КОЛЛЕКТИВНЫЕ ВОЗБУЖДЕНИЯ В АЛЬФА-СПИРАЛЬНОЙ МОЛЕКУЛЕ БЕЛКА

Translated title of the contribution: Collective excitations in alpha-helical protein molecule

V. N. Kadantsev, A. N. Goltsov

    Research output: Contribution to journalArticle

    Abstract

    Continuous energy supply, a necessary condition for life, excites a state far from thermodynamic equilibrium, in particular coherent electric polar vibrations depending on water ordering in the cell. The collective, low-frequency vibrational excitations in protein macromolecules in the terahertz frequency region are suggested to orchestrate many protein processes such as
    enzymatic activity, electron/energy transport, conformation transitions and others. The most significant type of excitations is long-lived coherent vibronic modes and waves which are either spreading over large protein subdomains or being localised states. Two possible mechanisms of the formation of collective dynamic modes in the form of Fröhlich collective mode and Davydov soliton were previously suggested. We developed a unified quantum-mechanics approach to describe conditions of the formation of Fröhlich vibronic state and Davidov soliton in alphahelical protein molecules interacting with the environment. We distinguish three subsystems in the model, i.e., (i) oscillating peptide groups (PGs), interacting with (ii) the subsystem of side residuals of proteins, which in turn interacts with the environment (surrounding water), which is responsible for dissipation and fluctuation processes and modelled by a system of harmonic oscillators. It was shown that the equation of motion for dynamic variables of PG chain (phonon variables) can be transformed to the nonlinear Schrodinger equation for order parameters, which determines energy “pumping” due to protein interaction with a reservoir. Solution of the order parameter equation was shown to admit bifurcation into the solution corresponding to the formation of weak damped collective vibronic mode with growing amplitude. It was also shown that the solution corresponding to Davydov soliton can exist at certain boundary conditions in this bifurcation region.
    The suggested mechanism of emergent of macroscopic dissipative structures in the form of collective vibronic modes in proteins is discussed in connection with recent experimental data on long-lived collective protein excitation in the terahertz frequency region.
    Original languageRussian
    Pages (from-to)32-45
    Number of pages14
    JournalRussian Technological Journal
    Volume6
    Issue number2
    Publication statusPublished - 2018

    Fingerprint

    proteins
    excitation
    molecules
    solitary waves
    peptides
    thermodynamic equilibrium
    macromolecules
    harmonic oscillators
    water
    nonlinear equations
    quantum mechanics
    equations of motion
    pumping
    dissipation
    electron energy
    boundary conditions
    low frequencies
    vibration
    energy
    cells

    Cite this

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    title = "КОЛЛЕКТИВНЫЕ ВОЗБУЖДЕНИЯ В АЛЬФА-СПИРАЛЬНОЙ МОЛЕКУЛЕ БЕЛКА",
    abstract = "Continuous energy supply, a necessary condition for life, excites a state far from thermodynamic equilibrium, in particular coherent electric polar vibrations depending on water ordering in the cell. The collective, low-frequency vibrational excitations in protein macromolecules in the terahertz frequency region are suggested to orchestrate many protein processes such asenzymatic activity, electron/energy transport, conformation transitions and others. The most significant type of excitations is long-lived coherent vibronic modes and waves which are either spreading over large protein subdomains or being localised states. Two possible mechanisms of the formation of collective dynamic modes in the form of Fr{\"o}hlich collective mode and Davydov soliton were previously suggested. We developed a unified quantum-mechanics approach to describe conditions of the formation of Fr{\"o}hlich vibronic state and Davidov soliton in alphahelical protein molecules interacting with the environment. We distinguish three subsystems in the model, i.e., (i) oscillating peptide groups (PGs), interacting with (ii) the subsystem of side residuals of proteins, which in turn interacts with the environment (surrounding water), which is responsible for dissipation and fluctuation processes and modelled by a system of harmonic oscillators. It was shown that the equation of motion for dynamic variables of PG chain (phonon variables) can be transformed to the nonlinear Schrodinger equation for order parameters, which determines energy “pumping” due to protein interaction with a reservoir. Solution of the order parameter equation was shown to admit bifurcation into the solution corresponding to the formation of weak damped collective vibronic mode with growing amplitude. It was also shown that the solution corresponding to Davydov soliton can exist at certain boundary conditions in this bifurcation region. The suggested mechanism of emergent of macroscopic dissipative structures in the form of collective vibronic modes in proteins is discussed in connection with recent experimental data on long-lived collective protein excitation in the terahertz frequency region.",
    author = "Kadantsev, {V. N.} and Goltsov, {A. N.}",
    year = "2018",
    language = "Russian",
    volume = "6",
    pages = "32--45",
    journal = "Russian Technological Journal",
    issn = "2500-316X",
    publisher = "MIREA - Russian Technological University",
    number = "2",

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    КОЛЛЕКТИВНЫЕ ВОЗБУЖДЕНИЯ В АЛЬФА-СПИРАЛЬНОЙ МОЛЕКУЛЕ БЕЛКА. / Kadantsev, V. N.; Goltsov, A. N.

