Hidden protein folding pathways in free-energy landscapes uncovered by network analysis

Journal of Chemical Theory and Computation

Volumn 8, Issue 4, 2012, Pages 1176-1189

  Yin, Yanping ^a   Maisuradze, Gia G ^a   Liwo, Adam ^a,b   Scheraga, Harold A ^a  

^a Department of Obstetrics Gynecology   (United States)

^b UNIVERSITY OF GDA SK   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84859564623     PISSN: 15499618     EISSN: 15499626     Source Type: Journal    
DOI: 10.1021/ct200806n     Document Type: Article

References (64)

1. Frauenfelder, H.; Sligar, S. G.; Wolynes, P. G. The energy landscapes and motions of proteins Science 1991, 254, 1598-1630
2. Wales, D. J.; Scheraga, H. A. Global optimization of clusters, crystals, and biomolecules Science 1999, 285, 1368-1372
3. Brooks, C. L., III; Onuchic, J. N.; Wales, D. J. Taking a walk on a landscape Science 2001, 293, 612-613
4. Wales, D. J. Energy landscapes; Cambridge University Press: Cambridge, U.K., 2003; p 681.
5. Krivov, S.; Karplus, M. Hidden complexity of free energy surfaces for peptide (protein) folding Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 14766-14770
6. Altis, A.; Otten, M.; Nguyen, P. H..; Hegger, R.; Stock, G. Construction of the free energy landscape of biomolecules via dihedral angle principal component analysis J. Chem. Phys. 2008, 128, 245102
7. Maisuradze, G. G.; Liwo, A.; Scheraga, H. A. How adequate are one- and two-dimensional free energy landscapes for protein folding dynamics? Phys. Rev. Lett. 2009, 102, 238102
8. Maisuradze, G. G.; Liwo, A.; Scheraga, H. A. Relation between free energy landscapes of proteins and dynamics J. Chem. Theory Comput. 2010, 6, 583-595
9. Hegger, R.; Altis, A.; Nguyen, P. H.; Stock, G. How complex is the dynamics of peptide folding? Phys. Rev. Lett. 2007, 98, 028102
10. Zhou, R.; Berne, B. J.; Germain, R. The free energy landscape for β hairpin folding in explicit water Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 14931-14936
11. Zhou, R.; Parida, L.; Kapila, K.; Mudur, S. PROTERAN: animated terrain evolution for visual analysis of patterns in protein folding trajectory Bioinformatics 2007, 23, 99-106
12. Newman, M. E. J. The structure and function of complex networks SIAM Rev. 2003, 45, 167-256
13. Krivov, S.; Karplus, M. Free energy disconnectivity graphs: Application to peptide models J. Chem. Phys. 2002, 117, 10894-10903
14. Rao, F.; Caflisch, A. The protein folding network J. Mol. Biol. 2004, 342, 299-306
15. Gfeller, D.; De Los Rios, P.; Caflisch, A.; Rao, F. Complex network analysis of free-energy landscapes Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 1817-1822
16. Stillinger, F.; Weber, T. Hidden structure in liquids Phys. Rev. A 1983, 28, 2408-2416
17. Rao, F.; Karplus, M. Protein dynamics investigated by inherent structure analysis Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 9152-9157
18. Liwo, A.; Arlukowicz, P.; Czaplewski, C.; Oldziej, S.; Pillardy, J.; Scheraga, H. A. A method for optimizing potential-energy functions by a hierarchical design of the potential-energy landscape: Application to the UNRES force field Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 1937-1942
19. Oldziej, S.; Liwo, A.; Czaplewski, C.; Pillardy, J.; Scheraga, H. A. Optimization of the UNRES force field by hierarchical design of the potential-energy landscape. 2. Off-lattice tests of the method with single proteins J. Phys. Chem. B 2004, 108, 16934-16949
20. Gouda, H.; Torigoe, H.; Saito, A.; Sato, M.; Arata, Y.; Shimada, I. Three-dimensional solution structure of the B domain of staphylococcal protein A: comparisons of the solution and crystal structures Biochemistry 1992, 31, 9665-9672
21. Liwo, A.; Pincus, M. R.; Wawak, R. J.; Rackovsky, S.; Scheraga, H. A. Prediction of protein conformation on the basis of a search for compact structure: Test on avian pancreatic polypeptide Protein Sci. 1993, 2, 1715-1731
