Multiscale free energy simulations: An efficient method for connecting classical MD simulations to QM or QM/MM free energies using non-Boltzmann Bennett reweighting schemes

Journal of Chemical Theory and Computation

Volumn 10, Issue 4, 2014, Pages 1406-1419

  König, Gerhard ^a   Hudson, Phillip S ^b   Boresch, Stefan ^c   Woodcock, H Lee ^b  

^a NATIONAL HEART LUNG AND BLOOD INSTITUTE   (United States)

^b UNIVERSITY OF SOUTH FLORIDA   (United States)

^c UNIVERSITY OF VIENNA   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84898491607     PISSN: 15499618     EISSN: 15499626     Source Type: Journal    
DOI: 10.1021/ct401118k     Document Type: Article

References (129)

1. Oostenbrink, C.; van Gunsteren, W. Free energies of ligand binding for structurally diverse compounds Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 6750-6754
2. Mobley, D. L.; Graves, A. P.; Chodera, J. D.; McReynolds, A. C.; Shoichet, B. K.; Dill, K. A. Predicting absolute ligand binding free energies to a simple model site J. Mol. Biol. 2007, 371, 1118-1134
3. Shirts, M. R.; Mobley, D. L.; Chodera, J. D.; Pande, V. S. Accurate and efficient corrections for missing dispersion interactions in molecular simulations J. Phys. Chem. B 2007, 111, 13052-13063
4. de Ruiter, A.; Oostenbrink, C. Efficient and Accurate Free Energy Calculations on Trypsin Inhibitors J. Chem. Theory Comput. 2012, 8, 3686-3695
5. de Ruiter, A.; Boresch, S.; Oostenbrink, C. Comparison of thermodynamic integration and Bennett's acceptance ratio for calculating relative protein-ligand binding free energies J. Comput. Chem. 2013, 34, 1024-1034
6. Deng, Y.; Roux, B. Computations of standard binding free energies with molecular dynamics simulations J. Phys. Chem. B 2009, 113, 2234-2246
7. Shirts, M. R.; Pitera, J. W.; Swope, W. C.; Pande, V. S. Extremely precise free energy calculations of amino acid side chain analogs: Comparison of common molecular mechanics force fields for proteins J. Chem. Phys. 2003, 119, 5740-5761
8. Pitera, J. W.; van Gunsteren, W. F. One-Step Perturbation Methods for Solvation Free Energies of Polar Solutes J. Phys. Chem. B 2001, 105, 11264-11274
9. Seeliger, D.; de Groot, B. Protein Thermostability Calculations Using Alchemical Free Energy Simulations Biophys. J. 2010, 98, 2309-2316
10. König, G.; Bruckner, S.; Boresch, S. Absolute Hydration Free Energies of Blocked Amino Acids: Implications for Protein Solvation and Stability Biophys. J. 2013, 104, 453-462
11. a Difference: Phenol in Aqueous Solution J. Am. Chem. Soc. 1996, 118, 4912-4913
12. Li, G.; Cui, Q. pKa Calculations with QM/MM Free Energy Perturbations J. Phys. Chem. B 2003, 107, 14521-14528
13. Riccardi, D.; Schaefer, P.; Cui, Q. pKa calculations in solution and proteins with QM/MM free energy perturbation simulations: a quantitative test of QM/MM protocols J. Phys. Chem. B 2005, 109, 17715-17733
14. Riccardi, D.; Cui, Q. pKa analysis for the zinc-bound water in human carbonic anhydrase II: Benchmark for ″multiscale″ QM/MM simulations and mechanistic implications J. Phys. Chem. A 2007, 111, 5703-5711
15. Ghosh, N.; Cui, Q. pKa of residue 66 in Staphylococal nuclease. I. Insights from QM/MM simulations with conventional sampling J. Phys. Chem. B 2008, 112, 8387-8397
