The ONIOM method: Its foundation and applications to metalloenzymes and photobiology

Wiley Interdisciplinary Reviews: Computational Molecular Science

Volumn 2, Issue 2, 2012, Pages 327-350

  Chung, Lung Wa ^a   Hirao, Hajime ^a   Li, Xin ^a   Morokuma, Keiji ^a,b  

^a KYOTO UNIVERSITY   (Japan)

^b EMORY UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84857095543     PISSN: 17590876     EISSN: 17590884     Source Type: Journal    
DOI: 10.1002/wcms.85     Document Type: Review

References (123)

1. van der Vaart A, Gogonea V, Dixon SL, Merz KM Jr. Linear scaling molecular orbital calculations of biological systems using the semiempirical divide and conquer method. J Comput Chem 2000, 21:1494-1504.
2. Warshel A, Levitt M. Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. J Mol Biol 1976, 103:227-249.
3. - exchange reaction and gas phase protonation of polyethers. J Comput Chem 1986, 7:718-730.
4. Field MJ, Bash PA, Karplus M. A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations. J Comput Chem 1990, 11:700-733.
5. Lin H, Truhlar DG. QM/MM: what have we learned, where are we, and where do we go from here? Theor Chem Acc 2007, 117:185-199.
6. Senn HM, Thiel W. QM/MM methods for biological systems. Top Curr Chem 2007, 268:173-290.
7. Hu H, Yang W. Free energies of chemical reactions in solution and in enzymes with ab initio quantum mechanics/molecular mechanics methods. Annu Rev Phys Chem 2008, 59:573-601.
8. Senn HM, Thiel W. QM/MM methods for biomolecular systems. Angew Chem Int Ed 2009, 48:1198-1229.
9. Maseras F, Morokuma K. IMOMM: a new integrated ab initio + molecular mechanics geometry optimization scheme of equilibrium structures and transition states. J Comput Chem 1995, 16:1170-1179.
10. -. J Chem Phys 1996, 105:1959-1967.
11. 2 oxidative addition. J Phys Chem 1996, 100:19357-19363.
12. Dapprich S, Komáromi I, Byun S, Morokuma K, Frisch MJ. A new ONIOM implementation in Gaussian98. Part I. The calculation of energies, gradients, vibrational frequencies and electric field derivatives. J Mol Struct (Theochem) 1999, 1:461-462.
13. Vreven T, Morokuma K. On the application of the IMOMO (Integrated Molecular Orbital + Molecular Orbital) method. J Comput Chem 2000, 21:1419-1432.
14. Karadakov PB, Morokuma K. ONIOM as an efficient tool for calculating NMR chemical shielding constants in large molecules. Chem Phys Lett 2000, 317:589-559.
15. Morokuma K, Musaev DG, Vreven T, Basch H, Torrent M, Khoroshun, DV. Model studies of the structures, reactivities, and reaction mechanisms of metalloenzymes IBM. J Res & Dev 2001, 45:367-395.
16. Vreven T, Mennucci B, da Silva CO, Morokuma K, Tomasi J. The ONIOM-PCM method: combining the hybrid molecular orbital method and the polarizable continuum model for solvation. Application to the geometry and properties of a merocyanine in solution. J Chem Phys 2001, 115:62-72.
17. Vreven T, Morokuma K, Farkas Ö, Schlegel HB, Frisch MJ. Geometry optimization with QM/MM, ONIOM and other combined methods. I. Microiterations and constraints. J Comput Chem 2003, 24:760-769.
18. Vreven T, Frisch MJ, Kudin KN, Schlegel HB, Morokuma K. Geometry optimization with QM/MM methods. II. Explicit quadratic coupling. Mol Phys 2006, 104:701-714.
19. Vreven T, Byun KS, Komáromi I, Dapprich S, Montgomery JA Jr, Morokuma K, Frisch MJ. Combining quantum mechanics methods with molecular mechanics methods in ONIOM. J Chem Theory Comput 2006, 2:815-826.
20. Vreven T, Morokuma K. Hybrid methods: ONIOM(QM:MM) and QM/MM. Annu Rep Comput Chem 2006, 2:35-51.
21. Li X, Chung LW, Morokuma K. Modeling photobiology using quantum mechanics (QM) and quantum mechanics/molecular mechanics (QM/MM) calculations. In: Reimers JR, ed. Computational Methods for Large Systems: Electronic Structure Approaches for Biotechnology and Nanotechnology. New York: John Wiley & Sons; 2010, 342-373.
