Photosynthesis Research

, Volume 102, Issue 2–3, pp 455–470

The MoD-QM/MM methodology for structural refinement of photosystem II and other biological macromolecules

  • Eduardo M. Sproviero
  • Michael B. Newcomer
  • José A. Gascón
  • Enrique R. Batista
  • Gary W. Brudvig
  • Victor S. Batista
Review

Abstract

Quantum mechanics/molecular mechanics (QM/MM) hybrid methods are currently the most powerful computational tools for studies of structure/function relations and structural refinement of macrobiomolecules (e.g., proteins and nucleic acids). These methods are highly efficient, since they implement quantum chemistry techniques for modeling only the small part of the system (QM layer) that undergoes chemical modifications, charge transfer, etc., under the influence of the surrounding environment. The rest of the system (MM layer) is described in terms of molecular mechanics force fields, assuming that its influence on the QM layer can be roughly decomposed in terms of electrostatic interactions and steric hindrance. Common limitations of QM/MM methods include inaccuracies in the MM force fields, when polarization effects are not explicitly considered, and the approximate treatment of electrostatic interactions at the boundaries between QM and MM layers. This article reviews recent advances in the development of computational protocols that allow for rigorous modeling of electrostatic interactions in extended systems beyond the common limitations of QM/MM hybrid methods. We focus on the moving-domain QM/MM (MoD-QM/MM) methodology that partitions the system into many molecular domains and obtains the electrostatic and structural properties of the whole system from an iterative self-consistent treatment of the constituent molecular fragments. We illustrate the MoD-QM/MM method as applied to the description of photosystem II as well as in conjunction with the application of spectroscopically constrained QM/MM optimization methods, based on high-resolution spectroscopic data (extended X-ray absorption fine structure spectra, and exchange coupling constants).

