1932

Abstract

Hybrid quantum mechanical/molecular mechanical (QM/MM) methods have become indispensable tools for the study of biomolecules. In this article, we briefly review the basic methodological details of QM/MM approaches and discuss their applications to various energy transduction problems in biomolecular machines, such as long-range proton transports, fast electron transfers, and mechanochemical coupling. We highlight the particular importance for these applications of balancing computational efficiency and accuracy. Using several recent examples, we illustrate the value and limitations of QM/MM methodologies for both ground and excited states, as well as strategies for calibrating them in specific applications. We conclude with brief comments on several areas that can benefit from further efforts to make QM/MM analyses more quantitative and applicable to increasingly complex biological problems.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-biophys-111622-091140
2023-05-09
2024-04-27
Loading full text...

Full text loading...

/deliver/fulltext/biophys/52/1/annurev-biophys-111622-091140.html?itemId=/content/journals/10.1146/annurev-biophys-111622-091140&mimeType=html&fmt=ahah

Literature Cited

  1. 1.
    Antes I, Thiel W. 1999. Adjusted connection atoms for combined quantum mechanical and molecular mechanical methods. J. Phys. Chem. A 103:9290–95
    [Google Scholar]
  2. 2.
    Astumian RD, Mukherjee S, Warshel A. 2016. The physics and physical chemistry of molecular machines. Phys. Chem. Chem. Phys. 17:1719–41
    [Google Scholar]
  3. 3.
    Baiz CR, Blasiak B, Bredenbeck J, Cho M, Choi JH et al. 2020. Vibrational spectroscopic map, vibrational spectroscopy, and intermolecular interaction. Chem. Rev. 120:7152–218
    [Google Scholar]
  4. 4.
    Bannwarth C, Caldeweyher E, Ehlert S, Hansen A, Pracht P et al. 2020. Extended tight-binding quantum chemistry methods. WIREs Comput. Mol. Sci. 11:e01493
    [Google Scholar]
  5. 5.
    Barros EP, Ries B, Boselt L, Champion C, Riniker S. 2022. Recent developments in multiscale free energy simulations. Curr. Opin. Struct. Biol. 72:55–62
    [Google Scholar]
  6. 6.
    Berta D, Buigues PJ, Badaoui M, Rosta E. 2020. Cations in motion: QM/MM studies of the dynamic and electrostatic roles of H+ and Mg2+ ions in enzyme reactions. Curr. Opin. Struct. Biol. 61:198–206
    [Google Scholar]
  7. 7.
    Blumberger J. 2015. Recent advances in the theory and molecular simulation of biological electron transfer reactions. Chem. Rev. 115:2011191–238
    [Google Scholar]
  8. 8.
    Bold BM, Sokolov M, Maity S, Wanko M, Dohmen PM et al. 2020. Benchmark and performance of long-range corrected time-dependent density functional tight binding (LC-TD-DFTB) on rhodopsins and light-harvesting complexes. Phys. Chem. Chem. Phys. 22:10500–18
    [Google Scholar]
  9. 9.
    Bondanza M, Nottoli M, Cupellini L, Lipparini F, Mennucci B. 2020. Polarizable embedding QM/MM: the future gold standard for complex (bio)systems?. Phys. Chem. Chem. Phys. 22:14433–48
    [Google Scholar]
  10. 10.
    Borshchevskiy V, Kovalev K, Round E, Efremov R, Astashkin R et al. 2022. True-atomic-resolution insights into the structure and functional role of linear chains and low-barrier hydrogen bonds in proteins. Nat. Struct. Mol. Biol. 29:440–50
    [Google Scholar]
  11. 11.
    Brunk E, Rothlisberger U. 2015. Mixed quantum mechanical/molecular mechanical molecular dynamics simulations of biological systems in ground and electronically excited states. Chem. Rev. 115:6217–63
    [Google Scholar]
  12. 12.
    Bustamante C, Keller D, Oster G. 2001. The physics of molecular motors. Acc. Chem. Res. 34:412–20
    [Google Scholar]
  13. 13.
    Cai XH, Haider K, Lu JX, Radik S, Son CY et al. 2018. Network analysis of a proposed exit pathway for protons to the P-side of cytochrome c oxidase. Biochem. Biophys. Acta Bioenerg. 1859:997–1005
    [Google Scholar]
  14. 14.
    Chen MS, Zuehlsdorff TJ, Morawietz T, Isborn CM, Markland TE. 2020. Exploiting machine learning to efficiently predict multidimensional optical spectra in complex environments. J. Phys. Chem. Lett. 11:7559–68
    [Google Scholar]
  15. 15.
    Christensen AS, Kubař T, Cui Q, Elstner M. 2016. Semi-empirical quantum mechanical methods for non-covalent interactions for chemical and biochemical applications. Chem. Rev. 116:5301–37
    [Google Scholar]
  16. 16.
    Chung LW, Sameera WMC, Ramozzi R, Page AJ, Hatanaka M et al. 2015. The ONIOM method and its applications. Chem. Rev. 115:5678–769
    [Google Scholar]
  17. 17.