22. Chung LW, Li X, Morokuma K. Modeling enzymatic reactions in metalloenzymes and photobiology by quantum mechanics (QM) and quantum mechanics/molecular mechanics (QM/MM) calculations. In: Matta CF, ed. Quantum Biochemistry. Weinheim: Wiley-VCH; 2010, 85-130.
23. (Accessed December 18, 2010).
24. Voth GA. Coarse-Graining of Condensed Phase and Biomolecular Systems. Boca Raton, FL: CRC Press; 2008.
25. Wanko M, Hoffmann M, Frauenheim T, Elstner M. Effect of polarization on the opsin shift in rhodopsins. 1. A combined QM/QM/MM model for bacteriorhodopsin and pharaonis sensory rhodopsin II. J Phys Chem B 2008, 112:11462-11467.
26. Byun K, Mo Y, Gao J. New insight on the origin of the unusual acidity of Meldrum's acid from ab initio and combined QM/MM simulation study. J Am Chem Soc 2001, 123:3974-3979.
27. Marti S, Moliner V, Tunon 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.
28. Liang W, Chapman CT, Frisch MJ, Li X. Geometry optimization with multilayer methods using least-squares minimization. J Chem Theory Comput 2010, 6:3352-3357.
29. Maeda S, Ohno K, Morokuma K. An automated and systematic transition structure explorer in large flexible molecular systems based on combined global reaction route mapping and microiteration methods. J Chem Theory Comput 2009, 5:2734-2743.
30. Vreven T, Morokuma K. Investigation of the S0-S1 excitation in bacteriorhodopsin with the ONIOM(MOMM) hybrid method. Theor Chem Acc 2003, 109:125-132.
31. Zheng G Lundberg M Jakowski J Vreven T Frisch MJ Morokuma K. Implementation and benchmark tests of the DFTB method and its application in the ONIOM method. Int J Quantum Chem 2009, 109:1841-1854.
32. Kawatsu T, Lundberg M, Morokuma K. Protein free energy corrections in ONIOM QM:MM modeling: a case study for isopenicillin n synthase (IPNS). J Chem Theory Comput 2011, 7:390.
33. Tao P, Fisher JF, Shi Q, Vreven T, Mobashery S, Schlegel HB. Matrix metalloproteinase 2 inhibition: combined quantum mechanics and molecular mechanics studies of the inhibition mechanism of (4-phenoxyphenyl-sulfonyl)methylthiirane and its oxirane analogue. Biochemistry 2009, 48:9839-9847.
34. Hayashi S, Ohmine I. Proton transfer in bacteriorhodopsin: structure, excitation, IR spectra, and potential energy surface analyses by an ab initio QM/MM method. J Phys Chem B 2000, 104:10678-10691.
35. Wang B, Truhlar DG. Combined quantum mechanical and molecular mechanical methods for calculating potential energy surfaces: tuned and balanced redistributed-charge algorithm. J Chem Theory Comput 2010, 6:359-369.
36. Mayhall NJ, Raghavachari K. Charge transfer across ONIOM QM:QM boundaries: the impact of model system preparation. J Chem Theory Comput 2010, 6:3131-3136.
37. Lin H, Truhlar DG. Redistributed charge and dipole schemes for combined quantum mechanical and molecular mechanical calculations. J Phys Chem A 2005, 109:3991-4004.
38. Sherwood P de Vries AH Collins SJ Greatbanks SP Burton NA Vincent MA Hillier IH. Computer simulation of zeolite structure and reactivity using embedded cluster methods. Faraday Discuss 1997, 106:79-92.
39. Hratchian HP, Parandekar PV, Raghavachari K, Frisch MJ, Vreven T. QM:QM electronic embedding using Mulliken atomic charges: energies and analytic gradients in an ONIOM framework. J Chem Phys 2008, 128:34107.
40. 1, 2 excitation energies of cyclic alkenes and enones. Chem Phys Lett 1996, 263:393-400.
41. 1 excited state photoisomerization path of a retinal protonated Schiff base. J Chem Phys 2000, 113:2969-2975.
42. Bearpark MJ, Larkin SM, Vreven T. Searching for conical intersections of potential energy surfaces with the ONIOM method: application to previtamin D. J Phys Chem A 2009, 112:7286-7295.
