Electrosoliton dynamics in a thermalized molecular chain
https://doi.org/10.32362/2500-316X-2020-8-1-43-57
Abstract
The possibility of the electrosoliton formation in α-helical proteins which represents a localized state of an extra electron bound with the deformation region of the α-helix arising due to the electron interaction with chain of peptide groups is investigated in a quasiclassical approximation. Two possible mechanisms of the formation of collective dynamic modes in the form of Fröhlich collective mode and Davydov soliton were previously suggested by the authors. In this paper, we developed a unified quantum-mechanics approach to describe conditions of the formation of the Fröhlich vibronic state and Davydov soliton in α-helical protein molecules interacting with the environment. The concept of "soliton" is used not only in the strict mathematical sense, i.e. in the case of completely integrable Hamiltonian systems, but also to describe dynamically stable, nonlinear collective structures. Davydov solitons are stable due to a small probability of the dissipation of its energy into thermal energy which provides a high efficiency of soliton transport of energy, charges, and conformation changes in biosystems at a physiological temperature of 310 K.
Electrosolitons can be formed if the value of electron–phonon interaction (EPI) parameter exceeds a certain threshold. One of the most important characteristics of the electrosoliton’s state is the coupling energy of a quasi-particle (exciton or electron) with molecular chain deformation, which also determines the soliton stability. Dynamic equations describing the motion of a one-dimensional electrosoliton in the continuum approximation are a self-consistent system which includes the time-dependent Schrödinger equation with a deformation potential and an inhomogeneous linear wave equation for this potential. This system, known as the Zakharov system, has significance in physics and, generally, describes the nonlinear interaction of two physical subsystems: fast and slow. Zakharov equations have a well-known soliton solution in the hyperbolic secant form, describing the envelope profile of the high-frequency vibrations of a fast subsystem, which can propagate with any subsonic velocity. The suggested mechanism of emergent of macroscopic dissipative structures in the form of electrosolitons in α-helical proteins is discussed in connection with recent experimental data on long-lived collective protein excitation in the terahertz frequency region.
About the Authors
V. N. Kadantsev
MIREA – Russian Technological University
Russian Federation
Russian Federation
Vasiliy N. Kadantsev – Dr. Sci. (Physics and Mathematics), Professor of the Department of Biocybernetic Systems and Technologies, Institute of Cybernetics
78, Vernadskogo pr., Moscow 119454
A. N. Goltsov
School of Applied Sciences, Abertay University
United Kingdom
United Kingdom
Alexey N. Goltsov – Dr. Sci. (Physics and Mathematics), Lecturer. Scopus Author ID: 56234051200
Dundee
M. A. Kondakov
MIREA – Russian Technological University
Russian Federation
Russian Federation
Mikhail A. Kondakov – Postgraduate Student of the Department of Biocybernetics Systems and Technologies in the Institute of Cybernetics
78, Vernadskogo pr., Moscow 119454
References
1. Vol՚kenshtein M.V. Biofizika (Biophysics). St. Petersburg: Lan՚; 2008. 608 p. (in Russ.). ISBN 978-5-8114-0851-1
2. Serdyuk I., Zakkai N., Zakkai Dzh. Metody v molekulyarnoi biofizike: struktura, funktsiya, dinamika: uchebnoe posobie: v 2-kh t. (Methods in molecular biophysics: structure, function, dynamics: a training manual: in 2 v.). T. 1. Moscow: KDU; 2009. 568 p. (in Russ.). ISBN 978-5-98227-453-3.
3. Szent-Gyorgyi A. Bioenergetics. New York: Acad. Press; 1957. 143 p.
4. Jordan P. Über die physikalische Structure organischer Riesenmoleküule. Naturwissenschaften. 1938;26(42):693-694. https://doi.org/10.1007/BF01606595
5. Atanasov B.P., Postnikova G.B., Sadykov Yu.Kh., Vol'kenshtein M.V. An investigation of electron transport in hemoproteins. Molekulyarnaya biologiya = Molecular biology. 1977;11(3):537-544 (in Russ.)
6. Hoi W.G.J., Van Duijnen P.T., Berendsen H.J.C. The alpha-helix dipoles and the properties of proteins. Nature. 1978;273:443-446. https://doi.org/10.1038/273443a0
7. Ukrainskii I.I., Mironov S.I. O prirode zony provodimosti v peptidnykh tsepyakh (On the nature of the conduction band in peptide chains). Preprint AN USSR. ITF-78-6Ip. Kiev: ITF; 1978. 18 р. (in Russ.)
