Simulation-Based Approaches for Determining Membrane Permeability of Small Compounds

Journal of Chemical Information and Modeling

Volumn 56, Issue 4, 2016, Pages 721-733

  Lee, Christopher T ^a   Comer, Jeffrey ^b   Herndon, Conner ^c   Leung, Nelson ^d   Pavlova, Anna ^c   Swift, Robert V ^a   Tung, Chris ^d   Rowley, Christopher N ^e   Amaro, Rommie E ^a   Chipot, Christophe ^f,g   Wang, Yi ^d   Gumbart, James C ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b KANSAS STATE UNIVERSITY   (United States)

^c GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^d CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^e MEMORIAL UNIVERSITY OF NEWFOUNDLAND   (Canada)

^f UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^g University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BAYESIAN NETWORKS; BENZOIC ACID; INFERENCE ENGINES; LIPID BILAYERS; MOLECULAR DYNAMICS; UREA;

ADAPTIVE BIASING FORCES; BAYESIAN INFERENCE; MEMBRANE PERMEABILITY; MOLECULAR DYNAMICS SIMULATIONS; NUMERICAL CALCULATION; POSITION DEPENDENTS; POTENTIAL OF MEAN FORCE; SIMULATION BASED APPROACHES;

MECHANICAL PERMEABILITY;

BENZOIC ACID; CODEINE; DIMYRISTOYLPHOSPHATIDYLCHOLINE; LIPID BILAYER; UREA;

BAYES THEOREM; CELL MEMBRANE PERMEABILITY; CHEMISTRY; CONFORMATION; LIPID BILAYER; METABOLISM; MOLECULAR MODEL;

BAYES THEOREM; BENZOIC ACID; CELL MEMBRANE PERMEABILITY; CODEINE; DIMYRISTOYLPHOSPHATIDYLCHOLINE; LIPID BILAYERS; MODELS, MOLECULAR; MOLECULAR CONFORMATION; UREA;

EID: 84969180414     PISSN: 15499596     EISSN: 1549960X     Source Type: Journal    
DOI: 10.1021/acs.jcim.6b00022     Document Type: Article

References (99)

