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Understanding and Improving Free Energy Calculations in Molecular Simulations: Error Analysis and Reduction Methods

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Free Energy Calculations

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References

  1. Leach, A.R., Molecular Modelling, Principles and Applications, Prentice Hall: London, 2001

    Google Scholar 

  2. Zwanzig, R.W., High-temperature equation of state by a perturbation method, J. Chem. Phys. 1954, 22, 1420-1426

    Article  CAS  Google Scholar 

  3. Jarzynski, C., Equilibrium free-energy differences from nonequilibrium measurements: a master equation approach, Phys. Rev. E 1997, 56, 5018-5035

    Article  CAS  Google Scholar 

  4. Jarzynski, C., Nonequilibrium equality for free energy differences, Phys. Rev. Lett. 1997,78,2690-2693

    Article  CAS  Google Scholar 

  5. Crooks, G.E., Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences, Phys. Rev. E 1999, 60, 2721-2726

    Article  CAS  Google Scholar 

  6. Crooks, G.E., Nonequilibrium measurements of free energy differences for microscop-ically reversible Markovian systems, J. Stat. Phys. 1998, 90, 1481-1487

    Article  Google Scholar 

  7. Frenkel, D., Smit, B., Understanding Molecular Simulation: From Algorithms to Applications, Academic: San Diego, 2002

    Google Scholar 

  8. Beveridge, D.L., DiCapua, F.M., Free energy via molecular simulation: applications to chemical and biomolecular systems, Annu. Rev. Biophys. Chem. 1989, 18, 431-492

    Article  CAS  Google Scholar 

  9. Kollman, P., Free energy calculations: applications to chemical and biochemical phenomena, Chem. Rev. 1993, 32, 2395-2417

    Article  Google Scholar 

  10. Wang, W. et al., Biomolecular simulations: recent developments in force fields, simu-lations of enzyme catalysis, protein-ligand, protein-protein, and protein-nucleic acid noncovalent interactions, Annu. Rev. Biophys. Biomol. Struct. 2001, 30, 211-243

    Article  CAS  Google Scholar 

  11. Hendrix, D.A., Jarzynski, C., A ‘fast growth’ method of computing free energy differ-ences, J. Chem. Phys. 2001, 114, 5974-5981

    Article  CAS  Google Scholar 

  12. Hummer, G., Fast-growth thermodynamic integration: error and efficiency analysis, J. Chem. Phys. 2001, 114, 7330-7337.

    Article  CAS  Google Scholar 

  13. Hummer, G., Fast-growth thermodynamics integration: results for sodium ion hydration, Mol. Simul. 2002, 28, 81-90

    Article  CAS  Google Scholar 

  14. Zuckerman, D.M., Woolf, T.B., Theory of a systematic computational error in free energy differences, Phys. Rev. Lett. 2002, 89

    Google Scholar 

  15. Zuckerman, D.M., Woolf, T.B., Overcoming finite sampling errors in fast-switching free-energy estimates: extrapolative analysis of a molecular system, Chem. Phys. Lett. 2002,351,445-453

    Article  CAS  Google Scholar 

  16. Sun, S.X., Equilibrium free energies from path sampling of nonequilibrium trajectories, J. Chem. Phys. 2003, 118, 5769-5775

    Article  CAS  Google Scholar 

  17. Gore, J., Ritort, F., Bustamante, C., Bias and error in estimates of equilibrium free-energy differences from nonequilibrium measurements, Proc. Natl Acad. Sci. USA 2003,100,12564-12569

    Article  CAS  Google Scholar 

  18. Park, S. et al., Free energy calculation from steered molecular dynamics simulations using Jarzynski’s equality, J. Chem. Phys. 2003, 119, 3559-3566

    Article  CAS  Google Scholar 

  19. Liphardt, J. et al., Equilibrium information from nonequilibrium measurements in an experimental test of Jarzynski’s equality, Science 2002, 296(5574), 1832-1835

    Article  CAS  Google Scholar 

  20. Hummer, G., Szabo, A., Free energy reconstruction from nonequilibrium single-molecule pulling experiments, Proc. Natl Acad. Sci. USA 2001, 98, 3658-3661

    Article  CAS  Google Scholar 

  21. Lavery, R. et al., Structure and mechanics of single biomolecules: experiment and simulation, J. Phys. Condens. Matter 2002, 14, R383-R414

