Hybrid quantum and classical methods for computing kinetic isotope effects of chemical reactions in solutions and in enzymes

Methods in Molecular Biology

Volumn 443, Issue , 2008, Pages 37-62

  Gao, Jiali ^a   Major, Dan T ^a   Fan, Yao ^a   Lin, Yen Lin ^a   Ma, Shuhua ^a   Wong, Kin Yiu ^a  

^a University of Minnesota

Author keywords

Combined QM MM; Dual level potential; Enzyme kinetics; Kinetic isotope effects; Path integral simulations; PI FEP UM; Solvent effects

Indexed keywords

EID: 84934437616     PISSN: 10643745     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-1-59745-177-2_3     Document Type: Article

References (128)

1. Sumner, J. B. (1926) "THE ISOLATION AND CRYSTALLIZATION OF THE ENZYME UREASE. PRELIMINARY PAPER," J. Biol. Chem. 69, 435-441.
2. Pauling, L. (1946) "Molecular architecture and biological reactions," Chem. Eng. News 24, 1375.
3. Schowen, R. L. (1978) in Transition States of Biochemical Processes (Gandour, R. D., and Schowen, R. L., Eds.) pp 77-114, Plenum Press, New York.
4. Gao, J., Ma, S., Major, D. T, Nam, K., Pu, J., and Truhlar, D. G. (2006) "Mechanisms and free energies of enzymatic reactions," Chem. Rev. 106, 3188-3209.
5. Garcia-Viloca, M., Gao, J., Karplus, M., and Truhlar, D. G. (2004) "How enzymes work: Analysis by modern rate theory and computer simulations," Science 303, 186-195.
6. Villa, J. and Warshel, A. (2001) "Energetics and dynamics of enzymatic reactions," J. Phys. Chem. B 105, 7887-7907.
7. Gao, J. and Truhlar, D. G. (2002) "Quantum mechanical methods for enzyme kinetics," Ann. Rev. Phys. Chem. 53, 467-505.
8. Pu, J., Gao, J., and Truhlar, D. G. (2006) "Multidimensional tunneling, recrossing, and the transmission coefficient for enzymatic reactions," Chem. Rev. 106, 3140-3169.
9. Wolfenden, R. and Snider, M. J. (2001) "The depth of chemical time and the power of enzymes as catalysts," Acc. Chem. Res. 34, 938-945.
10. Snider, M. G., Temple, B. S., and Wolfenden, R. (2004) "The path to the transition state in enzyme reactions: A survey of catalytic efficiencies," J. Phys. Org. Chem. 17, 586-591.
11. Truhlar, D. G., Garrett, B. C., and Klippenstein, S. J. (1996) "Current status of transition-state theory," J. Phys. Chem. 100, 12771-12800.
12. Fernandez-Ramos, A., Miller, J. A., Klippenstein, S. J., and Truhlar, D. G. (2006) "Modeling the kinetics of bimolecular reactions," Chem. Rev. 106, 4518-4584.
13. Bennett, C. H. (1977) "Molecular dynamics and transition state theory: the simulation of infrequent events," ACS Symp. Ser. 46, 63-97.
14. Chandler, D. (1978) "Statistical mechanics of isomerization dynamics in liquids and the transition state approximation," J. Chem. Phys. 68, 2959-2970.
15. Neria, E. and Karplus, M. (1997) "Molecular dynamics of an enzyme reaction: proton transfer in TIM," Chem. Phys. Lett. 267, 26-30.
16. Nam, K., Prat-Resina, X., Garcia-Viloca, M., Devi-Kesavan, L. S., and Gao, J. (2004) "Dynamics of an enzymatic substitution reaction in haloalkane dehalogenase," J. Am. Chem. Soc. 126, 1369-1376.
17. Voth, G. A. and Hochstrasser, R. M. (1996) "Transition state dynamics and relaxation processes in solutions: a frontier of physical chemistry," J. Phys. Chem. 100, 13034-13049.