1. Tanford, C. Interfacial Free Energy and the Hydrophobic Effect Proc. Natl. Acad. Sci. U. S. A. 1979, 76, 4175-4176 10.1073/pnas.76.9.4175
2. Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes; John Wiley & Sons Inc.: New York, 1970.
3. Kola, I.; Landis, J. Can the Pharmaceutical Industry Reduce Attrition Rates? Nat. Rev. Drug Discovery 2004, 3, 711-715 10.1038/nrd1470
4. Tsaioun, K.; Bottlaender, M.; Mabondzo, A. ADDME-Avoiding Drug Development Mistakes Early: Central Nervous System Drug Discovery Perspective BMC Neurol. 2009, 9 (Suppl 1) S1 10.1186/1471-2377-9-S1-S1
5. Kansy, M.; Senner, F.; Gubernator, K. Physicochemical High Throughput Screening: Parallel Artificial Membrane Permeation Assay in the Description of Passive Absorption Processes J. Med. Chem. 1998, 41, 1007-1010 10.1021/jm970530e
6. Avdeef, A. the Rise of PAMPA Expert Opin. Drug Metab. Toxicol. 2005, 1, 325-342 10.1517/17425255.1.2.325
7. Artursson, P.; Palm, K.; Luthman, K. Caco-2 Monolayers in Experimental and Theoretical Predictions of Drug Transport Adv. Drug Delivery Rev. 2012, 64, 280-289 10.1016/j.addr.2012.09.005
8. van Breemen, R. B.; Li, Y. Caco-2 Cell Permeability Assays to Measure Drug Absorption Expert Opin. Drug Metab. Toxicol. 2005, 1, 175-185 10.1517/17425255.1.2.175
9. Hansch, C. Quantitative Relationships Between Lipophilic Character and Drug Metabolism Drug Metab. Rev. 1972, 1, 1-14 10.3109/03602537208993906
10. Hansch, C. a Quantitative Approach to Biochemical Structure-Activity Relationships Acc. Chem. Res. 1969, 2, 232-239 10.1021/ar50020a002
11. Stouch, T. R.; Kenyon, J. R.; Johnson, S. R.; Chen, X.-Q.; Doweyko, A.; Li, Y. In Silico ADME Tox: Why Models Fail J. Comput.-Aided Mol. Des. 2003, 17, 83-92 10.1023/A:1025358319677
12. Swift, R. V.; Amaro, R. E. Back to the Future: Can Physical Models of Passive Membrane Permeability Help Reduce Drug Candidate Attrition and Move Us Beyond QSPR? Chem. Biol. Drug Des. 2013, 81, 61-71 10.1111/cbdd.12074
13. Paloncýová, M.; Fabre, G.; DeVane, R. H.; Trouillas, P.; Berka, K.; Otyepka, M. Benchmarking of Force Fields for Molecule-Membrane Interactions J. Chem. Theory Comput. 2014, 10, 4143-4151 10.1021/ct500419b
14. Wang, L.; Wu, Y.; Deng, Y.; Kim, B.; Pierce, L.; Krilov, G.; Lupyan, D.; Robinson, S.; Dahlgren, M. K.; Greenwood, J.; Romero, D. L.; Masse, C.; Knight, J. L.; Steinbrecher, T.; Beuming, T.; Damm, W.; Harder, E.; Sherman, W.; Brewer, M.; Wester, R.; Murcko, M.; Frye, L.; Farid, R.; Lin, T.; Mobley, D. L.; Jorgensen, W. L.; Berne, B. J.; Friesner, R. A.; Abel, R. Accurate and Reliable Prediction of Relative Ligand Binding Potency in Prospective Drug Discovery by Way of a Modern Free-Energy Calculation Protocol and Force Field J. Am. Chem. Soc. 2015, 137, 2695-2703 10.1021/ja512751q
15. Vitalini, F.; Mey, A. S. J. S.; Noé, F.; Keller, B. G.; Vitalini, F.; Mey, A. S. J. S.; Noé, F.; Keller, B. G. Dynamic Properties of Force Fields J. Chem. Phys. 2015, 142, 084101 10.1063/1.4909549
16. Finkelstein, A.; Cass, A. Permeability and Electrical Properties of Thin Lipid Membranes J. Gen. Physiol. 1968, 52, 145-172 10.1085/jgp.52.1.145
