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QM and QM/MM Simulations of Proteins

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Biomolecular Simulations

Part of the book series: Methods in Molecular Biology ((MIMB,volume 924))

Abstract

Molecular dynamics simulations of biomolecules have matured into powerful tools of structural biology. In addition to the commonly used empirical force field potentials, quantum mechanical descriptions are gaining popularity for structure optimization and dynamic simulations of peptides and proteins. In this chapter, we introduce methodological developments such as the QM/MM framework and linear-scaling QM that make efficient calculations on large biomolecules possible. We identify the most common scenarios in which quantum descriptions of peptides and proteins are employed, such as structural refinement, force field development, treatment of unusual residues, and predicting spectroscopic and exited state properties. The benefits and shortcomings of QM potentials, in comparison to classical force fields, are discussed, with special emphasis on the sampling problems of protein conformational space. Finally, recent examples of QM/MM calculations in light-sensitive membrane proteins illustrate typical applications of the reviewed methods.

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References

  1. Karplus M, McCammon J (2002) Molecular dynamics simulations of biomolecules. Nat Struct Biol 9:646–652

    PubMed  CAS  Google Scholar 

  2. van Gunsteren WF et al. (2006) Biomolecular modeling: goals, problems, perspectives. Angew Chemie Int Ed 45:4064–4092

    Google Scholar 

  3. MacKerell A et al. (1998) All-atom empirical potential for molecular modeling and dynamics studies of proteins. J Phys Chem B 102:3586–3616

    CAS  Google Scholar 

  4. van Gunsteren WF, Billeter SR, Eising AA, Hunenberger PH, Kruger P, Mark AE, Scott WRP, Tironi IG (1996) Biomolecular simulation: the GROMOS manual and user guide. vdf Hochschulverlag, ETH Zurich

    Google Scholar 

  5. Shaw DE, Maragakis P, Lindorff-Larsen K, Piana S, Dror RO, Eastwood MP, Bank JA, Jumper JM, Salmon JK, Shan Y, Wriggers W (2010) Atomic-level characterization of the structural dynamics of proteins. Science 330:341–346

    PubMed  CAS  Google Scholar 

  6. Porezag D, Frauenheim T, Kohler T, Seifert G, Kaschner R (1995) Construction of tight-binding-like potentials on the basis of density-functional theory—application to carbon. Phys Rev B 51:12947–12957

    CAS  Google Scholar 

  7. Elstner M, Porezag D, Jungnickel G, Elsner J, Haugk M, Frauenheim T, Suhai S, Seifert G (1998) Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties. Phys Rev B 58:7260–7268

    CAS  Google Scholar 

  8. Grotendorst J, Attig N, Bluegel S, Marx D (eds) (2009) Multiscale simulation methods in molecular sciences. Publication series of the John von Neumann Institute for computing

    Google Scholar 

  9. Lee T, York D (eds) (2008) Models for biocatalysis: modern techniques and applications. Springer, Berlin

    Google Scholar 

  10. Riccardi D, Schaefer P, Yang Y, Yu H, Ghosh N, Prat-Resina X, Konig P, Li G, Xu D, Guo H, Elstner M, Cui Q (2006) Development of effective quantum mechanical/molecular mechanical (QM/MM) methods for complex biological processes. J Phys Chem B 110:6458–6469

    PubMed  CAS  Google Scholar 

  11. Elstner M, Cui Q (2009) Multi-scale methods for the description of chemical events in biological systems. Publication Series of the John von Neumann Institute for Computing

    Google Scholar 

  12. Gogonea V, Suarez D, van der Vaart A, Merz K (2001) New developments in applying quantum mechanics to proteins. Curr Op Struct Biol 11:217–223

    CAS  Google Scholar 

  13. Goedecker S (1999) Linear scaling electronic structure methods. Rev Mod Phys 71:1085–1123

    CAS  Google Scholar 

  14. Yang W (1991) Direct calculation of electron-density in density-functional theory. Phys Rev Lett 66:1438–1441

    PubMed  CAS  Google Scholar 

  15. Yang W, Lee T (1995) A density-matrix divide-and-conquer approach for electronic-structure calculations of large molecules. J Chem Phys 103:5674–5678

    CAS  Google Scholar 

  16. Dixon S, Merz K (1996) Semiempirical molecular orbital calculations with linear system size scaling. J Chem Phys 104:6643–6649

    CAS  Google Scholar 

  17. Kitaura K, Ikeo E, Asada T, Nakano T, Uebayasi M (1999) Fragment molecular orbital method: an approximate computational method for large molecules. Chem Phys Lett 313:701–706

    CAS  Google Scholar 

  18. Nakano T, Kaminuma T, Sato T, Fukuzawa K, Akiyama Y, Uebayasi M, Kitaura K (2002) Fragment molecular orbital method: use of approximate electrostatic potential. Chem Phys Lett 351:475–480

    CAS  Google Scholar 

  19. Fedorov D, Kitaura K (2006) The three-body fragment molecular orbital method for accurate calculations of large systems. Chem Phys Lett 433:182–187

    CAS  Google Scholar 

  20. Gao A, Zhang D, Zhang J, Zhang Y (2004) An efficient linear scaling method for ab initio calculation of electron density of proteins. Chem Phys Lett 394:293–297

    CAS  Google Scholar 

  21. He X, Zhang J (2005) A new method for direct calculation of total energy of protein. J Chem Phys 122:031103

    Google Scholar 

  22. Zhang D, Zhang J (2003) Molecular fractionation with conjugate caps for full quantum mechanical calculation of protein-molecule interaction energy. J Chem Phys 119:3599–3605

    CAS  Google Scholar 

  23. Rezac J, Salahub D (2010) Multilevel fragment-based approach (MFBA): a novel hybrid computational method for the study of large molecules. J Comp Theor Comput 6:91–99

    CAS  Google Scholar 

  24. Stewart J (1996) Application of localized molecular orbitals to the solution of semiempirical self-consistent field equations. Int J Quant Chem 58:133–146

    CAS  Google Scholar 

  25. Ochsenfeld C, Kussmann J, Lambrech D (2007) Linear-scaling methods in quantum chemistry. Wiley-VCH, New York

    Google Scholar 

  26. He X, Merz K (2010) Divide and conquer Hartree–Fock calculations on proteins. J Comp Theor Comput 6:405–411

    CAS  Google Scholar 

  27. Titmuss S, Cummins P, Bliznyuk A, Rendell A, Gready J (2000) Comparison of linear-scaling semiempirical methods and combined quantum mechanical/molecular mechanical methods applied to enzyme reactions. Chem Phys Lett 320:169–176