18. Alhambra, C, Corchado, J., Sanchez, M. L., Garcia-Viloca, M., Gao, J., and Truhlar, D. G. (2001) "Canonical variational theory for enzyme kinetics with the protein mean force and multidimensional quantum mechanical tunneling dynamics. Theory and application to liver alcohol dehydrogenase," J. Phys. Chem. B 105, 11326-11340.
19. Valleau, J. R and Torrie, G. M. (1977) in Modern Theoretical Chemistry (Berne, B. J., Ed.) pp 169-194, Plenum, New York.
20. Jorgensen, W. L. (1989) "Free energy calculations: a breakthrough for modeling organic chemistry in solution," Acc. Chem. Res. 22, 184-189.
21. Hwang, J. K., King, G., Creighton, S., and Warshel, A. (1988) "Simulation of free energy relationships and dynamics of SN2 reactions in aqueous solution," J. Am. Chem. Soc. 110, 5297-5311.
22. Gertner, B. J., Bergsma, J. P., Wilson, K. R., Lee, S., and Hynes, J. T. (1987) "Nonadiabatic solvation model for SN2 reactions in polar solvents," J. Chem. Phys. 86, 1377-1386.
23. Gao, J. (1996) "Hybrid quantum mechanical/molecular mechanical simulations: an alternative avenue to solvent effects in organic chemistry," Acc. Chem. Res. 29, 298-305.
24. Muller, R. P. and Warshel, A. (1995) "Ab initio calculations of free energy barriers for chemical reactions in solution," J. Phys. Chem. 99, 17516-17524.
25. Mo, Y. and Gao, J. (2000) "Ab initio QM/MM simulations with a molecular orbital-valence bond (MOVB) method: application to an SN2 reaction in water," J. Comput. Chem. 21, 1458-1469.
26. Truhlar, D. G. and Garrett, B. C. (2000) "Multidimensional transition state theory and the validity of Grote-Hynes theory," J. Phys. Chem. B 104, 1069-1072.
27. Truhlar, D. G., Gao, J., Alhambra, C., Garcia-Viloca, M., Corchado, J., Sanchez, M. L., and Villa, J. (2002) "The incorporation of quantum effects in enzyme kinetics modeling," Acc. Chem. Res. 35, 341-349.
28. MacKerell, A. D., Jr., Bashford, D., Bellott, M., Dunbrack, R. L., 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. C, Stote, R., Straub, J., Watanabe, M., Wiorkiewicz-Kuczera, J., Yin, D., and Karplus, M. (1998) "All-atom empirical potential for molecular modeling and dynamics studies of proteins," J. Phys. Chem. B 102, 3586-3616.
29. Ponder, J. W. and Case, D. A. (2003) "Advances in Protein Chemisty", edited by V. Daggett, QM/MM and related approaches, Adv. Protein Chem. 66, 27-85.
30. Gao, J. and Xia, X. (1992) "A prior evaluation of aqueous polarization effects through Monte Carlo QM-MM simulations," Science 258, 631-635.
31. Gao, J. (1995) in Rev. Comput. Chem. (Lipkowitz, K. B., and Boyd, D. B., Eds.) Methods and applications of combined QM/MM methods, pp 119-185, VCH, New York.
32. Chandrasekhar, J., Smith, S. F, and Jorgensen, W. L. (1984) "SN2 reaction profiles in the gas phase and aqueous solution," J. Am. Chem. Soc. 106, 3049-3050.
33. Gao, J. (1991) "A priori computation of a solvent-enhanced SN2 reaction profile in water: the Menshutkin reaction," J. Am. Chem. Soc. 113, 7796-7797.
34. Donini, O., Darden, T, and Kollman, P. A. (2000) "QM-FE calculations of aliphatic hydrogen abstraction in citrate synthase and in solution: reproduction of the effect of enzyme catalysis and demonstration that an enolate rather than an enol is formed," J. Am. Chem. Soc. 122, 12270-12280.