Keywords

Quantum mechanics Molecular mechanics Photosystem II EXAFS MoD-QM/MM 

Abbreviations

BS

Broken symmetry

DFT

Density functional theory

DNA

Deoxyribonucleic acid

EE

Electronic-embedding

ESP

Electrostatic potential

EXAFS

Extended X-ray absorption fine structure

FTIR

Fourier Transform Infrared Spectroscopy

MEP

Minimum energy path

MoD-QM/MM

Moving-domain QM/MM

OEC

Oxygen-evolving complex

P-EXAFS

Polarized extended X-ray absorption fine structure

PSII

Photosystem II

QM/MM

Quantum mechanics–molecular mechanics

SC-QM/MM

Spectroscopically constrained QM/MM

References

  1. Ankudinov AL, Ravel B, Rehr JJ, Conradson SD (1998) Real-space multiple-scattering calculation and interpretation of X-ray-absorption near-edge structure. Phys Rev B 58:7565–7576CrossRefGoogle Scholar
  2. Ankudinov AL, Bouldin CE, Rehr JJ, Sims J, Hung H (2002) Parallel calculation of electron multiple scattering using Lanczos algorithms. Phys Rev B 65:104–107CrossRefGoogle Scholar
  3. Ashley CA, Doniach S (1975) Theory of extended X-ray absorption-edge fine-structure (EXAFS) in crystalline solids. Phys Rev B 11:1279–1288CrossRefGoogle Scholar
  4. Bouldin C, Sims J, Hung H, Rehr JJ, Ankudinov AL (2001) Rapid calculation of X-ray absorption near edge structure using parallel computation. X-Ray Spectrom 30:431–434CrossRefGoogle Scholar
  5. Britt RD, Peloquin JM, Campbell KA (2000) Pulsed and parallel-polarization EPR characterization of the photosystem II oxygen-evolving complex. Annu Rev Biophys Biomol Struct 29:463–495CrossRefPubMedGoogle Scholar
  6. Britt RD, Campbell KA, Peloquin JM, Gilchrist ML, Aznar CP, Dicus MM, Robblee J, Messinger J (2004) Recent pulsed EPR studies of the photosystem II oxygen-evolving complex: implications as to water oxidation mechanisms. Biochim Biophys Acta 1655:158–171CrossRefPubMedGoogle Scholar
  7. Broyden CG (1970) Convergence of single-rank quasi-Newton methods. Math Comput 24:365–382CrossRefGoogle Scholar
  8. Brudvig GW, Crabtree RH (1986) Mechanism for photosynthetic O2 evolution. Proc Natl Acad Sci USA 83:4586–4588CrossRefPubMedGoogle Scholar
  9. Cooper SR, Calvin M (1977) Mixed-valence interactions in di-μ-oxo bridged manganese complexes. J Am Chem Soc 99:6623–6630CrossRefGoogle Scholar
  10. Cooper SR, Dismukes GC, Klein MP, Calvin M (1978) Mixed-valence interactions in di-μ-oxo bridged manganese complexes: electron-paramagnetic resonance and magnetic-susceptibility studies. J Am Chem Soc 100:7248–7252CrossRefGoogle Scholar
  11. Cornell WD, Cieplak P, Bayly CI, Gould IR, Merz KM, Ferguson DM, Spellmeyer DC, Fox T, Caldwell JW, Kollman PA (1995) A second generation force-field for the simulation of proteins, nucleic-acids, and organic-molecules. J Am Chem Soc 117:5179–5197CrossRefGoogle Scholar
  12. Dapprich S, Komaromi I, Byun KS, Morokuma K, Frisch MJ (1999) A new ONIOM implementation in Gaussian98. Part I. The calculation of energies, gradients, vibrational frequencies and electric field derivatives. THEOCHEM J Mol Struct 461:1–21CrossRefGoogle Scholar
  13. Dau H, Iuzzolino L, Dittmer J (2001) The tetra-manganese complex of photosystem II during its redox cycle: X-ray absorption results and mechanistic implications. Biochim Biophys Acta 1503:24–39CrossRefPubMedGoogle Scholar
  14. Dau H, Liebisch P, Haumann M (2004) The structure of the manganese complex of photosystem II in its dark-stable S1-state-EXAFS results in relation to recent crystallographic data. Phys Chem Chem Phys 6:4781–4792CrossRefGoogle Scholar