17. Diamond, J. M.; Katz, Y. Interpretation of Nonelectrolyte Partition Coefficients Between Dimyristoyl Lecithin and Water J. Membr. Biol. 1974, 17, 121-154 10.1007/BF01870176
18. Marrink, S.-J.; Berendsen, H. J. C. Simulation of Water Transport Through a Lipid Membrane J. Phys. Chem. 1994, 98, 4155-4168 10.1021/j100066a040
19. Torrie, G.; Valleau, J. Nonphysical Sampling Distributions in Monte Carlo Free-Energy Estimation: Umbrella Sampling J. Comput. Phys. 1977, 23, 187-199 10.1016/0021-9991(77)90121-8
20. Rodriguez-Gomez, D.; Darve, E.; Pohorille, A. Assessing the Efficiency of Free Energy Calculation Methods J. Chem. Phys. 2004, 120, 3563-3578 10.1063/1.1642607
21. Darve, E.; Pohorille, A. Calculating Free Energies Using Average Force J. Chem. Phys. 2001, 115, 9169 10.1063/1.1410978
22. Darve, E.; Rodríguez-Gómez, D.; Pohorille, A. Adaptive Biasing Force Method for Scalar and Vector Free Energy Calculations J. Chem. Phys. 2008, 128, 144120 10.1063/1.2829861
23. Wei, C.; Pohorille, A. Permeation of Nucleosides Through Lipid Bilayers J. Phys. Chem. B 2011, 115, 3681-3688 10.1021/jp112104r
24. Laio, A.; Parrinello, M. Escaping Free-Energy Minima Proc. Natl. Acad. Sci. U. S. A. 2002, 99, 12562-12566 10.1073/pnas.202427399
25. Wang, F.; Landau, D. Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States Phys. Rev. Lett. 2001, 86, 2050-2053 10.1103/PhysRevLett.86.2050
26. Swendsen, R. H.; Wang, J. S. Replica Monte Carlo Simulation of Spin-Glasses Phys. Rev. Lett. 1986, 57, 2607-2609 10.1103/PhysRevLett.57.2607
27. Xiang, T.-X.; Anderson, B. D. Liposomal Drug Transport: A Molecular Perspective from Molecular Dynamics Simulations in Lipid Bilayers Adv. Drug Delivery Rev. 2006, 58, 1357-1378 10.1016/j.addr.2006.09.002
28. Wilson, M. A.; Pohorille, A. Mechanism of Unassisted Ion Transport Across Membrane Bilayers J. Am. Chem. Soc. 1996, 118, 6580-6587 10.1021/ja9540381
29. Grossfield, A.; Woolf, T. B. Interaction of Tryptophan Analogs with POPC Lipid Bilayers Investigated by Molecular Dynamics Calculations Langmuir 2002, 18, 198-210 10.1021/la0106485
30. Ulander, J.; Haymet, A. D. J. Permeation Across Hydrated DPPC Lipid Bilayers: Simulation of the Titrable Amphiphilic Drug Valproic Acid Biophys. J. 2003, 85, 3475-3484 10.1016/S0006-3495(03)74768-7
31. Bemporad, D.; Essex, J. W.; Luttmann, C. Permeation of Small Molecules Through a Lipid Bilayer: A Computer Simulation Study J. Phys. Chem. B 2004, 108, 4875-4884 10.1021/jp035260s
32. MacCallum, J. L.; Bennett, W. F. D.; Tieleman, D. P. Partitioning of Amino Acid Side Chains into Lipid Bilayers: Results from Computer Simulations and Comparison to Experiment J. Gen. Physiol. 2007, 129, 371-377 10.1085/jgp.200709745
33. Johansson, A. C. V.; Lindahl, E. Position-Resolved Free Energy of Solvation for Amino Acids in Lipid Membranes from Molecular Dynamics Simulations Proteins: Struct., Funct., Genet. 2008, 70, 1332-1344 10.1002/prot.21629
34. MacCallum, J. L.; Bennett, W. F. D.; Tieleman, D. P. Distribution of Amino Acids in a Lipid Bilayer from Computer Simulations Biophys. J. 2008, 94, 3393-4304 10.1529/biophysj.107.112805
