ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Netrebko A. V., Netrebko N. V., Romanovsky Y. M., Hurgin J. I., Shidlovskaja E. G. Complicated modulations regimes and stochastic vibrations in cluster dynamic models of macromolecules. Izvestiya VUZ. Applied Nonlinear Dynamics, 1994, vol. 2, iss. 3, pp. 26-43. DOI: 10.18500/0869-6632-1994-2-3-26-43

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon 1994no3-4p026.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
539.194
DOI: 
10.18500/0869-6632-1994-2-3-26-43

Complicated modulations regimes and stochastic vibrations in cluster dynamic models of macromolecules

Autors: 
Netrebko Aleksej Vasilevich, Lomonosov Moscow State University
Netrebko Nina Vladimirovna, Lomonosov Moscow State University
Romanovsky Yuri Mihajlovich, Lomonosov Moscow State University
Hurgin Jurij Isaakovich, Lomonosov Moscow State University
Shidlovskaja Ekaterina Gennadevna, Lomonosov Moscow State University
Abstract: 

The possibility of realization of «marked» degrees of freedom when the system motion occurs in narrow area of coordinate plane was considered within the framework of a simplest cluster model of an enzyme molecule. Under certain conditions the motion of the system becomes complex and perhaps stochastic and the spectrum of oscillations becomes more rich. The role of the interaction potential curve shapes of the system is discussed. It was shown that energy transfer associated with complicated modulations in a two-dimensional system takes place even for small oscillations with amplitudes approximately equal to 0.1 A°.

