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Free Energy Calculations: Approximate Methods for Biological Macromolecules

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Free Energy Calculations

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References

  1. Gilson, M.; Given, J.; Bush, B.; McCammon, J.A., The statistical-thermodynamic basis for computation of binding affinities: a critical review, Biophys. J. 1997, 72, 1047-1069

    CAS  Google Scholar 

  2. Fersht, A., Structure and Mechanism in Protein Science: A Guide to Enzyme Catalysis and Protein Folding, Freeman: New York, 1999

    Google Scholar 

  3. Tembe, B.; McCammon, J.A., Ligand-receptor interactions, Comput. Chem. 1984, 8, 281-283

    CAS  Google Scholar 

  4. Reinhardt, W.P.; Miller, M.A.; Amon, L.A., Why is it so difficult to simulate entropies, free energies, and their differences? Acc. Chem. Res. 2001, 34, 607-614

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  6. Simonson, T. Free energy calculations. in Computational Biochemistry & Biophysics, Becker, O.; Mackerell Jr., A.; Roux, B.; Watanabe, M., Eds. Marcel Dekker: New York, 2001, ch. 9

    Google Scholar 

  7. Miyamoto, S.; Kollman, P., Absolute and relative binding free energy calculations of the interaction of biotin and its analogs with streptavidin using molecular dynamics/free energy perturbation approaches, Proteins 1993, 16, 226-245

    CAS  Google Scholar 

  8. Lamb, M.L.; Jorgensen, W.J., Computational approaches to molecular recognition, Curr. Opin. Chem. Biol. 1997, 1, 449-457

    CAS  Google Scholar 

  9. Woo, H.J.; Roux, B., Calculation of absolute protein ligand binding free energy from computer simulations, Proc. Natl Acad. Sci. USA 2005, 102, 6825-6830

    CAS  Google Scholar 

  10. Alvarez, J.; Shoichet, B., Virtual Screening in Drug Discovery, CRC: West Palm Beach, FL, USA, 2005

    Google Scholar 

  11. Roux, B.; Simonson, T., Implicit solvent models, Biophys. Chem. 1999, 78, 1-20

    CAS  Google Scholar 

  12. Simonson, T.; Archontis, G.; Karplus, M., Free energy simulations come of age: the protein-ligand recognition problem, Acc. Chem. Res. 2002, 35, 430-437

    CAS  Google Scholar 

  13. Aqvist, J.; Luzhkov, V.B.; Brandsal, B.O., Ligand binding affinities from MD simula-tions, Acc. Chem. Res. 2002, 35, 358-365

    Google Scholar 

  14. Aqvist, J.; Osterberg, F.; Almlof, M.; Feierberg, I.; Luzhkov, V.B.; Brandsal, B.O., Free energy calculations and ligand binding, Adv. Prot. Chem. 2003, 66, 123-158

    Google Scholar 

  15. Wong, C.F.; McCammon, J.A., Protein simulation and drug design, Adv. Prot. Chem. 2003,66,87-121

    CAS  Google Scholar 

  16. Jorgensen, W.L., The many roles of computation in drug discovery, Science 2003, 303, 1813-1818

    Google Scholar 

  17. Warshel, A.; Levitt, M., Theoretical studies of enzymic reactions: dielectric, electro-static and steric stabilization of the carbonium ion in the reaction of lysozyme, J. Mol. Biol. 1976, 103, 227

    CAS  Google Scholar 

  18. Bashford, D.; Karplus, M., The pKa ’s of ionizable groups in proteins: atomic detail from a continuum electrostatic model, Biochemistry 1990, 29, 10219-10225

    CAS  Google Scholar 

  19. Antosiewicz, J.; McCammon, J.A.; Gilson, M., The determinants of pKa ’s in proteins, Biochemistry 1996, 35, 7819-7833

    CAS  Google Scholar 

  20. Schaefer, M.; Vlijmen, H.W.T. van; Karplus, M., Electrostatic contributions to molecu-lar free energies in solution, Adv. Prot. Chem. 1998, 51, 1-57

    CAS  Google Scholar 

  21. Beveridge, D.; DiCapua, F., Free energy via molecular simulation: applications to chemical and biomolecular systems, Ann. Rev. Biophys. Chem. 1989, 18, 431-492

