Abstract
Motivated by several long-lasting mechanistic questions for biomolecular proton pumps, we have engaged in developing hybrid quantum mechanical/molecular mechanical (QM/MM) methods that allow an efficient and reliable description of long-range proton transport in transmembrane proteins. In this review, we briefly discuss several relevant issues: the need to develop a “multi-scale” generalized solvent boundary potential (GSBP) for the analysis of chemical events in large trans-membrane proteins, approaches to validate such a protocol, and the importance of improving the flexibility of QM/MM Hamiltonian. Several recent studies of model and realistic protein systems are also discussed to help put the discussions into context. Collectively, these studies suggest that the QM/MM-GSBP framework based on an approximate density functional theory (SCC-DFTB) as QM holds the promise to strike the proper balance between computational efficiency, accuracy and generality. With additional improvements in the methodology and recent developments by others, especially powerful sampling techniques, this “multi-scale” framework will be able to help unlock the secrets of proton pumps and other biomolecular machines.
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References
Nicholls DG, Ferguson SJ. Bioenergetics 3. Academic Press, New York, 2002
Hill TL. Free Energy Transduction in Biology. Academic Press, New York, 1977
Hosler JP, Ferguson-Miller S, Mills DA. Energy transduction: Proton transfer through the respiratory complexes. Annu Rev Biochem, 2006, 75: 165–187
Brzezinski P, Gennis RB. Cytochrome c oxidase: Exciting progress and remaining mysteries. J Bioenerg Biomember, 2008, 40: 521–531
Kaila VR, Verkhovsky MV, Wikström M. Proton-coupled electron transfer in cytochrome c oxidase. Chem Rev, 2010, 110: 7062–7081
Schliwa M (Ed). Molecular Motors. Wiley-VCH, 2002
Quenneville J, Popovic DM, Stuchebrukhov AA. Combined DFT and electrostatics study of the proton pumping mechanism in cytochrome c oxidase. Biochim Biophys Acta, 2006, 1757: 1035–1046
Kaila VRI, Sharma V, Wikström M. The identity of the transient proton loading site of the proton-pumping mechanism of cytochrome c oxidase. Biochim Biophys Acta Bioeng, 2011, 1807: 80–84
Lee HJ, Svahn E, Swanson JMJ, Lepp H, Voth GA, Brzezinski P, Gennis RB. Intricate role of water in proton transport through cytochrome c oxidase. J Am Chem Soc, 2010, 132: 16225–16239
Olsson MHM, Warshel A. Monte carlo simulations of proton pumps: On the working principles of the biological valve that controls proton pumping in cytochrome c oxidase. Proc Natl Acad Sci USA, 2006, 103(17): 6500–6505
Pisliakov AV, Sharma PK, Chu ZT, Haranczyk M, Warshel A. Electrostatic basis for the unidirectionality of the primary proton transfer in cytochrome c oxidase. Proc Natl Acad Sci USA, 2008, 105: 7726–7731
Hammes-Schiffer S, Stuchebrukhov AA. Theory of coupled electron and proton transfer reactions. Chem Rev, 2010, 110: 6939–6960
Siegbahn PEM, Blomberg MRA. Quantum chemical studies of proton-coupled electron transfer in metalloenzymes. Chem Rev, 2010, 110: 7040–7061
Yang S, Cui Q. Glu-286 rotation and water wire reorientation are unlikely the gating elements for proton pumping in cytochrome c oxidase. Biophys J, 2011, 101: 61–69
Cui Q. Theoretical and computational studies of vectorial processes in biological systems. Special Issue on New Perspectives in Theoretical Chemistry. Theor Chem Acc, 2006, 116: 51–59
