Journal of Molecular Modeling

, Volume 14, Issue 8, pp 735–746

A dynamic view of enzyme catalysis

Original Paper

Abstract

Recent experimental advances have shown that enzymes are flexible molecules, and point to a direct link between dynamics and catalysis. Movements span a wide time range, from nano- to milli-seconds. In this paper we introduce two aspects of enzyme flexibility that are treated with two appropriate techniques. First, transition path sampling is used to obtain an unbiased picture of the transition state ensemble in chorismate mutase, as well as its local flexibility and the energy flow during the chemical step. Second, we consider the binding and release of substrates in L-rhamnulose-1-phosphate aldolase. We have calculated the normal modes of the enzyme with the elastic network model. The lowest frequency modes generate active site deformations that change the coordination number of the catalytic zinc ion. The coordination lability of zinc allows the binding and release of substrates. Substitution of zinc by magnesium blocks the exchange of ligands.

Keywords

Enzyme catalysis Enzyme dynamics Transition path sampling Energy relaxation QM/MM Chorismate mutase Aldolase 

Supplementary material

894_2008_283_MOESM1_ESM.pdf (528 kb)
ESM 1(PDF 528 kb)

References

  1. 1.
    Agarwal P (2005) Role of protein dynamics in reaction rate enhancement by enzymes. J Am Chem Soc 127(43):15248–15256CrossRefGoogle Scholar
  2. 2.
    Agarwal PK, Billeter SR, Rajagopalan PR, Benkovic SJ, Hammes-Schiffer S (2002) Network of coupled promoting motions in enzyme catalysis. Proc Natl Acad Sci USA 301:2794–2799CrossRefGoogle Scholar
  3. 3.
    Antoniou D, Basner J, Núñez S, Schwartz SD (2006) Computational and theoretical methods to explore the relation between enzyme dynamics and catalysis. Chem Rev 106(8):3170–3187CrossRefGoogle Scholar
  4. 4.
    Astumian D (2002) Protein conformational fluctuations and free-energy transduction. Appl Phys A 75(2):193–206CrossRefGoogle Scholar
  5. 5.
    Basner JE, Schwartz SD (2005) How enzyme dynamics helps catalyze a reaction in atomic detail: a transition path sampling study. J Am Chem Soc 127:13822–13831CrossRefGoogle Scholar
  6. 6.
    Benkovic SJ, Hammes-Schiffer S (2003) A perspective on enzyme catalysis. Science 301:1196–1202CrossRefGoogle Scholar
  7. 7.
    Bennett CH (1976) Efficient estimation of free energy differences from monte carlo data. J Comput Phys 22(2):245–268CrossRefGoogle Scholar
  8. 8.
    Berendsen HJ, Hayward S (2000) Collective protein dynamics in relation to function. Curr Opin Struct Biol 10:165–169CrossRefGoogle Scholar
  9. 9.
    Bernado P, Blackledge M (2004) Local dynamic amplitudes on the protein backbone from dipolar couplings: toward the elucidation of slower motions in biomolecules. J Am Chem Soc 125(25):7760–7761CrossRefGoogle Scholar
  10. 10.
    Bock C, Katz A, Markham G, Glusker J (1999) Manganese as a replacement for magnesium and zinc: functional comparison of the divalent ions. J Am Chem Soc 121(32):7360–7372CrossRefGoogle Scholar
  11. 11.
    Bolhuis PG, Chandler D, Dellago C, Geissler PL (2002) Transition path sampling: Throwing ropes over rough mountain passes, in the dark. Annu Rev Phys Chem 53:291–318CrossRefGoogle Scholar
  12. 12.
    Bolhuis PG, Dellago C, Chandler D (2000) Reaction coordinates of biomolecular isomerization. Proc Natl Acad Sci USA 97(11):5877–5882CrossRefGoogle Scholar