    Cignoni E, Cupellini L, Menucci B. 2022. A fast method for electronic couplings in embedded multichromophoric systems. J. Phys. Condens. Matter 34:304004
    [Google Scholar]
  18. 18.
    Cui K, Yethiraj A, Schmidt JR. 2019. Influence of charge scaling on the solvation properties of ionic liquid solutions. J. Phys. Chem. B 123:9222–29
    [Google Scholar]
  19. 19.
    Cui Q. 2016. Quantum mechanical methods in biochemistry and biophysics. J. Chem. Phys. 145:140901
    [Google Scholar]
  20. 20.
    Cui Q, Pal T, Xie L. 2021. Biomolecular QM/MM simulations: What are some of the “burning issues''?. J. Phys. Chem. B 125:689–702
    [Google Scholar]
  21. 21.
    Dahl PJ, Yi SM, Gu Y, Acharya A, Shipps C et al. 2022. A 300-fold conductivity increase in microbial cytochrome nanowires due to temperature-induced restructuring of hydrogen bonding networks. Sci. Adv. 8:19eabm7193
    [Google Scholar]
  22. 22.
    Das D, Eurenius KP, Billings EM, Sherwood P, Chatfield DC et al. 2002. Optimization of quantum mechanical molecular mechanical partitioning schemes: Gaussian delocalization of molecular mechanical charges and the double link atom method. J. Chem. Phys. 117:10534–47
    [Google Scholar]
  23. 23.
    Das S, Nam K, Major DT 2018. Rapid convergence of energy and free energy profiles with quantum mechanical size in quantum mechanical–molecular mechanical simulations of proton transfer in DNA. J. Chem. Theory Comput. 14:31695–705
    [Google Scholar]
  24. 24.
    Demapan D, Kussman J, Ochsenfeld C, Cui Q. 2022. Factors that determine the variation of equilibrium and kinetic properties of QM/MM enzyme simulations: QM region, conformation and boundary condition. J. Chem. Theory Comput. 18:2530–42
    [Google Scholar]
  25. 25.
    Deng J, Cui Q. 2022. Electronic polarization is essential for the stabilization and dynamics of buried ion pairs in staphylococcal nuclease mutant. J. Am. Chem. Soc. 144:4594–610
    [Google Scholar]
  26. 26.
    Donati E, Genna V, De Vivo M. 2020. Recruiting mechanism and functional role of a third metal ion in the enzymatic activity of 5' structure-specific nucleases. J. Am. Chem. Soc. 142:2823–34
    [Google Scholar]
  27. 27.
    Dreuw A, Head-Gordon M. 2005. Single-reference ab initio methods for the calculation of excited states of large molecules. Chem. Rev. 105:114009–37
    [Google Scholar]
  28. 28.
    Duboué-Dijon E, Javanainen M, Delcroix P, Jungwirth P, Martinez-Seara H. 2020. A practical guide to biologically relevant molecular simulations with charge scaling for electronic polarization. J. Chem. Phys. 153:050901
    [Google Scholar]
  29. 29.
    E W, Vanden-Eijnden E 2010. Transition-path theory and path-finding algorithms for the study of rare events. Annu. Rev. Phys. Chem. 61:391–420
    [Google Scholar]
  30. 30.
    Field MJ, Bash PA, Karplus M. 1990. A combined quantum-mechanical and molecular mechanical potential for molecular-dynamics simulations. J. Comput. Chem. 11:6700–33
    [Google Scholar]
  31. 31.
    Flaig D, Beer M, Ochsenfeld C. 2012. Convergence of electronic structure with the size of the QM region: example of QM/MM NMR shieldings. J. Chem. Theory Comput. 8:72260–71
    [Google Scholar]
  32. 32.
    Frähmcke J, Wanko M, Phatak P, Mroginski A, 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 114:11338–52
    [Google Scholar]
  33. 33.
    Freier E, Wolf S, Gerwert K. 2011. Proton transfer via a transient linear water-molecule chain in a membrane protein. PNAS 108:11435–39
    [Google Scholar]
  34. 34.
    Gao J. 1996. Methods and applications of combined quantum mechanical and molecular mechanical potentials. Reviews in Computational Chemistry, Vol. VII KB Lipkowitz, DB Boyd 119–85. New York: Wiley
    [Google Scholar]
  35. 35.
    Gao JL, Amara P, Alhambra C, Field MJ. 1998. A generalized hybrid orbital (GHO) method for the treatment of boundary atoms in combined QM/MM calculations. J. Phys. Chem. A 102:4714–21
    [Google Scholar]
  36. 36.
    Gao JL, Truhlar DG. 2002. Quantum mechanical methods for enzyme kinetics. Annu. Rev. Phys. Chem. 53:467–505
    [Google Scholar]
  37. 37.
    Gao Y, Yang W 2016. Capture of a third Mg2+ is essential for catalyzing DNA synthesis. Science 352:1334–37
    [Google Scholar]
  38. 38.