  15. DeRose VJ, Mukerji I, Latimer MJ, Yachandra VK, Sauer K, Klein MP (1994) Comparison of the manganese oxygen-evolving complex in photosystem II of Spinach and Synechococcus Sp with multinuclear manganese model compounds by X-ray-absorption spectroscopy. J Am Chem Soc 116:5239–5249CrossRefGoogle Scholar
  16. Dykstra CE (1993) Electrostatic interaction potentials in molecular-force fields. Chem Rev 93:2339–2353CrossRefGoogle Scholar
  17. Fan LY, Ziegler T (1991) The influence of self-consistency on nonlocal density functional calculations. J Chem Phys 94:6057–6063CrossRefGoogle Scholar
  18. Ferreira KN, Iverson TM, Maghlaoui K, Barber J, Iwata S (2004) Architecture of the photosynthetic oxygen-evolving center. Science 303:1831–1838CrossRefPubMedGoogle Scholar
  19. Flank AM, Weininger M, Mortenson LE, Cramer SP (1986) Single-crystal EXAFS of nitrogenase. J Am Chem Soc 108:1049–1055CrossRefGoogle Scholar
  20. Fletcher R (1970) A new approach to variable metric algorithms. Comput J 13:317–322CrossRefGoogle Scholar
  21. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery Jr JA, 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 B.04. Gaussian, Inc., Wallingford, CTGoogle Scholar
  22. Gascon JA, Leung SSF, Batista ER, Batista VS (2006a) A self-consistent space-domain decomposition method for QM/MM computations of protein electrostatic potentials. J Chem Theory Comput 2:175–186CrossRefGoogle Scholar
  23. Gascon JA, Sproviero EM, Batista VS (2006b) Computational studies of the primary phototransduction event in visual rhodopsin. Acc Chem Res 39:184–193CrossRefPubMedGoogle Scholar
  24. Goldfarb D (1970) A family of variable-metric methods derived by variational means. Math Comput 24:23–26CrossRefGoogle Scholar
  25. Haumann M, Junge W (1999) Evidence for impaired hydrogen-bonding of tyrosine YZ in calcium-depleted photosystem II. Biochim Biophys Acta 1411:121–133CrossRefPubMedGoogle Scholar
  26. Haumann M, Muller C, Liebisch P, Iuzzolino L, Dittmer J, Grabolle M, Neisius T, Meyer-Klaucke W, Dau H (2005) Structural and oxidation state changes of the photosystem II manganese complex in four transitions of the water oxidation cycle (S0→S1, S1→S2, S2→S3, and S3, S4→S0) characterized by X-ray absorption spectroscopy at 20 K and room temperature. Biochemistry 44:1894–1908CrossRefPubMedGoogle Scholar
  27. Hendry G, Wydrzynski T (2002) The two substrate-water molecules are already bound to the oxygen-evolving complex in the S2 state of photosystem II. Biochemistry 41:13328–13334CrossRefPubMedGoogle Scholar
  28. Hendry G, Wydrzynski T (2003) 18O isotope exchange measurements reveal that calcium is involved in the binding of one substrate-water molecule to the oxygen-evolving complex in photosystem II. Biochemistry 42:6209–6217CrossRefPubMedGoogle Scholar
  29. Hillier W, Wydrzynski T (2004) Substrate water interactions within the photosystem II oxygen evolving complex. Phys Chem Chem Phys 6:4882–4889CrossRefGoogle Scholar
  30. Hillier W, Wydrzynski T (2008) 18O-Water exchange in photosystem II: substrate binding and intermediates of the water splitting cycle. Coord Chem Rev 252:306–317CrossRefGoogle Scholar
  31. Hoganson CW, Babcock GT (1997) A metalloradical mechanism for the generation of oxygen from water in photosynthesis. Science 277:1953–1956CrossRefPubMedGoogle Scholar
  32. Jaguar (2003) Jaguar 5.5. Schrodinger LLC, Portland, ORGoogle Scholar
  33. Kronig RD (1931) The quantum theory of dispersion in metallic conductors II. In: Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character, vol 133, pp 255–265Google Scholar