    CAS  Google Scholar 

  28. Zhang R, Lev B, Cuervo J, Noskov S, Salahub D (2010) A guide to QM/MM methodology and applications. Adv Quant Chem 59:353–400

    CAS  Google Scholar 

  29. Zhang Y, Kua J, McCammon J (2003) Influence of structural fluctuation on enzyme reaction energy barriers in combined quantum mechanical/molecular mechanical studies. J Phys Chem B 107:4459–4463

    CAS  Google Scholar 

  30. Klahn M, Braun-Sand S, Rosta E, Warshel A (2005) On possible pitfalls in ab initio quantum mechanics/molecular mechanics minimization approaches for studies of enzymatic reactions. J Phys Chem B 109:15645–15650

    PubMed  Google Scholar 

  31. Kollman P (1993) Free-energy calculations—applications to chemical and biochemical phenomena. Chem Rev 93:2395–2417

    CAS  Google Scholar 

  32. March N, Matthai C (2010) The application of quantum chemistry and condensed matter theory in studying amino-acids, protein folding and anticancer drug technology. Theo Chem Acc 125:193–201

    CAS  Google Scholar 

  33. van Mourik T (2004) First-principles quantum chemistry in the life sciences. Phil Trans Royal Soc A 362:2653–2670

    Google Scholar 

  34. Beachy M, Chasman D, Murphy R, Halgren T, Friesner R (1997) Accurate ab initio quantum chemical determination of the relative energetics of peptide conformations and assessment of empirical force fields. J Am Chem Soc 119:5908–5920

    CAS  Google Scholar 

  35. Wei D, Guo H, Salahub D (2001) Conformational dynamics of an alanine dipeptide analog: an ab initio molecular dynamics study. Phys Rev E 64:011907

    CAS  Google Scholar 

  36. Frey R, Coffin J, Newton S, Ramek M, Cheng V, Momany F, Schafer L (1992) Importance of correlation-gradient geometry optimization for molecular conformational-analyses. J Am Chem Soc 114:5369–5377

    CAS  Google Scholar 

  37. Ramek M, Cheng V, Frey R, Newton S, Schafer L (1991) The case of glycine continued—some contradictory SCF results. J Mol Struct Theochem 81:1–10

    CAS  Google Scholar 

  38. Nagai Y, Nakanishi T, Okamoto H, Takeda K, Furukawa Y, Usui K, Mihara H (2005) IR study on stacking manner of peptide nanorings in peptide nanotubes. Jpn J Appl Phys 44:7654–7661

    CAS  Google Scholar 

  39. Abdali S, Niehaus T, Jalkanen K, Cao X, Nafie L, Frauenheim T, Suhai S, Bohr H (2003) Vibrational absorption spectra, DFT and SCC-DFTB conformational study and analysis of [Leu]enkephalin. Phys Chem Chem Phys 5:1295–1300

    CAS  Google Scholar 

  40. Jalkanen K, Jurgensen V, Claussen A, Rahim A, Jensen G, Wade R, Nardi F, Jung C, Degtyarenko I, Nieminen R, Herrmann F, Knapp-Mohammady M, Niehaus T, Frimand K, Suhai S (2006) Use of vibrational spectroscopy to study protein and DNA structure, hydration, and binding of biomolecules: a combined theoretical and experimental approach. Int J Quant Chem 106:1160–1198

    CAS  Google Scholar 

  41. Bour P, Sopkova J, Bednarova L, Malon P, Keiderling T (1997) Transfer of molecular property tensors in Cartesian coordinates: a new algorithm for simulation of vibrational spectra. J Comp Chem 18:646–659

    CAS  Google Scholar 

  42. Scott A, Radom L (1996) Harmonic vibrational frequencies: an evaluation of Hartree–Fock, Moller–Plesset, quadratic configuration interaction, density functional theory, and semiempirical scale factors. J Phys Chem 100:16502–16513

    CAS  Google Scholar 

  43. Jalkanen K, Suhai S (1996) N-acetyl-L-alanine N’-methylamide: a density functional analysis of the vibrational absorption and vibrational circular dichroism spectra. Chem Phys 208:81–116

    CAS  Google Scholar 

  44. Kubelka J, Keiderling T (2001) Differentiation of beta-sheet-forming structures: ab initio-based simulations of IR absorption and vibrational CD for model peptide and protein beta-sheets. J Am Chem Soc 123:12048–12058

    PubMed  CAS  Google Scholar 

  45. Kubelka J, Silva R, Keiderling T (2002) Discrimination between peptide 3(10)- and alpha-helices. Theoretical analysis of the impact of alpha-methyl substitution on experimental spectra. J Am Chem Soc 124:5325–5332

    CAS  Google Scholar 

  46. Kubelka J, Huang R, Keiderling T (2005) Solvent effects on IR and VCD spectra of helical peptides: DFT-based static spectral simulations with explicit water. J Phys Chem B 109:8231–8243

    PubMed  CAS  Google Scholar 

  47. Silva R, Yasui S, Kubelka J, Formaggio F, Crisma M, Toniolo C, Keiderling T (2002) Discriminating 3(10)- from alpha helices: vibrational and electronic CD and IR absorption study of related Aib-containing oligopeptides. Biopolymers 65:229–243

    PubMed  CAS  Google Scholar 

  48. Bour P, Kubelka J, Keiderling T (2002) Ab initio quantum mechanical models of peptide helices and their vibrational spectra. Biopolymers 65:45–59

    PubMed  CAS  Google Scholar 

  49. Bour P, Keiderling T (2003) Empirical modeling of the peptide amide I band IR intensity in water solution. J Chem Phys 119:11253–11262

    CAS  Google Scholar 

  50. Bour P, Keiderling T (2004) Structure, spectra and the effects of twisting of beta-sheet peptides. A density functional theory study. J Mol Struct Theochem 675:95–105

    CAS  Google Scholar 

  51. Bour P, Keiderling T (2005) Vibrational spectral simulation for peptides of mixed secondary structure: method comparisons with the TrpZip model hairpin. J Phys Chem B 109:23687–23697

    PubMed  CAS  Google Scholar 

  52. Ireta J, Neugebauer J, Scheffler M, Rojo A, Galvan M (2003) Density functional theory study of the cooperativity of hydrogen bonds in finite and infinite alpha-helices. J Phys Chem B 107:1432–1437