  13. 13.
    Brothers EN, Suarez D, Deerfield DW II, Merz KM Jr (2004) PM3-compatible zinc parameters optimized for metalloenzyme active sites. J Comput Chem 25(14):1677–1692CrossRefGoogle Scholar
  14. 14.
    Chandler D (1998) Barrier crossings: classical theory of rare but important events. In: Berne B, Cicotti G, Coker DF (eds) Classical and quantum dynamics in condensed phase simulations. World Scientific, Singapore, pp 3–23Google Scholar
  15. 15.
    Chook YM, Gray JV, Ke H, Lipscomb WN (1994) The monofunctional chorismate mutase from bacillus subtilis. Structure determination of chorismate mutase and its complexes with a transition state analog and prephenate, and implications for the mechanism of the enzymatic reaction. J Mol Biol 240:476–500CrossRefGoogle Scholar
  16. 16.
    Chook YM, Ke H, Lipscomb WN (1993) Crystal structures of the monofunctional Chorismate Mutase from Bacillus subtilis and its complex with a transition state analog. Proc Natl Acad Sci USA 90:8600–8603CrossRefGoogle Scholar
  17. 17.
    Crehuet R, Field M (2007) A transition path sampling study of the reaction catalyzed by the enzyme chorismate mutase. J Phys Chem B 111(20):5708–5718CrossRefGoogle Scholar
  18. 18.
    Crehuet R, Field MJ, Pellegrini E (2004) Transition events in one dimension. Phys Rev E 69:012,101CrossRefGoogle Scholar
  19. 19.
    Crehuet R, Jimenez A (2008) Work in preparationGoogle Scholar
  20. 20.
    Cui Q, Bahar I (2006) Normal mode analysis. Theory and applications to biological and chemical systems. Mathematical and computational biology series. Chapman & Hall/CRC, Boca RatonGoogle Scholar
  21. 21.
    Dellago C, Bolhuis PG, Csajka FS, Chandler D (1998) Transition path sampling and the calculation of rate constants. J Chem Phys 108(5):1964–1977CrossRefGoogle Scholar
  22. 22.
    Dellago C, Bolhuis PG, Geissler PL (2002) Transition path sampling. Adv Chem Phys 123:1–86CrossRefGoogle Scholar
  23. 23.
    Dreyer MK, Schulz GE (1996) Refined high-resolution structure of the metal-ion dependent l-fuculose-1-phosphate aldolase (class II) from Escherichia coli. Acta Crystallogr, D Biol Crystallogr 52(6):1082–1091CrossRefGoogle Scholar
  24. 24.
    Dudev T, Lim C (2000) Metal binding in proteins: The effect of the dielectric medium. J Phys Chem B 104(15):3692–3694CrossRefGoogle Scholar
  25. 25.
    Eisenmesser EZ, Bosco DA, Akke M, Kern D (2002) Enzyme dynamics during catalysis. Science 295(5559):1520–1523CrossRefGoogle Scholar
  26. 26.
    Eisenmesser EZ, Millet O, Labeikovsky W, Korzhnev DM, Wolf-Watz M, Bosco DA, Skalicky JJ, Kay LE, Kern D (2005) Intrinsic dynamics of an enzyme underlies catalysis. Nature 438(7064):117–121CrossRefGoogle Scholar
  27. 27.
    Elstner M, Cui Q, Munih P, Kaxiras E, Frauenheim T, Karplus M (2003) Modeling zinc in biomolecules with the self consistent charge-density functional tight binding (scc-dftb) method: applications to structural and energetic analysis. J Comput Chem 24(5):565–581CrossRefGoogle Scholar
  28. 28.
    Engelkamp H, Hatzakis NS, Hofkens J, Schryver FCD, Nolte RJM, Rowan AE (2006) Do enzymes sleep and work? Chem Commun 9:935–940Google Scholar
  29. 29.
    Field MJ (1999) A practical introducction to the simulation of molecular systems. Cambridge University Press, Cambridge, UKGoogle Scholar
  30. 30.