  34. Kronig RD, Penney WG (1931) Quantum mechanics of electrons on crystal lattices. In: Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character, vol 130, pp 499–513Google Scholar
  35. Lee PA, Pendry JB (1975) Theory of the extended X-ray absorption fine structure. Phys Rev B 11:2795–2811CrossRefGoogle Scholar
  36. Limburg J, Vrettos JS, Liable-Sands LM, Rheingold AL, Crabtree RH, Brudvig GW (1999) A functional model for O–O bond formation by the O2-evolving complex in photosystem II. Science 283:1524–1527CrossRefPubMedGoogle Scholar
  37. Loll B, Kern J, Saenger W, Zouni A, Biesiadka J (2005) Towards complete cofactor arrangement in the 3.0 Å resolution structure of photosystem II. Nature 438:1040–1044CrossRefPubMedGoogle Scholar
  38. Lundberg M, Siegbahn PEM (2004) Theoretical investigations of structure and mechanism of the oxygen-evolving complex in PSII. Phys Chem Chem Phys 6:4772–4780CrossRefGoogle Scholar
  39. Lundberg M, Blomberg MRA, Siegbahn PEM (2003) Modeling water exchange on monomeric and dimeric Mn centers. Theor Chem Acc 110:130–143Google Scholar
  40. Manchanda R, Brudvig GW, Degala S, Crabtree RH (1994) Improved syntheses and structure of (Mn(III)Mn(IV)(O)2(Phen)4 (ClO4)3·2CH3COOH·2H2O. Inorg Chem 33:5157–5160CrossRefGoogle Scholar
  41. Maseras F, Morokuma K (1995) IMOMM: a new integrated ab initio plus molecular mechanics geometry optimization scheme of equilibrium structures and transition-states. J Comput Chem 16:1170–1179CrossRefGoogle Scholar
  42. McEvoy JP, Brudvig GW (2004) Structure-based mechanism of photosynthetic water oxidation. Phys Chem Chem Phys 6:4754–4763CrossRefGoogle Scholar
  43. Menikarachchi LC, Gascon JA (2008) Optimization of cutting schemes for the evaluation of molecular electrostatic potentials in proteins via moving-domain QM/MM. J Mol Model 14:479–487CrossRefPubMedGoogle Scholar
  44. Messinger J (2004) Evaluation of different mechanistic proposals for water oxidation in photosynthesis on the basis of Mn4OxCa structures for the catalytic site and spectroscopic data. Phys Chem Chem Phys 6:4764–4771CrossRefGoogle Scholar
  45. Messinger J, Badger M, Wydrzynski T (1995) Detection of one slowly exchanging substrate water molecule in the S3 state of photosystem II. Proc Natl Acad Sci USA 92:3209–3213CrossRefPubMedGoogle Scholar
  46. Newcomer MB, Ragain CM, Gascón JA, Batista ER, Strobel SA, Loria JP, Batista VS (2009) A self-consistent MOD-QM/MM structural refinement method: characterization of hydrogen bonding in the oxytricha nova G-quadruplex. J Chem Theory Comput (submitted)Google Scholar
  47. Noodleman L (1981) Valence bond description of anti-ferromagnetic coupling in transition-metal dimers. J Chem Phys 74:5737–5743CrossRefGoogle Scholar
  48. Noodleman L, Case DA (1992) Density functional theory of spin polarization and spin coupling in iron–sulfur clusters. Adv Inorg Chem 38:423–470CrossRefGoogle Scholar
  49. Noodleman L, Davidson ER (1986) Ligand spin polarization and antiferromagnetic coupling in transition-metal dimers. Chem Phys 109:131–143CrossRefGoogle Scholar
  50. Noodleman L, Peng CY, Case DA, Mouesca JM (1995) Orbital interactions, electron delocalization and spin coupling in iron–sulfur clusters. Coord Chem Rev 144:199–244CrossRefGoogle Scholar
  51. Nugent JHA, Rich AM, Evans MCW (2001) Photosynthetic water oxidation: towards a mechanism. Biochim Biophys Acta 1503:138–146CrossRefPubMedGoogle Scholar
  52. Pantazis DA, Orio M, Petrenko T, Zein S, Bill E, Lubitz W, Messinger J, Neese F (2009) A new quantum chemical approach to the magnetic properties of oligonuclear transition-metal complexes: application to a model for the tetranuclear manganese cluster of photosystem II. Chem Eur J 15:5108–5123CrossRefGoogle Scholar