    CAS  Google Scholar 

  53. Ireta J, Neugebauer J, Scheffler M, Rojo A, Galvan M (2005) Structural transitions in the polyalanine alpha-helix under uniaxial strain. J Am Chem Soc 127:17241–17244

    PubMed  CAS  Google Scholar 

  54. Ireta J, Scheffler M (2009) Density functional theory study of the conformational space of an infinitely long polypeptide chain. J Chem Phys 131:085104

    PubMed  Google Scholar 

  55. Wieczorek R, Dannenberg J (2005) Enthalpies of hydrogen-bonds in alpha-helical peptides. An ONIOM DFT/AM1 study. J Am Chem Soc 127:14534–14535

    PubMed  CAS  Google Scholar 

  56. Salvador P, Asensio A, Dannenberg JJ (2007) The effect of aqueous solvation upon alpha-helix formation for polyalanines. J Phys Chem B 111:7462–7466

    PubMed  CAS  Google Scholar 

  57. Tsai MIH, Xu Y, Dannenberg JJ (2009) Ramachandran revisited. DFT energy surfaces of diastereomeric trialanine peptides in the gas phase and aqueous solution. J Phys Chem B 113:309–318

    CAS  Google Scholar 

  58. Plumley JA, Dannenberg JJ (2010) The importance of hydrogen bonding between the glutamine side chains to the formation of amyloid VQIVYK Parallel beta-sheets: an ONIOM DFT/AM1 Study. J Am Chem Soc 132:1758–1759

    PubMed  CAS  Google Scholar 

  59. Kaminsky J, Jensen F (2007) Force field modeling of amino acid conformational energies. J Comp Theor Comput 3:1774–1788

    CAS  Google Scholar 

  60. Csontos J, Palermo N, Murphy R, Lovas S (2008) Calculation of weakly polar interaction energies in polypeptides using density functional and local Moller-Plesset perturbation theory. J Comp Chem 29:1344–1352

    CAS  Google Scholar 

  61. Wang Z Wu C Lei H Duan Y (2007) Accurate ab initio study on the hydrogen-bond pairs in protein secondary structures. J Comp Theor Comput 3:1527–1537

    CAS  Google Scholar 

  62. Han W, Jalkanen K, Elstner M, Suhai S (1998) Theoretical study of aqueous N-acetyl-L-alanine N ’-methylamide: structures and Raman, VCD, and ROA spectra. J Phys Chem B 102:2587–2602

    CAS  Google Scholar 

  63. Thar J, Zahn S, Kirchner B (2008) When is a molecule properly solvated by a continuum model or in a cluster ansatz? a first-principles simulation of alanine hydration. J Phys Chem B 112:1456–1464

    PubMed  CAS  Google Scholar 

  64. Hudaky I, Hudaky P, Perczel A (2004) Solvation model induced structural changes in peptides. A quantum chemical study on Ramachandran surfaces and conformers of alanine diamide using the polarizable continuum model. J Comp Chem 25:1522–1531

    CAS  Google Scholar 

  65. Wang Z, Duan Y (2004) Solvation effects on alanine dipeptide: a MP2/cc-pVTZ//MP2/6-31G** study of (Phi, Psi) energy maps and conformers in the gas phase, ether, and water. J Comp Chem 25:1699–1716

    CAS  Google Scholar 

  66. Jono R, Watanabe Y, Shimizu K, Terada T (2010) Multicanonical ab Inito QM/MM molecular dynamics simulation of a peptide in an aqueous environment. J Comp Chem 31:1168–1175

    CAS  Google Scholar 

  67. Kwac K, Lee K, Han J, Oh K, Cho M (2008) Classical and quantum mechanical/molecular mechanical molecular dynamics simulations of alanine dipeptide in water: comparisons with IR and vibrational circular dichroism spectra. J Chem Phys 128:105106

    PubMed  Google Scholar 

  68. Nemukhin A, Grigorenko B, Bochenkova A, Kovba V, Epifanovsky E (2004) Structures of the peptide-water complexes studied by the hybrid quantum mechanical-molecular mechanical (QM/MM) technique. Struct Chem 15:3–9

    CAS  Google Scholar 

  69. Han W, Elstner M, Jalkanen K, Frauenheim T, Suhai S (2000) Hybrid SCC-DFTB/molecular mechanical studies of H-bonded systems and of N-acetyl-(L-Ala)(n) N ’-methylamide helices in water solution. Int J Quant Chem 78:459–479

    CAS  Google Scholar 

  70. Hugosson H, Laio A, Maurer P, Rothlisberger U (2006) A comparative theoretical study of dipeptide solvation in water. J Comp Chem 27:672–684

    CAS  Google Scholar 

  71. Degtyarenko I, Jalkanen K, Gurtovenko A, Nieminen R (2007) L-alanine in a droplet of water: a density-functional molecular dynamics study. J Phys Chem B 111:4227–4234

    PubMed  CAS  Google Scholar 

  72. Jalkanen K, Elstner M, Suhai S (2004) Amino acids and small peptides as building blocks for proteins: comparative theoretical and spectroscopic studies. J Mol Struct Theochem 675:61–77

    CAS  Google Scholar 

  73. Jalkanen KJ, Degtyarenko IM, Nieminen RM, Cao X, Nafie LA, Zhu F, Barron LD (2008) Role of hydration in determining the structure and vibrational spectra of L-alanine and N-acetyl L-alanine N ’-methylamide in aqueous solution: a combined theoretical and experimental approach. Theor Chem Acc 119:191–210

    CAS  Google Scholar 

  74. Gaigeot M (2009) Unravelling the conformational dynamics of the aqueous alanine dipeptide with first-principle molecular dynamics. J Phys Chem B 113:10059–10062

    PubMed  CAS  Google Scholar 

  75. Headgordon T, Headgordon M, Frisch M, Brooks C, Pople J (1991) Theoretical-study of blocked glycine and alanine peptide analogs. J Am Chem Soc 113:5989–5997

    CAS  Google Scholar 

  76. Deng Z, Polavarapu P, Ford S, Hecht L, Barron L, Ewig C, Jalkanen K (1996) Solution-phase conformations of N-acetyl-N’-methyl-L-alaninamide from vibrational Raman optical activity. J Phys Chem 100:2025–2034