    CAS  Google Scholar 

  22. van Gunsteren, W.; Beutler, T.C.; Fraternali, F.; King, P.M.; Mark, A.E.; Smith, P.E., Computation of free energy in practice: choice of approximations and accuracy limiting factors. In Computer Simulation of Biomolecular Systems, van Gunsteren, W.; Weiner, P.; Wilkinson, A., Eds. Escom Science: Leiden, 1993, pp. 315-348

    Google Scholar 

  23. Fowler, R.H.; Guggenheim, E.A., Statistical Thermodynamics, Cambridge University Press: Cambridge, 1939

    Google Scholar 

  24. Zwanzig, F., High-temperature equation of state by a perturbation method. I. Non-polar gases , J. Chem. Phys. 1954, 22, 1420

    CAS  Google Scholar 

  25. Liu, H.; Mark, A.; van Gunsteren, W.F., Estimating the relative free energy of different molecular states with respect to a single reference state, J. Phys. Chem. 1996, 100, 9485-9494

    CAS  Google Scholar 

  26. von Mises, R., Mathematical Theory of Probability and Statistics, Academic: New York, 1964

    Google Scholar 

  27. Jorgensen, W.; Buckner, K.; Boudon, S.; Tirado-Rives, J., 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

    CAS  Google Scholar 

  28. Roux, B.; Nina, M.; Pomes, R.; Smith, J., Thermodynamic stability of water molecules in the Bacteriorhodopsin proton channel: a molecular dynamics and free energy pertur-bation study, Biophys. J. 1996, 71, 670-681

    CAS  Google Scholar 

  29. Wong, C.; McCammon, J.A., Dynamics and design of enzymes and inhibitors, J. Am. Chem. Soc. 1986, 108, 3830-3832

    CAS  Google Scholar 

  30. Wong, C.F.; Thacher, T.; Rabitz, H., Systematic sensitivity analysis. In Reviews in Computational Chemistry, Lipkowitz, K.; Boyd, D., Eds. Wiley: New York, 1998, pp. 281-326

    Google Scholar 

  31. Radmer, R.J.; Kollman, P.A., The application of three approximate free energy calcula-tions methods to structure based ligand design: trypsin and its complex with inhibitors., J. Comput. Aided Mol. Des. 1998, 12, 215-227

    CAS  Google Scholar 

  32. Sch äfer, H.; Mark, A.; van Gunsteren, W.F., Estimating relative free energies from a single ensemble: hydration free energies, J. Comput. Chem. 1999, 20, 1604-1617

    Google Scholar 

  33. Oostenbrink, C.; Pitera, J.W.; van Lipzig, M.M.H.; Meerman, J.H.N.; van Gunsteren, W.F., Simulations of the estrogen receptor ligand-binding domain: affinity of natural ligands and xenoestrogens, J. Med. Chem. 2000, 43, 4594-4605

    CAS  Google Scholar 

  34. Oostenbrink, C.; van Gunsteren, W.F., Free energies of binding of polychlorinated biphenyls to the estrogen receptor in a single simulation, Proteins 2004, 54, 237-246

    CAS  Google Scholar 

  35. Simonson, T., Free energy of particle insertion. An exact analysis of the origin singu-larity for simple liquids, Molec. Phys. 1993, 80, 441-447

    CAS  Google Scholar 

  36. Resat, H.; Mezei, M., Studies on free energy calculations. II. A theoretical approach to molecular solvation, J. Chem. Phys. 1994, 222, 6126-6140

    Google Scholar 

  37. Wong, C.F.; Hunenberger, P.H.; Akamine, P.; Narayana, N.; Diller, T.; McCammon, J.A.; Taylor, S.; Xuong, N.H., Computational analysis of PKA-balanol interactions, J. Med. Chem. 2001, 44, 1530-1539

    CAS  Google Scholar 

  38. Mordasini, T.Z.; McCammon, J.A., Calculations of relative hydration free energies: a comparative study using thermodynamic integration and an extrapolation method based on a single reference state, J. Phys. Chem. B 2000, 104, 360-367

    CAS  Google Scholar 

  39. Kong, X.; Brooks, C.L., λ-dynamics: a new approach to free energy calculations, J. Chem. Phys. 1996, 105, 2414-2423

    Google Scholar 

  40. Pomes, R.; Eisenmesser, E.; Post, C.B.; Roux, B., Calculating excess chemical potentials using dynamic simulations in the fourth dimension, J. Chem. Phys. 1999, 111, 3387-3395