16. Li, G.; Zhang, X.; Cui, Q. Free Energy Perturbation Calculations with Combined QM/MM Potentials Complications, Simplifications, and Applications to Redox Potential Calculations J. Phys. Chem. B 2003, 107, 8643-8653
17. Blumberger, J.; Sprik, M. Quantum versus classical electron transfer energy as reaction coordinate for the aqueous Ru2+/Ru3+ redox reaction Theor. Chem. Acc. 2005, 115, 113-126
18. Borhani, D. W.; Shaw, D. E. The future of molecular dynamics simulations in drug discovery J. Comput.-Aided Mol. Des. 2012, 26, 15-26
19. Mobley, D. L. Let's get honest about sampling J. Comput.-Aided Mol. Des. 2012, 26, 93-95
20. Nicholls, A.; Mobley, D. L.; Guthrie, J. P.; Chodera, J. D.; Bayly, C. I.; Cooper, M. D.; Pande, V. S. Predicting small-molecule solvation free energies: An informal blind test for computational chemistry J. Med. Chem. 2008, 51, 769-779
21. Guthrie, J. P. A Blind Challenge for Computational Solvation Free Energies: Introduction and Overview J. Phys. Chem. B 2009, 113, 4501-4507
22. Geballe, M. T.; Skillman, A. G.; Nicholls, A.; Guthrie, J. P.; Taylor, P. J. The SAMPL2 blind prediction challenge: introduction and overview J. Comput.-Aided Mol. Des. 2010, 24, 259-279
23. Muddana, H. S.; Varnado, C. D.; Bielawski, C. W.; Urbach, A. R.; Isaacs, L.; Geballe, M. T.; Gilson, M. K. Blind prediction of host-guest binding affinities: a new SAMPL3 challenge J. Comput.-Aided Mol. Des. 2012, 26, 475-487
24. Klimovich, P. V.; Mobley, D. L. Predicting hydration free energies using all-atom molecular dynamics simulations and multiple starting conformations J. Comput.-Aided Mol. Des. 2010, 24, 307-316
25. König, G.; Brooks, B. R. Predicting binding affinities of host-guest systems in the SAMPL3 blind challenge: the performance of relative free energy calculations J. Comput.-Aided Mol. Des. 2012, 26, 543-550
26. Gallicchio, E.; Levy, R. M. Prediction of SAMPL3 host-guest affinities with the binding energy distribution analysis method (BEDAM) J. Comput.-Aided Mol. Des. 2012, 26, 505-516
27. Lawrenz, M.; Wereszczynski, J.; Ortiz-Sánchez, J. M.; Nichols, S. E.; McCammon, J. A. Thermodynamic integration to predict host-guest binding affinities J. Comput.-Aided Mol. Des. 2012, 26, 569-576
28. Mobley, D. L.; Liu, S.; Cerutti, D. S.; Swope, W. C.; Rice, J. E. Alchemical prediction of hydration free energies for SAMPL J. Comput.-Aided Mol. Des. 2012, 26, 551-562
29. Stanton, R. V.; Hartsough, D. S.; Merz, K. M. Calculation of solvation free energies using a density functional/molecular dynamics coupled potential J. Phys. Chem. 1993, 97, 11868-11870
30. Reddy, M. R.; Singh, U. C.; Erion, M. D. Development of a quantum mechanics-based free-energy perturbation method: use in the calculation of relative solvation free energies J. Am. Chem. Soc. 2004, 126, 6224-6225
31. Reddy, M. R.; Singh, U. C.; Erion, M. D. Ab initio quantum mechanics-based free energy perturbation method for calculating relative solvation free energies J. Comput. Chem. 2007, 28, 491-494
32. Riccardi, D.; Schaefer, P.; Yang, Y.; Yu, H.; Ghosh, N.; Prat-Resina, X.; König, P.; Li, G.; Xu, D.; Guo, H.; Elstner, M.; Cui, Q. Development of effective quantum mechanical/molecular mechanical (QM/MM) methods for complex biological processes J. Phys. Chem. B 2006, 110, 6458-6469
33. Yang, W.; Cui, Q.; Min, D.; Li, H. QM/MM Alchemical Free Energy Simulations: Challenges and Recent Developments; Annual Reports in Computational Chemistry; Elsevier: 2010; Vol. 6.