35. Bauer, B. A.; Lucas, T. R.; Meninger, D. J.; Patel, S. Water Permeation Through DMPC Lipid Bilayers Using Polarizable Charge Equilibration Force Fields Chem. Phys. Lett. 2011, 508, 289-294 10.1016/j.cplett.2011.04.052
36. Tejwani, R. W.; Davis, M. E.; Anderson, B. D.; Stouch, T. R. Functional Group Dependence of Solute Partitioning to Various Locations Within a DOPC Bilayer: A Comparison of Molecular Dynamics Simulations with Experiment J. Pharm. Sci. 2011, 100, 2136-2146 10.1002/jps.22441
37. MacCallum, J. L.; Bennett, W. F. D.; Tieleman, D. P. Transfer of Arginine into Lipid Bilayers Is Nonadditive Biophys. J. 2011, 101, 110-117 10.1016/j.bpj.2011.05.038
38. Paloncýová, M.; Berka, K.; Otyepka, M. Convergence of Free Energy Profile of Coumarin in Lipid Bilayer J. Chem. Theory Comput. 2012, 8, 1200-1211 10.1021/ct2009208
39. Riahi, S.; Rowley, C. N. Why Can Hydrogen Sulfide Permeate Cell Membranes? J. Am. Chem. Soc. 2014, 136, 15111-15113 10.1021/ja508063s
40. Carpenter, T. S.; Kirshner, D. A.; Lau, E. Y.; Wong, S. E.; Nilmeier, J. P.; Lightstone, F. C. a Method to Predict Blood-Brain Barrier Permeability of Drug-like Compounds Using Molecular Dynamics Simulations Biophys. J. 2014, 107, 630-641 10.1016/j.bpj.2014.06.024
41. Issack, B. B.; Peslherbe, G. H. Effects of Cholesterol on the Thermodynamics and Kinetics of Passive Transport of Water Through Lipid Membranes J. Phys. Chem. B 2015, 119, 9391-9400 10.1021/jp510497r
42. Bemporad, D.; Luttmann, C.; Essex, J. W. Behaviour of Small Solutes and Large Drugs in a Lipid Bilayer from Computer Simulations Biochim. Biophys. Acta, Biomembr. 2005, 1718, 1-21 10.1016/j.bbamem.2005.07.009
43. Comer, J.; Schulten, K.; Chipot, C. Calculation of Lipid-Bilayer Permeabilities Using an Average Force J. Chem. Theory Comput. 2014, 10, 554-564 10.1021/ct400925s
44. Ghaemi, Z.; Minozzi, M.; Carloni, P.; Laio, A. a Novel Approach to the Investigation of Passive Molecular Permeation Through Lipid Bilayers from Atomistic Simulations J. Phys. Chem. B 2012, 116, 8714-8721 10.1021/jp301083h
45. Parisio, G.; Stocchero, M.; Ferrarini, A. Passive Membrane Permeability: Beyond the Standard Solubility-Diffusion Model J. Chem. Theory Comput. 2013, 9, 5236-5246 10.1021/ct400690t
46. Kirmizialtin, S.; Elber, R. Revisiting and Computing Reaction Coordinates with Directional Milestoning J. Phys. Chem. A 2011, 115, 6137-6148 10.1021/jp111093c
47. Vanden-Eijnden, E.; Venturoli, M.; Ciccotti, G.; Elber, R. on the Assumptions Underlying Milestoning J. Chem. Phys. 2008, 129, 174102 10.1063/1.2996509
48. Májek, P.; Elber, R. Milestoning Without a Reaction Coordinate J. Chem. Theory Comput. 2010, 6, 1805-1817 10.1021/ct100114j
49. Bello-Rivas, J. M.; Elber, R. Exact Milestoning J. Chem. Phys. 2015, 142, 094102 10.1063/1.4913399
50. Cardenas, A. E.; Jas, G. S.; DeLeon, K. Y.; Hegefeld, W. A.; Kuczera, K.; Elber, R. J. Unassisted Transport of N-Acetyl-L-Tryptophanamide Through Membrane: Experiment and Simulation of Kinetics J. Phys. Chem. B 2012, 116, 2739-2750 10.1021/jp2102447
51. Cardenas, A. E.; Elber, R. Modeling Kinetics and Equilibrium of Membranes with Fields: Milestoning Analysis and Implication to Permeation J. Chem. Phys. 2014, 141, 054101 10.1063/1.4891305
