Recent developments in methodologies for calculating the entropy and free energy of biological systems by computer simulation

Current Opinion in Structural Biology

Volumn 17, Issue 2, 2007, Pages 181-186

  Meirovitch, Hagai ^a  

^a UNIVERSITY OF PITTSBURGH SCHOOL OF MEDICINE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CYCLOPEPTIDE; PROTEIN;

BIOLOGY; CALCULATION; COMPUTER SIMULATION; ENERGY; ENTROPY; METHODOLOGY; MOLECULAR DYNAMICS; POPULATION; PRIORITY JOURNAL; PROTEIN FOLDING; REVIEW; SURFACE PROPERTY; THERMODYNAMICS;

COMPUTER SIMULATION; ENTROPY; MODELS, BIOLOGICAL; MULTIPROTEIN COMPLEXES; PROTEIN FOLDING; SYSTEMS BIOLOGY; THERMODYNAMICS;

EID: 34147133371     PISSN: 0959440X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sbi.2007.03.016     Document Type: Review

References (68)

1. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., and Teller E. Equation of state calculations by fast computing machines. J Chem Phys 21 (1953) 1087-1092
2. Alder B.J., and Wainwright T.E. Studies of molecular dynamics. I. General method. J Chem Phys 31 (1959) 459-466
3. McCammon J.A., Gelin B.R., and Karplus M. Dynamics of folded proteins. Nature 267 (1977) 585-590
4. Getzoff E.D., Geysen H.M., Rodda S.J., Alexander H., Tainer J.A., and Lerner R.A. Mechanisms of antibody binding to a protein. Science 235 (1987) 1191-1196
5. Rini J.M., Schulze-Gahmen U., and Wilson I.A. Structural evidence for induced fit as a mechanism for antibody- antigen recognition. Science 255 (1992) 959-965
6. Constantine K.L., Friedrichs M.S., Wittekind M., Jamil H., Chu C.H., Parker R.A., Goldfarb V., Mueller L., and Farmer B.T. Backbone and side chain dynamics of uncomplexed human adipocyte and muscle fatty acid-binding proteins. Biochemistry 37 (1998) 7965-7980
7. Beveridge D.L., and DiCapua F.M. Free energy via molecular simulation: applications to chemical and biomolecular systems. Annu Rev Biophys Biophys Chem 18 (1989) 431-492
8. Kollman P.A. Free energy calculations: applications to chemical and biochemical phenomena. Chem Rev 93 (1993) 2395-2417
9. Jorgensen W.L. Free energy calculations: a breakthrough for modeling organic chemistry in solution. Acc Chem Res 22 (1989) 184-189
10. Meirovitch H. Calculation of the free energy and entropy of macromolecular systems by computer simulation. In: Lipkowitz K.B., and Boyd D.B. (Eds). Reviews in Computational Chemistry 12 (1998), Wiley-VCH 1-74
11. Gilson M.K., Given J.A., Bush B.L., and McCammon J.A. The statistical thermodynamic basis for computing of binding affinities: a critical review. Biophys J 72 (1997) 1047-1069
12. Boresch S., Tettinger F., Leitgeb M., and Karplus M. Absolute binding free energies: a qualitative approach for their calculation. J Phys Chem B 107 (2003) 9535-9551
13. Garcia A.E., and Sanbonmatsu K.Y. Exploring the energy landscape of a beta hairpin in explicit solvent. Proteins 42 (2001) 345-354
14. Nguyen P.H., Stock G., Mittag E., Hu C.K., and Li M.S. Free energy landscape and folding mechanism of a β-hairpin in explicit water: a replica exchange molecular dynamics study. Proteins 61 (2005) 795-808
15. Lange O.F., and Grubmüller H. Collective Langevin dynamics of conformational motions in proteins. J Chem Phys 124 (2006) 214903-214918
16. Kumar S., Rosenberg J.M., Bouzida D., Swendsen R.H., and Kolmann P.A. Multidimensional free energy calculations using the weighted histogram analysis method. J Comput Chem 16 (1995) 1339-1350
17. Fleischman S.H., and Brooks III C.L. Thermodynamics of aqueous solvation: solution properties of alcohols and alkanes. J Chem Phys 87 (1987) 3029-3037
18. Peter C., Oostenbrink C., van Dorp A., and van Gunsteren W.F. Estimating entropies from molecular dynamics simulations. J Chem Phys 120 (2004) 2652-2661
19. Wan S., Stote R.H., and Karplus M. Calculation of the aqueous solvation energy and entropy, as well as free energy of simple polar solutes. J Chem Phys 121 (2004) 9539-9548
20. Fasnacht M., Swendsen R.H., and Rosenberg J.M. Adaptive integration method for Monte Carlo simulations. Phys Rev E Stat Nonlin Soft Matter Phys 69 (2004) 056704-056715. The efficient AIM method is introduced.