34. Yang, W.; Bitetti-Putzer, R.; Karplus, M. Chaperoned alchemical free energy simulations: a general method for QM, MM, and QM/MM potentials J. Chem. Phys. 2004, 120, 9450-9453
35. Min, D.; Chen, M.; Zheng, L.; Jin, Y.; Schwartz, M. A.; Sang, Q.-X. A.; Yang, W. Enhancing QM/MM molecular dynamics sampling in explicit environments via an orthogonal-space-random-walk-based strategy J. Phys. Chem. B 2011, 115, 3924-3935
36. Min, D.; Zheng, L.; Harris, W.; Chen, M.; Lv, C.; Yang, W. Practically Efficient QM/MM Alchemical Free Energy Simulations: The Orthogonal Space Random Walk Strategy J. Chem. Theory Comput. 2010, 6, 2253-2266
37. Kästner, J.; Senn, H.; Thiel, S.; Otte, N.; Thiel, W. QM/MM free-energy perturbation compared to thermodynamic integration and umbrella sampling: Application to an enzymatic reaction J. Chem. Theory Comput. 2006, 2, 452-461
38. Polyak, I.; Benighaus, T.; Boulanger, E.; Thiel, W. Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation J. Chem. Phys. 2013, 139, 064105-064116
39. Senn, H. M.; Thiel, W. QM/MM methods for biomolecular systems Angew. Chem., Int. Ed. 2009, 48, 1198-1229
40. Nam, K.; Gao, J.; York, D. M. An Efficient Linear-Scaling Ewald Method for Long-Range Electrostatic Interactions in Combined QM/MM Calculations J. Chem. Theory Comput. 2005, 1, 2-13
41. Štrajbl, M.; Hong, G.; Warshel, A. Ab Initio QM/MM Simulation with Proper Sampling: ″First Principle″ Calculations of the Free Energy of the Autodissociation of Water in Aqueous Solution J. Phys. Chem. B 2002, 106, 13333-13343
42. Plotnikov, N. V.; Kamerlin, S. C. L.; Warshel, A. Paradynamics: an effective and reliable model for ab initio QM/MM free-energy calculations and related tasks J. Phys. Chem. B 2011, 115, 7950-7962
43. Gao, J.; Xia, X. A priori evaluation of aqueous polarization effects through Monte Carlo QM-MM simulations Science 1992, 258, 631-635
44. Gao, J.; Luque, F. J.; Orozco, M. Induced dipole moment and atomic charges based on average electrostatic potentials in aqueous solution J. Chem. Phys. 1993, 98, 2975-2982
45. Luzhkov, V.; Warshel, A. Microscopic models for quantum mechanical calculations of chemical processes in solutions: LD/AMPAC and SCAAS/AMPAC calculations of solvation energies J. Comput. Chem. 1992, 13, 199-213
46. Wesolowski, T.; Warshel, A. Ab Initio Free Energy Perturbation Calculations of Solvation Free Energy Using the Frozen Density Functional Approach J. Phys. Chem. 1994, 98, 5183-5187
47. Gao, J.; Freindorf, M. Hybrid ab Initio QM/MM Simulation of N -Methylacetamide in Aqueous Solution J. Phys. Chem. A 1997, 101, 3182-3188
48. Kollman, P. Free energy calculations: Applications to chemical and biochemical phenomena Chem. Rev. 1993, 93, 2395-2417
49. Chandrasekhar, J.; Smith, S. F.; Jorgensen, W. L. SN2 reaction profiles in the gas phase and aqueous solution J. Am. Chem. Soc. 1984, 106, 3049-3050
50. Chandrasekhar, J.; Smith, S. F.; Jorgensen, W. L. Theoretical examination of the SN2 reaction involving chloride ion and methyl chloride in the gas phase and aqueous solution J. Am. Chem. Soc. 1985, 107, 154-163