  53. Pecoraro VL, Baldwin MJ, Gelasco A (1994) Interaction of manganese with dioxygen and its reduced derivatives. Chem Rev 94:807–826CrossRefGoogle Scholar
  54. Robblee JH, Cinco RM, Yachandra VK (2001) X-ray spectroscopy-based structure of the Mn cluster and mechanism of photosynthetic oxygen evolution. Biochim Biophys Acta 1503:7–23CrossRefPubMedGoogle Scholar
  55. Ruettinger WF, Ho DM, Dismukes GC (1999) Protonation and dehydration reactions of the Mn4O4L6 cubane and synthesis and crystal structure of the oxidized cubane Mn4O4L6 +: a model for the photosynthetic water oxidizing complex. Inorg Chem 38:1036–1037CrossRefPubMedGoogle Scholar
  56. Sarneski JE, Thorp HH, Brudvig GW, Crabtree RH, Schulte GK (1990) Assembly of high-valent oxomanganese clusters in aqueous solution. Redox equilibrium of water-stable Mn3O4 4+ and Mn2O2 3+ complexes. J Am Chem Soc 112:7255–7260CrossRefGoogle Scholar
  57. Sayers DE, Stern EA, Lytle FW (1971) New technique for investigating noncrystalline structures: Fourier analysis of extended X-ray absorption fine structure. Phys Rev Lett 27:1204–1207CrossRefGoogle Scholar
  58. Schlegel HB (1987) Optimization of equilibrium geometries and transition structures. Adv Chem Phys 67:249–285CrossRefGoogle Scholar
  59. Schlodder E, Witt HT (1999) Stoichiometry of proton release from the catalytic center in photosynthetic water oxidation: reexamination by a glass electrode study at pH 5.5–7.2. J Biol Chem 274:30387–30392CrossRefPubMedGoogle Scholar
  60. Scott RA, Hahn JE, Doniach S, Freeman HC, Hodgson KO (1982) Polarized X-ray absorption-spectra of oriented plastocyanin single-crystals: investigation of methionine copper coordination. J Am Chem Soc 104:5364–5369CrossRefGoogle Scholar
  61. Shanno DF (1970) Conditioning of quasi-Newton methods for function minimization. Math Comput 24:647–656CrossRefGoogle Scholar
  62. Soderhjelm P, Ryde U (2006) Combined computational and crystallographic study of the oxidised states of NiFe hydrogenase. THEOCHEM J Mol Struct 770:199–219CrossRefGoogle Scholar
  63. Sproviero EM, Gascon JA, McEvoy JP, Brudvig GW, Batista VS (2006a) Characterization of synthetic oxomanganese complexes and the inorganic core of the O2-evolving complex in photosystem II: evaluation of the DFT/B3LYP level of theory. J Inorg Biochem 100:786–800CrossRefPubMedGoogle Scholar
  64. Sproviero EM, Gascon JA, McEvoy JP, Brudvig GW, Batista VS (2006b) QM/MM models of the O2-evolving complex of photosystem II. J Chem Theory Comput 2:1119–1134CrossRefGoogle Scholar
  65. Sproviero EM, Gascon JA, McEvoy JP, Brudvig GW, Batista VS (2007) Structural models of the oxygen-evolving complex of photosystem II. Curr Opin Struct Biol 17:173–180CrossRefPubMedGoogle Scholar
  66. Sproviero EM, Brudvig GW, Batista VS (2008a) A P-EXAFS molecular refinement protocol. J Phys Chem (in preparation)Google Scholar
  67. Sproviero EM, Gascon JA, McEvoy JP, Brudvig GW, Batista VS (2008b) Computational studies of the O2-evolving complex of photosystem II and biomimetic oxomanganese complexes. Coord Chem Rev 252:395–415CrossRefPubMedGoogle Scholar
  68. Sproviero EM, Gascon JA, McEvoy JP, Brudvig GW, Batista VS (2008c) A model of the oxygen evolving center of photosystem II predicted by structural refinement based on EXAFS simulations. J Am Chem Soc 130:6728–6730CrossRefPubMedGoogle Scholar
  69. Sproviero EM, Gascon JA, McEvoy JP, Brudvig GW, Batista VS (2008d) QM/MM study of the catalytic cycle of water splitting in photosystem II. J Am Chem Soc 130:3428–3442CrossRefPubMedGoogle Scholar