    CAS  Google Scholar 

  77. Rommelmohle K, Hofmann H (1993) Conformation dynamics in peptides—quantum-chemical calculations and molecular-dynamics simulations on N-acetylalanyl-N’-methylamide. J Mol Struct Theochem 104:211–219

    Google Scholar 

  78. Elstner M, Jalkanen K, Knapp-Mohammady M, Frauenheim T, Suhai S (2000) DFT studies on helix formation in N-acetyl-(L-alanyl)(n)-N ’-methylamide for n=1–20. Chem Phys 256:15–27

    CAS  Google Scholar 

  79. Mohle K, Hofmann H, Thiel W (2001) Description of peptide and protein secondary structures employing semiempirical methods. J Comp Chem 22:509–520

    CAS  Google Scholar 

  80. Elstner M, Jalkanen K, Knapp-Mohammady M, Frauenheim T, Suhai S (2001) Energetics and structure of glycine and alanine based model peptides: approximate SCC-DFTB, AM1 and PM3 methods in comparison with DFT, HF and MP2 calculations. Chem Phys 263:203–219

    CAS  Google Scholar 

  81. Hu H, Elstner M, Hermans J (2003) Comparison of a QM/MM force field and molecular mechanics force fields in simulations of alanine and glycine “dipeptides” (Ace-Ala-Nme and Ace-Gly-Nme) in water in relation to the problem of modeling the unfolded peptide backbone in solution. Protein Struct Funct Genet 50:451–463

    CAS  Google Scholar 

  82. Seabra G, Walker R, Elstner M, Case D, Roitberg A (2007) Implementation of the SCC-DFTB method for hybrid QM/MM simulations within the amber molecular dynamics package. J Phys Chem A 111:5655–5664

    Google Scholar 

  83. Torras J, Seabra G, Deumens E, Trickey S, Roitberg A (2008) A versatile AMBER-Gaussian QM/MM interface through PUPIL. J Comp Chem 29:1564–1573

    CAS  Google Scholar 

  84. Elstner M, Frauenheim T, Suhai S (2003) An approximate DFT method for QM/MM simulations of biological structures and processes. J Mol Struct Theochem 632:29–41

    CAS  Google Scholar 

  85. Nemukhin A, Grigorenko B, Bochenkova A, Topol I, Burt S (2002) A QM/MM approach with effective fragment potentials applied to the dipeptide-water structures. J Mol Struct Theochem 581:167–175

    CAS  Google Scholar 

  86. Elstner M, Frauenheim T, Kaxiras E, Seifert G, Suhai S (2000) A self-consistent charge density-functional based tight-binding scheme for large biomolecules. Phys Stat Sol B 217:357–376

    CAS  Google Scholar 

  87. Seabra G, Walker R, Roitberg A (2009) Are current semiempirical methods better than force fields? a study from the thermodynamics perspective. J Phys Chem A 113:11938–11948

    CAS  Google Scholar 

  88. Echenique P, Alonso J (2008) Efficient model chemistries for peptides. I. General framework and a study of the heterolevel approximation in RHF and MP2 with Pople split-valence basis sets. J Comp Chem 29:1408–1422

    CAS  Google Scholar 

  89. Hornak V, Abel R, Okur A, Strockbine B, Roitberg A, Simmerling C (2006) Comparison of multiple amber force fields and development of improved protein backbone parameters. Protein Struct Funct Genet 65:712–725

    CAS  Google Scholar 

  90. Kang Y (2006) Conformational preferences of non-prolyl and prolyl residues. J Phys Chem B 110:21338–21348

    PubMed  CAS  Google Scholar 

  91. Huang Z, Yu W, Lin Z (2006) First-principle studies of gaseous aromatic amino acid histidine. J Mol Struct Theochem 801:7–20

    CAS  Google Scholar 

  92. Makshakova O, Ermakova E (2010) Computational study of hydrogen-bonding complex formation of helical polypeptides with water molecule. J Mol Struct Theochem 942:7–14

    CAS  Google Scholar 

  93. Riccardi D, Li G, Cui Q (2004) Importance of van der Waals interactions in QM/MM Simulations. J Phys Chem B 108:6467–6478

    PubMed  CAS  Google Scholar 

  94. Valdes H, Pluhackova K, Pitonak M, Rezac J, Hobza P (2008) Benchmark database on isolated small peptides containing an aromatic side chain: comparison between wave function and density functional theory methods and empirical force field. Phys Chem Chem Phys 10:2747–2757

    PubMed  CAS  Google Scholar 

  95. Valdes H, Spiwok V, Rezac J, Reha D, Abo-Riziq A, de Vries M, Hobza P (2008) Potential-energy and free-energy surfaces of glycyl-phenylalanyl-alanine (GFA) tripeptide: experiment and theory. Chemistry Eur J 14:4886–4898

    CAS  Google Scholar 

  96. Valdes H, Pluhackova K, Hobza P (2009) Phenylalanyl-glycyl-phenylalanine tripeptide: a model system for aromatic-aromatic side chain interactions in proteins. J Comp Theor Comput 5:2248–2256

    CAS  Google Scholar 

  97. McKinney B, Urban J (2010) Fluoroolefins as peptidie mimetics. 2. A computational study of the conformational ramifications of peptide bond replacement. J Phys Chem A 114:1123–1133

    PubMed  CAS  Google Scholar 

  98. Zhu X, Yethiraj A, Cui Q (2007) Establishing effective simulation protocols for beta- and alpha/beta-mixed peptides. I. QM and QM/MM models. J Comp Theor Comput 3:1538–1549

    CAS  Google Scholar 

  99. 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

    PubMed  CAS  Google Scholar 

  100. Field M, Bash P, Karplus M (1990) A combined quantum-mechanical and molecular mechanical potential for molecular-dynamics simulations. J Comp Chem 11:700–733

    CAS  Google Scholar 

  101. Gao J, Xia X (1992) A priori evaluation of aqueous polarization effects through monte-carlo QM-MM simulations. Science 258:631–635

    PubMed  CAS  Google Scholar 

  102. Shurki A, Warshel A (2003) Structure/function correlations of proteins using MM, QM/MM, and related approaches: methods, concepts, pitfalls, and current progress. Protein Sim 66:249–313

    CAS  Google Scholar 

  103. Oldfield E (2005) Quantum chemical studies of protein structure. Phil Trans Royal Soc B 360:1347–1361

    CAS  Google Scholar 

  104. Senn H, Thiel W (2007) QM/MM methods for biological systems. Top Curr Chem 268:173–290

    CAS  Google Scholar 

  105. Carloni P, Rothlisberger U, Parrinello M (2002) The role and perspective of a initio molecular dynamics in the study of biological systems. Acc Chem Res 35:455–464