51. Thiel, W.; Voityuk, A. A. Extension of MNDO to d Orbitals: Parameters and Results for the Second-Row Elements and for the Zinc Group J. Phys. Chem. 1996, 100, 616-626
52. Das, D.; Eurenius, K. P.; Billings, E. M.; Sherwood, P.; Chatfield, D. C.; Hodoscek, M.; Brooks, B. R. Optimization of quantum mechanical molecular mechanical partitioning schemes: Gaussian delocalization of molecular mechanical charges and the double link atom method J. Chem. Phys. 2002, 117, 10534-10547
53. Lyne, P. D.; Hodoscek, M.; Karplus, M. A Hybrid QM-MM Potential Employing Hartree-Fock or Density Functional Methods in the Quantum Region J. Phys. Chem. A 1999, 103, 3462-3471
54. Luque, F. J.; Reuter, N.; Cartier, A.; Ruiz-López, M. F. Calibration of the Quantum/Classical Hamiltonian in Semiempirical QM/MM AM1 and PM3Methods J. Phys. Chem. A 2000, 104, 10923-10931
55. Tuttle, T.; Thiel, W. OMx-D: semiempirical methods with orthogonalization and dispersion corrections. Implementation and biochemical application Phys. Chem. Chem. Phys. 2008, 10, 2159-2166
56. Repasky, M. P.; Chandrasekhar, J.; Jorgensen, W. L. PDDG/PM3 and PDDG/MNDO: Improved semiempirical methods J. Comput. Chem. 2002, 23, 1601-1622
57. Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, T.; Suhai, S.; Seifert, G. Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties Phys. Rev. B 1998, 58, 7260-7268
58. Lonsdale, R.; Hoyle, S.; Grey, D. T.; Ridder, L.; Mulholland, A. J. Determinants of reactivity and selectivity in soluble epoxide hydrolase from quantum mechanics/molecular mechanics modeling Biochemistry 2012, 51, 1774-1786
59. Bowman, A. L.; Grant, I. M.; Mulholland, A. J. QM/MM simulations predict a covalent intermediate in the hen egg white lysozyme reaction with its natural substrate Chem. Commun. 2008, 37, 4425-4427
60. Claeyssens, F.; Harvey, J. N.; Manby, F. R.; Mata, R. A.; Mulholland, A. J.; Ranaghan, K. E.; Schütz, M.; Thiel, S.; Thiel, W.; Werner, H.-J. High-accuracy computation of reaction barriers in enzymes Angew. Chem., Int. Ed. 2006, 45, 6856-6859
61. Lonsdale, R.; Harvey, J. N.; Mulholland, A. J. Inclusion of Dispersion Effects Significantly Improves Accuracy of Calculated Reaction Barriers for Cytochrome P450 Catalyzed Reactions Phys. Chem. Lett. 2010, 1, 3232-3237
62. Li, H.; Yang, W. Sampling enhancement for the quantum mechanical potential based molecular dynamics simulations: A general algorithm and its extension for free energy calculation on rugged energy surface J. Chem. Phys. 2007, 126, 114104
63. Woods, C. J.; Manby, F. R.; Mulholland, A. J. An efficient method for the calculation of quantum mechanics/molecular mechanics free energies J. Chem. Phys. 2008, 128, 014109
64. Rod, T. H.; Ryde, U. Accurate QM/MM Free Energy Calculations of Enzyme Reactions: Methylation by Catechol O -Methyltransferase J. Chem. Theory Comput. 2005, 1, 1240-1251
65. Rod, T.; Ryde, U. Quantum Mechanical Free Energy Barrier for an Enzymatic Reaction Phys. Rev. Lett. 2005, 94, 138302
66. Heimdal, J.; Ryde, U. Convergence of QM/MM free-energy perturbations based on molecular-mechanics or semiempirical simulations Phys. Chem. Chem. Phys. 2012, 14, 12592-12604
