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Vibrational energy flow across heme–cytochrome c and cytochrome c–water interfaces

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Abstract

We examine vibrational energy transfer across the heme–protein and protein–solvent interfaces of cytochrome c, using, as appropriate, classical, semiclassical, and quantum approaches. To characterize energy flow across the interface between the heme and the rest of cytochrome c, we calculate communication maps for the protein in its native structure as well as two structures with Met80 dissociated from the heme at 300 K. The response to excess energy in the heme is mediated by covalent and hydrogen bonds to the heme, as well as several through-space interactions, including those involving the dissociated Met80. This observation suggests no energy flow bottleneck between the heme and Met80 that would impede rebinding kinetics at 300 K. We examine the possibility of additional bottlenecks to energy flow by calculating the temperature dependence of the ergodicity threshold in an imidazole-ligated Fe-porphyrin system that constitutes the core of the heme–histidine complex. The ergodic threshold, which we calculate quantum mechanically, corresponds to a temperature of about 140 K. We also address the flow of excess vibrational energy from the protein to the solvent. We calculate the thermal boundary conductance between cytochrome c and water semiclassically over a range of temperatures and find that the protein–water interface poses no greater resistance to thermal flow than the protein itself.

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References

  1. Leitner DM, Straub JE (2009) Proteins: energy, heat and signal flow. Taylor and Francis Press, New York

    Google Scholar 

  2. Smock RG, Gierasch LM (2009) Sending signals dynamically. Science 324:198–203

    Article  CAS  Google Scholar 

  3. Fujisaki H, Straub JE (2005) Vibrational energy relaxation in proteins. Proc Natl Acad Sci (USA) 102:7626–7631

    Article  Google Scholar 

  4. Leitner DM (2008) Energy flow in proteins. Ann Rev Phys Chem 59:233–259

    Article  CAS  Google Scholar 

  5. Gunasekaran K, Ma B, Nussinov R (2004) Is allostery an intrinsic property of all dynamic proteins? Proteins Struct Func Bioinform 57:433–443

    Article  CAS  Google Scholar 

  6. Nussinov R, Tsai C-J (2012) Allostery in disease and in drug discovery. Cell 153:293–305

    Article  Google Scholar 

  7. Agarwal PK (2005) Role of protein dynamics in reaction rate enhancement by enzymes. J Am Chem Soc 127:15248–15256

    Article  CAS  Google Scholar 

  8. Fang C, Frontiera RR, Tran R, Mathies RA (2009) Mapping GFP structure evolution during proton transfer with femtosecond Raman spectroscopy. Nature 462:200–205

    Article  CAS  Google Scholar 

  9. Buchli B, Waldauer SA, Walser R, Donten ML, Pfister R, Bloechliger N, Steiner S, Caflisch A, Zerbe O, Hamm P (2013) Kinetic response of a photoperturbed allosteric protein. Proc Natl Acad Sci USA 110:11725–11730

    Article  CAS  Google Scholar 

  10. Nagy AM, Raicu V, Miller RJD (2005) Nonlinear optical studies of heme protein dynamics: implications for proteins as hybrid states of matter. Biochim Biophys Acta 1749:148–172

    Article  CAS  Google Scholar 

  11. Sagnella DE, Straub JE, Jackson TA, Lim M, Anfinrud PA (1999) Vibrational population relaxation of carbon monoxide in the heme pocket of carbonmonoxy myoglobin: comparison of time-resolved mid-IR absorbance experiments and molecular dynamics simulations. Proc Natl Acad Sci USA 96:14324–14329

    Article  CAS  Google Scholar 

  12. Henry ER, Eaton WA, Hochstrasser RM (1986) Molecular dynamics simulations of cooling in laser-excited heme proteins. Proc Natl Acad Sci USA 83:8982–8986

    Article  CAS  Google Scholar 

  13. Lian T, Locke B, Kholodenko Y, Hochstrasser RM (1994) Energy flow from solute to solvent probed by femtosecond ir spectroscopy: malachite green and heme protein solutions. J Phys Chem 98:11648–11656