    Garczarek F, Gerwert K. 2006. Functional waters in intraprotein proton transfer monitored by FTIR difference spectroscopy. Nature 439:109–12
    [Google Scholar]
  39. 39.
    Gaus M, Cui Q, Elstner M. 2014. Density functional tight binding (DFTB): application to organic and biological molecules. WIREs Comput. Mol. Sci. 4:49–61
    [Google Scholar]
  40. 40.
    Genna V, Vidossich P, Ippoliti E, Carloni P, De Vivo M. 2016. A self-activated mechanism for nucleic acid polymerization catalyzed by DNA/RNA polymerases. J. Am. Chem. Soc. 138:14592–98
    [Google Scholar]
  41. 41.
    Ghosh N, Prat-Resina X, Gunner M, Cui Q 2009. Microscopic pKa analysis of Glu286 in cytochrome c oxidase (Rhodobacter sphaeroides): toward a calibrated molecular model. Biochemistry 48:2468–85
    [Google Scholar]
  42. 42.
    Gillet N, Berstis L, Wu XJ, Gajdos F, Heck A et al. 2016. Electronic coupling calculations for bridge-mediated charge transfer using constrained density functional theory (CDFT) and effective Hamiltonian approaches at the density functional theory (DFT) and fragment-orbital density functional tight binding (FODFTB) level. J. Chem. Theory Comput. 12:4793–805
    [Google Scholar]
  43. 43.
    Gillet N, Elstner M, Kubař T. 2018. Coupled-perturbed DFTB-QM/MM metadynamics: application to proton-coupled electron transfer. J. Chem. Phys. 149:7072328
    [Google Scholar]
  44. 44.
    Gómez-Flores CL, Maag D, Kansari M, Vuong VQ, Irle S et al. 2022. Accurate free energies for complex condensed-phase reactions using an artificial neural network corrected DFTB/MM methodology. J. Chem. Theory Comput. 18:21213–26
    [Google Scholar]
  45. 45.
    Goyal P, Ghosh N, Phatak P, Clemens M, Gaus M et al. 2011. Proton storage site in bacteriorhodopsin: new insights from QM/MM simulations of microscopic pK(a) and infrared spectra. J. Am. Chem. Soc. 133:14981–97
    [Google Scholar]
  46. 46.
    Goyal P, Lu J, Yang S, Gunner MR, Cui Q. 2013. Changing hydration level in an internal cavity modulates the proton affinity of a key glutamate in cytochrome c oxidase. PNAS 110:18886–91
    [Google Scholar]
  47. 47.
    Goyal P, Yang S, Cui Q 2015. Microscopic basis for kinetic gating in cytochrome c oxidase: insights from QM/MM analysis. Chem. Sci. 6:826–41
    [Google Scholar]
  48. 48.
    Gregory MT, Gao Y, Cui Q, Yang W 2021. Multiple deprotonation paths of the nucleophile 3'-OH in the DNA synthesis reaction. PNAS 118:e2103990118
    [Google Scholar]
  49. 49.
    Gunner MR, Amin M, Zhu X, Lu J. 2013. Molecular mechanisms for generating transmembrane proton gradients. Biochim. Biophys. Acta Bioeng. 1827:892–913
    [Google Scholar]
  50. 50.
    Guo Y, Beyle FE, Bold BM, Watanabe HC, Koslowski A et al. 2016. Active site structure and absorption spectrum of channelrhodopsin-2 wild-type and C128T mutant. Chem. Sci. 7:63879–91
    [Google Scholar]
  51. 51.
    Hill TL. 1977. Free Energy Transduction in Biology New York: Acad. Press
  52. 52.
    Hoffmann M, Wanko M, Strodel P, König PH, Frauenheim T et al. 2006. Color tuning in rhodopsins: the mechanism for the spectral shift between bacteriorhodopsin and sensory rhodopsin II. J. Am. Chem. Soc. 128:3310808–18
    [Google Scholar]
  53. 53.
    Holub D, Lamparter T, Elstner M, Gillet N. 2019. Biological relevance of charge transfer branching pathways in photolyases. Phys. Chem. Chem. Phys. 21:3117072–81
    [Google Scholar]
  54. 54.
    Hou G, Zhu X, Elstner M, Cui Q. 2012. A modified QM/MM Hamiltonian with the self-consistent-charge density-functional-tight-binding theory for highly charged QM regions. J. Chem. Theory Comp. 8:4293–304
    [Google Scholar]
  55. 55.
    Hu H, Yang WT. 2008. Free energies of chemical reactions in solution and in enzymes with ab initio quantum mechanics/molecular mechanics methods. Annu. Rev. Phys. Chem. 59:573–601
    [Google Scholar]
  56. 56.
    Inakollu VSS, Geerke DP, Rowley CN, Yu H. 2020. Polarisable force fields: What do they add in biomolecular simulations?. Curr. Opin. Struct. Biol. 61:182–90
    [Google Scholar]
  57. 57.
    Jacquemin D, Perpète EA, Scuseria GE, Ciofini I, Adamo C. 2008. TD-DFT performance for the visible absorption spectra of organic dyes: conventional versus long-range hybrids. J. Chem. Theory Comput. 4:1123–35
    [Google Scholar]
  58. 58.