52. Neale, C.; Bennett, W. F. D.; Tieleman, D. P.; Pomès, R. Statistical Convergence of Equilibrium Properties in Simulations of Molecular Solutes Embedded in Lipid Bilayers J. Chem. Theory Comput. 2011, 7, 4175-4188 10.1021/ct200316w
53. Neale, C.; Hsu, J. C. Y.; Yip, C. M.; Pomès, R. Indolicidin Binding Induces Thinning of a Lipid Bilayer Biophys. J. 2014, 106, L29-L31 10.1016/j.bpj.2014.02.031
54. Bochicchio, D.; Panizon, E.; Ferrando, R.; Monticelli, L.; Rossi, G. Calculating the Free Energy of Transfer of Small Solutes into a Model Lipid Membrane: Comparison Between Metadynamics and Umbrella Sampling J. Chem. Phys. 2015, 143, 144108 10.1063/1.4932159
55. Izrailev, S.; Stepaniants, S.; Balsera, M.; Oono, Y.; Schulten, K. Molecular Dynamics Study of Unbinding of the Avidin-Biotin Complex Biophys. J. 1997, 72, 1568-1581 10.1016/S0006-3495(97)78804-0
56. Sotomayor, M.; Schulten, K. Single-Molecule Experiments in Vitro and in Silico Science 2007, 316, 1144-1148 10.1126/science.1137591
57. Walter, A.; Gutknecht, J. Monocarboxylic Acid Permeation Through Lipid Bilayer Membranes J. Membr. Biol. 1984, 77, 255-264 10.1007/BF01870573
58. Gallucci, E.; Micelli, S.; Lippe, C. Non-Electrolyte Permeability Across Thin Lipid Membranes Arch. Int. Physiol. Biochim. 1971, 79, 881-887 10.3109/13813457109104847
59. Orbach, E.; Finkelstein, A. the Nonelectrolyte Permeability of Planar Lipid Bilayer Membranes J. Gen. Physiol. 1980, 75, 427-436 10.1085/jgp.75.4.427
60. Marrink, S. J. S.; Berendsen, H. H. J. C. Permeation Process of Small Molecules Across Lipid Membranes Studied by Molecular Dynamics Simulations J. Phys. Chem. 1996, 100, 16729-16738 10.1021/jp952956f
61. Holland, B. W.; Gray, C. G.; Tomberli, B. Calculating Diffusion and Permeability Coefficients with the Oscillating Forward-Reverse Method Phys. Rev. E 2012, 86, 036707 10.1103/PhysRevE.86.036707
62. Mamonov, A. B.; Kurnikova, M. G.; Coalson, R. D. Diffusion Constant of K+ Inside Gramicidin A: A Comparative Study of Four Computational Methods Biophys. Chem. 2006, 124, 268-278 10.1016/j.bpc.2006.03.019
63. Wilson, M. A.; Pohorille, A.; Pratt, L. R. Molecular Dynamics Test of the Brownian Description of Na+ Motion in Water J. Chem. Phys. 1985, 83, 5832 10.1063/1.449663
64. Berne, B. J.; Borkovec, M.; Straub, J. E. Classical and Modern Methods in Reaction Rate Theory J. Phys. Chem. 1988, 92, 3711-3725 10.1021/j100324a007
65. Woolf, T. B.; Roux, B. Conformational Flexibility of O-Phosphorylcholine and O-Phosphorylethanolamine: A Molecular Dynamics Study of Solvation Effects J. Am. Chem. Soc. 1994, 116, 5916-5926 10.1021/ja00092a048
66. Hummer, G. Position-Dependent Diffusion Coefficients and Free Energies from Bayesian Analysis of Equilibrium and Replica Molecular Dynamics Simulations New J. Phys. 2005, 7, 34-34 10.1088/1367-2630/7/1/034
67. Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press, 1989; p 385.
68. Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kale, L.; Schulten, K. Scalable Molecular Dynamics with NAMD J. Comput. Chem. 2005, 26, 1781-1802 10.1002/jcc.20289
