Low-frequency collective motion in proteins and DNA

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Low-frequency collective motion in proteins and DNA refers to the application of statistical thermodynamics to understand low-frequency vibrations in biomolecules.[1]

The concept was first proposed by Professors Kuo-Chen Chou (周国城) and Nian-Yi Chen (陈念贻) in studying the binding interaction between proteins such as insulin and insulin receptor.[2] It was noted by them that enumerating the known explanations for the free energy change, such as translational and rotational entropy, hydrogen bonds, van der Waals interactions, and hydrophobic interactions, did not fully account for the observed free energy change for the reaction. It was inferred that the deficit could be explained by the creation of extra vibrational modes with very low wave numbers in the range of 10–100 cm−1, corresponding to the range of terahertz frequency (3×1011 to 3×1012 Hz).[2][3][4]

Subsequently, the aforementioned low-frequency modes have been indeed observed by Raman spectroscopy for a number of protein molecules[5][6] and different types of DNA.[7][8][9] These observed results have also been further confirmed by neutron scattering experiments.[10][11][12][13]

Experimental results[edit]

The beta-barrel protein GFP has been shown by coherent neutron scattering to undergo collective motions of the secondary structural units at ~1 THz.[11] These motions are thought to be sensitive to local rigidity within proteins, revealing beta structures to be generically more rigid than alpha or disordered proteins.[12][13]

Quasi-continuum model[edit]

The quasi-continuum model is one model developed to identify and analyze this kind of low-frequency motions in protein and DNA molecules. This model operates on an intermediate level of complexity between the elastic global model, which treats the biomolecule as a continuous elastic sphere, and atomistic normal mode methods.[14] It treats the biomolecule's backbone as a continuous mass distribution, with discrete interactions representing hydrogen bonds modeling the effects of internal conformation. This has the advantage of being simpler than explicit-atom methods, and providing a much more intuitive physical picture of the dynamics involved.[4]

It has been successfully used to simulate various low-frequency collective motions in protein and DNA molecules, such as accordion-like motion, pulsation or breathing motion, as reflected by the fact that the low-frequency wave numbers thus derived were quite close to the experimental observations.[15][16][17][18]

Application to biological functions and medical treatments[edit]

Many biological functions and their profound dynamic mechanisms can be revealed through the low-frequency collective motion or resonance in protein and DNA molecules, such as cooperative effects,[19][20] allosteric transition,[21] and intercalation of drugs into DNA.[22] In this regard, some phenomenological theories[23] were established. Meanwhile, the solitary wave motion was also used to address the internal motion during microtubule growth.[24] The relationship between solitons—a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it travels at constant speed—and the low-frequency phonons in proteins have been discussed in a recent paper.[25]

This kind of low-frequency collective motion has also been observed in calmodulin by NMR,[26] and applied in medical treatments.[27]