21. Jarzynski C. Nonequilibrium equality for free energy differences. Phys Rev Lett 78 (1997) 2690-2693
22. Ytreberg F.M., and Zuckerman D.M. Efficient use of nonequilibrium measurement to estimate free energy differences for molecular systems. J Comput Chem 25 (2004) 1749-1759
23. Ytreberg F.M., and Zuckerman D.M. Single-ensemble nonequilibrium path-sampling estimates of free energy differences. J Chem Phys 120 (2004) 10876-10879
24. Jarzynski C. Rare events and convergence of exponentially averaged work values. Phys Rev E Stat Nonlin Soft Matter Phys 73 (2006) 046105-046110
25. Wu D., and Kofke D.A. Rosembluth-sampled nonequilibrium work method for calculation of free energies in molecular simulation. J Chem Phys 122 (2005) 204104-204113
26. Oberhofer H., Dellago C., and Geissler P. Biased sampling of nonequilibrium trajectories: can fast switching simulations outperform conventional free energy calculations methods?. J Phys Chem B 109 (2005) 6902-6915
27. Lechner W., Oberhofer H., Dellago C., and Geissler P. Equilibrium free energies from fast-switching trajectories with large time step. J Chem Phys 124 (2006) 044113
28. MacFadyen J., and Andricioaei I. A skewed-momenta method to efficiently generate conformational-transition trajectories. J Chem Phys 123 (2005) 074107-074109
29. Adib A.B. Free energy surfaces from nonequilibrium processes without work measurement. J Chem Phys 124 (2006) 144111-144115
30. Shirts M.R., and Pande V.S. Comparison of efficiency and bias of free energies computed by exponential averaging, the Bennett acceptance ratio, and thermodynamics integration. J Chem Phys 122 (2005) 144107-144116. The authors developed theoretical estimates of the bias and variance of Jarzynski's identity, TI and Bennett's method, and compared their efficiency.
31. Bennett C.H. Efficient estimation of free energy differences from Monte Carlo data. J Comput Phys 22 (1976) 245-268
32. Jayachandran G., Shirts M.R., Park S., and Pande V.J. Parallelized-over-parts computation of absolute binding free energy with docking and molecular dynamics. J Chem Phys 125 (2006) 084901-084912
33. Ytreberg F.M., Swendsen R.H., and Zuckerman D.M. Comparison of free energy methods for molecular simulations. J Chem Phys 125 (2006) 184114. A detailed study of the performance of nine free energy methods is presented.
34. Zhang D., Gullingsrud J., and McCammon J.A. Potential of mean force for a acetylcholine unbinding from the alpha7 nicotinic acetylcholine receptor ligand-binding domain. J Am Chem Soc 128 (2006) 3019-3026
35. Xiong H., Crespo A., Marti M., Estrin D., and Roitberg A.E. Free energy calculations with non-equilibrium methods: applications of the Jarzynski relationship. Theor Chem Acc 116 (2006) 338-346
36. Gō N., and Scheraga H.A. Analysis of the contribution of internal vibrations to the statistical weights of equilibrium conformations of macromolecules. J Chem Phys 51 (1969) 4751-4767
37. Gō N., and Scheraga H.A. On the use of classical statistical mechanics in the treatment of polymer chain conformation. Macromolecules 9 (1976) 535-542
38. Hagler A.T., Stern P.S., Sharon R., Becker J.M., and Naider F. Computer simulation of the conformational properties of oligopeptides. Comparison of theoretical methods and analysis of experimental results. J Am Chem Soc 101 (1979) 6842-6852
39. Karplus M., and Kushick J.N. Method for estimating the configurational entropy of macromolecules. Macromolecules 14 (1981) 325-332
40. Chang C.E., Chen W., and Gilson M.K. Evaluating the accuracy of the quasiharmonic approximation. J Chem Theory Comput 1 (2005) 1017-1028. This paper describes a detailed study of the performance of the QH method.
41. Chang C.E., and Gilson M.K. Tork: conformational analysis method for molecules and complexes. J Comput Chem 24 (2003) 1987-1998
42. Chen W., Chang C.E., and Gilson M.K. Concepts in receptor optimization: targeting the RGD peptide. J Am Chem Soc 128 (2005) 4675-4684
43. Schlitter J. Estimation of absolute and relative entropies of macromolecules using the covariance matrix. Chem Phys Lett 215 (1993) 617-621
44. Schäfer H., Mark A.E., and van Gunsteren W.F. Absolute entropies from molecular dynamics simulation trajectories. J Chem Phys 113 (2000) 7809-7817