69. Tuckerman, M. Statistical Mechanics: Theory and Molecular Simulation; Oxford University Press: Oxford, 2010; p 720.
70. Hub, J. S.; de Groot, B. L.; van der Spoel, D. g-wham-a Free Weighted Histogram Analysis Implementation Including Robust Error and Autocorrelation Estimates J. Chem. Theory Comput. 2010, 6, 3713-3720 10.1021/ct100494z
71. Neale, C.; Madill, C.; Rauscher, S.; Pomès, R. Accelerating Convergence in Molecular Dynamics Simulations of Solutes in Lipid Membranes by Conducting a Random Walk Along the Bilayer Normal J. Chem. Theory Comput. 2013, 9, 3686-3703 10.1021/ct301005b
72. Türkcan, S.; Alexandrou, A.; Masson, J.-B. a Bayesian Inference Scheme to Extract Diffusivity and Potential Fields from Confined Single-Molecule Trajectories Biophys. J. 2012, 102, 2288-2298 10.1016/j.bpj.2012.01.063
73. Comer, J.; Chipot, C.; González-Nilo, F. D. Calculating Position-Dependent Diffusivity in Biased Molecular Dynamics Simulations J. Chem. Theory Comput. 2013, 9, 876-882 10.1021/ct300867e
74. Dorairaj, S.; Allen, T. W. on the Thermodynamic Stability of a Charged Arginine Side Chain in a Transmembrane Helix Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 4943-4948 10.1073/pnas.0610470104
75. Chowdhary, J.; Harder, E.; Lopes, P. E. M.; Huang, L.; MacKerell, A. D., Jr.; Roux, B. A Polarizable Force Field of Dipalmitoylphosphatidylcholine Based on the Classical Drude Model for Molecular Dynamics Simulations of Lipids J. Phys. Chem. B 2013, 117, 9142-9160 10.1021/jp402860e
76. Wang, L.-P.; Head-Gordon, T.; Ponder, J. W.; Ren, P.; Chodera, J. D.; Eastman, P. K.; Martinez, T. J.; Pande, V. S. Systematic Improvement of a Classical Molecular Model of Water J. Phys. Chem. B 2013, 117, 9956-9972 10.1021/jp403802c
77. Orsi, M.; Essex, J. W. Permeability of Drugs and Hormones Through a Lipid Bilayer: Insights from Dual-Resolution Molecular Dynamics Soft Matter 2010, 6, 3797-3808 10.1039/c0sm00136h
78. Comer, J.; Schulten, K.; Chipot, C. Diffusive Models of Membrane Permeation with Explicit Orientational Freedom J. Chem. Theory Comput. 2014, 10, 2710-2718 10.1021/ct500209j
79. Kulkarni, A. S.; Hopfinger, A. J. Membrane-Interaction QSAR Analysis: Application to the Estimation of Eye Irritation by Organic Compounds Pharm. Res. 1999, 16, 1245-1253 10.1023/A:1014853731428
80. Tseng, Y. J.; Hopfinger, A. J.; Esposito, E. X. The Great Descriptor Melting Pot: Mixing Descriptors for the Common Good of QSAR Models J. Comput.-Aided Mol. Des. 2012, 26, 39-43 10.1007/s10822-011-9511-4
81. Wu, E. L.; Cheng, X.; Jo, S.; Rui, H.; Song, K. C.; Dávila-Contreras, E. M.; Qi, Y.; Lee, J.; Monje-Galvan, V.; Venable, R. M.; Klauda, J. B.; Im, W. CHARMM-GUI Membrane Builder Toward Realistic Biological Membrane Simulations J. Comput. Chem. 2014, 35, 1997-2004 10.1002/jcc.23702
82. Hu, Y.; Ou, S.; Patel, S. Free Energetics of Arginine Permeation into Model DMPC Lipid Bilayers: Coupling of Effective Counterion Concentration and Lateral Bilayer Dimensions J. Phys. Chem. B 2013, 117, 11641-11653 10.1021/jp404829y
83. Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of Simple Potential Functions for Simulating Liquid Water J. Chem. Phys. 1983, 79, 926 10.1063/1.445869