    Article  CAS  Google Scholar 

  22. Radmer, R.J., Kollman, P.A., Free energy calculation methods: a theoretical and empir-ical comparison of numerical errors and a new method for qualitative estimates of free energy changes, J. Comput. Chem. 1997, 18, 902-919

    Article  CAS  Google Scholar 

  23. Lu, N.D., Accuracy and precision of free-energy calculations via molecular simula-tion. Department Chemical Engineering, University of Buffalo, State University of New York: Buffalo, NY, 2002

    Google Scholar 

  24. Lu, N.D., Kofke, D.A., Accuracy of free-energy perturbation calculations in molecular simulation. I. Modeling, J. Chem. Phys. 2001, 114, 7303-7311

    Article  CAS  Google Scholar 

  25. Lu, N.D., Kofke, D.A., Accuracy of free-energy perturbation calculations in molecular simulation. II. Heuristics, J. Chem. Phys. 2001, 115, 6866-6875

    Article  CAS  Google Scholar 

  26. Lu, N.D., Kofke, D.A., Optimal intermediates in staged free-energy calculations, J. Chem. Phys. 1999, 111, 4414-4423

    Article  CAS  Google Scholar 

  27. Lu, N.D., Kofke, D.A., Adhikari, J., Variational formula for the free energy based on incomplete sampling in a molecular simulation, Phys. Rev. E 2003, 68, 026122

    Article  Google Scholar 

  28. Zuckerman, D.M., Woolf, T.B., Systematic finite sampling inaccuracy in free energy differences and other nonlinear quantities, J. Stat. Phys. 2004, 114, 1303-1323

    Article  Google Scholar 

  29. Bendat, J.S., Piersol, A.G., Random Data: Analysis and Measurement Procedures, Wiley: New York, 1971

    Google Scholar 

  30. Efron, B., Tibshirani, R.J., An Introduction to the Bootstrap, Chapman & Hall/CRC: New York, 1993

    Google Scholar 

  31. Kofke, D.A., Cummings, P.T., Quantitative comparison and optimization of methods for evaluating the chemical potential by molecular simulation, Mol. Phys. 1997, 92, 973-996

    Article  CAS  Google Scholar 

  32. Kofke, D.A., Cummings, P.T., Precision and accuracy of staged free-energy perturbation methods for computing the chemical potential by molecular simulation, Fluid Phase Equilibria 1998, 150, 41-49

    Article  Google Scholar 

  33. Wood, R.H., Muhlbauer, W.C.F., Thompson, P.T., Systematic errors in free energy perturbation calculations due to a finite sample of configuration space: sample-size hysteresis, J. Phys. Chem. 1991, 95, 6670-6675

    Article  CAS  Google Scholar 

  34. Hummer, G., Calculation of free-energy differences from comptuer simulations of initial and final states, J. Chem. Phys. 1996, 105, 2004

    Google Scholar 

  35. Lu, N.D., Woolf, T.B., Kofke, D.A., Improving the efficiency and reliability of free energy perturbation calculations using overlap sampling methods, J. Comput. Chem. 2004,25,28-39

    Article  CAS  Google Scholar 

  36. Shing, K.S., Gubbins, K.E., The chemical potential in dense fluids and fluid mixtures via computer simulation, Mol. Phys. 1982, 46, 1109-1128

    Article  CAS  Google Scholar 

  37. Allen, M.P., Simulation and phase diagrams. In: Proceedings of the Euroconference on Computer simulation in Condensed Matter Physics and Chemistry, Binder, K., Ciccotti, G., Eds. European Union, 1996, pp. 255-284

    Google Scholar 

  38. Lu, N.D., Kofke, D.A., Simple model for insertion/deletion asymmetry of free-energy calculations. In: Foundations of Molecular Modeling and Simulation, Cummings, P., Westmoreland, P., Eds. AIChE Symposium Series, 2001, pp. 146-149

    Google Scholar 

  39. Jorgensen, W.L., Ravimohan, C., Monte Carlo simulation of differences in free energies of hydration, J. Chem. Phys. 1985, 83, 3050-3054

    Article  CAS  Google Scholar 

  40. Pearlman, D.A., A comparison of alternative approaches to free energy calculations, J. Phys. Chem. 1994, 98, 1487-1493

