Theory of binless multi-state free energy estimation with applications to protein-ligand binding

Journal of Chemical Physics

Volumn 136, Issue 14, 2012, Pages

  Tan, Zhiqiang ^a   Gallicchio, Emilio ^b   Lapelosa, Mauro ^b,c   Levy, Ronald M ^b  

^a RUTGERS UNIVERSITY   (United States)

^b RUTGERS UNIVERSITY   (United States)

^c Drexel University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACCEPTANCE RATIO; BIN SIZE; BINDING FREE ENERGY; CONVEX FUNCTIONS; DISTRIBUTED INTERACTION; ENERGY ESTIMATION; EQUILIBRIUM DISTRIBUTIONS; FINITE NUMBER; INTERACTION POTENTIALS; MULTI STATE; OPTIMIZATION ALGORITHMS; SELF-CONSISTENCY; SOFT-CORE POTENTIALS; STATISTICAL LITERATURE; WEIGHTED HISTOGRAM ANALYSIS METHOD;

ALGORITHMS; BINDING ENERGY; FREE ENERGY;

ESTIMATION;

LIGAND; PROTEIN;

ARTICLE; CHEMICAL STRUCTURE; METABOLISM; PROTEIN BINDING; STATISTICAL MODEL; THERMODYNAMICS;

LIGANDS; LIKELIHOOD FUNCTIONS; MODELS, MOLECULAR; PROTEIN BINDING; PROTEINS; THERMODYNAMICS;

EID: 84859951540     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3701175     Document Type: Article

References (41)