45. Andricioaei I., and Karplus M. On the calculation of entropy from covariance matrices of the atomic fluctuations. J Chem Phys 115 (2001) 6289-6292
46. Carlsson J., and Åqvist J. Absolute and relative entropies from computer simulation with applications to ligand binding. J Phys Chem B 109 (2005) 6448-6456
47. Wang J., and Brüschweiler R. 2D entropy of discrete molecular ensembles. J Chem Theory Comput 2 (2006) 18-24. A new interesting version of the QH method is put forward.
48. White R.P., and Meirovitch H. Lower and upper bounds for the absolute free energy by the hypothetical scanning Monte Carlo method: application to liquid argon and water. J Chem Phys 121 (2004) 10889-10904. The complete theory of the HSMC(D) method is developed, with applications to liquid argon and water.
49. White R.P., and Meirovitch H. Free volume hypothetical scanning molecular dynamics method for the absolute free energy of liquids. J Chem Phys 2006 (2006) 204108-204113
50. White R.P., and Meirovitch H. Calculation of the entropy of random coil polymers with the hypothetical scanning Monte Carlo method. J Chem Phys 123 (2005) 214908-214911
51. Cheluvaraja S., and Meirovitch H. Calculation of the entropy and free energy by the hypothetical scanning Monte Carlo method: application to peptides. J Chem Phys 122 (2005) 054903-054914
52. n) can be compromised significantly due to cancellation of errors.
53. Stoessel J.P., and Nowak P. Absolute free energies in biomolecular systems. Macromolecules 23 (1990) 1961-1965
54. Tyka M.D., Clarke A.R., and Sessions R.B. An efficient path-independent method for free energy calculations. J Phys Chem B 110 (2006) 17212-17220. A new method for calculating the absolute free energy based on a harmonic reference state and TI is outlined.
55. Ytreberg F.M., and Zuckerman D.M. Simple estimation of absolute free energies for biomolecules. J Chem Phys 124 (2006) 104105. The authors introduce a reference state whose absolute free energy is defined exactly numerically.
56. Voter A.F. A Monte Carlo method for determining free energy differences and transition state theory rate constants. J Chem Phys 82 (1985) 1890-1899
57. Ytreberg F.M., and Zuckerman D.M. Peptide conformational equilibria computed via a single-stage shifting protocol. J Phys Chem B 109 (2005) 9096-9103
58. Rodinger T., Howell P.L., and Pomes R. Absolute free energy calculations by thermodynamic integration in four spatial dimensions. J Chem Phys 123 (2005) 034104-034111
59. Blondel A. Ensemble variance in free energy calculations by thermodynamic integration: theory, optimal "alchemical" path, and practical solutions. J Comput Chem 25 (2004) 985-993
60. Huang L., and Makarov D.E. On the calculation of absolute free energy from molecular-dynamics or Monte Carlo data. J Chem Phys 124 (2006) 064108-064109
61. Darian E., Hnizdo V., Fedorowicz A., Singh H., and Demchuck E. Estimation of the absolute internal-rotation entropy of molecules with two torsional degrees of freedom from stochastic simulations. J Comput Chem 26 (2005) 651-660
62. Ohkubo Y.Z., and Thorpe I.F. Evaluating the conformational entropy of macromolecules using an energy decomposition approach. J Chem Phys 124 (2006) 024910-024916
63. Lee M.S., and Olson M.A. Calculation of absolute protein-ligand binding affinity using path and endpoint approaches. Biophys J 90 (2006) 864-877
64. Woo H.J., and Roux B. Calculation of absolute protein-ligand binding free energy from computer simulation. Proc Natl Acad Sci USA 102 (2005) 6825-6830
65. Rosta E., Klähn M., and Warshel A. Toward accurate ab initio QM/MM calculations of free energy profiles of enzymatic reactions. J Phys Chem B 110 (2006) 2934-2941
66. Abreu C.R.A., and Escobedo F.A. A general framework for non-Boltzmann Monte Carlo sampling. J Chem Phys 124 (2006) 054116
67. Gospodinov I.D., and Escobedo F.A. Multicanonical schemes for mapping out free- energy landscapes of single-component and multicomponent systems. J Chem Phys 122 (2005) 164103-164110
68. Chopra M., Muller M., and de Pablo J.J. Order-parameter-based Monte Carlo simulation of crystallization. J Chem Phys 124 (2006) 134102-134108