    Article  CAS  Google Scholar 

  41. Pearlman, D.A., Govinda, R., Free energy calculations: methods and applications. In: Encyclopedia of Computational Chemistry, Schleyer, P., Ed. Wiley: Chichester, 1998

    Google Scholar 

  42. Pearlman, D.A., Kollman, P.A., A new method for carrying out free energy perturbation calculations: dynamically modified windows, J. Chem. Phys. 1989, 90, 2460-2470

    Article  CAS  Google Scholar 

  43. Lu, N. et al., Using overlap and funnel sampling to obtain accurate free energies from nonequilibrium work measurements, Phys. Rev. E 2004

    Google Scholar 

  44. Lu, N.D., Singh, J.K., Kofke, D.A., Appropriate methods to combine forward and reverse free energy perturbation averages, J. Chem. Phys. 2003, 118, 2977-2984

    Article  CAS  Google Scholar 

  45. Torrie, G.M., Valleau, J.P., Nonphysical sampling distributions in Monte Carlo free-energy estimation: umbrella sampling, J. Comput. Phys. 1977, 23, 187-199

    Article  Google Scholar 

  46. Valleau, J.P., Torrie, J.A., A guide for Monte Carlo for statistical mechanics. In: Statis-tical Mechanics, Part A, Berne, B., Ed. Plenum: New York, 1977, pp. 169-194

    Google Scholar 

  47. Henchman, R.H., Essex, J.W., Free energies of hydration using restrained electrostatic potential derived charges via free energy perturbations and linear response, J. Comput. Chem. 1999, 20, 499-510

    Article  CAS  Google Scholar 

  48. Wood, R.H., Estimation of errors in free energy calculations due to the lag between the Hamiltonian and the system configuration, J. Phys. Chem. 1991, 95, 4838-4842

    Article  CAS  Google Scholar 

  49. Jorgensen, W.L. et al., Efficient computation of absolute free energies of binding by computer simulations. Application to the methane dimer in water, J. Chem. Phys. 1988, 89,3742-3746

    Article  CAS  Google Scholar 

  50. Chipot, C. et al., Molecular dynamics free energy perturbation calculations: influence of nonbonded parameters on the free energy of hydration of charged and neutral species, J. Phys. Chem. 1994, 98, 11362-11372

    Article  CAS  Google Scholar 

  51. Jacucci, G., Quirke, N., Monte-Carlo Calculation of the free-energy difference between hard and soft core diatomic liquids, Mol. Phys. 1980, 40, 1005-1009

    Article  CAS  Google Scholar 

  52. Mezei, M., Test of overlap ratio metho on the calculation of the aqueous hydration free energy difference between acetone and dimethyl amine, Mol. Phys. 1988, 65, 219-223

    Article  CAS  Google Scholar 

  53. Deitrick, G.L., Scriven, L.E., Davis, H.T., Efficient molecular simulation of chemical potentials, J. Chem. Phys. 1989, 90, 2370-2385

    Article  CAS  Google Scholar 

  54. Lu, N.D., Woolf, T.B., Overlap perturbation methods for computing alchemical free energy changes: variants, generalizations and evaluations, Mol. Phys. 2004, 102, 173-181

    Article  CAS  Google Scholar 

  55. Bennett, C.H., Efficient estimation of free energy differences from Monte Carlo data, J. Comput. Phys. 1976, 22, 245-268

    Article  Google Scholar 

  56. Crooks, G.E., Path-ensemble averages in systems driven far from equilibrium, Phys. Rev. E 2000, 61, 2361-2366

    Article  CAS  Google Scholar 

  57. Kobrak, M.N., Systematic and statistical error in histogram-based free energy calculations, J. Comput. Chem. 2003, 24, 1437-1446

    Article  CAS  Google Scholar 

  58. Ytreberg, F.M., Zuckerman, D.M., Efficient use of nonequilibrium measurement to estimate free energy differences for molecular systems, J. Comput. Chem. 2004, 25, 1749-1759

    Article  CAS  Google Scholar 

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Lu, N., Woolf, T.B. (2007). Understanding and Improving Free Energy Calculations in Molecular Simulations: Error Analysis and Reduction Methods. In: Chipot, C., Pohorille, A. (eds) Free Energy Calculations. Springer Series in CHEMICAL PHYSICS, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38448-9_6

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