Theoretical Chemistry Accounts

, Volume 128, Issue 4–6, pp 769–782 | Cite as

Vibrational dynamics of polyatomic molecules in solution: assignment, time evolution and mixing of instantaneous normal modes

  • Adrián Kalstein
  • Sebastián Fernández-Alberti
  • Adolfo Bastida
  • Miguel Angel Soler
  • Marwa H. Farag
  • José Zúñiga
  • Alberto Requena
Regular Article

Abstract

Intramolecular vibrational dynamics of polyatomic molecules in solution can be addressed through normal mode analysis based on either equilibrium normal modes (ENMs) or instantaneous normal modes (INMs). While the former offers a straightforward way of examining experimental spectra, the latter provides a decoupled short-time description of the vibrational motions of the molecule. In order to reconcile both representations, a realistic assignment of the INMs in terms of the ENMs is needed. In this paper, we describe a novel method to assign the INMs using the ENMs as templates, which provides a unique relationship between the two sets of normal modes. The method is based specifically on the use of the so-called Min-Cost or Min-Sum algorithm, duly adapted to our problem, to maximize the overlaps between the two sets of modes. The identification of the INMs as the system evolves with time then allows us to quantify the vibrational energy stored in each INM and so monitor the flows of intramolecular vibrational energy within the solute molecule. We also discuss the degree of mixing of the INMs and characterize the way they change with time by means of the corresponding autocorrelation functions. The usefulness of the method is illustrated by carrying out equilibrium molecular dynamics (MD) simulations of the deuterated N-methylacetamide (NMAD) molecule in D2O solution.

Keywords

Equilibrium normal modes Instantaneous normal modes Vibrational energy relaxation Biomolecules in solution 

Notes

Acknowledgments

This work was partially supported by the Ministerio de Educación y Ciencia of Spain under Project CTQ2007-66528/BQU and CONSOLIDER CSD2009-00038, by the Fundación Séneca del Centro de Coordinación de la Investigación de la Región de Murcia under Project 08735/PI/08, by the Universidad Nacional de Quilmes, and by CONICET. M.A.S. and M.H.F. both acknowledge fellowships provided by the Ministerio de Educación y Ciencia of Spain, and A.K. acknowledges a fellowship provided by CONICET.