    PubMed  CAS  Google Scholar 

  106. Challacombe M, Schwegler E (1997) Linear scaling computation of the Fock matrix. J Chem Phys 106:5526–5536

    CAS  Google Scholar 

  107. Van Alsenoy C, Yu C, Peeters A, Martin J, Schafer L (1998) Ab initio geometry determinations of proteins. 1. Crambin. J Phys Chem A 102:2246–2251

    Google Scholar 

  108. Scuseria G (1999) Linear scaling density functional calculations with Gaussian orbitals. J Phys Chem A 103:4782–4790

    CAS  Google Scholar 

  109. Tsuda K, Kaneko H, Shimada J, Takada T (2001) Ab initio MO studies of interaction mechanisms of Protein Kinase C with cell membranes. Comp Phys Comm 142:140–143

    CAS  Google Scholar 

  110. Sato F, Yoshihiro T, Era M, Kashiwagi H (2001) Calculation of all-electron wavefunction of hemoprotein cytochrome c by density functional theory. Chem Phys Lett 341:645–651

    CAS  Google Scholar 

  111. Inaba T, Tahara S, Nisikawa N, Kashiwagi H, Sato F (2005) All-electron density functional calculation on insulin with quasi-canonical localized orbitals. J Comp Chem 26:987–993

    CAS  Google Scholar 

  112. Nakanishi I, Fedorov D, Kitaura K (2007) Molecular recognition mechanism of FK506 binding protein: an all-electron fragment molecular orbital study. Protein Struct Funct Genet 68:145–158

    CAS  Google Scholar 

  113. Inaba T, Tsunekawa N, Hirano T, Yoshihiro T, Kashiwagi H, Sato F (2007) Density functional calculation of the electronic structure on insulin hexamer. Chem Phys Lett 434:331–335

    CAS  Google Scholar 

  114. Pichierri F (2005) Insights into the interplay between electronic structure and protein dynamics: the case of ubiquitin. Chem Phys Lett 410:462–466

    CAS  Google Scholar 

  115. Exner T, Mezey P (2003) Ab initio quality properties for macromolecules using the ADMA approach. J Comp Chem 24:1980–1986

    CAS  Google Scholar 

  116. Gogonea V, Merz K (1999) Fully quantum mechanical description of proteins in solution. Combining linear scaling quantum mechanical methodologies with the Poisson-Boltzmann equation. J Phys Chem A 103:5171–5188

    CAS  Google Scholar 

  117. van der Vaart A, Suarez D, Merz K (2000) Critical assessment of the performance of the semiempirical divide and conquer method for single point calculations and geometry optimizations of large chemical systems. J Chem Phys 113:10512–10523

    Google Scholar 

  118. Van der Vaart A, Gogonea V, Dixon S, Merz K (2000) Linear scaling molecular orbital calculations of biological systems using the semiempirical divide and conquer method. J Comp Chem 21:1494–1504

    Google Scholar 

  119. Zhang D, Zhang J (2004) Full ab initio computation of protein-water interaction energies. J Theor Comp Chem 3:43–49

    CAS  Google Scholar 

  120. Dixon S, Merz K (1997) Fast, accurate semiempirical molecular orbital calculations for macromolecules. J Chem Phys 107:879–893

    CAS  Google Scholar 

  121. Elstner M (2006) The SCC-DFTB method and its application to biological systems. Theo Chem Acc 116:316–325

    CAS  Google Scholar 

  122. Liu H, Elstner M, Kaxiras E, Frauenheim T, Hermans J, Yang W (2001) Quantum mechanics simulation of protein dynamics on long timescale. Protein Struct Funct Genet 44:484–489

    CAS  Google Scholar 

  123. Engh R, Huber R (1991) Accurate bond and angle parameters for X-ray protein-structure refinement. Acta Cryst A 47:392–400

    Google Scholar 

  124. Yu N, Yennawar H, Merz K (2005) Refinement of protein crystal structures using energy restraints derived from linear-scaling quantum mechanics. Acta Cryst D 61:322–332

    Google Scholar 

  125. Yu N, Li X, Cui G, Hayik S, Merz K (2006) Critical assessment of quantum mechanics based energy restraints in protein crystal structure refinement. Prot Sc 15:2773–2784

    CAS  Google Scholar 

  126. Canfield P, Dahlbom M, Hush N, Reimers J (2006) Density-functional geometry optimization of the 150 000-atom photosystem-I trimer. J Chem Phys 124:024301

    PubMed  Google Scholar 

  127. Stewart J (2009) Application of the PM6 method to modeling proteins. J Mol Model 15:765–805

    PubMed  CAS  Google Scholar 

  128. Wollacott A, Merz K (2007) Assessment of semiempirical quantum mechanical methods for the evaluation of protein structures. J Comp Theor Comput 3:1609–1619

    CAS  Google Scholar 

  129. He X, Fusti-Molnar L, Cui G, Merz K (2009) Importance of Dispersion and Electron Correlation in ab Initio Protein Folding. J Phys Chem B 113:5290–5300

    PubMed  CAS  Google Scholar 

  130. Morozov A, Misura K, Tsemekhman K, Baker D (2004) Comparison of quantum mechanics and molecular mechanics dimerization energy landscapes for pairs of ring-containing amino acids in proteins. J Phys Chem B 108:8489–8496

    CAS  Google Scholar 

  131. Masia M (2008) Ab initio based polarizable force field parametrization. J Chem Phys 128:184107

    PubMed  Google Scholar 

  132. Mackerell A, Feig M, Brooks C (2004) Extending the treatment of backbone energetics in protein force fields: limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations. J Comp Chem 25:1400–1415

    CAS  Google Scholar 

  133. Okiyama Y, Watanabe H, Fukuzawa K, Nakano T, Mochizuki Y, Ishikawa T, Ebina K, Tanaka S (2009) Application of the fragment molecular orbital method for determination of atomic charges on polypeptides. II. Towards an improvement of force fields used for classical molecular dynamics simulations. Chem Phys Lett 467:417–423

    CAS  Google Scholar 

  134. Thomas A, Milon A, Brasseur R (2004) Partial atomic charges of amino acids in proteins. Protein Struct Funct Genet 56:102–109