67. Hu, H.; Lu, Z.; Yang, W. QM/MM Minimum Free Energy Path: Methodology and Application to Triosephosphate Isomerase J. Chem. Theory Comput. 2007, 3, 390-406
68. Zeng, X.; Hu, H.; Hu, X.; Cohen, A. J.; Yang, W. Ab initio quantum mechanical/molecular mechanical simulation of electron transfer process: fractional electron approach J. Chem. Phys. 2008, 128, 124510
69. Hu, H.; Lu, Z.; Parks, J. M.; Burger, S. K.; Yang, W. Quantum mechanics/molecular mechanics minimum free-energy path for accurate reaction energetics in solution and enzymes: sequential sampling and optimization on the potential of mean force surface J. Chem. Phys. 2008, 128, 034105
70. Hu, H.; Yang, W. Elucidating solvent contributions to solution reactions with ab initio QM/MM methods J. Phys. Chem. B 2010, 114, 2755-2759
71. Zacharias, M.; Straatsma, T. P.; McCammon, J. A. Separation-Shifted Scaling, a New Scaling Method for Lennard-Jones Interactions in Thermodynamic Integration J. Chem. Phys. 1994, 100, 9025-9031
72. Beutler, T. C.; Mark, A. E.; van Schaik, R. C.; Gerber, P. R.; van Gunsteren, W. F. Avoiding Singularities and Numerical Instabilities in Free Energy Calculations Based on Molecular Simulations Chem. Phys. Lett. 1994, 222, 529-539
73. Zwanzig, R. W. High-Temperature Equation Of State By A Perturbation Method. 1. Nonpolar Gases J. Chem. Phys. 1954, 22, 1420-1426
74. Zhang, Y.; Liu, H.; Yang, W. Free energy calculation on enzyme reactions with an efficient iterative procedure to determine minimum energy paths on a combined ab initio QM/MM potential energy surface J. Chem. Phys. 2000, 112, 3483-3492
75. Mart, S.; Moliner, V.; Tuñón, I.; Williams, I. H. Computing kinetic isotope effects for chorismate mutase with high accuracy. A new DFT/MM strategy J. Phys. Chem. B 2005, 109, 3707-3710
76. Martí, S.; Moliner, V.; Tuñón, I. Improving the QM/MM Description of Chemical Processes: A Dual Level Strategy to Explore the Potential Energy Surface in Very Large Systems J. Chem. Theory Comput. 2005, 1, 1008-1016
77. Bentzien, J.; Muller, R. P.; Florián, J.; Warshel, A. Hybrid ab Initio Quantum Mechanics/Molecular Mechanics Calculations of Free Energy Surfaces for Enzymatic Reactions: The Nucleophilic Attack in Subtilisin J. Phys. Chem. A 1998, 102, 2293-2301
78. Frushicheva, M. P.; Warshel, A. Towards quantitative computer-aided studies of enzymatic enantioselectivity: the case of Candida antarctica lipase A ChemBioChem 2012, 13, 215-223
79. Heimdal, J.; Ryde, U. Convergence of QM/MM free-energy perturbations based on molecular-mechanics or semiempirical simulations Phys. Chem. Chem. Phys. 2012, 14, 12592-12604
80. Fox, S. J.; Pittock, C.; Tautermann, C. S.; Fox, T.; Christ, C.; Malcolm, N. O. J.; Essex, J. W.; Skylaris, C.-K. Free energies of binding from large-scale first-principles quantum mechanical calculations: application to ligand hydration energies J. Phys. Chem. B 2013, 117, 9478-9485
81. Beierlein, F. R.; Michel, J.; Essex, J. W. A Simple QM/MM Approach for Capturing Polarization Effects in Protein-Ligand Binding Free Energy Calculations J. Phys. Chem. B 2011, 115, 4911-4926
82. Lu, N.; Kofke, D. A.; Woolf, T. B. Improving the efficiency and reliability of free energy perturbation calculations using overlap sampling methods J. Comput. Chem. 2004, 25, 28-40