    Jindal G, Warshel A. 2016. Exploring the dependence of QM/MM calculations of enzyme catalysis on the size of the QM region. J. Phys. Chem. B 120:379913–21
    [Google Scholar]
  59. 59.
    Jing Z, Liu C, Cheng SY, Qi R, Walker BD et al. 2019. Polarizable force fields for biomolecular simulations: recent advances and applications. Annu. Rev. Biophys. 48:371–94
    [Google Scholar]
  60. 60.
    Kaila VRI. 2021. Resolving chemical dynamics in biological energy conversion: long-range proton-coupled electron transfer in respiratory complex I. Acc. Chem. Res. 54:4462–73
    [Google Scholar]
  61. 61.
    Kamerlin SCL, Sharma PK, Prasad RB, Warshel A. 2013. Why nature really chose phosphate. Q. Rev. Biophys. 46:1–132
    [Google Scholar]
  62. 62.
    Koenig P, Ghosh N, Hoffman M, Elstner M, Tajkhorshid E et al. 2006. Towards theoretical analysis of long-range proton transfer kinetics in biomolecular pumps. J. Phys. Chem. A 110:548–63
    [Google Scholar]
  63. 63.
    König PH, Hoffmann M, Frauenheim T, Cui Q. 2005. A critical evaluation of different QM/MM frontier treatments with SCC-DFTB as the QM method. J. Phys. Chem. B 109:9082–95
    [Google Scholar]
  64. 64.
    Krämer M, Dohmen PM, Xie WW, Holub D, Christensen AS, Elstner M. 2021. Charge and exciton transfer simulations using machine-learned Hamiltonians. J. Chem. Theory Comput. 16:4061–70
    [Google Scholar]
  65. 65.
    Kranz JJ, Elstner M, Aradi B, Frauenheim T, Lutsker V et al. 2017. Time-dependent extension of the long-range corrected density functional based tight-binding method. J. Chem. Theory Comput. 13:41737–47
    [Google Scholar]
  66. 66.
    Kubař T, Elstner M. 2013. Efficient algorithms for the simulation of non-adiabatic electron transfer in complex molecular systems: application to DNA. Phys. Chem. Chem. Phys. 15:5794–813
    [Google Scholar]
  67. 67.
    Kubař T, Elstner M. 2013. A hybrid approach to simulation of electron transfer in complex molecular systems. J. Royal Soc. Interface 10:20130415
    [Google Scholar]
  68. 68.
    Kubař T, Woiczikowski PB, Cuniberti G, Elstner M. 2008. Efficient calculation of charge-transfer matrix elements for hole transfer in DNA. J. Phys. Chem. B 112:7937–47
    [Google Scholar]
  69. 69.
    Kulik HJ, Zhang J, Klinman JP, Martínez TJ. 2016. How large should the QM region be in QM/MM calculations? The case of catechol O-methyltransferase. J. Phys. Chem. B 120:4411381–94
    [Google Scholar]
  70. 70.
    Lagardere L, Jolly LH, Lipparini F, Aviat F, Stamm B et al. 2018. Tinker-HP: a massively parallel molecular dynamics package for multiscale simulations of large complex systems with advanced point dipole polarizable force fields. Chem. Sci. 9:956–72
    [Google Scholar]
  71. 71.
    Lahav Y, Noy D, Schapiro I. 2021. Spectral tuning of chlorophylls in proteins: electrostatics versus ring deformation. Phys. Chem. Chem. Phys. 23:116544–51
    [Google Scholar]
  72. 72.
    Lassila JK, Zalatan JG, Herschlag D. 2011. Biological phosphoryl transfer reactions: understanding mechanism and catalysis. Annu. Rev. Biochem. 80:669–702
    [Google Scholar]
  73. 73.
    LeBard DN, Martin DR, Lin S, Woodbury NW, Matyushov DV. 2013. Protein dynamics to optimize and control bacterial photosynthesis. Chem. Sci. 4:4127–36
    [Google Scholar]
  74. 74.
    Lee S, Liang RB, Voth GA, Swanson JMJ. 2016. Computationally efficient multiscale reactive molecular dynamics to describe amino acid deprotonation in proteins. J. Chem. Theory Comput. 12:879–91
    [Google Scholar]
  75. 75.
    Lemkul JA, Huang J, Roux B, MacKerell AD Jr. 2016. An empirical polarizable force field based on the classical Drude oscillator model: development history and recent applications. Chem. Rev. 116:4983–5013
    [Google Scholar]
  76. 76.
    Leontyev IV, Stuchebrukhov AA. 2011. Accounting for electronic polarization in non-polarizable force fields. Phys. Chem. Chem. Phys. 13:2613–26
    [Google Scholar]
  77. 77.
    Li CH, Voth GA. 2021. Using constrained density functional theory to track proton transfers and to sample their associated free energy surface. J. Chem. Theory Comput. 17:5759–65
    [Google Scholar]
  78. 78.