Riccardi D, Yang S, Cui Q. Proton transfer function of carbonic anhydrase: Insights from QM/MM simulations. Biochim Biophys Acta, 2010, 1804: 342–351
Kato M, Pisliakov AV, Warshel A. The barrier for proton transport in aqauporins as a challenge for electrostatic models: The role of protein relaxation in mutational calculations. Proteins Struct Funct Bioinfor, 2006, 64: 829–844
Swanson JMJ, Maupin CM, Chen HN, Petersen MK, Xu JC, Wu YJ, Voth GA. Proton solvation and transport in aqueous and biomolecular systems: Insights from computer simulations. J Phys Chem B, 2007, 111: 4300–4314
Siegbahn PEM, Blomberg MRA. Energy diagrams and mechanism for proton pumping in cytochrome c oxidase. Biochim Biophys Acta, 2007, 1767: 1143–1156
Kaila VRI, Verkhovsky MI, Hummer G, Wikstrom M. Glutamic acid 242 is a valve in the proton pump of cytochrome c oxidase. Proc Acad Natl Sci USA, 2008, 105(17): 6255–6259
Gunner MR, Mao J, Song Y, Kim J. Factors influencing the energetics of electron and proton transfers in proteins what can be learned from calculations? Biochim Biophys Acta, 2006, 1757: 942–968
Ghosh N, Prat-Resina X, Cui Q. Towards a reliable molecular model of cytochrome c oxdiase: Insights from microscopic pK a calculations. Biochemistry, 2009, 48: 2468–2485
Schaefer P, Riccardi D, Cui Q. Reliable treatment of electrostatics in combined QM/MM simulation of macromolecules. J Chem Phys, 2005, 123: 014905
Riccardi D, Schaefer P, Yang Y, Yu H, Ghosh N, Prat-Resina X, König P, Li G, Xu D, Guo H, Elstner M, Cui Q. Development of effective quantum mechanical/molecular mechanical (QM/MM) methods for complex biological processes (Feature Article). J Phys Chem B, 2006, 110: 6458–6469
Im W, Bernéche S, Roux B. Generalized solvent boundary potential for computer simulations. J Chem Phys, 20011, 14(7): 2924–2937
Brooks CL, Karplus M. Deformable stochastic boundaries in molecular-dynamics. J Chem Phys, 1983, 79(12): 6312–6325
Qin L, Hiser C, Mulichak A, Garavito RM, Ferguson-Miller S. Identification of conserved lipid/detergent-binding sites in a high-resolution structure of the membrane protein cytochrome c oxidase. Proc Natl Acad Sci USA, 2006, 103: 16117–16122
Rou B. Influence of the membrane potential on the free energy of an intrinsic protein. Biophys J, 1997, 73: 2980–2989
Riccardi D, Schaefer P, Cui Q. pK a calculations in solution and proteins with QM/MM free energy perturbation simulations. J Phys Chem B, 2005, 109: 17715–17733
Riccardi D, Cui Q. pK a analysis for the zinc-bound water in human carbonic anhydrase II: Benchmark for “multi-scale” QM/MM simulations and mechanistic implications. J Phys Chem A, 2007, 111: 5703–5711
Benighaus T, Thiel W. Efficiency and accuracy of the generalized solvent boundary potential for hybrid QM/MM simulations: Implementation for semiempirical Hamiltonians. J Chem Theo Comp, 2008, 4: 1600–1609
Schutz CN, Warshel A. What are dielectric “constants” of proteins and how to validate electrostatic models? Proteins Struct Funct Genet, 2001, 44: 400–417
Simonson T. Electrostatics and dynamics of proteins. Rep Prog Phys 2003, 66: 737–787
Guest WC, Cashman NR, Plotkin SS. A theory for the anisotropic and inhomogeneous dielectric properties of proteins. Phys Chem Chem Phys, 2011, 13: 6286–6295
Li G, Zhang X, Cui Q. Free energy perturbation calculations with combined QM/MM potentials complications, simplifications, and applications to redox potential calculations. J Phys Chem B, 2003, 107: 8643–8653