83. Shirts, M. R.; Pande, V. S. Comparison of efficiency and bias of free energies computed by exponential averaging, the Bennett acceptance ratio, and thermodynamic integration J. Chem. Phys. 2005, 122, 144107-1-144107-16
84. Bruckner, S.; Boresch, S. Efficiency of Alchemical Free Energy Simulations I: Practical Comparison of the Exponential Formula, Thermodynamic Integration and Bennett's Acceptance Ratio Method J. Comput. Chem. 2011, 32, 1303-1319
85. Bruckner, S.; Boresch, S. Efficiency of Alchemical Free Energy Simulations II: Improvements for Thermodynamic Integration J. Comput. Chem. 2011, 32, 1320-1333
86. Bennett, C. H. Efficient Estimation of Free Energy Differences from Monte Carlo Data J. Comput. Phys. 1976, 22, 245-268
87. Kirkwood, J. G. Statistical Mechanics of Fluid Mixtures J. Chem. Phys. 1935, 3, 300-313
88. König, G.; Bruckner, S.; Boresch, S. Unorthodox Uses of Bennett's Acceptance Ratio Method J. Comput. Chem. 2009, 30, 1712-1718
89. Pohorille, A.; Jarzynski, C.; Chipot, C. Good Practices in Free-Energy Calculations J. Phys. Chem. B 2010, 114, 10235-10253
90. Rosta, E.; Klähn, M.; Warshel, A. Towards accurate ab initio QM/MM calculations of free-energy profiles of enzymatic reactions J. Phys. Chem. B 2006, 110, 2934-2941
91. König, G.; Boresch, S. Non-Boltzmann Sampling and Bennett's Acceptance Ratio Method: How to Profit from Bending the Rules J. Comput. Chem. 2011, 32, 1082-1090
92. Zwanzig, R. W. High-Temperature Equation of State by a Perturbation Method. I. Nonpolar Gases J. Chem. Phys. 1954, 22, 1420-1426
93. Jorgensen, W. L.; Thomas, L. L. Perspective on Free-Energy Perturbation Calculations for Chemical Equilibria J. Chem. Theory Comput. 2008, 4, 869-876
94. Shirts, M. R.; Pitera, J. W.; Swope, W. C.; Pande, V. S. Extremely precise free energy calculations of amino acid side chain analogs: Comparison of common molecular mechanics force fields for proteins J. Chem. Phys. 2003, 119, 5740-5761
95. Torrie, G. M.; Valleau, J. P. Non-physical sampling distributions in Monte-Carlo free energy estimation-umbrella sampling J. Comput. Phys. 1977, 23, 187-199
96. Wereszczynski, J.; McCammon, J. A. Using Selectively Applied Accelerated Molecular Dynamics to Enhance Free Energy Calculations J. Chem. Theory Comput. 2010, 6, 3285-3292
97. Straatsma, T. P.; McCammon, J. A. Treatment of rotational isomeric states. III. The use of biasing potentials J. Chem. Phys. 1994, 101, 5032-5039
98. Leitgeb, M.; Schröder, C.; Boresch, S. Alchemical Free Energy Calculations and Multiple Conformational Substates J. Chem. Phys. 2005, 122, 084109
99. Mobley, D. L.; Dill, K. A.; Chodera, J. D. Treating Entropy and Conformational Changes in Implicit Solvent Simulations of Small Molecules J. Phys. Chem. B 2008, 112, 938-946
100. Brooks, B.; Brooks, C., III; Mackerell, A., Jr.; Nilsson, L.; Petrella, R.; Roux, B.; Won, Y.; Archontis, G.; Bartels, C.; Boresch, S.; Caflisch, A.; Caves, L.; Cui, Q.; Dinner, A.; Feig, M.; Fischer, S.; Gao, J.; Hodoscek, M.; Im, W.; Kuczera, K.; Lazaridis, T.; Ma, J.; Ovchinnikov, V.; Paci, E.; Pastor, R.; Post, C.; Pu, J.; Schaefer, M.; Tidor, B.; Venable, R.; Woodcock, H.; Wu, X.; Yang, W.; York, D.; Karplus, M. CHARMM: The Biomolecular Simulation Program J. Comput. Chem. 2009, 30, 1545-1614
101. Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M. CHARMM: A program for macromolecular energy, minimization and dynamics calculations J. Comput. Chem. 1983, 4, 187-217
102. MacKerell, A. D., Jr.; Bashford, D.; Bellott, M.; Dunbrack, R. L., Jr.; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S.; Joseph-McCarthy, D.; Kuchnir, L.; Kuczera, K.; Lau, F. T. K.; Mattos, C.; Michnick, S.; Ngo, T.; Nguyen, D. T.; Prodhom, B.; Reiher, W. E., III; Roux, B.; Schlenkrich, M.; Smith, J.; Stote, R.; Straub, J.; Watanabe, M.; Wiorkiewicz-Kuczera, J.; Yin, D.; Karplus, M. All-atom empirical potential for molecular modeling and dynamics studies of protein J. Phys. Chem. B 1998, 102, 3586-3616
103. Shao, Y.; Molnar, L. F.; Jung, Y.; Kussmann, J.; Ochsenfeld, C.; Brown, S. T.; Gilbert, A. T. B.; Slipchenko, L. V.; Levchenko, S. V.; O'Neill, D. P.; DiStasio, R. A., Jr.; Lochan, R. C.; Wang, T.; Beran, G. J. O.; Besley, N. A.; Herbert, J. M.; Lin, C. Y.; Van Voorhis, T.; Chien, S. H.; Sodt, A.; Steele, R. P.; Rassolov, V. A.; Maslen, P. E.; Korambath, P. P.; Adamson, R. D.; Austin, B.; Baker, J.; Byrd, E. F. C.; Dachsel, H.; Doerksen, R. J.; Dreuw, A.; Dunietz, B. D.; Dutoi, A. D.; Furlani, T. R.; Gwaltney, S. R.; Heyden, A.; Hirata, S.; Hsu, C.-P.; Kedziora, G.; Khalliulin, R. Z.; Klunzinger, P.; Lee, A. M.; Lee, M. S.; Liang, W.; Lotan, I.; Nair, N.; Peters, B.; Proynov, E. I.; Pieniazek, P. A.; Rhee, Y. M.; Ritchie, J.; Rosta, E.; Sherrill, C. D.; Simmonett, A. C.; Subotnik, J. E.; Woodcock, H. L., III; Zhang, W.; Bell, A. T.; Chakraborty, A. K.; Chipman, D. M.; Keil, F. J.; Warshel, A.; Hehre, W. J.; Schaefer, H. F., III; Kong, J.; Krylov, A. I.; Gill, P. M. W.; Head-Gordon, M. Advances in methods and algorithms in a modern quantum chemistry program package Phys. Chem. Chem. Phys. 2006, 8, 3172-3191
104. Woodcock, H. L., III; Hodoscek, M.; Gilbert, A. T. B.; Gill, P. M. W.; Schaefer, H. F., III; Brooks, B. R. Interfacing Q-chem and CHARMM to perform QM/MM reaction path calculations J. Comput. Chem. 2007, 28, 1485-1502
105. Pearlman, D. A. A Comparison of Alternative Approaches to Free Energy Calculations J. Phys. Chem. 1994, 98, 1487-1493
106. Boresch, S.; Karplus, M. The Role of Bonded Terms in Free Energy Simulations: 1. Theoretical Analysis J. Phys. Chem. A 1999, 103, 103-118
107. Tembe, B. L.; McCammon, J. A. Ligand-receptor interactions Comput. Chem. 1984, 8, 281-283
108. Woodcock, H. L.; Miller, B. T.; Hodoscek, M.; Okur, A.; Larkin, J. D.; Ponder, J. W.; Brooks, B. R. MSCALE: A General Utility for Multiscale Modeling J. Chem. Theory Comput. 2011, 7, 1208-1219
109. Boresch, S.; Karplus, M. The Role of Bonded Terms in Free Energy Simulations. 2. Calculation of Their Influence on Free Energy Differences of Solvation J. Phys. Chem. A 1999, 103, 119-136
110. Hoover, W. G. Canonical Dynamics: Equilibrium Phase-Space Distributions Phys. Rev. A 1985, 31, 1695-1697
111. Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. A smooth particle mesh Ewald method J. Chem. Phys. 1995, 103, 8577-8593
112. Lee, M. S.; Feig, M.; Salsbury, F. R.; Brooks, C. L., III. New analytic approximation to the standard molecular volume definition and its application to generalized born calculations J. Comput. Chem. 2003, 23, 1348-1356
113. Zhao, Y.; Truhlar, D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other function Theor. Chem. Acc. 2007, 120, 215-241
114. Becke, A. D. A new mixing of Hartree-Fock and local-density-functional theories J. Chem. Phys. 1993, 98, 1372-1377
115. Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density Phys. Rev. B 1988, 37, 785-789
116. Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions J. Phys. Chem. B 2009, 113, 6378-6396
117. Gordon, M. S.; Schmidt, M. W. In Theory and Applications of Computational Chemistry: the first forty years; Dykstra, C. E.; Frenking, G.; Kim, K. S.; Scuseria, G. E., Eds.; Elsevier: Amsterdam, 2005; pp 1167-1189.
118. Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal Solvation Model Based on the Generalized Born Approximation with Asymmetric Descreening J. Chem. Theory Comput. 2009, 5, 2447-2464
119. Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Generalized Born Solvation Model SM12 J. Chem. Theory Comput. 2013, 9, 609-620
120. Villa, A.; Mark, A. E. Calculation of the free energy of solvation for neutral analogs of amino acid side chains J. Comput. Chem. 2002, 23, 548-553
121. Deng, Y. Q.; Roux, B. Hydration of amino acid side chains: Nonpolar and electrostatic contributions calculated from staged molecular dynamics free energy simulations with explicit water molecules J. Phys. Chem. B 2004, 108, 16567-16576
122. Vanommeslaeghe, K.; Hatcher, E.; Acharya, C.; Kundu, S.; Zhong, S.; Shim, J.; Darian, E.; Guvench, O.; Lopes, P.; Vorobyov, I.; Mackerell, A. D. CHARMM general force field: A force field for drug-like molecules compatible with the CHARMM all-atom additive biological force fields J. Comput. Chem. 2010, 31, 671-690
123. 2 Dihedral Angles J. Chem. Theory Comput. 2012, 8, 3257-3273
124. Beveridge, D. L.; DiCapua, F. M. In Computer Simulation of Biomolecular Systems; van Gunsteren, W. F.; Weiner, P. K., Eds.; ESCOM Science: Leiden, 1989; pp 1-26.
125. Ben-Naim, A.; Marcus, Y. J. Solvation thermodynamics of nonionic solutes J. Chem. Phys. 1984, 81, 2016-2027
126. Lin, C. Y.; Gilbert, A. T. B.; Gill, P. M. W. Calculating molecular vibrational spectra beyond the harmonic approximation Theor. Chem. Acc. 2007, 120, 23-35
127. Nicholls, A.; Mobley, D. L.; Guthrie, J. P.; Chodera, J. D.; Bayly, C. I.; Cooper, M. D.; Pande, V. S. Predicting Small-Molecule Solvation Free Energies: An Informal Blind Test for Computational Chemistry J. Med. Chem. 2008, 51, 769-779
128. Mobley, D. L.; Bayly, C. I.; Cooper, M. D.; Shirts, M. R.; Dill, K. A. Small Molecule Hydration Free Energies in Explicit Solvent: An Extensive Test of Fixed-Charge Atomistic Simulations J. Chem. Theory Comput. 2009, 5, 350-358
129. Mobley, D. L.; Liu, S.; Cerutti, D. S.; Swope, W. C.; Rice, J. E. Alchemical prediction of hydration free energies for SAMPL J. Comput.-Aided Mol. Des. 2012, 26, 551-562