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).
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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
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 58:7565–7576
Ankudinov AL, Bouldin CE, Rehr JJ, Sims J, Hung H (2002) Parallel calculation of electron multiple scattering using Lanczos algorithms. Phys Rev B 65:104–107
Ashley CA, Doniach S (1975) Theory of extended X-ray absorption-edge fine-structure (EXAFS) in crystalline solids. Phys Rev B 11:1279–1288
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 30:431–434
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 29:463–495
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 1655:158–171
Broyden CG (1970) Convergence of single-rank quasi-Newton methods. Math Comput 24:365–382
Brudvig GW, Crabtree RH (1986) Mechanism for photosynthetic O2 evolution. Proc Natl Acad Sci USA 83:4586–4588
Cooper SR, Calvin M (1977) Mixed-valence interactions in di-μ-oxo bridged manganese complexes. J Am Chem Soc 99:6623–6630
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 100:7248–7252
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 117:5179–5197
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 461:1–21
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 1503:24–39
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 6:4781–4792
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 116:5239–5249
Dykstra CE (1993) Electrostatic interaction potentials in molecular-force fields. Chem Rev 93:2339–2353
Fan LY, Ziegler T (1991) The influence of self-consistency on nonlocal density functional calculations. J Chem Phys 94:6057–6063
Ferreira KN, Iverson TM, Maghlaoui K, Barber J, Iwata S (2004) Architecture of the photosynthetic oxygen-evolving center. Science 303:1831–1838
Flank AM, Weininger M, Mortenson LE, Cramer SP (1986) Single-crystal EXAFS of nitrogenase. J Am Chem Soc 108:1049–1055
Fletcher R (1970) A new approach to variable metric algorithms. Comput J 13:317–322
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, CT
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 2:175–186
Gascon JA, Sproviero EM, Batista VS (2006b) Computational studies of the primary phototransduction event in visual rhodopsin. Acc Chem Res 39:184–193
Goldfarb D (1970) A family of variable-metric methods derived by variational means. Math Comput 24:23–26
Haumann M, Junge W (1999) Evidence for impaired hydrogen-bonding of tyrosine YZ in calcium-depleted photosystem II. Biochim Biophys Acta 1411:121–133
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 44:1894–1908
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 41:13328–13334
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 42:6209–6217
Hillier W, Wydrzynski T (2004) Substrate water interactions within the photosystem II oxygen evolving complex. Phys Chem Chem Phys 6:4882–4889
Hillier W, Wydrzynski T (2008) 18O-Water exchange in photosystem II: substrate binding and intermediates of the water splitting cycle. Coord Chem Rev 252:306–317
Hoganson CW, Babcock GT (1997) A metalloradical mechanism for the generation of oxygen from water in photosynthesis. Science 277:1953–1956
Jaguar (2003) Jaguar 5.5. Schrodinger LLC, Portland, OR
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 255–265
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 499–513
Lee PA, Pendry JB (1975) Theory of the extended X-ray absorption fine structure. Phys Rev B 11:2795–2811
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 283:1524–1527
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 438:1040–1044
Lundberg M, Siegbahn PEM (2004) Theoretical investigations of structure and mechanism of the oxygen-evolving complex in PSII. Phys Chem Chem Phys 6:4772–4780
Lundberg M, Blomberg MRA, Siegbahn PEM (2003) Modeling water exchange on monomeric and dimeric Mn centers. Theor Chem Acc 110:130–143
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 33:5157–5160
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 16:1170–1179
McEvoy JP, Brudvig GW (2004) Structure-based mechanism of photosynthetic water oxidation. Phys Chem Chem Phys 6:4754–4763
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 14:479–487
Messinger J (2004) Evaluation of different mechanistic proposals for water oxidation in photosynthesis on the basis of Mn4O x Ca structures for the catalytic site and spectroscopic data. Phys Chem Chem Phys 6:4764–4771
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 92:3209–3213
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)
Noodleman L (1981) Valence bond description of anti-ferromagnetic coupling in transition-metal dimers. J Chem Phys 74:5737–5743
Noodleman L, Case DA (1992) Density functional theory of spin polarization and spin coupling in iron–sulfur clusters. Adv Inorg Chem 38:423–470
Noodleman L, Davidson ER (1986) Ligand spin polarization and antiferromagnetic coupling in transition-metal dimers. Chem Phys 109:131–143
Noodleman L, Peng CY, Case DA, Mouesca JM (1995) Orbital interactions, electron delocalization and spin coupling in iron–sulfur clusters. Coord Chem Rev 144:199–244
Nugent JHA, Rich AM, Evans MCW (2001) Photosynthetic water oxidation: towards a mechanism. Biochim Biophys Acta 1503:138–146
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 15:5108–5123
Pecoraro VL, Baldwin MJ, Gelasco A (1994) Interaction of manganese with dioxygen and its reduced derivatives. Chem Rev 94:807–826
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 1503:7–23
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 38:1036–1037
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 112:7255–7260
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 27:1204–1207
Schlegel HB (1987) Optimization of equilibrium geometries and transition structures. Adv Chem Phys 67:249–285
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 274:30387–30392
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 104:5364–5369
Shanno DF (1970) Conditioning of quasi-Newton methods for function minimization. Math Comput 24:647–656
Soderhjelm P, Ryde U (2006) Combined computational and crystallographic study of the oxidised states of NiFe hydrogenase. THEOCHEM J Mol Struct 770:199–219
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 100:786–800
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 2:1119–1134
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 17:173–180
Sproviero EM, Brudvig GW, Batista VS (2008a) A P-EXAFS molecular refinement protocol. J Phys Chem (in preparation)
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 252:395–415
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 130:6728–6730
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 130:3428–3442
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 363:1149–1156
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 25:4743–4750
Stern EA (1974) Theory of extended X-ray-absorption fine-structure. Phys Rev B 10:3027–3037
Thorp HH, Brudvig GW (1991) The physical inorganic-chemistry of manganese relevant to photosynthetic oxygen evolution. New J Chem 15:479–490
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 462:379–390
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 88:322–328
Vreven T, Morokuma K (2000a) On the application of the IMOMO (integrated molecular orbital plus molecular orbital) method. J Comput Chem 21:1419–1432
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 113:2969–2975
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 103:227–249
Yachandra VK (2002) Structure of the manganese complex in photosystem II: insights from X-ray spectroscopy. Phil Trans R Soc Lond Ser B 357:1347–1357
Yachandra VK, Sauer K, Klein MP (1996) Manganese cluster in photosynthesis: where plants oxidize water to dioxygen. Chem Rev 96:2927–2950
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 127:14974–14975
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 314:821–825
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 363:1139–1147
Acknowledgements
V. S. Batista acknowledges a generous allocation of DOE supercomputer time from the National Energy Research Scientific Computing Center (NERSC) and financial support from the Grants NSF ECCS # 0404191, DOE DE-FG02-07ER15909, NIH 2R01-GM043278 and the US-Israel BSF R08164. G. W. Brudvig acknowledges support from NIH GM32715.
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Sproviero, E.M., Newcomer, M.B., Gascón, J.A. et al. The MoD-QM/MM methodology for structural refinement of photosystem II and other biological macromolecules. Photosynth Res 102, 455–470 (2009). https://doi.org/10.1007/s11120-009-9467-6
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DOI: https://doi.org/10.1007/s11120-009-9467-6