Konig PH, Hoffmann M, Frauenheim T, Cui Q. A critical evaluation of different QM/MM frontier treatments using SCC-DFTB as the QM method. J Phys Chem B, 2005, 109: 9082–9095
Frenkel D, Smit B. Understanding Molecular Simulations: from Algorithms to Applications. Academic Press, San Diego, 1996
Li G, Cui Q. pKa calculations with QM/MM free energy perturbations. J Phys Chem B, 2003, 107: 14521–14528
Ghosh N, Cui Q. pKa of residue 66 in staphylococal nuclease: Insights from QM/MM simulations with conventional sampling. J Phys Chem B, 2008, 112: 8387–8397
Goyal P, Ghosh N, Phatak P, Clemens M, Gaus M, Elstner M, Cui Q. Proton storage site in bacteriorhodopsin: New insights from QM/MM simulations of microscopic pK a and infrared spectra. J Am Chem Soc, In press
Elstner M, Porezag D, Jungnickel G, Elsner J, Haugk M, Frauenheim T, Suhai S, Seifert G. Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties. Phys Rev B, 58(11) (1998) 7260–7268
MacKerell AD Jr, et al. All-atom empirical potential for molecular modeling and dynamics studies of proteins. J Phys Chem B, 1998, 102: 3586–3616
Range K, Riccardi D, Elstner M, Cui Q, York D. Benchmark calculations of proton affinities and gas phase basicities of molecules important in the study of biological phosphoryl transfer. Phys Chem Chem Phys, 2005, 7: 3070–3079
Yang Y, Yu H, York D, Cui Q, Elstner M. Extension of the self-consistent charge density-functional tight-binding method: Third-order expansion of the density functional theory total energy and introduction of a modified effective coulomb interaction. 2007, J Phys Chem A, 111: 10861–10873
Gaus M, Cui Q, Elstner M. Dftb3: Extension of the self-consistent-charge density-functional tight-binding method (SCC-DFTB). J Chem Theor Comp, 2011, 7: 931–948
Simonson T. Gaussian fluctuations and linear response in an electron transfer protein. Proc Natl Acad Sci USA, 2002, 99: 6544–6549
Sulpizi M, Sprik M. Acidity constants from vertical energy gaps: Density functional theory based molecular dynamics implementation. Phys Chem Chem Phys, 2008, 10: 5238–3249
Song Y, Michonova-Alexova E, Gunner GM. Calculated proton uptake on anaerobic reduction of cytochrome c oxidase: Is the reaction electroneutral? Biochemistry, 2006, 45: 7959–7975
Simonson T, Carlsson J, Case DA. Proton binding to proteins: pK a calculations with explicit and implicit solvent models. J Am Chem Soc, 2004, 126: 4167–4180
Damjanovic A, Schlessman JL, Fitch CA, García AE, García-Moreno B. Role of flexibility and polarity as determinants of the hydration of internal cavities and pockets in proteins. Biophys J, 2007, 93: 2791–804
Isom DG, Castaneda CA, Velu PD, Garcia-Moreno BE. Charges in the hydrophobic interior of proteins. Proc Natl Acad Sci USA, 2010, 107: 16096–16100
Damjanovic A, Wu XW, Garcia-Moreno B, Brooks BR. Backbone relaxation coupled to the ionization of internal groups in proteins: A self-guided langevin dynamics study. Biophys J, 2008, 95(9): 4091–4101
Zheng LQ, Chen MG, Yang W. Random walk in orthogonal space to achieve efficient free-energy simulation of complex systems. Proc Natl Acad Sci USA, 2008, 105: 20227–20232
Dwyer JJ, Gittis AG, Karp DA, Lattman EE, Spencer DS, Stites WE, Garcia-Moreno B. High apparent dielectric constants in the interior of a protein reflect water penetration. Biophys J, 2000, 79(3): 1610–1620