    Liang RB, Swanson JMJ, Peng YX, Wikström M, Voth GA. 2016. Multiscale simulations reveal key features of the proton-pumping mechanism in cytochrome c oxidase. PNAS 113:7420–25
    [Google Scholar]
  79. 79.
    Liao QH, Kulkarni Y, Sengupta U, Petrovic D, Mulholland AJ et al. 2018. Loop motion in triosephosphate isomerase is not a simple open and shut case. J. Am. Chem. Soc. 140:15889–903
    [Google Scholar]
  80. 80.
    List NH, Curutchet C, Knecht S, Mennucci B, Kongsted J. 2013. Toward reliable prediction of the energy ladder in multichromophoric systems: a benchmark study on the FMO light-harvesting complex. J. Chem. Theory Comput. 9:114928–38
    [Google Scholar]
  81. 81.
    Loco D, Lagardere L, Adjoua O, Piquemal JP. 2021. Atomistic polarizable embeddings: energy, dynamics, spectroscopy, and reactivity. Acc. Chem. Res. 54:2812–22
    [Google Scholar]
  82. 82.
    Loco D, Polack E, Capresa S, Lagardere L, Lipparini F et al. 2016. A QM/MM approach using the amoeba polarizable embedding: from ground state energies to electronic excitations. J. Chem. Theory Comput. 12:3654–61
    [Google Scholar]
  83. 83.
    Lonsdale R, Mulholland A. 2014. QM/MM modelling of drug-metabolizing enzymes. Curr. Top. Med. Chem. 14:111339–47
    [Google Scholar]
  84. 84.
    Lu X, Ovchinnikov V, Roston DR, Demapan D, Cui Q. 2017. Regulation and plasticity of catalysis in enzymes: insights from analysis of mechanochemical coupling in myosin. Biochemistry 56:1482–97
    [Google Scholar]
  85. 85.
    Lu Y, Kundu M, Zhong D. 2020. Effects of nonequilibrium fluctuations on ultrafast short-range electron transfer dynamics. Nat. Commun. 11:2822
    [Google Scholar]
  86. 86.
    Lüdemann G, Solov'yov I, Kubař T, Elstner M. 2015. Solvent driving force ensures fast formation of a persistent and well-separated radical pair in plant cryptochrome. J. Am. Chem. Soc. 137:31147–56
    [Google Scholar]
  87. 87.
    Maag D, Mast T, Elstner M, Cui Q, Kubař T. 2021. O to bR transition in bacteriorhodopsin occurs through a proton hole mechanism. PNAS 118:e2024803118
    [Google Scholar]
  88. 88.
    Mai S, Menger MFSJ, Marazzi M, Stolba DL, Monari A, González L. 2020. Competing ultrafast photoinduced electron transfer and intersystem crossing of Re(CO)3(Dmp)(His124)(Trp122)]+ in Pseudomonas aeruginosa azurin: a nonadiabatic dynamics study. Theor. Chem. Acc. 139:365
    [Google Scholar]
  89. 89.
    Maity S, Bold BM, Prajapati JD, Sokolov M, Kubař T et al. 2020. DFTB/MM molecular dynamics simulations of the FMO light-harvesting complex. J. Phys. Chem. Lett. 11:208660–67
    [Google Scholar]
  90. 90.
    Maity S, Daskalakis V, Elstner M, Kleinekathöfer U. 2021. Multiscale QM/MM molecular dynamics simulations of the trimeric major light-harvesting complex II. Phys. Chem. Chem. Phys. 23:127407–17
    [Google Scholar]
  91. 91.
    Major DT, Gao J. 2007. An integrated path integral and free-energy perturbation-umbrella sampling method for computing kinetic isotope effects of chemical reactions in solution and in enzymes. J. Chem. Theory Comput. 3:3949–60
    [Google Scholar]
  92. 92.
    Manigrasso J, De Vivo M, Palermo G. 2021. Controlled trafficking of multiple and diverse cations prompts nucleic acid hydrolysis. ACS Catal 11:8786–97
    [Google Scholar]
  93. 93.
    Matyushov DV. 2013. Protein electron transfer: dynamics and statistics. J. Chem. Phys. 139:2025102
    [Google Scholar]
  94. 94.
    McCullagh M, Saunders MG, Voth GA. 2014. Unraveling the mystery of ATP hydrolysis in actin filaments. J. Am. Chem. Soc. 136:13053–58
    [Google Scholar]
  95. 95.
    Mehmood R, Kulik HJ. 2020. Both configuration and QM region size matter: zinc stability in QM/MM models of DNA methyltransferase. J. Chem. Theory Comput. 16:3121–34
    [Google Scholar]
  96. 96.
    Mokhtari DA, Appel MJ, Fordyce PM, Herschlag D. 2021. High throughput and quantitative enzymology in the genomic era. Curr. Opin. Struct. Biol. 71:259–73
    [Google Scholar]
  97. 97.
    Mugnai ML, Hyeon C, Hinczewski M, Thirumalai D. 2020. Theoretical perspectives on biological machines. Rev. Mod. Phys. 92:025001
    [Google Scholar]
  98. 98.