References

  1. 1.
    Hill JR, Ziegler CJ, Suslick KS, Dlott DD, Rella CW, Fayer MD (1996) Tuning the vibrational relaxation of co bound to heme and metalloporphyrin complexes. J Phys Chem 100:18023–18032CrossRefGoogle Scholar
  2. 2.
    Hamm P, Lim MH, Hochstrasser RM (1998) Structure of the amide i band of peptides measured by femtosecond nonlinear-infrared spectroscopy. J Phys Chem B 102 (31):6123–6138CrossRefGoogle Scholar
  3. 3.
    Peterson KA, Rella CW, Engholm JR, Schwettman HA (1999) Ultrafast vibrational dynamics of the myoglobin amide i band. J Phys Chem B 103(3):557–561CrossRefGoogle Scholar
  4. 4.
    Dlott DD (2001) Vibrational energy redistribution in polyatomic liquids: 3d infrared-raman spectroscopy. Chem Phys 266:149CrossRefGoogle Scholar
  5. 5.
    Iwaki L, Dlott DD (2001) Vibrational energy transfer in condensed phases. In: Moore JH, Spencer ND (eds) Encyclopedia of chemical physics and physical chemistry. IOP Publishing Ltd, Bristol, p 2717Google Scholar
  6. 6.
    Fayer MD (2001a) Fast protein dynamics probed with infrared vibrational echo experiments. Annu Rev Phys Chem 52:315CrossRefGoogle Scholar
  7. 7.
    Fayer MD (2001b) Ultrafast infrared and Raman spectroscopy. Marcel Dekker Inc, New YorkCrossRefGoogle Scholar
  8. 8.
    Cremeens ME, Fujisaki H, Zhang Y, Zimmermann J, Sagle LB, MAtsuda S, Dawson PE, Straub JE, Romesberg FE (2006) Efforts toward developing direct probes of protein dynamics. J Am Chem Soc 128:6028–6029CrossRefGoogle Scholar
  9. 9.
    Shigeto S, Dlott DD (2007) Vibrational relaxation of an amino acid in aqueous solution. Chem Phys Lett 447:134–139CrossRefGoogle Scholar
  10. 10.
    Wang ZH, Carter JA, Lagutchev A, Koh YK, Seong N-H, Cahill DG, Dlott DD (2007) Ultrafast flash thermal conductance of molecular chains. Science 317:787CrossRefGoogle Scholar
  11. 11.
    Shigeto S, Pang Y, Fang Y, Dlott DD (2008) Vibrational relaxation of normal and deuterated liquid nitromethane. J Phys Chem B 112:232–241CrossRefGoogle Scholar
  12. 12.
    Schade M, Moretto A, Crisma M, Toniolo C, Hamm P (2009) Vibrational energy trasnport in pepetide helices after excitation of c-d modes in leu-d 10. J Phys Chem A 113:13393–13397Google Scholar
  13. 13.
    Fang Y, Shigeto S, Seong N, Dlott D (2009) Vibrational energy dynamics of glycine, n-methylacetamide, and benzoate anion in aqueous (d2o) solution. J Phys Chem A 113(1):75–84CrossRefGoogle Scholar
  14. 14.
    Nguyen PH, Stock G (2003) Nonequilibrium molecular-dynamics study of the vibrational energy relaxation of peptides in water. J Chem Phys 119(21):11350–11358CrossRefGoogle Scholar
  15. 15.
    Frauenfelder H, Bishop AR, Garcia A, Perelson A, Schuster P, Sherrington D, Swart PJ (1997) Landscape paradigms in physics and biology: Concepts, structures, and dynamics. North-Holand, AmsterdamGoogle Scholar
  16. 16.
    Frauenfelder H, McMahon BH, Austin RH, Chu K, Groves JT (2001) The role of structure, energy landscape, dynamics, and allostery in the enzymatic function of myoglobin. Proc Natl Acad Sci USA 98:2370–2374CrossRefGoogle Scholar
  17. 17.
    Frauenfelder H, McMahon BH, Fenimore PW (2003) Myoglobin: The hydrogen atom of biology and a paradigm of complexity. Proc Natl Acad Sci 100:8615–8617CrossRefGoogle Scholar
  18. 18.
    Lubchenko V, Wolynes PG, Frauenfelder H (2005) Mosaic energy landscapes of liquids and the control of protein conformational dynamics by glass-forming solvents. J Phys Chem B 109:7488–7499CrossRefGoogle Scholar