1. A. M. Ferrenberg and R. H. Swendsen, "Optimized Monte Carlo data analysis," Phys. Rev. Lett. 63, 1195-1198 (1989).
2. E. Gallicchio, M. Andrec, A. K. Felts, and R. M. Levy, "Temperature weighted histogram analysis method, replica exchange, and transition paths," J. Phys. Chem. B 109, 6722-6731 (2005). (Pubitemid 40538440)
3. Free Energy Calculations. Theory and Applications in Chemistry and Biology, Springer Series in Chemical Physics, edited by C. Chipot and A. Pohorille (Springer, Berlin/Heidelberg, 2007).
4. M. E. J. Newman and G. T. Barkema, Monte Carlo Methods in Statistical Physics (Oxford University Press, New York, 1999).
5. C. Bartels andM. Karplus, "Multidimensional adaptive umbrella sampling: Application to main chain and side chain peptide conformations," J. Comput. Chem. 18, 1450-1462 (1997). (Pubitemid 127637343)
6. F. Zhu and G. Hummer, "Convergence and error estimation in free energy calculations using the weighted histogram analysis method," J. Comput. Chem. (in press).
7. C. J. Geyer, "Estimating normalizing constants and reweighting mixtures in Markov chain Monte Carlo," Technical report, University of Minnesota, School of Statistics, 1994.
8. X.-L. Meng and W. H. Wong, "Simulating ratios of normalizing constants via a simple identity: A theoretical explanation," Stat. Sin. 6, 831-860 (1996).
9. A. Kong, P. McCullagh, X.-L. Meng, D. Nicolae, and Z. Tan, "A theory of statistical models for Monte Carlo integration," J R. Stat. Soc. Ser. B (Stat. Methodol.) 65, 585-618 (2003).
10. Z. Tan, "On a likelihood approach for Monte Carlo integration," J. Am. Stat. Assoc. 99(468), 1027-1036 (2004). (Pubitemid 39665948)
11. M. R. Shirts and J. D. Chodera, "Statistically optimal analysis of samples from multiple equilibrium states," J. Chem. Phys. 129(12), 124105 (2008).
12. C. H. Bennett, "Efficient estimation of free energy differences from Monte Carlo data," J. Comput. Phys. 22(2), 245-268 (1976).
13. N. Lu, J. K. Singh, and D. A. Kofke, "Appropriate methods to combine forward and reverse free-energy perturbation averages," J. Chem. Phys. 118(7), 2977-2984 (2003).
14. P. Billingsley, Probability and Measure (Wiley, New York, 1995).
15. J. Nocedal and S. J. Wright, Numerical Optimization (Springer-Verlag, New York, 1999).
16. R. Gill, Y. Vardi, and J. Wellner, "Large sample theory of empirical distributions in biased sampling models," Ann. Stat. 16, 1069-1112 (1988).
17. M. R. Chernick, Bootstrap Methods: A Guide for Practitioners and Researchers, 2nd ed. (Wiley, Hoboken, NJ, 2008).
18. E. Gallicchio and R. M. Levy, "Recent theoretical and computational advances for modeling protein-ligand binding affinities," in Advances in Protein Chemistry and Structural Biology (Academic, 2011), Vol. 85, pp. 27-80.
19. M. K. Gilson, J. A. Given, B. L. Bush, and J. A. McCammon, "The statistical-thermodynamic basis for computation of binding affinities: A critical review," Biophys. J. 72, 1047-1069 (1997). (Pubitemid 27113632)
20. D. L. Mobley and K. A. Dill, "Binding of small-molecule ligands to proteins: 'what you see' is not always 'what you get'," Structure (London) 17(4), 489-498 (2009).
21. Y. Deng and B. Roux, "Computations of standard binding free energies with molecular dynamics simulations," J. Phys. Chem. B 113(8), 2234-2246 (2009).
22. J. Michel and J. W. Essex, "Prediction of protein-ligand binding affinity by free energy simulations: assumptions, pitfalls, and expectations," J. Comput.-Aided Mol. Des. 24(8), 639-658 (2010).
23. J. D. Chodera, D. L. Mobley, M. R. Shirts, R. W. Dixon, K. Branson, and V. S. Pande, "Alchemical free energy methods for drug discovery: Progress and challenges," Curr. Opin. Struct. Biol. 21, 150-160 (2011).
24. M. R. Shirts and V. S. Pande, "Comparison of efficiency and bias of free energies computed by exponential averaging, the Bennett acceptance ratio, and thermodynamic integration," J. Chem. Phys. 122(14), 144107 (2005).
25. A. Pohorille, C. Jarzynski, and C. Chipot, "Good practices in free-energy calculations," J. Phys. Chem. B 114(32), 10235-10253 (2010).
26. T. Steinbrecher, D. L.Mobley, and D. A. Case, "Nonlinear scaling schemes for Lennard-Jones interactions in free energy calculations," J. Chem. Phys. 127(21), 214108 (2007).
27. T. Steinbrecher, I. Joung, and D. A. Case, "Soft-core potentials in thermodynamic integration: Comparing one- and two-step transformations," J. Comput. Chem. 32(15), 3253-3263 (2011).
28. F. P. Buelens and H. Grubmüller, "Linear-scaling soft-core scheme for alchemical free energy calculations," J. Comput. Chem. 33(1), 25-33 (2012).
29. E. Gallicchio, M. Lapelosa, and R. M. Levy, "Binding energy distribution analysis method (BEDAM) for estimation of protein-ligand binding affinities," J. Chem. Theory Comput. 6(9), 2961-2977 (2010).
30. M. Lapelosa, E. Gallicchio, and R. M. Levy, "Conformational transitions and convergence of absolute binding free energy calculations," J. Chem. Theory Comput. 8, 47-60 (2012).
31. S. Kumar, D. Bouzida, R. H. Swendsen, P. A. Kollman, and J. M. Rosenberg, "The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method," J. Comput. Chem. 13, 1011-1021 (1992).
32. E. Gallicchio and R.M. Levy, "Advances in all atom sampling methods for modeling protein-ligand binding affinities," Curr. Opin. Struct. Biol. 21(2), 161-166 (2011).
33. C. D. Christ, A. E. Mark, and W. F. Van Gunsteren, "Basic ingredients of free energy calculations: a review," J. Comput. Chem. 31(8), 1569-1582 (2010).
34. E. Gallicchio and R. M. Levy, "Prediction of sampl3 host-guest affinities with the binding energy distribution analysis method (BEDAM)," J. Comp.-Aided Mol. Des. (in press).
35. H. Paliwal and M. R. Shirts, "A benchmark test set for alchemical free energy transformations and its use to quantify error in common free energy methods," J. Chem. Theory Comput. 7(12), 4115-4134 (2011).
36. W. Janke, "Statistical analysis of simulations: Data correlations and error estimation," in Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms (John von Neumann Institute for Computing, Jülich, Germany, 2002), pp. 423-445.
37. D. A. Holt, J. I. Luengo, D. S. Yamashita, H. J. Oh, A. L. Konialian, H. K. Yen, L.W. Rozamus,M. Brandt, and M. J. Bossard, "Design, synthesis, and kinetic evaluation of high-affinity fkbp ligands and the x-ray crystal structures of their complexes with fkbp12," J. Am. Chem. Soc. 115(22), 9925-9938 (1993).
38. J. Wang, Y. Deng, and B. Roux, "Absolute binding free energy calculations using molecular dynamics simulations with restraining potentials," Biophys. J. 91(8), 2798-2814 (2006). (Pubitemid 44526470)
39. H. Fujitani, Y. Tanida, M. Ito, J. Guha, C. D Snow, M. R. Shirts, E. J. Sorin, and V. S. Pande, "Direct calculation of the binding free energies of fkbp ligands," J. Chem. Phys. 123(8), 084108 (2005).
40. C. J. Geyer, Trust region optimization, R package 0.1-2., 2009, see http://www.stat.umn.edu/geyer/trust/.
41. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, New York, 1993).