22. Liwo, A.; Oldziej, S.; Pincus, M. R.; Wawak, R. J.; Rackovsky, S.; Scheraga, H. A. A united-residue force field for off-lattice protein-structure simulations. I. Functional forms and parameters of long-range side-chain interaction potentials from protein crystal data J. Comput. Chem. 1997, 18, 849-873
23. Liwo, A.; Pincus, M. R.; Wawak, R. J.; Rackovsky, S.; Oldziej, S.; Scheraga, H. A. A united-residue force field for off-lattice protein-structure simulation. II: Parameterization of local interactions and determination of the weights of energy terms by Z-score optimization J. Comput. Chem. 1997, 18, 874-887
24. α virtual bonds in polypeptides from the ab initio energy surfaces of terminally-blocked glycine, alanine, and proline J. Phys. Chem. A 2003, 107, 8035-8046
25. Liwo, A.; Oldziej, S.; Czaplewski, C.; Kozlowska, U.; Scheraga, H. A. Parametrization of backbone-electrostatic and multibody contributions to the UNRES force field for protein-structure prediction from ab initio energy surfaces of model systems J. Phys. Chem. B 2004, 108, 9421-9438
26. Oldziej, S.; Lagiewka, J.; Liwo, A.; Czaplewski, C.; Chinchio, M.; Nanias, M.; Scheraga, H. A. Optimization of the UNRES force field by hierarchical design of the potential-energy landscape. 3. Use of many proteins in optimization J. Phys. Chem. B 2004, 108, 16950-16959
27. Liwo, A.; Khalili, M.; Czaplewski, C.; Kalinowski, S.; Oldziej, S.; Wachucik, K.; Scheraga, H. A. Modification and optimization of the united-residue (UNRES) potential energy function for canonical simulations. I. Temperature dependence of the effective energy function and tests of the optimization method with single training proteins J. Phys. Chem. B 2007, 111, 260-285
28. Boczko, E. M.; Brooks, C. L., III. First principles calculation of the free energy surface for folding of a three helix bundle protein Science 1995, 269, 393-396
29. Guo, Z.; Brooks, C. L., III; Boczko, E. M. Exploring the folding free energy surface of a three-helix bundle protein Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 10161-10166
30. Bai, Y.; Karimi, A.; Dyson, H. J.; Wright, P. E. Absence of a stable intermediate on the folding pathway of Protein A (B domain) Protein Sci. 1997, 6, 1449-1457
31. Alonso, D. O. V.; Daggett, V. Staphylococcal protein A: Unfolding pathways, unfolded states, and differences between the B and E domains Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 133-138
32. Berriz, G. F.; Shakhnovich, E. I. Characterization of the folding kinetics of a three-helix bundle protein via a minimalist Langevin model J. Mol. Biol. 2001, 310, 673-685
33. Myers, J. K.; Oas, T. G. Preorganized secondary structure as an important determinant of fast protein folding Nat. Struct. Biol. 2001, 8, 552-558
34. Ghosh, A.; Elber, R.; Scheraga, H. A. An atomically detailed study of the folding pathways of protein A with the stochastic difference equation Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 10394-10398
35. Jang, S.; Kim, E.; Shin, S.; Pak, Y. Ab initio folding of helix bundle proteins using molecular dynamics simulations J. Am. Chem. Soc. 2003, 125, 14841-14846
36. Garcia, A. E.; Onuchic, J. N. Folding a protein in a computer: An atomic description of the holding/unfolding of protein A Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 13898-13903
37. Vila, J. A.; Ripoll, D. R.; Scheraga, H. A. Atomically detailed folding simulation of the B domain of staphylococcal protein A from random structures Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 14812-14816
38. Dimitriadis, G.; Drysdale, A.; Myers, J. K.; Arora, P.; Radford, S. E.; Oas, T. G.; Smith, D. A. Microsecond folding dynamics of the F13W G29A mutant of the B domain of staphylococcal protein A by laser-induced temperature jump Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 3809-3814