43. Caricato M, Vreven T, Trucks GW, Frisch MJ. Link atom bond length effect in ONIOM excited state calculations. J Chem Phys 2010, 133:054104.
44. Manuscript in preparation.
45. Hopkins BW, Tschumper GS. A Multicentered approach to integrated QM/QM calculations. Applications to multiply hydrogen bonded systems. J Comput Chem 2003, 24:1563-1568.
46. Tully JC. Molecular dynamics with electronic transitions. J Chem Phys 1990, 93:1061-1071.
47. Riccardi D Schaefer P Yang Y Yu HB Ghosh N Prat-Resina X König P Li G Xu D Guo H et al. Development of effective quantum mechanical/molecular mechanical (QM/MM) methods for complex biological processes. J Phys Chem B 2006, 110:6458-6469.
48. Rega N Iyengar SS Voth GA Schlegel HB Vreven T Frisch MJ. Hybrid ab-initio/empirical molecular dynamics: combining the ONIOM scheme with the atom-centered density matrix propagation (ADMP) approach. J Phys Chem B 2004, 108:4210-4220.
49. Car R, Parrinello M. Unified approach for molecular dynamics and density-functional theory. Phys Rev Lett 1985, 55:2471-2474.
50. Matsubara T, Dupuis M, Aida M. The ONIOM molecular dynamics method for biochemical applications: cytidine deaminase. Chem Phys Lett 2007, 437:138-142.
51. Sumner I, Iyengar SS. Combining quantum wavepacket ab initio molecular dynamics with QM/MM and QM/QM techniques: implementation blending ONIOM and empirical valence bond theory. J Chem Phys 2008, 129:054109.
52. Kerdcharoen T, Morokuma K. ONIOM-XS: an extension of the ONIOM method for molecular simulation in condensed phase. Chem Phys Lett 2002, 355:257-262.
53. Bulo RE, Ensing B, Sikkema J, Visscher L. Toward a practical method for adaptive QM/MM simulations. J Chem Theory Comput 2009, 5:2212-2221.
54. Li X, Chung LW, Mizuno H, Miyawaki A, Morokuma K. Primary events of photodynamics in reversible photoswitching fluorescent protein Dronpa. J Phys Chem Lett 2010, 1:3328-3333.
55. Li X, Chung LW, Mizuno H, Miyawaki A, Morokuma K. A theoretical study on the nature of on- and off-States of reversibly photoswitching fluorescent protein Dronpa: absorption, emission, protonation, and Raman. J Phys Chem B 2010, 114:1114-1126.
56. Bollinger JM Jr, Diao Y, Matthews ML, Xing G, Krebs C. myo-Inositol oxygenase: a radical new pathway for O2 and C-H activation at a nonheme diiron cluster. Dalton Trans 2009, 905-914.
57. Xing G Diao Y Hoffart LM Barr EW Prabhu KS Arner RJ Reddy CC Krebs C Bollinger JM Jr. Evidence for C-H cleavage by an iron-superoxide complex in the glycol cleavage reaction catalyzed by myo-inositol oxygenase. Proc Natl Acad Sci USA 2006, 103:6130-6135.
58. Hirao H, Morokuma K. Insights into the (superoxo)Fe(III)Fe(III) intermediate and reaction mechanism of myo-inositol oxygenase: DFT and ONIOM(DFT:MM) study. J Am Chem Soc 2009, 131:17206-17214.
59. Minor W, Steczko J, Stec B, Otwinowski Z, Bolin JT, Walter R, Axelrod B. Crystal structure of soybean lipoxygenase L-1 at 1.4 Å resolution. Biochemistry 1996, 35:10687-10701.
60. Tomchick DR, Phan P, Cymborowski M, Minor W, Holman TR. Structural and functional characterization of second-coordination sphere mutants of soybean lipoxygenase-1. Biochemistry 2001, 40:7509-7517.
61. Pavlosky MA, Solomon EI. Near-IR CD/MCD spectral elucidation of two forms of the non-heme active site in native ferrous soybean lipoxygenase-1: correlation to crystal structures and reactivity. J Am Chem Soc 1994, 116:11610-11611.
62. Pavlosky MA, Zhang Y, Westre TE, Gan QF, Pavel EG, Campochiaro C, Hedman B, Hodgson KO, Solomon EI. Near-infrared circular dichroism, magnetic circular dichroism, and X-ray absorption spectral comparison of the non-heme ferrous active sites of plant and mammalian 15-lipoxygenases. J Am Chem Soc 1995, 117:4316-4327.