84. Klauda, J. B.; Venable, R. M.; Freites, J. A.; O'Connor, J. W.; Tobias, D. J.; Mondragon-Ramirez, C.; Vorobyov, I.; MacKerell, A. D.; Pastor, R. W. Update of the CHARMM All-Atom Additive Force Field for Lipids: Validation on Six Lipid Types J. Phys. Chem. B 2010, 114, 7830-7843 10.1021/jp101759q
85. 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 10.1002/jcc.21367
86. Vanommeslaeghe, K.; Raman, E. P.; MacKerell, A. D. Automation of the CHARMM General Force Field (CGenFF) II: Assignment of Bonded Parameters and Partial Atomic Charges J. Chem. Inf. Model. 2012, 52, 3155-3168 10.1021/ci3003649
87. Vanommeslaeghe, K.; MacKerell, A. D. Automation of the CHARMM General Force Field (CGenFF) I: Bond Perception and Atom Typing J. Chem. Inf. Model. 2012, 52, 3144-3154 10.1021/ci300363c
88. Koopman, E. A.; Lowe, C. P. Advantages of a Lowe-Andersen Thermostat in Molecular Dynamics Simulations J. Chem. Phys. 2006, 124, 204103 10.1063/1.2198824
89. Lowe, C. P. an Alternative Approach to Dissipative Particle Dynamics Europhys. Lett. 1999, 47, 145-151 10.1209/epl/i1999-00365-x
90. Feller, S. E.; Zhang, Y.; Pastor, R. W.; Brooks, B. R. Constant Pressure Molecular Dynamics Simulation: The Langevin Piston Method J. Chem. Phys. 1995, 103, 4613 10.1063/1.470648
91. Miyamoto, S.; Kollman, P. A. Settle: An Analytical Version of the SHAKE and RATTLE Algorithm for Rigid Water Models J. Comput. Chem. 1992, 13, 952-962 10.1002/jcc.540130805
92. Darden, T.; York, D.; Pedersen, L. Particle Mesh Ewald: An Nlog(N) Method for Ewald Sums in Large Systems J. Chem. Phys. 1993, 98, 10089 10.1063/1.464397
93. Hénin, J.; Fiorin, G.; Chipot, C.; Klein, M. L. Exploring Multidimensional Free Energy Landscapes Using Time-Dependent Biases on Collective Variables J. Chem. Theory Comput. 2010, 6, 35-47 10.1021/ct9004432
94. Kumar, S.; Rosenberg, J. M.; Bouzida, D.; Swendsen, R. H.; Kollman, P. A. the Weighted Histogram Analysis Method for Free-Energy Calculations on Biomolecules. I. the Method J. Comput. Chem. 1992, 13, 1011-1021 10.1002/jcc.540130812
95. Tan, Z.; Gallicchio, E.; Lapelosa, M.; Levy, R. M. Theory of Binless Multi-State Free Energy Estimation with Applications to Protein-Ligand Binding J. Chem. Phys. 2012, 136, 144102 10.1063/1.3701175
96. Chodera, J. D.; Swope, W. C.; Pitera, J. W.; Seok, C.; Dill, K. A. Use of the Weighted Histogram Analysis Method for the Analysis of Simulated and Parallel Tempering Simulations J. Chem. Theory Comput. 2007, 3, 26-41 10.1021/ct0502864
97. Sugita, Y.; Okamoto, Y. Replica-Exchange Molecular Dynamics Method for Protein Folding Chem. Phys. Lett. 1999, 314, 141-151 10.1016/S0009-2614(99)01123-9
98. Minoukadeh, K.; Chipot, C.; Lelievre, T. Potential of Mean Force Calculations: A Multiple-Walker Adaptive Biasing Force Approach J. Chem. Theory Comput. 2010, 6, 1008-1017 10.1021/ct900524t
99. Comer, J.; Phillips, J. C.; Schulten, K.; Chipot, C. Multiple-Replica Strategies for Free-Energy Calculations in NAMD: Multiple-Walker Adaptive Biasing Force and Walker Selection Rules J. Chem. Theory Comput. 2014, 10, 5276-5285 10.1021/ct500874p