    Article  CAS  Google Scholar 

  14. Gnanasekaran R, Agbo JK, Leitner DM (2011) Communication maps computed for homodimeric hemoglobin: computational study of water-mediated energy transport in proteins. J Chem Phys 135:065103

    Article  Google Scholar 

  15. Champion PM (2005) Following the flow of energy in biomolecules. Science 310:980–982

    Article  CAS  Google Scholar 

  16. Sagnella DE, Straub JE (2001) Directed energy “funneling” mechanism for heme cooling following ligand photolysis or direct excitation in solvated carbonmonoxy myoglobin. J Phys Chem B 105:7057–7063

    Article  CAS  Google Scholar 

  17. Takayanagi M, Okumura H, Nagaoka M (2007) Anisotropic structural relaxation and its correlation with the excess energy diffusion in the incipient process of photodissociated MbCO: high-resolution analysis via ensemble perturbation method. J Phys Chem B 111:864–869

    Article  CAS  Google Scholar 

  18. Nagaoka M, Yu I, Takayanagi M (2009) Energy flow analysis in proteins via ensemble molecular dynamics simulations: time-resolved vibrational analysis and surficial Kirkwood-Buff Theory. In: Leitner DM, Straub JE (eds) Proteins: energy, heat and signal flow. Taylor & Francis Group, CRC Press, Boca Raton, pp 169–196

    Google Scholar 

  19. Mizutani Y, Kitagawa T (1997) Direct observation of cooling of heme upon photodissociation of carbonmonoxy myoglobin. Science 278:443–446

    Article  CAS  Google Scholar 

  20. Koyama M, Neya S, Mizutani Y (2006) Role of heme propionates of myoglobin in vibrational energy relaxation. Chem Phys Lett 430:404–408

    Article  CAS  Google Scholar 

  21. Sato A, Mizutani Y (2005) Picosecond structural dynamics of myoglobin following photodissociation of carbon monoxide as revealed by ultraviolet time-resolved resonance Raman spectroscopy. Biochem 44:14709–14714

    Article  CAS  Google Scholar 

  22. Ye X, Demidov A, Champion PM (2002) Measurements of the photodissociation quantum yields of MbNO and MbO2 and the vibrational relaxation of the six-coordinate heme species. J Am Chem Soc 124:5914–5924

    Article  CAS  Google Scholar 

  23. Ow Y-LP, Green DR, Hao Z, Mak TW (2008) Cytochrome c: functions beyond respiration. Nat Rev Mol Cell Biol 9:532–542

    Article  CAS  Google Scholar 

  24. Vos MH (2008) Ultrafast dynamics of ligands within heme proteins. Biochim Biophys Acta 1777:15–31

    Article  CAS  Google Scholar 

  25. Zang C, Stevens JA, Link JJ, Guo L, Wang L, Zhong D (2009) Ultrafast proteinquake dynamics in cytochrome c. J Am Chem Soc 131:2846–2852

    Article  CAS  Google Scholar 

  26. Fujii N, Mizuno M, Mizutani Y (2011) Direct observation of vibrational energy flow in cytochrome c. J Phys Chem B 115:13057–13064

    Article  CAS  Google Scholar 

  27. Zhang P, Malolepsza E, Straub JE (2012) Dynamics of methionine ligand rebinding in cytochrome c. J Phys Chem B 116:6980–6990

    Article  CAS  Google Scholar 

  28. Zhang P, Ahn SW, Straub JE (2013) “Strange kinetics” in the temperature dependence of methionine ligand rebinding dynamics in cytochrome c. J Phys Chem B 117:7190–7202

    Article  CAS  Google Scholar 

  29. Bu L, Straub JE (2003) Simulating vibrational energy flow in proteins: relaxation rate and mechanism for heme cooling in cytochrome c. J Phys Chem B 107:12339–12345