63. Hirao H, Morokuma K. What is the real nature of ferrous soybean lipoxygenase-1? A new two-conformation model based on combined ONIOM(DFT:MM) and multireference configuration interaction characterization. J Phys Chem Lett 2010, 1:901-906.
64. Sugimoto H, Oda SI, Otsuki T, Hino T, Yoshida T, Shiro Y. Crystal structure of human indoleamine 2, 3-dioxygenase: catalytic mechanism of O2 incorporation by a heme-containing dioxygenase. Proc Natl Acad Sci USA 2006, 103:2611-2616.
65. Forouhar E, Anderson JLR, Mowat CG, Vorobiev SM, Hussain A, Abashidze M, Bruckmann C, Thackray SJ, Seetharaman J, Tucker T, et al. Molecular insights into substrate recognition and catalysis by tryptophan 2, 3-dioxygenase. Proc Natl Acad Sci USA 2007, 104:473-478.
66. Chung LW, Li X, Sugimoto H, Shiro Y, Morokuma K. Density functional theory study on a missing piece in understanding of heme chemistry: the reaction mechanism for indoleamine 2, 3-dioxygenase and tryptophan 2, 3-dioxygenase. J Am Chem Soc 2008, 130:12298-12309.
67. Chung LW, Li X, Sugimoto H, Shiro Y, Morokuma K. ONIOM study on a missing piece in our understanding of heme chemistry: bacterial tryptophan 2, 3-dioxygenase with dual oxidants. J Am Chem Soc 2010, 132:11993-12005.
68. Chauhan N, Thackray SJ, Rafice SA, Eaton G, Lee M, Efimov I, Basran J, Jenkins PR, Mowat CG, Chapman SK, et al. Reassessment of the reaction mechanism in the heme dioxygenases. J Am Chem Soc 2009, 131:4186-4187.
69. Lewis-Ballester A, Batabyal D, Egawa T, Lu C, Lin Y, Marti MA, Capece L, Estrin DA, Yeh SR. Evidence for a ferryl intermediate in a heme-based dioxygenase. Proc Natl Acad Sci USA 2009, 106:17371-17376.
70. Banerjee R. Radical carbon skeleton rearrangements: catalysis by coenzyme B12-dependent mutases. Chem Rev 2003, 103:2083-2094.
71. Jensen KP, Ryde U. How the Co-C bond is cleaved in coenzyme B12 enzymes: a theoretical study. J Am Chem Soc 2005, 127:9117-9128.
72. Kozlowski PM, Kamachi T, Toraya T, Yoshizawa K. Does Cob(II)alamin act as a conductor in coenzyme B12 dependent mutases? Angew Chem Int Ed 2007, 46:980-983.
73. Sharma PK, Chu ZT, Olsson MHM, Warshel A. A new paradigm for electrostatic catalysis of radical reactions in vitamin B12 enzymes. Proc Natl Acad Sci USA 2007, 104:9661-9666.
74. Li X, Chung LW, Paneth P, Morokuma K. DFT and ONIOM(DFT:MM) studies on Co-C bond cleavage and hydrogen transfer in B12-dependent methylmalonyl-CoA mutase. Stepwise or concerted mechanism. J Am Chem Soc 2009, 131:5115-5125.
75. Kwiecien RA, Khavrutskii IV, Musaev DG, Morokuma K, Banerjee R, Paneth P. Computational insights into the mechanism of radical generation in B12-dependent methylmalonyl-CoA mutase. J Am Chem Soc 2006, 128:1287-1292.
76. N2 reaction at nitrogen: the effect of explicitly including solvent polarization. J Chem Theory Comput 2007, 3:1499-1409.
77. Gascon JA, Leung SFS, Batista ER, Batista VS. A self-consistent space-domain decomposition method for QM/MM computations of protein electrostatic potentials. J Chem Theory Comput 2006, 2:175-186.
78. Zhang Y, Lin H, Truhlar DG. Self-consistent polarization of the boundary in the redistributed charge and dipole scheme for combined quantum mechanical and molecular mechanical calculations. J Chem Theory Comput 2007, 3:1378-1398.
79. Morokuma K, Wang Q, Vreven T. Performance evaluation of the three-layer ONIOM method: case study for a zwitterionic peptide. J Chem Theory Comput 2006, 2:1317-1324.