Denisov VP, Schlessman JL, Garcia-Moreno B, Halle B. Stabilization of internal charges in a protein: Water penetration or conformational change? Biophys J, 2004, 87(6): 3982–3994
Karp DA, Gittis AG, Stahley MR, Fitch CA, Stites WE, Garcia-Moreno B. High apparent dielectric constant inside a protein reflects structural reorganization coupled to the ionization of an internal asp. Biophys J, 2007, 92(6): 2041–2053
Leontyev IV, Stuchebrukhov AA. Electronic continuum model for molecular dynamics simulations of biological molecules. J Chem Theor Comp, 2010, 6: 1498–1508
Brooks BR, Brooks III CL, Mackerell AD, Nilsson L, Petrella RJ, Roux B, Won Y, Archontis G, Bartels C, Boresch S, Caflisch A, Caves L, Cui Q, Dinner AR, Feig M, Fischer S, Gao J, Hodoscek M, Im W, Kuczera K, Lazaridis T, Ma J, Ovchinnikov V, Paci E, Pastor RW, Post CB, Pu JZ, Schaefer M, Tidor B, Venable RM, Woodcock HL, Wu X, Yang W, York DM, Karplus M. Charmm: The biomolecular simulation program. J Comp Chem, 2009, 30: 1545–1614
Stote R, Karplus SDJM. On the treatment of electrostatics interactions in biomolecular simulations. J Chim Phys, 1991, 88: 2419–2433
Steinbach PJ, Brooks BR. New spherical-cutoff methods for long-range forces in macro-molecular simulation. J Comput Chem, 1994, 15: 667–683
Kato M, Warshel A. Using a charging coordinate in studies of ionozation induced partial unfolding. J Phys Chem B, 2006, 110: 11566–11570
Park S. Comparison of the serial and parallel algorithms of generalized ensemble simulations: An analytical approach. Phys Rev E, 2008, 77: 016709
Wang FG, Landau DP. Efficient, multiple-range random walk algorithm to calculate the density of states. Phys Rev Lett, 2001, 86: 2050–2053
Gao YQ. An integrate-over-temperature approach for enhanced sampling. J Chem Phys, 2008, 128(6): 064105
Gao YQ. Self-adaptive enhanced sampling in the energy and trajectory spaces: Accelerated thermodynamics and kinetic calculations. J Chem Phys, 2008, 128(13): 134111
Phatak P, Ghosh N, Yu H, Cui Q, M Elstner. Amino acids with an intermolecular proton bond as the proton storage site in bacteriorhodopsin. Proc Acad Natl Sci USA, 2008, 105: 19672–19677
Li HZ, Fajer M, Yang W. Simulated scaling method for localized enhanced sampling and simultaneous “alchemical” free energy simulations: A general method for molecular mechanical, quantum mechanical, and quantum mechanical/molecular mechanical simulations. J Chem Phys, 2007, 126: 024106
Garczarek F, Gerwert K. Functional waters in intraprotein proton transfer monitored by ftir difference spectroscopy. Nature, 2006, 439: 109–112
Brown LS, Sasaki J, Kandori H, Maeda A, Needleman R, Lanyi JK. Glutamic acid 204 is the terminal proton release group at the extracellular surface of bacteriorhodopsin. J Biol Chem, 1995, 270: 27122–27126
Balashov SP, Imasheva ES, Ebrey TG, Chen N, Menick DR, Crouch RK. Glutamate-194 to Cysteine mutation inhibits fast light-induced proton release in bacteriorhodopsin. Biochemistry, 1997, 36: 8671–8676
Richter HT, Brown LS, Needleman R, Lanyi JK. A linkage of the pK a's of Asp-85 and Glu-204 forms part of the reprotonation switch of bacteriorhodopsin. Biochemistry, 1996, 35: 4054–4062
Essen LO, Siegert R, Lehmann WD, Oesterhelt D. Lipid patches in membrane protein oligomers: Crystal structure of the bacteriorhodopsinlipid complex. Proc Natl Acad Sci USA, 1998, 95: 11673–11678
Zscherp C, Schlesinger R, Tittor J, Oesterhelt D, Heberle J. In situ determination of transient pK a changes of internal amino acids of bacteriorhodopsin by using time-resolved attenuated total reflection fourier-transform infrared spectroscopy. Proc Natl Acad Sci USA, 1999, 96: 5498–5503