    In: Russian Technological Journal, Vol. 6, No. 2, 2018, p. 32-45.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - КОЛЛЕКТИВНЫЕ ВОЗБУЖДЕНИЯ В АЛЬФА-СПИРАЛЬНОЙ МОЛЕКУЛЕ БЕЛКА

    AU - Kadantsev, V. N.

    AU - Goltsov, A. N.

    PY - 2018

    Y1 - 2018

    N2 - Continuous energy supply, a necessary condition for life, excites a state far from thermodynamic equilibrium, in particular coherent electric polar vibrations depending on water ordering in the cell. The collective, low-frequency vibrational excitations in protein macromolecules in the terahertz frequency region are suggested to orchestrate many protein processes such asenzymatic activity, electron/energy transport, conformation transitions and others. The most significant type of excitations is long-lived coherent vibronic modes and waves which are either spreading over large protein subdomains or being localised states. Two possible mechanisms of the formation of collective dynamic modes in the form of Fröhlich collective mode and Davydov soliton were previously suggested. We developed a unified quantum-mechanics approach to describe conditions of the formation of Fröhlich vibronic state and Davidov soliton in alphahelical protein molecules interacting with the environment. We distinguish three subsystems in the model, i.e., (i) oscillating peptide groups (PGs), interacting with (ii) the subsystem of side residuals of proteins, which in turn interacts with the environment (surrounding water), which is responsible for dissipation and fluctuation processes and modelled by a system of harmonic oscillators. It was shown that the equation of motion for dynamic variables of PG chain (phonon variables) can be transformed to the nonlinear Schrodinger equation for order parameters, which determines energy “pumping” due to protein interaction with a reservoir. Solution of the order parameter equation was shown to admit bifurcation into the solution corresponding to the formation of weak damped collective vibronic mode with growing amplitude. It was also shown that the solution corresponding to Davydov soliton can exist at certain boundary conditions in this bifurcation region. The suggested mechanism of emergent of macroscopic dissipative structures in the form of collective vibronic modes in proteins is discussed in connection with recent experimental data on long-lived collective protein excitation in the terahertz frequency region.

    AB - Continuous energy supply, a necessary condition for life, excites a state far from thermodynamic equilibrium, in particular coherent electric polar vibrations depending on water ordering in the cell. The collective, low-frequency vibrational excitations in protein macromolecules in the terahertz frequency region are suggested to orchestrate many protein processes such asenzymatic activity, electron/energy transport, conformation transitions and others. The most significant type of excitations is long-lived coherent vibronic modes and waves which are either spreading over large protein subdomains or being localised states. Two possible mechanisms of the formation of collective dynamic modes in the form of Fröhlich collective mode and Davydov soliton were previously suggested. We developed a unified quantum-mechanics approach to describe conditions of the formation of Fröhlich vibronic state and Davidov soliton in alphahelical protein molecules interacting with the environment. We distinguish three subsystems in the model, i.e., (i) oscillating peptide groups (PGs), interacting with (ii) the subsystem of side residuals of proteins, which in turn interacts with the environment (surrounding water), which is responsible for dissipation and fluctuation processes and modelled by a system of harmonic oscillators. It was shown that the equation of motion for dynamic variables of PG chain (phonon variables) can be transformed to the nonlinear Schrodinger equation for order parameters, which determines energy “pumping” due to protein interaction with a reservoir. Solution of the order parameter equation was shown to admit bifurcation into the solution corresponding to the formation of weak damped collective vibronic mode with growing amplitude. It was also shown that the solution corresponding to Davydov soliton can exist at certain boundary conditions in this bifurcation region. The suggested mechanism of emergent of macroscopic dissipative structures in the form of collective vibronic modes in proteins is discussed in connection with recent experimental data on long-lived collective protein excitation in the terahertz frequency region.

    M3 - Article

    VL - 6

    SP - 32

    EP - 45

    JO - Russian Technological Journal

    JF - Russian Technological Journal

    SN - 2500-316X

    IS - 2

    ER -