    Article  CAS  Google Scholar 

  30. Zhang Y, Fujisaki H, Straub JE (2009) Mode specific vibrational energy relaxation of amide I and II modes in N-methylacetamide/water clusters: the intra- and inter-molecular energy transfer mechanisms. J Phys Chem A 113:3051–3060

    Article  CAS  Google Scholar 

  31. Zhang Y, Fujisaki H, Straub JE (2009) Direct evidence for mode-specific vibrational energy relaxation from quantum time-dependent perturbation theory. I. Five-coordinate ferrous iron porphydin model. J Chem Phys 130:025102

    Article  Google Scholar 

  32. Leitner DM (2001) Vibrational energy transfer in helices. Phys Rev Lett 87:188102

    Article  Google Scholar 

  33. Leitner DM, Wolynes PG (1996) Statistical properties of localized vibrational eigenstates. Chem Phys Lett 258:18–24

    Article  CAS  Google Scholar 

  34. Leitner DM, Wolynes PG (1997) Vibrational mixing and energy flow in polyatomic molecules: quantitative prediction using local random matrix theory. J Phys Chem A 101:541–548

    Article  CAS  Google Scholar 

  35. Keshavamurthy S (2013) Scaling perspective on intramolecular vibrational energy flow: analogies, insights and challenges. Adv Chem Phys 153:43–110

    CAS  Google Scholar 

  36. Semparithi A, Keshavamurthy S (2006) Intramolecular vibrational energy redistributions as diffusion in state space: classical-quantum correspondence. J Chem Phys 125:141101

    Article  Google Scholar 

  37. Leitner DM, Gruebele M (2008) A quantum model of restricted vibrational energy flow on the way to the transition state in unimolecular reactions. Mol Phys 106:433–442

    Article  CAS  Google Scholar 

  38. Gruebele M, Bigwood R (1998) Molecular vibrational energy flow: beyond the golden rule. Int Rev Phys Chem 17:91–145

    Article  CAS  Google Scholar 

  39. Bu L, Straub JE (2003) Vibrational energy relaxation of ‘tailored’ hemes in myoglobin following ligand photolysis supports energy funneling mechanism of heme ‘cooling’. J Phys Chem B 107:10634–10639

    Article  CAS  Google Scholar 

  40. Lervik A, Bresme F, Kjelstrup S, Bedeaux D, Rubi JM (2010) Heat transfer in protein–water interfaces. Phys Chem Chem Phys 12:1610–1617

    Article  CAS  Google Scholar 

  41. Leitner DM (2013) Thermal boundary conductance and rectification in molecules. J Phys Chem B 117:12820–12828

    Article  CAS  Google Scholar 

  42. Xu Y, Leitner DM (2014) Vibrational energy flow through the green fluorescent protein water interface: communication maps and thermal boundary conductance. J Phys Chem B. doi:10.1021/jp412141z

    Google Scholar 

  43. Leitner DM (2009) Frequency resolved communication maps for proteins and other nanoscale materials. J Chem Phys 130:195101

    Article  Google Scholar 

  44. Berne BJ, Borkovec M, Straub JE (1988) Classical and modern methods in reaction rate theory. J Phys Chem 92:3711–3725

    Article  CAS  Google Scholar 

  45. Leitner DM (2005) Heat transport in molecules and reaction kinetics: the role of quantum energy flow and localization. Adv Chem Phys 130B:205–256

    Google Scholar 

  46. Komatsuzaki T, Baba A, Kawai S, Toda M, Straub JE, Berry RS (2011) Ergodic problems for real complex systems in chemical physics. Adv Chem Phys 145:171–220

    CAS  Google Scholar 

  47. Leitner DM, Matsunaga Y, Li C-B, Komatsuzaki T, Shojiguchi A, Toda M (2011) Non-brownian phase space dynamics of molecules, the nature of their vibrational states, and non-RRKM kinetics. Adv Chem Phys 145:83–122

    CAS  Google Scholar 

  48. Li CB, Matsunaga Y, Toda M, Komatsuzaki T (2005) Phase space reaction network on a multisaddle energy landscape: HCN isomerization. J Chem Phys 123:184301