    Field MJ, Albe M, Bret C, Proust-de Martin F, Thomas A (2000) The Dynamo library for molecular simulations using hybrid quantum mechanical and molecular mechanical potentials. J Comput Chem 21(12):1088–1100CrossRefGoogle Scholar
  31. 31.
    Floquet N, Marechal JD, Badet-Denisot MA, Robert CH, Dauchez M, Perahia D (2006) Normal mode analysis as a prerequisite for drug design: application to matrix metalloproteinases inhibitors. FEBS Lett 580(22):5130–5136CrossRefGoogle Scholar
  32. 32.
    Frauenfelder H, Sligar S, Wolynes PG (1991) The energy landscapes and motions of proteins. Science 254:1598–1603CrossRefGoogle Scholar
  33. 33.
    Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA Jr, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene M, Li X, Knox JE, Hratchian HP, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA (2004) Gaussian 03, Revision C.02. Gaussian, Wallingford, CTGoogle Scholar
  34. 34.
    Fujisaki H, Bu L, Straub JE (2006) Probing vibrational energy relaxation in proteins using normal modes. In: Cui Q, Bahar I (eds) Normal mode analysis. Theory and applications to biological and chemical systems. Mathematical and computational biology series. Chapman & Hall/CRC, Boca Raton, pp 301–323Google Scholar
  35. 35.
    Fujisaki H, Straub JE (2005) Vibrational energy relaxation in proteins. Proc Natl Acad Sci USA 102(19):6726–6731CrossRefGoogle Scholar
  36. 36.
    Gamper M, Hilvert D, Kast P (2000) Probing the role of the c-terminus of Bacillus subtilis chorismate mutase by a novel random protein-termination strategy. Biochemistry 39:14087–14094CrossRefGoogle Scholar
  37. 37.
    Geissler PL, Dellago C, Chandler D (1999) Kinetic pathways of ion pair dissociation in water. J Phys Chem B 103:3706–3710CrossRefGoogle Scholar
  38. 38.
    Giacovazzo C, Monaco H, Artioli G, Viterbo D, Ferraris G, Gilli G, Zanotti G, Catti M (2002) Fundamentals of crystallography, 2nd edn. International Union of Crystallography Texts on Crystallography. Oxford University PressGoogle Scholar
  39. 39.
    Guimarães CRW, Repasky MP, Chandrasekhar J, Tirado-Rives J, Jorgensen WL (2003) Contributions of conformational compression and preferential transition state stabilisation to the rate enhancement by chorismate mutase. J Am Chem Soc 125:6892–6899CrossRefGoogle Scholar
  40. 40.
    Guimarães CRW, Udier-Blagović M, Tubert-Brohman I, Jorgensen WL (2005) Effects of Arg90 neutralization on the enzyme-catalyzed rearrangement of chorismate to prephanate. J Chem Theory Comput 1:617–625CrossRefGoogle Scholar
  41. 41.
    Guo H, Cui Q, Lipscomb WN, Karplus M (2001) Substrate conformational transitions in the active site of chorismate mutase: Their role in the catalytic mechanism. Proc Natl Acad Sci USA 98(16):9032–9037CrossRefGoogle Scholar
  42. 42.
    Hammes-Schiffer S (2002) Impact of enzyme motion on activity. Biochemistry 41(45):13335–13343CrossRefGoogle Scholar
  43. 43.
    Hänggi P (1990) Reaction–rate theory: fifty years after Kramers. Rev Mod Phys 62(2):251–341CrossRefGoogle Scholar
  44. 44.
    Higashi M, Hayashi S, Kato S (2007) Transition state determination of enzyme reaction on free energy surface: application to chorismate mutase. Chem Phys Lett 437:293–297CrossRefGoogle Scholar
  45. 45.
    Hinsen K (2000) The molecular modeling toolkit: a new approach to molecular simulations. J Comput Chem 21(2):79–85CrossRefGoogle Scholar
  46. 46.
    Hinsen K, Petrescu AJ, Dellerue S, Bellissent-Funel MC, Kneller GR (2000) Harmonicity in slow protein dynamics. Chem Phys 261(1–2):25–37CrossRefGoogle Scholar