    CAS  Google Scholar 

  135. Dupradeau F, Pigache A, Zaffran T, Savineau C, Lelong R, Grivel N, Lelong D, Rosanski W, Cieplak P (2010) The R.ED. tools: advances in RESP and ESP charge derivation and force field library building. Phys Chem Chem Phys 12:7821–7839

    PubMed  CAS  Google Scholar 

  136. Duan Y, Wu C, Chowdhury S, Lee M, Xiong G, Zhang W, Yang R, Cieplak P, Luo R, Lee T, Caldwell J, Wang J, Kollman P (2003) A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations. J Comp Chem 24:1999–2012

    CAS  Google Scholar 

  137. Bayly C, Cieplak P, Cornell W, Kollman P (1993) A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges—the RESP model. J Phys Chem 97:10269–10280

    CAS  Google Scholar 

  138. Laio A, VandeVondele J, Rothlisberger U (2002) D-RESP: dynamically generated electrostatic potential derived charges from quantum mechanics/molecular mechanics simulations. J Phys Chem B 106:7300–7307

    CAS  Google Scholar 

  139. Ercolessi F, Adams J (1994) Interatomic potentials from 1st-principles calculations—the force-matching method. Europhys Lett 26:583–588

    CAS  Google Scholar 

  140. Laio A, Bernard S, Chiarotti G, Scandolo S, Tosatti E (2000) Physics of iron at Earth’s core conditions. Science 287:1027–1030

    PubMed  CAS  Google Scholar 

  141. Izvekov S, Parrinello M, Burnham C, Voth G (2004) Effective force fields for condensed phase systems from ab initio molecular dynamics simulation: a new method for force-matching. J Chem Phys 120:10896–10913

    PubMed  CAS  Google Scholar 

  142. Akin-Ojo O, Song Y, Wang F (2008) Developing ab initio quality force fields from condensed phase quantum-mechanics/molecular-mechanics calculations through the adaptive force matching method. J Chem Phys 129:064108

    PubMed  Google Scholar 

  143. Maurer P, Laio A, Hugosson H, Colombo M, Rothlisberger U (2007) Automated parametrization of biomolecular force fields from quantum mechanics/molecular mechanics (QM/MM) simulations through force matching. J Comp Theor Comput 3:628–639

    CAS  Google Scholar 

  144. Bucher D, Guidoni L, Maurer P, Rothlisberger U (2009) Developing improved charge sets for the modeling of the KcsA K+ channel using QM/MM electrostatic potentials. J Comp Theor Comput 5:2173–2179

    CAS  Google Scholar 

  145. Bucher D, Rothlisberger U (2010) Molecular simulations of ion channels: a quantum chemist’s perspective. J Gener Phys 135:549–554

    CAS  Google Scholar 

  146. McMahon B, Stojkovic B, Hay P, Martin R, Garcia A (2000) Microscopic model of carbon monoxide binding to myoglobin. J Chem Phys 113:6831–6850

    CAS  Google Scholar 

  147. Marti M, Crespo A, Capece L, Boechi L, Bikiel D, Scherlis D, Estrin D (2006) Dioxygen affinity in heme proteins investigated by computer simulation. J Inorg Biochem 100:761–770

    PubMed  CAS  Google Scholar 

  148. Friesner R, Baik M, Gherman B, Guallar V, Wirstam M, Murphy R, Lippard S (2003) How iron-containing proteins control dioxygen chemistry: a detailed atomic level description via accurate quantum chemical and mixed quantum mechanics/molecular mechanics calculations. Coord Chem Rev 238:267–290

    Google Scholar 

  149. Xie H, Wu R, Zhou Z, Cao Z (2008) Exploring the interstitial atom in the FeMo cofactor of nitrogenase: insights from QM and QM/MM calculations. J Phys Chem B 112:11435–11439

    PubMed  CAS  Google Scholar 

  150. Babitzki G, Denschlag R, Tavan P (2009) Polarization effects stabilize Bacteriorhodopsin’s chromophore binding pocket: a molecular dynamics study. J Phys Chem B 113:10483–10495

    PubMed  CAS  Google Scholar 

  151. Hutter M, Reimers J, Hush N (1998) Modeling the bacterial photosynthetic reaction center. 1. Magnesium parameters for the semiempirical AM1 method developed using a genetic algorithm. J Phys Chem B 102:8080–8090

    CAS  Google Scholar 

  152. Hutter M, Hughes J, Reimers J, Hush N (1999) Modeling the bacterial photosynthetic reaction center. 2. A combined quantum mechanical molecular mechanical study of the structure of the cofactors in the reaction centers of purple bacteria. J Phys Chem B 103:4906–4915

    CAS  Google Scholar 

  153. Reimers J, Hughes J, Hush N (2000) Modeling the bacterial photosynthetic reaction center 3: interpretation of effects of site-directed mutagenesis on the special-pair midpoint potential. Biochemistry 39:16185–16189

    PubMed  CAS  Google Scholar 

  154. Hughes J, Hutter M, Reimers J, Hush N (2001) Modeling the bacterial photosynthetic reaction center. 4. The structural, electrochemical, and hydrogen-bonding properties of 22 mutants of Rhodobacter sphaeroides. J Am Chem Soc 123:8550–8563

    PubMed  CAS  Google Scholar 

  155. Reimers J, Shapley W, Hush N (2003) Modelling the bacterial photosynthetic reaction center. V. Assignment of the electronic transition observed at 2200 cm(-1) in the special-pair radical-cation as a second-highest occupied molecular orbital to highest occupied molecular orbital transition. J Chem Phys 119:3240–3248

    CAS  Google Scholar 

  156. Reimers J, Shapley W, Rendell A, Hush N (2003) Modelling the bacterial photosynthetic reaction center. VI. Use of density-functional theory to determine the nature of the vibronic coupling between the four lowest-energy electronic states of the special-pair radical cation. J Chem Phys 119:3249–3261

    CAS  Google Scholar 

  157. Reimers J, Hush N (2003) Modeling the bacterial photosynthetic reaction center. VII. Full simulation of the intervalence hole-transfer absorption spectrum of the special-pair radical cation. J Chem Phys 119:3262–3277

    CAS  Google Scholar 

  158. Yamasaki H, Takano Y, Nakamura H (2008) Theoretical investigation of the electronic asymmetry of the special pair cation radical in the photosynthetic type-II reaction center. J Phys Chem B 112:13923–13933