    Article  Google Scholar 

  49. Shojiguchi A, Li CB, Komatsuzaki T, Toda M (2007) Fractional behavior in multi-dimensional Hamiltonian systems describing reactions. Phys Rev E 76:056205

    Article  Google Scholar 

  50. Toda M (2005) Global aspects of chemical reactions in multidimensional phase space. Adv Chem Phys 130A:337–399

    Google Scholar 

  51. Ezra GS, Martens CC, Fried LE (1987) Semiclassical quantization of polyatomic molecules: some recent developments. J Phys Chem 91:3721–3730

    Article  CAS  Google Scholar 

  52. Uzer T (1991) Theories of intramolecular vibrational energy transfer. Phys Rep 199(2):73–146

    Article  CAS  Google Scholar 

  53. Keshavamurthy S, Ezra GS (1997) Eigenstate assignments and the quantum-classical correspondence for highly-excited vibrational states of the Baggot H2O Hamiltonian. J Chem Phys 107:156–179

    Article  CAS  Google Scholar 

  54. Leitner DM, Wolynes PG (1996) Vibrational relaxation and energy localization in polyatomics: effects of high-order resonances on flow rates and the quantum ergodicity transition. J Chem Phys 105:11226–11236

    Article  CAS  Google Scholar 

  55. Logan DE, Wolynes PG (1990) Quantum localization and energy flow in many-dimensional Fermi resonant systems. J Chem Phys 93:4994–5012

    Article  CAS  Google Scholar 

  56. Lervik A, Bresme F, Kjelstrup S (2009) Heat transfer in soft nanoscale interfaces: the influence of interface curvature. Soft Matter 5:2407–2414

    Article  CAS  Google Scholar 

  57. Nguyen PH, Park SM, Stock G (2010) Nonequilibrium molecular dynamics simulation of the energy transfer through a peptide helix. J Chem Phys 132:025102

    Article  Google Scholar 

  58. Nguyen PH, Hamm P, Stock G (2009) Nonequilibrium molecular dynamics simulation of photoinduced energy flow in peptides: theory meets experiment. In: Leitner DM, Straub JE (eds) Proteins: energy, heat and signal flow. Taylor & Francis Group, CRC Press, Boca Raton, pp 149–168

    Google Scholar 

  59. Yu X, Leitner DM (2003) Vibrational energy transfer and heat conduction in a protein. J Phys Chem B 107:1698–1707

    Article  CAS  Google Scholar 

  60. Yu X, Leitner DM (2005) Heat flow in proteins: computation of thermal transport coefficients. J Chem Phys 122:054902

    Article  Google Scholar 

  61. Botan V, Backus EHG, Pfister R, Moretto A, Crisma M, Toniolo C, Nguyen PH, Stock G, Hamm P (2007) Energy transport in peptide helices. Proc Natl Acad Sci USA 104:12749–12754

    Article  CAS  Google Scholar 

  62. Kholodenko Y, Volk M, Gooding E, Hochstrasser RM (2000) Energy dissipation and relaxation processes in deoxymyoglobin after photoexcitation in the Soret region. Chem Phys 259:71–87

    Article  CAS  Google Scholar 

  63. Helbing J, Devereux M, Nienhaus K, Nienhaus GU, Hamm P, Meuwly M (2012) Temperature dependence of the heat diffusivity of proteins. J Phys Chem A 116:2620–2628

    Article  CAS  Google Scholar 

  64. Müller-Werkmeister HM, Bredenbeck J (2014) A donor-acceptor pair for the real time study of vibrational energy transfer in proteins. Phys Chem Chem Phys 16:3261–3266

    Article  Google Scholar 

  65. Hopkins PE (2013) Thermal transport across solid interfaces with nanoscale imperfections: effects of roughness, disorder, dislocations and bonding on thermal boundary conductance (Review Article). ISRN Mech Eng, 2013: 682586

