Pseudosystematic conformational search. Application to cycloheptadecane

Journal of the American Chemical Society

Volumn 119, Issue 24, 1997, Pages 5657-5667

  Ngo, J Thomas ^a,b,c   Karplus, Martin ^a  

^a HARVARD UNIVERSITY   (United States)

^b Graduate Biophysics Program   (United States)

^c Interval Research Corporation   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CYCLOHEPTADECANE; CYCLOHEPTANE DERIVATIVE; UNCLASSIFIED DRUG;

ALGORITHM; ARTICLE; COMPUTER; CONFORMATION; INTERMETHOD COMPARISON; STEREOCHEMISTRY; SYSTEM ANALYSIS;

EID: 0030858712     PISSN: 00027863     EISSN: None     Source Type: Journal    
DOI: 10.1021/ja961132o     Document Type: Article

References (67)

1. Saunders, M.; Houk, K. N.; Wu, Y.-D.; Still, W. C.; Lipton, M.; Chang, G.; Guida, W. C. Comformations of cycloheptadecane: A comparison of methods for conformational searching. J. Am. Chem. Soc. 1990, 112, 1419-1427.
2. Brooks, C. L., III; Karplus, M.; Pettitt, B. M. Proteins. Advances in Chemical Physics; Wiley: New York, 1988; Vol. LXXI.
3. 2 torsional terms. J. Am. Chem. Soc. 1977, 99 (25), 8127-8132.
4. Gotō, H.; Ōsawa, E. An efficient algorithm for searching low-energy conformers of cyclic and acyclic molecules. J. Chem. Soc., Perkin Trans. 2 1993, pages 187-198.
5. Ngo, J. T. Global Optimization for Articulated Figures: Molecular Structure Prediction and Motion Synthesis for Animation. Ph.D. Thesis, Harvard University, Cambridge, MA, June 1993.
6. Kolossvàry, I.; Guida, W. C. Comprehensive conformational analysis of the four- to twelve-membered ring cycloalkanes: Identification of the complete set of interconversion pathways on the MM2 potential energy hypersurface. J. Am. Chem. Soc. 1993, 113, 2107-2119.
7. Koča, J. Computer program CICADA - travelling along conformational potential energy hypersurface. J. Mol. Struct: THEOCHEM 1994, 308, 13-24.
8. Saunders, M. J. Stochastic exploration of molecular mechanics energy surfaces. Hunting for the global minimum. J. Am. Chem. Soc. 1987, 109, 3150.
9. Chang, G.; Guida, W. C.; Still, W. C. An internal coordinate Monte Carlo method for searching conformational space. J. Am. Chem. Soc. 1989, 11, 4379.
10. Lipton, M.; Still, W. C. The multiple minimum problem in molecular modeling. Tree searching internal coordinate conformational space. J. Comput. Chem. 1988, 9 (4), 343-355.
11. Gō, N.; Scheraga, H. A. Ring closure and local conformational deformations of chain molecules. Macromolecules 1970, 3 (2), 178-187.
12. Bruccoleri, R. E.; Karplus, M. Prediction of the folding of short polypeptide segments by uniform conformational sampling. Biopolymers 1987, 26, 137-168.
13. Korein, J. U. A Geometric Investigation of Reach. ACM Distinguished Dissertations; MIT Press: Cambridge, MA, 1985.
14. Howard, A. E.; Kollman, P. A. An analysis of current methodologies for conformational searching of complex molecules. J. Med. Chem. 1988, 31 (9), 1669-1675.
15. Li, Z.; Scheraga, H. A. Monte Carlo-Minimization approach to the multiple-minima problem in protein folding. Proc. Natl. Acad. Sci. U.S.A. 1987, 84, 6611-6615.
16. Caflisch, A.; Niederer, P.; Anliker, M. Monte Carlo Minimization with thermalization for global optimization of polypeptide conformation conformations in Cartesian coordinate space. Proteins: Struct., Funct. Genet. 1992, 14, 102-109.
17. Nayeem, A.; Vila, J.; Scheraga, H. A. A comparative study of the simulated-annealing and Monte Carlo-with-minimization approaches to the minimum-energy structures of polypeptides: [met]-enkephalin. J. Comput. Chem. 1991, 12 (5), 594-605.
18. Kirkpatrick, S.; Gelatt, C. D., Jr.; Vecchi, M. P. Optimization by simulated annealing. Science 1983, 220, 671-680.
19. Saunders, M. J. Stochastic search for the conformations of bicyclic hydrocarbons. J. Comput. Chem. 1989, 10 (2), 203-208.
20. Ferguson, D. M.; Raber, D. J. A new approach to probing conformational space with molecular mechanics: Random incremental pulse search. J. Am. Chem. Soc. 1989, 111 (12), 4371-4378.
21. Berg, B. A.; Neuhaus, T. Multicanonical algorithms for first-order phase transitions. Phys. Lett. 1991, B267(2), 249-253.