  1. ^ Chou KC (1988). "Low-frequency collective motion in biomacromolecules and its biological functions". (secondary). Biophysical Chemistry. 30 (1): 3–48. doi:10.1016/0301-4622(88)85002-6. PMID 3046672.; Chou KC (March 1994). "Errata" (PDF). Biophysical Chemistry. 49 (2): 183. doi:10.1016/0301-4622(94)85002-X.
  2. ^ a b Chou KC, Chen NY (1977). "The biological functions of low-frequency phonons". (primary). Scientia Sinica. 20 (4): 447–457.
  3. ^ Chothia C, Janin J (Aug 1975). "Principles of protein-protein recognition". (primary). Nature. 256 (5520): 705–8. Bibcode:1975Natur.256..705C. doi:10.1038/256705a0. PMID 1153006.
  4. ^ a b Sinkala Z (Aug 2006). "Soliton/exciton transport in proteins". (primary). Journal of Theoretical Biology. 241 (4): 919–27. CiteSeerX doi:10.1016/j.jtbi.2006.01.028. PMID 16516929.
  5. ^ Painter PC, Mosher LE, Rhoads C (Jul 1982). "Low-frequency modes in the Raman spectra of proteins". (primary). Biopolymers. 21 (7): 1469–72. doi:10.1002/bip.360210715. PMID 7115900.
  6. ^ Turton, David A.; Senn, Hans Martin; Harwood, Thomas; Lapthorn, Adrian J.; Ellis, Elizabeth M.; Wynne, Klaas (2014-06-03). "Terahertz underdamped vibrational motion governs protein-ligand binding in solution" (PDF). Nature Communications. 5: ncomms4999. Bibcode:2014NatCo...5E3999T. doi:10.1038/ncomms4999. PMID 24893252.
  7. ^ Painter PC, Mosher LE, Rhoads C (1981). "Low-frequency modes in the Raman spectrum of DNA". (primary). Biopolymers. 20: 243–247. doi:10.1002/bip.1981.360200119.
  8. ^ Urabe H, Tominaga Y (Dec 1982). "Low-lying collective modes of DNA double helix by Raman spectroscopy". (primary). Biopolymers. 21 (12): 2477–81. doi:10.1002/bip.360211212. PMID 7150706.
  9. ^ González-Jiménez, Mario; Ramakrishnan, Gopakumar; Harwood, Thomas; Lapthorn, Adrian J.; Kelly, Sharon M.; Ellis, Elizabeth M.; Wynne, Klaas (2016-06-01). "Observation of coherent delocalized phonon-like modes in DNA under physiological conditions". Nature Communications. 7: ncomms11799. Bibcode:2016NatCo...711799G. doi:10.1038/ncomms11799. PMC 4895446.
  10. ^ Martel P (1992). "Biophysical aspects of neutron scattering from vibrational modes of proteins". (secondary). Progress in Biophysics and Molecular Biology. 57 (3): 129–79. doi:10.1016/0079-6107(92)90023-Y. PMID 1603938.
  11. ^ a b Nickels JD, Perticaroli S, O'Neill H, Zhang Q, Ehlers G, Sokolov AP (Nov 2013). "Coherent neutron scattering and collective dynamics in the protein, GFP". (primary). Biophysical Journal. 105 (9): 2182–7. Bibcode:2013BpJ...105.2182N. doi:10.1016/j.bpj.2013.09.029. PMC 3824694. PMID 24209864.
  12. ^ a b Perticaroli S, Nickels JD, Ehlers G, O'Neill H, Zhang Q, Sokolov AP (Oct 2013). "Secondary structure and rigidity in model proteins". (primary). Soft Matter. 9 (40): 9548–56. Bibcode:2013SMat....9.9548P. doi:10.1039/C3SM50807B. PMID 26029761.
  13. ^ a b Perticaroli S, Nickels JD, Ehlers G, Sokolov AP (Jun 2014). "Rigidity, secondary structure, and the universality of the boson peak in proteins". (primary). Biophysical Journal. 106 (12): 2667–74. Bibcode:2014BpJ...106.2667P. doi:10.1016/j.bpj.2014.05.009. PMC 4070067. PMID 24940784.
  14. ^ Thirumuruganandham S, Urbassek H (2009). "Low-frequency vibrational modes and infrared absorbance of red, blue and green opsin". (primary). Journal of Molecular Modeling. 15 (12): 1545. doi:10.1007/s00894-009-0577-z.
  15. ^ Chou KC (Dec 1983). "Identification of low-frequency modes in protein molecules". (primary). The Biochemical Journal. 215 (3): 465–9. doi:10.1042/bj2150465. PMC 1152424. PMID 6362659.
  16. ^ Chou KC (Jul 1984). "Low-frequency vibrations of DNA molecules". (primary). The Biochemical Journal. 221 (1): 27–31. doi:10.1042/bj2210027. PMC 1143999. PMID 6466317.
  17. ^ Chou KC (Aug 1985). "Low-frequency motions in protein molecules. Beta-sheet and beta-barrel". (primary). Biophysical Journal. 48 (2): 289–97. Bibcode:1985BpJ....48..289C. doi:10.1016/S0006-3495(85)83782-6. PMC 1329320. PMID 4052563.
  18. ^ Chou KC, Maggiora GM, Mao B (Aug 1989). "Quasi-continuum models of twist-like and accordion-like low-frequency motions in DNA". (primary). Biophysical Journal. 56 (2): 295–305. Bibcode:1989BpJ....56..295C. doi:10.1016/S0006-3495(89)82676-1. PMC 1280479. PMID 2775828.
  19. ^ Chou KC, Chen NY, Forsen S (1981). "The biological functions of lowfrequency phonons: 2. Cooperative effects". (primary). Chemica Scripta. 18: 126–132.
  20. ^ Chou KC (Jun 1989). "Low-frequency resonance and cooperativity of hemoglobin". (primary). Trends in Biochemical Sciences. 14 (6): 212–3. doi:10.1016/0968-0004(89)90026-1. PMID 2763333.
  21. ^ Chou KC (Aug 1984). "The biological functions of low-frequency vibrations (phonons). 4. Resonance effects and allosteric transition". (primary). Biophysical Chemistry. 20 (1–2): 61–71. doi:10.1016/0301-4622(84)80005-8. PMID 6487745.
  22. ^ Chou KC, Mao B (Nov 1988). "Collective motion in DNA and its role in drug intercalation". (primary). Biopolymers. 27 (11): 1795–815. doi:10.1002/bip.360271109. PMID 3233332.
  23. ^ Chou KC, Kiang YS (Aug 1985). "The biological functions of low-frequency vibrations (phonons) 5. A phenomenological theory". (primary). Biophysical Chemistry. 22 (3): 219–35. doi:10.1016/0301-4622(85)80045-4. PMID 4052576.
  24. ^ Chou KC, Zhang CT, Maggiora GM (Jan 1994). "Solitary wave dynamics as a mechanism for explaining the internal motion during microtubule growth". (primary). Biopolymers. 34 (1): 143–53. doi:10.1002/bip.360340114. PMID 8110966.
  25. ^ Sinkala Z (Aug 2006). "Soliton/exciton transport in proteins". (primary). Journal of Theoretical Biology. 241 (4): 919–27. CiteSeerX doi:10.1016/j.jtbi.2006.01.028. PMID 16516929.
  26. ^ Chou JJ, Li S, Klee CB, Bax A (Nov 2001). "Solution structure of Ca(2+)-calmodulin reveals flexible hand-like properties of its domains". (primary). Nature Structural Biology. 8 (11): 990–7. doi:10.1038/nsb1101-990. PMID 11685248.
  27. ^ Gordon GA (Sep 2007). "Designed electromagnetic pulsed therapy: clinical applications". (secondary). Journal of Cellular Physiology. 212 (3): 579–82. doi:10.1002/jcp.21025. PMID 17577213.