  66. Buldum A, Leitner DM, Ciraci S (1999) Thermal conduction through a molecule. Europhys Lett 47:208–212

    Article  CAS  Google Scholar 

  67. Segal D, Nitzan A, Hänggi P (2003) Thermal conductance through molecular wires. J Chem Phys 119:6840–6855

    Article  CAS  Google Scholar 

  68. Leitner DM, Wolynes PG (2000) Heat flow through an insulating nanocrystal. Phys Rev E 61:2902–2908

    Article  CAS  Google Scholar 

  69. Allen PB, Feldman JL (1993) Thermal conductivity of disordered harmonic solids. Phys Rev B 48:12581–12588

    Article  CAS  Google Scholar 

  70. Xu Y, Leitner DM (2014) Communication maps of vibrational energy transport in photoactive yellow protein. J Phys Chem A. doi:10.1021/jp411281y

    Google Scholar 

  71. Ishikura T, Yamato T (2006) Energy transfer pathways relevant for long-range intramolecular signaling of photosensory protein revealed by microscopic energy conductivity analysis. Chem Phys Lett 432:533–537

    Article  CAS  Google Scholar 

  72. Ota N, Agard DA (2005) Intramolecular signaling pathways revealed by modeling anisotropic thermal diffusion. J Mol Biol 351:345–354

    Article  CAS  Google Scholar 

  73. Gnanasekaran R, Xu Y, Leitner DM (2010) Dynamics of water clusters confined in proteins: a molecular dynamics simulation study of interfacial waters in a dimeric hemoglobin. J Phys Chem B 114:16989–16996

    Article  CAS  Google Scholar 

  74. Yu X, Leitner DM (2003) Anomalous diffusion of vibrational energy in proteins. J Chem Phys 119:12673–12679

    Article  CAS  Google Scholar 

  75. Yu X, Leitner DM (2006) Thermal conductivity computed for vitreous silica and methyl-doped silica above the plateau. Phys Rev B 74:184305

    Article  Google Scholar 

  76. Swartz ET, Pohl RO (1989) Thermal boundary resistance. Rev Mod Phys 61:605–668

    Article  Google Scholar 

  77. Yu X, Leitner DM (2005) Thermal transport coefficients for liquid and glassy water computer from a harmonic aqueous glass. J Chem Phys 123:104503

    Article  Google Scholar 

  78. Bigwood R, Gruebele M, Leitner DM, Wolynes PG (1998) The vibrational energy flow transition in organic molecules: theory meets experiment. Proc Natl Acad Sci USA 95:5960–5967

    Article  CAS  Google Scholar 

  79. Agbo JK, Leitner DM, Myshakin EM, Jordan KD (2007) Quantum energy flow and the kinetics of water shuttling between hydrogen bonding sites on trans-formanilide (TFA). J Chem Phys 127:064315

    Article  Google Scholar 

  80. Acharya H, Mozdzierz NJ, Keblinski P, Garde S (2012) How chemistry, nanoscale roughness, and the direction of heat flow affect thermal conductance of solid–water interfaces. Ind Eng Chem Res 51:1767–1773

    Article  CAS  Google Scholar 

  81. Agbo JK, Gnanasekaran R, Leitner DM (2014) Communication maps: exploring energy transport through proteins and water. Isr J Chem. doi:10.1002/ijch.201300139

  82. Volkov AM, vanNuland NAJ (2012) Electron transfer interactome of cytochrome c. PLoS Comput Biol 8:e1002807

    Article  CAS  Google Scholar 

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Acknowledgments

Support from the National Science Foundation (NSF CHE-0910669 and CHE-1361776 to DML, CHE-1114676 to JES) is gratefully acknowledged.

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Correspondence to John E. Straub or David M. Leitner.

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Dedicated to Professor Greg Ezra and published as part of the special collection of articles celebrating his 60th birthday.

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Agbo, J.K., Xu, Y., Zhang, P. et al. Vibrational energy flow across heme–cytochrome c and cytochrome c–water interfaces. Theor Chem Acc 133, 1504 (2014). https://doi.org/10.1007/s00214-014-1504-7

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