    CAS  Google Scholar 

  41. Simonson, T.; Perahia, D.; Br ünger, A.T., Microscopic theory of the dielectric properties of proteins., Biophys. J. 1991, 59, 670-690

    CAS  Google Scholar 

  42. Simonson, T.; Perahia, D., Microscopic dielectric properties of cytochrome c from molecular dynamics simulations in aqueous solution, J. Am. Chem. Soc. 1995, 117, 7987-8000

    CAS  Google Scholar 

  43. Del Buono, G.S.; Figueirido, F.E.; Levy, R., Intrinsic pKa ’s of ionizable residues in proteins: an explicit solvent calculation for lysozyme, Proteins 1994, 20, 85-97

    CAS  Google Scholar 

  44. Simonson, T.; Wong, C.; Br ünger, A.T., Classical and quantum simulations of trypto-phan in solution, J. Phys. Chem. A 1997, 101, 1935-1945

    CAS  Google Scholar 

  45. Simonson, T.; Archontis, G.; Karplus, M., Continuum treatment of long-range interac-tions in free energy calculations. Application to protein-ligand binding, J. Phys. Chem. B 1997, 101, 8349-8362

    Google Scholar 

  46. Ceccarelli, M.; Marchi, M., Simulation and modeling of the Rhodobacter spaeroides bacterial reaction center, J. Phys. Chem. B 2003, 107, 1423-1431

    CAS  Google Scholar 

  47. Simonson, T., Gaussian fluctuations and linear response in an electron transfer protein, Proc. Natl Acad. Sci. USA 2002, 99, 6544-6549

    CAS  Google Scholar 

  48. Simonson, T.; Carlsson, J.; Case, D.A., Proton binding to proteins: pKa calculations with explicit and implicit solvent models, J. Am. Chem. Soc. 2004, 126, 4167-4180

    CAS  Google Scholar 

  49. Chandler, D., Introduction to Modern Statistical Mechanics, Oxford University Press: Oxford, 1987

    Google Scholar 

  50. Hansen, J.P.; McDonald, I., Theory of Simple Liquids, Academic: New York, 1986

    Google Scholar 

  51. Landau, L.; Lifschitz, E., Statistical Mechanics, Pergamon: New York, 1980

    Google Scholar 

  52. Warshel, A., Dynamics of reactions in polar solvents. Semiclassical trajectory studies of electron transfer and proton transfer studies, J. Phys. Chem. 1982, 86, 2218-2224

    CAS  Google Scholar 

  53. Gehlen, J.N.; Marchi, M.; Chandler, D., Dynamics affecting the primary charge transfer in photosynthesis, Science 1994, 263, 499

    CAS  Google Scholar 

  54. Marcus, R., Electron transfer reactions in chemistry: theory and experiment. In Protein Electron Transfer (1996), Bendall, D., Ed., BIOS Scientific: Oxford, pp. 249-272

    Google Scholar 

  55. Marcus, R., Chemical and electro-chemical electron transfer theory, Ann. Rev. Phys. Chem. 1964, 15, 155-196

    CAS  Google Scholar 

  56. Marcus, R., On the theory of shifts and broadening of electronic spectra of polar solutes in polar media, J. Chem. Phys. 1965, 43, 1261-1274

    CAS  Google Scholar 

  57. Muegge, I.; Qi, P.X.; Wand, A. J.; Chu, Z. T.; Warshel, A., Reorganization energy of cytochrome c revisited, J. Phys. Chem. B 1997, 101, 825-836

    CAS  Google Scholar 

  58. Simonson, T.; Archontis, G.; Karplus, M., A Poisson-Boltzmann study of charge inser-tion in an enzyme active site: the effect of dielectric relaxation, J. Phys. Chem. B 1999, 103,6142-6156

    CAS  Google Scholar 

  59. Sham, Y.Y.; Chu, Z.T.; Warshel, A., Consistent calculations of pKa ’s of ionizable residues in proteins: semi-microscopic and microscopic approaches, J. Phys. Chem. B 1997,101,4458-4472

    CAS  Google Scholar 

  60. Warshel, A.; Sussman, F.; King, G., Free energy changes in solvated proteins: micro-scopic calculations using a reversible charging process, Biochemistry 1986, 25, 8368-8372