  47. 47.
    Hixon M, Sinerius G, Schneider A, Walter C, Fessner WD, Schloss JV (1996) Quo vadis photorespiration: atale of two aldolases. FEBS Lett 392(3):281–284CrossRefGoogle Scholar
  48. 48.
    Hur S, Bruice TC (2002) The mechanism of catalysis of the chorismate to prephenate reaction by the Escherichia coli mutase enzyme. Proc Natl Acad Sci USA 99(3):1176–1181CrossRefGoogle Scholar
  49. 49.
    Hur S, Bruice TC (2003) Enzymes do what is expected (chalcone isomerase versus chorismate mutase). J Am Chem Soc 125:1472–1473CrossRefGoogle Scholar
  50. 50.
    Hur S, Bruice TC (2003) Just a near attack conformer for catalysis (chorismate to prephenate rearrangements in water, antibody, enzymes, and their mutants). J Am Chem Soc 125:10540–10542CrossRefGoogle Scholar
  51. 51.
    Hur S, Bruice TC (2003) The near attack conformation approach to the study of the chorismate to prephenate reaction. Proc Natl Acad Sci USA 100(21):12015–12020CrossRefGoogle Scholar
  52. 52.
    Ishida T, Fedorov D, Kitaura K (2006) All electron quantum chemical calculation of the entire enzyme system confirms a collective catalytic device in the chorismate mutase reaction. J Phys Chem B 110(3):1457–1463CrossRefGoogle Scholar
  53. 53.
    Jarzynski C (1997) Nonequilibrium equality for free energy differences. Phys Rev Lett 78(14):2690–2693CrossRefGoogle Scholar
  54. 54.
    Joerger AC, Gosse C, Fessner WD, Schulz GE (2000) Catalytic action of fuculose 1-phosphate aldolase (class II) as derived from structure-directed mutagenesis. Biochemistry 39(20):6033–6041CrossRefGoogle Scholar
  55. 55.
    Jorgensen WL, Maxwell DS, Tirado-Rives J (1996) Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids. J Am Chem Soc 118:11225–11236CrossRefGoogle Scholar
  56. 56.
    Käb G, Schröder C, Schwarzer D (2002) Intramolecular vibrational redistribution and energy relaxation in solution: a molecular dynamics approach. Phys Chem Chem Phys 4:271CrossRefGoogle Scholar
  57. 57.
    Kästner J, Thiel W (2005) Bridging the gap between thermodynamic integration and umbrella sampling provides a novel analysis method: “umbrella integration”. J Chem Phys 123(14):144104. DOI 10.1063/1.2052648 CrossRefGoogle Scholar
  58. 58.
    Kay LE (1998) Protein dynamics from NMR. Nat Struct Biol 5:513–517CrossRefGoogle Scholar
  59. 59.
    Kimura E, Gotoh T, Koike T, Shiro M (1999) Dynamic enolate recognition in aqueous solution by zinc(II) in a phenacyl-pendant cyclen complex: Implications for the role of zinc(II) in class II aldolases. J Am Chem Soc 121(6):1267–1274CrossRefGoogle Scholar
  60. 60.
    Kondrashov DA, Van Wynsberghe AW, Bannen RM, Cui Q, Phillips GN Jr (2007) Protein structural variation in computational models and crystallographic data. Structure 15(2):169–177CrossRefGoogle Scholar
  61. 61.
    Kroemer M, Merkel I, Schulz GE (2003) Structure and catalytic mechanism of l-rhamnulose-1-phosphate aldolase. Biochemistry 42(36):10560–10568CrossRefGoogle Scholar
  62. 62.
    Kumar S, Rosenberg JM, Bouzida D, Swendsen RH, Kollman PA (1992) The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method. J Comput Chem 13(8):1011–1021CrossRefGoogle Scholar
  63. 63.
    Lee YS, Worthington SE, Krauss M, Brooks BR (2002) Reaction mechanism of chorismate mutase studied by the combined potentials of quantum mechanics and molecular mechanics. J Phys Chem B 106:12059–12065CrossRefGoogle Scholar