80. Torrent M, Vreven T, Musaev DG, Morokuma K. Effects of the protein environment on the structure and energetics of active sites of metalloenzymes. oniom study of methane monooxygenase and ribonucleotide reductase. J Am Chem Soc 2002, 124:192-193.
81. Zheng G, Witek HA, Bobadova-Parvanova P, Irle S, Musaev DG, Prabhakar R, Morokuma K. Parameter calibration of transition-metal elements for the spin-polarized self-consistent-charge density-functional tight-binding (DFTB) Method: Sc, Ti, Fe, Co, and Ni. J Chem Theory Comput 2007, 3:1349-1367.
82. Lundberg M, Sasakura Y, Zheng G, Morokuma K. Case studies of ONIOM(DFT:DFTB) and ONIOM(DFT:DFTB:MM) for enzymes and enzyme mimics. J Chem Theory Comput 2010, 6:1413-1427.
83. Shaner NC, Patterson GH, Davidson MW. Advances in fluorescent protein technology. J Cell Sci 2007, 120:4247-4260.
84. Ando R, Mizuno H, Miyawaki A. Regulated fast nucleocytoplasmic shuttling observed by reversible protein highlighting. Science 2004, 306:1370-1373.
85. Ando R, Hama H, Yamamoto-Hino M, Mizuno H, Miyawaki A. An optical marker based on the UV-induced green-to-red photoconversion of a fluorescent protein. Proc Natl Acad Sci USA 2002, 99:12651-12656.
86. Mizuno H, Mal TK, Wälchli M, Kikuchi A, Fukano T, Ando R, Jeyakanthan J, Taka J, Shiro Y, Ikura M, et al. Light-dependent regulation of structural flexibility in a photochromic fluorescent protein. Proc Natl Acad Sci USA 2008, 105:9927-9932.
87. Andresen M, Stiel AC, Trowitzsch S, Weber G, Eggeling C, Wahl MC, Hell SW, Jakobs S. Structural basis for reversible photoswitching in Dronpa. Proc Natl Acad Sci USA 2007, 104:13005-13009.
88. Schäfer LV, Groenhof G, Boggio-Pasqua M, Robb MA, Grubmüller H. Protein environment controls photoswitching of the asFP595 chromophore. PLoS Comput Biol 2008, 4:e1000034.
89. Li X, Chung LW, Mizuno H, Miyawaki A, Morokuma K. Competitive mechanistic pathways for green-to-red photoconversion in the fluorescent protein Kaede: a computational study. J Phys Chem B 2010, 114:16666-16675.
90. Hoffmann M, Wanko M, Strodel P, König PH, Frauenheim T, Schulten K, Thiel W, Tajkhorshid E, Elstner M. et al. Color tuning in rhodopsins: the mechanism for the spectral shift between bacteriorhodopsin and sensory rhodopsin II. J Am Chem Soc 2006, 128:10808-10818.
91. Altun A, Yokoyama S, Morokuma K. Mechanism of spectral tuning going from retinal in vacuo to bovine rhodopsin and its mutants: multireference ab initio quantum mechanics/molecular mechanics studies. J Phys Chem B 2008, 112:16883-16890.
92. q-coupled GPCR-insights from structural and spectral tuning studies on squid rhodopsin. Chem Eur J 2010, 16:1744-1749.
93. Gascón A, Sproviero EM, Batista VS. Computational studies of the primary phototransduction event in visual rhodopsin. Acc Chem Res 2006, 39:39-184.
94. Hayashi S, Tajkhorshid E, Schulten K. Photochemical reaction dynamics of the primary event of vision studied by means of a hybrid molecular simulation. Biophys J 2009, 96:403-416.
95. Polli D, Altoè P, Weingart O, Spillane KM, Manzoni C, Brida D, Tomasello G, Orlandi G, Kukura P, Mathies RA, et al. Conical intersection dynamics of the primary photoisomerization event in vision. Nature 2010, 467:440-443.
96. Tao P, Schlegel HB. A toolkit to assist ONIOM calculations. J Comput Chem 2010, 31:2363-2369.
97. Hratchian HP, Frisch MJ. Integrating steepest-descent reaction pathways for large molecules. J Chem Phys 2011, 134:204103.