    CAS  Google Scholar 

  61. Kirkwood, J., Statistical mechanics of fluid mixtures, J. Chem. Phys. 1935, 3, 300-313

    CAS  Google Scholar 

  62. Reiss, H., Scaled particle methods in the statistical thermodynamics of fluids, Adv. Chem. Phys. 1965, 9, 1-84

    Google Scholar 

  63. McQuarrie, D., Statistical Mechanics, Harper and Row: New York, 1975

    Google Scholar 

  64. Stillinger, F., Structure in aqueous solutions of nonpolar solutes from the standpoint of scaled-particle theory, J. Sol. Chem. 1973, 2, 141-158

    CAS  Google Scholar 

  65. Pierotti, R.A., A scaled particle theory of aqueous and nonaqueous solutions, Chem. Rev. 1976, 76, 717-726

    CAS  Google Scholar 

  66. Tanford, C., The Hydrophobic Effect, Wiley: New York, 1980

    Google Scholar 

  67. Tolman, R.C., Consideration of the Gibbs theory of surface tension, J. Chem. Phys. 1948,16,758-774

    CAS  Google Scholar 

  68. Postma, J.; Berendsen, H.; Haak, J., Thermodynamics of cavity formation in water. A molecular dynamics study, Far. Symp. Chem. Soc. 1982, 17, 55-67

    Google Scholar 

  69. Straatsma, T.; Berendsen, H.; Postma, J., Free energy of hydrophobic hydration: a mole-cular dynamics study of noble gases in water, J. Chem. Phys. 1986, 85, 6720

    CAS  Google Scholar 

  70. Pratt, L.; Pohorille, A., Theory of hydrophobicity: transient cavities in molecular liq-uids, Proc. Natl Acad. Sci. USA 1992, 89, 2995-2999

    CAS  Google Scholar 

  71. Hummer, G.; Garde, S.; Garcia, A.E.; Pohorille, A.; Pratt, L.R., An information theory model of hydrophobic interactions, Proc. Natl Acad. Sci. USA 1996, 93, 8951-8955

    CAS  Google Scholar 

  72. Pratt, L.R.; Pohorille, A., Hydrophobic effects and modeling of biophysical aqueous solution interfaces, Chem. Rev. 2002, 102, 2671-2691

    CAS  Google Scholar 

  73. Sitkoff, D.; Sharp, K.; Honig, B., Accurate calculation of hydration free energies using macroscopic solvent models, J. Phys. Chem. 1994, 98, 1978-1988

    CAS  Google Scholar 

  74. Simonson, T.; Br ünger, A.T., Solvation free energies estimated from macroscopic con-tinuum theory: an accuracy assessment, J. Phys. Chem. 1994, 98, 4683-4694

    CAS  Google Scholar 

  75. Kollman, P.A.; Massova, I.; Reyes, C.; Kuhn, B.; Huo, S.; Chong, L.; Lee, M.; Lee, T.; Duan, Y.; Wang, W.; Donini, O.; Cieplak, P.; Srinivasan, J.; Case, D.A.; Cheatham, T.E., Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models, Acc. Chem. Res. 2000, 33, 889-897

    CAS  Google Scholar 

  76. Gallicchio, E.; Kubo, M.M.; Levy, R.M., Enthalpy-entropy and cavity decomposition of alkane hydration free energies: numerical results and implications for theories of hydrophobic hydration, J. Phys. Chem. B 2000, 104, 6271-6285

    CAS  Google Scholar 

  77. Shurki, A.; Warshel, A., Structure/function correlations of proteins using MM, QM/MM and related approaches: methods, concepts, pitfalls, and current progress, Adv. Prot. Chem. 2003, 66, 249-313

    CAS  Google Scholar 

  78. Born, M., Volumen und hydrationsw ärme der ionen, Zeit. Phys. 1920, 1, 45-48

    CAS  Google Scholar 

  79. Kirkwood, J., Theory of solutions of molecules containing widely separated charges with special application to zwitterions, J. Chem. Phys. 1934, 2, 351-361

    CAS  Google Scholar 

  80. Onsager, L., Electric moments of molecules in liquids, J. Am. Chem. Soc. 1936, 58, 1486

    CAS  Google Scholar 

  81. Jean-Charles, A.; Nicholls, A.; Sharp, K.; Honig, B.; Tempzyck, A.; Hendrickson, T.; Still, W.C., Electrostatic contributions to solvation energies: comparison of free energy perturbation and continuum calculations., J. Am. Chem. Soc. 1991, 113, 1454-1455