35. Zhang, Y. K., Liu, H. Y., and Yang, W. T. (2000) "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. 112, 3483-3492.
36. Liu, H., Lu, Z., Cisneros, G. A., and Yang, W. (2004) "Parallel iterative reaction path optimization in ab initio quantum mechanical/molecular mechanical modeling of enzyme reactions," J. Chem. Phys. 121, 697-706.
37. Warshel, A. and Weiss, R. M. (1980) "An empirical valence bond approach for comparing reactions in solutions and in enzymes," J. Am. Chem. Soc. 102, 6218-6226.
38. Warshel, A. (1991) Computer Modeling of Chemical Reactions in Enzymes and Solutions, Wiley, New York.
39. Aaqvist, J., Fothergill, M., and Warshel, A. (1993) "Computer simulation of the carbon dioxide/bicarbonate interconversion step in human carbonic anhydrase I," J. Am. Chem. Soc. 115, 631-635.
40. Kim, Y., Corchado, J. C., Villa, J., Xing, J., and Truhlar, D. G. (2000) "Multiconfiguration molecular mechanics algorithm for potential energy surfaces of chemical reactions," J. Chem. Phys. 112, 2718-2735.
41. Olsson, M. H. M. and Warshel, A. (2004) "Solute solvent dynamics and energetics in enzyme catalysis: the SN2 reaction of dehalogenase as a general benchmark," J. Am. Chem. Soc. 126, 15167-15179.
42. Warshel, A. (2003) "Computer simulations of enzyme catalysis: Methods, progress, and insights," Ann. Rev. Biophys. Biomol. Struct. 32, 425-443.
43. Aqvist, J. and Warshel, A. (1993) "Simulation of enzyme reactions using valence bond force fields and other hybrid quantum/classical approaches," Chem. Rev. 93, 2523-2544.
44. Warshel, A., Sharma, P. K., Kato, M., Xiang, Y, Liu, H., and Olsson, M. H. M. (2006) "Electrostatic basis for enzyme catalysis," Chem. Rev. 106, 3210-3235.
45. Mo, Y., Zhang, Y., and Gao, J. (1999) "A simple electrostatic model for trisilylamine: theoretical examinations of the n→ sigma. Negative hyperconjugation, p.pi.→d.pi. bonding, and stereoelectronic interaction," J. Am. Chem. Soc. 121, 5737-5742.
46. Mo, Y. and Gao, J. (2000) "An ab initio molecular orbital-valence bond (MOVB) method for simulating chemical reactions in solution," J. Phys. Chem. A 104, 3012-3020.
47. Gao, J. and Mo, Y. (2000) "Simulation of chemical reactions in solution using an ab initio molecular orbital-valence bond model," Prog. Theor. Chem. Phys. 5, 247-268.
48. Gao, J., Garcia-Viloca, M., Poulsen, T. D., and Mo, Y (2003) "Solvent effects, reaction coordinates, and reorganization energies on nucleophilic substitution reactions in aqueous solution," Adv. Phys. Org. Chem. 38, 161-181.
49. Albu, T. V., Corchado, J. C., and Truhlar, D. G. (2001) "Molecular mechanics for chemical reactions: a standard strategy for using multiconfiguration molecular mechanics for variational transition state theory with optimized multidimensional tunneling," J. Phys. Chem. A 105, 8465-8487.
50. Liu, H., Elstner, M., Kaxiras, E., Fraunheim, T., Hermans, J., and Yang, W. (2001) "Quantum mechanics simulation of protein dynamics on long timescale," Proteins: Struct., Funct. Gen. 44, 484-489.
51. Monard, G. and Merz, K. M., Jr. (1999) "Combined quantum mechanical/molecular mechanical methodologies applied to biomolecular systems," Acc. Chem. Res. 32, 904-911.
52. Car, R. and Parrinello, M. (1985) "Unified approach for molecular dynamics and density-functional theory," Phys. Rev. Lett. 55, 2471-2474.