    PubMed  CAS  Google Scholar 

  159. Sinnecker S, Flores M, Lubitz W (2006) Protein-cofactor interactions in bacterial reaction centers from Rhodobacter sphaeroides R-26: effect of hydrogen bonding on the electronic and geometric structure of the primary quinone. A density functional theory study. Phys Chem Chem Phys 8:5659–5670

    CAS  Google Scholar 

  160. Nonella M, Mathias G, Eichinger M, Tavan P (2003) Structures and vibrational frequencies of the quinones in Rb. sphaeroides derived by a combined density functional/molecular mechanics approach. J Phys Chem B 107:316–322

    CAS  Google Scholar 

  161. Drews J (2000) Drug discovery: a historical perspective. Science 287:1960–1964

    PubMed  CAS  Google Scholar 

  162. Steinbrecher T, Labahn A (2010) Towards accurate free energy calculations in ligand protein-binding studies. Curr Med Chem 17:767–785

    PubMed  CAS  Google Scholar 

  163. Moustakas D, Lang P, Pegg S, Pettersen E, Kuntz I, Brooijmans N, Rizzo R (2006) Development and validation of a modular, extensible docking program: DOCK 5. J Comp Aided Mol Design 20:601–619

    CAS  Google Scholar 

  164. T.J.A. Ewing IK (1997) Critical evaluation of search algorithms for automated molecular docking and database screening. J Comp Chem 18:1175–1189

    Google Scholar 

  165. Morris G, Goodsell D, Halliday R, Huey R, Hart W, Belew R, Olson A (1998) Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function. J Comp Chem 19:1639–1662

    CAS  Google Scholar 

  166. Rarey M, Kramer B, Lengauer T (1996) A fast flexible docking method using an incremental construction algorithm. J Mol Biol 261:470–489

    PubMed  CAS  Google Scholar 

  167. Kramer B, Rarey M, Lengauer T (1999) Evaluation of the FLEXX incremental construction algorithm for protein-ligand docking. Protein Struct Funct Genet 37:228–241

    CAS  Google Scholar 

  168. Jones G, Willett P, Glen R, Leach A, Taylor R (1997) Development and validation of a genetic algorithm for flexible docking. J Mol Biol 267:727–748

    PubMed  CAS  Google Scholar 

  169. Friesner R, Banks J, Murphy R, Halgren T, Klicic J, Mainz D, Repasky M, Knoll E, Shelley M, Perry J, Shaw D, Francis P, Shenkin P (2004) Glide: a new approach for rapid, accurate docking and scoring. 1. Method and assessment of docking accuracy. J Med Chem 47:1739–1749

    PubMed  CAS  Google Scholar 

  170. Halgren T, Murphy R, Friesner R, Beard H, Frye L, Pollard W, Banks J (2004) Glide: a new approach for rapid, accurate docking and scoring. 2. Enrichment factors in database screening. J Med Chem 47:1750–1759

    PubMed  CAS  Google Scholar 

  171. Villar R, Gil M, Garcia J, Martinez-Merino V (2005) Are AM1 ligand-protein binding enthalpies good enough for use in the rational design of new drugs? J Comp Chem 26:1347–1358

    CAS  Google Scholar 

  172. Nikitina E, Sulimov V, Zayets V, Zaitseva N (2004) Semiempirical calculations of binding enthalpy for protein-ligand complexes. Int J Quant Chem 97:747–763

    CAS  Google Scholar 

  173. Raha K, Merz K (2005) Large-scale validation of a quantum mechanics based scoring function: predicting the binding affinity and the binding mode of a diverse set of protein-ligand complexes. J Med Chem 48:4558–4575

    PubMed  CAS  Google Scholar 

  174. Vasilyev V, Bliznyuk A (2004) Application of semiempirical quantum chemical methods as a scoring function in docking. Theo Chem Acc 112:313–317

    CAS  Google Scholar 

  175. Li J, Reynolds C (2009) A quantum mechanical approach to ligand binding - Calculation of ligand-protein binding affinities for stromelysin-1 (MMP-3) inhibitors. Can J Chem 87:1480–1484

    CAS  Google Scholar 

  176. Peters M, Raha K, Merz K (2006) Quantum mechanics in structure-based drug design. Curr Op Drug Disc 9:370–379

    CAS  Google Scholar 

  177. Wang M, Wong C (2007) Rank-ordering protein-ligand binding affinity by a quantum mechanics/molecular mechanics/Poisson-Boltzmann-surface area model. J Chem Phys 126:026101

    PubMed  Google Scholar 

  178. Heady L, Fernandez-Serra M, Mancera R, Joyce S, Venkitaraman A, Artacho E, Skylaris C, Ciacchi L, Payne M (2006) Novel structural features of CDK inhibition revealed by an ab initio computational method combined with dynamic simulations. J Med Chem 49:5141–5153

    PubMed  CAS  Google Scholar 

  179. Fukuzawa K, Kitaura K, Uebayasi M, Nakata K, Kaminuma T, Nakano T (2005) Ab initio quantum mechanical study of the binding energies of human estrogen receptor alpha with its ligands: an application of fragment molecular orbital method. J Comp Chem 26:1–10

    CAS  Google Scholar 

  180. Fischer B, Fukuzawa K, Wenzel W (2008) Receptor-specific scoring functions derived from quantum chemical models improve affinity estimates for in-silico drug discovery. Protein Struct Funct Genet 70:1264–1273

    CAS  Google Scholar 

  181. Neugebauer J (2009) Subsystem-based theoretical spectroscopy of biomolecules and biomolecular assemblies. ChemPhysChem 10:3148–3173

    PubMed  CAS  Google Scholar 

  182. Schapiro I, Ryazantsev MN, Ding WJ, Huntress MM, Melaccio F, Andruniow T, Olivucci M (2010) Computational photobiology and beyond. Austr J Chem 63:413–429

    CAS  Google Scholar 

  183. Mata RA (2010) Application of high level wavefunction methods in quantum mechanics/molecular mechanics hybrid schemes. Phys Chem Chem Phys 12:5041–5052

    PubMed  CAS  Google Scholar 

  184. Hoffmann M, Wanko M, Strodel P, Koenig PH, Frauenheim T, Schulten K, Thiel W, Tajkhorshid E, Elstner M (2006) Color tuning in rhodopsins: the mechanism for the spectral shift between bacteriorhodopsin and sensory rhodopsin II. J Am Chem Soc 128:10808–10818

