Designing potential energy functions for protein folding

Current Opinion in Structural Biology

Volumn 9, Issue 2, 1999, Pages 184-188

  Hao, Ming Hong ^a,b   Scheraga, Harold A ^b  

^a BIP Inc   (United States)

^b Department of Population Medicine and Diagnostic Sciences   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

PROTEIN;

ALGORITHM; MOLECULAR MODEL; PRIORITY JOURNAL; PROTEIN FOLDING; REVIEW; THERMODYNAMICS;

EID: 0033117762     PISSN: 0959440X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0959-440X(99)80026-8     Document Type: Article

References (40)

1. Onuchic JN, Luthey-Schulten Z, Wolynes PG: Theory of protein folding: The energy landscape perspective. Annu Rev Phys Chem 1997, 48:545-600.
2. Dill KA, Chan HS: From Levinthal to pathways to funnels. Nat Struct Biol 1997, 4:10-19.
3. Levitt M, Gerstein M, Huang E, Subbiah S, Tsai J: Protein folding: The endgame. Annu Rev Biochem 1997, 66:549-579.
4. Shakhnovich EI: Protein design: A perspective from simple tractable models. Fold Des 1998, 3:R45-R58.
5. Go N: Theoretical studies of protein folding. Annu Rev Biophys Bioeng 1983, 12:183-210.
6. Bryngelson JD, Wolynes PG: Spin glasses and the statistical mechanics of protein folding. Proc Natl Acad Sci USA 1987, 84:7524-7528.
7. Shakhnovich E, Farztdinov G, Gutin AM, Karplus M: Protein folding bottlenecks: A lattice Monte-Carlo simulation. Phys Rev Lett 1991, 67:1665-1667.
8. Shakhnovich EI: Proteins with selected sequences fold into unique native conformation. Phys Rev Lett 1994, 72:3907-3910.
9. Goldstein RA, Luthey-Schulten ZA, Wolynes PG: Optimal protein- folding codes from spin-glass theory. Proc Natl Acad Sci USA 1992, 89:4918-4922.
10. Bowie JU, Lüthy R, Eisenberg D: A method to identify protein sequences that fold into a known three-dimensional structure. Science 1991, 253:164-170.
11. Shakhnovich EI, Gutin AM: A new approach to the design of stable proteins. Protein Eng 1993, 6:793-800.
12. Nymeyer H, Garcia AE, Onuchic JN: Folding funnels and frustration in off-lattice minimalist protein landscapes. Proc Natl Acad Sci USA 1998, 95:5921-5928. The folding transition of off-lattice models of proteins with optimized sequences were studied. The results were analyzed within the framework of the energy landscape theory of protein folding, using techniques developed previously for studying simple cubic-lattice proteins. As the more quantitative measure of the models, that is, the density of states, was not calculated, however, it is difficult to draw conclusions about whether the off-lattice models studied are any different from simple cubic-lattice models.
13. Klimov DK, Thirumalai D: Cooperativity in protein folding: From lattice models with side chains to real proteins. Fold Des 1998, 3:127-139. The behavior of the cooperative folding of proteins was studied within a square lattice (in two dimensions) of 15-mers. The free-energy landscape of the systems was characterized both in energy space and along an order parameter of folding. It is reported that the models with sidechains exhibit stronger cooperativity in folding than the same models without sidechains. The conclusion of this study is not completely convincing because the two systems compared (with and without sidechains) have different sizes in their conformational spaces; the number of conformations for the model with sidechains is larger by a factor of 2202 than that without sidechains. The strength of the cooperativity may depend on the size of the systems.
14. Mirny LA, Abkevich VI, Shakhnovich EI: How evolution makes proteins fold quickly. Proc Natl Acad Sci USA 1998, 95:4976-4981. Sequences of fast-folding model proteins defined on a cubic lattice were generated using an evolution-like selection process that favors fast-folding sequences. The main conclusion of the study is that fast-folding protein models are characterized by possessing a core of conserved residues as a folding nucleus. The simulation results are compared to the behavior of one real protein.