8. Takano Т., Swanson R., Kallai О.В., Dickerson R.E. Conformational changes upon reduction of cytochrome с. Cold Spring Harbor Symp. Quant. Biol. 1972;36:397-404. https://doi.org/10.1101/SQB.1972.036.01.051
9. Takeno S. Vibron solitons in one-dimensional molecular crystals. Prog. Theor. Phys. 1984;71(2):395-398. https://doi.org/10.1143/PTP.71.395
10. Frohlich H. On the theory of superconductivity: the one-dimensional cases. Proc. Roy. Soс. 1954;223(1154):296-305. https://doi.org/10.1098/rspa.1954.0116
11. Frohlich H. Electron in lattice fields. Advance in Phys. 1954;3(11):325-361. https://doi.org/10.1080/00018735400101213
12. Davydov A.S. Influence of electron-phonon interaction on the motion of an electron in a one-dimensional molecular system. Theor. Math. Phys. 1979;40(3): 831-840. https://doi.org/10.1007/BF01032070
13. Turner I.E., Anderson Y.E., Pox K. Energy eigenvalues and eigen-functions for an electron in an electric-dipole field. Phys. Rev. 1968;174(1):81-89. https://doi.org/10.1103/PhysRev.174.81
14. Davydov A.S. Kvantovaya teoriya dvizheniya kvazichastitsy v molekulyarnoi tsepi s uchetom teplovykh kolebanii (A quantum theory of the motion of a quasiparticle in a molecular chain, taking into account thermal vibrations). Kiev: ITF; 1985. 37 р. (in Russ.).
15. Lupichev L.N., Savin A.V., Kadantsev V.N. Sinergetika molekulyarnykh sistem. Dinamicheskie svoistva dispersionnykh struktur (Synergetics of molecular systems. Dynamic properties of dispersion structures). LAMBERT Academic Publishing; 2012. 396 р. (in Russ.). ISBN-13978-3-659-22114-9.
16. Lupichev L.N., Savin A.V., Kadantsev V.N. Synergetics of Molecular Systems. Springer Series in Synergetics. Springer International Publishing; 2015. 332 p. ISBN 978-3-319-08194-6. https://doi.org/10.1007/978-3-319-08195-3
17. Kadantsev V.N., Kondakov М.А. Collective excitations in α-helix protein molecule interacting with environment. International Forum on Chemical, Biological, Agricultural, Pharmacy and Health Sciences: Conference Proceedings, May 31th, 2017, Madrid, Spain: Scientific public organization «Professional science»; 2017. Р. 164
18. Kadantsev V.N., Goltsov A.N. Collective excitations in alpha-helical protein molecule. Rossiiskii tekhnologicheskii zhurnal = Russian Technological Journal. 2018;6(2):32-45 (in Russ.). https://doi.org/10.32362/2500316X-2018-6-2-32-45
19. Kadantsev V.N., Goltsov A. Collective excitations in alpha-helical protein structures interacting with environment. BioRxiv. 2019. https://doi.org/10.1101/457580
20. Landau L.D., Lifshits E.M. Kvantovaya mekhanika (Quantum mechanics). Moscow: Fizmatgiz; 1963. 702 p. (in Russ.).
21. Landau L.D., Pekar S.I. The effective mass of the polaron. Zhurnal ehksperimental'noi i teoreticheskoi fiziki = Journal of Experimental and Theoretical Physics. 1948;18:419. (in Russ.).
22. Davydov A.S. Solitons in molecular systems. Kiev: Naukova dumka; 1984. 288 p. (in Russ.).
23. Pettit R.M., Ge W., Kumar P., Luntz-Martin D.R., Schultz J.T., Neukirch L.P., Bhattacharya M., Vamivakas A.N. An optical tweezer phonon laser. Nat. Photonics. 2019;13(6):402-405 https://doi.org/10.1038/s41566-019-0395-5
24. Romero-Isart O., Pflanzer A.C., Blaser F., Kaltenbaek R., Kiesel N., Aspelmeyer M., Cirac J.I. Large quantum superpositions and interference of massive nanometer-sized objects. Phys. Lett. 2011;107(2):Article No. 020405. https://doi.org/10.1103/PhysRevLett.107.020405
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1. Fig. 2. Calculation results of the capture of an excess electron placed at the initial moment of time on the first molecule of the chain by an acoustic soliton with energy E = 0.49 eV. At the initial moment of time, the soliton is excited by the displacem | |
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Kadantsev V.N., Goltsov A.N., Kondakov M.A. Electrosoliton dynamics in a thermalized molecular chain. Russian Technological Journal. 2020;8(1):43-57. (In Russ.) https://doi.org/10.32362/2500-316X-2020-8-1-43-57
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