53. Tuckerman, M. E., Laasonen, K., Sprik, M., and Parrinello, M. (1994) "Ab initio simulations of water and water ions," J. Phys.: Conden. Matter 6, A93-A100.
54. Sprik, M., Hutter, J., and Parrinello, M. (1996) "Ab initio molecular dynamics simulation of liquid water: comparison of three gradient-corrected density functionals," J. Chem. Phys. 105, 1142-1152.
55. Rothlisberger, U., Carloni, P., Doclo, K., and Parrinello, M. (2000) "A comparative study of galactose oxidase and active site analogs based on QM/MM Car-Parrinello simulations," J Biol Inorg Chem 5, 236-250.
56. Rohrig, U. F, Guidoni, L., and Rothlisberger, U. (2005) Chem Phys Chem 6, 1836.
57. York, D. M., Lee, T.-S., and Yang, W. (1998) "Quantum mechanical treatment of biological macromolecules in solution using linear-scaling electronic structure methods," Phys. Rev. Lett. 80, 5011-5014.
58. Titmuss, S. J., Cummins, P. L., Rendell, A. P., Bliznyuk, A. A., and Gready, J. E. (2002) "Comparison of linear-scaling semiempirical methods and combined quantum mechanical/molecular mechanical methods for enzymic reactions. II. An energy decomposition analysis," J. Comput. Chem. 23, 1314-1322.
59. Van der Vaart, A. and Merz, K. M., Jr. (1999) "The role of polarization and charge transfer in the solvation of biomolecules," J. Am. Chem. Soc. 121, 9182-9190.
60. Stewart, J. J. P. (1996) "Application of localized molecular orbitais to the solution of semiempirical self-consistent field equations," Int. J. Quantum Chem. 58, 133-146.
61. Gao, J. and Thompson, M. A. (1998) Combined Quantum Mechanical and Molecular Mechanical Methods, Vol. 712, American Chemical Society, Washington, DC.
62. Warshel, A. and Levitt, M. (1976) "Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme," J. Mol. Biol. 103, 227-249.
63. Singh, U. C. and Kollman, P. A. (1986) "A combined ab initio quantum mechanical and molecular mechanical method for carrying out simulations on complex molecular systems: applications to the CH3C1 + Cl-exchange reaction and gas phase protonation of polyenes.," J. Comput. Chem. 7, 718-730.
64. Tapia, O., Lluch, J. M., Cardenas, R., and Andres, J. (1989) "Theoretical study of solvation effects on chemical reactions. A combined quantum chemical/Monte Carlo study of the Meyer-Schuster reaction mechanism in water," J. Am. Chem. Soc. 111, 829-835.
65. Field, M. J., Bash, P., A., and Karplus, M. (1990) "A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations," J. Comput. Chem. 11, 700-733.
66. Gao, J. (1992) "Absolute free energy of solvation from Monte Carlo simulations using combined quantum and molecular mechanical potentials," J. Phys. Chem. 96, 537-540.
67. Stanton, R. V, Hartsough, D. S., and Merz, K. M., Jr. (1993) "Calculation of solvation free energies using a density functional/molecular dynamics coupled potential," J. Phys. Chem. 97, 11868-11870.
68. Freindorf, M. and Gao, J. (1996) "Optimization of the Lennard-Jones parameters for a combined ab initio quantum mechanical and molecular mechanical potential using the 3-21G basis set.," J. Comput. Chem. 17, 386-395.
69. Hillier, I. H. (1999) "Chemical reactivity studied by hybrid QM/MM methods," Theochem 463, 45-52.
70. Morokuma, K. (2002) Phil. Trans. Roy. Soc. London, Ser. A 360, 1149.
71. Warshel, A. and Karplus, M. (1972) "Calculation of ground and excited state potential surfaces of conjugated molecules. I. Formulation and parametrization," J. Amer. Chem. Soc. 94, 5612-5625.