15. Govindarajan S, Goldstein RA: On the thermodynamic hypothesis of protein folding. Proc Natl Acad Sci USA 1998, 95:5545-5549. The thermodynamic hypothesis of protein folding, that is, that the native state is the global free-energy minimum, was studied from the perspective of sequence optimization in an evolution process. It was found that a sequence evolution process, in which mutations that keep the kinetic foldability of the sequence are retained, will result in proteins that satisfy the thermodynamic hypothesis of protein folding.
16. Mirny LA, Shakhnovich EI: How to derive a protein folding potential? A new approach to an old problem. J Mol Biol 1996, 264:1164-1179.
17. Hao MH, Scheraga HA: How optimization of potential functions affects protein folding. Proc Natl Acad Sci USA 1996, 93:4984-4989.
18. Hao MH, Scheraga HA: Optimizing potential functions for protein folding. J Phys Chem 1996, 100:14540-14548.
19. Koretke KK, Luthey-Schulten Z, Wolynes PG: Self-consistently optimized statistical mechanical energy functions for sequence structure alignment. Protein Sci 1996, 5:1043-1059.
20. Koretke KK, Luthey-Schulten Z, Wolynes PG: Self-consistently optimized energy functions for protein structure prediction by molecular dynamics. Proc Natl Acad Sci USA 1998, 95:2932-2937. In this paper, a general strategy is proposed for optimizing the energy parameters of a potential function by taking into account both the major determinant and the secondary contributions. The methods for sampling the misfolded conformations of protein models and the approach for treating the heterogeneity of different proteins in the optimization are also provided. Tests of the method on an ensemble of eight proteins are described and reasonably good results for folding are reported.
21. Chiu TL, Goldstein RA: Optimizing energy potentials for success in protein tertiary structure prediction. Fold Des 1998, 3:223-228. An alternative procedure is proposed for optimizing a potential energy function for an ensemble of proteins. The average success of folding all the proteins in the training set is maximized in this approach.
22. Kolinski A, Galazka W, Skolnick J: Monte Carlo studies of the thermodynamics and kinetics of reduced protein models. Application to small helical, beta and alpha-beta proteins. J Chem Phys 1998, 108:2608-2617. This paper is one of a series of publications from the same group, in which a general strategy for deriving a potential energy function for the folding of more realistic models of proteins is developed.
23. Rooman M, Gilis D: Different derivations of knowledge-based potentials and analysis of their robustness and context-dependent predictive power. Eur J Biochem 1998, 254:135-143. The authors present a comprehensive study of all physically reasonable ways of deriving the energy parameters from the observed frequency of contacts among different types of residues in the native structures of proteins. The performance and robustness of the different formulations were evaluated. The paper concludes that the main problem limiting the performance of database-derived potentials is their lack of universality (or general accuracy for different protein types). This problem also appears to exist, to some degree, in the potentials optimized in order to achieve foldability conditions for various protein models.
24. Du R, Grosberg AY, Tanaka T: Models of protein interactions: How to choose one. Fold Des 1998, 3:203-211. This paper analyzes the differences and similarities among five different sets of database-derived energy parameters. It is found that two-letter coded potentials, taken from the two major principal components of the full contact potential, are a poor representation of the original full interactions.
25. Skolnick J, Kolinski A, Ortiz AR: MONSSTER: A method for folding globular proteins with a small number of distance restraints. J Mol Biol 1997, 265:217-241. A hybrid potential, combining the conventional force-field and distance restraints, was used in Monte Carlo algorithms for folding proteins. The technique has the potential to utilize different experimental/empirical information, such as NMR data, secondary-structure prediction and homology modeling, in order to enhance the performance of computer algorithms for protein folding.