Key words: 
-
Acknowledgments: 
The authors express their deep gratitude to Professor W. Ebeling of the Humboldt University (Berlin) for useful discussions and valuable comments.
Reference: 
  1. Karplus М. Dynamics of Proteins. Ber. Bunsenges. Phys. Chem. 1982;86:386-395. DOI: 10.1002/bbpc.19820860511.
  2. Chernavskii DS, Khurgin YuI, Shnol SE. About elastic deformations of protein - enzyme. Mol. Biol. 1967;1(3):419-424.
  3. Chernavskii DS, Khurgin YuI, Shnol SE. The concept of “protein-machine” and ee consequences. Mol. Biophys. 1987;20(5):1356.
  4. Romanovsky YuM, Chikishev AYu, Khurgin Yul. Subglobular Motion and Proton Transfer Model in the a-Chymotrypsin Molecule. J. Mol. Catalysis. 1988;47(2-3):235-240. DOI: 10.1016/0304-5102(88)85047-8.
  5. Romanovskii YuМ, Khurgin YuI, Chikishev АYu, Tereshko VМ. Use of a cluster model of proteins to analyse the attenuation of small oscillations induced by EHF irradiation. In: Devyatkov ND, Betskii OV, editors. Millimetre Waves in Medicine. M.: Institute of Radio Electronics AS USSR; 1991. P. 400.
  6. Romanovskii YuМ, Khurgin YuI, Chikishev АYu, Tereshko VМ. Cluster dynamics of protein and its relationship with functional activity. In: Lopushanskii AI, editor. Thermodynamics of irreversible processes. М.: Nauka; 1992. P. 177.
  7. Netrebko NV, Romanovsky YuМ, Shidlovskaya EG, Tereshko VM. Damping in the models for molecular dynamics. SPIE. Laser Applications in Life Sciences. 1990. Vol. 1403. P. 512. DOI:  10.1117/12.57394.
  8. Chikishev AYu, Khurgin Yul, Romanovsky YuM, Shidlovskaya EG. Cluster model of protein molecule. In: SPIE. 1990. Vol. 1403. Laser Applications in Life Sciences. P. 517. DOI: 10.1117/12.57397.
  9. Fersht A. Enzyme structure and mechanism. Reading: WH Freeman; 1977. 371 p.
  10. Romanovskii YuМ, Tikhomirova NК, Khurgin YuI. Electromechanical model of the Enzyme-substract complex. Biophys. 1979;24(3):442-447.
  11. Ebeling W, Romanovsky YuM. Energie Transfer and Chaotic Oscillations in Enzyme Catalysis. Z. Phys. Chem. Leipzig 1985;266(1):836-843. DOI: 10.1515/zpch-1985-266103.
  12. Welch GR, Somogyi B, Damjanovich S. The Role of Protein Fluctuation in Enzyme Action: A Review. Prog. Biophys. Mol. Biol. 1982;39:109-146. DOI: 10.1016/0079-6107(83)90015-9.
  13. Havsteen В. A New Principle of Enzyme Catalysis: Coupled Vibrations Facilitate Conformational Changes. J. Theor. Biol. 1989;140(1):101-127. DOI: 10.1016/S0022-5193(89)80032-3.
  14. Havsteen В. A stochastic attractor participates in chymotrypsin catalysis. A new facet of enzyme catalysis. J. Theor. Biol. 1991;151(4):557-571. DOI:  10.1016/S0022-5193(05)80370-4.
  15. Khurgin YuI. Hydration of globular proteins. Rus. J. Gen. Chem. 1976;6:619.
  16. Rubin. АB. Biophysics. Vol. I. M.: Vysshaya Shkola; 1987. 319 p.
  17. Chernavskaya NМ, Chernavskii DS. Tunnelling Electron Transport in Photosynthesis. M.: Moscow Uni8versity Press; 1977. 175 p.
  18. Davydov АS. Solitons in molecular systems. Kiev: Naukova dumka; 1984. 288 p.
  19. Ebeling W, Jenssen M, Romanovskii YuM. 100 Years Arrhenius Low and Recent Developments in Reaction Theory. In: Ebeling W, Ulbricht H, editors. Irreversible Processes and Selforganization. Vol. 23. Leipzig: Teubner-Texte zur Physik;1989. P. 7-24.
  20. Ebeling W, Jensen М. Soliton dynamics and energy trapping in enzyme catalysis. Z. Phys. Chem. 1988;2690(1):1-7. DOI: 10.1515/zpch-1988-26903.
  21. Gotlib YuYa, Darinskii АА, Svetlov YuЕ. Physical Kinetics of Macromolecules. Leningrad: Khimiya; 1986. 271 p.
  22. Avbelj F, Moult J. et al. Molecular Dynamics Study of the Structure and Dynamics of a Protein Molecular in a Crystalline Tonic Environment, Streptomyces griseus Protease A. Biochemistry. 1990;29(37):8658-8676. DOI: 10.1021/bi00489a023.
  23. Conrad M. Unstable Electron Pairing and the Energy Loan Model of Enzyme Catalysis. J. Theor. Biol. 1979;79(2):137-156. DOI: 10.1016/0022-5193(79)90243-1.
  24. Dashevskii VG. Conformational Analysis of Macromolecules. М.: Nauka; 1987. 272 p.
  25. Polozov RV. Semi-Empirical Force Field Method in Conformational Analysis of Biopolymers. М.: Nauka; 1981. 119 p.
  26. Birktoft JJ, Blow DM. Structure of crystalline -chymotrypsin. V. The atomic structure of tosyl- -chymotrypsin at 2 A resolution.. J. Mol. Biol. 1972;68(2):187-240. DOI: 10.1016/0022-2836(72)90210-0.
  27. Tsukada H, Blow D. Structure of a — Chymotrypsin Refined at 1-68 А Resolution. J. Mol. Biol. 1985;184(4):703-711. DOI: 10.1016/0022-2836(85)90314-6.
  28. Brown H, Eifus S, Small E, Peticolas WL. Conformationally Dependent Low-Frequency Motion of Proteins by Laser RAMAN-spectroscopy. PNAS USA. 1972;69(6):1467-1469. DOI: 10.1073/pnas.69.6.1467.
  29. Volkenshtein МV. Biophysics. М.: Nauka; 1988. 590 p.
  30. Blumenfeld LA. Physics of Bioenergetic Рrоcesses. Berlin: Springer; 1983. 132 p. DOI: 10.1007/978-3-642-68525-5.
  31. Schimansky—Geier L, Zulicke Ch. Harmonic noise: Effect on bistable systems. Z. Phys. В.: Condensed Matter. 1990;79:451-460. DOI:  10.1007/bf01437657.
  32. Neimark YuI, Landa PS. Stochastic and Chaotic Osciliations. Dordrecht: Springer; 1992. 500 p. DOI: 10.1007/978-94-011-2596-3.
  33. Pippard АB. The Physics of Vibration. Cambridge: Cambridge University Press; 1989. 656 p.
  34. Stratonovich RL, Polyakova МS. Elements of Molecular Physics, Thermodynamics and Statistical Physics. М.: Moscow University Press; 1981. 176 p.
Received: 
16.02.1994
Accepted: 
01.04.1994
Published: 
24.11.1994
  • 1929 reads