98. Ochsenfeld C, Kussmann J, Lambrecht DS. Linear-scaling methods in quantum chemistry. Rev Comput Chem 2007, 23:1-82.
99. Werner H-J, Pflüger K. On the selection of domains and orbital pairs in local correlation treatments. Annu Rep Comput Chem 2006, 2:53-80.
100. Weigend F, Kattannek M, Ahlrichs R. Approximated electron repulsion integrals: Cholesky decomposition versus resolution of the identity methods. J Chem Phys 2009, 130:164106.
101. Chan GKL, Zgid D. The density matrix renormalization group in quantum chemistry. Annu Rep Comput Chem 2009, 5:149-162.
102. Stewart JJP. Optimization of parameters for semiempirical methods V: modification of NDDO approximations and application to 70 elements. J Mol Model 2007, 13:1173-1213.
103. Repasky MP, Chandrasekhar J, Jorgensen WL. DDG/PM3 and PDDG/MNDO: improved semiempirical methods. J Comput Chem 2002, 23:1601-1622.
104. Silva-Junior MR, Thiel W. Benchmark of electronically excited states for semiempirical methods: MNDO, AM1, PM3, OM1, OM2, OM3, INDO/S, and INDO/S2. J Chem Theory Comput 2010, 6:1546-1564.
105. Ufimtsev IS, Martínez TJ. Quantum chemistry on graphical processing units. 1. Strategies for two-electron integral evaluation. J Chem Theory Comput 2008, 4:222-231.
106. 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.
107. Sugita Y, Okamoto Y. Replica-exchange molecular dynamics method for protein folding. Chem Phys Lett 1999, 314:141-151.
108. Laio A, Parrinello M. Escaping free-energy minima. Proc Natl Acad Sci USA 2002, 99:12562-12566.
109. Siegel JB, Zanghellini A, Lovick HM, Kiss G, Lambert AR, St Clair JL, Gallaher JL, Hilvert D, Gelb MH, Stoddard BL, et al. Computational design of an enzyme catalyst for a stereoselective bimolecular Diels-Alder reaction. Science 2010, 329:309-313.
110. Ananikov VP, Musaev DG, Morokuma K. Real size of ligands, substrates and catalysts: studies of structure, reactivity and selectivily by ONIOM and other hybrid computational approaches. J Mol Catal A 2010, 24:104-119.
111. Lundberg M, Morokuma K. Determining transition states in bioinorganic reactions. In: Solomon EI, King RB, Scott RA, eds. Computational Inorganic and Bioinorganic Chemistry. Chichester: John Wiley & Sons; 2009, 17-31.
112. (Accessed December 18, 2010).
113. Clemente F, Vreven T, Frisch MJ. Getting the most out of ONIOM: guidelines and pitfalls. In: Matta C, ed. Quantum Biochemistry. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA; 2008, 61-83.
114. Hu H, Yang WT. Development and application of ab initio QM/MM methods for mechanistic simulation of reactions in solution and in enzymes. J Mol Struct (Theochem) 2009, 898:17-30.
115. Friesner RA, Guallar V. Ab initio quantum chemical and mixed quantum mechanics/molecular mechanics (QM/MM) methods for studying enzymatic catalysis. Annu Rev Phys Chem 2005, 56:389-427.
116. Garcia-Viloca M, Gao J, Karplus M, Truhlar DG. How enzymes work: analysis by modern rate theory and computer simulations. Science 2004, 303:186-195.
117. Gao J, Truhlar DG. Quantum mechanical methods for enzyme kinetics. Annu Rev Phys Chem 2002, 53:467-505.
118. Monard G, Merz KM Jr. Combined quantum mechanical/molecular mechanical methodologies applied to biomolecular systems. Acc Chem Res 1999, 32:904-911.
119. Warshel A. Computer simulations of enzyme catalysis. Annu Rev Biophys Biomol Struct 2003, 32:425-443.
120. Shaik S, Kumar D, de Visser SP, Altun A, Thiel W. A theoretical perspective on structure and mechanism of cytochrome p450 enzymes. Chem Rev 2005, 105:2279-2328.
121. Siegbahn PEM, Borowski T. Modeling enzymatic reactions involving transition metals. Acc Chem Res 2006, 39:729-738.
122. Robb MA, Garavelli M, Olivucci M, Bernardi F. A computational strategy for organic photochemistry. Rev Comput Chem 2000, 15:87-146.
123. Hu L, Söderhjelm P, Ryde U. On the convergence of QM/MM energies. J Chem Theory Comput 2011, 7:761-777.