  19. 19.
    Moritsugu K, Miyashita O, Kidera A (2000) Vibrational energy transfer in a protein molecule. Phys Rev Lett 85:3970–3973CrossRefGoogle Scholar
  20. 20.
    Roitberg A, Gerber BB, Ratner MA (1997) A vibrational eigenfunction of a protein: Anharmonic coupled-mode ground and fundamental excited states of bpti. J Phys Chem B 101:1700–1706CrossRefGoogle Scholar
  21. 21.
    Hayward S, Kitao A, Go N (1994) Harmonic and anharmonic aspects in the dynamics of bpti: A normal mode analysis and principal component analysis. Protein Sci 3:936–943CrossRefGoogle Scholar
  22. 22.
    Go N, Noguti T, Nishikawa T (1983) Dynamics of a small globular protein in terms of low-frequency vibrational-modes. Proc Natl Acad Sci USA 80:3696CrossRefGoogle Scholar
  23. 23.
    Hayward S, Kitao A, Go N (1995) Harmonicity and anharmonicity in protein dynamics: A normal mode analysis and principal component analysis. Proteins 23:177–186CrossRefGoogle Scholar
  24. 24.
    Ohmine I, Tanaka H (1990) Potential energy surfaces for water dynamics. II. Vibrational mode excitations, mixing and relaxations. J Chem Phys 93:8138–8147CrossRefGoogle Scholar
  25. 25.
    Ohmine I, Tanaka H (1993) Fluctuation, relaxations, and hydration in liquid water. hydrogen-bond rearrangement dynamics. Chem Rev 93:2545–2566CrossRefGoogle Scholar
  26. 26.
    Sagnella DE, Straub JE (1999) A study of vibrational relaxation of b-state carbon monoxide in the heme pocket of photolyzed carboxymyoglobin. Biophys J 77:70–84CrossRefGoogle Scholar
  27. 27.
    Rao F, Karplus M (2010) Protein dynamics investigated by inherent structure analysis. Proc Natl Acad Sci USA 107:9152–9157CrossRefGoogle Scholar
  28. 28.
    Elber R, Karplus M (1987) Multiple conformational states of proteins: A molecular dynamics analysis of myoglobin. Science 235:318CrossRefGoogle Scholar
  29. 29.
    Fujisaki H, Stock G (2008) Dynamic treatment of vibrational energy relaxation in a heterogeneous and fluctuating environment. J Chem Phys 129(13):134110CrossRefGoogle Scholar
  30. 30.
    Levy RM, Perahia D, Karplus M (1982) Molecular-dynamics of an alpha-helical polypeptide-temperature-dependence and deviation from harmonic behavior. Proc Natl Acad Sci USA 79:1346–1350CrossRefGoogle Scholar
  31. 31.
    Karplus M, Kushick J (1981) Method for estimating the configurational entropy of macromolecules. Macromolecules 14:325–332CrossRefGoogle Scholar
  32. 32.
    Levy RM, Karplus M, Kushick J, Perahia D (1984) Evaluation of the configurational entropy for proteins—Application to molecular-dynamics simulations of an alpha-helix. Macromolecules 17:1370–1374CrossRefGoogle Scholar
  33. 33.
    Buchner M, Ladanyi B, Stratt RM (1992) The short-time dynamics of molecular liquids. Instantaneous-normal-mode theory. J Chem Phys 97:8522–8535CrossRefGoogle Scholar
  34. 34.
    Goodyear G, Stratt RM (1997) The short-time intramolecular dynamics of solutes in liquids. 2. Vibrational population relaxation. J Chem Phys 107:3098–3120CrossRefGoogle Scholar
  35. 35.
    Keyes T (1997) Instantaneous normal mode approach to liquid state dynamics. J Phys Chem A 101:2921–2930CrossRefGoogle Scholar
  36. 36.
    David EF, Stratt RM (1998) The anharmonic features of the short-time dynamics of fluids: The time evolution and mixing of instantaneous normal modes. J Chem Phys 109:1375–1390CrossRefGoogle Scholar
  37. 37.
    Stratt RM (2001) The molecular mechanism behind the vibrational population relaxation of small molecules in liquids. In: Fayer MD (eds) Ultrafast infrared and Raman spectroscopy. Marcel Dekker Inc, New York, pp. 149–190Google Scholar