26. Ortiz AR, Kolinski A, Skolnick J: Fold assembly of small proteins using Monte Carlo simulations driven by restraints derived from multiple sequence alignments. J Mol Biol 1998, 277:419-448.
27. Keasar C, Tobi D, Elber R, Skolnick J: Coupling the folding of homologous proteins. Proc Natl Acad Sci USA 1998, 95:5880-5883.
28. Kolinski A, Skolnick J: Lattice Models of Protein Folding, Dynamics and Thermodynamics. Austin, TX: RG Landes; 1996.
29. Socci ND, Onuchic JN: Kinetic and thermodynamic analysis of protein-like heteropolymers: Monte Carlo histogram technique. J Chem Phys 1995, 103:4732-4744.
30. Hao MH, Scheraga HA: Monte Carlo simulation of a first order transition for protein folding. J Phys Chem 1994, 98:4940-4948.
31. Chung MS, Neuwald AF, Wilbur WJ: A free energy analysis by unfolding applied to 125-mers on a cubic lattice. Fold Des 1998, 3:51-65. A method is proposed for calculating the free-energy profile of protein models based on restricted Monte Carlo simulations and conformational sampling over a restricted conformational window. The calculated free-energy profile is used to characterize the foldability of protein models. The method was tested on cubic-lattice proteins with 27-mer and 125-mer chain lengths.
32. Hao MH, Scheraga HA: Molecular mechanisms for cooperative folding of proteins. J Mol Biol 1998, 277:973-983. The molecular mechanisms for the cooperative folding of prevailing protein models represented by simple cubic-lattice chains and more realistic protein models are compared. The free-energy landscapes of these two systems are characterized by the density of states as a function of energy. The variation of the free energy of the systems with other folding order parameters can be inferred from the correlation of the latter with the energy. Important differences between the origins of cooperativity in the folding transitions between the two representative protein models are identified. The relationship between the different folding mechanisms and the force-fields is investigated. It is concluded that, in order to obtain a folding behavior that is similar to that of realistic proteins, more sophisticated force-fields and protein models are required.
33. Hao MH, Scheraga HA: Characterization of foldable protein models: Thermodynamics, folding kinetics and force field. J Chem Phys 1997, 107:8089-8102. An analytical treatment of the thermodynamics and kinetics of the folding transitions of two types of protein models is presented. The basic characteristics of these protein models are derived from previous computer simulation results and it is shown that these two types of models correspond to quantitatively different systems at the analytical mean-field level of description.
34. Hao MH, Scheraga HA: Theory of two-state cooperative folding of proteins. Accounts Chem Res 1998, 31:433-440. The mechanism of the cooperative folding of single-domain proteins is inferred from computer simulation results of representative protein models and theoretical analyses.
35. •] than to the simple cubic- lattice protein models.
36. Honig B, Cohen FE: Adding backbone to protein folding: Why proteins are polypeptides. Fold Des 1996, 1:R17-R20.
37. Liwo A, Pincus MR, Wawak RJ, Rackovsky S, Scheraga HA: Prediction of protein conformation on the basis of a search for compact structures; test on avian pancreatic polypeptide. Protein Sci 1993, 2:1715-1731.
38. Lee J, Liwo A, Scheraga HA: Energy-based ab initio protein folding by conformational space annealing and off-lattice united-residue force field: Application to the 10-55 fragment of staphylococcal protein A and to apo calbindin D9K. Proc Nail Acad Sci USA 1999, in press.
39. Liwo A, Kazmierkiewicz R, Czaplewski C, Groth M, Oldziej S, Wawak RJ, Rackovsky S, Pincus MR, Scheraga HA: United-residue force field for off-lattice protein-structure simulations; III. Origin of backbone hydrogen-bonding cooperativity in united-residue potentials. J Comput Chem 1998, 19:259-276.
40. Lee J, Scheraga HA, Rackovsky S: New optimization method for conformational energy calculations on polypeptides: conformational space annealing. J Comput Chem 1997, 18:1222-1232.