39. Sato, S.; Religa, T. L.; Daggett, V.; Fersht, A. R. Testing protein-folding simulations by experiment: B domain of protein A Proc Natl. Acad. Sci. USA 2004, 101, 6952-6956
40. Liwo, A.; Khalili, M.; Scheraga, H. A. Ab initio simulations of protein-folding pathways by molecular dynamics with the united-residue model of polypeptide chains Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 2362-2367
41. Khalili, M.; Liwo, A.; Jagielska, A.; Scheraga, H. A. Molecular dynamics with the United-Residue model of polypeptide chains. II. Langevin and Berendsen-Bath dynamics and tests on model α-helical systems J. Phys. Chem. B 2005, 109, 13798-13810
42. Cheng, S.; Yang, Y.; Wang, W.; Liu, H. J. Transition state ensemble for the folding of B domain of protein A: A comparison of distributed molecular dynamics simulation with experiments J. Phys. Chem. B 2005, 109, 23645-23654
43. Khalili, M.; Liwo, A.; Scheraga, H. A. Kinetic studies of folding of the B-domain of staphylococcal protein A with molecular dynamics and a united-residue (UNRES) model of polypeptide chains J. Mol. Biol. 2006, 355, 536-547
44. Jagielska, A.; Scheraga, H. A. Influence of temperature, friction, and random forces on folding of the B-domain of staphylococcal protein A: All- atom molecular dynamics in implicit solvent J. Comput. Chem. 2007, 28, 1068-1082
45. Maisuradze, G. G.; Liwo, A.; Oldziej, S.; Scheraga, H. A. Evidence, from simulations, of a single state with residual native structure at the thermal denaturation midpoint of a small globular protein J. Am. Chem. Soc. 2010, 132, 9444-9452
46. Berendsen, H. J. C.; Postma, J. P. M; van Gunsteren, W. F.; Dinola, A.; Haak, J. R. Molecular dynamics with coupling to an external bath J. Chem. Phys. 1984, 81, 3684-3690
47. Gibson, D.; Kleinberg, J.; Raghavan, P. Inferring web communities from link topology; ACM Press: New York, 1998.
48. Newman, M. E. J. The structure of scientific collaboration networks Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 404-409
49. Barabasi, A. L.; Oltvai, Z. N. Network biology: understanding the cell's functional organizations Nat. Rev. Genet. 2004, 5, 101-113
50. Girvan, M.; Newman, M. E. J. Community structure in social and biological networks Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 7821-7826
51. Clauset, A.; Newman, M. E. J.; Moore, C. Finding community structure in very large networks Phys. Rev. E 2004, 70, 066111
52. Van Dongen, S. Graph clustering by flow simulation. PhD thesis, University of Utrecht: Utrecht, The Netherlands, May 2000.
53. Enright, A. J.; Van Dongen, S.; Ouzounis, C. A. An efficient algorithm for large scale detection of protein families Nucleic Acids Res. 2002, 30, 1575-1584
54. Ohgushi, M.; Wada, A. "Molten-globule state": a compact form of globular proteins with mobile side-chains FEBS Lett. 1983, 164, 21-24
55. Bondy, J. A.; Murty, U. S. R. Graph Theory with Applications; Macmillan: London, 1976.
56. Harary, F. Graph Theory; Perseus: Cambridge, MA, 1995.
57. Bollobas, B. Modern Graph Theory; Springer: New York, 1998.
58. Richard, B. On a Routing Problem Quarterly of Applied Mathematics 1958, 16, 87-90
59. Dijkstra, E. W. A note on two problems in connexion with graphs Numerische Math. 1959, 1, 269-271
60. Floyd, R. W. Algorithm 97: Shortest Path Commun. ACM 1962, 5, 345
61. Hart, P. E.; Nilsson, N. J.; Raphael, B. Correction to "A Formal Basis for the Heuristic Determination of Minimum Cost Paths" SIGART Newsletter 1972, 37, 28-29
62. Newman, M. E. J. Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality Phys. Rev. E 2001, 64, 016132
63. Privalov, P. L.; Khechinashvili, N. N. A thermodynamic approach to the problem of stabilization of globular protein structure: a calorimetric study J. Mol. Biol. 1974, 86, 665-684
64. Eastwood, M. P.; Hardin, C.; Luthey-Schulten, Z.; Wolynes, P. G. Statistical mechanical refinement of protein structure prediction schemes: Cumulant expansion approach J. Chem. Phys. 2002, 117, 4602-4615