  38. 38.
    Garberoglio G, Vallauri R (2002) Instantaneous normal mode analysis of short-time dynamics in hydrogen-bonded liquids. Physica A 314:492–500CrossRefGoogle Scholar
  39. 39.
    Kramer N, Buchner M, Dorfmuller T (1998) Normal mode dynamics in simple liquids. J Chem Phys 109:1912–1919CrossRefGoogle Scholar
  40. 40.
    Moore PB, Ji XD, Ahlborn H, Space B (1998) An instantaneous normal mode theory of condensed phase absortion: The vibrational spectrum of condensed cs2 from bpiling to freezing. Chem Phys Lett 296:259–265CrossRefGoogle Scholar
  41. 41.
    Ahlborn H, Ji XD, Space B, Moore PB (1999) A combined instantaneous normal mode and time correlation function description of the infrarred vibrational spectrum of ambient water. J Chem Phys 111:10622–10632CrossRefGoogle Scholar
  42. 42.
    Ji XD, Alhborn H, Space B, Moore PB, Zhou Y, Constantine S, Ziegler LD (2000) A combined instantaneous normal mode and time correlation function description of the optical Kerr effect and Raman spectroscopy of liquid cs2. J Chem Phys 112:4186–4192CrossRefGoogle Scholar
  43. 43.
    Perry A, Ahlborn H, Space B, Moore PB (2003) A combined time correlation function and instantaneous normal mode study of the sum frequency generation spectroscopy of the water/vapor interface. J Chem Phys 118:8411–8419CrossRefGoogle Scholar
  44. 44.
    Deng YQ, Ladanyi BM, Stratt RM (2002) High-frequency vibrational energy relaxation in liquids: The foundations of instantaneous-pair theory and some generalizations. J Chem Phys 117:10752–10767CrossRefGoogle Scholar
  45. 45.
    Bu L, Straub JE (2003) Vibrational frequency shifts and relaxation rates for a selected vibrational mode in cytochrome c. Biophys J 85:1429–1439CrossRefGoogle Scholar
  46. 46.
    Fujisaki H, Yagi K, Straub JE, Stock G (2009) Quantum and classical vibrational relaxation dynamics of n-methylacetamide on ab initio potential energy surfaces. Int J Quant Chem 109:2047–2057CrossRefGoogle Scholar
  47. 47.
    Schulz R, Krishnana M, Daidone I, Smith JC (2009) Instantaneous normal modes and the protein glass transition. Biophys J 96:476–484CrossRefGoogle Scholar
  48. 48.
    Bastida A, Soler MA, Zúñiga J, Requena A, Kalstein A, Fernandez-Alberti S (2010) Instantaneous normal modes, resonances and assignments in the vibrational relaxation of the amide i mode of n-methylacetamide-d in aqueous (d2o) solution. J Chem Phys 132:224501CrossRefGoogle Scholar
  49. 49.
    Bastida A, Soler MA, Zúñiga J, Requena A, Fernández-Alberti S, Kalstein A (in press) Molecular dynamics simulations and instantaneous normal mode analysis of the vibrational relaxation of the C–H stretching modes of n-methylacetamide-d in liquid deuterated water. J Phys Chem A (in press)Google Scholar
  50. 50.
    Cho M, Fleming GR, Saito S, Ohmine I, Stratt RM (1994) Instantaneous normal-mode analysis of liquid water. J Chem Phys 100:6672–6683CrossRefGoogle Scholar
  51. 51.
    Ladanyi BM, Klein S (1996) Contributions of rotation and translation to polarizability anisotropy and solvation dynamics in acetonitrile. J Chem Phys 105:1552–1561CrossRefGoogle Scholar
  52. 52.
    Stratt RM, Cho M (1994) The short-time dynamics of solvation. J Chem Phys 100:6700–6708CrossRefGoogle Scholar
  53. 53.
    Kalbfleisch TS, Ziegler LD, Keyes T (1996) An instantaneous normal mode analysis of solvation: Methyl iodide in high pressure gases. J Chem Phys 105:7034–7046CrossRefGoogle Scholar