22. Hansmann, U. H. E., Okamoto, Y. Prediction of peptide conformation by multicanonical algorithm: New approach to the multiple-minima problem. J. Comput. Chem. 1993, 14 (11), 1333-1338.
23. van Gunsteren, W. F.; Berendsen, H. J. C. Algorithms for macromolecular dynamics of constraint dynamics. Mol. Phy. 1977, 34 (5), 1311-1327.
24. Swindoll, R. D.; Haile, J. M. A multiple time-step method for molecular dynamics simulations of fluids of chain molecules. J. Comput. Phys. 1984, 53 (2), 289-298.
25. Teleman, O.; Jönsson, B. Vectorizing a general purpose molecular dynamics simulation program. J. Comput. Chem. 1986, 7 (1), 58-66.
26. Tuckerman, M. E.; Martyna, G. J.; Berne, B. J. Molecular dynamics algorithm for condensed systems with multiple time scales. J. Chem. Phys. 1990 1990, 93 (2), 1287-1291.
27. Tuckerman, M. E.; Berne, B. J.; Rossi, A. Molecular dynamics algorithm for multiple time scales: Systems with disparate masses. J. Chem. Phys. 1990, 94 (2), 1465-1469.
28. Tuckerman, M. E.; Berne, B. J. Molecular dynamics in systems with multiple time scales: Systems with stiff and soft degrees of freedom and with short- and long-range forces. J. Chem. Phys. 1991, 95 (11), 8362-8364.
29. Tuckerman, M. E.; Martyna, G. J.; Berne, B. J. Molecular dynamics algorithm for multiple time scales: Systems with long-range forces. J. Chem. Phys. 1991, 94 (10), 6811-6815.
30. Tuckerman, M. E.; Berne, B. J.; Martyna, G. J. Reversible multiple time scale molecular dynamics. J. Chem. Phys. 1992, 97 (3), 1990-2001.
31. Watanabe, M.; Karplus, M. Dynamics of molecules with internal degrees of freedom by multiple time-step methods. J. Chem. Phys. 1993, 99, 8063.
32. Némethy, G.; Pottle, M. S.; Scheraga, H. A. Energy parameters in polypeptides. 9. Updating of geometrical parameters, nonbonded interactions, and hydrogen bond interactions for the naturally occurring amino acids. J. Phys. Chem. 1983, 87, 1883.
33. Momany, F. A.; McGuire, R. F.; Burgess, A. W.; Scheraga, H. A. Energy parameters in polypeptides. VII. Geometric parameters, partial atomic charges, nonbonded interactions, hydrogen bond interactions, and intrinsic torsional potentials for the naturally occurring amino acids. J. Phys. Chem. 1975, 79 (22), 2361-2381.
34. Durup, J. Protein molecular dynamics constrained to slow modes. Theoretical approach based on a hierarchy of local modes with a set of holonomic constraints: The method and its tests on citrate synthase. J. Phys. Chem. 1991, 95, 1817-1829.
35. Mazur, A. K.; Dorofeev, V. E.; Abagyan, R. A. Derivation and testing of explicit equations of motion for polymers described by internal coordinates. J. Comput. Phys. 1991, 92, 261-272.
36. Head-Gordon, T.; Brooks, C. L., III. Virtual rigid body dynamics. Biopolymers 1991, 31, 77-100.
37. Surles, M. C. An algorithm with linear complexity for interactive, physically-based modeling of large proteins. Comput. Graphics 1992, 26 (2), 221-230.
38. Morley, S. D.; Jackson, D. E.; Saunders, M. R.; Vinter, J. G. DMC: A multifunctional hybrid dynamics/Monte Carlo simulation algorithm for the evaluation of conformational space. J. Comput. Chem. 1992, 13 (6), 693-703.
39. Elofsson, A.; Le Grand, S. M.; Eisenberg, D. Local moves: An efficient algorithm for simulation of protein folding. Proteins: Struct., Funct., Genet. 1995, 23, 73-82.
40. Dudek, M. J.; Scheraga, H. A. Protein structure prediction using a combination of sequence homology and global energy minimization I. Global energy minimization of surface loops. J. Comput. Chem. 1990, 11 (1), 121-151.
41. Crippen, G. M. Exploring the conformational space of cycloalkanes by linearized embedding. J. Comput. Chem. 1992, 13 (3), 351-361.
42. 38
43. -1. This causes the maximum values of the rotational and translational components of Λ(T̂) to have similar magnitude.
44. Strang, G. Linear Algebra and Its Applications, 2nd ed.; Academic Press: New York, 1976.
45. Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes in C. The Art of Scientific Computing; Cambridge University Press: Cambridge, U.K., 1988.
46. 13 can arise only at the beginning of the pseudosystematic search, when the first random structure is generated. It is easily overcome by bending the extended structure in any direction, or by choosing a new random starting structure.