72. Bash, P. A., Field, M. J., and Karplus, M. (1987) "Free energy perturbation method for chemical reactions in the condensed phase: a dynamic approach based on a combined quantum and molecular mechanics potential," J. Am. Chem. Soc. 109, 8092-8094.
73. Gao, J. (1995) "An automated procedure for simulating chemical reactions in solution. Application to the decarboxylation of 3-carboxybenzisoxazole in water," J. Am. Chem. Soc. 117, 8600-8607.
74. Wu, N., Mo, Y, Gao, J., and Pai, E. F. (2000) "Electrostatic stress in catalysis: structure and mechanism of the enzyme orotidine monophosphate decarboxylase," Proc. Natl. Acad. Sci. U.S.A. 97, 2017-2022.
75. Gao, J. (1994) "Computation of intermolecular interactions with a combined quantum mechanical and classical approach," ACS Symp. Ser. 569, 8-21.
76. Dewar, M. J. S., Zoebisch, E. G., Healy, E. F, and Stewart, J. J. P. (1985) "Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model," J. Am. Chem. Soc. 107, 3902-3909.
77. Stewart, J. J. P. (1989) "Optimization of parameters for semiempirical methods I. Method," J. Comp. Chem. 10, 209-220.
78. Orozco, M., Luque, F. J., Habibollahzadeh, D., and Gao, J. (1995) "The polarization contribution to the free energy of hydration. [Erratum to document cited in CA122:299891]," J. Chem. Phys. 103, 9112.
79. Major, D. T., York, D. M., and Gao, J. (2005) "Solvent polarization and kinetic isotope effects in nitroethane deprotonation and implications to the nitroalkane oxidase reaction," J. Am. Chem. Soc. 127, 16374-16375.
80. Gao, J. (1994) "Monte Carlo quantum mechanical-configuration interaction and molecular mechanics simulation of solvent effects on the n → pi.* blue shift of acetone," J. Am. Chem. Soc. 116, 9324-9328.
81. Gao, J. and Byun, K. (1997) "Solvent effects on the n → pi* transition of pyrimidine in aqueous solution," Theor. Chem. Acc. 96, 151-156.
82. Garcia-Viloca, M., Truhlar, D. G., and Gao, J. (2003) "Importance of substrate and cofactor polarization in the active site of dihydrofolate reductase," J. Mol. Biol. 327, 549-560.
83. Byun, K., Mo, Y, and Gao, J. (2001) "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. 123, 3974-3979.
84. Maseras, F. and Morokuma, K. (1995) "IMOMM: a new integrated ab initio + molecular mechanics geometry optimization scheme of equilibrium structures and transition states," J. Comput. Chem. 16, 1170-1179.
85. Mulholland, A. J. (2001) "The QM/MM approach to enzymatic reactions," Theor. Comput. Chem. 9, 597-653.
86. Zwanzig, R. (1954) "High-temperature equation of state by a perturbation method. I. Nonpolar gases," J. Chem. Phys. 22, 1420-1426.
87. Jorgensen, W. L. and Ravimohan, C. (1985) "Monte Carlo simulation of differences in free energies of hydration," J. Chem. Phys. 83, 3050-3054.
88. Kollman, P. (1993) "Free energy calculations: Applications to chemical and biochemical phenomena," Chem. Rev. 93, 2395-2417.
89. Simonson, T. (2001) in Computational Biochemistry and Biophysics (Becker, O. M., MacKerell, A. D., Jr., Roux, B., and Watanabe, M., Eds.) pp. 169-197. Dekker, New York.
90. Espinosa-Garcia, J., Corchado, J. C., and Truhlar, D. G. (1997) "importance of quantum effects for C-H bond activation reactions," J. Am. Chem. Soc. 119, 9891-9896.
91. Alhambra, C., Gao, J., Corchado, J. C., Villa, J., and Truhlar, D. G. (1999) "Quantum mechanical dynamical effects in an enzyme-catalyzed proton transfer reaction," J. Am. Chem. Soc. 121, 2253-2258.