  54. 54.
    Egorov SA, Stephens MD, Skinner JL (1996) Absorption line shapes and solvation dynamics of ch3i in supercritical ar. J Chem Phys 107:10485–10491CrossRefGoogle Scholar
  55. 55.
    Ladanyi BM, Stratt RM (1995) Short-time dynamics of solvation—Linear solvation theory for polar-solvents. J Phys Chem 99:2502–2511CrossRefGoogle Scholar
  56. 56.
    Ladanyi BM, Stratt RM (1996) Short-time dynamics of solvation: Relationship between polar and nonpolar solvation. J Phys Chem 100:1266–1282CrossRefGoogle Scholar
  57. 57.
    Woutersen S, Mu Y, Stock G, Hamm P (2001) Subpicosecond conformational dynamics of small peptides probed by two-dimensional vibrational spectroscopy. Proc Natl Acad Sci USA 98:11254CrossRefGoogle Scholar
  58. 58.
    Zanni MT, Asplund MC, Hochstrasser RM (2001) Two-dimensional heterodyned and stimulated infrared photon echoes of n-methylacetamide-d. J Chem Phys 114:4579–4590CrossRefGoogle Scholar
  59. 59.
    Woutersen S, Pfister R, Hamm P, Mu Y, Kosov DS, Stock G (2002) Peptide conformational heterogeneity revealed from nonlinear vibrational spectroscopy and molecular-dynamics simualtions. J Chem Phys 117:6833–6840CrossRefGoogle Scholar
  60. 60.
    Rubtsov IV, Wang J, Hochstrasser RM (2003) Vibrational coupling between amide-i and amide-a modes revealed by femtosecond two color infrared spectroscopy. J Phys Chem A 107:3384–3396CrossRefGoogle Scholar
  61. 61.
    DeCamp MF, DeFlores L, McCracken JM, Tokmakoff A, Kwac K, Cho M (2005) Amide i vibrational dynamics of n-methylacetamide in polar solvents: The role of electrostatic interactions. J Phys Chem B 109(21):11016–11026CrossRefGoogle Scholar
  62. 62.
    DeFlores LP, Ganim Z, Ackley SF, Chung HS, Tokmakoff A (2006) The anharmonic vibrational potential and relaxation pathways of the amide I and II modes of n-methylacetamide. J Phys Chem B 110(38):18973–18980CrossRefGoogle Scholar
  63. 63.
    Gregurick SK, Chaban GM, Gerber RB (2002) Ab initio and improved empirical potentials for the calculation of the anharmonic vibrational states and intramolecular mode coupling of n-methylacetamide. J Phys Chem A 106(37):8696–8707CrossRefGoogle Scholar
  64. 64.
    Kwac K, Cho M (2003) Molecualr dynamics simualtion study of n-methylacetamide in water. I. Amide I mode frequency fluctuation. J Chem Phys 119:2247–2255CrossRefGoogle Scholar
  65. 65.
    Schmidt JR, Corcelli SA, Skinner JL (2004) Ultrafast vibrational spectroscopy of water and aqueus n-methylacetamide. Comparison of different electronic structure/molecular dynamics approaches. J Chem Phys 121:8887–8896CrossRefGoogle Scholar
  66. 66.
    Hayashi T, Zhuang W, Mukamel S (2005) Electrostatic DFT map for the complete vibrational amide band of NMA. J Phys Chem A 109:9747–9759CrossRefGoogle Scholar
  67. 67.
    Fujisaki H, Zhang Y, Straub JE (2006) Time-dependent perturbation theory for vibrational energy relaxation and dephasing in peptides and proteins. J Chem Phys 124(14):144910CrossRefGoogle Scholar
  68. 68.
    Fujisaki H, Yagi K, Hirao K, Straub JE (2007) Quantum dynamics of n-methylacetamide studied by the vibrational configuration interaction method. Chem Phys Lett 443:6–11CrossRefGoogle Scholar
  69. 69.
    Goodyear G, Stratt RM (1996) The short time intramolecular dynamics of solutes in liquids. I. An instantaneous normal mode theory for friction. J Chem Phys 105:10050–10071CrossRefGoogle Scholar
  70. 70.