    CAS  Google Scholar 

  82. Nina, M.; Beglov, D.; Roux, B., Atomic radii for continuum electrostatics calculations based on molecular dynamics free energy simulations, J. Phys. Chem. B 1997, 101, 5239-5248

    CAS  Google Scholar 

  83. Jackson, J.D., Classical Electrodynamics, Wiley: New York, 1975

    Google Scholar 

  84. Landau, L.; Lifschitz, E., Electrodynamics of Continuous Media, Pergamon: New York, 1980

    Google Scholar 

  85. Warwicker, J.; Watson, H., Calculation of the electrostatic potential in the active site cleft due to α helix dipoles, J. Mol. Biol. 1982, 157, 671-679

    CAS  Google Scholar 

  86. Klapper, I.; Hagstrom, R.; Fine, R.; Sharp, K.; Honig, B., Focussing of electric fields in the active site of Cu-Zn superoxide dismutase, Proteins 1986, 1, 47

    CAS  Google Scholar 

  87. Holst, M.J.; Baker, N.A.; Wang, F., Adaptive multilevel finite element solution of the Poisson-Boltzmann equation I: algorithms and examples, J. Comp. Chem. 2000, 21, 1319-1342

    CAS  Google Scholar 

  88. Simonson, T., Electrostatics and dynamics of proteins, Rep. Prog. Phys. 2003, 66, 737-787

    CAS  Google Scholar 

  89. Fr öhlich, H., Theory of Dielectrics, Clarendon: Oxford, 1949

    Google Scholar 

  90. Juffer, A.; Botta, E.; van Keulen, B.; van der Ploeg, A.; Berendsen, H., The electric potential of a macromolecule in a solvent: a fundamental approach, J. Comp. Phys. 1991,97,144

    CAS  Google Scholar 

  91. Ghosh, A.; Rapp, C.S.; Friesner, R.A., Generalized Born model based on a surface area formulation, J. Phys. Chem. B 1998, 102, 10983-10990

    CAS  Google Scholar 

  92. Aqvist, J.; Median, C.; Samuelsson, J.E., A new method for predicting binding affinity in computer-aided drug design, Prot. Eng. 1994, 7, 385-391

    CAS  Google Scholar 

  93. Basu, G.; Kitao, A.; Kuki, A.; Go, N., Protein electron transfer reorganization energy from normal mode analysis. 1. Theory, J. Phys. Chem. B 1998, 102, 2076-2084

    CAS  Google Scholar 

  94. Gilson, M.; Honig, B., Calculation of the total electrostatic energy of a macromolecu-lar system: solvation energies, binding energies, and conformational analysis, Proteins 1988,4,7-18

    CAS  Google Scholar 

  95. Carlson, H.A.; Jorgensen, W.L., An extended linear response method for determining free energies of hydration, J. Phys. Chem. 1995, 99, 10667-10673

    CAS  Google Scholar 

  96. Jones-Hertzog, D.K.; Jorgensen, W.L., Binding affinities for sulfonamide inhibitors with human thrombin using Monte Carlo simulations with a linear response method, J. Med. Chem. 1997, 40, 1539-1549

    CAS  Google Scholar 

  97. Lamb, M.L.; Tirado-Rives, J.; Jorgensen, W.L., Estimation of the binding affinities of FKBP12 inhibitors using a linear response method, Bioorg. Med. Chem. 1999, 7, 851-860

    CAS  Google Scholar 

  98. McDonald, N.A.; Carlson, H.A.; Jorgensen, W.L., Free energies of solvation in chloro-form and water from a linear response approach, J. Phys. Org. Chem. 1997, 10, 563-576

    CAS  Google Scholar 

  99. Graffner-Nordberg, M.; Kolmodin, K.; Aqvist, J.; Queener, S.F.; Hallberg, A., Design, synthesis, computational prediction, and biological evaluation of ester soft drugs as inhibitors of dihydrofolate reductase from Pneumocystis carinii, J. Med. Chem. 2001, 44,2391-2402

    CAS  Google Scholar 

  100. Ljungberg, K.B.; Marelius, J.; Musil, D.; Svensson, P.; Norden, B.; Aqvist, J., Computational modelling of inhibitor binding to human thrombin, Eur. J. Pharm. Sci. 2001, 12,441-446

