
64. Wales DJ, Doye JPK (1997) Global optimization by basin-hopping and the lowest energy structures of lennard-jones clusters containing up to 110 atoms. J Phys Chem A 101: 5111-5116.
65. Dellago C, Bolhuis PG, Csajka FS, Chandler D (1998) Transition path sampling and the calculation of rate constants. J Chem Phys 108: 1964.
66. Bolhuis PG, Chandler D, Dellago C, Geissler PL (2002) Transition path sampling: Throwing ropes over rough mountain passes, in the dark. Annu Rev Phys Chem 53: 291-318.
67. Murrell JN, Laidler KJ (1968) Symmetries of activated complexes. Trans Faraday Soc 64: 371.
68. Nocedal J (1980) Updating quasi-newton matrices with limited storage. Mathematics of Computation 35: 773-782.
69. Liu D, Nocedal J (1989) On the limited memory bfgs method for large scale optimization. Math Prog 45: 503-528.
70. Munro LJ, Wales DJ (1999) Defect migration in crystalline silicon. Phys Rev B 59: 3969-3980.
71. Carr JM, Trygubenko SA, Wales DJ (2005) Finding pathways between distant local minima. J Chem Phys 122: 234903.
72. Tirion MM (1996) Large amplitude elastic motions in proteins from a singleparameter, atomic analysis. Phys Rev Lett 77: 1905.
73. Kearsley SK (1989) On the orthogonal transformation used for structural comparisons. Acta Cryst A 45: 208-210.
74. Pelzer H, Wigner E (1932) The speed constansts of the exchange reactions. Z Phys Chem B 15: 445.