    Ladanyi BM, Stratt RM (1998) The short-time dynamics of vibrational relaxation in molecular liquids. J Phys Chem A 102:1068–1082CrossRefGoogle Scholar
  71. 71.
    Carpaneto G, Martello S, Toth P (1988) Algorithms and codes for the assigment problem. Ann Oper Res 13:193–223CrossRefGoogle Scholar
  72. 72.
    Nakamura M, Tamura K, Murakami S (1995) Isotope effects on thermodynamic properties: Mixtures of x(d2o or h2o) + (1 − x)ch3cn at 298.15 k. Thermochim Acta 253:127–136CrossRefGoogle Scholar
  73. 73.
    Cornell WD, Cieplak P, Bayly CI, Gould IR, Merz KM Jr, Ferguson DM, Spellmeyer DC, Fox T, Caldwell JW, Kollman PA (1995) A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J Am Chem Soc 117:5179–5197CrossRefGoogle Scholar
  74. 74.
    MacKerell AD Jr, Bashford D, Bellott M, Dunbrack RL Jr, Evanseck JD, Field MJ, Fischer S, Gao J, Guo H, Ha S, Joseph-McCarthy D, Kuchnir L, Kuczera K, Lau FTK, Mattos C, Michnick S, Ngo T, Nguyen DT, Prodhom B, Reiher WE III, Roux B, Schlenkrich M, Smith JC, Stote R, Straub J, Watanabe M, Wiórkiewicz-Kuczera J, Yin D, Karplus M (1998) All-atom empirical potential for molecular modeling and dynamics studies of proteins. J Phys Chem B 102(18):3586–3616CrossRefGoogle Scholar
  75. 75.
    Pappu RV, Hart RK, Ponder JW (1998) Analysis and application of potential energy smoothing and search methods for global optimization. J Phys Chem B 102:9725–9742CrossRefGoogle Scholar
  76. 76.
    Allen MP, Tildesley DJ (1987) Computer simulation of liquids. Oxford Science Publications, OxfordGoogle Scholar
  77. 77.
    Svanberg M (1997) An improved leap-frog rotational algorithm. Mol Phys 92:1085Google Scholar
  78. 78.
    Rey-Lafon M, Forel MT, Garrigou-Lagrange C (1973) Discussion des modes normaux des groupements amides cis et trans partir des champs de force du δ-valrolactame et du n-methylacetamide. Spectr Acta 29A:471–486CrossRefGoogle Scholar
  79. 79.
    Ataka S, Takeuchi H, Tasumi M (1984) Infrared studies of the less stable cis form of n-methylformamide and n-methylacetamide in low-temperature nitrogen matrices and vibrational analyses of the trans and cis forms of these molecules. J Mol Struct 113:147–160CrossRefGoogle Scholar
  80. 80.
    Berendsen HJC, Postma JPM, van Gunsteren WF, DiNola A, Haak JR (1984) Molecular-dynamics with coupling to an external bath. J Chem Phys 81:3684CrossRefGoogle Scholar
  81. 81.
    Raff LM (1988) Projection methods for obtaining intramolecular energy-transfer rates from classical trajectory results—Application to 1,2-difluoroethane. J Chem Phys 89(9):5680–5691CrossRefGoogle Scholar
  82. 82.
    Kabadi VN, Rice BM (2004) Molecular dynamics simualtions of normal mode vibrational energy transfer in liquid nitromethane. J Phys Chem A 108:532–540CrossRefGoogle Scholar
  83. 83.
    Bell RJ, Dean P, Hibbins-Butler C (1970) localization of normal modes in vitreous silica, germania and beryllium fluoride. J Phys C: Solid St Phys 3:2111–2118CrossRefGoogle Scholar
  84. 84.
    Taraskin SN, Elliott SR (1999) Anharmonicity and localization of atomic vibrations in vitreous silica. Phys Rev B 59:8572–8585CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Adrián Kalstein
    • 1
  • Sebastián Fernández-Alberti
    • 1
  • Adolfo Bastida
    • 2
  • Miguel Angel Soler
    • 2
  • Marwa H. Farag
    • 2
  • José Zúñiga
    • 2
  • Alberto Requena
    • 2
  1. 1.Universidad Nacional de QuilmesBernalArgentine
  2. 2.Departamento de Química FísicaUniversidad de MurciaMurciaSpain

Personalised recommendations