92. Billeter, S. R., Webb, S. P., Iordanov, T., Agarwal, P. K., and Hammes-Schiffer, S. (2001) "Hybrid approach for including electronic and nuclear quantum effects in molecular dynamics simulations of hydrogen transfer reactions in enzymes," J. Chem. Phys. 114, 6925-6936.
93. Garcia-Viloca, M., Alhambra, C., Truhlar, D. G., and Gao, J. (2001) "Inclusion of quantum-mechanical vibrational energy in reactive potentials of mean force," J. Chem. Phys. 114, 9953-9958.
94. Hammes-Schiffer, S. (1998) "Mixed quantum/classical dynamics of hydrogen transfer reactions," J. Phys. Chem. A 102, 10443-10454.
95. Webb, S. P. and Hammes-Schiffer, S. (2000) "Fourier grid Hamiltonian multiconfigurational self-consistent-field: A method to calculate multidimensional hydrogen vibrational wavefunctions," J. Chem. Phys. 113, 5214-5227.
96. Alhambra, C., Corchado, J., Sanchez, M. L., Gao, J., and Truhlar, D. G. (2000) "Quantum dynamics of hydride transfer in enzyme catalysis," J. Am. Chem. Soc. 122, 8197-8203.
97. Hwang, J.-K. and Warshel, A. (1996) "How important are quantum mechanical nuclear motions in enzyme catalysis?," J. Am. Chem. Soc. 118, 11745-11751.
98. Liu, Y. P., Lynch, G. C., Truong, T. N., Lu, D. H., Truhlar, D. G., and Garrett, B. C. (1993) "Molecular modeling of the kinetic isotope effect for the [1,5]-sigmatropic rearrangement of cis-1,3-pentadiene," J. Am. Chem. Soc. 115, 2408-2415.
99. Liu, Y. P., Lu, D. H., Gonzalez-Lafont, A., Truhlar, D. G., and Garrett, B. C. (1993) "Direct dynamics calculation of the kinetic isotope effect for an organic hydrogen-transfer reaction, including corner-cutting tunneling in 21 dimensions," J. Am. Chem. Soc. 115, 7806-7817.
100. Garrett, B. C., Truhlar, D. G., Wagner, A. F., and Dunning, T. H., Jr. (1983) "Variational transition state theory and tunneling for a heavy-light-heavy reaction using an ab initio potential energy surface. Atomic chlorine-37 + hydrogen chloride [H(D)35C1] .fwdarw. hydrogen chloride [H(D)37C1] + atomic chlorine-35," J. Chem. Phys. 78, 4400-4413.
101. Fernandez-Ramos, A. and Truhlar, D. G. (2001) "Improved algorithm for corner-cutting tunneling calculations," J. Chem. Phys. 114, 1491-1496.
102. Feynman, R. P. and Hibbs, A. R. (1965) Quantum Mechanics and Path Integrals, McGraw-Hill, New York.
103. Gillan, M. J. (1988) "The quantum simulation of hydrogen in metals," Phil. Mag. A 58, 257-283.
104. Voth, G. A., Chandler, D., and Miller, W. H. (1989) "Rigorous formulation of quantum transition state theory and its dynamical corrections," J. Chem. Phys. 91, 7749-7760.
105. Messina, M., Schenter, G. K., and Garrett, B. C. (1993) "Centroid-density, quantum rate theory: variational optimization of the dividing surface," J. Chem. Phys. 98, 8525-8536.
106. Cao, J. and Voth, G. A. (1994) "The formulation of quantum statistical mechanics based on the Feynman path centroid density. V. Quantum instantaneous normal mode theory of liquids,"J. Chem. Phys. 101, 6184-6192.
107. Hwang, J. K. and Warshel, A. (1993) "A quantized classical path approach for calculations of quantum mechanical rate constants,"J. Phys. Chem. 97, 10053-10058.
108. Thomas, A., Jourand, D., Bret, C., Amara, P., and Field, M. J. (1999) "Is there a covalent intermediate in the viral neuraminidase reaction? A hybrid potential free-energy study," J. Am. Chem. Soc. 121, 9693-9702.