  64. 64.
    Ma J (2006) Applications of normal mode analysis in structural refinement of supramolecular complexes. In: Cui Q, Bahar I (eds) Normal mode analysis. Theory and applications to biological and chemical systems. Mathematical and computational biology series. Chapman & Hall/CRC, Boca Raton, pp 137–154Google Scholar
  65. 65.
    Markwick P, Bouvignies G, Blackledge M (2007) Exploring multiple timescale motions in protein gb3 using accelerated molecular dynamics and nmr spectroscopy. J Am Chem Soc 129(15):4724–4730CrossRefGoogle Scholar
  66. 66.
    Martí S, Andrés J, Moliner V, Silla E, Tuñón I, Bertrán J (2003) Conformational equilibrium of chorismate. A QM/MM theoretical study combining statistical simulations and geometry optimisations in gas phase and in aqueous solution. Theochem 632:197–206CrossRefGoogle Scholar
  67. 67.
    Martí S, Andrés J, Moliner V, Silla E, Tuñón I, Bertrán J (2004) A comparative study of Claisen and Cope rearrangements catalyzed by chorismate mutase. An insight into enzymatic efficiency: transition state stabilization or substrate preorganization? J Am Chem Soc 126:311–319CrossRefGoogle Scholar
  68. 68.
    Martí S, Andrés J, Moliner V, Silla E, Tuñón I, Bertrán J, Field MJ (2001) A hybrid potential reaction path and free energy study of the chorismate mutase reaction. J Am Chem Soc 123:1709–1712CrossRefGoogle Scholar
  69. 69.
    McCammon JA, Gelin BR, Karplus M (1977) Dynamics of folded proteins. Nature 267:585–590CrossRefGoogle Scholar
  70. 70.
    Min W, English BP, Luo G, Cherayil BJ, Kou SC, Xie XS (2005) Fluctuating enzymes: lessons from single-molecule studies. Acc Chem Res 38(12):923–931CrossRefGoogle Scholar
  71. 71.
    Ming D, Kong Y, Lambert MA, Huang Z, Ma J (2002) How to describe protein motion without amino acid sequence and atomic coordinates. Proc Natl Acad Sci USA 99(13):8620–8625CrossRefGoogle Scholar
  72. 72.
    Neufeld AA, Schwarzer D, Schröeder J, Troe J (2003) Molecular dynamics approach to vibrational energy relaxation. Quantum-classical versus purely classical non-equilibrium simulations. J Chem Phys 119:2502–2512CrossRefGoogle Scholar
  73. 73.
    Noonan RC, Carter CW, Bagdassarian CK (2002) Enzymatic conformational fluctuations along the reaction coordinate of cytidine deaminase. Protein Sci 11:1424–1434CrossRefGoogle Scholar
  74. 74.
    Núñez S, Wing C, Antoniou D, Schramm V, Schwartz S (2006) Insight into catalytically relevant correlated motions in human purine nucleoside phosphorylase. J Phys Chem A 110(2):463–472CrossRefGoogle Scholar
  75. 75.
    Parak FG (2003) Physical aspects of protein dynamics. Rep Prog Phys 66:103–129CrossRefGoogle Scholar
  76. 76.
    Ranaghan KA, Ridder L, Szefczyk B, Sokalski WA, Hermann JC, Mulholland AJ (2003) Insights into enzyme catalysis from QM/MM modelling: transition state stabilisation in chorismate mutase. Mol Phys 101(17):2695–2714CrossRefGoogle Scholar
  77. 77.
    Ranaghan KE, Ridder L, Szefczyk B, Sokalski WA, Hermann JC, Mulholland AJ (2004) Transition state stabilisation and substrate strain in enzyme catalysis: ab initio QM/MM modelling of the chorismate mutase reaction. Org Biomol Chem 2(7):968–980CrossRefGoogle Scholar
  78. 78.
    Repasky MP, Guimarães CRW, Chandrasekhar J, Tirado-Rives J, Jorgensen WL (2003) Investigation of solvent effects for the Claisen rearrangement of chorismate to prephenate: mechanistic interpretation via near attack conformations. J Am Chem Soc 125:6663–6672CrossRefGoogle Scholar