    CAS  Google Scholar 

  101. Wall, I.D.; Leach, A.R.; Salt, D.W.; Ford, M.G.; Essex, J.W., Binding constants of neuraminidase inhibitors: an investigation of the linear interaction energy method, J. Med. Chem. 1999, 42, 5142-5152

    CAS  Google Scholar 

  102. Ostrovsky, D.; Udier-Blagovic, M.; Jorgensen, W.L., Analyses of activity for factor Xα inhibitors based on Monte Carlo simulations, J. Med. Chem. 2003, 46, 5691-5699

    CAS  Google Scholar 

  103. Kroeger-Smith, M.B.; Hose, B.M.; Hawkins, A.; Lipchock, J.; Farnsworth, D.W.; Rizzo, R.C.; Tirado-Rives, J.; Arnold, E.; Zhang, W.; Hughes, S.H.; Jorgensen, W.L.; Michedja, C.J.; Smith, R.H., Molecular modeling calculations of HIV-1 reverse transcriptase nonnucleoside inhibitors: correlation of binding energy with biological activity for novel 2-aryl-substituted benzimidazole analogues, J. Med. Chem. 2003, 46, 1940-1947

    CAS  Google Scholar 

  104. Kubinyi, H.; Folkers, G.; Martin, Y.C., 3D QSAR in Drug Design: Volume 2: Ligand-Protein Interactions and Molecular Similarity, Springer: Berlin, Heidelberg, New York, 2000

    Google Scholar 

  105. Zhou, R.; Friesner, R.A.; Ghosh, A.; Rizzo, R.C.; Jorgensen, W.L.; Levy, R.M., New linear interaction method for binding affinity calculations using a continuum solvent model, J. Phys. Chem. B 2001, 105, 10388-10397

    CAS  Google Scholar 

  106. Sham, Y.Y.; Shao, Z.T.; Tao, H.; Warshel, A., Examining methods for calculations of binding free energies: LRA, LIE and PDLD/S-LRA calculations of ligand binding to an HIV protease, Proteins 2000, 39, 393-407

    CAS  Google Scholar 

  107. Schaefer, M.; Froemmel, C., A precise analytical method for calculating the electrostatic energy of macromolecules in aqueous solution, J. Mol. Biol. 1990, 216, 1045-1066

    CAS  Google Scholar 

  108. Hendsch, Z.; Tidor, B., Electrostatic interactions in the GCN4 leucine zipper: substan-tial contributions arise from intramolecular interactions enhanced on binding, Prot. Sci. 1999,8,1381-1392

    CAS  Google Scholar 

  109. Archontis, G.; Simonson, T.; Karplus, M., Binding free energies and free energy components from molecular dynamics and Poisson-Boltzmann calculations. Application to amino acid recognition by aspartyl-tRNA synthetase, J. Mol. Biol. 2001, 306, 307-327

    CAS  Google Scholar 

  110. Schapira, M.; Totrov, M.; Abagyan, R., Prediction of the binding energy for small mole-cules, peptides and proteins, J. Molec. Recog. 1999, 12, 177-190

    CAS  Google Scholar 

  111. Huron, M.J.; Claverie, P., Calculation of the interaction energy of one molecule with its whole surroundings. I. Method and application to pure nonpolar compounds., J. Phys. Chem. 1972, 76, 2123-2133

    CAS  Google Scholar 

  112. Claverie, P.; Daudey, J.P.; Langlet, J.; Pullman, B.; Piazzola, D.; Huron, M.J., Studies of solvent effects. 1. Discrete, continuum, and discrete-continuum models and their comparison for some simple cases: NH4 , CH3 OH, and substituted NH4 , J. Phys. Chem. 1978,82,405-418

    CAS  Google Scholar 

  113. Floris, F.M.; Tomasi, J.; Pascal-Ahuir, J.L., Dispersion and repulsion contributions to the solvation energy: refinements to a simple computational model in the continuum approximation, J. Comp. Chem. 1991, 12, 784-791

    CAS  Google Scholar 

  114. Srinivasan, J.; Cheatham, T.E.; Cieplak, P.; Kollman, P.A.; Case, D.A., Continuum solvent studies of the stability of DNA, RNA, and phosphoramidate-DNA helices, J. Am. Chem. Soc. 1998, 120, 9401-9409

    CAS  Google Scholar 

  115. Simonson, T., Macromolecular electrostatics: continuum models and their growing pains, Curr. Opin. Struct. Biol. 2001, 11, 243-252