    Muhlbauer ME, Saura P, Nuber F, Di Luca A, Friedrich T, Kaila VRI 2020. Water-gated proton transfer dynamics in respiratory complex I. J. Am. Chem. Soc. 142:13718–28
    [Google Scholar]
  99. 99.
    Naseem-Khan S, Lagardere L, Narth C, Cisneros GA, Ren P et al. 2022. Development of the quantum-inspired SIBFA many-body polarizable force field: enabling condensed-phase molecular dynamics simulations. J. Chem. Theory Comput. 18:3607–21
    [Google Scholar]
  100. 100.
    Nicholls DG, Ferguson SJ. 2002. Bioenergetics New York: Acad. Press. , 3rd ed..
  101. 101.
    Nishimura Y, Nakai H. 2019. DCDFTBMD: divide-and-conquer density functional tight-binding program for huge-system quantum mechanical molecular dynamics simulations. J. Comput. Chem. 40:1538–49
    [Google Scholar]
  102. 102.
    Nitzan A. 2014. Chemical Dynamics in Condensed Phases: Relaxation, Transfer, and Reactions in Condensed Molecular Systems Oxford, UK: Oxford Univ. Press
  103. 103.
    Noe F, Tkatchenko A, Müller KR, Clementi C. 2020. Machine learning for molecular simulation. Annu. Rev. Phys. Chem. 71:361–90
    [Google Scholar]
  104. 104.
    Pang Z, Sokolov M, Kubař T, Elstner M. 2022. Unravelling the mechanism of glucose binding in a protein-based fluorescence probe: molecular dynamics simulation with a tailor-made charge model. Phys. Chem. Chem. Phys. 24:42441–53
    [Google Scholar]
  105. 105.
    Parac M, Grimme S. 2002. Comparison of multireference Møller-Plesset theory and time-dependent methods for the calculation of vertical excitation energies of molecules. J. Phys. Chem. A 106:6844–50
    [Google Scholar]
  106. 106.
    Phatak P, Ghosh N, Yu H, Cui Q, Elstner M. 2008. Amino acids with an intermolecular proton bond as the proton storage site in bacteriorhodopsin. PANS 105:19672–77
    [Google Scholar]
  107. 107.
    Pisliakov AV, Sharma PK, Chu ZT, Haranczyk M, Warshel A. 2008. Electrostatic basis for the unidirectionality of the primary proton transfer in cytochrome c oxidase. PNAS 105:7726–31
    [Google Scholar]
  108. 108.
    Priess M, Göddeke H, Groenhof G, Schäfer LV. 2018. Molecular mechanism of ATP hydrolysis in an ABC transporter. ACS Central Sci 4:1334–43
    [Google Scholar]
  109. 109.
    Raper AT, Reed AJ, Suo ZC. 2018. Kinetic mechanism of DNA polymerases: contributions of conformational dynamics and a third divalent metal ion. Chem. Rev. 118:6000–25
    [Google Scholar]
  110. 110.
    Reinhardt CR, Konstantinovsky D, Soudackov AV, Hammes-Schiffer S. 2022. Kinetic model for reversible radical transfer in ribonucleotide reductase. PNAS 119:e2202022119
    [Google Scholar]
  111. 111.
    Reuter N, Dejaegere A, Maigret B, Karplus M. 2000. Frontier bonds in QM/MM methods: a comparison of different approaches. J. Phys. Chem. A 104:1720–35
    [Google Scholar]
  112. 112.
    Riccardi D, Schaefer P, Cui Q. 2005. pKa calculations in solution and proteins with QM/MM free energy perturbation simulations. J. Phys. Chem. B 109:17715–33
    [Google Scholar]
  113. 113.
    Richter R, Foerster JM, Schelter I, Kümmel S. 2020. Self-interaction correction, electrostatic, and structural influences on time-dependent density functional theory excitations of bacteriochlorophylls from the light-harvesting complex 2. J. Chem. Phys. 153:2441–53
    [Google Scholar]
  114. 114.
    Rizzi A, Carloni P, Parrinello M. 2021. Targeted free energy perturbation revisited: accurate free energies from mapped reference potentials. J. Phys. Chem. Lett. 12:9449–54
    [Google Scholar]
  115. 115.
    Roston D, Cui Q. 2016. Substrate and transition state binding in alkaline phosphatase exhibited by computational analysis of isotope effects. J. Am. Chem. Soc. 138:11946–57
    [Google Scholar]
  116. 116.
    Roston D, Demapan D, Cui Q. 2019. Extensive free energy simulations identify water as the base in nucleotide addition by DNA polymerase. PNAS 116:25048–56
    [Google Scholar]
  117. 117.
    Roston D, Lu X, Fang D, Demapan D, Cui Q. 2018. Analysis of phosphoryl transfer enzymes with QM/MM free energy simulations. Methods Enzymol 607:53–90
    [Google Scholar]
  118. 118.