47. Our implicit assumption is that the average time required to minimize each structure would be no higher, given the same hardware, software, and energy minimization parameters, than the time required when a different search technique is employed. This assumption is reasonable because, unlike the trial structures produced by the Cartesian and torsional Monte Carlo searches, the trial structures produced by the pseudosystematic search contain no unfavorable bond lengths and angles and, because of the use of operations that respect the kinematics of the molecule, are unlikely to contain unfavorable torsional values.
48. 1).
49. 1 two conformers are deemed identical if all of their torsions match within 10° after 1 of the 68 possible symmetry operations.
50. 1) increased to just below 3.002 kcal/mol. If the coordinates obtained by Saunders et al. are reminimized, all energies of corresponding conformers match those obtained here to at least 0.0001 kcal/ mol precision. The results reported here employ the 3.002 kcal/mol threshold.
51. Shakhnovich, E. I.; Gutin, A. M. Implications of thermodynamics of protein folding for evolution of primary sequences. Nature 1990, 346, 773-775.
52. missed.
53. Wiberg, K. B.; Murcko, M. A. Rotational barriers. 2. Energies of alkane rotamers. An examination of gauche interactions. J. Am. Chem. Soc. 1988, 110, 8029-8038.
54. Dunbrack Jr., R. L.; Karplus, M. Conformational analysis of the backbone-dependent rotamer preferences of protein sidechains. Nat. Struct. Biol. 1994, 1, 334-340.
55. 1 report that sequences of four contiguous anti torsions appear twice among their conformers within 2 kcal/mol of the purported global minimum and 18 times among their conformers within the 3 kcal/ mol bound.
56. 1 was found.
57. The algorithm is also easily parallelized, especially for MIMD parallel machines and workstation clusters. If the generation and energy minimization of one trial structure are assigned to each processor, then the total number of processors that can be utilized effectively at any given stage in the search is 34 times the number of known, unvisited solutions. At the beginning of the search, this number can be as low as 34, but soon afterward it rises into the thousands.
58. Ngo, J. T.; Marks, J. Computational complexity of a problem in molecular-structure prediction. Protein Eng. 1992, 5 (4), 313-321.
59. Garey, M. R.; Johnson, D. S. Computers and Intractability: A Guide to the Theory of NP-Completeness; W. H. Freeman and Co.: San Francisco, CA, 1979. P is the set of problems that can be solved exactly by a deterministic machine in polynomial time. NP is the set of problems that can be solved exactly by a non-deterministic machine in polynomial time.
60. This empirical observation does not contradict the theoretical result; any NP-hard problem can have special cases that are solved relatively easily. What the result prohibits (unless P = NP) is the existence of a conformational search algorithm that can be guaranteed to complete in polynomial time for all molecules.
61. Monge, A., Friesner, R. A.; Honig, B. An algorithm to generate low-resolution protein tertiary structures from knowledge of secondary structure. Proc. Natl. Acad. Sci. 1994, 91, 5027-5029.
62. Gunn, J. R.; Monge, A.; Friesner, R. A.; Marshall, C. H. Hierarchical algorithm for computer modeling of protein tertiary structure: Folding of myoglobin to 6.2å resolution. J. Phys. Chem. 1994, 98, 702-711.
63. target is a constant transformation determined by the required position and orientation.
64. Derrida, B. Random-energy model: An exactly solvable model of disordered systems. Phys. Rev. B 1981, 24 (5), 2613-2624.
65. Rechenberg, I. Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution; Frommann-Holzboog Verlag: Stuttgart, 1973.
66. Bäck, T.; Hoffmeister, F.; Schwefel, H.-P. A survey of evolution strategies. In Proceedings of the 4th International Conference on Genetic Algorithms, San Mateo, CA, 1991; Belew, R. K., Booker, L. B., Eds.; Morgan Kaufmann: San Mateo, CA, 1991; pp 2-9.
67. Choquet-Bruhat, Y.; Dewitt-Morette, C.; Dillard-Bleick, M. Analysis, Manifolds, and Physics: Part I; North-Holland: Amsterdam, 1982.