Garczarek F, Brown LS, Lanyi JK, Gerwert K. Proton binding within a membrane protein by a protonated water cluster. Proc Natl Acad Sci USA, 2005, 102: 3633–3638
Headrick JM, Diken EG, Walters RS, Hammer NI, Christie RA, Cui J, Myshakin EM, Duncan MA, Johnson MA, Jordan KD. Spectral signatures of hydrated proton vibrations in water clusters. Science, 2005, 308: 1765–1769
Spassov VZ, Luecke H, Gerwert, K, Bashford D. pK a calculations suggest storage of an excess proton in a hydrogen-bonded water network in bacteriorhodopsin. J Mol Biol, 2001, 312: 203–219
Mathias G, Marx, D. Structures and spectral signatures of protonated water networks in bacteriorhodopsin. Proc Natl Acad Sci USA, 2007, 104: 6980–6985
Balashov S. Protonation reactions and their coupling in bacteriorhodopsin. Biochim Biophys Acta, 2000, 1469: 75–95
Balashov SP, Imasheva E, Govindjee R, Ebrey TG. Titration of aspartate-85 in bacteriorhodopsin: What it says about the mechanisms of chromophore isomerization and proton release. Biophhys J, 1996, 70: 473–481
Balashov SP, Govindjee R, Kono M, Imasheva E, Mishra S, Ebrey TG, Crouch R, Menick DR, Feng Y. The pK a of aspartate-85 and control of thermal isomerization and proton release in arginine-82 to lysine mutant of bacteriorhodopsin. Biochemistry, 1995, 34: 8820–8834
Cui Q, Elstner M, Kaxiras E, Frauenheim Th, Karplus M. A QM/MM implementation of the self consistent charge density functional tight binding (SCC-DFTB) method. J Phys Chem B, 2001, 105(2): 569–585
Yu H, Cui Q. The vibrational spectra of protonated water clusters: A benchmark for SCC-DFTB. J Chem Phys, 2007, 127: 234504
Kim YC, Wikström M, Hummer G. Kinetic gating of the proton pump in cytochrome c oxidase. Proc Natl Acad Sci USA, 2009, 106: 13707–13712
Riccardi D, Koenig P, Guo H, Cui Q. Proton transfer in carbonic anhydrase is controlled by electrostatics rather than the orientation of the acceptor. Biochemistry, 2008, 47: 2369–2378
Voth GA. Computer simulation of proton solvation and transport in aqueous and biomolecular systems. Acc Chem Res, 2006, 39: 143–150
Marx D, Tuckerman ME, Hutter J, Parrinello M. The nature of the hydrated excess proton in water. Nature, 1999, 397: 601–604
Bondar AN, Fischer S, Smith JC, Elstner M, Suhai S. Key role of electrostatic interactions in bacteriorhodopsin proton transfer. J Am Chem Soc, 2004, 126: 14668–14677
König P, Ghosh N, Hoffman M, Elstner M, Tajkhorshid E, Frauenheim T, Cui Q. Towards theoretical analysis of long-range proton transfer kinetics in biomolecular pumps. J Phys Chem A (Truhlar Issue), 2006, 110: 548–563
Phatak P, Frahmcke JS, Wanko M, Hoffmann M, Strodel P, Smith JC, Suhai S, Bondar AN, Elstner M. Long-distance proton transfer with a break in the bacteriorhodopsin active site. J Am Chem Soc, 2009, 131: 7064–7078
Sattelmeyer KW, Tirado-Rives J, Jorgensen W. Comparison of SCC-DFTB and NDDO-based semiempirical molecular orbital methods for organic molecules. J Phys Chem A, 2006, 110: 13551–13559
Otte N, Scholten M, Thiel W. Looking at self-consistent-charge density functional tight binding from a semiempirical perspective. J Phys Chem A, 2007, 111: 5751–5755
Kruger T, Elstner M, Schiffels P, Frauenheim T. Validation of the density functional based tight-binding approximation method for the calculation of reaction energies and other data. J Chem Phys, 2005, 122: 114110