    Rouhani S, Cartailler JP, Facciotti MT, Walian P, Needleman R et al. 2001. Crystal structure of the D85S mutant of bacteriorhodopsin: model of an O-like photocycle intermediate. J. Mol. Biol. 313:3615–28
    [Google Scholar]
  119. 119.
    Roux B 2011. Molecular Machines Singapore: World Sci.
  120. 120.
    Samara NL, Yang W 2018. Cation trafficking propels RNA hydrolysis. Nat. Struct. Mol. Biol. 25:715–21
    [Google Scholar]
  121. 121.
    Schulz CE, van Gastel M, Pantazis DA, Neese F. 2021. Converged structural and spectroscopic properties for refined QM/MM models of azurin. Inorg. Chem. 60:7399–412
    [Google Scholar]
  122. 122.
    Senn HM, Thiel W. 2009. QM/MM methods for biomolecular systems. Angew. Chem. Int. Ed. 48:1198–229
    [Google Scholar]
  123. 123.
    Shen L, Yang WT. 2018. Molecular dynamics simulations with quantum mechanics/molecular mechanics and adaptive neural networks. J. Chem. Theory. Comput. 14:1442–55
    [Google Scholar]
  124. 124.
    Sirohiwal A, Pantazis DA. 2021. Electrostatic profiling of photosynthetic pigments: implications for directed spectral tuning. Phys. Chem. Chem. Phys. 23:4324677–84
    [Google Scholar]
  125. 125.
    Sivak DA, Crooks GE. 2012. Thermodynamic metrics and optimal paths. Phys. Rev. Lett. 108:190602
    [Google Scholar]
  126. 126.
    Sokolov M, Bold BM, Kranz JJ, Höfener S, Niehaus TA, Elstner M. 2021. Analytical time-dependent long-range corrected density functional tight binding (TD-LC-DFTB) gradients in DFTB+: implementation and benchmark for excited-state geometries and transition energies. J. Chem. Theory Comput. 17:42266–82
    [Google Scholar]
  127. 127.
    Son CY, Yethiraj A, Cui Q. 2017. Cavity hydration dynamics in cytochrome c oxidase and functional implications. PNAS 114:E8830–36
    [Google Scholar]
  128. 128.
    Song Y, Gunner MR. 2014. Halorhodopsin pumps Cl and bacteriorhodopsin pumps protons by a common mechanism that uses conserved electrostatic interactions. PNAS 111:4616377–82
    [Google Scholar]
  129. 129.
    Stevens DR, Hammes-Schiffer S. 2018. Exploring the role of the third active site metal ion in DNA polymerase η with QM/MM free energy simulations. J. Am. Chem. Soc. 140:8965–69
    [Google Scholar]
  130. 130.
    Stoddart JF. 2017. Mechanically interlocked molecules (MIMs)—molecular shuttles, switches, and machines (Nobel Lecture). Angew. Chem. Int. Ed. 56:11094–125
    [Google Scholar]
  131. 131.
    Sun R, Sode O, Dama JF, Voth GA. 2017. Simulating protein mediated hydrolysis of ATP and other nucleoside triphosphates by combining QM/MM molecular dynamics with advances in metadynamics. J. Chem. Theory Comput. 13:2332–41
    [Google Scholar]
  132. 132.
    Swanson JMJ. 2022. Multiscale kinetic analysis of proteins. Curr. Opin. Struct. Biol. 72:169–75
    [Google Scholar]
  133. 133.
    Sweeney HL, Houdusse A. 2010. Structural and functional insights into the myosin motor mechanism. Annu. Rev. Biophys. 39:539–57
    [Google Scholar]
  134. 134.
    Thirumalai D, Hyeon C, Zhuravlev PI, Lorimer GH. 2019. Symmetry, rigidity, and allosteric signaling: from monomeric proteins to molecular machines. Chem. Rev. 119:6788–821
    [Google Scholar]
  135. 135.
    Tripathi R, Forbert H, Marx D. 2019. Settling the long-standing debate on the proton storage site of the prototype light-driven proton pump bacteriorhodopsin. J. Phys. Chem. B 123:9598–608
    [Google Scholar]
  136. 136.
    Tripathi R, Glaves R, Marx D. 2017. The GTPase hGBP1 converts GTP to GMP in two steps via proton shuttle mechanisms. Chem. Sci. 8:371–80
    [Google Scholar]
  137. 137.
    Troisi A. 2011. The speed limit for sequential charge hopping in molecular materials. Org. Electron. 12:1988–91
    [Google Scholar]
  138. 138.
    Unarta IC, Zhu LZ, Tse CKM, Cheung PPH, Yu J, Huang XH 2018. Molecular mechanisms of RNA polymerase II transcription elongation elucidated by kinetic network models. Curr. Opin. Struct. Biol. 49:54–62
    [Google Scholar]
  139. 139.
    Valsson O, Tiwary P, Parrinello M. 2016. Enhancing important fluctuations: rare events and metadynamics from a conceptual viewpoint. Annu. Rev. Phys. Chem. 67:159–84
    [Google Scholar]
  140. 140.
    van Wonderen JH, Hall CR, Jiang X, Adamczyk K, Carof A et al. 2019. Ultrafast light-driven electron transfer in a Ru(II)tris(bipyridine)-labeled multiheme cytochrome. J. Am. Chem. Soc. 141:3815190–200
    [Google Scholar]
  141. 141.