  70. Sproviero EM, Shinopoulos K, Gascon JA, McEvoy JP, Brudvig GW, Batista VS (2008e) QM/MM computational studies of substrate water binding to the oxygen evolving complex of Photosystem II. Phil Trans R Soc Lond B 363:1149–1156CrossRefGoogle Scholar
  71. Stebler M, Ludi A, Burgi HB (1986) (Phen)2Mn(IV)(μ-O)2Mn(III)(Phen)2(PF6)3CH3CN and (Phen)2Mn(IV)(μ-O)2Mn(IV)(Phen)2 (ClO4)4CH3CN (Phen = 1,10-Phenanthroline): crystal-structure analyses at 100-K, interpretation of disorder, and optical, magnetic, and electrochemical results. Inorg Chem 25:4743–4750CrossRefGoogle Scholar
  72. Stern EA (1974) Theory of extended X-ray-absorption fine-structure. Phys Rev B 10:3027–3037CrossRefGoogle Scholar
  73. Thorp HH, Brudvig GW (1991) The physical inorganic-chemistry of manganese relevant to photosynthetic oxygen evolution. New J Chem 15:479–490Google Scholar
  74. Tsutsui Y, Wasada H, Funahashi S (1999) Reaction mechanism of water exchange on di- and trivalent cations of the first transition series and structural stability of seven-coordinate species. J Mol Struct THEOCHEM 462:379–390CrossRefGoogle Scholar
  75. Versluis L, Ziegler T (1988) The determination of molecular-structures by density functional theory: the evaluation of analytical energy gradients by numerical-integration. J Chem Phys 88:322–328CrossRefGoogle Scholar
  76. Vreven T, Morokuma K (2000a) On the application of the IMOMO (integrated molecular orbital plus molecular orbital) method. J Comput Chem 21:1419–1432CrossRefGoogle Scholar
  77. Vreven T, Morokuma K (2000b) The ONIOM (our own N-layered integrated molecular orbital plus molecular mechanics) method for the first singlet excited (S-1) state photoisomerization path of a retinal protonated Schiff base. J Chem Phys 113:2969–2975CrossRefGoogle Scholar
  78. Warshel A, Levitt M (1976) Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of carbonium-ion in reaction of lysozyme. J Mol Biol 103:227–249CrossRefPubMedGoogle Scholar
  79. Yachandra VK (2002) Structure of the manganese complex in photosystem II: insights from X-ray spectroscopy. Phil Trans R Soc Lond Ser B 357:1347–1357CrossRefGoogle Scholar
  80. Yachandra VK, Sauer K, Klein MP (1996) Manganese cluster in photosynthesis: where plants oxidize water to dioxygen. Chem Rev 96:2927–2950CrossRefPubMedGoogle Scholar
  81. Yano J, Pushkar Y, Glatzel P, Lewis A, Sauer K, Messinger J, Bergmann U, Yachandra V (2005) High-resolution Mn EXAFS of the oxygen-evolving complex in photosystem II: structural implications for the Mn4Ca cluster. J Am Chem Soc 127:14974–14975CrossRefPubMedGoogle Scholar
  82. Yano J, Kern J, Sauer K, Latimer MJ, Pushkar Y, Biesiadka J, Loll B, Saenger W, Messinger J, Zouni A, Yachandra VK (2006) Where water is oxidized to dioxygen: structure of the photosynthetic Mn4Ca cluster. Science 314:821–825CrossRefPubMedGoogle Scholar
  83. Yano J, Kern J, Pushkar Y, Sauer K, Glatzel P, Bergmann U, Messinger J, Zouni A, Yachandra VK (2008) High-resolution structure of the photosynthetic Mn4Ca catalyst from X-ray spectroscopy. Phil Trans R Soc Lond B 363:1139–1147CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Eduardo M. Sproviero
    • 1
  • Michael B. Newcomer
    • 1
  • José A. Gascón
    • 1
    • 2
  • Enrique R. Batista
    • 3
  • Gary W. Brudvig
    • 1
  • Victor S. Batista
    • 1
  1. 1.Department of ChemistryYale UniversityNew Haven06520-8107USA
  2. 2.Department of ChemistryUniversity of ConnecticutStorrsUSA
  3. 3.Theoretical DivisionLos Alamos National LaboratoryLos AlamosUSA

Personalised recommendations