Riccardi D, König P, Prat-Resina X, Yu H, Elstner M, Frauenheim T, Cui Q. “Proton holes” in long-range proton transfer reactions in solution and enzymes: A theoretical analysis. J Am Chem Soc, 2006, 128: 16302–16311
Elstner M. SCC-DFTB: What is the proper degree of self-consistency? J Phys Chem A, 2007, 111: 5614–5621
Riccardi D, Li G, Cui Q. The importance of van der Waals interactions in QM/MM simulations. J Phys Chem B, 2004, 108: 6467–6478
Malolepsza E, Morokuma HA, Morokuma K, Accurate vibrational frequencies using the selfconsistent-charge density-functional tight-binding method. Chem Phys Lett, 2005, 412: 237–243
Goyal P, Elstner M, Cui Q. Application of the SCC-DFTB method to neutral and protonated water clusters and bulk water. J Phys Chem B, 2011, 115: 6790–6805
Yang Y, Yu H, Cui Q. Extensive conformational changes are required to turn on Atp hydrolysis in myosin. J Mol Biol, 2008, 381: 1407–1420
Yang Y, Cui Q. Does water relayed proton transfer play a role in phosphoryl transfer reactions? A theoretical analysis of uridine 3′-m-nitrobenzyl phosphate isomerization in water and tert-butanol. J Phys Chem B, 2009, 113: 4930–4933 NIHMS:103392
Field MJ, Bash PA, Karplus M. A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations. J Comput Chem, 1990, 11(6): 700–733
Freindorg M, Gao J. 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, 1996, 17(3): 386–395
Bash PA, Ho LL, MacKerell Jr AD, Levine D, Hallstrom P. Progress toward chemical accuracy in the computer simulation of condensed phase reactions. Proc Natl Acad Sci USA, 1996, 93: 3698–3703
Yang Y, Yu H, York D, Elstner M, Cui Q. Description of phosphate hydrolysis reactions with the self-consistent-charge density-functional-tight-binding (SCC-DFTB) theory 1 parameterization. J Chem Theory Comput, 2008, 4(12): 2067–2084
Giese TJ, York DM. Charge-dependent model for many-body polarization, exchange, and dispersion interactions in hybrid quantum mechanical/molecular mechanical calculations. J Chem Phys, 2007, 127: 194101
Thiel W. Perspectives on semiempirical molecular orbital theory. Adv Chem Phys, 1996, 93: 703–757
Das D, Eurenius KP, Billings EM, Sherwood P, Chattfield DC, Hodošček, M, Brooks BR. Optimization of quantum mechanical molecular mechanical partitioning schemes: Gaussian delocalization of molecular mechanical charges and the double link atom method. J Chem Phys, 2002, 117: 10534–10547
Wang B, Truhlar DG. Including charge penetration effects in molecular modeling. J Chem Theo Comp, 2010, 6: 3330–3342
Min DH, Zheng LQ, Harris W, Chen MG, Lv C, Yang W. Practically efficient QM/MM alchemical free energy simulations: The orthogonal space random walk strategy. J Chem Theor Comput, 2010, 6: 2253–2266
Johansson MP, Kaila VRI, Laakkonen L. Charge parameterization of the metal centers in cytochrome c oxidase. J Comutp Chem, 2008, 29: 753–767
Wolf S, Freier E, Potschies M, Hofmann E, Gerwert K. Directional proton transfer in membrane proteins achieved through protonated protein-bound water molecules: a proton diode. Angew Chem Int Ed, 2010, 49: 6889–6893
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Riccardi, D., Zhu, X., Goyal, P. et al. Toward molecular models of proton pumping: Challenges, methods and relevant applications. Sci. China Chem. 55, 3–18 (2012). https://doi.org/10.1007/s11426-011-4458-9
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DOI: https://doi.org/10.1007/s11426-011-4458-9