109. Makarov, D. E. and Topaler, M. (1995) "Quantum transition-state theory below the crossover temperature," Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 52, 178-188.
110. Messina, M., Schenter, G. K., and Garrett, B. C. (1995) "A variational centroid density procedure for the calculation of transmission coefficients for asymmetric barriers at low temperature," J. Chem. Phys. 103, 3430-3435.
111. Mills, G., Schenter, G. K., Makarov, D.E., and Jonsson, H. (1997) "Generalized path integral based quantum transition state theory," Chem. Phys. Lett. 278, 91-96.
112. Jang, S. and Voth, G. A. (2000) "A relationship between centroid dynamics and path integral quantum transition state theory," J. Chem. Phys. 112, 8747-8757. Erratum: 2001. 114, 1944.
113. Feierberg, I., Luzhkov, V., and Aqvist, J. (2000) "Computer simulation of primary kinetic isotope effects in the proposed rate-limiting step of the glyoxalase I catalyzed reaction," J. Biol. Chem. 275, 22657-22662.
114. Sprik, M., Klein, M. L., and Chandler, D. (1985) "Staging: a sampling technique for the Monte Carlo evaluation of path integrals," Phys. Rev. B 31, 4234-4244.
115. Major, D. T. and Gao, J. (2005) "Implementation of the bisection sampling method in path integral simulations," J. Mol. Graph. Model. 24, 121-127.
116. Major, D. T., Garcia-Viloca, M., and Gao, J. (2006) "Path integral simulations of proton transfer reactions in aqueous solution using combined QM/MM potentials," J. Chem. Theory Comput. 2, 236-245.
117. Ceperley, D. M. (1995) "Path integrals in the theory of condensed helium," Rev. Mod. Phys. 67, 279-355.
118. Major, D. T., Nam, K., and Gao, J. (2006) "Transition state stabilization and a-amino carbon acidity in alanine racemase," J. Am. Chem. Soc. 128, 8114-8115.
119. Major, D. T. and Gao, J. (2007) "An integrated path intergral and free-energy perturbationumbrella sampling method for computing kinetic isotope effects of chemical reactions in solution and in enzymes," J. Chem. Theory Comput. 3, 949-960.
120. Ramirez, R. (1997) "Dynamics of quantum particles of by path-integral centroid simulations: The symmetric Eckart barrier," J. Chem. Phys. 107, 3550-3557.
121. Johnston, H. S. (1966) Gas Phase Reaction Rate Theory, Ronald Press, New York.
122. Shavitt, I. (1959) "Calculation of the rates of the ortho-para conversions and isotope exchanges in hydrogen," J. Chem. Phys. 31, 1359.
123. Rishavy, M. A. and Cleland, W. W. (2000) "Determination of the mechanism of orotidine 5'-monophosphate decarboxylase by isotope effects," Biochemistry 39, 4569-4574.
124. Nam, K., Gao, J., and York, D. M. (2005) "An efficient linear-scaling ewald method for long-range electrostatic interactions in combined QM/MM calculations," J. Chem. Theory Comput. 1, 2-13.
125. Toney, M. D. (2005) "Reaction specificity in pyridoxal phosphate enzymes," Arch. Biochem. Biophys. 433, 279-283.
126. Ondrechen, M. J., Briggs, J. M., and McCammon, J. A. (2001) "A model for enzymesubstrate interaction in alanine racemase," J. Am. Chem. Soc. 123, 2830-2834.
127. Major, D. T. and Gao, J. (2006) "A combined quantum mechanical and molecular mechanical study of the reaction mechanism and a-amino acidity in alanine racemase," J. Am. Chem. Soc. 128, 16345-16357.
128. Spies, M. A., Woodward, J. J., Watnik, M. R., and Toney, M. D. (2004) "Alanine racemase free energy profiles from global analyses of progress curves," J. Am. Chem. Soc. 126, 7464-7475.