    CAS  Google Scholar 

  116. Jencks, W.P., Catalysis in Chemistry and Enzymology, Dover: New York, 1986

    Google Scholar 

  117. Schutz, C.N.; Warshel, A., What are the dielectric ‘constants’ of proteins and how to validate electrostatic models?, Proteins 2001, 8, 211-217

    Google Scholar 

  118. Simonson, T.; Perahia, D., Internal and interfacial dielectric properties of cytochrome c from molecular dynamics simulations in aqueous solution, Proc. Natl Acad. Sci. USA 1995,92,1082-1086

    CAS  Google Scholar 

  119. Chong, L.T.; Duan, Y.; Wang, L.; Massova, I.; Kollman, P., Molecular dynamics and free energy calculations applied to affinity maturation in antibody 48G7, Proc. Natl Acad. Sci. USA 1999, 96, 14330-14335

    CAS  Google Scholar 

  120. Hunenberger, P.; Helms, V.; Narayana, N.; Taylor, S.S.; McCammon, J.A., Determinants of ligand binding to cAMP-dependent protein kinase, Biochemistry 1999, 38, 2358-2366

    CAS  Google Scholar 

  121. Massova, I.; Kollman, P., Computational alanine scanning to probe protein-protein interactions: a novel approach to evaluate binding free energies, J. Am. Chem. Soc. 1999,121,8133-8143

    CAS  Google Scholar 

  122. Sims, P.A.; Wong, C.F.; Vuga, D.; McCammon, J.A.; Sefton, B.F., Relative contributions of desolvation, inter- and intramolecular contributions to binding affinity in protein kinase systems, J. Comput. Chem. 2005, 26, 668-681

    CAS  Google Scholar 

  123. Roux, B.; MacKinnon, R., The cavity and pore helices in the KcsA K+ channel: electrostatic stabilization of monovalent cations, Science 1999, 285, 100-102

    CAS  Google Scholar 

  124. Eberini, I.; Baptista, A.M.; Gianazza, E.; Fraternali, F.; Beringhelli, T., Reorganization in apo- and holo-β -lactoglobulin upon protonation of Glu89: molecular dynamics and pKa calculations, Proteins 2004, 54, 744-758

    CAS  Google Scholar 

  125. Archontis, G.; Simonson, T., Proton binding to proteins: a free energy component analysis using a dielectric continuum model, Biophys. J. 2005, 88, 3888-3904

    CAS  Google Scholar 

  126. Baptista, A.M.; Martel, P.J.; Soares, C.M., Simulation of electron-proton coupling with a Monte-Carlo method: application to cytochrome c3 using continuum electrostatics, Biophys. J. 1999, 76, 2978-2998

    CAS  Google Scholar 

  127. Ullmann, M., The coupling of protonation and reduction in proteins with multiple redox centers: theory, computational method and application to cytochrome c3 , J. Phys. Chem. B 2000, 104, 6293-6301

    CAS  Google Scholar 

  128. Ishikita, H.; Morra, G.; Knapp, E.W., Redox potential of quinones in photosynthetic reaction centers from Rhodobacter sphaeroides: dependence on protonation of Glu-L212 and Asp-L213, Biochemistry 2003, 42, 3882-3892

    CAS  Google Scholar 

  129. Kollman, P.A., Free energy calculations: applications to chemical and biochemical phenomena, Chem. Rev. 1993, 93, 2395

    Google Scholar 

  130. Mackerell, A.D.; Bashford, D.; Bellott, M.; Dunbrack, R.L.; Evanseck, J.; Field, M.J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S.; Joseph, D.; Kuchnir, L.; Kuczera, K.; Lau, F.T.K.; Mattos, C.; Michnick, S.; Ngo, T.; Nguyen, D.T.; Prodhom, B.; Reiher, W.E.; Roux, B.; Smith, J.; Stote, R.; Straub, J.; Watanabe, M.; Wiorkiewicz-Kuczera, J.; Yin, D.; Karplus, M., An all-atom empirical potential for molecular modelling and dynamics study of proteins, J. Phys. Chem. B 1998, 102, 3586-3616

    CAS  Google Scholar 

  131. Ben Naim, A.; Marcus, Y., Solvation thermodynamics of nonionic solutes, J. Chem. Phys. 1984, 81, 2016-2027

    CAS  Google Scholar 

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Simonson, T. (2007). Free Energy Calculations: Approximate Methods for Biological Macromolecules. 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_12

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