    PubMed  CAS  Google Scholar 

  185. Babitzki G, Mathias G, Tavan P (2009) The infrared spectra of the retinal chromophore in bacteriorhodopsin calculated by a DFT/MM approach. J Phys Chem B 113:10496–10508

    PubMed  CAS  Google Scholar 

  186. Mroginski MA, Mark F, Thiel W, Hildebrandt P (2007) Quantum mechanics/molecular mechanics calculation of the Raman spectra of the phycocyanobilin chromophore in alpha-c-phycocyanin. Biophys J 93:1885–1894

    PubMed  CAS  Google Scholar 

  187. Mroginski MA, von Stetten D, Escobar FV, Strauss HM, Kaminski S, Scheerer P, Guenther M, Murgida DH, Schmieder P, Bongards C, Gaertner W, Mailliet J, Hughes J, Essen LO, Hildebrandt P (2009) Chromophore structure of cyanobacterial phytochrome Cph1 in the Pr state: reconciling structural and spectroscopic data by QM/MM calculations. Biophys J 96:4153–4163

    PubMed  CAS  Google Scholar 

  188. Mroginski MA, Kaminski S, Hildebrandt P (2010) Raman spectra of the phycoviolobilin cofactor in phycoerythrocyanin calculated by QM/MM methods. ChemPhysChem 11:1265–1274

    PubMed  CAS  Google Scholar 

  189. Schmitz M, Tavan P (2004) Vibrational spectra from atomic fluctuations in dynamics simulations. I. Theory, limitations, and a sample application. J Chem Phys 121:12233–12246

    PubMed  CAS  Google Scholar 

  190. Schmitz M, Tavan P (2004) Vibrational spectra from atomic fluctuations in dynamics simulations. II. Solvent-induced frequency fluctuations at femtosecond time resolution. J Chem Phys 121:12247–12258

    CAS  Google Scholar 

  191. Kaminski S, Gaus M, Phatak P, von Stetten D, Elstner M, Mroginski MA (2010) Vibrational Raman spectra from the self-consistent charge density functional tight binding method via classical time-correlation functions. J Chem Theor Comput 6:1240–1255

    CAS  Google Scholar 

  192. Yu H, Cui Q (2007) The vibrational spectra of protonated water clusters: a benchmark for self-consistent-charge density-functional tight binding. J Chem Phys 127:234504

    PubMed  Google Scholar 

  193. Phatak P, Ghosh N, Yu H, Cui Q, Elstner M (2008) Amino acids with an intermolecular proton bond as proton storage site in bacteriorhodopsin. Proc Natl Acad Sci USA 105:19672–19677

    PubMed  CAS  Google Scholar 

  194. Xu Z, Mei Y, Duan L, Zhang D (2010) Hydrogen bonds rebuilt by polarized protein-specific charges. Chem Phys Lett 495:151–154

    CAS  Google Scholar 

  195. Duan LL, Mei Y, Zhang QG, Zhang JZH (2009) Intra-protein hydrogen bonding is dynamically stabilized by electronic polarization. J Chem Phys 130:115102

    PubMed  Google Scholar 

  196. Fraehmcke JS, Wanko M, Phatak P, Mroginski MA, Elstner M (2010) The protonation state of glu181 in rhodopsin revisited: interpretation of experimental data on the basis of QM/MM calculations. J Phys Chem B 114:11338–11352

    CAS  Google Scholar 

  197. Wanko M, Hoffmann M, Strodel P, Koslowski A, Thiel W, Neese F, Frauenheim T, Elstner M (2005) Calculating absorption shifts for retinal proteins: Computational challenges. J Phys Chem B 109:3606–3615

    PubMed  CAS  Google Scholar 

  198. Dreuw A, Head-Gordon M (2005) Single-reference ab initio methods for the calculation of excited states of large molecules. Chem Rev 105:4009–4037

    PubMed  CAS  Google Scholar 

  199. Dreuw A (2006) Quantum chemical methods for the investigation of photoinitiated processes in biological systems: theory and applications. ChemPhysChem 7:2259–2274

    PubMed  CAS  Google Scholar 

  200. Wanko M, Garavelli M, Bernardi F, Niehaus T, Frauenheim T, Elstner M (2004) A global investigation of excited state surfaces within time-dependent density-functional response theory. J Chem Phys 120:1674–1692

    PubMed  CAS  Google Scholar 

  201. Wanko M, Hoffmann M, Frauenheim T, Elstner M (2008) Effect of polarization on the opsin shift in rhodopsins. 1. A combined QM/QM/MM model for bacteriorhodopsin and pharaonis sensory rhodopsin II. J Phys Chem B 112:11462–11467

    PubMed  CAS  Google Scholar 

  202. Wanko M, Hoffmann M, Fraehmcke J, Frauenheim T, Elstner M (2008) Effect of polarization on the opsin shift in rhodopsins. 2. Empirical polarization models for proteins. J Phys Chem B 112:11468–11478

    PubMed  CAS  Google Scholar 

  203. Soederhjelm P, Husberg C, Strambi A, Olivucci M, Ryde U (2009) Protein influence on electronic spectra modeled by multipoles and polarizabilities. J Chem Theor Comput 5:649–658

    Google Scholar 

  204. Wanko M (2008) Ph.D. thesis, Technical University of Braunschweig, Germany

    Google Scholar 

  205. Phatak P, Fraehmcke JS, Wanko M, Hoffmann M, Strodel P, Smith JC, Suhai S, Bondar AN, Elstner M (2009) Long-distance proton transfer with a break in the bacteriorhodopsin active site. J Am Chem Soc 131:7064–7078

    PubMed  CAS  Google Scholar 

  206. Xie W, Gao J (2007) Design of a next generation force field: the X-POL potential. J Chem Theor Comput 3:1890–1900

    CAS  Google Scholar 

  207. Gresh N, Cisneros GA, Darden TA, Piquemal JP (2007) Anisotropic, polarizable molecular mechanics studies of inter- and intramoecular interactions and ligand-macromolecule complexes. A bottom-up strategy. J Chem Theor Comput 3:1960–1986

    CAS  Google Scholar 

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Steinbrecher, T., Elstner, M. (2013). QM and QM/MM Simulations of Proteins. In: Monticelli, L., Salonen, E. (eds) Biomolecular Simulations. Methods in Molecular Biology, vol 924. Humana Press, Totowa, NJ. https://doi.org/10.1007/978-1-62703-017-5_5

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