  79. 79.
    Daniel RM, Dunn RV, Finney JL, Smith JC (2003) The role of dynamics in enzyme activity. Annu Rev Biophys Biomol Struct 32:69–92CrossRefGoogle Scholar
  80. 80.
    Rueda M, Chacon P, Orozco M (2007) Thorough validation of protein normal mode analysis: a comparative study with essential dynamics. Structure 15(5):565–575CrossRefGoogle Scholar
  81. 81.
    Shirts MR, Pande VS (2005) Comparison of efficiency and bias of free energies computed by exponential averaging, the bennett acceptance ratio, and thermodynamic integration. J Chem Phys 122(14):144,107CrossRefGoogle Scholar
  82. 82.
    Smiley RD, Hammes GG (2006) Single molecule studies of enzyme mechanisms. Chem Rev 106(8):3080–3094CrossRefGoogle Scholar
  83. 83.
    Sousa SF, Fernandes PA, Ramos MJ (2007) Comparative assessment of theoretical methods for the determination of geometrical properties in biological zinc complexes. J Phys Chem B 111(30):9146–9152CrossRefGoogle Scholar
  84. 84.
    Szefczyk B, Claeyssens F, Mulholland AJ, Sokalski WA (2007) Quantum chemical analysis of reaction paths in chorismate mutase: conformational effects and electrostatic stabilization. Int J Quantum Chem 107(12):2274–2285CrossRefGoogle Scholar
  85. 85.
    Tama F, Wriggers W, Brooks CL III (2002) Exploring global distortions of biological macromolecules and assemblies from low-resolution structural information and elastic network theory. J Mol Biol 321(2):297–305CrossRefGoogle Scholar
  86. 86.
    Teague SJ (2003) Implications of protein flexibility for drug discovery. Nat Rev Drug Discov 2(7):527–541CrossRefGoogle Scholar
  87. 87.
    Torrie G, Valleau J (1977) Nonphysical sampling distributions in monte carlo free-energy estimation:umbrella sampling. J Comput Phys 23(2):187–199CrossRefGoogle Scholar
  88. 88.
    Tozzini V (2005) Coarse-grained models for proteins. Curr Opin Struct Biol 15(2):144–150CrossRefGoogle Scholar
  89. 89.
    Villà J, Warshel A (2001) Energetics and dynamics of enzymatic reactions. J Phys Chem B 105:7887–7907CrossRefGoogle Scholar
  90. 90.
    Štrajbl M, Shurki A, Kato M, Warshel A (2003) Apparent NAC effect in chorismate mutase reflects electrostatic transition state stabilisation. J Am Chem Soc 125:10228–10237CrossRefGoogle Scholar
  91. 91.
    Warshel A, Sharma PK, Kato M, Xiang Y, Liu H, Olsson MHM (2006) Electrostatic basis for enzyme catalysis. Chem Rev 106(8):3210–3235CrossRefGoogle Scholar
  92. 92.
    Williams RJ (1995) Energised (entatic) states of groups and of secondary structures in proteins and metalloproteins. Eur J Biochem 234(2):363–381CrossRefGoogle Scholar
  93. 93.
    Yang LW, Bahar I (2005) Coupling between catalytic site and collective dynamics: a requirement for mechanochemical activity of enzymes. Structure 13(6):893–904CrossRefGoogle Scholar
  94. 94.
    Zhang BW, Jasnow D, Zuckerman DM (2007) Transition-event durations in one-dimensional activated processes. J Chem Phys 126:074504CrossRefGoogle Scholar
  95. 95.
    Zhang X, Zhang X, Bruice TC (2005) A definitive mechanism for chorismate mutase. Biochemistry 44(31):10443–10448CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Departament de Química de Pèptids i ProteïnesInstitut d´Investigacions Químiques i Ambientals de Barcelona (IIQAB–CSIC)BarcelonaSpain

Personalised recommendations