    Vennelakanti V, Nazemi A, Mehmood R, Steeves AH, Kulik HJ. 2022. Harder, better, faster, stronger: large-scale QM and QM/MM for predictive modeling in enzymes and proteins. Curr. Opin. Struct. Biol. 72:9–17
    [Google Scholar]
  142. 142.
    Wang W, Cao SQ, Zhu LZ, Huang XH. 2018. Constructing Markov state models to elucidate the functional conformational changes of complex biomolecules. WIREs Comput. Mol. Sci. 8:e1343
    [Google Scholar]
  143. 143.
    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. 120:1674–92
    [Google Scholar]
  144. 144.
    Wanko M, Hoffmann M, Frähmcke 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 112:11468–78
    [Google Scholar]
  145. 145.
    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 112:11462–67
    [Google Scholar]
  146. 146.
    Wanko M, Hoffmann M, Strodel P, Koslowski A, Thiel W et al. 2005. Calculating absorption shifts for retinal proteins: computational challenges. J. Phys. Chem. B 109:3606–15
    [Google Scholar]
  147. 147.
    Warshel A, Chu ZT. 2001. Nature of the surface crossing process in bacteriorhodopsin: computer simulations of the quantum dynamics of the primary photochemical event. J. Phys. Chem. B 105:9857–71
    [Google Scholar]
  148. 148.
    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. 103:2227–49
    [Google Scholar]
  149. 149.
    Weber C, Cole DJ, O'Regan DD, Payne MC 2014. Renormalization of myoglobin-ligand binding energetics by quantum many-body effects. PNAS 111:5790–95
    [Google Scholar]
  150. 150.
    Welke K, Watanabe HC, Wolter T, Gaus M, Elstner M. 2013. QM/MM simulations of vibrational spectra of bacteriorhodopsin and channelrhodopsin-2. Phys. Chem. Chem. Phys. 15:186651–59
    [Google Scholar]
  151. 151.
    Woiczikowski PB, Steinbrecher T, Kubař T, Elstner M. 2011. Nonadiabatic QM/MM simulations of fast charge transfer in Escherichia coli DNA photolyase. J. Phys. Chem. B 115:329846–63
    [Google Scholar]
  152. 152.
    Wolf S, Freier E, Cui Q, Gerwert K. 2015. Infrared spectral marker bands characterizing a transient water wire inside a hydrophobic membrane protein. J. Chem. Phys. 141:22D524
    [Google Scholar]
  153. 153.
    Wolter T, Elstner M, Fischer S, Smith JC, Bondar AN. 2015. Mechanism by which untwisting of retinal leads to productive bacteriorhodopsin photocycle states. J. Phys. Chem. B 119:62229–40
    [Google Scholar]
  154. 154.
    Wolter T, Welke K, Phatak P, Bondar AN, Elstner M. 2013. Excitation energies of a water-bridged twisted retinal structure in the bacteriorhodopsin proton pump: a theoretical investigation. Phys. Chem. Chem. Phys. 15:3012582–90
    [Google Scholar]
  155. 155.
    Wu Q, Van Voorhis T. 2005. Direct optimization method to study constrained systems within density-functional theory. Phys. Rev. A 72:024502
    [Google Scholar]
  156. 156.
    Wu Q, Van Voorhis T. 2006. Constrained density functional theory and its application in long-range electron transfer. J. Chem. Theory Comput. 2:3765–74
    [Google Scholar]
  157. 157.
    Wu Q, Van Voorhis T. 2006. Direct calculation of electron transfer parameters through constrained density functional theory. J. Phys. Chem. A 110:299212–18
    [Google Scholar]
  158. 158.
    Wu WJ, Yang W, Tsai MD. 2017. How DNA polymerases catalyze replication and repair with contrasting fidelity. Nat. Rev. Chem. 1:0068
    [Google Scholar]
  159. 159.
    Yagi K, Ito S, Sugita Y. 2021. Exploring the minimum-energy pathways and free-energy profiles of enzymatic reactions with QM/MM calculations. J. Phys. Chem. B 125:4701–13
    [Google Scholar]
  160. 160.
    Zhang LF, Wang H, E W 2018. Reinforced dynamics for enhanced sampling in large atomic and molecular systems. J. Chem. Phys. 148:124113
    [Google Scholar]
  161. 161.
    Zhang Y. 2006. Pseudobond ab initio QM/MM approach and its applications to enzyme reactions. Theor. Chem. Acc. 116:43–50
    [Google Scholar]
  162. 162.
    Zheng YQ, Cui Q. 2017. Microscopic mechanisms that govern the titration response and pKa values of buried residues in staphylococcal nuclease mutants. Proteins 85:268–81
    [Google Scholar]
/content/journals/10.1146/annurev-biophys-111622-091140
Loading
/content/journals/10.1146/annurev-biophys-111622-091140
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error